Grade 6

Module 1: Ratios and Unit Rates

Eureka MathDesmos Math 6–A1
Topic A Representing and Reasoning About Ratios 
Lesson 1: Ratios
Lesson 2: Ratios
Unit 2
Lesson 1: Pizza Maker [Free lesson]
Lesson 2: Ratio Rounds (Print available)
Lesson 3: Equivalent Ratios
Lesson 4: Equivalent Ratios
Unit 2
Lesson 3: Rice Ratios
Lesson 4: Fruit Lab [Free lesson]
Lesson 5: Balancing Act
Lesson 7: Mixing Paint, Part 1
Lesson 8 World Records (Print available)
Lesson 11 Community Life (Print available)
Practice Day 1 (Print available)
Lesson 5: Solving Problems by Finding Equivalent Ratios
Lesson 6: Solving Problems by Finding Equivalent Ratios
Unit 2
Lesson 5 Balancing Act
 
Lesson 7: Associated Ratios and the Value of a Ratio
Lesson 8: Equivalent Ratios Defined Through the Value of a Ratio
Unit 2
Lesson 6: Product Prices (Print available)
Lesson 7: Mixing Paint, Part 1
Topic B Collections of Equivalent Ratios 
Lesson 9: Tables of Equivalent RatiosUnit 2
Lesson 6: Product Prices (Print available)
Lesson 7: Mixing Paint, Part 1
Lesson 10: The Structure of Ratio Tables-Additive and MultiplicativeUnit 2
Lesson 10: Balloons
Lesson 11: Community Life (Print available)
Lesson 11: Comparing Ratios Using Ratio TablesUnit 2
Lesson 10: Balloons
Lesson 12: From Ratio Tables to Double Number Line DiagramsUnit 2
Lesson 6: Product Prices (Print available)
Lesson 8: World Records (Print available)
Lesson 12: Mixing Paint, Part 2
Lesson 14: Lunch Waste (Print available)
Practice Day 2 (Print available)
Lesson 13: From Ratio Tables to Equations Using the Value of a Ratio 
Lesson 14: From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane 
Lesson 15: A Synthesis of Representations of Equivalent Ratio Collections 
Topic C Unit Rates 
Lesson 16: From Ratio to RatesUnit 2
Lesson 8: World Records (Print available)
 
Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]
Lesson 6: Welcome to the Robot Factory
Lesson 17: From Rates to Ratios 
Lesson 18: Finding a Rate by Dividing Two QuantitiesUnit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]
Lesson 6: Welcome to the Robot Factory
Lesson 7: More Soft Serve
Lesson 19: Comparison Shopping-Unit Price and Related Measurement Conversions
Lesson 20: Comparison Shopping-Unit Price and Related Measurement Conversions
Lesson 21: Getting the Job Done—Speed, Work, and Measurement Units
Lesson 22: Getting the Job Done—Speed, Work, and Measurement Units
Unit 3
Lesson 2: Counting Classrooms
Lesson 3: Pen Pals
Lesson 23: Problem-Solving Using Rates, Unit Rates, and Conversions.Unit 3
Lesson 13: A Country as a Village
Topic D Percent 
Lesson 24: Percent and Rates per 100Unit 3
Lesson 8: Lucky Duckies [Free lesson]
Lesson 9: Bicycle Goals
Lesson 25: A Fraction as a Percent 
Lesson 26: Percent of a Quantity.Unit 3
Lesson 10: What´s Missing? (Print available)
Lesson 11: Cost Breakdown
Lesson 27: Solving Percent Problems
Lesson 28: Solving Percent Problems
Lesson 29: Solving Percent Problems
Unit 3
Lesson 10: What´s Missing? (Print available)
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Lesson 13: A Country as a Village
Practice Day 2 (Print available)

Module 2: Arithmetic Operations Including Division of Fractions

Lesson 1: Interpreting Division of a Fraction by a Whole Number—Visual Models.Unit 4
Lesson 2: Making Connections (Print available)
Lesson 2: Interpreting Division of a Whole Number by a Fraction —Visual Models.Unit 4
Lesson 1: Cookie Cutter
Lesson 3: Flour Planner [Free lesson]
Lesson 4: Flower Planters
Lesson 5: Garden Bricks (Print available)
Lesson 3: Interpreting and Computing Division of a Fraction by a Fraction—More Models
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—More Models
Unit 4
Lesson 5: Garden Bricks
Lesson 6: Fill the Gap [Free lesson]
Lesson 7: Break It Down
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 10: Swap Meet (Print available)
Practice Day
Lesson 5: Creating Division Stories. 
Lesson 6: More Division Stories. 
Lesson 7: The Relationship Between Visual Fraction Models and Equations 
Lesson 8: Dividing Fractions and Mixed NumbersUnit 4
Lesson 5: Garden Bricks (Print available)
Lesson 6: Fill the Gap [Free lesson]
Topic B Multi-Digit Decimal Operations—Adding, Subtracting, and Multiplying
Lesson 9: Sums and Differences of DecimalsUnit 5
Lesson 2: Decimal Diagrams [Free lesson]
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 10: The Distributive Property and the Products of DecimalsUnit 5
Lesson 5: Decimal Multiplication
Lesson 6: Multiplying with Areas
Lesson 7: Multiplication Methods (Print available)
Lesson 11: Fraction Multiplication and the Products of DecimalsUnit 5
Lesson 7: Multiplication Methods (Print available)
Topic C Dividing Whole Numbers and Decimals
Lesson 12: Estimating Digits in a Quotient 
Lesson 13: Dividing Multi-Digit Numbers Using the AlgorithmUnit 5
Lesson 9: Long Division Launch
Practice Day 1 (Print available)
Practice Day 2 (Print available)
Lesson 14: The Division Algorithm—Converting Decimal Division into Whole Number Division Using Fractions. 
Lesson 15: The Division Algorithm—Converting Decimal Division into Whole Number Division Using Mental Math 
Topic D Number Theory—Thinking Logically About Multiplicative Arithmetic 
Lesson 16: Even and Odd Numbers 
Lesson 17: Divisibility Tests for 3 and 9 
Lesson 18: Least Common Multiple and Greatest Common FactorUnit 5
Lesson 14: Common Multiples
Lesson 15: Common Factors
Practice Day 2 (Print available)
Lesson 19: The Euclidean Algorithm as an Application of the Long Division Algorithm 

Module 3: Rational Numbers

Lesson 1: Positive and Negative Numbers on the Number Line—Opposite Direction and ValueUnit 7Lesson 2: Digging Deeper
Lesson 2: Real-World Positive and Negative Numbers and Zero.
Lesson 3: Real-World Positive and Negative Numbers and Zero.
Unit 7 Lesson 4: Sub-Zero
Lesson 4: The Opposite of a Number
Lesson 5: The Opposite of a Number’s Opposite
Lesson 6: Rational Numbers on the Number Line
Unit 7Lesson 2: Digging Deeper
Topic B Order and Absolute Value
Lesson 7: Ordering Integers and Other Rational Numbers
Lesson 8: Ordering Integers and Other Rational Numbers
Lesson 9: Comparing Integers and Other Rational Numbers
Unit 7Lesson 3: Order in the Class (Print available) [Free lesson]
Lesson 10: Writing and Interpreting Inequality Statements Involving Rational Numbers 
Lesson 11: Absolute Value—Magnitude and Distance
Lesson 12: The Relationship Between Absolute Value and Order
Unit 7Lesson 5: Distance on the Number Line
Lesson 13: Statements of Order in the Real World. 
Topic C Rational Numbers and the Coordinate Plane 
Lesson 14: Ordered Pairs
Lesson 15: Locating Ordered Pairs on the Coordinate Plane
Unit 7Lesson 9: Sand Dollar SearchLesson 10: The A-maze-ing Coordinate PlaneLesson 11: Polygon Maker
Lesson 16: Symmetry in the Coordinate Plane. 
Lesson 17: Drawing the Coordinate Plane and Points on the PlaneLesson 10: The A-maze-ing Coordinate Plane
Lesson 18: Distance on the Coordinate PlaneUnit 7Lesson 11: Polygon Maker
Lesson 19: Problem Solving and the Coordinate PlaneUnit 7Lesson 12: Graph Telephone (Print available)Practice Day 2 (Print available)

Module 4: Expressions and Equations

Topic A Relationships of the Operations 
Lesson 1: The Relationship of Addition and Subtraction 
Lesson 2: The Relationship of Multiplication and Division 
Lesson 3: The Relationship of Multiplication and Addition. 
Lesson 4: The Relationship of Division and Subtraction 
Topic B Special Notations of Operations 
Lesson 5: ExponentsUnit 6Lesson 10: PowersLesson 11: Exponent Expressions (Print available)Practice Day 2 (Print available)
Lesson 6: The Order of Operations 
Topic C Replacing Letters and Numbers 
Lesson 7: Replacing Letters with Numbers
Lesson 8: Replacing Numbers with Letters
Unit 6Lesson 7: Border TilesLesson 12: Squares and Cubes
Topic D Expanding, Factoring, and Distributing Expressions 
Lesson 9: Writing Addition and Subtraction ExpressionsUnit 6Lesson 6: Vari-applesLesson 8: Products and Sums [Free lesson]Lesson 9: Products, Sums, and Differences
Lesson 10: Writing and Expanding Multiplication Expressions
Lesson 11: Factoring Expressions
Lesson 12: Distributing Expressions
Unit 6Lesson 8: Products and Sums [Free lesson]Lesson 9: Products, Sums, and Differences
Lesson 13: Writing Division Expressions 
Lesson 14: Writing Division Expressions 
Topic E Expressing Operations in Algebraic Form 
Lesson 15: Read Expressions in Which Letters Stand for Numbers
Lesson 16: Write Expressions in Which Letters Stand for Numbers
Lesson 17: Write Expressions in Which Letters Stand for Numbers
Unit 6Lesson 6: Vari-applesLesson 7: Border Tiles
Topic F Writing and Evaluating Expressions and Formulas 
Lesson 18: Writing and Evaluating Expressions—Addition and Subtraction
Lesson 19: Substituting to Evaluate Addition and Subtraction Expressions
Lesson 20: Writing and Evaluating Expressions—Multiplication and Division
Lesson 21: Writing and Evaluating Expressions—Multiplication and Addition
Unit 6Lesson 7: Border TilesLesson 8: Products and Sums [Free lesson]Lesson 9: Products, Sums, and DifferencesLesson 12: Squares and Cubes
Lesson 22: Writing and Evaluating Expressions—ExponentsUnit 6Lesson 10: PowersLesson 11: Exponent Expressions (Print available)Lesson 12: Squares and CubesPractice Day 2 (Print available)
Topic G Solving Equations 
Lesson 23: True and False Number Sentences
Lesson 24: True and False Number Sentences
Unit 6Lesson 1: Weight for It [Free lesson]
Lesson 25: Finding Solutions to Make Equations TrueUnit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five Equations
Lesson 26: One-Step Equations—Addition and SubtractionUnit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five EquationsLesson 3: Hanging Around
Lesson 27: One-Step Equations—Multiplication and Division
Lesson 28: Two-Step Problems—All Operations
Lesson 29: Multi-Step Problems—All Operations
Unit 6Lesson 3: Hanging AroundLesson 4: Hanging It UpLesson 5: Swap and Solve
Topic H Applications of Equations 
Lesson 30: One-Step Problems in the Real World
Lesson 31: Problems in Mathematical TermsLesson Lesson 32: Multi-Step Problems in the Real World
Unit 6Lesson 3: Hanging AroundLesson 4: Hanging It UpLesson 5: Swap and SolvePractice Day 1 (Print available)
Lesson 33: From Equations to Inequalities
Lesson 34: Writing and Graphing Inequalities in Real-World Problems
Unit 7Lesson 6: Tunnel Travel [Free lesson]Lesson 7: Comparing WeightsLesson 8: Shira´s Solutions

Module 5: Area, Surface Area, and Volume Problems

Topic A: Area of Triangles, Quadrilaterals, and Polygons
Lesson 1: The Area of Parallelograms Through Rectangle FactsUnit 1Lesson 3: Exploring Parallelograms (Print available) [Free lesson]Lesson 4: Off the Grid
Lesson 2: The Area of Right Triangles
Lesson 3: The Area of Acute Triangles Using Height and Base
Unit 1Lesson 5: Exploring Triangles (Print available)Lesson 6: Triangles and ParallelogramsLesson 7: Off the Grid, Part 2
Lesson 4: The Area of All Triangles Using Height and BaseUnit 1Lesson 6: Triangles and ParallelogramsLesson 7: Off the Grid, Part 2
Lesson 5: The Area of Polygons Through Composition and DecompositionUnit 1Lesson 2: LettersLesson 8: Pile of PolygonsPractice Day 1 (Print available)
Lesson 6: Area in the Real World 
Topic B Polygons on the Coordinate Plane 
Lesson 7: Distance on the Coordinate PlaneUnit 1Lesson 8: Pile of Polygons
Lesson 8: Drawing Polygons in the Coordinate PlaneUnit 7Lesson 11: Polygon Maker
Lesson 9: Determining Perimeter and Area of Polygons on the Coordinate PlaneUnit 1Lesson 8: Pile of Polygons
Lesson 10: Distance, Perimeter, and Area in the Real World 
Topic C Volume of Right Rectangular Prisms 
Lesson 11: Volume with Fractional Edge Lengths and Unit CubesUnit 4Lesson 11: Classroom ComparisonsLesson 12: Puzzling Areas (Print available) [Free lesson]Lesson 13: Volume ChallengesLesson 14: Planter Planner (Print available)
Lesson 12: From Unit Cubes to the Formulas for Volume  
Lesson 13: The Formulas for Volume 
Lesson 14: Volume in the Real WorldUnit 4Lesson 14: Planter Planner (Print available)
Topic D Nets and Surface Area 
Lesson 15: Representing Three-Dimensional Figures Using Nets
Lesson 16: Constructing Nets
Lesson 17: From Nets to Surface Area
Unit 1Lesson 10: Plenty of PolyhedraLesson 11: Nothing But Nets (Print available)Lesson 13: Take It To Go (Print available)
Lesson 18: Determining Surface Area of Three-Dimensional FiguresUnit 1Lesson 9: Renata´s Stickers [Free lesson]Lesson 10: Plenty of PolyhedraLesson 11: Nothing But Nets (Print available)Lesson 13: Take It To Go (Print available)Practice Day 2 (Print available)
Lesson 19: Surface Area and Volume in the Real World 
Lesson 19a: Addendum Lesson for Modeling―Applying Surface Area and Volume to Aquariums 
Lesson 3: The Area of Acute Triangles Using Height and BaseUnit 1Lesson 5 Exploring TrianglesLesson 6 Triangles and ParallelogramsLesson 7 Off the Grid, Part 2

Module 6: Statistics

Topic A Understanding Distributions 
Lesson 1: Posing Statistical QuestionsUnit 8 Lesson 1: Screen TimeLesson 2: Dot Plots
Lesson 2: Displaying a Data Distribution
Lesson 3: Creating a Dot Plot
Unit 8 Lesson 2: Dot PlotsLesson 3: Minimum Wage (Print available) [Free lesson]Lesson 4: Lots More Dots
Lesson 4: Creating a Histogram
Lesson 5: Describing a Distribution Displayed in a Histogram
Unit 8Lesson 5: The Plot Thickens [Free lesson]Lesson 6: DIY Histograms (Print available)
Topic B Summarizing a Distribution That Is Approximately Symmetric Using the Mean and Mean Absolute Deviation 
Lesson 6: Describing the Center of a Distribution Using the Mean
Lesson 7: The Mean as a Balance Point
Unit 8Lesson 7: Snack Time
Lesson 8: Variability in a Data DistributionUnit 8Lesson 8: Pop It!
Topic 9: The Mean Absolute Deviation (MAD).Unit 8Lesson 9: Hoops
Lesson 10: Describing Distributions Using the Mean and MAD
Lesson 11: Describing Distributions Using the Mean and MAD
Unit 8Lesson 10 Hollywood Part 1Practice Day 1 (Print available)
Topic C Summarizing a Distribution That Is Skewed Using the Median and the Interquartile Range 
Lesson 12: Describing the Center of a Distribution Using the MedianUnit 8Lesson 11: Toy Cars [Free lesson]Lesson 12: In the News
Lesson 13: Describing Variability Using the Interquartile Range (IQR)Unit 8Lesson 13: Pumpkin Patch
Lesson 14: Summarizing a Distribution Using a Box Plot
Lesson 15: More Practice with Box Plots
Unit 8Lesson 14: Car, Plane, Bus, or Train? (Print available)
Lesson 16: Understanding Box PlotsUnit 8Lesson 14: Car, Plane, Bus, or Train? (Print available)Lesson 15: Hollywood Part 2Lesson 16: Hollywood Part 3 (Print available)Practice Day 2 (Print available)
Topic D Summarizing and Describing Distributions 
Lesson 17: Developing a Statistical Project 
Lesson 18: Connecting Graphical Representations and Numerical SummariesUnit 8Lesson 5: The Plot Thickens [Free lesson]
Lesson 19: Comparing Data DistributionsUnit 8Lesson 15: Hollywood Part 2
Lesson 20: Describing Center, Variability, and Shape of a Data Distribution from a Graphical Representation
Lesson 21: Summarizing a Data Distribution by Describing Center, Variability, and Shape
Unit 8Lesson 16: Hollywood Part 3 (Print available)
Lesson 22: Presenting a Summary of a Statistical Project 
Lesson 3: Creating a Dot PlotUnit 8Lesson 2 Dot PlotsLesson 3 Minimum Wage [Free lesson]Lesson 4 Lots More Dots

Grade 7

Module 1: Ratios and Proportional Relationships

Eureka MathDesmos Math 6–A1
Topic A Proportional Relationships 
Lesson 1: An Experience in Relationships as Measuring RateUnit 2
Lesson 1: Paint [Free lesson]
Lesson 2: Balloon Float
 
Unit 4
Lesson 1: Mosaics [Free lesson]
Lesson 2: Peach Cobbler (Print available)
Lesson 2: Proportional RelationshipsUnit 2  
Lesson 2: Balloon Float
Lesson 3: Sugary Drinks (Print available)
 
Unit 4
Lesson 3: Sticker Sizes
Lesson 3: Identifying Proportional and Non-Proportional Relationships in Tables
Lesson 4: Identifying Proportional and Non-Proportional Relationships in Tables
Unit 2
Lesson 2: Balloon Float
Lesson 3: Sugary Drinks (Print available)
Lesson 4: Robot Factory
Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs
Lesson 6: Identifying Proportional and Non-Proportional Relationships in Graphs
Unit 2
Lesson 8: Dino Pops [Free lesson]
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations (Print available)
Lesson 12: Water Efficiency
Topic B Unit Rate and the Constant of Proportionality 
Lesson 7: Unit Rate as the Constant of ProportionalityUnit 2
Lesson 2: Balloon Float
Lesson 8: Representing Proportional Relationships with Equations
Lesson 9: Representing Proportional Relationships with Equations
Unit 2
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available) [Free lesson]
Lesson 7: All Kinds of Equations
Lesson 10: Interpreting Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops [Free lesson]
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations (Print available)
Lesson 12: Water Efficiency
Topic C Ratios and Rates Involving Fractions 
Lesson 11: Ratios of Fractions and Their Unit Rates
Lesson 12: Ratios of Fractions and Their Unit Rates
Unit 2
Lesson 3: Sugary Drinks (Print available)
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two [Free lesson]
Lesson 13: Finding Equivalent Ratios Given the Total QuantityUnit 2  
Lesson 2: Balloon Float
Lesson 3: Sugary Drinks (Print available)
Lesson 14: Multi-Step Ratio Problems 
Lesson 15: Equations of Graphs of Proportional Relationships Involving FractionsUnit 2
Lesson 8: Dino Pops [Free lesson]
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations
Lesson 12: Water Efficiency
Topic D Ratios of Scale Drawings 
Lesson 16: Relating Scale Drawings to Ratios and RatesUnit 1
Lesson 1: Scaling Machines [Free lesson]
Lesson 17: The Unit Rate as the Scale FactorUnit 1
Lesson 2: Scaling Robots
Lesson 3: Make It Scale
Lesson 4: Scale Factor Challenges
Practice Day 1 (Print available)
Lesson 18: Computing Actual Lengths from a Scale DrawingUnit 1
Lesson 6: Introducing Scale
Lesson 7: Will It Fit? (Print available) [Free lesson]
Lesson 19: Computing Actual Areas from a Scale DrawingUnit 1
Lesson 5: Tiles
Lesson 6: Introducing Scale
Lesson 7: Will It Fit? (Print available) [Free lesson]
Lesson 8: Scaling States (Print available)
Lesson 20: An Exercise in Creating a Scale Drawing
Lesson 21: An Exercise in Changing Scales
Lesson 22: An Exercise in Changing Scales
Unit 1
Lesson 8: Scaling States (Print available)
Lesson 9: Scaling Buildings
Lesson 10: Room Redesign (Print available)
Practice Day 2 (Print available)

Module 2: Rational Numbers

Topic A Addition and Subtraction of Integers and Rational Numbers 
Lesson 1: Opposite Quantities Combine to Make ZeroUnit 5
Lesson 1: Floats and Anchors [Free lesson]
Lesson 2: Using the Number Line to Model the Addition of Integers
Lesson 3: Understanding Addition of Integers
Lesson 4: Efficiently Adding Integers and Other Rational Numbers
Lesson 5: Understanding Subtraction of Integers and Other Rational Numbers
Unit 5
Lesson 2: More Floats and Anchors
Lesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 5: Number Puzzles
Lesson 10: Integer Puzzles [Free lesson]
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)
Lesson 6: The Distance Between Two Rational Numbers 
Lesson 7: Addition and Subtraction of Rational NumbersUnit 5
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 5: Number Puzzles
Lesson 10; Integer Puzzles [Free lesson]
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)
Practice Day 1 (Print available)
Lesson 8: Applying the Properties of Operations to Add and Subtract Rational Numbers 
Lesson 9: Applying the Properties of Operations to Add and Subtract Rational Numbers 
Topic B Multiplication and Division of Integers and Rational Numbers 
Lesson 10: Understanding Multiplication of Integers
Lesson 11: Develop Rules for Multiplying Signed Numbers
Unit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Practice Day 2 (Print available)
Lesson 12: Division of IntegersUnit 5
Lesson 8: Speeding Turtles
Lesson 13: Converting Between Fractions and Decimals Using Equivalent Fractions 
Lesson 14: Converting Rational Numbers to Decimals Using Long DivisionUnit 4
Lesson 13: Decimal Deep Dive (Print available)
Lesson 15: Multiplication and Division of Rational NumbersUnit 5
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)
Practice Day 2 (Print available)
Lesson 16: Applying the Properties of Operations to Multiply and Divide Rational Numbers 
Topic C Applying Operations with Rational Numbers to Expressions and Equations 
Lesson 17: Comparing Tape Diagram Solutions to Algebraic SolutionsUnit 6
Lesson 2: Smudged Receipts
Lesson 3: Equations
Lesson 4: Seeing Structure (Print available)
Lesson 18: Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers
Lesson 19: Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers
Unit 5
Lesson 9 Expressions
Lesson 20: Investments—Performing Operations with Rational Numbers
Lesson 21: If-Then Moves with Integer Number Cards
Lesson 22: Solving Equations Using Algebra
Lesson 23: Solving Equations Using Algebra
Unit 6
Lesson 3: Equations
Lesson 4: Seeing Structure (Print available)
Lesson 6: Balancing Equations
Lesson 7: Keeping It True (Print available)
Lesson 12: Community Day (Print available)
 
Unit 5
Lesson 3: Bumpers

Module 3: Expressions and Equations

Topic A Use Properties of Operations to Generate Equivalent Expressions 
Lesson 1: Generating Equivalent Expressions
Lesson 2: Generating Equivalent Expressions
Unit 5 Lesson 9: Expressions (Print available)Unit 6Lesson 9: Always-Equal MachinesLesson 11: Equation Roundtable (Print available)
Lesson 3: Writing Products as Sums and Sums as Products
Lesson 4: Writing Products as Sums and Sums as Products
Unit 6 Lesson 2: Smudged ReceiptsLesson 6: Balancing EquationsLesson 7: Keeping It True (Print available)Lesson 8: Factoring and ExpandingLesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available)Lesson 12: Community Day (Print available)
Lesson 5: Using the Identity and Inverse to Write Equivalent Expressions 
Lesson 6: Collecting Rational Number Like Terms 
Topic B Solve Problems Using Expressions, Equations, and Inequalities 
Lesson 7: Understanding EquationsUnit 6Lesson 2: Smudged ReceiptsLesson 5: Balancing MovesLesson 6: Balancing Equations
Lesson 8: Using If-Then Moves in Solving Equations
Lesson 9: Using If-Then Moves in Solving Equations
Unit 6Lesson 2: Smudged ReceiptsLesson 6: Balancing EquationsLesson 7: Keeping It True (Print available)Lesson 8: Factoring and Expanding (Print available)Lesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available)Lesson 12: Community Day (Print available)Practice Day 1 (Print available)
Lesson 10: Angle Problems and Solving EquationsUnit 7Lesson 2: Friendly Angles [Free lesson]Lesson 3: Angle DiagramsLesson 4: Missing Measures (Print available) [Free lesson]
Lesson 11: Angle Problems and Solving Equations 
Lesson 12: Properties of Inequalities
Lesson 13: Inequalities
Lesson 14: Solving Inequalities
Unit 6Lesson 14: Unbalanced HangersLesson 15: Budgeting (Print available)Lesson 16: Shira the Sheep [Free lesson]Lesson 17: Write Them and Solve Them (Print available)
Lesson 15: Graphing Solutions to InequalitiesUnit 6Lesson 13: I Saw the SignsPractice Day 2 (Print available)
Topic C Use Equations and Inequalities to Solve Geometry Problems 
Lesson 16: The Most Famous Ratio of AllUnit 3Lesson 2: Is It a Circle?Lesson 3: Measuring Around [Free lesson]
Lesson 17: The Area of a CircleUnit 3Lesson 5: Area StrategiesLesson 6: Radius Squares (Print available)Lesson 7: Why Pi? (Print available)Lesson 8: Area Challenges [Free lesson]Lesson 9: Circle vs. SquarePractice Day 2 (Print available)
Lesson 18: More Problems on Area and CircumferenceUnit 3Lesson 4: Perimeter ChallengesLesson 5: Area StrategiesLesson 6: Radius Squares (Print available)Lesson 7: Why Pi? (Print available)Lesson 8: Area Challenges [Free lesson]Lesson 9: Circle vs. Square
Lesson 19: Unknown Area Problems on the Coordinate Plane
Lesson 20: Composite Area Problems
Unit 3Lesson 4: Perimeter ChallengesPractice Day 2 (Print available)
Lesson 21: Surface Area
Lesson 22: Surface Area
Lesson 23: The Volume of a Right Prism
Lesson 24: The Volume of a Right Prism
Unit 7Lesson 10: Simple PrismsLesson 11: More Complicated Prisms Lesson 12: Surface Area Strategies (Print Available)Lesson 13: Popcorn PossibilitiesPractice Day 2 (Print available)
Lesson 25: Volume and Surface Area
Lesson 26: Volume and Surface Area
Unit 7Lesson 13: Popcorn PossibilitiesPractice Day 2

Module 4: Percent and Proportional Relationships

Topic A Finding the Whole 
Lesson 1: PercentUnit 4Lesson 1: Mosaics [Free lesson]Lesson 2: Peach Cobbler (Print available)Lesson 3: Sticker Sizes
Lesson 2: Part of a Whole as a PercentUnit 4Lesson 1: Mosaics [Free lesson]Lesson 2: Peach Cobbler (Print available)
Lesson 3: Comparing Quantities with PercentUnit 4Lesson 1: Mosaics [Free lesson]Lesson 2: Peach Cobbler (Print available)Lesson 3: Sticker Sizes
Lesson 4: Percent Increase and DecreaseUnit 4Lesson 4: More and LessLesson 5: All the EquationsLesson 6: 100% (Print available)Lesson 7: Percent machines [Free lesson]Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Lesson 5: Finding One Hundred Percent Given Another Percent 
Lesson 6: Fluency with PercentsUnit 4Lesson 7: Percent machines [Free lesson]Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Topic B Percent Problems Including More Than One Whole 
Lesson 7: Markup and Markdown ProblemsUnit 4Lesson 7: Percent machines [Free lesson]Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Lesson 8: Percent Error Problems
Lesson 9: Problem Solving When the Percent Changes
Unit 4Lesson 4: More and LessLesson 5: All the EquationsLesson 6: 100% (Print available)Lesson 7: Percent machines [Free lesson]Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Lesson 10: Simple Interest 
Lesson 11: Tax, Commissions, Fees, and Other Real-World Percent ApplicationsUnit 4Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]Practice Day (Print available)
Topic C Scale Drawings 
Lesson 12: The Scale Factor as a Percent for a Scale Drawing 
Lesson 13: Changing ScalesUnit 1Lesson 1: Scaling Machines [Free lesson]Lesson 2: Scaling RobotsLesson 3: Make It ScaleLesson 4: Scale Factor ChallengesLesson 5: TilesLesson 6: Introducing ScaleLesson 7: Will It Fit? (Print available) [Free lesson]Lesson 8: Scaling States (Print available)Lesson 9: Scaling BuildingsLesson 10: Room Redesign (Print available)Practice Day 1 (Print available)Practice Day 2 (Print available) Unit 3Lesson 1 Toothpicks
Lesson 14: Computing Actual Lengths from a Scale DrawingUnit 1Lesson 6: Introducing ScaleLesson 7: Will It Fit? (Print available) [Free lesson]Lesson 8: Scaling States (Print available)Lesson 9: Scaling BuildingsLesson 10: Room Redesign (Print available) Unit 3Lesson 1: Toothpicks
Lesson 15: Solving Area Problems Using Scale DrawingsUnit 1Lesson 5: Tiles
Topic D Population, Mixture, and Counting Problems Involving Percents 
Lesson 16: Population ProblemsUnit 8Lesson 10: Crab Island [Free lesson]Lesson 11: Headlines
Lesson 17: Mixture Problems 
Lesson 18: Counting Problems 

Module 5: Statistics and Probability

Topic A Calculating and Interpreting Probabilities 
Lesson 1: Chance ExperimentsUnit 8Lesson 1: How Likely? (Print available) [Free lesson]Lesson 2: Prob-bear-bilities [Free lesson]Lesson 3: Mystery Bag
Lesson 2: Estimating Probabilities by Collecting Data
Lesson 3: Chance Experiments with Equally Likely Outcomes
Lesson 4: Calculating Probabilities for Chance Experiments with Equally Likely Outcomes
Unit 8Lesson 3: Mystery BagLesson 4: Spin ClassLesson 5: Is It Fair?Lesson 6: Fair Games
Lesson 5: Chance Experiments with Outcomes That Are Not Equally LikelyUnit 8Lesson 4: Spin ClassLesson 5: Is It Fair?Lesson 6: Fair GamesLesson 7: Weather or Not
Lesson 6: Using Tree Diagrams to Represent a Sample Space and to Calculate ProbabilitiesUnit 8Lesson 6: Fair GamesLesson 7: Weather or Not
Lesson 7: Calculating Probabilities of Compound EventsUnit 8Lesson 8: Simulate It! (Print available)Lesson 9: Car, Bike, or Train? (Print available)Practice Day 1 (Print available)
Topic B Estimating Probabilities 
Lesson 8: The Difference Between Theoretical Probabilities and Estimated Probabilities
Lesson 9: Comparing Estimated Probabilities to Probabilities Predicted by a Model
Unit 8Lesson 6: Fair GamesLesson 7: Weather or NotLesson 8: Simulate It! (Print available)Lesson 9: Car, Bike, or Train? (Print available)
Lesson 10: Conducting a Simulation to Estimate the Probability of an EventUnit 8Lesson 7: Weather or NotLesson 8: Simulate It! (Print available)Lesson 9: Car, Bike, or Train? (Print available)
Lesson 11: Conducting a Simulation to Estimate the Probability of an Event
Lesson 12: Applying Probability to Make Informed Decisions
Unit 8Lesson 7: Weather or NotLesson 8: Simulate It! (Print available)
Topic C Random Sampling and Estimating Population Characteristics 
Lesson 13: Populations, Samples, and Generalizing from a Sample to a PopulationUnit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 10: Crab Island [Free lesson]Lesson 11: HeadlinesLesson 12: Flower Power
Lesson 14: Selecting a Sample
Lesson 15: Random Sampling
Lesson 16: Methods for Selecting a Random Sample
Unit 8Lesson 10: Crab Island [Free lesson]Lesson 11: Headlines
Lesson 17: Sampling VariabilityUnit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 13: Plots and Samples
Lesson 18: Sampling Variability and the Effect of Sample Size
Lesson 19: Understanding Variability When Estimating a Population Proportion
Unit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 13: Plots and SamplesLesson 14: School Newspaper (Print available)
Lesson 20: Estimating a Population Proportion 
Topic D Comparing Populations 
Lesson 21: Why Worry About Sampling Variability?Unit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 13: Plots and SamplesLesson 14: School Newspaper (Print available)
Lesson 22: Using Sample Data to Compare the Means of Two or More Populations
Lesson 23: Using Sample Data to Compare the Means of Two or More Populations
Unit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 10: Crab Island [Free lesson]Lesson 13: Plots and SamplesLesson 14: School Newspaper (Print available)Lesson 15: Asthma Rates (Print available)

Module 6: Geometry

Topic A Unknown Angles 
Lesson 1: Complementary and Supplementary AnglesUnit 7Lesson 2: Friendly Angles [Free lesson]Lesson 3: Angle Diagrams
Lesson 2: Solving for Unknown Angles Using Equations
Lesson 3: Solving for Unknown Angles Using Equations
Lesson 4: Solving for Unknown Angles Using Equations
Unit 7Lesson 1: PinwheelsLesson 2: Friendly AnglesLesson 3: Angle DiagramsLesson 4: Missing Measures (Print available) [Free lesson]
Topic B Constructing Triangles 
Lesson 5: Identical TrianglesUnit 7Lesson 6: Is It Enough?Lesson 7: More Than One
Lesson 6: Drawing Geometric ShapesUnit 7Lesson 6: Is It Enough?Lesson 7: More Than OneLesson 8: Can You Draw It? (Print available)
Lesson 7: Drawing Parallelograms 
Lesson 8: Drawing TrianglesUnit 7Lesson 5: Can You Build It? [Free lesson]Lesson 6: Is It Enough?Lesson 7: More Than OneLesson 8: Can You Draw It? (Print available)Practice Day 1 (Print available)
Lesson 9: Conditions for a Unique Triangle―Three Sides and Two Sides and the Included
Lesson 10: Conditions for a Unique Triangle—Two Angles and a Given Side Angle
Unit 7Lesson 8: Can You Draw It? (Print available)
Lesson 11: Conditions on Measurements That Determine a TriangleUnit 7Lesson 5: Can You Build It? [Free lesson]Lesson 6: Is It Enough?Lesson 7: More Than OneLesson 8: Can You Draw It? (Print available)Practice Day 1 (Print available)
Lesson 12: Unique Triangles―Two Sides and a Non-Included Angle 
Lesson 13: Checking for Identical Triangles
Lesson 14: Checking for Identical Triangles
Unit 7Lesson 6: Is It Enough?Lesson 7: More Than OnePractice Day 1
Lesson 15: Using Unique Triangles to Solve Real-World and Mathematical Problems 
Topic C Slicing Solids 
Lesson 16: Slicing a Right Rectangular Prism with a Plane
Lesson 17: Slicing a Right Rectangular Pyramid with a Plane
Lesson 18: Slicing on an Angle
Unit 7Lesson 9: Slicing Solids
Lesson 19: Understanding Three-Dimensional Figures 
Topic D Problems Involving Area and Surface Area 
Lesson 20: Real-World Area ProblemsUnit 3Lesson 5: Area Strategies
Lesson 21: Mathematical Area ProblemsUnit 3Lesson 5: Area StrategiesLesson 6: Radius Squares (Print available)
Lesson 22: Area Problems with Circular RegionsUnit 3Lesson 5: Area StrategiesLesson 8: Area Challenges [Free lesson]
Lesson 23: Surface Area
Lesson 24: Surface Area
Unit 7Lesson 12: Surface Area Strategies (Print available)Lesson 13: Popcorn Possibilities
Topic E Problems Involving Volume 
Lesson 25: Volume of Right PrismsUnit 7Lesson 10: Simple PrismsLesson 11: More Complicated PrismsLesson 13: Popcorn Possibilities
Lesson 26: Volume of Composite Three-Dimensional ObjectsUnit 7Lesson 11: More Complicated Prisms
Lesson 27: Real-World Volume ProblemsUnit 7Lesson 13: Popcorn Possibilities

Grade 8

Module 1: Integer Exponents and Scientific Notation

Eureka MathDesmos Math 6–A1
Topic A Exponential Notation and Properties of Integer Exponents 
Lesson 1: Exponential NotationUnit 7 Lesson 1 Circles [Free lesson]Lesson 2 Combining Exponents
Lesson 2: Multiplication of Numbers in Exponential Form
Lesson 3: Numbers in Exponential Form Raised to a Power
Unit 7 Lesson 2 Combining ExponentsLesson 3 Power Pairs (Print available) [Free lesson]Lesson 4 Rewriting Powers
Lesson 4: Numbers Raised to the Zeroth Power
Lesson 5: Negative Exponents and the Laws of Exponents
Unit 7 Lesson 5 Zero and Negative ExponentsLesson 6 Write a Rule (Print available)Practice Day 1 (Print available)
Lesson 6: Proofs of Laws of Exponents 
Topic B Magnitude and Scientific Notation 
Lesson 7: MagnitudeUnit 7 Lesson 7 Scales and Weights
Lesson 8: Estimating QuantitiesUnit 7 Lesson 7: Scales and WeightsLesson 8: Point ZapperLesson 9: Use Your Powers
Lesson 9: Scientific Notation
Lesson 10: Operations with Numbers in Scientific Notation
Unit 7 Lesson 10: Solar System [Free lesson]Lesson 11: Balance the Scales [Free lesson]Lesson 13: Star Power
Lesson 11: Efficacy of Scientific NotationUnit 7 Lesson 13: Star Power
Lesson 12: Choice of Unit 
Lesson 13: Comparison of Numbers Written in Scientific Notation and Interpreting Scientific Notation Using TechnologyUnit 7  Lesson 13: Star Power Practice Day 2 (Print available)

Module 2: The Concept of Congruence

Topic A Definitions and Properties of the Basic Rigid Motions 
Lesson 1: Why Move Things Around?
Lesson 2: Definition of Translation and Three Basic Properties
Unit 1Lesson 1: Transformers [Free lesson]Lesson 2: Spinning, Flipping, Sliding [Free lesson]
Lesson 3: Translating LinesUnit 1Lesson 1: Transformers [Free lesson]Lesson 2: Spinning, Flipping, Sliding [Free lesson] Unit 3Lesson 6: Translations
Lesson 4: Definition of Reflection and Basic Properties
Lesson 5: Definition of Rotation and Basic Properties
Lesson 6: Rotations of 180 Degrees
Unit 1Lesson 1: Transformers [Free lesson]Lesson 2: Spinning, Flipping, Sliding [Free lesson]Lesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting Coordinated
Topic B Sequencing the Basic Rigid Motions 
Lesson 7: Sequencing Translations
Lesson 8: Sequencing Reflections and Translations
Unit 1Lesson 3: Transformation GolfLesson 6: Connecting the Dots [Free lesson]
Lesson 9: Sequencing Rotations
Lesson 10: Sequences of Rigid Motions
Unit 1Lesson 3: Transformation GolfLesson 6: Connecting the Dots [Free lesson]Lesson 13: Tessellate [Free lesson]Practice Day
Topic C Congruence and Angle Relationships 
Lesson 11: Definition of Congruence and Some Basic PropertiesUnit 1 Lesson 7: Are They the Same?Lesson 8: No Bending, No StretchingLesson 9: Are They Congruent?Practice Day
Lesson 12: Angles Associated with Parallel LinesUnit 1 Lesson 10: Transforming Angles  
Lesson 13: Angle Sum of a TriangleUnit 1 Lesson 11: Tearing It Up (Print available)
Lesson 14: More on the Angles of a TriangleUnit 1 Lesson 11: Tearing It Up (Print available)Lesson 12: Puzzling It Out [Free lesson]
Topic D: The Pythagorean Theorem 
Lesson 15: Informal Proof of the Pythagorean TheoremUnit 8Lesson 7: Pictures to Prove It
Lesson 16: Applications of the Pythagorean TheoremUnit 8Lesson 10: Taco TruckPractice Day 2 (Print available)

Module 3: Similarity

Topic A Dilation 
Lesson 1: What Lies Behind “Same Shape”?Unit 2Lesson 1: Sketchy Dilations [Free lesson]Lesson 2: Dilation Mini Golf [Free lesson]
Lesson 2: Properties of Dilations
Lesson 3: Examples of Dilations
Unit 2Lesson 1: Sketchy Dilations [Free lesson]Lesson 2: Dilation Mini Golf [Free lesson]Lesson 3: Match My DilationLesson 4: Dilations on a Plane (Print available)
Lesson 4: Fundamental Theorem of Similarity
Lesson 5: First Consequences of FTS
Unit 2Lesson 5: Transformations Golf with DilationsLesson 6: Social Scavenger Hunt (Print available) [Free lesson]
Lesson 6: Dilations on the Coordinate PlaneUnit 8Lesson 4: Dilations on a Plane (Print available)
Lesson 7: Informal Proofs of Properties of Dilations 
Topic B Similar Figures 
Lesson 8: Similarity
Lesson 9: Basic Properties of Similarity
Unit 2Lesson 5: Transformations Golf with DilationsLesson 6: Social Scavenger Hunt (Print available) [Free lesson]
Lesson 10: Informal Proof of AA Criterion for SimilarityUnit 2Lesson 7: Are Angles Enough?
Lesson 11: More About Similar TrianglesUnit 2Lesson 7: Are Angles Enough?Lesson 8: Shadows
Lesson 12: Modeling Using SimilarityUnit 2Lesson 8: ShadowsLesson 9: Water SlideLesson 10: Points on a PlanePractice Day 
Topic C The Pythagorean Theorem 
Lesson 13: Proof of the Pythagorean TheoremUnit 8Lesson 6: The Pythagorean TheoremLesson 7: Pictures to Prove ItLesson 8: Triangle-Tracing Turtle [Free lesson]
Lesson 14: The Converse of the Pythagorean TheoremUnit 8 Lesson 9: Make It Right

Module 4: Linear Equations

Topic A Writing and Solving Linear Equations 
Lesson 1: Writing Equations Using Symbols 
Lesson 2: Linear and Nonlinear Expressions in x 
Lesson 3: Linear Equations in xUnit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)
Lesson 4: Solving a Linear EquationUnit 4Lesson 3: Balanced MovesLesson 4: More Balanced MovesLesson 4: More Balanced Moves (Print available)Lesson 5: Equation Roundtable (Print available) [Free lesson]Lesson 6: Strategic Solving (Print available)
Lesson 5: Writing and Solving Linear EquationsUnit 3Lesson 1: Turtle Time Trials Unit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)Lesson 5: Equation Roundtable (Print available) [Free lesson]Lesson 6: Strategic Solving (Print available)
Lesson 6: Solutions of a Linear EquationUnit 3Lesson 10: Solutions Unit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)Lesson 5: Equation Roundtable (Print available) [Free lesson]Lesson 6: Strategic Solving (Print available)
Lesson 7: Classification of SolutionsUnit 4Lesson 7: All, Some, or None?
Lesson 8: Linear Equations in Disguise 
Lesson 9: An Application of Linear Equations 
Topic B Linear Equations in Two Variables and Their GraphsUnit 3Lesson 2: Water TankLesson 3: PostersLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Lesson 10: A Critical Look at Proportional RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson]Lesson 2: Water TankLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 7: Water CoolerLesson 8: Landing PlanesLesson 9: Coin Capture
Lesson 11: Constant RateUnit 2Lesson 9: Water SlideLesson 10: Points on a PlanePractice Day  Unit 3Lesson 3: PostersLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations Unit 4Lesson 8: When Are They the Same?
Lesson 12: Linear Equations in Two VariablesUnit 3Lesson 3: PostersLesson 6: Translations Unit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)
Lesson 13: The Graph of a Linear Equation in Two VariablesUnit 3 Lesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: TranslationsLesson 7: Water CoolerLesson 10: SolutionsLesson 11: Pennies and Quarters
Lesson 14: The Graph of a Linear Equation―Horizontal and Vertical LinesUnit 3 Lesson 9: Coin CapturePractice Day  [Free lesson]
Topic C Slope and Equations of Lines 
Lesson 15: The Slope of a Non-Vertical LineUnit 3Lesson 5: Flags [Free lesson]Lesson 6: TranslationsLesson 7: Water CoolerLesson 8: Landing Planes
Lesson 16: The Computation of the Slope of a Non-Vertical LineUnit 3Lesson 7: Water CoolerLesson 8: Landing Planes
Lesson 17: The Line Joining Two Distinct Points of the Graph 𝑦 = 𝑚x + 𝑏 Has Slope mUnit 3Lesson 7: Water Cooler
Lesson 18: There Is Only One Line Passing Through a Given Point with a Given SlopeUnit 3Lesson 5: Flags [Free lesson]Lesson 7: Water Cooler
Lesson 19: The Graph of a Linear Equation in Two Variables Is a LineUnit 3Lesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Lesson 20: Every Line Is a Graph of a Linear EquationUnit 3Lesson 3: PostersLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Lesson 21: Some Facts About Graphs of Linear Equations in Two VariablesUnit 3Lesson 3: PostersLesson 6: TranslationsPractice Day 
Lesson 22: Constant Rates RevisitedUnit 2Lesson 9: Water SlideLesson 10: Points on a Plane Unit 3Lesson 1: Turtle Time Trials [Free lesson]Lesson 2: Water TankLesson 3: Posters
Lesson 23: The Defining Equation of a LineUnit 3Lesson 10: SolutionsLesson 11: Pennies and Quarters
Topic D Systems of Linear Equations and Their Solutions 
Lesson 24: Introduction to Simultaneous EquationsUnit 4Lesson 7: All, Some, or None?Lesson 8: When Are They the Same?Lesson 13: All, Some, or None? Part 2
Lesson 25: Geometric Interpretation of the Solutions of a Linear SystemUnit 4  Lesson 9: On or Off the Line?Lesson 10: On Both LinesLesson 11: Make Them Balance [Free lesson]Lesson 12: Line Zapper [Free lesson]Lesson 13: All, Some, or None? Part 2Practice Day 2 (Print available)
Lesson 26: Characterization of Parallel LinesUnit 3 Lesson 6: Translations
Lesson 27: Nature of Solutions of a System of Linear EquationsUnit 4  Lesson 9: On or Off the Line?
Lesson 28: Another Computational Method of Solving a Linear System 
Lesson 29: Word Problems 
Lesson 30: Conversion Between Celsius and Fahrenheit 
Topic E Pythagorean Theorem 
Lesson 31: System of Equations Leading to Pythagorean Triples 

Module 5: Examples of Functions from Geometry

Topic A Functions 
Lesson 1: The Concept of a FunctionUnit 5 Lesson 1: Turtle Crossing [Free lesson]Lesson 2: Guess My Rule [Free lesson]
Lesson 2: Formal Definition of a FunctionUnit 5 Lesson 1: Turtle Crossing [Free lesson]Lesson 2: Guess My Rule [Free lesson] Lesson 3: Function or Not?
Lesson 3: Linear Functions and ProportionalityUnit 3Lesson 1: Turtle Time Trials [Free lesson] Unit 5Lesson 4: Window Frames
Lesson 4: More Examples of FunctionsUnit 5Lesson 3: Function or Not?Lesson 4: Window Frames
Lesson 5: Graphs of Functions and EquationsUnit 5Lesson 4: Window FramesLesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 6: Graphs of Linear Functions and Rate of ChangeUnit 2Lesson 9: Water SlideLesson 10: Points on a Plane Unit 3Lesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Lesson 7: Comparing Linear Functions and GraphsUnit 5Lesson 3: PostersLesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 8: Graphs of Simple Nonlinear Functions 
Topic B Volume 
Lesson 9: Examples of Functions from GeometryUnit 8Lesson 1: Tilted SquaresLesson 2: From Squares to Roots
Lesson 10: Volumes of Familiar Solids—Cones and CylindersUnit 5Lesson 10: Volume LabLesson 11: Cylinders [Free lesson]Lesson 12: Scaling CylindersLesson 13: Cones [Free lesson]Lesson 14: Missing Dimensions (Print available)
Lesson 11: Volume of a SphereUnit 5 Lesson 15: Spheres Practice Day 2 (Print available)

Module 6: Linear Functions

Topic A Linear Functions 
Lesson 1: Modeling Linear RelationshipsUnit 5 Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 2: Interpreting Rate of Change and Initial ValueUnit 2Lesson 9: Water SlideLesson 10: Points on a Plane Unit 3Lesson 1: Turtle Time Trials [Free lesson]Lesson 2: Water TankLesson 3: PostersLesson 4: Stacking Cups
Lesson 3: Representations of a LineUnit 5Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 4: Increasing and Decreasing Functions
Lesson 5: Increasing and Decreasing Functions
Unit 5Lesson 1: Turtle Crossing [Free lesson]Lesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing Stories
Topic B Bivariate Numerical Data 
Lesson 6: Scatter Plots
Lesson 7: Patterns in Scatter Plots
Unit 6 Lesson 1: Click BattleLesson 2: Wing SpanLesson 3: Robots [Free lesson]Practice Day 1 (Print available) [Free lesson]
Lesson 8: Informally Fitting a LineUnit 6 Lesson 4: Dapper Cats [Free lesson]Lesson 5: Fit Fights [Free lesson]Lesson 6: Interpreting SlopesLesson 7: Scatter Plot CityLesson 8: Animal BrainsPractice Day 1 (Print available) [Free lesson]Practice Day 2 (Print available)
Lesson 9: Determining the Equation of a Line Fit to Data 
Topic C Linear and Nonlinear Models 
Lesson 10: Linear Models
Lesson 11: Using Linear Models in a Data Context
Unit 5 Lesson 4: Window FramesLesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing StoriesUnit 6 Lesson 6: Interpreting SlopesLesson 8: Animal BrainsPractice Day 2 (Print available)
Lesson 12: Nonlinear Models in a Data Context 
Topic D Bivariate Categorical Data 
Lesson 13: Summarizing Bivariate Categorical Data in a Two-Way TableUnit 6 Lesson 9: Tasty Fruit
Lesson 14: Association Between Categorical VariablesUnit 6 Lesson 10: Finding Associations [Free lesson] Lesson 11: Federal Budgets Practice Day 3

Module 7: Introduction to Irrational Numbers Using Geometry

Topic A Square and Cube Roots 
Lesson 1: The Pythagorean TheoremUnit 8
Lesson 6: The Pythagorean Theorem
Lesson 2: Square RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Lesson 3: Existence and Uniqueness of Square Roots and Cube RootsUnit 8
Lesson 5: Filling Cubes
Lesson 4: Simplifying Square RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Practice Day 1 (Print available)
Lesson 5: Solving Equations with Radicals 
Topic B Decimal Expansions of Numbers 
Lesson 6: Finite and Infinite Decimals
Lesson 7: Infinite Decimals
Lesson 8: The Long Division Algorithm
Lesson 9: Decimal Expansions of Fractions, Part 1
Lesson 10: Converting Repeating Decimals to Fractions
Unit 8
Lesson 12: Fractions to Decimals
Lesson 13: Decimals to Fractions
Lesson 11: The Decimal Expansion of Some Irrational Numbers 
Lesson 12: Decimal Expansions of Fractions, Part 2 
Lesson 13: Comparing Irrational NumbersUnit 8
Lesson 14: Hit the Target
Lesson 14: Decimal Expansion of π 
Topic C The Pythagorean Theorem 
Lesson 15: Pythagorean Theorem, RevisitedUnit 8
Lesson 6: The Pythagorean Theorem
Lesson 7: Pictures to Prove It
Lesson 16: Converse of the Pythagorean TheoremUnit 8
Lesson 9: Make It Right
Lesson 17: Distance on the Coordinate PlaneUnit 8
Lesson 11: Pond Hopper
Lesson 18: Applications of the Pythagorean TheoremUnit 8
Lesson 10: Taco Truck [Free lesson]
Practice Day 2 (Print available)
Topic D Applications of Radicals and Roots 
Lesson 19: Cones and Spheres 
Lesson 20: Truncated Cones 
Lesson 21: Volume of Composite Solids 
Lesson 22: Average Rate of Change 
Lesson 23: Nonlinear Motion 

Grade 6

Unit 1: Area and Surface Area

Illustrative MathematicsDesmos Math 6–A1
Topic A: Reasoning to Find Area 
Lesson 1: Tiling the PlaneUnit 1
Lesson 1: Shapes on a Plane [Free lesson]
Lesson 2: Finding Area by Decomposing and Rearranging
Lesson 3: Reasoning to Find Area
Unit 1
Lesson 2: Letters
Topic 2: Parallelograms
Lesson 4: Parallelograms
Lesson 5: Bases and Heights of Parallelograms
Lesson 6: Area of Parallelograms
Unit 1
Lesson 3: Exploring Parallelograms (Print available) [Free lesson]
Lesson 4: Off the Grid
Topic 3: Triangles
Lesson 7: From Parallelograms to TrianglesUnit 1
Lesson 3: Exploring Parallelograms (Print available) [Free lesson]
Lesson 4: Off the Grid
Lesson 6: Triangles and Parallelograms
Lesson 8: Area of TrianglesUnit 1
Lesson 5: Exploring Triangles (Print available)
Lesson 9: Formula for the Area of a Triangle
Lesson 10: Bases and Heights of Triangles
Unit 1
Lesson 4: Off the Grid
Lesson 6: Triangles and Parallelograms
Topic 4: Polygons
Lesson 11: PolygonsUnit 1
Lesson 2: Letters
Lesson 8: Pile of Polygons
Practice Day 1 (Print available)
Unit 7
Lesson 11: Polygon Maker
Topic 5: Surface Area
Lesson 12: What is Surface Area?Unit 1
Lesson 9: Renata´s Stickers [Free lesson]
Lesson 13: PolyhedraUnit 1Lesson 10: Plenty of Polyhedra
Lesson 14: Nets and Surface AreaUnit 1
Lesson 10: Plenty of Polyhedra
Lesson 11: Nothing But Nets (Print available)
Lesson 13: Take It To Go
Lesson 15: More Nets, More Surface AreaUnit 1
Lesson 10: Plenty of Polyhedra
Lesson 11: Nothing But Nets (Print available)
Lesson 12: Face Value
Lesson 13: Take It To Go (Print available)
Practice Day 2 (Print available)
Lesson 16: Distinguishing Between Surface Area and Volume
Topic 6: Squares and Cubes 
Lesson 17: Squares and CubesUnit 6
Lesson 12: Squares and Cubes
Lesson 18: Surface Area of a Cube 
Topic 7: Let’s Put It to Work 
Lesson 19: Designing a TentUnit 1
Lesson 13: Take It To Go (Print available)

Unit 2: Introducing Ratios

Topic 1: Introducing Ratios
Lesson 1: Introducing Ratios and Ratio LanguageUnit 2Lesson 1: Pizza Maker [Free lesson]Lesson 2: Ratio Rounds (Print available)
Lesson 2: Representing Ratios with DiagramsUnit 2Lesson 1: Pizza Maker [Free lesson]Lesson 2: Ratio Rounds (Print available)Lesson 3: Rice Ratios (Print available)
Topic 2: Equivalent Ratios
Lesson 3: RecipesUnit 2Lesson 1: Pizza Maker [Free lesson]Lesson 3: Rice Ratios (Print available)
Lesson 4: Color MixturesUnit 2Lesson 7: Mixing Paint, Part 1Lesson 12: Mixing paint, Part 2
Lesson 5: Defining Equivalent RatiosUnit 2Lesson 3: Rice Ratios (Print available)Lesson 4: Fruit Lab [Free lesson]Lesson 11: Community LifePractice Day 1 (Print available)
Topic 3: Representing Equivalent ratios
Lesson 6: Introducing Double Number Line DiagramsUnit 2Lesson 5: Balancing Act
Lesson 7: Creating Double Line DiagramsUnit 2Lesson 5: Balancing ActLesson 6: Product prices (Print available)
Lesson 8: How Much for One?Unit 2Lesson 6: Product prices (Print available)
Lesson 9: Constant SpeedUnit 2Lesson 8: World Records (Print available)
Lesson 10: Comparing Situations by Examining RatiosUnit 2Lesson 7: Mixing Paint, Part 1 
Topic 4: Solving Ratio and Rate Problems
Lesson 11: Representing Ratios with TablesUnit 2Lesson 9: Disaster Preparation [Free lesson]
Lesson 12: Navigating a Table of Equivalent Ratios
Lesson 13: Tables and Double Line Diagrams
Unit 2Lesson 6: Product prices (Print available)Lesson 7: Mixing Paint, Part 1
Lesson 14: Solving Equivalent Ratio ProblemsUnit 2Lesson 6: Product prices (Print available)Lesson 7: Mixing Paint, Part 1Lesson 10: BalloonsLesson 11: Community Life (Print available)
Topic 5: Part-Part-Whole Ratios
Lesson 15: Part-Part-Whole RatiosUnit 2Lesson 12: Mixing paint, Part 2Lesson 13: City Planning
Lesson 16: Solving More Ratio ProblemsUnit 2Lesson 13: City PlanningLesson 14: Lunch Waste (Print available)
Topic 6: Let’s Put It to Work 
Lesson 17: A Fermi ProblemUnit 2Lesson 13: City PlanningLesson 14: Lunch Waste (Print available)Practice Day 2 (Print available)

Unit 3: Rates and Percentages

Topic 1: Units of Measurement 
Lesson 1: The Burj KhalifaUnit 3
Lesson 4: Model Trains
Topic 2: Unit Conversion
Lesson 2: Anchoring Units of MeasurementUnit 3
Lesson 1: Many Measurements (Print available) [Free lesson]
Lesson 3: Measuring with Different-Sized Units
Lesson 4: Converting Units
Unit 3
Lesson 2: Counting Classrooms
Lesson 3: Pen Pals
Topic 3: Rates
Lesson 5: Comparing Speeds and PricesUnit 2
Lesson 8: World Records (Print available) 

Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]
Lesson 6: Welcome to the Robot Factory
Lesson 6: Interpreting Rates
Lesson 7: Equivalent Ratios Have the Same Unit Rates
Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]
Lesson 8: More About Constant SpeedUnit 2
Lesson 8: World Records (Print available) 

Unit 3
Lesson 4: Model Trains
Lesson 9: Solving Rate ProblemsUnit 3
Lesson 7: More Soft Serve
Topic 4: Percentages
Lesson 10: What Are percentagesUnit 3
Lesson 8: Lucky Duckies [Free lesson]
Lesson 9: Bicycle Goals
Lesson 11: Percentages and Double Number LinesUnit 3
Lesson 9: Bicycle Goals
Lesson 10: What’s Missing? (Print available)
Lesson 12: Percentages and Tape DiagramsUnit 3
Lesson 10: What’s Missing? (Print available)
Lesson 13: Benchmark percentagesUnit 3
Lesson 8: Lucky Duckies [Free lesson]
Lesson 14: Solving Percentage Problems
Lesson 15: Finding This Percent of That
Lesson 16: Finding the Percentage
Unit 3
Lesson 10: What’s Missing? (Print available)
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Lesson 13: A Country as a Village
Topic 5: Let’s Put It to Work 
Lesson 17: Painting a RoomUnit 3
Lesson 13: A Country as a Village
Lesson 7: Equivalent Ratios Have the Same Unit RatesUnit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]

Unit 4: Dividing Fractions

Topic 1: Making Sense of Division 
Lesson 1: Size of Divisor and Size of Quotient
Lesson 2: Meanings of Division
Unit 4Lesson 1: Cookie Cutter
Lesson 3: Interpreting Division SituationsUnit 4Lesson 2: Making Connections (Print available)
Topic 2: Meanings of Fraction Division
Lesson 4: How Many Groups (Part 1)Unit 4Lesson 3: Flour Planner [Free lesson]Lesson 4: Flower Planters 
Lesson 5: How Many Groups (Part 2)Unit 4Lesson 5: Garden Bricks (Print available)
Lesson 6: Using Diagrams to Find the Number of GroupsUnit 4Lesson 5: Garden Bricks (Print available)Lesson 6: Fill the Gap [Free lesson]
Lesson 7: What Fraction of a Group?
Lesson 8: How Much in Each Group? (Part 1)
Lesson 9: How Much in Each Group? (Part 2)
Unit 4Lesson 8: Potting Soil
Topic 3: Algorithm for Fraction Division
Lesson 10: Dividing by Unit and Non-Unit FractionsUnit 4Lesson 7: Break It DownLesson 8: Potting SoilLesson 9: Division Challenges 
Lesson 11: Using an Algorithm to Divide FractionsUnit 4Lesson 9: Division ChallengesPractice Day
Topic 4: Fractions in Lengths, Areas, and Volumes
Lesson 12: Fractional LengthsUnit 4Lesson 11: Classroom Comparisons
Lesson 13: Rectangles with Fractional Side LengthsUnit 4Lesson 12: Puzzling Areas (Print available) [Free lesson]
Lesson 14: Fractional Lengths in Triangles and Prisms
Lesson 15: Volume of PrismsUnit 4Lesson 13: Volume Challenges
Topic 5: Let’s Put It to Work
Lesson 16: Solving Problems with FractionsUnit 4Lesson 10: Swap Meet (Print available)
Lesson 17: Fitting Boxes into BoxesUnit 4Lesson 14: Planter Planner (Print available)

Unit 5: Arithmetic in Base Ten

Topic 1: Warming Up to Decimals 
Lesson 1: Using Decimals in a Shopping ContextUnit 5Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Topic 2: Adding and Subtracting Decimals
Lesson 2: Using Decimals to Represent Addition and SubtractionUnit 5Lesson 3: Fruit by the PoundLesson 4: Missing Digits
Lesson 3: Adding and Subtracting Decimals with Few Non-Zero DigitsUnit 5Lesson 4: Missing Digits
Lesson 4: Adding and Subtracting Decimals with Many Non-Zero Digits 
Topic 3: Multiplying Decimals
Lesson 5: Decimal Points in ProductsUnit 5Lesson 5: Decimal Multiplication
Lesson 6: Methods for Multiplying DecimalsUnit 5Lesson 5: Decimal MultiplicationLesson 6: Multiplying with AreasLesson 7: Multiplication methods (Print available)
Lesson 7: Using Diagrams to Represent MultiplicationUnit 5Lesson 5: Decimal MultiplicationLesson 6: Multiplying with Areas
Lesson 8: Calculating Products of DecimalsUnit 5Lesson 6: Multiplying with Areas
Topic 4: Dividing Decimals
Lesson 9: Using the Partial Quotients MethodUnit 5Lesson 8: Division Diagrams
Lesson 10: Using Long DivisionUnit 5Lesson 8: Division DiagramsLesson 9: Long Division Launch (Print available)Lesson 10: Return of the Long Division (Print available)
Lesson 11: Dividing Numbers That Result in Decimals
Lesson 12: Dividing Decimals by Whole Numbers
Lesson 13: Dividing Decimals by Decimals
Unit 5Lesson 9: Long Division Launch (Print available)Lesson 10: Return of the Long Division (Print available)
Topic 5: Let’s Put It to Work
Lesson 14: Using Operations on Decimals to Solve ProblemsUnit 5Lesson 11: Movie Time [Free lesson]
Lesson 15: Making and Measuring Boxes
Lesson 12: Dividing Decimals by Whole Numbers 
Lesson 13: Dividing Decimals by DecimalsUnit 5Lesson 9: Long Division Launch (Print available)Lesson 10: Return of the Long Division (Print available)

Unit 6: Expressions and Equations

Lesson 1: Tape Diagrams and Equations
Lesson 2: Truth and Equations
Unit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five Equations (Print available)
Lesson 3: Staying in BalanceUnit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five Equations (Print available)Lesson 3: Hanging Around
Lesson 4: Practice Solving Equations and Representing Situations with EquationsUnit 6Lesson 3: Hanging AroundLesson 4: Hanging It UpLesson 5: Swap and Solve (Print available)
Lesson 5: A New Way to Interpret a and bUnit 6Lesson 4: Hanging It UpLesson 5: Swap and Solve (Print available)
Topic 2: Equal and Equivalent
Lesson 6: Write Expressions Where Letters Stand for NumbersUnit 6Lesson 6: Vari-applesLesson 7: Border Tiles
Lesson 7: Revisit PercentagesUnit 3Lesson 10: What’s Missing?Lesson 11: Cost BreakdownLesson 12: More Bicycle Goals
Lesson 8: Equal and EquivalentUnit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five Equations (Print available)Lesson 3: Hanging AroundLesson 6: Vari-apples
Topic 9: The Distributive Property, Part 1Unit 6Lesson 8: Products and Sums [Free lesson]
Lesson 10: The Distributive Property, Part 2
Lesson 11: The Distributive Property, Part 3
Unit 6Lesson 8: Products and Sums [Free lesson]Lesson 9: Products, Sums, and Differences (Print available)
Topic 3: Expressions with Exponents
Lesson 12: Meaning of ExponentsUnit 6Lesson 10: PowersLesson 11: Exponent Expressions (Print available)
Lesson 13: Expressions with Exponents
Lesson 14: Evaluating Expressions with Exponents
Lesson 15: Equivalent Exponential Expressions
Unit 6Lesson 11: Exponent Expressions (Print available)Lesson 12: Squares and Cubes
Topic 4: Relationships Between Quantities 
Lesson 16: Two Related Quantities, Part 1
Lesson 17: Two Related Quantities, Part 2
Lesson 18: More Relationships
Unit 6Lesson 13: Turtles All the WayLesson 14: Representing RelationshipsLesson 15: Connecting Representations (Print available)
Topic 5: Let’s Put It to Work
Lesson 19: Tables, Equations, and Graphs, Oh My!Unit 6Lesson 16: Subway fares (Print available) [Free lesson]

Unit 7: Rational Numbers

Topic 1: Positive and Negative Numbers
Lesson 1: Positive and Negative NumbersUnit 7Lesson 1: Can You Dig In [Free lesson]Lesson 2: Digging Deeper
Lesson 2: Points on the Number LineUnit 7Lesson 2: Digging Deeper
Lesson 3: Comparing Positive and Negative Numbers
Lesson 4: Ordering Rational Numbers
Unit 7Lesson 3: Order in the Class (Print available) [Free lesson]
Lesson 5: Using Negative Numbers to make Sense of ContextsUnit 7 Lesson 4: Sub-Zero
Lesson 6: Absolute Value of Numbers
Lesson 7: Comparing Numbers and Distance from Zero
Unit 7Lesson 5: Distance on the Number Line
Topic 2: Inequalities
Lesson 8: Writing and Graphing InequalitiesUnit 7Lesson 13: Popcorn Possibilities
Lesson 9: Solutions of Inequalities
Lesson 10: Interpreting Inequalities
Unit 7Lesson 6: Tunnel Travel [Free lesson]Lesson 7: Comparing WeightsLesson 8: Shira´s Solutions
Topic 3: The Coordinate Plane
Lesson 11: Points on the Coordinate Plane
Lesson 12: Constructing the Coordinate Plane
Unit 7Lesson 9: Sand Dollar SearchLesson 10: The A-maze-ing Coordinate Plane
Lesson 13: Interpreting Points on a Coordinate PlaneUnit 7Lesson 9: Sand Dollar SearchLesson 10: The A-maze-ing Coordinate PlaneLesson 11: Polygon Maker
Lesson 14: Distances on a Coordinate PlaneUnit 7Lesson 11: Polygon MakerLesson 12: Graph Telephone (Print available)
Lesson 15: Shapes on the Coordinate PlaneUnit 1Lesson 1: Shapes on a Plane [Free lesson]Lesson 2: LettersLesson 5: Exploring Triangles (Print available)Lesson 6: Triangles and ParallelogramsUnit 7Lesson 3: Exploring Parallelograms (Print available)Lesson 11: Polygon MakerLesson 12: Graph Telephone (Print available)
Topic 4: Common Factors and Common Multiples
Lesson 16: Common FactorsUnit 5Lesson 15: Common factors
Lesson 17: Common MultiplesUnit 5Lesson 14: Common Multiples
Lesson 18: Using Common Multiples and Common FactorsUnit 5Lesson 14: Common MultiplesLesson 15: Common factorsPractice Day 2 (Print available)
Topic 5: Let’s Put It to Work
Lesson 19: Drawing on the Coordinate PlaneUnit 7Lesson 11: Polygon MakerLesson 12: Graph Telephone (Print available)

Unit 8: Data Sets and Distributions

Topic 1: Data, Variability, and Statistical Questions
Lesson 1: Got Data?
Lesson 2: Statistical Questions
Unit 8Lesson 1: Screen TimeLesson 2: Dot Plots
Topic 2: Dot Plots and Distributions
Lesson 3: Representing Data Graphically
Lesson 4: Dot Plots
Lesson 5: Using Dot Plots to Answer Statistical Questions
Unit 8Lesson 2: Dot PlotsLesson 3: Minimum Wage (Print available) [Free lesson]Lesson 4: Lots More Dots
Lesson 6: Interpreting Histograms
Lesson 7: Using Histograms to Answer Statistical Questions
Lesson 8: Describing Distributions on Histograms
Unit 8Lesson 5: The Plot Thickens [Free lesson]Lesson 6: DIY Histograms (Print available)
Topic 3: Measures of Center and Variability
Lesson 9: Mean
Lesson 10: Finding and Interpreting the Mean as a Balance Point
Unit 8Lesson 7: Snack Time
Lesson 11: Variability and MADUnit 8Lesson 8: Pop It!
Lesson 12: Using Mean and MAD to Make ComparisonsUnit 8Lesson 9: Hoops
Topic 4: Median and IQR
Lesson 13: MedianUnit 8Lesson 11: Toy Cars [Free lesson]Lesson 12: In the News
Lesson 14: Comparing Mean and MedianUnit 8Lesson 12: In the News
Lesson 15: Quartiles and Interquartile RangeUnit 8Lesson 13: Pumpkin Patch
Lesson 16: Box PlotsUnit 8Lesson 14: Car, Plane, Bus, or Train? (Print available)
Lesson 17: Using Box PlotsUnit 8Lesson 14: Car, Plane, Bus, or Train? (Print available)Lesson 15: Hollywood Part 2Lesson 16: Hollywood Part 3 (Print available)Practice Day 2 (Print available)
Topic 5: Let’s Put It to Work
Lesson 18: Using Data to Solve ProblemsUnit 8Lesson 16: Hollywood Part 3 (Print available)

Unit 9: Putting It All Together

Topic 1: Making Connections
Lesson 1: Fermi Problems
Lesson 2: In Our Class Were the World
Unit 3Lesson 13: A Country as a Village
Lesson 3: Rectangle MadnessUnit 5Lesson 14: Common MultiplesLesson 15: Common factors
Topic 2: Voting
Lesson 4: How Do We Choose?Unit 2Lesson 13: City PlanningLesson 14: Lunch Waste (Print available)
Lesson 5: More than Two ChoicesUnit 3Lesson 13: A Country as a Village
Lesson 6: Picking RepresentativesUnit 8Lesson 16: Hollywood Part 3 (Print available)

Grade 7

Unit 1: Scale Drawings

Illustrative MathematicsDesmos Math 6–A1
Topic 1: Scaled Copies 
Lesson 1: What are Scaled Copies?Unit 1Lesson 1: Scaling Machines [Free lesson]
Lesson 2: Corresponding Parts and Scale FactorsUnit 1Lesson 2: Scaling Robots Unit 3Lesson 1: Toothpicks
Lesson 3: Making Scaled Copies
Lesson 4: Scaled Relationship
Unit 1Lesson 3: Make It Scale Unit 4Lesson 3: Sticker Sizes
Lesson 5: The Size and the Scale FactorUnit 1Lesson 4: Scale Factor Challenges
Lesson 6: Scaling and AreaUnit 1Lesson 5: TilesPractice Day 1 (Print available)
Topic 2: Scale Drawings 
Lesson 7: Scale DrawingsUnit 1Lesson 6: Introducing ScaleLesson 7: Will It Fit? (Print available) [Free lesson]
Lesson 8: Scale Drawings and Maps 
Lesson 9: Creating Scale Drawings
Lesson 10: Changing Scales in Scale Drawings
Unit 1Lesson 8: Scaling StatesLesson 9: Scaling BuildingsLesson 10: Room Redesign (Print available)
Lesson 11: Scales without Units 
Lesson 12: Units in Scale DrawingsUnit 1Lesson 8: Scaling StatesLesson 9: Scaling BuildingsLesson 10: Room Redesign (Print available)Practice Day 2 (Print available)
Topic 3: Let’s Put It to Work
Lesson 13: Draw It to ScaleUnit 1Lesson 10: Room Redesign (Print available)

Unit 2: Introducing Proportional Relationships

Topic 1: Representing Proportional Relationships with Tables
Lesson 1: One of These Things Is Not Like the OthersUnit 2Lesson 1: Paint [Free lesson] 
Lesson 2: Introducing Proportional Relationships with TablesUnit 2Lesson 2: Balloon FloatLesson 3: Sugary Drinks (Print available)Lesson 4: Robot Factory
Lesson 3: More About Constant of ProportionalityUnit 2Lesson 3: Sugary Drinks (Print available)Unit 4Lesson 3: Sticker Sizes
Topic 2: Representing Proportional Relationships with Equations 
Lesson 4: Proportional Relationships with EquationsUnit 2Lesson 4: Robot FactoryLesson 5: SnapshotsLesson 6: Two and Two (Print available) [Free lesson]Lesson 7: All Kinds of Equations
Lesson 5: Two Equations for Each Relationship
Lesson 6: Using Equations to Solve Problems
Unit 2Lesson 6: Two and Two (Print available) [Free lesson]Lesson 7: All Kinds of EquationsPractice Day
Topic 3: Comparing Proportional and Nonproportional Relationships 
Lesson 7: Comparing Relationships with TablesUnit 2Lesson 2: Balloon FloatLesson 3: Sugary Drinks (Print available)Lesson 4: Robot Factory
Lesson 8: Comparing Relationships with EquationsUnit 2Lesson 4: Robot FactoryLesson 5: SnapshotsLesson 6: Two and Two (Print available) [Free lesson]Lesson 7: All Kinds of EquationsLesson 11: Four RepresentationsLesson 12: Water Efficiency
Lesson 9: Solving Problems About Proportional RelationshipsUnit 2Lesson 12: Water Efficiency
Topic 4: Representing Proportional Relationships with Graphs
Lesson 10: Introducing Graphs of Proportional Relationships
Lesson 11: Interpreting Graphs of Proportional Relationships
Lesson 12: Using Graphs to Compare Relationships
Lesson 13: Two Graphs for Each Relationship
Unit 2Lesson 8: Dino Pops [Free lesson]Lesson 9: Gallon ChallengeLesson 10: Three TurtlesLesson 11: Four RepresentationsLesson 12: Water Efficiency
Topic 5: Let’s Put It to Work
Lesson 14: For RepresentationsUnit 2Lesson 11: Four Representations (Print available)
Lesson 15: Using Water EfficiencyUnit 2Lesson 12: Water Efficiency

Unit 3: Measuring Circles

Topic 1: Circumference of a Circle 
Lesson 1: How Well Can You Measure?Unit 3Lesson 1: Toothpicks
Lesson 2: Exploring Circles
Lesson 3: Exploring Circumference
Lesson 4: Applying Circumference
Unit 3Lesson 2: Is It a Circle?Lesson 3: Measuring Around [Free lesson]
Lesson 5: Circumference and Wheels 
Topic 2: Area of a Circle
Lesson 6: Estimating AreasUnit 3Lesson 5: Area Strategies
Lesson 7: Exploring the Area of a Circle
Lesson 8: Relating Area to Circumference
Unit 3Lesson 5: Area StrategiesLesson 6: Radius Squares (Print available)Lesson 7: Why Pi?Lesson 8: Area Challenges [Free lesson]Lesson 9: Circle vs. SquarePractice Day 2 (Print available)
Lesson 9: Applying Area of CirclesUnit 3Lesson 6: Radius Squares (Print available)
Topic 3: Let’s Put It to Work
Lesson 10: Distinguishing Circumference and AreaUnit 3Lesson 7: Why Pi?
Lesson 11: Stained-Glass WindowsUnit 3Lesson 5: Area StrategiesLesson 6: Radius Squares (Print available)

Unit 4: Proportional Relationships and Percentages

Topic 1: Proportional Relationships with Fractions 
Lesson 1: Lots of Flags
Lesson 2: Ratios and Rates with Fractions
Lesson 3: Revisiting Proportional Relationships
Lesson 4: Half as Much Again
Unit 4Lesson 1: Mosaics [Free lesson]Lesson 2: Peach Cobbler (Print available)Lesson 3: Sticker Sizes
Lesson 5: Say It with Decimals 
Topic 2: Percent Increase and Decrease 
Lesson 6: Increasing and DecreasingUnit 4Lesson 4: More and LessLesson 5: All the EquationsLesson 6: 100% (Print available)Lesson 7: Percent machines [Free lesson]Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Lesson 7: One Hundred percentUnit 4Lesson 6: 100% (Print available)
Lesson 8: Percent Increase and Decrease with EquationsUnit 4Lesson 5: All the Equations
Lesson 9: More and Less than 1% 
Topic 3: Applying Percentages
Lesson 10: Tax and Tip
Lesson 11: Percentage Contexts
Unit 4Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Lesson 12: Finding the PercentagesUnit 4Lesson 4: More and Less
Lesson 13: Measurement Error
Lesson 14: Percent Error
Lesson 15: Error Intervals
Unit 4Lesson 11: Bookcase Builder
Topic 4: Let’s Put It to Work 
Lesson 16: Posing Percent ProblemsUnit 4Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]Practice Day

Unit 5: Rational Number Arithmetic

Topic 1: Interpreting Negative Numbers 
Lesson 1: Interpreting Negative NumbersUnit 5Lesson 1: Floats and Anchors [Free lesson]
Topic 2: Adding and Subtracting Rational Numbers
Lesson 2: Changing Temperatures
Lesson 3: Changing Elevation
Unit 5Lesson 2: More Floats and AnchorsLesson 3: BumpersLesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 4: Money and Debts 
Lesson 5: Representing SubtractionUnit 5Lesson 5: Number Puzzles
Lesson 6: Subtracting Rational Numbers
Lesson 7: Adding and Subtracting to Solve Problems
Unit 5Lesson 3: BumpersLesson 4: Draw Your Own (Print available) [Free lesson]Lesson 5: Number PuzzlesLesson 10: Integer Puzzles [Free lesson]Lesson 11: Changing TemperaturesLesson 13: Solar Panels and More (Print available)Practice Day 1 (Print available)
Topic 3: Multiplying and Dividing Rational Numbers
Lesson 8: Position, Speed, and Direction
Lesson 9: Multiplying Rational Numbers
Lesson 10: Multiply!
Unit 5Lesson 7: Back in Time
Lesson 11: Dividing Rational NumbersUnit 5Lesson 8: Speeding Turtles
Lesson 12: Negative Rates 
Topic 4: Four Operations with Rational Numbers 
Lesson 13: Expressions with Rational NumbersUnit 5Lesson 9: Expressions (Print available)
Lesson 14: Solving Problems with Rational NumbersLesson 11: Changing Temperatures
Lesson 12: Arctic Ice Sea (Print available)
Lesson 13: Solar Panels and More (Print available)
Topic 5: Solving Equations When There Are Negative Numbers 
Lesson 15: Making and Measuring Boxes 
Lesson 16: Representing Contexts with Equations 
Topic 6: Let’s Put It to Work 
Lesson 17: The Stock market

Unit 6: Expressions, Equations, and Inequalities

Topic 1: Representing Situations of the Form px + q and p(+ q) = r
Lesson 1: Relationships Between Quantities
Unit 2 Lesson 1: Paint [Free lesson] Lesson 2: Balloon Float
Unit 4 Lesson 1: Mosaics [Free lesson] Lesson 2: Peach Cobbler (Print available)
Unit 6 Lesson 1: Toothpicks and Tiles
Lesson 2: Reasoning about Contexts with Tape Diagrams
Lesson 3: Reasoning about Equations with Tape Diagrams
Lesson 4: Reasoning about Equations and Tape Diagrams (Part 1)
Lesson 5: Reasoning about Equations and Tape Diagrams (Part 2)
Unit 6Lesson 2: Smudged ReceiptsLesson 3: EquationsLesson 4: Seeing Structure (Print available)
Lesson 6: Distinguishing between Two Types of SituationsUnit 6Lesson 6: Balancing EquationsLesson 7: Keeping It True (Print available)
Topic 2: Solving Equations of the Form px + q and p(+ q) = and Problems That lead to Those Equations 
Lesson 7: Reasoning about Solving Equations (Part 1)Unit 6Lesson 5: Balancing MovesLesson 6: Balancing EquationsLesson 7: Keeping It True (Print available) 
Lesson 8: Reasoning about Solving Equations (Part 2)Unit 6Lesson 5: Balancing MovesLesson 6: Balancing EquationsLesson 7: Keeping It True (Print available)Lesson 9: Always-Equal Machines
Topic 9 Dealing with Negative Numbers 
Lesson 10: Different Options for Solving One EquationUnit 6Lesson 7: Keeping It True (Print available)Lesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available)
Lesson 11: Using Equations to Solve ProblemsUnit 6Lesson 12: Community Day (Print available)
Lesson 12: Solving Problems about Percent Increase or DecreaseUnit 4Lesson 10: Cost of College (Print available)
Topic 3: Inequalities 
Lesson 13: Reintroducing InequalitiesUnit 6Lesson 13: I Saw the SignsLesson 15: BudgetingLesson 16: Shira the Sheep [Free lesson]
Lesson 14: Finding Solutions to Inequalities in Context
Lesson 15: Efficiency Solving Inequalities
Unit 6Lesson 14: Unbalanced HangersLesson 15 Budgeting (Print available)Lesson 16: Shira the Sheep [Free lesson]Lesson 17: Write Them and Solve Them (Print available)
Lesson 16: Interpreting Inequalities
Lesson 17: Modeling with Inequalities
Unit 6Lesson 16: Shira the Sheep [Free lesson]Lesson 17: Write Them and Solve Them (Print available)Practice Day 2 (Print available)
Topic 4: Writing Equivalent Expressions 
Lesson 18: Subtraction in Equivalent ExpressionsUnit 6Lesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available) 
Lesson 19: Expanding and FactoringUnit 6Lesson 8: Factoring and Expanding (Print available)Lesson 11: Equation Roundtable (Print available)
Lesson 20: Combining Like Terms (Part 1)
Lesson 21: Combining Like Terms (Part 2)
Lesson 22: Combining Like Terms (Part 3)
Unit 6Lesson 2: Smudged ReceiptsLesson 6: Balancing EquationsLesson 8: Factoring and Expanding (Print available)Lesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available)Practice Day 1 (Print available)
Topic 5: Let’s Put It to Work
Lesson 23: Applications of ExpressionsUnit 6Lesson 12: Community Day (Print available)

Unit 7: Angles, Triangles, and Prisms

Topic 1: Angle Relationships
Lesson 1:Relationships of Angles
Unit 7 Lesson 1: Pinwheels Lesson 2: Friendly Angles [Free lesson] Lesson 3: Angle Diagrams
Lesson 2: Adjacent Angles
Lesson 3: Nonadjacent Angles
Unit 7Lesson 2: Friendly Angles [Free lesson]Lesson 3: Angle Diagrams
Lesson 4: Solving for Unknown AnglesUnit 7Lesson 2: Friendly Angles [Free lesson]Lesson 3: Angle DiagramsLesson 4: Missing Measures (Print available)
Lesson 5: Using Equations to Solve for Unknown AnglesUnit 7Lesson 3: Angle DiagramsLesson 4: Missing Measures (Print available) [Free lesson]
Topic 2: Drawing Polygons with Given Conditions 
Lesson 6: Building Polygons (Part 1)
Lesson 7: Building Polygons (Part 2)
Unit 7Lesson 6: Is It Enough?
Lesson 8: Triangles with 3 Common MeasuresUnit 7Lesson 13: Popcorn Possibilities
Lesson 9: Drawing Triangles (Part 1)
Lesson 10: Drawing Triangles (Part 2)
Unit 7Lesson 5: Can You Build It? [Free lesson]Lesson 6: Is It Enough?Lesson 7: More Than OneLesson 8: Can You Draw It? (Print available)Practice Day 1 (Print available)
Topic 3: Solid Geometry
Lesson 11: Slicing SolidsUnit 7Lesson 9: Slicing Solids
Lesson 12: Volume of Right PrismsUnit 7Lesson 10: Simple Prisms
Lesson 13: Decomposing Bases for AreasUnit 7Lesson 11: More Complicated Prisms
Lesson 14: Surface Area of Right PrismsUnit 7Lesson 10: Simple PrismsLesson 11: More Complicated PrismsLesson 12: Surface Area Strategies (Print available)
Lesson 15: Distinguishing Volume and Surface Area
Lesson 16: Applying Volume and Surface AreaUnit 7Lesson 13: Popcorn Possibilities
Topic 4: Let’s Put It to Work
Lesson 17: Building Prisms

Unit 8: Probability and Sampling

Topic 1: Probabilities of Single Step Events
Lesson 1: Mystery Bags
Lesson 2: Chance Experiments
Lesson 3: What Are Probabilities?
Unit 8 Lesson 1: How Likely? (Print available) [Free lesson] Lesson 2: Prob-bear-bilities [Free lesson] Lesson 3: Mystery Bag
Lesson 4: Estimating Probabilities Through Repeated ExperimentsUnit 8Lesson 4: Spin ClassLesson 5: Is It Fair?Lesson 6: Fair Games
Lesson 5: More Estimating ProbabilitiesUnit 8Lesson 6: Fair GamesLesson 7: Weather or NotLesson 9: Car, Bike, or Train? (Print available)
Lesson 6: Estimating Probabilities Using SimulationUnit 8Lesson 6: Fair GamesLesson 7: Weather or NotLesson 8: Simulate ItLesson 9: Car, Bike, or Train? (Print available)
Topic 2: Probabilities of Multi-step Events
Lesson 7: Simulating Multi-step EventsUnit 8Lesson 7: Weather or NotLesson 8: Simulate ItLesson 9: Car, Bike, or Train? (Print available)
Lesson 8: Keeping Track of All Possible OutcomesUnit 8Lesson 4: Spin ClassLesson 5: Is It Fair?Lesson 6: Fair Games
Topic 9: Multi-step experiments
Lesson 10: Designing SimulationsUnit 8Lesson 7: Weather or NotLesson 8: Simulate ItLesson 9: Car, Bike, or Train? (Print available)
Topic 3: Sampling
Lesson 11: Comparing Groups
Lesson 12: Larger Populations
Lesson 13: What Makes a Good Sample?
Lesson 14: Sampling in a Fair Way
Unit 8Lesson 10: Crab Island [Free lesson]Lesson 11: Headlines
Topic 4: Using Samples
Lesson 15: Estimating Population Measures of Center
Lesson 16: Estimating Population Proportions
Unit 8 Lesson 9: Car, Bike, or Train? (Print available)Lesson 10: Crab Island [Free lesson]Lesson 11: HeadlinesLesson 12: Flower Power
Lesson 17: More about Sampling Variability
Lesson 18: Comparing Populations Using Samples
Lesson 19: Comparing Populations with Friends
Unit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 10: Crab Island [Free lesson]Lesson 13: Plots and SamplesLesson 14: School Newspaper (Print available)Lesson 15: Asthma Rates (Print available)
Topic 5: Let’s Put It to Work
Lesson 20: Memory TestUnit 8Lesson 14: School Newspaper (Print available)Lesson 15: Asthma Rates (Print available)

Grade 8

Unit 1: Rigid Transformations and Congruence

Illustrative MathematicsDesmos Math 6–A1
Topic 1: Rigid Transformations 
Lesson 1: Moving in the PlaneUnit 1Lesson 1: Transformers [Free lesson]
Lesson 2: Naming the MovesUnit 1Lesson 2: Spinning, Flipping, Sliding [Free lesson]
Lesson 3: Grid MovesUnit 1Lesson 3: Transformation GolfLesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting CoordinatedUnit 3Lesson 6: Translations
Lesson 4: Making the MovesUnit 1Lesson 1: Transformers [Free lesson]Lesson 2: Spinning, Flipping, Sliding [Free lesson]Lesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting Coordinated
Lesson 5: Coordinate MovesUnit 1Lesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting Coordinated
Lesson 6: Describing TransformationsUnit 1Lesson 5: Getting CoordinatedLesson 6: Connecting the Dots [Free lesson]
Topic 2: Properties of Rigid Transformations 
Lesson 7: No Bending or StretchingUnit 1Lesson 7: No Bending, No Stretching
Lesson 8: Rotation PatternsUnit 1Lesson 1: Transformers [Free lesson]Lesson 2: Spinning, Flipping, Sliding [Free lesson]Lesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting Coordinated
Lesson 9: Moves in Parallel
Lesson 10: Composing Figures
Unit 1 Lesson 10: Transforming Angles
Topic 3: Congruence 
Lesson 11: What is the Same?
Lesson 12: Congruent Polygons
Lesson 13: Congruence
Unit 1 Lesson 7: Are They the Same?Lesson 9: Are They Congruent?Practice Day (Print available)
Topic 4: Angles in a Triangle
Lesson 14: Alternate Interior Angles
Lesson 15: Adding the Angles in a Triangle
Unit 1 Lesson 11: Tearing It Up (Print available)
Lesson 16: Parallel Lines and the Angles in a TriangleUnit 1 Lesson 10: Transforming Angles
Topic 5: Let’s Put It to Work
Lesson 17: Rotate and TessellateLesson 13: Tessellate [Free lesson]

Unit 2: Dilations, Similarity, and Introducing Slope

Topic 1: Dilations
Lesson 1: Projecting and ScalingUnit 2Lesson 1: Sketchy Dilations [Free lesson]Lesson 2: Dilation Mini Golf (Print available) [Free lesson]
Lesson 2: Circular Grid
Lesson 3: Dilations with No Grid
Lesson 4: Dilations on a Square Grid
Lesson 5: More Dilations
Unit 2Lesson 1: Sketchy Dilations [Free lesson]Lesson 2: Dilation Mini Golf (Print available) [Free lesson]Lesson 3: Match My DilationLesson 4: Dilations on a Plane
Topic 2: Similarity 
Lesson 6: SimilarityUnit 2Lesson 5: Transformations Golf with DilationsLesson 6: Social Scavenger Hunt (Print available) [Free lesson]
Lesson 7: Similar Polygons 
Lesson 8: Similar Triangles
Lesson 9: Side Length Quotients in Similar Triangles
Unit 2Lesson 7: Are Angles Enough?Lesson 8: Shadows
Topic 3: Slope
Lesson 10: Meet SlopeUnit 2Lesson 9: Water SlideLesson 10: Points on a PlanePractice Day (Print available)Unit 3Lesson 3: PostersLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations Unit 4Lesson 8: When Are They the Same?
Lesson 11: Writing Equations of LinesUnit 3Lesson 3: PostersLesson 6: TranslationsLesson 10: SolutionsLesson 11: Pennies and Quarters Unit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)
Lesson 12: Using Equations of LinesUnit 3Lesson 9: Coin Capture
Topic 4: Let’s Put It to Work
Lesson 13: The Shadow KnowsUnit 2Lesson 8: Shadows

Unit 3: Linear Relationships

Topic 1: Proportional Relationships 
Lesson 1: Understanding Proportional RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson]
Lesson 2: Graphs of Proportional RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson]Lesson 2: Water Tank Unit 5Lesson 4: Window Frames
Lesson 3: Representing Proportional RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson] Unit 5Lesson 4: Window FramesLesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 4: Comparing Proportional RelationshipsUnit 3Lesson 3: Posters
Topic 2: Representing Linear Relationships
Lesson 5: Introduction to Linear RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson]Lesson 4: Stacking CupsUnit 5Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 6: More Linear RelationshipsUnit 5Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 7: Representations of Linear RelationshipsUnit 3Lesson 5: Flags [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 8: Translating mx + bUnit 3Lesson 3: PostersLesson 6: Translations
Topic 3: Finding Slopes 
Lesson 9: Slopes Don’t Have to be PositiveUnit 3Lesson 5: Flags [Free lesson]Lesson 6: TranslationsLesson 7: Water CoolerLesson 8: Landing Planes
Lesson 10: Calculating SlopeUnit 3Lesson 7: Water CoolerLesson 8: Landing Planes
Lesson 11: Equations of All Kinds of LinesUnit 3Lesson 3: PostersLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Topic 4: Linear Equations 
Lesson 12: Solutions to Linear EquationsUnit 3Lesson 3: PostersLesson 6: TranslationsLesson 10: Solutions Unit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)
Lesson 13: More Solutions to Linear EquationsUnit 3 Lesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: TranslationsLesson 7: Water CoolerLesson 10: Solutions
Topic 5: Let’s Put It to Work 
Lesson 14: Using Linear Relations to Solve ProblemsUnit 3 Lesson 11: Pennies and Quarters

Unit 4: Linear Equations and Linear Systems

Topic 1: Puzzle Problems 
Lesson 1: Number PuzzlesUnit 4Lesson 1: Number machines
Topic 2: Linear Equation in One Variable 
Lesson 2: Keeping the Equation BalancedUnit 4Lesson 2: Keep It Balanced
Lesson 3: Balanced MovesUnit 4Lesson 3: Balanced Moves
Lesson 4: More Balanced MovesUnit 4Lesson 4: More Balanced Moves (Print available)
Lesson 5: Solving Any Linear EquationUnit 4Lesson 4: More Balanced Moves (Print available)Lesson 5: Equation Roundtable (Print available) [Free lesson]Lesson 6: Strategic Solving (Print available)
Lesson 6: Strategic SolvingUnit 4Lesson 5: Equation Roundtable (Print available) [Free lesson]Lesson 6: Strategic Solving (Print available)
Lesson 7: All, Some, or No Solutions
Lesson 8: How many Solutions?
Unit 4Lesson 7: All, Some, or None?
Lesson 9: When Are They the SameUnit 4Lesson 8: When Are They the Same?
Topic 3: Systems of Linear Equations
Lesson 10: On or Off the Line?Unit 4Lesson 7: All, Some, or None?Lesson 8: When Are They the Same?Lesson 13: All, Some, or None? Part 2
Lesson 11: On Both of the Lines
Lesson 12: Systems of Equations
Lesson 13: Solving Systems of Equations
Unit 4 Lesson 9: On or Off the Line?Lesson 10: On Both LinesLesson 11: Make Them Balance [Free lesson]Lesson 12: Line Zapper [Free lesson]Lesson 13: All, Some, or None? Part 2Practice Day 2 (Print available)
Lesson 14: Solving More Systems 
Lesson 15: Writing Systems of EquationsUnit 4 Lesson 14: Strategic Solving, Part 2 (Print available)
Topic 4: Let’s Put It to Work 
Lesson 16: Posing Problems with Systems of EquationsUnit 4 Lesson 14: Strategic Solving, Part 2 (Print available)

Unit 5: Functions and Volume

Topic 1: Inputs and Outputs 
Lesson 1: Inputs and OutputsUnit 5Lesson 1: Turtle Crossing [Free lesson]Lesson 2: Guess My Rule [Free lesson]
Lesson 2: Introduction to FunctionsUnit 5Lesson 1: Turtle Crossing [Free lesson]Lesson 2: Guess My Rule [Free lesson]Lesson 3: Function or Not?
Topic 2: Representing and Interpreting Functions 
Lesson 3: Equations of FunctionsUnit 3Lesson 1: Turtle Time Trials [Free lesson] Unit 5Lesson 3: Function or Not?Lesson 4: Window Frames
Lesson 4: Tables, Equations, and Graphs of Functions
Lesson 5: More Graphs of Functions
Unit 5Lesson 4: Window FramesLesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 6: Even More Graphs of Functions 
Lesson 7: Connecting Representations of FunctionsUnit 5Lesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: (Print available)Charge!
Topic 3: Linear Functions and Rates of Change
Lesson 8: Linear FunctionsUnit 2Lesson 9: Water SlideLesson 10: Points on a PlaneUnit 3Lesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Lesson 9: Linear ModelsUnit 5Lesson 3: PostersLesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 10: Piecewise Linear FunctionsUnit 5Lesson 9: Piecing It Together
Topic 4: Cylinder and Cones 
Lesson 11: Filling Containers 
Lesson 12: How Much Will Fit? 
Lesson 13: The Volume of a CylinderUnit 5Lesson 10: Volume LabLesson 11: Cylinders [Free lesson]Lesson 12: Scaling Cylinders
Lesson 14: Finding Cylinder DimensionsUnit 5Lesson 10: Volume LabLesson 11: Cylinders [Free lesson]Lesson 12: Scaling CylindersLesson 14: Missing Dimensions (Print available)
Lesson 15: The Volume of a ConeUnit 5Lesson 10: Volume LabLesson 13: Cones [Free lesson]Lesson 14: Missing Dimensions (Print available)
Lesson 16: Finding Cone DimensionsUnit 5Lesson 12: Scaling CylindersLesson 13: Cones [Free lesson]Lesson 14: Missing Dimensions (Print available)
Topic 5: Dimensions and Spheres 
Lesson 17: Scaling One DimensionUnit 5Lesson 12: Scaling Cylinders
Lesson 18: Scaling Two Dimensions 
Lesson 19: Estimating a Hemisphere 
Lesson 20: The Volume of a Sphere
Lesson 21: Cylinders, Cones, and Spheres
Unit 5Lesson 15: SpheresPractice Day 2 (Print available)
Topic 6: Let’s Put It to Work 
Lesson 22: Volume As a Function of …Unit 5Lesson 15: Spheres

Unit 6: Associations in Data

Topic 1: Does This Predict That? 
Lesson 1: Organizing DataUnit 6 Lesson 1: Click Battle
Lesson 2: Plotting DataUnit 6 Lesson 2: Wing Span
Topic 2: Associations in Numerical Data 
Lesson 3: What a Point in a Scatter Plot MeansUnit 6 Lesson 1: Click BattleLesson 2: Wing SpanLesson 3: Robots [Free lesson]Lesson 7: Scatter Plot City
Lesson 4: Fitting a LineUnit 6 Lesson 4: Dapper Cats [Free lesson]Lesson 5: Fit Fights [Free lesson]Lesson 6: Interpreting SlopesLesson 8: Animal BrainsPractice Day 1 (Print available) [Free lesson]Practice Day 2 (Print available)
Lesson 5: Describing Trends in Scatter PlotsUnit 6 Lesson 1: Click BattleLesson 2: Wing SpanLesson 3: Robots [Free lesson]Lesson 7: Scatter Plot City(Print available)Practice Day 1 [Free lesson]
Lesson 6: The Slope of a Fitted LineUnit 6 Lesson 6: Interpreting SlopesLesson 7: Scatter Plot CityPractice Day 1 (Print available) [Free lesson]Practice Day 2 (Print available)
Lesson 7: Observing More patterns in Scatter PlotsUnit 6 Lesson 1: Click BattleLesson 2: Wing SpanLesson 3: Robots [Free lesson]Lesson 7: Scatter Plot City
Lesson 8: Analyzing Bivariate DataUnit 6Lesson 9: Tasty Fruit
Topic 3: Associations in Categorical data 
Lesson 9: Looking for AssociationsUnit 6Lesson 10: Finding Associations [Free lesson]Lesson 11: Federal BudgetsPractice Day 3 (Print available)
Lesson 10: Using Data Displays to Find associationsUnit 6Lesson 10: Finding Associations [Free lesson]Lesson 9: Tasty Fruit
Topic 4: Let’s Put It to Work
Lesson 11: Gone in 30 SecondsUnit 6Lesson 11: Federal Budgets

Unit 7: Exponents and Scientific Notation

Topic 1: Exponent Review 
Lesson 1: Exponent ReviewUnit 7 Lesson 1: Circles [Free lesson]Lesson 2: Combining Exponents
Topic 2: Exponent Rules 
Lesson 2: Multiplying Powers of 10
Lesson 3: Powers of Powers of 10
Lesson 4: Dividing Powers of 10
Unit 7 Lesson 3: Power Pairs (Print available) [Free lesson]Lesson 4: Rewriting Powers  
Lesson 5: Negative Exponents with Powers of 10Unit 7 Lesson 5: Zero and Negative ExponentsLesson 6: Write a Rule (Print available)Practice Day 1 (Print available)
Lesson 6: What about Other Bases? 
Lesson 7: Practice with Rational Bases
Lesson 8: Combining Bases 
Topic 3: Scientific Notation 
Lesson 9: Describing Large and Small Numbers using Powers of 10Unit 7 Lesson 7: Scales and Weights
Lesson 10: Representing Large Numbers on the Number Line
Lesson 11: Representing Small Numbers on the Number Line
Unit 7 Lesson 8: Point Zapper
Lesson 12: Applications of Arithmetic with Powers of 10Unit 7  Lesson 8: Point ZapperLesson 9: Use Your Powers
Lesson 13: Defining Scientific Notation
Lesson 14: Multiplying, Dividing, and Estimating with Scientific Notation
Unit 7 Lesson 10: Solar System [Free lesson]Lesson 11: Balance the Scales [Free lesson]Lesson 13: Star Power
Lesson 15: Adding and Subtracting with Scientific NotationUnit 7 Lesson 10: Solar System [Free lesson]Lesson 11: Balance the Scales [Free lesson]Lesson 12: City LightsLesson 13: Star Power
Topic 4: Let’s Put It to Work
Lesson 16: Is a Smartphone Smart Enough to Go to the Moon?Lesson 13: Star Power Practice Day 2 (Print available)

Unit 8: Pythagorean Theorem and Irrational Numbers

Topic 1: Side Lengths and Areas of Squares
Lesson 1: The Areas of Squares and Their Side LengthsUnit 8Lesson 1: Tilted Squares
Lesson 2: Side Lengths and AreasUnit 8Lesson 2: From Squares to RootsLesson 3: Between Squares
Lesson 3: Rational and Irrational Numbers
Lesson 4: Square Roots on the Number Line
Lesson 5: Reasoning about Square RootsUnit 8Lesson 2: From Squares to RootsLesson 3: Between SquaresLesson 4: Root Down [Free lesson]Practice Day 1 (Print available)
Topic 2: The Pythagorean Theorem
Lesson 6: Finding Side Lengths of TrianglesUnit 8Lesson 6: The Pythagorean TheoremLesson 7: Pictures to Prove ItLesson 8: Triangle-Tracing Turtle [Free lesson]
Lesson 7: A Proof of the Pythagorean TheoremUnit 8Lesson 7: Pictures to Prove It
Lesson 8: Finding Unknown Side LengthsUnit 8Lesson 11: Pond Hopper
Lesson 9: The ConverseUnit 8Lesson 9: Make It Right
Lesson 10: Applications of the Pythagorean TheoremUnit 8Lesson 10: Taco Truck [Free lesson]
Lesson 11: Finding Distances in the Coordinate PlaneUnit 8Lesson 11: Pond Hopper
Topic 3: Side Lengths and Volumes of Cubes
Lesson 12: Edge Lengths and Volumes
Lesson 13: Cube Roots
Unit 8Lesson 5: Filling Cubes
Topic 4: Decimal Representation of Rational and Irrational Numbers
Lesson 14: Decimal Representation of Rational and Numbers
Lesson 15: Infinite Decimal expansions
Unit 8Lesson 12: Fractions to DecimalsLesson 13: Decimals to Fractions
Topic 5: Let’s Put It to Work
Lesson 16: When Is the Same Size Not the Same Size?Unit 8Lesson 10: Taco Truck [Free lesson]

Unit 9: Putting It All Together

Topic 1: Tessellations
Lesson 1: Tessellations of the Plane
Lesson 2: Regular Tessellations
Lesson 3: Tessellating Polygons
Topic 2: The Weather
Lesson 4: What Influences Temperature?
Lesson 5: Plotting the Weather
Lesson 6: Using and Interpreting a Mathematical Model

Grade 6

Chapter 1: Use Positive Rational Numbers

enVision MathDesmos Math 6–A1
Lesson 1: Fluently Add, Subtract, and Multiply DecimalsUnit 5
Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Lesson 2: Decimal Diagrams [Free lesson]
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 5: Decimal Multiplication
Lesson 12: Budget Vehicles (Print available)
Practice Day 1 (Print available)
Lesson 2: Fluently Divide Whole Numbers and DecimalsUnit 5
Lesson 8: Division Diagrams
Lesson 9: Long Division Launch (Print available)
Lesson 10: Return of the Long Division (Print available)
Lesson 11: Movie Time [Free lesson]
Lesson 12: Budget Vehicles (Print available)
Practice Day 2
Lesson 3: Multiply FractionsUnit 4
Lesson 12: Puzzling Areas (Print available) [Free lesson]
Lesson 13: Volume Challenges
Lesson 14: Planter Planner (Print available)
Lesson 4: Understand Division with FractionsUnit 4
Lesson 1: Cookie Cutter
Lesson 2: Making Connections (Print available)
Lesson 3: Flour Planner [Free lesson]
Lesson 4: Flower Planters
Practice Day (Print available)
Lesson 5: Divide Fractions by fractionsUnit 4
Lesson 5: Garden Bricks (Print available)
Lesson 7: Break It Down
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 14: Planter planner (Print available)
Practice Day (Print available)
Lesson 6: Divide Mixed NumbersUnit 4
Lesson 5 Garden Bricks (Print available)
Lesson 6 Fill the Gap [Free lesson]
Lesson 11 Classroom Comparisons
Lesson 7: Solve Problems with Rational NumbersLesson 3: Flour Planner [Free lesson]
Lesson 4: Flower Planters
Lesson 5: Garden Bricks (Print available)
Lesson 10: Swap Meet (Print available)

Chapter 2: Integers and Rational Numbers

Lesson 1: Understand IntegersUnit 7
Lesson 1: Can You Dig it In [Free lesson]
Lesson 4 Sub-Zero
Lesson 2: Represent Rational Numbers on the Number LineUnit 7
Lesson 2: Digging Deeper
Lesson 3: Order in the Class (Print available) [Free lesson]
Practice Day 1
Lesson 3: Absolute Values of Rational NumbersUnit 7
Lesson 5: Distance on the Number Line
Practice Day 1 (Print available)
Lesson 4: Represent Rational Numbers on the Coordinate Plane 
Lesson 5: Find Distances on the Coordinate Plane
Lesson 6: Represent Polygons on the Coordinate Plane
Unit 7
Lesson 11: Polygon Maker

Chapter 3: Numeric and Algebraic Expressions

Chapter 4: Represent and Solve Equations and Inequalities

Lesson 1: Understand Equations and SolutionsUnit 6
Lesson 1: Weight for It [Free lesson]
Lesson 3: Hanging Around
Lesson 13: Turtles All the Way
Lesson 2: Apply Properties of Equality
Lesson 3: Write and Solve Addition and Subtraction Equations
Lesson 4: Write and Solve Multiplication and Division Equations
Unit 6
Lesson 3: Hanging Around
Lesson 4: Hanging It Up
Lesson 5: Swap and Solve (Print available)
Practice Day 1 (Print Available)
Lesson 5: Write and Solve Equations with Rational NumbersUnit 6
Lesson 4; Hanging It Up
Lesson 5: Swap and Solve (Print available)
Lesson 6: Understand and Write InequalitiesUnit 7
Lesson 6: Tunnel Travel [Free lesson]
Lesson 7: Comparing Weights
Lesson 7: Solve InequalitiesUnit 7
Lesson 8: Shira’s Solutions
Lesson 8: Understand Dependent and Independent VariablesUnit 6
Lesson 13: Turtles All the Way
Lesson 9: Use Patterns to Write and Solve Equations
Lesson 10: Relate Tables, Graphs, and Equations
Unit 6
Lesson 13: Turtles All the Way
Lesson 14: Representing Relationships
Lesson 15: Connecting Representations (Print available)
Lesson 16: Subway Fares (Print available) [Free lesson]
Practice Day 2 (Print available)

Chapter 5: Understand and Use Ratio and Rate

Chapter 6: Understand and Use Percent

Lesson 1: Understand PercentUnit 3
Lesson 8: Lucky Duckies [Free lesson]
Lesson 2: Relate Fractions, Decimals, and PercentsUnit 5
Lesson 13: Grocery Prices (Print available)
Lesson 3: Represent Percents Greater Than 100 or Less than 1 
Lesson 4: Estimate to Find Percent 
Lesson 5: Find the Percent of a Number
Lesson 6: Find the Whole Given a Part and the Percent
Unit 3
Lesson 9: Bicycle Goals
Lesson 10: What’s Missing?
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Practice Day 2 (Print Available)

Chapter 7: Solve Area, Surface Area, and Volume Problems

Chapter 8: Display, Describe, and Summarize data

Grade 7

Chapter 1: Rational Number Operations

enVision MathDesmos Math 6–A1
Lesson 1: Relate Integers and Their OppositesUnit 5
Lesson 1: Floats and Anchors [Free lesson]
Lesson 2: Understand Rational NumbersUnit 4
Lesson 13: Decimal Deep Dive (Print available)
Lesson 3: Add Integers
Lesson 4: Subtract Integers
Unit 5
Lesson 2: More Floats and Anchors
Lesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 5: Number Puzzles
Lesson 10: Integer Puzzles [Free lesson]
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)
Lesson 5: Add and Subtract Rational NumbersUnit 5
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 5: Number Puzzles
Lesson 10: Integer Puzzles [Free lesson]
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)
Practice Day 1 (Print available)
Lesson 6: Multiply IntegersUnit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Practice Day 2 (Print available)
Lesson 7: Multiply Rational NumbersUnit 5
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)
Practice Day 2 (Print available)
Lesson 8: Divide IntegersUnit 5
Lesson 8: Speeding Turtles
Lesson 9: Divide Rational NumbersUnit 5
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)
Practice Day 2 (Print available)
Lesson 10 Solve Problems with Rational NumbersUnit 5
Lesson 11: Changing Temperatures
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)

Chapter 2: Analyze and Use Proportional Relationships

Lesson 1: Connect Ratios, Rates, and Unit Rates 
Lesson 2: Determine Unit Rates with Ratios of Fractions 
Lesson 3: Understand Proportional Relationships: Equivalent RatiosUnit 2
Lesson 1: Paint [Free lesson]
Lesson 2: Balloon Float
Lesson 4: Describe Proportional Relationships: Constant of ProportionalityUnit 2
Lesson 3: Sugary Drinks (Print available)
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available) [Free lesson]
Lesson 7: All Kinds of Equations
Lesson 10: Three Turtles
Practice Day (Print available)
Unit 3
Lesson 1 Circumference of a Circle
Lesson 5: Graph Proportional RelationshipsUnit 2
Lesson 8: Dino Pops [Free lesson]
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations (Print available)
Lesson 6: Apply Proportional Reasoning to Solve ProblemsUnit 2
Lesson 11: Four Representations (Print available)
Lesson 12: Water Efficiency

Chapter 3: Analyze and Solve Percent Problems

Chapter 4: Generate Equivalent Expressions

Chapter 5: Solve Problems Using Equations and Inequalities

Chapter 6: Use Sampling to Draw Inferences About Populations

Chapter 7: Probability

Lesson 1: Understand Likelihood and ProbabilityUnit 8
Lesson 1 How Likely? (Print available) [Free lesson]
Lesson 2 Prob-bear-bilities [Free lesson]
Lesson 3 Mystery Bag
Lesson 2: Understand Theoretical Probability
Lesson 3: Understand Experimental Probability
Unit 8
Lesson 4: Spin Class
Lesson 5: Is It Fair?
Lesson 6: Fair Games
Lesson 4: Use Probability ModelsUnit 8
Lesson 6: Fair Games
Lesson 7: Weather or Not
Lesson 8: Simulate It
Lesson 9: Car, Bike, or Train? (Print available)
Lesson 5: Determine Outcomes of Compound EventsUnit 8
Lesson 9: Car, Bike, or Train? (Print available)
Lesson 6: Find Probabilities of Compound Events
Lesson 7: Simulate Compound Events
Unit 8
Lesson 8: Simulate It
Lesson 9: Car, Bike, or Train? (Print available)
Practice Day 1 (Print Available)

Chapter 8: Solve Problems Involving Geometry

Lesson 1: Solve Problems Involving Scale DrawingsUnit 1 Lesson 1: Scaling Machines [Free lesson] Lesson 2: Scaling Robots Lesson 3: Make It Scale Lesson 4: Scale Factor Challenges Lesson 5: Tiles Lesson 6: Introducing Scale Lesson 7: Will It Fit? [Free lesson] Lesson 8: Scaling States Lesson 9: Scaling Buildings Lesson 10: Room Redesign Practice Day 1 Practice Day 2   Unit 3 Lesson 1: Toothpicks   Unit 4 Lesson 3: Sticker Sizes
Lesson 2: Draw Geometric FiguresUnit 7
Lesson 6: Is It Enough?
Lesson 3: Draw Triangles with Given ConditionsUnit 7
Lesson 5: Can You Build It? [Free lesson]
Lesson 6: Is It Enough?
Lesson 7: More Than One
Lesson 8: Can You Draw It?
Practice Day 1
Lesson 4: Solve Problems Using Angle RelationshipsUnit 7
Lesson 1: Pinwheels
Lesson 2: Friendly Angles [Free lesson]
Lesson 3: Angle Diagrams
Lesson 4: Missing Measures [Free lesson]
Lesson 5: Solve Problems Involving Circumference of a CircleUnit 3
Lesson 2: Is It a Circle?
Lesson 3: Measuring Around [Free lesson]
Lesson 4: Perimeter Challenges
Practice Day 1 (Print available) [Free lesson]
Lesson 6: Solve Problems Involving Area of a CircleUnit 3
Lesson 5: Area Strategies
Lesson 6: Radius Squares
Lesson 7: Why Pi?
Lesson 8: Area Challenges [Free lesson]
Lesson 9: Circle vs. Square
Practice Day 2
Lesson 7: Describe Cross SectionsUnit 7
Lesson 9: Slicing Solids
Lesson 8: Solve Problems Involving Surface AreaUnit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 12: Surface Area Strategies
Lesson 13: Popcorn Possibilities
Lesson 9: Solve Problems Involving VolumeUnit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 13: Popcorn Possibilities
Practice Day 2

Grade 8

Chapter 1: Real Numbers

enVision MathDesmos Math 6–A1
Lesson 1: Rational Numbers as DecimalsUnit 8
Lesson 12: Fractions to Decimals
Lesson 13: Decimals to Fractions
Lesson 2: Understand Irrational NumbersUnit 8
Lesson 14: Hit the Target
Lesson 3: Compare and Order Real Numbers 
Lesson 4: Evaluate Square Roots and Cube RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Lesson 5: Solve Equations Using Square Roots and Cube RootsUnit 8
Lesson 5: Filling Cubes
Practice Day 1 (Print available)
Lesson 6: Use Properties of Integer ExponentsUnit 7  
Lesson 2: Combining Exponents
Lesson 3: Power Pairs (Print available) [Free lesson]
Lesson 4: Rewriting Powers
Practice Day 1 (Print available)
Lesson 7: More Properties of Integer ExponentsUnit 7  
Lesson 5: Zero and Negative Exponents
Lesson 6: Write a Rule (Print available)
Lesson 8: Use Powers of 10 to Estimate QuotientsUnit 7  
Lesson 7: Scales and Weights
Lesson 8: Point Zapper
Lesson 9: Use Your Powers
Lesson 9: Understand Scientific NotationUnit 7  
Lesson 10: Solar System [Free lesson]
Lesson 11: Balance the Scales [Free lesson]
Lesson 13: Star Power
Practice Day 2 (Print available)

Chapter 2: Analyze and Solve Linear Equations

Lesson 1: Combine Like Terms to Solve EquationsUnit 4
Lesson 2: Keep It Balanced
Lesson 2: Solve Equations with Variables on Both SidesUnit 4
Lesson 3: Balanced Moves
Lesson 4: More Balanced Moves (Print available)
Lesson 3: Solve Multi-Step EquationsUnit 4
Lesson 3: Balanced Moves
Lesson 4: More Balanced Moves (Print available)
Lesson 5: Equation Roundtable (Print available) [Free lesson]
Lesson 6: Strategic Solving (Print available)
Lesson 4: Equations with No Solutions or Infinitely Many SolutionsUnit 4
Lesson 7: All, Some, or None?
Lesson 5: Compare Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials [Free lesson]
Lesson 2: Water Tank
Lesson 3: Posters
Lesson 6: Connect proportional Relationships and SlopeUnit 2
Lesson 9: Water Slide
Lesson 10: Points on a Plane
Practice Day 
 
Unit 3
Lesson 2: Water Tank
Lesson 4: Stacking Cups
Lesson 5: Flags [Free lesson]
Lesson 7: Water Cooler
Lesson 8: Landing Planes
Lesson 9: Coin Capture
Lesson 7: Analyze Linear Equations: y = mxUnit 3
Lesson 3: Posters
Lesson 6: Translations
Lesson 8: Understand the y-intercept of a LineUnit 3
Lesson 5: Flags [Free lesson]
Lesson 6: Translations
Lesson 9: Analyze Linear Equations: y = mx + bUnit 3  
Lesson 6: Translations
Lesson 7: Water Cooler
Practice Day 

Chapter 3: Use Functions to Model Relationships

Lesson 1: Understand Relations and FunctionsUnit 5
Lesson 1: Turtle Crossing [Free lesson]
Lesson 2: Guess My Rule [Free lesson]
Lesson 2: Connect Representations of FunctionsUnit 5
Lesson 3: Function or Not?
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 3: Compare Linear and Nonlinear FunctionsUnit 5
Lesson 4: Window Frames
Lesson 4: Construct Functions to Model Linear RelationshipsUnit 5
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 8: Charge! (Print available)
Lesson 5: Intervals of Increase and DecreaseUnit 5
Lesson 1: Turtle Crossing [Free lesson]
Lesson 6: Graphing Stories
Lesson 6: Sketch Functions from Verbal DescriptionsUnit 5  
Lesson 6: Graphing Stories

Chapter 4: Investigate Bivariate Data

Lesson 1: Construct and Interpret Scatter PlotsUnit 6  
Lesson 1: Click Battle
Lesson 2: Wing Span
Lesson 3: Robots [Free lesson]
Practice Day 1 (Print available) [Free lesson]
Lesson 2: Analyze Linear AssociationUnit 6  
Lesson 4: Dapper Cats [Free lesson]
Lesson 5: Fit Fights [Free lesson]
Lesson 7: Scatter Plot City
Lesson 3: Use Linear Models to Make PredictionsUnit 6  
Lesson 6: Interpreting Slopes
Lesson 8: Animal Brains
Practice Day 2 (Print available)
Lesson 4: Interpret Two-Way Frequency TablesUnit 6
Lesson 9: Tasty Fruit
Lesson 5: Interpret Two-Way Relative Frequency TablesUnit 6
Lesson 10: Finding Associations [Free lesson]
Lesson 11: Federal Budgets
Practice Day 3

Chapter 5: Analyze and Solve Systems of Linear Equations

Chapter 6: Congruence and Similarity

Chapter 7: Understand and Apply the Pythagorean Theorem

Lesson 1: Understand the Pythagorean TheoremUnit 8
Lesson 6: The Pythagorean Theorem
Lesson 7: Pictures to Prove It
Lesson 8: Triangle-Tracing Turtle [Free lesson]
Lesson 2: Understand the Converse of the Pythagorean TheoremUnit 8
Lesson 9: Make It Right
Lesson 3: Apply the Pythagorean Theorem to Solve ProblemsUnit 8
Lesson 10: Taco Truck [Free lesson]
Practice Day 2 (Print available)
Lesson 4: Find Distance in the Coordinate PlaneUnit 8
Lesson 11: Pond Hopper

Chapter 8: Solve Problems Involving Surface Area and Volume

Lesson 1: Find Surface Area of Three-Dimensional Figures 
Lesson 2: Find Volume of CylindersUnit 5
Lesson 10: Volume Lab
Lesson 11: Cylinders [Free lesson]
Lesson 14: Missing Dimensions (Print available)
Lesson 3: Find Volume of ConesUnit 5
Lesson 13: Cones [Free lesson]
Lesson 14: Missing Dimensions (Print available)
Lesson 4: Find Volume of SpheresUnit 5
Lesson 15: Spheres
Practice Day 2 (Print available)

S1-05: How does coding fit in the science classroom? A conversation with Aryanna Trejo of Code.org

Podcast cover titled "Science Connections" featuring Aryanna Trejo, Season 1, Episode 5. It includes abstract illustrations of a globe and telescope, discussing coding in the science classroom.

In this episode, Eric sits down with Aryanna Trejo, a professional learning specialist of Code.org. Aryanna shares her journey from working as an elementary teacher in New York City and Los Angeles to teaching other educators at Code.org. Eric and Aryanna chat about computer literacy within the science classroom, problem-solving skills, and ways to model productive struggle for students. Aryanna also shares ways to teach coding and computer literacy in schools, no matter the classroom’s technology level. Explore more from Science Connections by visiting our main page.

Download Transcript

Aryanna Trejo (00:00):

I would hear teachers saying things like, “Well, I just can’t do coding; this is too hard for me; the time has passed.” And I would ask them, “Would you say that to your student about math or English?” And they would always sheepishly go, “No.” And I’d say, “Well, be as kind to yourself as you would be to your student.”

Eric Cross (00:19):

Welcome to Science Connections. I’m your host, Eric Cross. My guest today is Aryanna Trejo. Aryanna is a member of the professional learning team at Code.org. Before joining Code.org, Aryanna led computer science professional development for elementary school teachers, and served as an instructional coach for new educators. She also taught fourth and fifth grade in both New York City and in Los Angeles. In this episode, we discuss Aryanna’s journey to Code.org, where she helps educators connect coding to real life, how to use a rubber duck to solve problems, and how coding and computer science principles can be taught to students in areas without access to the internet…or even a computer. I hope you enjoy my conversation with Aryanna Trejo. So I was born and raised here, and I saw that you went to UC San Diego.

Aryanna Trejo (01:11):

I did, I did. I actually just put a deposit down on an apartment in University Heights, ’cause I’m moving back.

Eric Cross (01:16):

You’re coming back?

Aryanna Trejo (01:17):

I’m coming back. Yeah.

Eric Cross (01:19):

So if you need a classroom to visit….

Aryanna Trejo (01:21):

I would love to do more classroom observations!

Eric Cross (01:24):

Are we doing this? Let’s do—we’re making this happen.

Aryanna Trejo (01:26):

We are. Yeah. So I’ll be there. I’m moving there in April. I actually grew up in Orange County too, so I’m like a very diehard SoCal person.

Eric Cross (01:35):

So I feel like I know the answer to, hopefully—Tupac or Biggie? ‘Cause you’re on the East Coast, and you’re on the West Coast.

Aryanna Trejo (01:40):

Yeah. I like Tupac, but I have more Biggie songs committed to memory. Which is not a lot. I have “Juicy” and “Hypnotized” memorized.

Eric Cross (01:53):

All right. So you’re just memorizing, and you have the Biggie songs memorized, but not the Tupac ones.

Aryanna Trejo (01:58):

No, but I do love Tupac songs. You know, it’s like, Biggie has the flow, but Tupac has the lyrics. Nobody’s—they both have something really amazing about them.

Eric Cross (02:06):

You know, I can respect that you broke it down into both of their strengths.

Aryanna Trejo (02:11):

Thanks for buttering me up before this interview. And not….

Eric Cross (02:15):

<laugh> Oh, we already started.

Aryanna Trejo (02:16):

Huh? We already started?

Eric Cross (02:17):

We’re already started. Yeah. We’re already into this.

Aryanna Trejo (02:19):

We’re into it.

Eric Cross (02:21):

You were in the classroom, fourth and fifth grade, and you were doing TFA.

Aryanna Trejo (02:26):

I did. I did Teach For America. I was 2012, New York City Corps. Right after graduation. ‘Cause I graduated UC San Diego in 2012. So graduation was on June 17th, and I touched down at JFK on June 19th.

Eric Cross (02:40):

Even though I wasn’t in TFA, I know a lot of the fellows that are in it. And there’s just some phenomenal teachers in there. How long were you doing elementary school when you were teaching?

Aryanna Trejo (02:49):

Yeah, I taught for—well, I did, three years of teaching fourth grade. Then there happened to be an instructional coach opening in my fourth year. I took that, did some instructional coaching within the same network, and then I moved back to LA and I taught fifth grade for a year.

Eric Cross (03:11):

  1. And what was it like now? Did you go to Code.org right after the classroom?

Aryanna Trejo (03:17):

No, I didn’t. No. I transitioned after teaching fifth grade for a year in downtown Los Angeles, in the Pico-Union neighborhood. I ended up getting this email out of the blue from someone who had actually found me through the Teach for America job site. ‘Cause I was hitting the pavement; I was really looking to transition out of the classroom. And she invited me to interview with this company called 9 Dots. And they taught computer science to kids K–6 throughout Los Angeles and Compton. And I was like, “Sure, no problem. Let’s do it.” So I interviewed, I got the job, and yeah, that’s how I transitioned to 9 Dots. And then after almost four years there, I transitioned to Code.org, with the same person. Actually, she moved over to Code.org first, and then she helped me get this job.

Eric Cross (04:07):

Oh, that’s happened a lot—like, that relationship kinda carries over.

Aryanna Trejo (04:11):

Yeah. We’re meant to be coworkers.

Eric Cross (04:13):

Yeah. Are you still? Is she still there? Are you both still together?

Aryanna Trejo (04:17):

Yeah, we’re on the same team and it’s nice. I saw her last night for Happy Hour, with another coworker who’s in LA. So we’re tight. And she’s a wonderful, wonderful mentor to me.

Eric Cross (04:28):

That’s great. Did you have computer-science background, when you were doing elementary school teaching? Did you have—

Aryanna Trejo (04:34):

No. <laugh> Not at all. When I was teaching in New York City, I had like four desktop computers in my classroom, and we rarely used them. Which was such a shame. And then when I moved to Los Angeles and taught fifth grade there, we were a one-to-one school, and the joys of that are just amazing. It was just really wonderful to, you know, get the students used to typing on the computer, using different software to submit their assignments. Getting creative—as creative as you can get—with Google Slides. You know, to show off what they know. And stuff like that. That’s all I had, though. And you know, when I transitioned to 9 Dots I was like, “Sure, why not? Let’s give a shot.” And I learned a lot. It was really interesting, yeah.

Eric Cross (05:26):

And so now at Code.org you are…well, so my journey with Code.org, I’ve been in the classroom for eight years. Still in the classroom as of…an hour ago, I was there. <Laugh> And I use Code.org, and I feel like I’ve checked it periodically, and I feel like it’s evolved over the gaps. And I’ve seen it. It’s become more robust in the things that they offer, over the years I’ve been an educator. Just to kind of…could you give a thumbnail sketch? Like, what is Code.org? Who’s it for? Who’s the target audience? What resources are there?

Aryanna Trejo (06:00):

Yeah. So it’s for everyone. It is a nonprofit that provides curriculum and training and a platform for teachers and students. We provide curriculum for K through 12. It’s completely free. And it comes with lesson plans, slideshows, all that. We focus specifically on underrepresented groups. So we have targeted measures for Black students, for Native American students, for students who identify as female. That’s a huge part of our mission. But we’re really working to expand access to computer science to as many students as we can.

Eric Cross (06:41):

One of the things I’m hearing in your story is you were teaching in Compton; you were in Bronx, New York. One of the reasons why I got into the classroom is because of educators, and the impact they made on me in exposing me to science and technologies I’d never had access to. And that intentionality, that you’re going about it…are there…not just the code, but how you bring that across to different groups…are there strategies, or are there ways to connect this idea of coding to diverse groups and diverse audiences? Or is it kind of, the curriculum applies for everyone? ‘Cause in science, when I’m teaching, I’m always trying to make what I’m doing relevant to the backgrounds of my students.

Aryanna Trejo (07:28):

Sure.

Eric Cross (07:28):

So I’m teaching biology, and I’m trying to make this kind of connection. Sometimes it’s more organic; sometimes it feels kind of forced. Because it’s just not always a nice fit. But it sounds like Code.org is really about inclusion. And in the numbers that I’ve seen for representation, in especially computer science software engineers, the groups that you’re focusing on are not necessarily represented in the professional workforce. At least disproportionately.

Aryanna Trejo (07:54):

Yeah, absolutely. Yeah, that’s correct.

Eric Cross (07:57):

And so how do you go about being intentional about reaching groups that we don’t see in, you know, the Silicon Valley software engineers? How do you start that? Like, at a young age, do you look for specific schools in specific areas to say, “We are going to bring this to the school. We’re going out to these populations of the cities”? Because we’re just not seeing…you know, on the map, we’re not seeing anybody really doing anything with coding here. Or we’re not seeing the numbers come out of these areas, out of these cities, of students who are going into STEM or going into computer science fields.

Aryanna Trejo (08:41):

Yeah. I don’t necessarily work on the recruitment side of it, is the issue, in my position. But I do work on the professional learning, that is brought out to teachers. And we have a huge focus on equity throughout the workshops that we create from K–12. It’s something we’re really passionate about. We definitely aim to prepare teachers to teach computer science. That’s a huge part of it. Knowing the content, but also thinking through, “What does recruitment look like at your school to make sure that the demographics of your classroom match the demographics of your entire school?” Also, thinking through, “How can we make sure that female students feel included in your classroom? How can we make sure that we are, giving students creativity to think about, or we are setting students up to be creative and think about the problems that are in their community, and how they can use computer science to solve them, or at least work towards them?”

Eric Cross (09:39):

So solving real-world problems and that inclusion aspect…are there things like…you were saying “female or students who identify as female”…are there things that teachers can do to ensure that they’re being more inclusive? Or to recruit, or encourage more female students to take part? One of the things I was thinking of, that I’ve seen, is I’ve seen coding kind of camps.

Aryanna Trejo (10:06):

Sure.

Eric Cross (10:08):

That were specifically for a female audience. And that seemed to help with recruitment. Is that something that you see on your side?

Aryanna Trejo (10:16):

That’s not something that we set up, no. But the curriculum that I work with is CS Principles. And it’s offered as an Advanced Placement course, as well as an AP class. So that’s a curriculum that’s designed for students who are in grades 10 through 12. And so at that point, we can really talk to teachers and ask them what the recruitment strategy is. But in terms of strategies that teachers can use to recruit those students…I mean, I’ve heard over and over from lots of different teachers who identify as female that they didn’t think that computer science was for them, until they saw a role model in that position. And so just being a role model for those students is really wonderful.

Eric Cross (11:00):

And I see it too, with—like, we do “Draw a Scientist” activity, which is like a popular science thing—

Aryanna Trejo (11:05):

Sure, yeah, I’m familiar.

Eric Cross (11:05):

But it’s the same thing, right? Like, it fleshes out. My students don’t draw themselves as scientists. They draw what they perceive, based on what television says. I imagine with computer science, it’s probably really similar, when you think about “What’s a software engineer look like?” Do students tend to draw themselves? Or is it even a mystery? Because I don’t even know what a software engineer looks like.

Aryanna Trejo (11:28):

Yeah, absolutely. Well, one of the things we love to do with our professional learning workshops is talk about understanding yourself, your identities, how they show up in the classroom as biases. And, you know, things like stereotype threat. We see that as really important to understand, and think through, and consider, before you step into the classroom. So that you’re not, you know, coddling certain groups of students because you don’t believe that they are able to be successful in computer science. Holding all the students to the same expectations and believing that they can succeed. And computer science, I think a lot of the times people have this conception of it being this utopian, bias-less, technocratic field. When in reality, everything has bias. And people talk about algorithmic bias and facial recognition, but also the people who created computers and computer languages have their own bias that comes through. And I think it’s really important to show students that. So that they can, one, know what they’re working with, and two, make sure that they can create products that reduce that bias.

Eric Cross (12:50):

It’s like…it’s not objective, just because we’re creating software. Like, once it gets to a point of being so sophisticated…I think, like, AI software, right? With facial recognition? And we’re seeing more and more articles come out about, you know, predicting trends based on historical data.

Aryanna Trejo (13:12):

Sure.

Eric Cross (13:13):

But then, the trends and things that they’re seeing tend to target things that have happened in the past. But it also doesn’t take into consideration a lot of other factors that can lead to certain groups or populations being identified. And I’ve seen some articles lately about how your code is really just representation of what you put into it. And like you just said, your bias—if you have that, conscious or unconscious—you’re gonna put that into your code. And the input is gonna be an impact, is gonna impact the output.

Aryanna Trejo (13:44):

Yeah, absolutely. Or even just—and I’m ashamed to say this, ’cause this is an idea that came to me just recently, through an article that I read—but computers themselves have bias. The hardware assumes that you have vision, that you can see the screen, that you are able-bodied, that you can use your hands to work the keyboard, the mouse, et cetera, and that you don’t have to use assistive technology. You know, there are small things like that, where we think that technology, like I said, is this utopian, futuristic science…but there are biases throughout.

Eric Cross (14:19):

You’re absolutely right. I’ve never even—I’ve never even considered that. Even though I do use assistive tech, and figure it out, I’ve never thought from the ground up, the process is built for an able-bodied, sighted, hearing person.

Aryanna Trejo (14:31):

Exactly.

Eric Cross (14:32):

To be able to engage with the hardware. And then these other things, these tertiary things that we kind of add on, so that you can do this, but it’s not designed from the ground up for people who are, you know, different audiences, physically. So I’m glad you brought that up, though. Now I’ve seen—and I haven’t done this—but I know Hour of Code is a big thing. And this is something that’s ongoing. Can you talk a little bit about what Hour of Code is? I know it’s, it’s a big thing for the classroom teachers.

Aryanna Trejo (15:08):

Yeah. So Hour of Code is really exciting, and it’s just blossomed from something small to something tremendous. This year is gonna be the 10th Hour of Code. So what it is, is it happens during CS Education Week in December, during Grace Hopper’s—or to honor Grace Hopper’s birthday. She was a computer scientist and Navy Admiral. And basically the aim of it is to get as many students on the computer doing an hour of code, and demystify what coding is. You know, to do seed-planting. To show teachers that this is something that you can facilitate for your students. And also to show students like, “Hey, computer science is something you can absolutely do. Not just for an hour, but more if you want.” So, yeah. Now it’s worldwide, and it’s really exciting.

Eric Cross (15:58):

That’s awesome. And I think about teachers and I still hear the apologetic—when I’m helping teachers in the classroom with education technology—the self-deprecating “I’m a dinosaur; I’m not good with tech,” which is never true. Like, they’re better than they even realize. And I feel like sometimes there’s still a stigma, too. It’s like <laugh> The Simpsons’ Comic Book Store Guy. The condescending tech support person—

Aryanna Trejo (16:27):

Sure.

Eric Cross (16:28):

—who has that tone. And so I feel like some people have been so negatively impacted by that person. So I know when I’m helping people, I actually try to go full-spectrum the other side. But I’m thinking about teachers’ barrier to entry. Sometimes code is like, “Whoa.” And I don’t teach computer science. Do you see those barriers to entry, or at least the perception of them? And then, what’s the reality for like someone listening, and going, “I’m a fourth grade teacher,” or “I’m a humanities teacher in ninth grade.” What’s the perception that you see, versus reality, with the teachers that you train? Is it much more accessible than we think? Or is there a level of sophistication that you have to have coming into it?

Aryanna Trejo (17:10):

No, not at all. I know computer science, and that says a lot! <Laugh> You know, I know my own corner of computer science. And you know, that’s me being self-deprecating, too. But I think learning computer science has helped me in so many different ways that I wasn’t expecting. I recently took the GRE in hopes of, you know, getting back into grad school. And I think just the way that computer science teaches you to search for bugs in your code, or errors, and kind of tirelessly look at a problem from multiple different angles, I was able to carry that into the math that I was doing. And I noticed just a huge difference in the way that I approached it, and the way that I was open to it. But you asked a great question, in regards to the barriers to technology. In my position at 9 Dots, I was working directly with teachers to lead professional development with them. Sometimes it would be a full day; sometimes it would be an hour after school. And the one thing that I always had in my back pocket that was really useful is that I would hear teachers saying things like, “Well, I just can’t do coding; this is too hard for me; the time has passed.” And I would ask them, “Would you say that to your student about math or English?” And they would always sheepishly go, “No.” And I’d say, “Well, be as kind to yourself as you would be to your student.” You know, it takes some patience and nobody’s gonna get it perfect 100 percent of the time. Have I banged my head against the wall trying to solve one tiny little syntax error in my code? Absolutely! But it feels absolutely phenomenal to fix that. And I was an English major in undergrad, and I had never done computer science before. So it’s something that becomes really satisfying.

Eric Cross (19:07):

Yeah, I imagine. I had someone—a trainer or a presenter—one time bring up the fact that our students rarely get to see us learn in real time.

Aryanna Trejo (19:19):

Yeah.

Eric Cross (19:19):

So we don’t get to ever really model failure. I mean, unless we’re in a classroom situation <laughs> in our failures, with classroom management. Then they see it, they see it! But they don’t get to see us model learning failure. And I don’t mean like failure—and yes, I know, “first attempt is learning,” and “no such thing as failure”—that’s not what I’m talking about. But just when we’re not successful with our code, and then we experience real-time frustration.

Aryanna Trejo (19:42):

Yep.

Eric Cross (19:42):

And they said that is actually a great learning experience for your students to watch you go through productive struggle. And that was really liberating for me. Because now I’m in the classroom, and I’m trying to go through it with my students, and the beautiful thing was, they started helping me. We were all trying to solve the problem. And then we had this authentic problem-solving experience. I think it was like a Scratch program, where we were trying to solve, trying to embed it somewhere, or something. And then, in the background of the class: “Mr. Cross! I got it! I figured it out!” And it was this really neat bonding experience. And I felt that—your ears get red, and you get hot, ’cause you’re not—

Aryanna Trejo (20:19):

Oh yeah.

Eric Cross (20:20):

You don’t know it! And you’re in front of 36 kids! And I said, “OK, I need to tell them how I feel.”

Aryanna Trejo (20:25):

Yeah.

Eric Cross (20:26):

So I said, “Now I feel really frustrated.” Like, “I want to go through this, and here’s my thoughts.” ‘Cause I knew that it would be helpful if they saw and would hear my thoughts. So I just did a quick think-aloud and I said, “In my head, <laugh> I want to just quit,” I said, “But I realize that this is the part where my learning’s happening. So I just want you all to hear what’s going on in my brain.” And now I feel like when I’m doing coding with my students, and it’s just basic coding, I feel much more comfortable, like, not knowing. But I needed someone to release me from that “I have to be the expert in everything” to do it.

Aryanna Trejo (21:06):

And teachers are used to being the experts. Right? And they should be. And coding is just such a different landscape. But I think once you kind of give over to the power of tinkering, I think it’s really gratifying. I love being able to…you can revise a sentence, and then read your paragraph back to yourself in English, and say, “OK, I get it.” But there’s something so gratifying about changing a line of code or a block and then being able to hit play and watch your program come to life, and say, “Hmm, that’s not quite what I wanted. Let’s try something different.”

Eric Cross (21:39):

I love your connection to tinkering. ‘Cause—I had never thought about it—’cause I love tinkering with my hands. But I always think about physical things. But coding is exactly that. It’s tinkering.

Aryanna Trejo (21:47):

It’s exactly that.

Eric Cross (21:47):

That’s exactly what it is.

Aryanna Trejo (21:49):

And a lot of it is, for me, especially when I’m trying something new, it’s guess-and-check. It’s like, “OK, that didn’t work. What if I add a semicolon here? Will it finally work? Or what if I add a ‘for’ loop? Will this get me what I want?” And it’s wonderful because you have that with students as well. Like, you have that record of their thinking, and you can ask them to go step-by-step and tell you, you know, “First, I added this, because I wanted the program to do this,” and so on and so forth. And so you have that record, but you can always get rid of it. Students often wanna get completely get rid of it. That’s something that I’ve noticed a lot as I’ve taught computer science. But, once you can get them to target the specific parts of the program, tinker with that, and continue, that’s a really wonderful learning space. There was also something you said about modeling failure. I love the fact that in computer science you can model failure for your students. You said to your students, “I’m getting frustrated.” I love that, because I never got that in math. Nobody ever showed me what it was like to be frustrated with graphing a parabola. Right? Like, my math teachers were always like, “Doot, doot, doot, here you go, you’re done!” <Laugh> And I would get so frustrated, because it didn’t come that easily to me. And I think there’s two parts to that. So there’s modeling the learning and the thinking and the productive struggle, but also there’s the identity of being a computer scientist and modeling what that looks like. So for me, when I get really frustrated with a program, I walk away. I take five minutes. I take a deep breath. I say, “I’m not gonna think about it in these five minutes.” And I come back to it. And I think once you start teaching computer science, you can facilitate that for students. And there’s so many different strategies that they can pick up. They can pick up rubber ducking, which is where they pick up a rubber duck or a similar object, and they talk to it as if they were a partner and talk through their code. And oftentimes, as you’re rubber ducking, you’re gonna find that error, because you’re explaining it to someone who’s a stand-in for a novice. And rubber ducking is a well-known strategy for computer scientists who make it their career. You know, there’s pair programming. Some students love pair programming; some students hate it. But the students start to build this identity about how they problem-solve. And how they approach failure. And I just love that.

Eric Cross (24:31):

I’m writing this down. Because the rubber-ducking strategy, I love. I just imagine my seventh graders, a bunch of 13-year-olds with, like, rubber on the desk. And not necessarily in coding, but I was thinking in my science class. And they’re working through a challenge, and they’re all looking at this duck, and they’re talking to it. But I just love the the idea of externalizing your thought process and talking through it yourself so that you can hopefully arrive at a conclusion. But it’s such a great practice, and this is something that’s been around for a long time, apparently. So.

Aryanna Trejo (24:59):

Yeah. Yeah. It’s a real thing. And you know, you can go low-fi. It doesn’t have to be a rubber duck. You can have students talk to their pencils or their imaginary friends. That’s not the issue; the issue is, you know, talking to somebody.

Eric Cross (25:10):

I know you support teachers. But I just wanted to…I was just curious about your typical day, what that’s like. And then what you do, how you support ’em.

Aryanna Trejo (25:15):

So, at my previous job at 9 Dots, I was in there with the teachers in the classrooms. I was coaching our internal staff who went out to co-teach with teachers. And I loved that. And I had such a great impact on a local scale. But now at Code.org, I have a much broader impact. But I don’t get to interface with—that’s such a tech-y word!—I don’t get to interact with—

Eric Cross (25:42):

You work at Code.org! You get to—

Aryanna Trejo (25:42):

I know! But I’m a teacher at heart, forever, right? That’s my identity that I forged when I was 22 years old. And a typical day looks like opening up my computer, taking a look at my calendar. I often have meetings to talk about, different things that we’re doing to support our facilitators who go out to our teachers and lead their workshops for them. I recently worked on a product that was designed for CS principles, teachers, to onboard to the course if they weren’t able to get into an in-person workshop. And it’s completely self-paced, so it gives teachers an on-ramp into the course. And now I’m working on some in-person workshop agendas. So I feel really wonderful that my work is going out to thousands of teachers. But at the same time, I really, really miss talking to teachers. Because that’s something that energizes me so much.

Eric Cross (26:46):

When should students start learning computer science? I feel like we see it in this kind of narrow lane. Like, this is computer science if you make an app. Can it be more than that? As far as like the benefit of computer science? And—I guess two-part question—when should students, one, start being exposed to it? And then two, what are some of the benefits beyond just, “I wanna just make an app”?

Aryanna Trejo (27:08):

I taught coding to kindergartners. It can start as early as you as you want it to. And it doesn’t necessarily need to be on the computer. A lot of students that I worked with didn’t have computers at home, were interacting with computers for the first time. And that’s a huge barrier, of course, to a lot of teachers. But there are so many unplugged lessons that you can do to start to start to have students think about algorithms, which is just a series of steps to complete to solve a problem. As long as a student can use a computer, I think they can do computer science. There are products out there like codeSpark, where students—and Code.org has these products too—where students are moving an avatar around a board, kind of like a quadrant to…you know, they feed the directions to a computer and then the computer enacts it for them. And with that, they can learn algorithms. You know, that is computer science. And a lot of people don’t see it that way, but it really is. And it starts to set students up for more complex thinking as they move on.

Eric Cross (28:13):

One of the biggest underserved communities, geographically, are students in rural areas.

Aryanna Trejo (28:20):

Yep.

Eric Cross (28:21):

They can be reservations; they can be places just not an urban area. Is there a way to serve our communities of students and bring these skills in an unplugged way?

Aryanna Trejo (28:32):

Yeah. Yeah. If you typed in “unplugged computer science lessons” to Google, you’ll have a ton of hits. And there are so many students out there—not just in rural areas. But there’s incarcerated students. It hurts my heart to even say those words, but in urban areas too. Like in my classroom, where I only had four desktop computers. Access is a real struggle. And there’s things, like I said, instead of moving an avatar around a grid on the computer, I used to have an actual mat that I would take out to my kindergarten classrooms, lay it out, and it would have a grid on it. And we’d have one of the students act as the avatar and the rest of the students would give them directions to get to a different point on the grid. And there, you’re building an algorithm or just a series of steps. Like I said, it’s not some fancy term to solve a problem. And there’s multiple ways to solve that problem, too. And I think investigating that can be a really good way to stretch those lessons.

Eric Cross (29:32):

It almost sounds like an oxymoron, but this low-tech computer science strategy. Develop these skills and then transfer that once you have access to the tools.

Aryanna Trejo (29:39):

Yeah. Yeah. Absolutely. And I think it’s a good way for students who need kinesthetic means to start to understand something, or just different learning styles, to start transferring that over.

Eric Cross (29:53):

I probably have students in the classroom where those kinesthetic moving things would help be a great way—or WILL be a great way—for them to learn the principles and the fundamentals of coding. Instead of only giving the option to just do the computer, actually giving them some choice. Or giving them a way to be able to manipulate things. We’re still in the system of education that’s still very siloed. It’s been the same way for a hundred years. We got math and then we got science and we got English. I’m wondering, how can a teacher fit this into their daily lessons? And then, do you have any experiences or stories or things that you’ve seen, just really creative ways that you’ve seen teachers incorporate this? Outside the norm of, “This is a computer science class; we’re just gonna code.” But have you seen it branch out? In the trainings that you’ve done?

Aryanna Trejo (30:40):

I’ve seen examples of that. I’ve seen a teacher use Scratch to demonstrate different climates of California, and show the different climates. This past year for Hour of Code, my friend Amy—the one who helped me move to 9 Dots and at Code.org—she created this incredible tutorial called Poetry Bot. And it was a way to get students to match the mood of the poem to some of the elements that were happening in the stage. So they would have different backgrounds show up at different parts of the poem. When the words would show up, they would have different sprites show up. They would have, sometimes, sounds. Or the text would show up with different animations. So there are cross-curricular opportunities everywhere, if you can be creative enough to find them, or if you beg, borrow, steal from other educators who are doing this incredible work out there.

Eric Cross (31:36):

Yeah. I say this all the time, but I’m an educational DJ, not an MC.

Aryanna Trejo (31:44):

Oh yeah.

Eric Cross (31:45):

So MCs write their lyrics and DJs remix with things that other people have done.

Aryanna Trejo (31:48):

Absolutely.

Eric Cross (31:48):

I was like, I’m a DJ. I was like, all day. Sometimes I’ll write a lyric, once or twice, but most of the time I’m remixing things. So teachers, if you’ve been out there and you got an awesome interdisciplinary thing, or you’ve incorporated coding and it’s something that’s traditionally not seen, please send it to us. Share it with us.

Aryanna Trejo (32:03):

Yeah. And there are so many different places where you can find that. We have a forum for Code.org, but there’s also CSTA, the Computer Science Teachers Association. You can join your local chapter and get to know other computer science teachers out there.

Eric Cross (32:19):

I guess…to wrap up, I’ve been using Scratch programming, the MIT website. My students do the basic animated name, CS First, stuff. But over the years, I’ve noticed that my students are coming in with a higher level of sophistication in Scratch to where now the differentiation…some of my students are just doing very basic…and then I have other students who’ve created full-on video games with complex…like, you look at their Scratch page and it’s just an amazing amount of blocks and integrations and things that they have. Is there anything on Code.org that could be a next step? That takes them beyond, maybe like the visuals? And if so, what would be a good next step, to take students to advance them to another platform? There’s so many coding languages out there, I feel like. Or I might not even be thinking about that the right way.

Aryanna Trejo (33:20):

No, I think you are. You know, we have three different curricula out on our website right now. We have CS Fundamentals, which is probably more in line with what you’re talking about. We have a free CS Discoveries curriculum, and that is designed for, grades, I believe, 6 through 10. And that would be a really good entry point, for both teachers and for students.

Eric Cross (33:44):

There’s a lot of new stuff that I hadn’t seen yet, a few years ago.

Aryanna Trejo (33:49):

Yeah.

Eric Cross (33:49):

So I was really excited.

Aryanna Trejo (33:50):

One thing that I do know is that CS Discovery has just added an artificial intelligence slash machine-learning unit, that you can just pick up and give to your students. You don’t have to go in order with CS Discoveries, like you do with CS Principles. And I’ve gone through some of those lessons. They are really rad. And I would’ve loved to have learned that when I was in middle school or high school. So yeah, we’re constantly thinking of how we can make things one, relevant to our students, and two relevant to what’s going on in the world.

Eric Cross (34:20):

So would I be overselling it if I said, “If you go through this, you’ll be able to create an AI or a neural net to do all your homework”?

Aryanna Trejo (34:26):

You would be overselling it.

Eric Cross (34:27):

I would be? OK. So what I’ll do is, I’ll wait until the end of the school year, and then introduce it, and then by the time they’ve realized it’s not true, they’ll be eighth graders.

Aryanna Trejo (34:35):

There you go. Good old bait-and-switch.

Eric Cross (34:37):

You’re amazing. Thank you for serving teachers, and for being part of such a great organization that puts out great stuff. So much free curricula for teachers to be able to use. Especially nowadays we hunt and scour the internet for those types of things. And to be able to bring computer literacy into the classroom, and with your focus of serving communities of underrepresented groups, it feels good to know that not only is it high-quality material, but it’s also trying to raise everyone up. Because ultimately when we have more people trying to solve a common problem, we come up with better solutions. And I was talking to somebody who was a materials engineer somewhere in Europe, and he said one of the things about the U.S., As he was critiquing me on this flight, critiquing the U.S., He said, “One of the things about your country is that you have a heterogeneous group of people who, in a group, when you have multiple perspectives attacking a problem, you come up with more novel solutions.” He says, “That’s one of the great things, is that there’s not necessarily just a hive mind.” And I think that that’s one of the great things. We uplift different communities, and we uplift women, people of color, people who, have backgrounds that parents didn’t go to college but have these amazing qualities and strengths. And we put everybody focusing on the same issue. We come up with novel solutions that we wouldn’t have come up with if only select groups were trying to look at it and solve it. And so—.

Aryanna Trejo (36:22):

Yeah.

Eric Cross (36:23):

And we couldn’t do that without organizations like yours, that help empower teachers. So.

Aryanna Trejo (36:27):

Yeah! You really said it.

Eric Cross (36:29):

You’re coming to my classroom when you’re back in San Diego?

Aryanna Trejo (36:31):

Yeah! I totally will. Yeah. Let’s make it happen.

Eric Cross (36:34):

Last question. If you think back in your schooling, your own schooling, K through college, is there a person or a teacher that had a big impact on you? Or a learning experience that had an impact on you? And it could be, you know, positive or negative. But something that impacted you, even to this day, that stands out to you, that you remember?

Aryanna Trejo (36:56):

This is a big diversion from the topics that we’re talking about. But in grades 10 through 12, my drama teacher, Mr. Byler, who I still talk with, was such a huge impression on me. Really wonderful. And I couldn’t tell you the teaching moves that he did that were wonderful. I don’t know much about his management. But I can tell you that he gave me space to be confident, and grow into myself, through drama productions. They were high school productions, so they weren’t amazing. But I just really came into myself in high school, because I had the confidence to get on stage. And he was just such a wonderful mentor to all of us. So, props to Mr. Byler.

Eric Cross (37:39):

Shout out to Mr. Byler for creating space for Aryanna to fly! Thanks for making time, after your workday, to talk with us and to share Code.org with teachers.

Aryanna Trejo (37:54):

Of course. Happy to.

Eric Cross (37:59):

Thanks so much for joining me and Aryanna today. We want to hear more about you. If you have any great lessons or ways to keep student engagement high, please email us at stem@amplify.com. Make sure to click subscribe wherever you listen to podcasts. And join our brand new Facebook group, Science Connections: The Community for some extra content.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Aryanna Trejo says about science

“I would hear teachers saying things like, ‘Well I just can’t do coding, it’s just too hard for me.’ And I would ask them…Would you say that to your student about math or English? Be as kind to yourself as you would be to your student.”

– Aryanna Trejo

Professional Learning Specialist, Code.org

Meet the guest

Aryanna is a member of the Code.org Professional Learning Team. Before joining Code.org, Aryanna led computer science professional development for K-6 teachers and served as an instructional coach for new educators. She also taught fourth and fifth grade in New York City and Los Angeles. In her spare time, Aryanna loves taking advantage of the California sunshine, creating wheel-thrown pottery, and hanging out with her dog Lola.

Person with curly hair smiling, standing in front of a brick wall. Circular frame with decorative star in the corner.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. Listen here!

Grade 6

Module 1: Ratios and Rates

Module 2: Fractions, Decimals, and Percents

Lesson 1: Understand PercentsUnit 3Lesson 8: Lucky Duckies [Free lesson]Lesson 9: Bicycle Goals
Lesson 2: Percents Greater Than 100% and Less Than 1% 
Lesson 3: Relate Fractions, Decimals, and PercentsUnit 5Lesson 2: Decimal Diagrams [Free lesson]Lesson 13: Grocery Prices (Print available)
Lesson 4: Find the Percent of a NumberUnit 3Lesson 10: What’s Missing? (Print available)Lesson 11: Cost Breakdown
Lesson 5: Estimate the Percent of a Number 
Lesson 6: Find the WholeUnit 3Lesson 10: What’s Missing? (Print available)

Module 3: Compute with Multi-Digit Numbers and Fractions

Module 4: Integers, Rational Numbers, and the Coordinate Plane

Lesson 1: Represent IntegersUnit 7Lesson 1: Can You Dig It [Free lesson]Lesson 4: Sub-Zero
Lesson 2: Opposites and Absolute ValueUnit 7Lesson 5: Distance on the Number Line
Lesson 3: Compare and Order IntegersUnit 7Lesson 2: Digging DeeperLesson 3: Order in the Class (Print available) [Free lesson]
Lesson 4: Rational NumbersUnit 7Lesson 2: Digging Deeper
Lesson 5: The Coordinate PlaneUnit 7Lesson 9: Sand Dollar SearchLesson 10: The A-maze-ing Coordinate Plane
Lesson 6: Graph Reflections of Points
Lesson 7: Absolute Value and DistanceUnit 7Lesson 5: Distance on the Number Line

Module 5: Numerical and Algebraic Expressions

Module 6: Relationships in Geometry

Module 7: Relationships Between Two Variables

Module 8: Area

Module 9: Volume and Surface Area

Module 10: Statistical Measures and Displays

Grade 7

Module 1: Proportional Relationships

Module 2: Solve Percent Problems

Module 3: Operations with Integers

Module 4: Operations with Rational Numbers

Module 5: Simplify Algebraic Expressions

Module 6: Write and Solve Equations

Lesson 1: Write and Solve One-Step EquationsUnit 6Lesson 3: EquationsLesson 4: Seeing Structure (Print available)Lesson 14: Unbalanced HangersLesson 15: BudgetingLesson 16: Shira the Sheep [Free lesson]Lesson 17: Write Them and Solve Them (Print available)
Lesson 2: Solve Two-Step Equations: px + q = r
Lesson 3: Write and Solve Two-Step Equations: px + q = r
Lesson 4: Solve Two-Step Equations: p(x + q) = r
Lesson 5: Write and Solve Two-Step Equations: p(x + q) = r
Unit 6Lesson 4: Seeing Structure (Print available)Lesson 6: Balancing EquationsLesson 7: Keeping It True (Print available)Lesson 12: Community Day (Print available)Practice Day 1 (Print available)

Module 7: Write and Solve Inequalities

Lesson 1: Solve One-Step Addition and Subtraction Inequalities
Lesson 2: Write and Solve One-Step Addition and Subtraction Inequalities
Lesson 3: Solve One-Step Multiplication and Division Inequalities
Lesson 4: Solve One-Step Multiplication and Division Inequalities with Negative Coefficients
Unit 6Lesson 14: Unbalanced HangersLesson 15: Budgeting (Print available)Lesson 16: Shira the SheepLesson 17: Write Them and Solve Them (Print available)
Lesson 5: Write and Solve One-Step Multiplication and Division InequalitiesUnit 6Lesson 15: Budgeting (Print available)
Lesson 6: Write and Solve Two-Step InequalitiesUnit 6Lesson 15: Budgeting (Print available)Lesson 16: Shira the Sheep [Free lesson]Lesson 17: Write Them and Solve Them (Print available)Practice Day 2 (Print available)

Module 8: Geometric Figures

Module 9: Measure Figures

Module 10: Probability

Lesson 1: Find Likelihoods
Lesson 2: Relative Frequency of Simple Events
Lesson 3: Theoretical Probability of Events
Unit 8Lesson 1: How Likely? (Print available) [Free lesson]Lesson 2: Prob-bear-bilities [Free lesson]Lesson 3: Mystery Bag
Lesson 4: Compare Probabilities of Simple EventsUnit 8Lesson 4: Spin ClassLesson 5: Is It Fair?
Lesson 5: Probability of Compound EventsUnit 8Lesson 6: Fair GamesLesson 7: Weather or NotLesson 8: Simulate It
Lesson 6: Simulate Chance EventsUnit 8Lesson 8: Simulate ItPractice Day 1 (Print available)

Module 11: Sampling and Statistics

Grade 8

Module 1: Exponents and Scientific Notation

Module 2: Real Numbers

Lesson 1: Terminating and Repeating DecimalsUnit 8
Lesson 12: Fractions to Decimals
Lesson 13: Decimals to Fractions
Lesson 2: RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Practice Day 1 (Print available)
Lesson 3: Real NumbersUnit 8
Lesson 14: Hit the Target
Lesson 4: Estimate Irrational NumbersUnit 8
Lesson 3: Between Squares
Lesson 5: Compare and Order Real NumbersUnit 8
Lesson 14: Hit the Target

Module 3: Solve Equations with Variables on Each Side

Module 4: Linear Relationships and Slope

Module 5: Functions

Module 6: Systems of Linear Equations

Lesson 1: Solve Systems of Equations by GraphingUnit 4 
Lesson 9: On or Off the Line?
Lesson 10: On Both Lines
Lesson 11: Make Them Balance [Free lesson]
Lesson 12: Line Zapper
Lesson 13: All, Some, or None? Part 2
(Print available)Practice Day 2 
Lesson 2: Determine Number of SolutionsUnit 4 
Lesson 13: All, Some, or None? Part 2
Lesson 3: Solve Systems of Equations by Substitution
Lesson 4: Solve Systems of Equations by Elimination
Lesson 5: Write and Solve Systems of EquationsUnit 4 
Lesson 14: Strategic Solving, Part 2 (Print available)

Module 7: Triangles and the Pythagorean Theorem

Lesson 1: Angle Relationships and Parallel LinesUnit 1 Lesson 10: Transforming Angles
Lesson 2: Angle Relationships and TrianglesUnit 1 Lesson 10: Transforming Angles Lesson 11: Tearing It Up (Print available)Lesson 12: Puzzling It Out [Free lesson]
Lesson 3: The Pythagorean TheoremUnit 8Lesson 6: The Pythagorean TheoremLesson 7: Pictures to Prove It
Lesson 4: Converse of the Pythagorean TheoremUnit 8Lesson 9: Make It Right
Lesson 5: Distance on the Coordinate PlaneUnit 8Lesson 11: Pond HopperPractice day 2 (Print available)

Module 8: Transformations

Module 9: Congruence and Similarity

Lesson 1: Congruence and Transformations
Lesson 2: Congruence and Corresponding Parts
Unit 1 Lesson 7: Are They the Same?Lesson 9: Are They Congruent?
Lesson 3: Similarity and TransformationsUnit 2Lesson 5: Transformations Golf with DilationsLesson 6: Social Scavenger Hunt (Print available) [Free lesson]
Lesson 4: Similarity and Corresponding PartsUnit 2Lesson 7: Are Angles Enough?Lesson 8: Shadows
Lesson 5: Indirect MeasurementUnit 2Lesson 8: Shadows

Module 10: Volume

Lesson 1: Volume of CylindersUnit 5Lesson 10: Volume LabLesson 11: Cylinders [Free lesson]Lesson 12: Scaling Cylinders
Lesson 2: Volume of ConesUnit 5Lesson 10: Volume LabLesson 13: Cones [Free lesson]Lesson 14: Missing Dimensions (Print available)
Lesson 3: Volume of SpheresUnit 5Lesson 15: Spheres
Lesson 4: Finding Missing DimensionsUnit 5Lesson 14: Missing Dimensions (Print available)
Lesson 5: Volume of Composite SolidsUnit 5Lesson 15: Spheres

Module 11: Scatter Plots and Two-Way Tables

S3-04: Using AI and ChatGPT in the science classroom

A graphic with the text "Science Connections" and "Amplify" features colorful circles and curved lines on a dark gray background.

In the latest episode of the Science Connections podcast, we explore AI in education and its impact on students. Listen as I sit down with teachers Donnie Piercey and Jennifer Roberts to discuss ChatGPT and how we can use it to build science and literacy skills in K–12 classrooms while preparing students for the real world.

And don’t forget to grab your Science Connections study guide to track your learning and find additional resources!

We hope you enjoy this episode and explore more from Science Connections by visiting our main page!

DOWNLOAD TRANSCRIPT

Jennifer Roberts (00:00:00):

If a kid graduates from school without knowing that AI exists, they’re not gonna be prepared for what they face out in the world.

Eric Cross (00:00:07):

Welcome to Science Connections. I’m your host, Eric Cross.

Eric Cross (00:00:12):

This season of the podcast, we’re making the case for everyone’s favorite underdog, science. Recently we’ve been highlighting the magic that can come from integrating science and literacy. So if you haven’t checked out those recent episodes, definitely go back in your feed after you’re done with this one. This time around, we’re going to deep dive into what artificial intelligence means for literacy instruction, and how science can be a force for good, in responsibly exposing students to AI. To help me out, I’m joined by two extremely accomplished educators. Jen Roberts, a veteran high-school English teacher from San Diego, who among many things runs the website LitAndTech.com. And I’m also joined by fifth-grade teacher Donnie Piercey. In addition to being Kentucky’s 2021 Teacher of the Year, Donnie also has an upcoming book about bringing AI into the classroom. Whether you’ve never heard of ChatGPT or whether you’re already using it every day, I think you’ll find this a valuable discussion about the intersection of science, English, and technology. Here’s Jen and Donnie.

Eric Cross (00:01:17):

So first off, welcome to the show. It’s good to see you all. What I wanna do is kind of start off by introducing both of you. And so we’ll just go K–12. So <laugh>, Donnie.

Jennifer Roberts (00:01:30):

Donnie goes first.

Eric Cross (00:01:31):

Donnie’s gonna go first. Donnie out in Kentucky. Just a little background. What do you teach; how long you’ve been in the classroom; and what are you having fun with right now?

Donnie Piercey (00:01:38):

Yeah, so my name is Donnie Piercey. I’m a fifth-grade teacher from Kentucky. Live and teach right here in Lexington, Kentucky, right in the center of the state. I’m the 2021 Kentucky Teacher of the Year. But I’ve been teaching elementary school for the past … I think this is year 16 or 17. It’s long enough where I’ve lost count, and I can’t even count on fingers anymore. My friends like to joke that I’ve taught long enough where now I can count down. You know, it’s like, “All right, only so many more years left.” But yeah, teach all subjects. Science definitely is one of the subjects that I don’t just try to squeeze into my day, but make sure that … it’s not even a devoted subject, but one that I definitely try to — don’t just have that set time, but also try to do some cross-curricular stuff with it. So definitely the rise of AI in these past few months, which feels like years by this point, has definitely played quite the role, in not just changing the way that I’ve been teaching science, but really all my subjects. So, excited to chat with y’all about it.

Eric Cross (00:02:47):

Nice. I’m excited that you’re here. And Jen?

Jennifer Roberts (00:02:51):

Hi, I’m Jen Roberts. I teach ninth-grade English at Point Loma High School, and that’s where I usually stop when I introduce myself. But for your sake—

Eric Cross (00:03:00):

I will keep introducing you if you stop there. <laugh>

Jennifer Roberts (00:03:04):

I am nationally board-certified in English Language Arts for early adolescence. I am the co-author of a book called Power Up: Making the Shift to 1:1 Teaching and Learning, from Stenhouse, with my fabulous co-author Diana Neebe. Shout out to Diana. I blog at LitAndTech.com about teaching and technology and literacy and the intersection of those things. And I’m looking forward to talking about how AI is showing up in my classroom and the fun things I’m doing with it.

Donnie Piercey (00:03:31):

And one of us is actually secretly a robot, and you have to guess which one.

Jennifer Roberts (00:03:35):

Have to guess which one. Yes. <laugh>

Eric Cross (00:03:37):

That would be super-meta. And you were the CUE — Computer-Using Educator — outstanding teacher or educator? Whatever. Either one. Of the year.

Jennifer Roberts (00:03:45):

I was the CUE ’22 Outstanding Educator. Yes. And I’ve won a few other things as well.

Eric Cross (00:03:53):

The gaming backpack.

Jennifer Roberts (00:03:54):

I’ve won a gaming backpack recently! Yes. I once won an iPad in a Twitter chat.

Eric Cross (00:03:58):

What?

Donnie Piercey (00:03:58):

What’s a gaming backpack? Hold on. We need to talk about that.

Jennifer Roberts (00:04:01):

We will talk about that. <laugh> And then, I was once a finalist for county Teacher of the Year. That’s as close as I got to Donnie. Donnie was the Kentucky Teacher of the Year. He got to go to the White House and stuff. That was exciting.

Donnie Piercey (00:04:13):

<laugh> I mean, to be fair, there’s only three million people in Kentucky, and about what, 50 million people that live in California? <Laugh> So odds are definitely stacked in my favor, I think.

Jennifer Roberts (00:04:23):

So you’re saying we’re even there? Is that, is that what you’re going for?

Donnie Piercey (00:04:25):

Yeah, evens out. Evens out.

Eric Cross (00:04:27):

So I’ve been looking forward to talking to you both for a while now, and talking about artificial intelligence. It’s like the big thing. And both of you, at different ends of the spectrum and in my life, have contributed to this. Donnie, you’ve been sharing so much great information online about how you’re using AI in elementary. Jen, you are the reason I got into education technology years ago, right when I was becoming a teacher. And so being able to talk with you both about it excites me a lot. So first off, for the listeners who may not have any experience with it — and there’s still a lot of people out there who have not been exposed to it, haven’t got their feet wet with it yet — I’m hoping we could start off maybe with an explanation of … we could do AI, ChatGPT, I know that’s the big one. But simply explaining what it is, just for the new person. And whoever wants to start off can tell us about it. Or maybe we’ll start … we’ll, let’s actually, let’s do this: Let’s continue going like K–12? So Donnie, maybe you could … what’s your pitch to the new person of, “Hey, this is what it is”?

Donnie Piercey (00:05:31):

All right. So, AI, artificial intelligence, probably the way that most people are exposed to it, at least since November when it launched, is through ChatGPT. Where if you Google it, you know it’s made by a company called OpenAI. The best way to describe what it is … when you go there for the first time, make an account, it’s free. You have like a little search window, looks like a Google search bar. And instead of searching for information, you can ask it to create stuff for you. So for example, like on Google search, you might type in a question like, “Who was the 19th president of the United States?” Where on ChatGPT, instead of just searching for information, it creates stuff for you. So you could say, you could ask it to, “Hey, write a poem about the 19th president of the United States.” Or, “Write a short little essay comparing, I don’t know, Frederick Douglass to Martin Luther King Jr.” And it would do that for you. You know, that’s most people’s first exposure to AI, at least in these past few months. Instead of … you know, it’s artificial intelligence, but it’s not just chatbots. There’s lots of other AI that exist out there.

Jennifer Roberts (00:06:47):

And I think that’s the thing: that people don’t realize how much AI is already in their lives.

Donnie Piercey (00:06:51):

For sure. Yeah.

Jennifer Roberts (00:06:52):

You know, they just haven’t seen … the term that I see being used a lot now is “generative AI.” AI that can produce something. It can produce writing, it can produce art, it can produce a script, it can produce a character. But the AI that has been helping you pick what to watch next on Netflix and the AI that’s helping Google help you get where you wanna go on Google Maps faster, those are forms of artificial intelligence as well.

Donnie Piercey (00:07:21):

Yeah. I mean, even those, when you get that that message in Gmail, and instead of having to type out that response that says, “Yeah, that sounds great,” you can just click the little button that says, “Yeah, that sounds great.” I mean, that’s been in Gmail for years, but that’s artificial intelligence too.

Eric Cross (00:07:39):

Absolutely. So why is it important, do you think, for educators to, to be familiar with it? Like, why are we all so excited about it?

Jennifer Roberts (00:07:47):

So, educators need to know what kids are into, and kids are obviously into ChatGPT. And anyone who’s an educator right now has probably already had something cross their desk — or more likely their computer screen — that was written by AI and passed off as a student’s own work. And that is, of course, the great fear among teachers everywhere, that this is what kids are just gonna do these days and they won’t be able to catch it and children won’t be doing their own work and this and this. But I think the big reason teachers need to know what’s going on is because teachers need to be futurists. Our clientele will live in the future. We teach kids, kids will become adults, adults will live in the world. And so if we’re not thinking about and trying to predict on some level what’s gonna happen 5, 10, 15 years from now … we might be wrong, but what if we’re right?

Jennifer Roberts (00:08:38):

And if we’re not at least trying to think about what is their future world gonna look like, then we’re not serving our students well. I did a whole night talk on that. So I think ChatGPT is part of that. I teach seniors. I had this moment of realization I felt a few months ago. I’m like, “This is gonna be the world they graduate into. They need to know what this is before they leave me.” If I don’t teach them how to use this well, and not the way they’re using it — which is to copy and paste the teacher’s assignment and drop it into ChatGPT and take whatever it spits out and turning that in without even looking at it — if I don’t teach ’em how to use it critically, if I don’t teach them how to write effective prompts, if I don’t teach them how to use the AI as a tool, as a collaborator, then they’re gonna graduate into a world where they lose out to people who do know how to do that. And I think the advantage goes to kids who have access and knowledge of what’s in front of them and what’s available, and can use all of the tools at their disposal. Because when you’re writing in school and you write with a collaborator, that could be considered cheating. But when you do that out in the adult world, that’s considered doing a good job. <Laugh> Being a team player. <Laugh> You know, adults don’t work alone for the most part. And adults are expected to churn out beautiful, perfect content no matter how they got there. So if I’m not teaching my kids how to use this, they’re not being ready. They’re not gonna be ready to be the adults that I want them to be.

Donnie Piercey (00:10:07):

A hundred percent agree. And I also believe … as you know, I teach elementary school. I also don’t think anybody is saying that on the first day of kindergarten, you hand a kid a Chromebook and load up an AI chatbot or ChatGPT and say, Hey, this thing’s gonna do all your work for you for the next 12 years; just coast through life. You don’t have to think creatively. You don’t have to learn how to develop a paragraph or learn how to write a speech or develop an idea. Like, I don’t think anybody’s saying that, because as an elementary school teacher, there’s many days when I’m like, “Y’all, we’re just putting the Chromebooks away today and we’re just gonna go old-school. We’re just gonna maybe just jot down five quick ideas and stand up and present those ideas to the class.”

Donnie Piercey (00:10:54):

Because while AI definitely will, like you were saying, Jen, play a significant role in the lives of our students who are, not just graduating, but the 10- and 11-year-olds in my classroom this year. A significant role in their lives. It’s also really important to recognize that we’re not saying that this means that “Hey, kids don’t have to work anymore.” They still have to put forth that effort. There’s still — one of the ways that you become a good writer is by trial and error. And sometimes that trial and error comes through talking to a teacher or talking like you were saying to a peer or collaborating with a peer and saying to them, “Well, this sentence here, this paragraph here, really doesn’t make sense.” And I do believe one of the ways — especially as AI starts to become more fine-tuned and starts to be embedded more and more in tools like Google Docs and Microsoft Word — is it’s almost going to be a tutor to students.

Donnie Piercey (00:11:56):

Mm-hmm. <affirmative> Where I could very easily see in a few years, or maybe a few months, who knows what Google or any of these other big companies has rolling out, where a student could highlight a paragraph that they wrote simply, and then say, “Hey, proofread this for me,” or “Check for coherence.” Or even just ask a simple question: “Does this paragraph make sense?” Because you can already do that. You can copy a paragraph over into a chatbot and say, “Hey, does this make sense?” You know, “Rate my idea from one to 10,” and it’ll do that for ’em.

Jennifer Roberts (00:12:26):

We did that last week <laugh>.

Donnie Piercey (00:12:28):

Yeah. Right. I mean, that’s the thing. That technology exists now. It’s just not totally embedded yet. But based on what I’ve read and what I’ve seen, that’s gonna happen sooner rather than later. And it’s really, really important that we teach our students that, “No, you’re not just gonna use this, this tool to cheat, but you can use this tool to help you become a more creative student.”

Jennifer Roberts (00:12:50):

This is the use case in my classroom. Can I talk about that? You ready for that?

Eric Cross (00:12:53):

Please.

Jennifer Roberts (00:12:54):

OK.

Eric Cross (00:12:54):

Please.

Jennifer Roberts (00:12:55):

So my ninth graders are writing a comparative analysis essay, where I took them to the student art gallery and I made them pick two pieces of completely unknown student art and take notes on it, so they could go back and write this essay. And as soon as we got back to class, I said, can ChatGPT write this for you? And they all kind of froze ’cause I didn’t tell them what ChatGPT was. And they weren’t sure if they were allowed to know or not. And finally one of them kind of bravely raised his hand and said, “No.” And I said, “Why not?” And he said, “Well, the AI hasn’t seen the art. How can it write an essay about art when the art is completely original that we just went and looked at?” I said, “It’s almost like I planned it that way, isn’t it?” And they laughed nervously. And then I said, “Does that mean it can’t help us with this assignment?” And they said, “Well, no — of course it can’t help us, because it has not seen the art.” And I said, “Well. …” And I open ChatGPT, and I typed in what they were trying to do: “I need to write a comparative analysis essay comparing two pieces of student art on these reasons. And I need to choose which one did it better, basically. Can you help me with an outline?” and ChatGPT produced a lovely outline. And I looked at that with my students and we looked at it together and I said, “This is what it gave us. Would this be helpful to you?” And they’re like, “Yeah, that would be helpful to us.” So we — to be clear here, I was the only one using ChatGPT in the room. They were not actually using it. We were using it together. I copied and pasted the outline that it gave us and put it in their learning management system where they could access it so they could use the outline that the robot provided, and then they could use that to make their own writing better. So then I let them write for a little while, and, after they’d written for a little while, I said, “Does anybody wanna let me share your first paragraph with ChatGPT and see what it thinks of how you’re doing?” And a brave student raised his hand and we took his paragraph and we put it in ChatGPT, and it spit back advice. We said, “This is what I have so far for my first paragraph. Do you have any advice for me?” And we gave it the writing, and the first piece of advice it gave back was very generic, you know, “Add a hook,” you know, like kind of thing. But after that, it started to get more specific about things he was actually doing in his writing. And it started to give him some feedback. And we looked at that together as a class. And I said, “Does any of that feedback help you?” And he said, “Oh yeah, absolutely. I’m gonna go add some revisions to my paragraph.” And other students did too. They looked at the feedback he got and used that to improve their writing. And so everybody went and revised. And I said, “Look, if you take what the robot gives you and you copy and paste it, and you turn it in as your own work, it’s gonna get flagged for plagiarism. And that’s not gonna go well. But if it gives you writing advice the same way I would give you writing advice, and you decide that advice is good, and you take that advice and you incorporate it into your own writing yourself, then the robot’s making you better, but you’re still the one doing your own writing.” And the writing they turned in from that assignment was, was better. It wasn’t written by ChatGPT; it was still about the student art that they found in the gallery. But I showed them a path. Like, it can help you with an outline, it can help you with feedback. Right? These are fair ways to use it that’s gonna make you better. And they really liked that. They really liked — no one had shown them that before. The idea that you don’t just take the teacher’s prompt and give it to it … like, these are new uses to students and worked well.

Eric Cross (00:16:17):

So right now, you both just laid out these ways that you’re using it. And I do this with people that I’m trying to introduce to ChatGPT or AI. ‘Cause I get excited. Anyone could write a 500-word persuasive essay on the use of color in The Great Gatsby or The Outsiders, and they can get something back within seconds. But for a lot of educators, it might feel like the sky is falling.

Donnie Piercey (00:16:43):

Oh, understandably! Understandably. I mean, that totally makes sense.

Eric Cross (00:16:49):

What would you say to them? Donnie, go ahead.

Donnie Piercey (00:16:51):

Yeah. Well, I feel like every teacher kind of goes through the same experience when they see like a generative chatbot. I mean, all these major companies are gonna start incorporating AI, the generative AI piece. And a lot of times, when they see it for the first time, two things. First they’ll say “Oh, but I’ll know that that’s not my students’ writing.” Which, frankly, I think is a good thing, because that tells me that the teachers know their students’ writing. They’ve seen them write in person. They’ve conferenced with them one-on-one. And if a student were to turn something in to me, who I know might be a struggling writer, maybe it’s not their strength, and all of a sudden they’re turning in this10-page dissertation-worthy thesis written at a PhD level, I’m like, “All right, man, you’re nine. Can we talk about where this came from?” <laugh> But I also don’t think that at like the heart, I don’t feel like kids want to cheat. I really don’t. I feel like sometimes like kids are in a situation where they’re like, “OK, I’ve got nothing left. I gotta get this assignment done.” And when those kind of things happen, that’s when we as teachers, we have those one-on-one conversations. Even when I showed my students ChatGPT and even some of the AI image-generating stuff for the first time, and I talked to them about, “What do y’all think about this?” Because, you know, they’re under 13. In my district, ChatGPT is blocked for students. Staff, we have access to it. And that’s just because one, it’s so new, and at the same time, we need to figure out, “What’s the best way they can go about using this tool?” But when we were talking about it as a class, you know, I didn’t want to ignore the elephant in the room. So I asked them, I said, “Hey, do you feel like this is something that you all would use to. …” I mean, I used the word. I said “cheat.” And to be honest, the majority of the students in my class, they were taken aback. They’re like, “What? You think we just would cheat all the time?” Right? <Laugh> And I’m like, “Oh, well good. I’m glad to know that integrity is still alive and well.” But yeah, that’s definitely my thoughts on it, as far as not only the student integrity piece — I think that that’s the big thing that you need to just bring up with your students. Because again, I like to think that I’ve seen my students write enough that if they were going to turn something in that wasn’t their voice, or it didn’t sound like them, like I could have that conversation. And don’t be surprised, too, if in the next … I don’t know, one month to a year, there’s lots of AI detectors that exist. A lot of them are these like third-party things. You can go ahead, but I would not be surprised if in the next year or so, like you start to see those AI detectors be built into Google Docs, into Microsoft Word, into even Canva. And honestly, it’s almost like a fail-safe button for teachers, that we could say “All right, this is telling me that this is 99% probably written by AI.” So you can have that conversation with a student that way.

Jennifer Roberts (00:20:03):

I mean, if you’re worried about it, Formative, right now, will even tell you if something is copy-and-pasted into the boxes that they give you for students to write in. I find that kids who cheat are desperate, you know. Especially at the high school level. They’re panic mode. And, and usually their panic comes from, “I have no idea how to even start this assignment.” And so part of what I wanna use ChatGPT for is to lower that barrier for them. Like, you’ve got an assignment, you don’t know where to start. Tell the robot, tell ChatGPT, about the assignment and ask it for a list of steps. You know, ask it for an outline. Ask it for a time management plan. I see so much tremendous potential for this to help many of my students with IEPs who have executive functioning issues.

Donnie Piercey (00:20:49):

Oh, a hundred percent, right?

Jennifer Roberts (00:20:51):

Yes, a hundred percent. This can be their personal assistant who, you know, instead of me sitting with them one-on-one and saying, you know, “This is the task you need to do, let’s break it down into these six discrete chunks,” the artificial intelligence can do that for them. And it can do that for teachers too. <laugh>

Donnie Piercey (00:21:09):

Jen, I was just thinking about, how long until we see like the phrase artificial intelligence written onto a student’s IEP? I could see that happening very, very soon.

Jennifer Roberts (00:21:20):

Right? They should be able to use that. And then, also, of course, all of its amazing beneficials for teachers. I had to completely rewrite a unit of my curriculum. I knew what I wanted to do. I had some ideas of things I wanted to put in there. And I resorted to, I went to EducationCopilot.com and typed in my stuff that I had: You know, what standards I wanted to cover, what outcomes I was hoping for mm-hmm. <affirmative>. And it generated an eight-week unit for me. And I actually told it then to go back and do it as a 12-week unit so that I’d have more stuff in there to go and cherry-pick to decide what I really wanted to do. But it gave me ideas. It gave me places to start. It saved me an hour of just brainstorming. And I don’t think that was cheating. I still got to go in and decide which ideas were valid. And I still got to … you know, I mean, I’m a teacher. Can I get accused of cheating? I don’t think that’s a thing. It’s—

Eric Cross (00:22:18):

That’s collaborating! It’s collaborating!

Donnie Piercey (00:22:20):

Collaborating! It’s a feature! It’s a feature.

Jennifer Roberts (00:22:22):

It’s Tony Stark talking to Jarvis. You know, they’re figuring it out together.

Donnie Piercey (00:22:26):

Oh, when you use the AI, Jennifer, do you call yours Jarvis? In my class we call him Jeeves. ‘Cause remember Ask Jeeves?

Jennifer Roberts (00:22:33):

I think Eric calls it Jarvis.

Eric Cross (00:22:35):

Yeah. Jarvis is gonna be the AI’s name when, when I can get that fully functioning. There are some things that you had said, I just wanna circle back on. Donnie, Jen — so what I heard was like, best intentions. The part you said about integrity and students wanting to cheat … even the mindset that we go in assuming our students, what they would want to do and assuming best intentions, really kind of frames how you look at this kind of technology. And then Jen, you kind of brought up why students cheat, and realizing that either they don’t feel equipped, or maybe it’s time management, or something else. But most people — and I believe this as an educator — most students want to learn, and they want to be able to perform and achieve. And when they cheat, it’s because they didn’t feel like they could, for whatever reason. Whether it’s it’s outside factors, whether it’s something internal, motivation, whatever it is.

Jennifer Roberts (00:23:24):

Or they were very disconnected and just didn’t care.

Eric Cross (00:23:27):

Sure.

Jennifer Roberts (00:23:27):

This is just busy work the teacher’s giving me, so I’m gonna give it very little of my time and energy. But I think, yeah, it can be that. But if the kid cares about it, if they wanna learn, they wanna learn, you know?

Eric Cross (00:23:40):

Right.

Jennifer Roberts (00:23:40):

This is the day of the internet. Any kid can learn anything they really want to learn. And we see that all the time in our classes. The kid who has zero interest in what I’m teaching in English, but he is an expert coder, and that’s what he wants to spend his time learning. He’s like, “Can I read this C++ book as my independent reading book?” And I’m like, “You know, actually, you can. Go ahead.” <Laugh>

Eric Cross (00:24:01):

Yeah. And for both of you, saying that this makes content more accessible … and I think Donnie, or Jen, you said something about IEPs. I actually put in having it write an IEP to see what would happen. I gave it a prompt for a student’s ability level and I asked it to create a plan. And then I asked it to create a rationale. And it did! And it was good! I went through and vetted it. And right now … you know, a lot of it is funny, ’cause the conversation I’m having with different teachers is kind of like the Wikipedia one. Remember when Wikipedia first got out and everyone was like trying to discourage everybody from using it, because, well, it could be changed by anybody? And now everyone’s like, “Oh, check Wikipedia, and then steal the sources, ’cause they’re already done for you.” Like, the mindset has shifted since then. And I was talking to someone and they said, “Well. …” And I said, “We can use AI, it could be a tutor, these other things. …” And they said, “Yeah, but what happens?” And then insert apocalyptic scenario. Like, what happens if you don’t have access to wifi? And it reminded me of, for some reason, cooking classes. So in the 1700s you probably had to be able to farm to be able to generate your food. Right? Like, you had to get it from somewhere. But if you take a culinary class now, you just go to the grocery store. And someone might say, “Well, but you should know how to farm, ’cause what if there was this worldwide apocalypse and nobody could go to the grocery stores?” <Laugh> And you’re like, “Well, balance of probability though.” You know, it’s like we’ve been really been living in these iterations of life, and I think this next step for some folks … like, we don’t even realize, even like something like bank statements, right? So many folks are paperless. And there’s always a what-if scenario. What if you need it and the internet goes down. But we get so used to to to technology advancing and making our lives different. This kind of seems like that next iteration. And I wanna ask you this question: Are we looking at like the next calculator? The next internet, with this tech? Or do you think it’s too early to say?

Donnie Piercey (00:26:01):

Well, I’ve seen a lot of people compare ChatGPT to a calculator. I’ve seen that pop up on social media. There’s, “Oh well, no, this is like when the calculator was invented. Everyone was up in arms about how ‘that’s not what math students should do.’ Math should be pencil and paper, math should be this.’” However, you can give a kid a calculator and you can give ’em a word problem and they can punch in all the numbers, but they could do the wrong operation or they could put the decimal point in the wrong place, ’cause the student is still the one who’s controlling what’s on the calculator. Where with AI, all you gotta do is just copy it and then paste it into the bot and it’ll spit out whatever the question asked it for. Whether it was, you know, a 500-word rationale or proof for something in geometry, or if it’s analyzing data on a chart, it’ll do all that.

Jennifer Roberts (00:27:00):

Yes. But it’s not that magical. It’s back to what Eric did with the IEP. He put in a prompt and then he knew enough to ask for a rationale and then he knew enough about IEPs to critically read the results he got and make sure they actually worked for what he needed. He had to know all that. He was an expert using it to do an expert thing. My husband’s a computer scientist; he got ChatGPT to help him write an app, and it was a new programming language to him, and he could put in the data and he could ask for things that I would’ve never thought to ask for. But because he knows the language of computer science, he knew what to ask for. And when it gave him results that were bad, he could see that, and he could say, “Yes, but do it again, but without this,” or “make this part more efficient.” He, again, knew what to ask for. So I think the generative AI is, as a partner with humans, a powerful thing. But if the human doesn’t know what they’re doing, yeah. You’re still not gonna get great results.

Donnie Piercey (00:28:03):

<laugh> And I think that’s why I’m coming at this from the elementary school perspective, right? Because in K–5 students are still learning, like, “Hey, where does the decimal point go?” They’re still learning, you know, if you’re dividing by a two-digit number, where does the first digit go, if you go in the old long-division algorithm? And so they’re still acquiring that base-level knowledge that … I don’t know, maybe this is similar to in Jurassic Park when Jeff Goldblum says, “It didn’t take any knowledge to attain,” you know, “they stood on the shoulders of geniuses,” that whole thing. Like they had to acquire the knowledge for themselves, was his whole point. And so that’s why I don’t think it’s exactly the same as the calculator. It is definitely going to change things, in a similar way that the calculator did. But to me it’s just a whole new animal. And I don’t know if it’s going to be like the next internet, Eric — if you’re gonna get little devices that have AI built into it, like a Star Wars kind of thing, like a droid or something that follows you around — all that would be kind of cool, not gonna lie. But whether it’s something that you’ll access through the internet, something that’s built into your TV, that part I don’t know. But I do know that there’s a reason why all of these apps and all these companies are investing so much — not just energy, but time and money into it. Because they’re recognizing. “OK, this really has the potential to change things.” But if used well, and used safely, to change people’s lives for the better.

Eric Cross (00:29:41):

So I definitely hear that you both agree with the statement that if AI ChatGPT was used in the classroom, it could be a force for good. And literacy development. And I wanna shift gears a bit and then come back to the AI. So with that said — and we’re gonna get into some best practices in a minute — in Science Connections right now in this season, we’re making the case for how science can do more in classrooms and in schools. And so I’m I’m curious about what both of you think about the role in science fostering a better future when it comes to AI and education. And this season we’re really talking a lot about literacy. You know, in schools, so often it’s taught in a siloed way. And Donnie, you’re doing multi-subject. Jen, you’re single-subject: English. And we’ve really been trying to make this case for how science can actually support literacy, and these skills that students are trying to develop. So we’re going a little old-school, kind of diving into your content specialty, but maybe even pre-AI, or maybe AI has a component in this. But Don, maybe we’ll start with you. How has science been a way that has been helpful for your own literacy instruction? I know you do a lot of science, because I see your Google Earth stuff and the thing you did with the solar systems back in the day. And I think —.

Donnie Piercey (00:30:54):

Oh my gosh! You remember my <laugh> … wow.

Eric Cross (00:30:58):

That was amazing!

Donnie Piercey (00:31:00):

We haven’t done that since the pandemic. But I had my students go out, and using Google Earth, we built a scale model. Each of the students partnered up and they planned out on Google Earth a scale model of the solar system. They picked an object from around their house and we talked about like, “Don’t pick something bigger than a beach ball, or else, you know, your Neptune’s gonna end up like 10 miles away.” But you know, they just picked like a small ball, like a basketball, soccer ball, something like that. Or football, for international friends. And then we calculated the size of every other planet. And then on Google Earth, using their front lawn as where the sun was, then we went and we calculated where other planets would be, and then we actually drove to those locations and like held up the objects that would represent Neptune, Jupiter, Saturn, and all that. But it was a lot of fun.

Eric Cross (00:31:59):

And is that still accessible? ‘Cause I know you have some websites that you put resources out there.

Donnie Piercey (00:32:03):

Yeah. Yeah, I can … I wanna say on my Resources page — Resources.MrPiercey.com — I’ve got a link on there to a couple of student examples that I can share. And if not, when we get off this call, I’m gonna go on and put them on there <laugh> so people can find it. I’ll even throw on there just the assignment itself. So if you wanted to copy that and do that with your students, you could.

Eric Cross (00:32:27):

Donnie, the reason why I brought that up is because I saw that you had posted that or shared it a long time ago, and I just thought it was the coolest thing that you could totally do with middle-school students or high-school students. Jen, when I became a teacher, you said, “We’re all teachers of literacy.”

Jennifer Roberts (00:32:43):

<laugh> Yeah. I think we forgot to tell them that I was one of your professors.

Eric Cross (00:32:47):

Yes. <Jennifer laughs> One of the people who’ve definitely influenced and shaped my teaching. And that statement has never left my mind: that we’re all teachers of literacy. And I want to ask you, at the high-school level, how can science educators, or how can science — how have you seen it, or how does it, support literacy, when it’s done right?

Jennifer Roberts (00:33:09):

Like I said, I think we’re all teachers of literacy, but I think literacy is bigger than just reading and writing. I don’t think someone is literate if they can’t talk somewhat knowledgeably about what’s happening with climate change. I don’t think someone’s literate if they don’t know what’s going on in the world. And I think so much of what’s going on in the world has to do with science. We’re doing that all the time. If I could teach English just by giving kids articles about science, things to read, that would make my day. Right? We would never read another piece of fiction again. It would all be, you know, what’s happening to the ice sheet in Greenland. My students thrive on reading non-fiction. And then whenever that non-fiction touches on science is even more interesting. And whenever I can get them writing about data, particularly their own data that they collected, I think that’s building those science literacy skills as well. So I think science and English blend together very, very well. I think the literacy aspects of that are fantastic. There are more subject-specific vocabulary words, advanced vocabulary words, in science than any other discipline. And I don’t see why those shouldn’t come up in English as well. You know, my seniors will do a unit at the end of the year on the new space race. Unless I replace it with a unit about generative AI, which I’m seriously considering doing, ’cause I think they really need to learn about bias in AI algorithms and things like that. And I would like to have them read a whole bunch about that stuff. And I wanna give them the open letter that all those CEOs signed that said that AI research should slow down, and make them part of that live conversation about what’s happening in that field. So science comes into that. You know, when we read Into the Wild, we start talking about a whole bunch of scientific concepts. And when it rains in Southern California, we pull up weather maps and look at radar and talk about that and how that works.

Donnie Piercey (00:34:59):

That’s like once every 10 years, Jen? <Laugh>

Jennifer Roberts (00:35:02):

Well, actually, this year it rained a lot. It rained a lot in San Diego. Which is actually very high-interest for them. ‘Cause they wanna know, is it gonna be raining at lunchtime?

Eric Cross (00:35:12):

Jen, you said something … you have your students writing about data?

Jennifer Roberts (00:35:16):

Oh yeah.

Eric Cross (00:35:17):

Can you tell me more about that?

Jennifer Roberts (00:35:19):

So, this is something we’ve done with the ninth grade team for a long time now, is writing about their own data. So it started with a unit about stereotypes and stereotype threat. And they would collect data individually and then they would enter that data into a Google form and then we would give them the spreadsheet of the aggregate data from the whole ninth grade. And then we morphed that unit into one about academic honesty, and they filled out a survey at the beginning of the unit about their feelings about academic honesty and about experiences with academic honesty and cheating and homework and things like that. And then we would do the unit. We’d do all the readings in the unit. And they’d have these “aha” moments about things that were happening at other schools. And then at the end of the unit, we would give them back their own aggregate data and ask them to write about whether or not academic honesty was an issue at our school. And then to support that answer with evidence from their own dataset. So they had that spreadsheet to comb through and figure out, you know, where am I gonna stand on this? We give them the multiple-choice questions we gave them as the graphs, in Google Slides, so that they could write about them and talk about them, too. So yeah, getting kids to write about data. And the the sentence frames we gave them were sentence frames out of, They Say, I Say, from the chapter on writing about science. And <laugh> as they write this stuff, they’re like, “I feel so smart writing this way.” And I’m like, “I know, ’cause you’re writing about big important topics!” Right? And writing about their own data come to think of it is another great way to make an assignment both very personal to them, but also make it ChatGPT-proof, you know, if you’re looking for something that kids can’t just hand to the robot, the robot doesn’t have that data set.

Eric Cross (00:37:08):

Absolutely. And Donnie, at the elementary level, do you, do you make connections between science and literacy? In your class? You talked about with math, definitely with the solar system, but now, I’m curious, what are your newer projects? What have you been working on lately?

Jennifer Roberts (00:37:23):

What’s up now, Donnie?

Eric Cross (00:37:24):

Yeah, what are you doing?

Donnie Piercey (00:37:25):

Oh, man. Well, let me think. I’m just trying to think of some fun projects that we’ve done this year. Science that we can tie in Literacy and also some student creation. Just recently we had a … so I’ve wanted to expose my students to famous scientists that weren’t just white dudes from Europe. So for this year, what I did — and I actually used AI for this — I went into ChatGPT and I asked for 64 famous scientists and it listed them all off. And then I asked it, like, how many of these were white? And I think it said like 61 of them. You know, it had like Neil DeGrasse Tyson, and a couple of other … I didn’t know who they were. So I’m like, “All right, so we need to make this more diverse and make this more equitable.” ‘Cause you know, with the student population in my classroom, try to find equal representation to make sure they can see themselves in some of these scientists. So, eventually got it narrowed down to where I had about 64 scientists. Half are women, half are men from all continents except Antarctica. I assigned these scientists to my students. Some got two; some got three. And their assignment was to go and one, do some individual research on this person, find out what they were famous for, what they were most well-known for, turn it actually into a persuasive piece, where I said, “Hey, you’re gonna have one slide.” And I’ll tell you why I gave him one slide in a minute. On that one slide, you’ve gotta convince the person who sees it that this scientist is the most important scientist since the dawn of creation. I said, “You could use images, text — I don’t care if they were famous for something that you didn’t even understand what it was. It’s a persuasive piece. You’re 10. Go all out. Add gifs, do that whole thing.

Eric Cross (00:39:21):

This is awesome.

Jennifer Roberts (00:39:21):

I wanna do this project.

Donnie Piercey (00:39:23):

And if you picked up on the number 64, and I did this in March, so what we did was throughout the weeks of March Madness of the women’s and men’s NCAA tournament, whenever a game was going on, we had another round of voting. I just paired ’em up. I was gonna like seed them, like 1 to 64 — that’s just way too much work for me <laugh>. So I just kind of did random kind of thing. But all the students had to do — they just saw the slides side-by-side, and the only question they had was, “Based on what you see here, who is the most important scientist? This person or this person?” And it eventually came down to Carl Sagan going up against Marie Curie.

Eric Cross (00:40:04):

OK, that’s a good matchup.

Donnie Piercey (00:40:06):

Yeah, well, the Marie Curie slide, they just liked the radium piece. So they added like some green glowing gifs. And I said, “Guys, it doesn’t always grow glow green.” But whatever. Anyway, eventually Carl Sagan, in case you wanted to know, according to the 10-year-olds in my classroom, is the most important scientist in the history of the world. So I don’t know if I agree with that per se — I think maybe Newton or somebody else might have had something else to say about it — but fun assignment. It was a unique way to expose my students to a bunch of ideas. I remember the student that I assigned Newton, the only thing that that she knew about Isaac Newton was “Didn’t he get hit in the head with an apple?” And I said, “Well, not exactly, I think you might have read or maybe seen too many like old-school cartoons or whatever.” But she ended up doing some research. She’s like, “Oh, I’ve heard of that before! That equal and opposite reaction thing.” Didn’t know what it meant. I had another student that just got really … you know, if you’ve ever been on one of those YouTube kicks where it’s just, you go like nine levels deep onto like, “What does this theorem mean?” Student sits in back of my classroom, I walked by one day and he’s just watching something on like the fifth dimension and what it might be. And I said, “Oh, your scientist got you started on that.” So definitely was a lot of fun. Unique way to combine reading, writing, but also expose my students to some ideas. And we’re definitely gonna do it again. I’ve actually done this assignment before. I picked 64 random elements on the periodic table. But their only slide that they have to make is “What’s your element? What is it used for? And then, why is this the most important element since the dawn of creation?” <Laugh> And, you know, there’s always that student that gets hydrogen. They’re just like “Sweet!” Right? They get excited about that one. <laugh>

Eric Cross (00:41:59):

Explosions.

Donnie Piercey (00:42:00):

Yeah. But then, for that kid who likes a challenge, or that student with the “gifted” label, you give them, like, einsteinium or palladium. Some of the more challenging ones. And they go all out with this. I didn’t use AI for that one, but it was kind of fun, and I figured it’d be neat to share an idea that another teacher could try.

Eric Cross (00:42:20):

Well you probably have at least two teachers right now that are gonna go and try that. And we’re both looking at you. So.

Donnie Piercey (00:42:24):

Go for it.

Eric Cross (00:42:25):

Thanks for that idea. I’m imagining my students coming in with jerseys with “neon.”

Donnie Piercey (00:42:29):

Oh yeah. <laugh>

Eric Cross (00:42:30):

“Neon” on it. Just all ’80s out.

Donnie Piercey (00:42:33):

The game behind it, too, is you tell kids — again, this is just so the 10-year-olds in my class don’t get their feelings hurt — but I say, “Hey, and if your element gets knocked out, you just have to start cheering for whoever beats you in the tournament.” So by the end, you kind of got half the class cheering for one and half the class cheering for whatever.

Jennifer Roberts (00:42:53):

So the only thing I got outta that whole story that I’ve got for you is, as a child I met Carl Sagan. That’s all I got.

Donnie Piercey (00:43:02):

For real?

Jennifer Roberts (00:43:02):

For real.

Donnie Piercey (00:43:03):

So did he talk with that cadence and tone?

Jennifer Roberts (00:43:06):

Yes.

Donnie Piercey (00:43:06):

Like in real life? Wow.

Jennifer Roberts (00:43:07):

Yes. My father was one of the cinematographers on the original Cosmos. And I got to go to the set a few times.

Donnie Piercey (00:43:14):

That’s incredible!

Jennifer Roberts (00:43:15):

I did not appreciate what I was seeing as a child. But as an adult, I’m like, “That was cool. I was there.”

Donnie Piercey (00:43:20):

“You can see my shadow off in the distance.”

Jennifer Roberts (00:43:23):

I mean, maybe that’s part of why I’ve always had an interest in science. I’ve always had fantastic science teachers. Every science teacher I ever had was amazing.

Donnie Piercey (00:43:31):

I credit mine to Mr. Wizard. I don’t know if you ever watched Mr. Wizard and Beakman’s World?

Eric Cross (00:43:35):

I remember Mr. Wizard. Yep. Yep. I definitely remember Mr. Wizard, Beakman’s World, all those. That was on Nickelodeon back in the day. I had to get up early to watch that one. But there’s a YouTube video—

Donnie Piercey (00:43:44):

Six am!

Eric Cross (00:43:44):

<laugh> It was! It was super-early! But there was one, Don, I don’t know if you’ve seen this on YouTube, but it said “Mr. Wizard Is Mean,” and it’s just clips of when he’s—

Donnie Piercey (00:43:56):

Yelling at kids!

Eric Cross (00:43:56):

Chastising. Or being really direct. It’s just one after another.

Donnie Piercey (00:44:02):

He always asked ’em a question and if the kid, you know, didn’t answer it right, he’d be like, “Well, you’re not right, but you’re wrong.” You know, whatever. <Laugh>

Eric Cross (00:44:14):

I have to make sure I’m not subconsciously saying Mr. Wizard quotes when I’m talking in the classroom, when things are happening. But yeah, that video’s hilarious. So I just want to bring us back to AI, and ask this question: Do you think science has a special role to play when it comes to teaching kids about AI responsibly? Does science have a special role in that?

Jennifer Roberts (00:44:36):

I think the responsible piece of AI I wanna teach my students about is the part about the bias in the algorithms and the bias in the training. And I want them to understand how it works, well enough to make informed decisions about how it impacts their lives.

Donnie Piercey (00:44:56):

Hmm.

Jennifer Roberts (00:44:57):

Because I do have concerns about a tool that was trained on the internet. And the answers it gives you is the average of the internet. And do we trust the internet? And the answer from kids is always, “Well sorta, no.” <Laugh> So I want them to understand the social science behind that.

Donnie Piercey (00:45:18):

Yeah. And just along that same point, having the students recognize that just because, you know, you copy-and-paste a question in, the answer it spits out might not always be correct. So, teaching them that just like you would with a source that you find about a topic that you’re researching, you’ve gotta fact-check.

Jennifer Roberts (00:45:44):

It’s just like being a good scientist. A good scientist wouldn’t always accept a single result or the first result. You know, you would look at multiple angles. You would try things different ways. Last week I took the article my seniors were reading about victim compensation after 9-11, and in front of them, I gave ChatGPT, I said, “Are you familiar with this article by Amanda Ripley? And ChatGPT came back and said, “Oh yes, this was written in the Atlantic in 2020 and it’s about these things, blah, blah blah.” And my students looked at that and went, “That’s not the article we read.” And I said, “I know. It got it wrong. That’s amazing!” Yeah. And I was so happy that it got it wrong! ‘Cause I wanted them to see that happen.

Donnie Piercey (00:46:21):

And I guess one of the big science questions there, or one of the big science components there, is that idea of inquiry. Right? It’s almost like you have to teach students how to ask those deep questions about what AI spits out.

Eric Cross (00:46:35):

All of those tips are great. And it leads me to this last question I want to ask. New teachers that are out there — it actually doesn’t even matter; new teachers, experienced teachers, all of us are kind of new at different levels of this race. We’re all kind of starting it together. I mean, it hit mainstream. We’re all getting exposed to it. You all really dive into it. When tech comes out, I know you two really like, “OK, how can we use this to transform education and do awesome things for kids?”

Donnie Piercey (00:47:04):

Usually, when new tech comes out, “How can this make my life easier?” is usually the question. Yeah.

Jennifer Roberts (00:47:09):

“How can I save myself time with this?” Yes.

Donnie Piercey (00:47:11):

“How can this result in me watching more TV and you know, less grading,” sometimes.

Eric Cross (00:47:16):

And I start there like you, but then I end up more time that I fill with another project. And I need to learn how to stop doing that. I’m like, “Oh! I got more free time! … to go take on this other task.”

Jennifer Roberts (00:47:28):

Oh, all of my tech adoption is driven by “how can I work less?”

Eric Cross (00:47:32):

So you’re you’re talking to a new teacher, teacher’s getting exposed to this, they’re starting the school year or they’re just getting their feet wet with it. What advice would you give them about AI, incorporated into content or even just best practices? Where you’re at right now in your own journey, and someone’s asking you about it —what would you share with ’em? And Jen, I want to start with you.

Jennifer Roberts (00:47:53):

So, the first thing I did is I was in the middle of grading, you know, 62 essays from my seniors about Into the Wild, when ChatGPT became a thing last November. And I wanted to see what would happen. So the first thing I did was take the prompt that I had given my students and gave it to ChatGPT, ’cause I had just graded a whole bunch of those essays and my brain was very attuned to what my rubric was doing and what I was expecting as the outcome. So I could take what ChatGPT gave me as that quote unquote “essay” and evaluate it critically. And I was ready to do that. So my first advice is take something you’re already asking students to do and ask ChatGPT to do the same thing. So that as you look at the student results, you can compare that to what ChatGPTgives you. If what you’re finding is that ChatGPT can generate something that would earn a decent grade from you, you might need to change that assignment. And it doesn’t need to be a big change, but it might need a tweak or something, so that it, it does rely on the student voice, the students to do something more personal. I’m finding very helpful in my classroom is having my kids do projects where they are recording themselves on — I like Flip. So they’re writing a scene together and they’re having to record the scene together. And I’m emphasizing more of the speaking roles than the writing roles necessarily. So yes, first, take something you’re already doing, paste in to ChatGPT, see what the results are, see how that fits with what your students are doing, and then do that for every assignment you give and just sort of see what comes out of that, and see which assignments are failing and which assignments are working. ‘Cause that’s gonna give you a sense, when you do see one of those results from your students, you’ll be able to recognize it. But it’ll also help you tweak your assignments and decide, “How can I make this a little more original or a little bit more authentic for my students?” And if the robot, if the AI, can’t generate a response, what could the AI do that would be helpful to your students? Would be my next question. So can you use the AI to help them generate an outline? Can you use the AI to help them generate a list of steps to help them get started? And when you’re comfortable enough doing that by yourself, then don’t be afraid to open it in front of your class. If it’s not blocked at your school site, which I hope it’s not. Because I think the advantage goes to kids who have access to this in the long run, or at least see what it is and know what it is. Right? Because if a kid graduates from school without knowing that AI exists, they’re not gonna be prepared for what they face out in the world. So give them a chance to see you using it. Model effectively using it. I have a blog post about that. I just wrote it. LitAndTech.com. You can check that out. “Introducing 9th graders to ChatGPT.” How it went, right? There’s a chart there you can have. It’s my very first draft of this, but it seems to be very popular. So, you know, show students how it can be used as their mentor. If I can’t come read your paragraph because I have 36 kids in my classroom and I cannot stop and read everybody’s first paragraph, can you, if you want to, give your first paragraph to ChatGPT and ask for advice? And will that advice be helpful to you? So showing students how it can be used responsibly is, I think, something every teacher should be doing right now. And don’t hold back just because you’re afraid you’re gonna be teaching them what this is. They know what this is. Right?

Donnie Piercey (00:51:13):

They know what it is.

Jennifer Roberts (00:51:13):

Especially if you teach high school. They know what it is. I’ve had parents thank me for showing them how to use it responsibly. You know, this can actually be a really useful tool, but if you’re trying to make it do your work for you, it will probably fail you. If you’re trying to use it to help you do your work, it will probably be helpful. Sort of the way I’m breaking it down for them at this point. You want the great metaphor? The great metaphor is if you build a robot and send it to the top of a mountain, did you climb that mountain? No. If you build a robot and ask it to help you get to the top of the mountain, and you and the robot go together, did you climb that mountain? Yes.

Eric Cross (00:51:53):

I like that. I’m thinking through this. I’m processing that now.

Donnie Piercey (00:51:57):

Me too.

Eric Cross (00:51:59):

Yeah. I just imagine a robot holding my hand climbing Mount Everest and I’m like, “Yeah, I did it.”

Donnie Piercey (00:52:04):

If I got a robot though, like I would have to dress it like Arnold Schwarzenegger in Terminator 2. Like I would just have to.

Eric Cross (00:52:10):

Of course.

Donnie Piercey (00:52:10):

Of course.

Eric Cross (00:52:13):

Donnie, same question. Advice. Teachers getting immersed into it. Tips. What would you say?

Donnie Piercey (00:52:20):

So, I would definitely agree with everything that Jen said. Just, if anything else, to familiarize yourself with it. Almost like pretend like it’s a student in your classroom and it’s answering questions, just so that way you can see what it can do. And you’re kind of training yourself, like, “Oh, well, if I ever need examples, exemplars.” If you’re in a writing piece and you don’t wanna sit there and write out four different types of student responses — you know, advanced writer, beginning writer, whatever — great way to to do that is you just—

Jennifer Roberts (00:52:48):

Oh yeah. We did that.

Donnie Piercey (00:52:48):

—copy the prompt in and give a beautifully written piece that a fifth grader would be impressed with. Boom. It’ll do it for you. In my classroom, the way that I approach it is I kinda look at AI as almost like this butler that I don’t have to pay. That if I need it to do something for me, it’s just bookmarked. I can click it. And I mean, sometimes I just talk to it like it’s a person. And it’s almost like, in the chat window, I’m just rambling at it, what I’m trying to do. And it’s almost like I’m talking to a coworker, and I’m trying to hedge out some ideas for a lesson. Simple example: For a science lesson, if you’re trying to come up with … let’s say you’re a fifth-grade — or, sorry, I teach fifth grade. Say you’re a seventh-grade science teacher. And you’re trying to teach the students in your class about Newton’s third law of motion. You know, every action [has an ] equal and opposite reaction. Look around your room. See what you have. Maybe look around and you’re like, “All right, I got a whiteboard, microscope, I’ve got magnets, a cylinder. …” And you just copy all this stuff into ChatGPT. Say, like, “Hey, I have all of these items. Cotton balls, peanut butter, whatever.” And say, “I’m trying to teach students Newton’s third law of motion. Give me some ideas of some ways I could teach it using some of these materials.” And it’ll do it! It’ll give you like five to 10 ideas!

Jennifer Roberts (00:54:15):

And then tell it what your students are into. Like, my students are really into basketball. Can you work that into this lesson?

Donnie Piercey (00:54:21):

Yeah! They’re into the Avengers! Hey, find some way to tie Spider-Man into this. You know, that was a pun that didn’t go so well. But, you know <laugh> figure out some way that you could incorporate this and it’ll do it. And Eric, like you said, it won’t be perfect. Right? But if anything else, if you’re a starting teacher and you’re trying to brainstorm ideas — try it.

Eric Cross (00:54:44):

And Donnie, as you were saying that, I was thinking — first, I imagined Spider-Man shooting cotton balls with peanut butter all over them — and then my mind went to having students have these items, like you were saying. And then they create labs, working alongside AI. To do inquiry. To create a lab about something, and then going and performing and collecting data. OK, that’s — now I wanna go do that tomorrow!

Donnie Piercey (00:55:10):

Listen, it is so easy to do. If you have an extra computer in your classroom. … We were talking about Jarvis and Iron Man and Tony Stark earlier. Make a new chat in ChatGPT. Tell it, “I want you to pretend that you are Tony Stark. Only answer questions as if you are Tony Stark.” Or “Pretend you’re Jarvis.” Whatever. “Stay in character the whole time. I’m going to have sixth grade students come up to you and ask you questions about science or forces of nature, and only answer questions like you’re Iron Man.” And guess what? You keep that station in your classroom. Students are working on a project — you know, in elementary school, a lot of times we’ll have that, “ask three before me” — you’re supposed to ask three friends before you go and bug the teacher. Well, maybe one of those “three before me” can be that little computer station, where they go up and ask Tony Stark a question, and then it answers them as Jarvis or Iron Man. I mean, we’re really just scratching the surface with all this AI stuff. And as more and more companies and more and more creatives are gonna start to realize everything that it can do, we’re gonna start to see it more and more. And hopefully we as teachers can really figure out how to use this tool to, of course, help students, but also help them be creative and explore and learn on their own.

Eric Cross (00:56:35):

That’s amazing. And just both of you are just dropping gems right now. And I wanna wrap up by saying — and I’ve said this before on earlier podcasts I’ve done — but at this phase in my life, the people that I’m the biggest fans of are teachers. And it’s true. I don’t mean that in a cliche way. When I watch celebrities and things like that, when I watch professional sports, that doesn’t fill me the way it used to when I was a kid. At this point, as a professional, I get inspired by other educators who are just doing awesome things. And when I think about educators who are doing that, you two are on that list of people that make me better. And when I get better, I can do better things for my kids. And so, one, I want to thank you for staying in the classroom and continue to support students. They’re so lucky to have you both. The second thing I wanted to say is, Jen, I wanna start with you. Where can people — and I know we said at the beginning — but where can people find the stuff that you put out? You got blogs, your social, your book.

Jennifer Roberts (00:57:28):

I got lots of social. Twitter, I’m JenRoberts1 on Twitter. And then my blog is LitAndTech.com. And then I’m on lots of the new social too, the Mastodons, the Spoutables, the Posts — those kinds of things — as just Jen Roberts, because I got in early and I got my real name without a 1. And there was some other one I’m on recently that I’ve forgotten about. But there’s lots of ’em. They’re fun. And I’m Jen Roberts. You can find me there.

Donnie Piercey (00:57:56):

And I’m SergeantPepperD on AOL, if anyone’s interested.

Eric Cross (00:58:00):

If you wanna hit Donnie up on AIM. <Laugh>

Donnie Piercey (00:58:03):

SergeantPepperD.

Jennifer Roberts (00:58:04):

You know, speaking of rock stars and people who do amazing things, I did write a blog post about using ChatGPT in the classroom, but I hear Donnie wrote a whole book.

Eric Cross (00:58:13):

Oh yeah. So, Donnie! Donnie, that’s a great segue. Thanks Jen. Donnie, how do people find out more? And can you tell us about this book you wrote, that’s coming out in the summer?

Donnie Piercey (00:58:22):

Yeah, so the book I wrote is called 50 Strategies for Integrating AI Into the Classroom. It’s published by Teacher Created Materials. They reached out to me. They had seen some of the stuff that I was doing, not just with ChatGPT, but also some image-generating AI stuff. You know, I got featured on Good Morning America, which was kind of cool. And they saw that and they said, ‘Hey, that looks really neat.” Reached out to me and asked me to write a book. And the idea behind the book, that launches this summer, it’s just 50 ideas, 50 prompts, different things that, as a classroom teacher, that you can do. So, you know, I think there’s so many AI books that are out there now. A lot of them are big ideas, which I think are important. Definitely important discussions that need to be, have around, the ethics of AI. What’s the role that AI should play in the classroom. But I just wanted to write a book, kind of like the discussion that, that Jen and I were just having, which is like, “Can we just share a whole bunch of ideas, different things that we could try with our students?” So definitely check it out. And I appreciate you giving me a shout-out too. That was cool, Eric. Thank you.

Eric Cross (00:59:35):

Of course. Definitely. And Donnie, your Twitter is again. …

Donnie Piercey (00:59:39):

Oh, @MrPiercey, M R P I E R C E Y.

Eric Cross (00:59:44):

Follow Donnie. Follow Jen. Tons of stuff on there. Both of you, thank you so much. For your time, for talking about students and how we can take care of them, science, literacy, AI. I hope we can talk about this again. I feel like even if in just six months, we might be saying different things. In a year, the landscape might completely change. And that makes it really fun. But thank you both for being on the show.

Jennifer Roberts (01:00:04):

Thank you for having us, Eric.

Donnie Piercey (01:00:05):

Thank you so much, Eric. We appreciate it, bud.

Eric Cross (01:00:10):

Thanks so much for listening to my conversation with Jen Roberts and Donnie Piercey. Jen Roberts is a veteran English teacher at San Diego’s Point Loma High School and author of the book Power Up: Making the Shift to 1:1 Teaching and Learning. You can keep up with her at LitAndTech.com. And Donnie Piercey is a fifth-grade teacher from Lexington, Kentucky. He hosts the podcast Teachers Passing Notes. Stay up-to-date with him at Resources.MrPiercey.com. And let us know what you think of this episode in our Facebook discussion group, Science Connections: The Community. Make sure you don’t miss any new episodes of Science Connections by subscribing to the show, wherever you get podcasts. And as always, we’d really appreciate it if you can leave us a review. It’ll help more people and AI robots find the show. You can find more information on all of Amplify’s shows on our podcast hub, Amplify.com/hub. Thanks again for listening.

Stay connected!

Join our community and get new episodes every other Wednesday!

We’ll also share new and exciting free resources for your classroom every month!

What Jennifer Roberts says about science

“If I’m not teaching my students how to use this, then they’re not going to turn into the adults we need them to be… If we’re not at least trying to think about what our future world is going to look like, then we’re not serving our students well.”

– Jennifer Roberts

High School English Teacher

Meet the guests

Jen Roberts is a Nationally Board Certified high school English teacher with 25+ years of experience teaching Social Science and English Language Arts in grades 7-12. She has had 1:1 laptops for her students since 2008 and is the co-author of Power Up: Making the Shift to 1:1 Teaching and Learning. A Google for Education Certified Innovator since 2011, Jen was named the CUE Outstanding Educator in 2022. Her interests include literacy instruction, standards based grading, and leveraging Google tools to make her teaching more efficient and effective.

A woman with light skin and blond hair stands outdoors, framed by illustrated graphics including a blue flask and curved lines. Green foliage is visible in the background.

Donnie Piercey, the 2021 Kentucky Teacher of the Year, is a fifth-grade teacher in Lexington, Kentucky.  With a passion for utilizing technology to promote student inquiry, learning, and engagement, he has been teaching since 2007. In addition to being in the classroom, he runs a podcast, Teachers Passing Notes that is produced by the Peabody Award winning GZMShows, and holds several recognitions, including a National Geographic Fellowship to Antarctica in 2018. His most recent work in Artificial Intelligence has not gone unnoticed, earning him multiple appearances on Good Morning America, the Associated Press, and PBS. His upcoming book, “50 Strategies for Integrating AI in the Classroom” published by Teacher Created Materials, is written for educators looking for practical classroom approaches to using AI. All told, Donnie has been invited to keynote and present at schools in thirty-three states and on five continents.

A man with short brown hair and a beard smiles at the camera, wearing a red shirt, framed by a circular graphic with a blue flask icon.
A laptop screen displays the “Science Connections: The Community” private group page, with science-themed icons decorating the background and edges.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. 

Eureka Math-NEW

To view this protected page, enter the password below:



S1-02: Community and joy within K–8 science instruction: Desiré Whitmore

Promotional graphic for "Science Connections" Season 1, Episode 2 featuring Desiré Whitmore, focusing on community and joy in K–8 science instruction.

In this episode, we join Eric Cross as he sits down with physicist and science education specialist, Desiré Whitmore. Listen in as Desiré explains her work at the Exploratorium, a public learning laboratory. Eric and Desiré discuss finding passion in science, the importance of meeting students we’re they’re at, and K–8 science instruction with real-life connections. Desiré chats with Eric about her work on supporting the science of teaching science content at the Exploratorium museum.

Explore more from Science Connections by visiting our main page.

Download Transcript

Desiré Whitmore (00:00):

I think it’s really amazing when we can realize as teachers, like, no, our job is not to just enforce rules on our students, right? Our job is to help students to achieve more learning.

Eric Cross (00:37):

Welcome to Science Connections. I’m your host, Eric Cross. My guest today is Desiré Whitmore. Desiré has held positions as a science curriculum specialist with Amplify Science, a professor of laser and photonics technology at Irvine Valley College, and is now the senior physics educator in the Teacher Institute at the Exploratorium in San Francisco. Her current work is focused on providing support and professional development to middle and high school science teachers to help them teach through inquiry. In this episode, we discussed Desiré’s pathway into physics, the impact of educators in her life, and the importance of representation for students in the classroom. I’m so excited for you to meet my physicist friend, Dr. Desiré Whitmore. All right. So just like a superhero, STEM superhero, you have an origin story and so—

Desiré Whitmore (01:36):

How long is this podcast gonna be? ‘Cause, you know, I can talk for days, so you—

Eric Cross (01:40):

I know, I know! But it’s, it’s…so, OK. We can give us a highlight. So, you know, 30 minutes. But what would be the origin story? You can start from any point in time, but what’s that journey like?

Desiré Whitmore (01:51):

I’m gonna start at the beginning, when I was really young, just because I think it’s important. Neither of my parents were college-educated. My mother didn’t finish high school. My father went back and got a GED later. But my father’s grandmother, her name was Claudia Pairs, and she was a teacher, right? So when I was a kid, she actually kind of raised me from, I don’t know, until I was around seven or eight. And so she was very important in who I became, I think because she taught me that college is important and she taught me to think. She taught me to ask questions. She taught me how to ask questions. Just the Exploratorium likes to do. Which is why I fit so well here. She taught me to always wonder and always think about things. And I remember as a kid, she taught me to count and read and write when I was, like, three. And she would always have bubbles at her house. And I was obsessed with bubbles. I thought bubbles were the coolest thing in the world. And just how you can take your breath and create this thing that now you can see, and it’s your breath, right? It’s your breath inside of a bubble and it’s flying around and it has all these cool colors, and then it would fly up and then eventually just pop. And you’re like, where did it go? Now my breath is just up there. Not understanding, as a kid, but my breath is always everywhere. I didn’t understand any of that, but I understood that my breath was inside of a bubble. That’s my earliest memory of thinking about science, was from that. And she was not a science teacher. She was—I don’t even know what she taught. I think she was an elementary school teacher, maybe. She died when I was 12. So I don’t have super-strong memories or of understanding who she was, only that she raised me and what she taught me as a kid. But that in itself really helped me because then when I was in the environment that I was in at home with my parents, which was not at all the environment she provided for me, I always had the things she taught me in my head, right? So I was always asking questions. My mother hated it. I was always taking things apart and putting them back together. So I used to take apart TVs and VCRs and vacuum cleaners and telephones, and my mother’s like, “Oh my God, I’m gonna murder you.” And she tried a couple times, too.

Eric Cross (04:25):

Did you ever put ’em back together and realize you had extra parts? You’re like, oh, hi.

Desiré Whitmore (04:29):

Oh yeah. All the time. Yeah. Yeah. VCRs have a lot of extra pieces. You’re like, “What do you even…it still works. It’s fine.” <laugh> You know? And vacuum cleaners too. They had a lot of extra parts, <laugh> all the time. And TVs. I should not have been playing with TVs. But like I said, I didn’t have a lot of parental, guidance as a child. So, like, whatever—I’m opening up TVs.

Eric Cross (04:54):

There’s a lot of open inquiry going on in your household. Yeah. Unsupervised.

Desiré Whitmore (04:59):

Unsupervised. But I didn’t know what it was or what it meant as a kid. I mean, I used to put things in the microwave. I did so many microwave experiments as a child, trying to cook different foods or melt different things. And so I think those kinds of experiences, where I was allowed to just be curious, kind of shaped who I am today. And then I kind of got into…you know, when I was in school, I loved math. In 10th grade, I had my first Black teacher, he was my chemistry teacher. His name was Mr. Strickland. And I was like, chemistry is cool, dude. And he was not the best teacher, but he was fun. Like you were saying, he was me, and he was talking to us the way I speak. And he was so like, just kind of chill and happy-go-lucky, I guess. But he wasn’t…he hadn’t taught chemistry in a long time. So he wasn’t a very good teacher. And me and one other kid in the class were in love with chemistry. And so we would read the book and do all the homework and he’d be in class lecturing and we’re like, “That’s not right, Mr. Strickland, like, what are you talking about?” And then he’d be like, “Oh, really, Desiré? Do you wanna teach the class, then?” And I’d be like, “Yeah.” And so I would go up and I would teach my chemistry class in high school, because the teacher was trying to make an example out of me. But he was also, I think, willing to be like, “I really don’t know.” And I really appreciated that. That he wasn’t just like, “I know all of the answers and you’re wrong.” Like, he wasn’t being a jerk, right? Like, the fact that I said, “Yes, I do wanna teach it,” and he actually let me do it? That’s pretty dope. And then I liked physics in my senior year in high school, but I didn’t think it was where I was gonna go or anything. I loved music and I loved math. Those were my two subjects.

Eric Cross (06:51):

What was it about math that resonated with you?

Desiré Whitmore (06:55):

I think it helped me understand the world a lot better. I didn’t have strong science teachers, I guess, growing up. It was a lot of reading out of books or watching laser discs in class. That’s how old I am.

Eric Cross (07:12):

Laser discs.

Desiré Whitmore (07:13):

Laser discs. And you know, so there wasn’t a lot of…I moved around a lot as a kid. I didn’t have this straight curriculum. You know, in one year, in the third grade, I went to three different schools.

Eric Cross (07:25):

Mm. Oh wow.

Desiré Whitmore (07:26):

It was kinda hard for me to latch onto school. But with math, because I could look at math and actually understand the world in it, I could see how math can be used to describe how things work.

Eric Cross (07:40):

I almost imagine, especially with so much transition in your life, it helped make sense of things. You had a lot of transition going on, but you were able to understand the world through the process of math. And then this early exposure, it kind of reminds me my own story too. Because there were these books that would do these cross sections of a cruise ship or a machine; that’s what got me really into engineering. Kind of How Stuff Works. I would watch that on Nova, How Stuff Works. I’d always be fascinated. Even Sesame Street had a segment where they would show you crayons and how the dye was added. You remember that?

Desiré Whitmore (08:19):

Yep. Yeah.

Eric Cross (08:20):

Young Desiré, doing photronics…photronics?

Desiré Whitmore (08:24):

Photonics.

Eric Cross (08:24):

Photonics. Photonics at home with the microwave and all these other things.

Desiré Whitmore (08:29):

Sure. How ’bout that.

Eric Cross (08:30):

<laugh> Right. And then loving math. So, early, I could see this combination, sort of this alchemy, happening inside you. And then, how did that lead to you becoming a physicist?

Desiré Whitmore (08:46):

It’s not as straightforward as it seems it should be. It’s obvious to everyone. <laugh>. But it wasn’t obvious to me. ‘Cause I wanted to be a lawyer. You know, because my parents weren’t educated, they didn’t really know…both of my parents and their subsequent spouses when they broke up—so my parents and my stepparents—are all bus drivers. And so they don’t know what options are. Right? So for them it’s like, “You have to be—you can be a doctor. You can be a lawyer. ‘Cause you’re smart. I know you’re smart, so you’re gonna be one of those things.” And I was like, “I don’t wanna be a doctor. That’s not actually interesting to me.” I did wanna be a teacher when I was younger, because I knew that my grandmother was one. But yeah, I went in and I was like, “I’m gonna be a lawyer. I’m gonna be a lawyer.” And then I go to college and I was like, ‘Eh, I don’t. I hate writing.” <Laugh> Like, I love reading, but I don’t writing. So I don’t think I wanna be a lawyer. I love music and I love math. I was originally going to major in music and math, but then I went to community college because I missed my opportunity to go to university for…long story. And so I’m at community college and I was like, “You know what? I’m gonna just do something new. I’m gonna be a marine biologist.” So my major was marine biology, and then they’re helping me pick out my classes. And they had zero math there. And I was like, “Pardon me. I think there’s a mistake, but I’m not taking any math.” And they were like, “No, you’re done with all your math. For marine biology, you only need calculus. And you took all of that in high school, so you’re done.” And I was like, “No, this is not gonna work for me, dude.” So I continued taking calculus anyway and moving on in math. And then I realized that biology wasn’t what I needed, but I did love my chemistry and I loved my physics classes. So I asked those teachers—chemistry, physics, and math teachers in community college, my professors—”I don’t wanna be a marine biologist and I don’t wanna be a lawyer. What do I do? What do you think I could study? I really like chemistry and math and physics.” And so all of them, all three of these professors told me, “Oh, it sounds chemical engineering would be good for you, so you should be a chemical engineer.” And I was like, “OK, cool. No problem.” That’s what I did. So I got my degree in chemical engineering. Right. And I finished community college, studying chemical engineering. I was like, “This is really cool. This is a lot of fun. I love engineering.” And then I transferred to UCLA as a chemical engineering major. And I was like, “I hate this.” <Laugh>. “I hate it a lot.” It was just…

Eric Cross (11:07):

What was it about chemical engineering that you were just not feeling anymore? What was it that just made you go, “nope”?

Desiré Whitmore (11:12):

It didn’t—at least the way it was taught to me—it wasn’t as as…exploratory, I guess. There wasn’t a lot of theory in it. There was just a lot of “OK, pull out a ruler and you’re gonna draw a thing and then this is how you’re gonna build a reactor.” And it didn’t seem very scientific to me. The science was missing. And don’t get me wrong, I understand, now that I have a degree in chemical engineering, that it’s not that chemical engineering is not scientific. But it’s that you build up the science and then you don’t focus on it. You focus on the engineering aspect of it. Which is, you have the science and the scientists will work on that aspect. But then how can WE do kind of larger batch chemistry. And for me, that was just less interesting. It was a lot of pushing buttons and just plug-and-play equations stuff. Instead of diving into first principles of why things happen in chemical engineering. There was no “why things happen”; it was “this is what happens, so this is the next step.”

Eric Cross (12:25):

You had to go so far into your academic career to realize that this is what chemical engineering is. And we were talking about representation, and not having examples or parents; your families were bus drivers. My mom was a receptionist and executive assistant, things like that. And I was the first of many, like you…we kind of had to go through and invest all this time and money to finally get to this place to realize, “This ain’t it.”

Desiré Whitmore (12:58):

This is not for me, yeah.

Eric Cross (12:59):

This is not for me. That was a long journey to get to that point.

Desiré Whitmore (13:03):

It was. Especially because I went through community college and I took a long time in community college, ’cause I was working full-time. So I was working full-time, going to community college. Took me a while. And then I finally get to UCLA. I’m like, “Yeah, I’m finally gonna get my degree and go make money!” And then I was like, “Ooh, no.” I mean, I could go and make money, don’t get me wrong. I could have graduated and made a ton of money. But I was not happy at all and I did not enjoy what I was doing. So, while I was in undergrad, I realized I don’t wanna do chemical engineering anymore. But what do I wanna do? But then I was taking…I took a quantum mechanics class. And that class blew my whole mind. And I was like, “This is the coolest thing that I’ve ever learned in my life, and this is what I wanna do.” And so I went and talked to my professor and I was like, “Can I work for you? Can I do research? Because this is amazing and I wanna do this.” I felt it was too late for me. I had been in school for so long and I was already kind of burnt out. So I was, “I’m not going to change my major. That’s just outta the question for me right now. It costs so much money for this degree and I don’t have—I’m not just gonna waste my time and keep working all these jobs.” So I had three jobs in college. And it was like, I worked at Radio Shack, I did research for this professor, and I worked in the library, the chemistry and physics library.

Eric Cross (14:28):

I love the fact that we’ve talked about laser discs; you said Radio Shack; and we talked about the analog internet of the encyclopedia salespeople. And I know all of those things. And I’ve been through all of those things together.

Desiré Whitmore (14:43):

Just in case people don’t know how old I am. <Laugh>

Eric Cross (14:47):

For our listeners who are way younger, yeah, this is how we grew up. This is how we—these things are extinct now. There’s this element of this kind of cultural connection. I think that we experience that. It kind of it flies under the radar. People don’t really realize it until you’re in an environment that’s different from what you’re used to. And you realize that, “Oh wow. this is not what I’m used to.” And the things that I’m finding funnier, the things that I connect with, it’s not what everybody else connects with. And as a teacher, it’s the same thing, right? Like, we go in the classroom and you know, you and I are rapping about laser discs and Radio Shack and I’m trying to talk to my kids about it. And they’re like, “Yo, Cross, what is that? Are you gonna give us a history lesson? What are these things?”

Desiré Whitmore (15:35):

Yeah.

Eric Cross (15:36):

And I found myself having to stay connected to pop culture, because I teach 12- and 13-year-olds all day. And it’s great for keeping things relevant for my students. But when I talk to my friends that are my peers, they’re like, unless they’re a teacher, they’re like, “I got no idea what you’re talking about.”

Desiré Whitmore (15:55):

Yeah. I have a friend who’s also a middle-school teacher and she’s always coming to me with all this. I’m like, “What are you talking about?” She did the Glow-up Challenge, but she did the Glow-down Challenge. So she invented a new thing. She’s like, “No, I couldn’t do Glow Up ’cause that’s too much. So I did the Glow-Down Challenge.” And it’s the cutest thing ever. And the students think it’s amazing. And I’m like, “That’s awesome. But I have no idea what the point of that is.” <Laugh>

Eric Cross (16:21):

And there’s this theme, too, that when we talk about teaching kids STEM, there’s this soft part of it, this relational piece of it that you mentioned, of this connective aspect that in a certain way kind of even superseded the content knowledge that your teacher even had at that point, where you’re going up and teaching the class. But just the fact that someone looked like you or spoke like you or connected with you in a certain way made a big difference to who you are as…well, the trajectory of where you went.

Desiré Whitmore (16:57):

Yeah.

Eric Cross (16:57):

“I like chemistry. It resonates with me.” And it’s something I think can get lost. And I think just to kind of a good segue, I use Amplify my classroom, and one of the reasons why is because of the representation that is in these videos. And you were part of crafting this for…was it the fifth grade?

Desiré Whitmore (17:21):

I mean, it was K–8. So I was—

Eric Cross (17:23):

OK, so you were doing the whole thing.

Desiré Whitmore (17:24):

Yeah, I was a part of the K–8 science team. My title was science curriculum specialist. But in reality I was hired to do the engineering internships, mostly. Which are middle school. And to be a sim developer. So sims K–8. I worked on several of them in both middle school and elementary. Yeah.

Eric Cross (17:47):

What was that like for you? When you were designing curriculum? ‘Cause as a teacher, it’s, you know, I think with teachers it’s kind of…I would consider myself, if I was gonna use hip hop as a metaphor, I’m more of a DJ than an MC. Where I wanna remix things that exist, versus, I don’t wanna write the lyrics in freestyle. So I don’t want to go and write the curriculum completely; I wanna take something that’s solid and then I want to go ahead and remix it. You are great at both. What was the process for you, being on that team, designing? How did you go about making, “OK, we’re gonna create this experience for kids”?

Desiré Whitmore (18:25):

It was, it was amazing. I learned so much, so much. It was the best job I had before I came to the Exploratorium. The process was amazing, because it wasn’t just me, right? It wasn’t just me. It was a whole team. And each unit had its own team. So we had a scientist, which I was the scientist we had. So we had a scientist; we had a literacy specialist, because it was really important to increase science literacy so that students understand not just that science exists, but “What are the terms that are used in science and how can I speak and act a scientist? What are the things that scientists actually do in their real life?” Then we had an assessment specialist and then we had a simulation specialist. And so, on the units that I was on, sometimes I was both the sim developer and the scientist, or sometimes I was just the sim developer and I got to work alongside another scientist, which was always fun. And so it was really nice, because I was working alongside master teachers. People who had been teaching for years, and they were able to help me better understand. ‘Cause I’ll come in and I’ll be like, “Yeah, there’s a unit on light waves, let’s come in and teach this unit on light waves!” <laugh> I was the sim developer and scientist on that unit, and there was another scientist working on the unit, but they were like, “Well, Desiré literally builds lasers, so I think she should be the science developer.” So we kinda had two science developers on that one, which was fun. But I come in and she’ll come in and she’ll be like, “Yeah, I think this is where we wanna go and this is what we wanna teach.” I’m like, “No way! Like, that’s not accurate, right?” And so I can come in, but then I’m coming in with all this crazy lingo, right? I’m up here. But then also I have taught kids about lasers and optics and photonics my whole career. So I’m also very capable of bringing it down to where kids need it to be. What I don’t know is how effective that is, right? When to do it and when not to do it. When to bring the level up; when to bring the level down. And so working alongside these other teachers and assessors really helped me to do that. And so for me it was just two years of deep learning experience. I learned—every single day at work, I learned something new. Which is something that I value and I’ve wanted in my career, my whole life. We made active decisions in that room. Like, “We want to interview scientists who are scientists of color or who have different abilities or who have different representations in all kinds of ways.” Right? And then we also have these fake internships, or not even the internships, but just in the general units. And we actively wrote scripts for those. And we actively wrote in those scripts, like, “This is a Black woman. This is an Indian woman. This is a Jewish man in a wheelchair.” Like, we specifically dictated exactly who we wanted in these videos, because we knew that representation was super-important and we knew that we wanted students to be able to connect.

Eric Cross (21:35):

Right. One of the things, I appreciate what I’m hearing a lot in that is the amount of intentionality that went into this. But even now as you’re reliving it, you’re still almost iterating on how could we improve it or how can we make it different or reach more people. And I think that goes towards when we’re talking about including more people and inclusion. Like, it’s not a binary thing. You’re always modifying; you’re always iterating; you’re always redesigning and improving to be more inclusive, to reach more students. Because you know, to your point, part of it is, “Yes, we wanna do this really awesome science curriculum,” but the other part of it is there’s more to it than just your content. And I think now more than ever…I use—we just finished the food bar unit. Metabolism. And in there there’s a simulator. They always ask me when I show the videos, “Are these, are these real people? Are these real situations?” And I tell ’em, “Well, the story is real, but these are all fictional actors. But what’s actually happening happens. It’s real.” And they get really into it. And I think one of the other things is with your simulations—especially the engineering units—there’s no one right answer. And so my students who want to go, “Mr. Cross, I wanna make the best bar! Perfect 10, best taste, cheapest!” And I’m like, “All right, good luck!”

Desiré Whitmore (23:06):

Yeah. Go do that.

Eric Cross (23:09):

Casue there’s something called trade-offs! It could happen! And they’re like, they’re trying. They get into the code. They try to open up the Inspect Element, when they feel like hackers.

Desiré Whitmore (23:17):

Yeah, they do. But these kids like, they’re so smart and they’re so resourceful. And I’m just thinking like, maybe that’s how we challenge them more, right? Sometimes we can give them these kinds of things where it’s like, “Go and create a program, ’cause that’s the level you’re at <laugh>. Go and create this program to do something similar that’s related to the work that we’re doing.”

Eric Cross (23:38):

I’ve had some of my own students redesign—I have one student who redesigns every assessment I give him. I give the project; I give the options for the final goal; and he always chooses—if I give three options, he always chooses option four. If I choose two options, he’s choosing option three. And so he’ll go into Google Sheets, he’ll pull all the data and then he’ll construct his own kind of spreadsheet with all the probabilities of different things.

Desiré Whitmore (24:06):

You tell this kid to make a GitHub right now <laugh> so that he can get a job as soon as he’s done with high school. <laugh>.

Eric Cross (24:12):

He’s amazing. And we did this one project where students had to design a Netflix show to show their understanding of metabolism. And they had to do four episodes. So I gave him a template. It’s not from me; it’s from, I think, EdTechPicks.org or something. And it looks like the whole Netflix splash page. They took photos, did the whole deal. He created NOTflix. Everyone else did Google Slides. His Google Slides was interactive. So when you clicked on different boxes, it actually took you to the next splash page of that show. I mean, it was….

Desiré Whitmore (24:48):

That’s fantastic.

Eric Cross (24:49):

It was, it was. I recorded his presentation. It was brilliant.

Desiré Whitmore (24:53):

But that’s amazing. And that speaks to your strengths as a teacher and why you’re an amazing teacher. Because you see the students and what they’re trying to do and you work with them; you meet them where they are. Right? There are so many teachers who would just be frustrated with that student. And it’d be like, “No, these are not your options. Your option was to do what I told you to do.” And there are many teachers who would do that. And I think it’s really amazing when we can realize as teachers, “No, our job is not to just enforce rules on our students. I mean, that is part of the job, because that’s what school was when it was created. But our job is to help students to achieve more learning in what we’re trying to do. And so the fact that you are so good with this student and that you encourage him to go above and beyond when he can, I think it’s so amazing.

Eric Cross (25:49):

Well, that brings me to my favorite group, organization, and the phase of your career of where you are now: The Exploratorium. And I wanted to kind of rap, talking about what you do now. Because the Exploratorium—I tell people, they go, what is that place? And maybe you can tell us what it is and then what you do. But for me, I’ll just tell everybody: It’s Disneyland for science teachers. And I love going there. I not only love going there because of what I receive from it professionally. Many of the PDs, I don’t even call ’em PDs—just communal learning experiences, that I’ve had that have been led by you and Lori and, and Tammy and the rest, and everybody that’s there have been incredible. And I have so much fun. Emotionally, I get excited when I go. When I’m on the plane, I’m like, “Here we go!” And then we go and we’re making fudge or we’re blowing darts with marshmallows across the room in the theme of Boba Fett. There’s just these rad things that are going on there. And it’s not like anything I’ve ever experienced before. So maybe we can close with talking about what the Exploratorium is, what you do there, for people who’ve never been and have been a part of it.

Desiré Whitmore (27:19):

I’m gonna give you what my definition of the Exploratorium is.

Eric Cross (27:21):

That’s what we want.

Desiré Whitmore (27:22):

So, the actual definition is, we are a public learning laboratory. We are known as the Museum of Art, Science and Human Perception. Cool. But, like, what does that all mean? Right? And I think your description of the Disneyland for science teachers, I think that’s a perfect description. ‘Cause for me, I tell people like, “Oh, I wanna go to the happiest place on earth.” And for me, that is the Exploratorium. And yes, I work there, and yes, it’s still true for me. So the Exploratorium is this huge museum. It’s an interactive science museum. And art—we have a lot of art. And it’s all about learning through doing. It’s not about learning science by going up to an exhibit and reading the little paper next to it. It’s like, no, you go up to an exhibit and you interact with it and you teach yourself science. The goal of the Exploratorium is really to help people understand that learning science, doing science, isn’t reserved for only scientists. Doing science is something that everyone in the world should and does do. And so helping people understand that everything we do is science is kind of the point of the Exploratorium to me.

Eric Cross (28:35):

Even the building itself…one of the other cool things too is, for people that don’t know, it’s the size of Costco or two.

Desiré Whitmore (28:43):

Yeah. Yeah.

Eric Cross (28:44):

It’s immense! And even the building itself teaches. Like, you have that whole workshop, dead-center in the middle of the floor where they’re designing things. It’s like inside-out. And then I remember going to the one experience where I think it was Eric who showed us that it’s one of the few facilities that is actually cooled by the Bay water. And there’s only a couple of those in the state that can do that. And it has a platinum rating, something wild that. So even just the building itself…everything that if they can extract every ounce of science teaching in that, it’s in there. And you are in a very important program for me. And can you talk a little bit about maybe what you’re doing in T.I.?

Desiré Whitmore (29:33):

So I am in the Teacher Institute. I’m a physicist in the Teacher Institute. And the Teacher Institute is a group of teachers and scientists. And our job is to basically support middle school and high school science teachers and teacher leaders in the state of California, but science teachers around the world, in their pursuit of science teaching. And by support, I mean we provide professional development. We provide other things, communities of practice, and we go and do workshops in certain places. We go to India to teach Tibetan monks and nuns science. And we go to Costa Rica to teach teachers all over the country of Costa Rica about science. And so our job is really, to help science teachers feel more secure in their science teaching and help to retain them in the field, because a good science teacher is so important in helping our students thrive. And so our job—and we take this very seriously—is to help science teachers thrive. And we are made up of PhD scientists and veteran classroom teachers. So we have on the one side teachers who have been teaching middle school or high school for years. One of my coworkers, Zeke, who I work with the most, he was a high school physics and environmental science teacher for 21 years before coming to the Exploratorium. And then me, I was never a classroom teacher. I was a professor; I was a physics professor at a community college, and I was a researcher. So my deep knowledge of physics and current knowledge of physics—or knowledge of current physics—combined with Zeke’s extremely experienced pedagogy is really how we work together as a team. And it’s not just Zeke, right? We’ve got a geologist on the team, Eric Muller. We’ve got Tammy, who’s a middle-school bio teacher. We’ve got, Julie Yu, who is a chemical engineer, PhD, and also a prior middle school teacher, former middle school teacher. We’ve got Hilleary Osheroff, who was a PhD biologist who used to work at the American Museum of Natural History. We’ve got Lori Lambertson, who was a middle-school math teacher. And so, you know, we all come together to bring our experiences both in and out of the classroom and in and out of the research lab to provide teachers with the best inquiry-driven stuff we can. And we’re very—we’re so equity-focused, because we believe that that’s important, right? We know that the impact of our work is, I think, why most of us are here. It’s why I’m here. In undergrad, my grad school, and my postdoc, I would go into classrooms. I would go into science museums and teach science to people. And I probably reached out to maybe…over that whole time, I would say a couple thousand people, right? Maybe a couple thousand people total. That’s great. But over 15 years of reaching out and only reaching a couple thousand people, that’s rough, right? And now I’m at the Exploratorium, and I know that if I reach one teacher, right? If I can teach one teacher…let’s say you. How many students do you have in your classes a year?

Eric Cross (33:11):

Two hundred a year.

Desiré Whitmore (33:12):

You have 200 students a year that you teach. So if you teach for 10 years, that’s 2000. That’s 2000 students. So I have, by teaching you today, assuming that I’m actually teaching you something that’s gonna be useful for you—

Eric Cross (33:29):

You do! And you are!

Desiré Whitmore (33:30):

You are going to be impacting these 2000 students over the next 10 years. And of course you’re gonna be in teaching for much longer than that. But let’s just say in 10 years, that payoff is so much higher, right? And you’re one teacher. But I have 30 of you in my workshop! And so if all of these 30 teachers each teach 2000 kids over the next 10 years, then I’m actually doing something. I’m actually changing the way that students see science, through changing the way that you see science. Right? And so I take my job very seriously, as we all do. Like, we’re so invested in our teachers. And it’s not that we don’t care about students, ’cause we absolutely do. But we understand that without good teachers, students aren’t going to be able to thrive, as often as they would otherwise. I was able to do it somehow. But I’m one. There are so many other kids who could have gone into science who didn’t because they felt they never connected to it. So our job is to try to help teachers connect to it. And an important part of that is allowing you all to experience science as a learner. We want you to play and have joyful experiences. We want you to enjoy science and to try to think about it from the perspective of your students. Walk in their shoes. So that when you then go back to your classroom, you are able to think about like, “Oh yeah, you know, my students totally asked the same question that I asked, or that another teacher asked in the workshop because they had the foresight to think about that’s what my students would ask.” Right?

Eric Cross (35:02):

Well, I think it’s really effective to create empathy for the learner. Because I find myself in that position. I don’t know if some kind of memory displacement field happens to me when I sit in those workshops, but Hillary will ask a question that I know the answer to and I’m like, “I don’t want to answer the question. I don’t—I might be wrong.” And I teach the subject! And I embody what it’s like to be a student. And when I leave, I might have to go back and reference exactly what the lesson was, but I remember how I felt when I didn’t know. And very rarely as teachers do we get put in positions like that. And so it helps me be in the position of my students emotionally, of what it’s like. Even even the intentionality of how do you ask questions and not showing an affect on your face when somebody says the right answer or the wrong answer.

Desiré Whitmore (35:55):

Well, I’m still learning that. I’m not great at it. Julie is the mast.

Eric Cross (35:59):

Julie’s got it nailed.

Desiré Whitmore (36:00):

I’m still trying to learn from her. She’s amazing. And I really would like to get there one day. But I’m still not there. I’ll be like, “Oh! Oh! Well, that’s…”. I have a terrible poker face. So I’ll be like, “Oh yeah, but you think that? Maybe…”. That’s a piece of it that’s really important, right? It’s this not giving away the answer, even when you have the right answer. Allowing people to ask the questions and explore and become invested in the problem, before giving away the answer. That’s something that I learn here at the Exploratorium. And like I said, I learn every day. And it’s something that I think is so important for us as teachers to learn and try to implement. Because oftentimes you’ll come and you’ll have students who are like, “I’m too stupid. I don’t know the answer.” And then somebody else will say the answer, and then the student is like, “Yeah, I was right. I’m too stupid.’” But it’s like no! But if you have that student actually think about it, then the student—once they do hear the right answer—they might be like, “Oh yeah, that would make sense.” Instead of “I’m stupid.” It’s like, no, this is, “I explored this and I figured it out on my own.”

Eric Cross (37:08):

Things keep coming back to how this experience and the process of them learning science even outweighs the content of it. ‘Cause the content is almost easier to share, it’s easier to get, you can look it up really quickly. But in your story and in many other people’s stories, the exposure, the experience, how they’re going through that process—I know that’s something that I’ve learned a lot in just watching. Not teaching science, but actually the science of teaching. Sitting in the workshops and watching how we’re treated as students, how you interact with us, and then being able to take that back to the classroom. And just to add onto the value that it’s created, I think one thing that it’s also done is given us community. And in addition to being able to impact students, it’s also been able to build resilience in teachers. Because we as teachers can feel very isolated. And especially now when things are incredibly difficult, and every teacher’s experiencing Covid and shutdowns and low staffing across the country in different ways, when you don’t feel you have community or people that you can connect with, it just makes everything feel exponentially harder. And you’ve done a great job at being able to build community with us in our community of practice. The Exploratorium has been able to do that. And it’s something that I’m super-grateful for probably more than anything else is that through these last two years, being able to connect really made me feel like, “OK, we’re gonna be able to do this.” And it’s not just about Cross or my other teacher in eighth grade or my sixth grade teacher who’s doing this. That message, I think, is really, really important. I wanna ask this: Was there a teacher or an experience that impacted you or inspired you throughout your educational career? You know, kindergarten all the way to college? Was there a moment or a person or anything that that really stuck with you, that you felt maybe influenced who you became? Met you where you were at? I know you mentioned your chemistry teacher at that point, but is there anyone else, or was it that person that was really the person who sticks out for you?

Desiré Whitmore (39:21):

There actually have been a few. Of course, the first is my great-grandmother, Claudia Pairs. But I think in the fourth and fifth grade I had the same teacher. She stayed with us going from fourth to fifth grade. And fourth grade was a new school for me. New town. I was the only Black child in the school, me and my sister. And my teacher recognized that I had no real help at home, I guess? And she really kind of…she saw that I was really smart. She would give me extra assignments when she could tell I was bored. It meant that someone outside of my house cared about me in a way that I didn’t feel cared about at home. Her name is Ms. Comet. Mrs. Comet.

Eric Cross (40:11):

Like…comet?

Desiré Whitmore (40:13):

Yeah. Mrs. Fran Comet. And I’ve tried looking her up as an adult and I can’t find her. But I work with so many teachers, and I know how hard teaching is and how degrading it can be…or demoralizing, I guess, to not be appreciated. And so I know what it feels to me when a student has reached out and shown me like, “Hey, I’m now in dental school,” or “I’m now getting a PhD in science,” and I’m just like….

Eric Cross (40:40):

I got a message this morning on Instagram from a student. And none of my students use their real names in their Instagram handles. So I got a message from Moonshine. <Laugh> And I was a seventh grade teacher. And through deduction, deductive reasoning, I figured out who it was. This person’s now in college and they responded in that…you know, you get one of those every once in a while. And I feel it just fills your tank. It’s just so important that we—it’s funny because, kind of to your point, we don’t realize who or how we’re making impacts on people. And in what ways. We just know that we are. And I tell other teachers, I said, “You have one of the few professions where you fall asleep worrying about other people’s kids.” And it’s the words that we speak, the things that we do, people are always watching. I know, no pressure, right!? Hopefully, someone listening can find Ms. Comet.

Desiré Whitmore (41:37):

Ms. Comet. Teacher at Buena Vista Elementary School back in the ’80s. But your talk about this impact, it reminds me of the thing I wanted to say, but I didn’t. But I’m gonna tell you right now. I mentioned how science was not a priority when I went to school, in my hometown. That’s Lancaster, California. But recently I got a phone call from a family friend and she was so excited. And she called me to tell me that her daughter was super-excited when she picked her up from school. Because I was in her classroom. She said, “Auntie Desiré was in my class today! And she works on lasers! And she does spectroscopy! And I wanna learn about spectroscopy now. So can we call Auntie Desiré?” And I was like, “Wait, what?” My friend was kind of confused. She’s like, “Desiré didn’t tell me she was in town.” She had no idea why her daughter was saying I was in her classroom, ’cause I was not physically there. And then I had to put the pieces together and I was like, “Oh my God, your daughter’s in eighth grade already.” It made me feel really old, ’cause I know this girl from a little baby. But I was like, “Oh my God, that’s the eighth grade unit on light waves for Amplify that I wrote, and I’m featured as the scientist.” Because we have real scientists in the units. And they featured me in that one, in my laser lab. And so this little girl who knows me really well, who lives in my hometown, is seeing representation in science. She doesn’t necessarily know I’m a scientist. She knows that—I don’t know what she knows about me. She just knows I’m Auntie Desiré and, you know, I like gumbo at Christmas. That’s what she knows about me. <Laugh>. And so she comes back and she’s so excited ’cause now she knows so much more about me. And she knows that if I can do it and I came from where she’s at, she can do it too. And she was super-excited. And I was just…it brought me to tears. I was just crying in the car. I was driving <laugh> at the time and I was like, “This is amazing. Work that I did is teaching you and all of your friends in this tiny little town that you live in. And that to me is so important because now this little girl knows that, like, she knows me as just a normal human right. Who likes Star Trek and Star Wars and The Owl House. And now she’s over here like, “Oh my gosh, this normal human wrote the science curriculum that I’m learning from.” Which I think is just so fantastic. And it really brought home for me kind of the importance of my work and why I’m doing what I’m doing. And that’s pretty awesome. And I get messages from Instagram, you know, from teachers who are like, “Hey, did you work on this? ‘Cause you were featured in the video, but did you write this light waves unit?” And I’m like, “Yeah.” And they’ll tell me, “I have students, this is their favorite unit. I’ve gotten notes from students saying, ‘This was my favorite unit in all of middle school.’” And I’m like, “Ohhhhhh!”<Laugh>

Eric Cross (44:33):

That story just gives me chills. Because I just can imagine how surreal that must feel. And you’re directly making that impact on those kids. And I’m glad that you shared that story so that everyone can hear it, because it’s a powerful story and I lived—I feel I was living it through you, just now, as you were discussing it.

Desiré Whitmore (44:54):

Yeah.

Eric Cross (44:54):

And I feel that way in the classroom to a small degree, because I get to have—when my students create posters of scientists that we don’t typically see, I’ve got you on my list of scientists, and I’m they’re like…And I’m like, “I can call her!” Like, “Mr. Cross, you KNOW her?!” I’m like, “Yeah, she’s a friend of mine! I was talking to her the other day!” And they’re like, “Whoa. She works with lasers?!”

Desiré Whitmore (45:17):

<Whispers> I do.

Eric Cross (45:18):

Desiré. I’ve held you for so long and—

Desiré Whitmore (45:23):

Yes, I’m sorry! I told you, I talk so much! I’m a teacher!

Eric Cross (45:26):

No! No, no, no, no. It was great! I wanna honor your time. Can you tell everybody where they can find out more about you again?

Desiré Whitmore (45:33):

So first off, you can find me on Twitter at Darth Science, D A R T H S C I E N C E, and you can also find me at Instagram at Dr. Laser Chick: D R dot laser chick. Even though I don’t post on Instagram that much. I also have a website, which is laser chick dot net. I’m still working on it. It’s not the best website yet. But, you know, it’ll, it’ll be better in the future.

Eric Cross (46:02):

Would you be willing to come back later on in the year and do a part two?

Desiré Whitmore (46:07):

Oh, for sure. Yeah. So I can actually finish telling you the story of how I got into physics! ‘Cause I totally didn’t. ‘Cause I’m all over the place.

Eric Cross (46:15):

So, everybody, cliffhanger! Next time she comes back, she’ll continue to tell us the story. Desiré, thank you so much.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Desiré Whitmore says about science

“I think it’s really amazing when we can realize as teachers… our job is not just to enforce rules on our students… our job is is to help students achieve more learning.”

– Desiré Whitmore

Senior Physics Educator, aka “LaserChick”, Exploratorium

Meet the guest

A Southern California native, Desiré earned an associate of science from Antelope Valley College, a bachelor of science in chemical engineering from UCLA, and a master of science and Ph.D. in chemical and material physics from UC Irvine. Her research focused on developing very fast laser and microscope systems that could capture molecules vibrating and rotating in real time. She was a postdoctoral fellow at UC Berkeley, where she designed and built attosecond lasers (the fastest laser pulses, which emit x-ray light, ever measured). At the Lawrence Hall of Science she wrote an all-digital K–8 science curriculum (Amplify Science), which aligned to the NGSS, with the Learning Design Group (LDG). Desiré left LDG to teach hands-on laser technology and physics courses at Irvine Valley College before joining the TI staff. She is the proud mom of Stella, a four-year-old boxer-pit mix. In her spare time, Desiré is restoring her 1967 VW bug.

Person with curly hair wearing a blue jacket, smiling at the camera with a blurred background.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. Listen here!

S1-06: Supporting students with a creative twist: A conversation with Kentucky Science Teacher of the Year, Shad Lacefield

In this episode, Eric sits down with the Kentucky Science Teacher of the Year, Shad Lacefield. Shad shares his experience teaching during the first year of the pandemic, where Shad dressed up in over 100 costumes to create a unique and engaging online learning experience for his students. Shad also explains ways he connects with his students to celebrate student success, as well as large-scale efforts he leads within his school to cultivate the love of learning science content. Explore more from Science Connections by visiting our main page.

Download Transcript

Shad Lacefield (00:00):
When you stay relevant, it’s being engaged with your students and figuring out, or what are, what are they liking? And every year it’s gonna be different. And that helps you stay relevant. When you have conversations and you build relationships with your kids,Eric Cross (00:13):
Welcome to science connections. I’m your host. Eric Cross. My guest today is Shad Layfield. Shad is a teacher at garden Springs elementary and a part-time professor at Asbury University in Kentucky during the first year of the pandemic, Mr. Layfield dressed up in over a hundred costumes to create a unique and engaging online learning experience for his students. He also created Vader visits, where he visited students at their homes, dressed as Darth Vader to celebrate their online successes and keep them encouraged. During a challenging time. In this episode, we discuss how creativity impacts engagement, transferring lessons learned from distance teaching back to in-person instruction, and how upper grades can apply the same principles to improve student learning. I hope you enjoy this discussion with shad lays field. So you’ve been in fourth grade for four years, and then you were in second grade and fifth grade. And so like how long have you been teaching for like total?

Shad Lacefield (01:09):
So this is my 15th year teaching.

Eric Cross (01:12):
Really? Yeah. You’ve been in the game for a while.

Shad Lacefield (01:15):
Yeah. Yep. It, it doesn’t, and it’s always surprising to parents too during that, that first like, come in and meet your teacher. And I walk in, I’m like, yeah, I’ve been teaching for 15 years and every time it gets ’em, they’re like no way. And I’m like, yeah,

Eric Cross (01:28):
That’s, that’s a good thing though. That’s a good thing. Right?

Eric Cross (01:31):
You know? So like, well the energy and then, and you’re just how you’re perceived. Like you’re, they’re just, I don’t know. It’s something about work with young people. Like it keeps you young.

Shad Lacefield (01:39):
That’s what it is. Absolutely.

Eric Cross (01:41):
So how did, how, like, what’s your origin story? Like, how did you become a teacher? Like what, what was it? Was it something like you knew second career, like right outta school? Like how did you end up in the classroom?

Shad Lacefield (01:53):
Yeah. No, and I love this question cause I’m a big Marvel and, and superhero. So origin stories are all, I love a good origin story. So I grew up on a 13 acre farm in a little bitty town called Gustin, Kentucky, and very early on, like we were instilled my parents, amazing, amazing parents. But they really instilled like a, a super important work ethic in our lives of like, it’s, it’s all about hard work and it’s important that you’re working hard in whatever it is that you do. And I’m one of six kids as well in my family.

Eric Cross (02:24):
Where are you in the–

Shad Lacefield (02:25):
I’m second to last.

Eric Cross (02:26):
Second to last. Okay. So you’re the second youngest.

Shad Lacefield (02:29):
Yes. Okay. And and so, and so growing up, like with that, like, you know, I worked in tobacco, I worked in hay, you know, we did things being on the farm and stuff like that. And within my family as well, there’s four boys. And so when I decided to go to college I was the first guy in my family to go to college. And the first and only boy that ended up going to college. And so it was like this big deal, like, oh, you know, we got one of our boys gonna go to college. So what is he gonna be? And I was like, well, if I’m gonna put forth the, the time and effort and then the financial strain that it would cause cuz we were not poor at all. My dad worked two jobs to make sure, but I really felt the responsibility of like, if I’m gonna go, I’m gonna work in a profession.

Shad Lacefield (03:09):
That’s gonna make a lot of money. And here I am as a teacher now. So I didn’t go to college to be a teacher. I actually was pre dentistry. I thought, now here’s a profession. You can, a lot of money. You don’t work weekends or holidays, you know, I can still be the doctor thing. And so I’m gonna be pre dentistry. But like all good origin stories. There was a, there was a flip. So in my first year I started working at the most majestic place that you will ever go. It’s called Squire, boon, caverns. It’s a cave in Southern Indiana. And it’s an amazingly beautiful little place. You have to like one lane highway, like road to go back there up and down. Like you, you think you’re never gonna make it. And if it rains too much, the bridge will flood and you actually can’t even get back there.

Shad Lacefield (03:52):
So that’s how we’re talking like way back in the sticks. But once you get back, back there totally worth it. And as part of the job you were a tour I also did grist mill demonstrations and gym mining adventures, or, you know, as they’re gym mining and stuff like that. And within that, I started working with school aged kids and on very large tours and stuff. And my manager at the time, Claudia, I’m still great friends with and we still take our kids back there. Every summer she, to me, you’re really good with kids. Like you’re really good with kids. We have this scout program that’s on the weekends. And then during the summers and you would be teaching kindergarten through eighth grade kids, geology and forestry. What do you think about doing that? And I said, well, right, let’s try that out. And then I got the teaching bug and it hit and I was like, oh my gosh, like I don’t wanna spend my life doing something that is all about money or, or that is like, this is where it’s at. Like, I love this, I enjoy this. I enjoy the response that I get when I’m talking. And kids are excited about learning and getting new information and learning new stuff. And so then I change my major and here I am now, all these years later teaching instead of being a dentist,

Eric Cross (05:04):
Are there, are there days, do you ever have days where you’re like, you know, dentistry, it’s still an option. Like I can, I can go back.

Shad Lacefield (05:12):
Oh, rare, rare occasions. Rarely. Yeah.

Eric Cross (05:16):
Okay. Yeah. All right. All right. Fair enough. I, I, I always joke and say that like we have, you know, sometimes I have my, my alternate job on the hard days, which is for me, it’s working at the gap where I just want to fold clothes and go home at the end of the day, you know, on those really rough days. And you know, it’s never the kids, right. It’s always other things. The kids are like the great part. And then there’s all these other things. And I just wanna work at the gap. I just wanna work at the gap. Fold some clothes. Yes, sir. Yes. Ma’am absolutely. I can find that size for you. And then I just go home cause about their job when they go home at the end of the day, when you work at the gap, at least sorry, gap workers. I’m sure hard of that, but my perception in my mind is that you close up shop and then you’re done. Yeah,

Shad Lacefield (05:52):
Absolutely. Like you said, they can turn it, like it’s a turnoff at the end. Exactly. As teachers we know, like you don’t ever turn it off, it’s always there.

Eric Cross (06:00):
Yeah. So one of the things that I was super excited about when I, when I first heard about you is I went on your website and there’s so many things I feel like I can just talk about your website and just the, the content that you’ve produced. I, I, there’s so many directions I can go. But one, one of the things I want to ask you is, is about that. Now, one of the things that’s on there, and this is coming from a fellow star wars, Fisha who finished Bobba FET and the Mandalorian recently and is Jones in four OB one to come out.

Shad Lacefield (06:33):
Oh, so yes,

Eric Cross (06:35):
I live in Southern California next to Disneyland visited Galaxy’s edge star wars. You have these things called VA Vader visits. And so what do you do in those? And like, where did you get the idea for these Vader visits?

Shad Lacefield (06:50):
So the costumes were bringing the kids into the classroom. But when they left my room because you would, we only had them for a certain amount of time. There was still a lot of extra work that they needed to get done. And what I was seeing was I could get them to come in and they were really engaged during my lesson. But then afterwards, when it came to work completion or getting things done, there was, it was starting to fall off. As you know, we were experiencing, you know, more and more craziness of what’s going on. So then as an incentive, I decided if you have everything turned in, by the end of the day, I’m gonna dress up in my Darth Vader outfit, full costume, the, you know, the, the full helmet, like everything. And I’m gonna show up to your house and we’re gonna hang out and play any game at all that you wanna play.

Shad Lacefield (07:34):
So then it was a way of rewarding. My kids for getting everything turned in. But same time I felt like it would also help me build a relationship with them. That was a very challenging part of online learning. Like, again, I want you to feel like you’re a part of my classroom. I wanna feel like I’m invested in you and wanna learn about you. And it was a commitment because some of those kids put me through the ringer, whether it was we’re gonna do gymnastics on a trampoline. And again, I’m in full costume doing gymnast on the trampoline, or we’re doing soccer drills with their soccer coach at their house playing football games. I mean, all kinds of stuff. I made a Yachty game for a kid that loves Harry Potter. And it was really a big part of getting work turned in because, and it’s the crazy thought they wanted to spend time with me. Like that’s what it was. And so it was like, yeah, absolutely. I’ll keep dressing up. I did over 50 plus Vater visits. It wasn’t just for my homeroom. It was for all of fourth grade. So I went over 50 visits and it was cool to see kids in their home and talk to them and meet their parents. It was a great opportunity for me to engage with parents as well. How is online learning, going, what can I do to support you? Do you guys have any questions and stuff like that? So

Eric Cross (08:39):
This thing of relationships is like leading to work completion, which isn’t, which isn’t always the, the thing that we think to as educators of like how, you know, work completion. A lot of times we think of like structures or you know, certain protocols that you do in class get work completion, but here you are addressing as Darth Vader. And, and you said students were turning in more work because they’re connected to, you saw an increase in, in yeah. Engagement.

Shad Lacefield (09:07):
And absolutely. And, and I remember even saying that to myself, like this is, this is what’s getting them. But it, it was, and as part of the Vader visit as well with the videos we recorded all of them and I said, I’m gonna make you a YouTube star. And so I would, I, I recorded them. I put ’em on my YouTube channel. And so a lot of the videos that are on my website, all those Vader visits are like the kids showing off and playing against the teacher. And I promise you, I didn’t take it easy on any one of those kids. Like when it was like a verse match, I went all out and I told ’em. I was like, if you beat me, you know, it’s gonna be like, you earned it.

Eric Cross (09:38):
What a great way to leverage, just what, what is relevant to our students? Like you used your platform and then now you’re showcasing them on your, you know, your platform or what you were using. And then they’re seeing each other. And I could just see, regardless of the grade level, like just students, like beam from, from getting that kind of positive praise through, through, you know a medium that doesn’t, that tends to be more of a, just content consumption, but you’re kind of watching other folks do stuff, but now it’s about them. Like, and they’re, they’re getting that attention directly. Now I have to ask about the Vader costume. Did you, did you buy it for this event or did you already have that Darth Vader costume in your closet?

Shad Lacefield (10:19):
I had parts of the costume, but not the complete costume. And honestly, the very first Vader visit I had, I had the Vader mask that makes sounds, and like you could talk and it makes you sound like Vader.

Eric Cross (10:29):
My dark saber is on order. Yes. And it keeps getting delayed from best buy. It’s supposed to arrive in April, but I do have dark staple and order that I ordered back in November. So the best to your point, I don’t know who doesn’t have one, I’m waiting for mine though.

Shad Lacefield (10:42):
There you go, come on. Best buy come through for us. So

Eric Cross (10:44):
You, you did all this investment in time and, and you created all this content, but then we went back in person. Were, were you able to bring this back into the classroom or any of the things that you had generated during distance learning back in the classroom? Or are you, are you using some of the things that you learned? Like what, or is it just completely separate and you’re just doing something completely different. Now

Shad Lacefield (11:04):
That’s a great question. So I still try to dress up at least once every week, if not once every other week just to make whatever we’re doing fun, cuz I already have costumes that were connected to the content that I was doing. So had I had made a character called captain Soundwave that will use when I’m teaching my amplify lessons over sound. And so then I, you know, I have that or I would have, you know, specific characters that were designed for certain lessons that I would do. And so I still

Eric Cross (11:32):
Lemme interrupt you real quick. Where did you get these character ideas from? Cause they are super creative. I clicked on one random one. And you have had like a, a knitted like skull cap and like some blue shiny like cloak and I like who is this guy? I think, is that him? Is that captain sound wave? That’s

Shad Lacefield (11:48):
That’s hilarious. That was, that was my attempted Elsa. Oh, that was yeah. Started buying more and more costumes and and making characters and putting costumes together. And so yeah, it just ends up being this thing where you never know when I’m gonna show up in a completely random costume and be like today, we’re getting ready to learn about how sedimentary rocks form. And I dressed in my rock outfit, which is the old school rock with the turtleneck and the gold chain with,

Eric Cross (12:16):
Wait, do you have a Fanny pack too?

Shad Lacefield (12:17):
I have a Fanny pack. Yes you have. Yep. You nailed it. And they’re like, what does this guy

Eric Cross (12:22):
Do? He raise the one eyebrow. Can you do the, the rock eyebrow? Oh yeah, you got this. Oh, people on the podcast. Can’t see. Chad’s got it down. He’s got it down. He’s got the, he’s got the eyebrow going. Okay, so you, so I feel like I can go on a tangent and talk about all your costumes that you have, but the thinking about this. So tons of engagement, younger people now taking like some of the principles that you’ve learned from this, how can, how can upper grades like bring this joy to their classroom? Like middle school students, you know, older kids sometimes, you know, they can, they’re still kids, but you know, they might not be the same thing as fourth graders. Like would you, do you have any ideas of like how teachers and upper grades can kind of take these elements that you’ve done and, and apply them?

Shad Lacefield (13:04):
Absolutely. So some of the things that you had talked about, like with YouTube can also be applied to like TikTok videos and things like that, that kids are, are willing to watch and, and be engaged in. And so those things, I feel like I’ve seen other middle and high school teachers really utilize in their classroom. But honestly, and this is a new initiative that we’ve started in our district. Minecraft has been something that a lot of kids play and are really engaged in and has shown an amazing engagement for all of our kids when it comes to science engagement, particularly. And so with that, so there’s 126 million active Minecraft players right now in the world. And Minecraft is one of the largest selling video games. The average age, cuz they’re always like, oh, Minecraft is for kids who actually the average age is like 24.

Shad Lacefield (13:51):
So a lot of the older kids are playing Minecraft as well with the younger kids. And with that in mind, it was a way when I looked at Minecraft and specifically like Minecraft educational edition came out and it was during COVID and it was free. So if you had a school email or it’s like the, what the go 365 account, you could get it for free and all of our kids got it for free. And so then, then we went from playing Minecraft on the computer as like a fun game to me looking at it and saying like, wait a minute. I feel like when I’m doing energy conversions, we can take Redstone and Minecraft and kids can now show how a simple system using different parts and devices can work and understand even more con creates how energy is converted from one form to another.

Shad Lacefield (14:39):
And so let’s make this a, a, a, an actual activity. Let’s take what I’m teaching in the classroom. And if they get done early as an enrichment piece, because there’s not a ton of science and enrichment activities at times for kids to be able to do, like, what do I do when I’m done, Minecraft ended up being that. And so I could have these elaborate worlds that I would build for them that they could then go and play and be super engaged in and show me way more on this Minecraft world, what they knew than what they were writing on paper sometimes, cuz I, you know, you’d get like a sentences out of them on paper, but then all of a sudden when they would build this elaborate system and you just had them record and talk, it was like, oh my gosh, you understand way more than I was thinking that you did with that last exit slip, an assessment that we did.

Shad Lacefield (15:25):
And so like, this is awesome. So then I went to my district and I actually proposed an idea what if we did tire Minecraft build challenges for the whole district? So our district has 37 elementary schools and I was like, I think this could be something that, you know, as we’re looking for science, curriculum engagement and making kids excited about learning science and stuff again, cuz that was always the hard part. I feel like sometimes with COVID everything kids lost this love of, of being in the classroom and, and, and learning and that it was like, you know, getting them to come back into the classroom and, and finding, learning fun again. It was like this, this started to get ’em excited and like, yeah, I get to play in Minecraft and I’m learning at the same time. And it was working for all kinds of content areas.

Shad Lacefield (16:07):
We’re doing a blast off to, to Mars. We it’s called blast off to us. We’re partnering with CLO of the future. They’re working with SpaceX. Our kids will actually get to send postcards to space and yes, it’s, it’s a super cool thing. And I love my district and all of the office of technology, individuals, Ashley Josh and Kelly for putting this together. And so it asks this question if you could a community in space, what would it be like? And the goal is that kids will write on the back what they want. And then we send this postcard off to space, they stamp it saying it’s been in space and the kids get to have it back and, and be able to use it. But what, what we decided, what we could do with Minecraft is what if they actually built the colony on Mars, like really research put time and effort into reading scientific articles about plants and how plants would grow and, and water and, and structures and apply all of that in a massive build challenge. And then that be, you know what we’re doing? That can be the answer to the question. And so it’s not just a couple sentences on a postcard, but it’s like a week or two week unit that pulls all this scientific content and standards that we’re working with and really allows kids to show so much creativity like on my Twitter I’ve been posting like pictures and stuff like that of some of the students builds. And I’m gonna continue to do that throughout the build challenge.

Eric Cross (17:26):
Now, are you using Minecraft EDU?

Shad Lacefield (17:28):
Yes. That is correct.

Eric Cross (17:29):
I love Minecraft EDU. Like it, it, you talking about it inspires me to, to try to dive back into it. One of the things sometimes I feel limited by is the time that I have and the things that we’re trying to cover. And it’s almost, it almost feels like we’re doing something wrong using a video game to teach, but it’s such a great educational tool. Like you said, you just said that students are able to show what they know in, in a way by creating something that’s different than if they would’ve just written it, but they’re actually creating, and this is one of the things, I guess you kind of hit on this, but I wanted to probe it a little more. Is do you have your students creating content like you do? Cause I kind of heard that they, you were, did you say that they were explaining or doing a video recording or describing it? How are they, how are they, how are they doing that work?

Shad Lacefield (18:17):
Yeah. So what they actually do is they’ll write a script and they will use Screencastify to record and then upload to Flipgrid. And then that way they can actually show their build to all of fourth grade. Since we weren’t allowed to be in the same class, like we were all departmentalized, so then we will have voting challenges. So after you record, you get to see everyone’s videos, you get to like and comment and leave feedback on their builds. So you can see what the other kids created. And then then from those initial videos and voting, we selected a certain of kids that then go on to the district level for our Minecraft build challenge. And then those videos are viewed by administration and other teachers to vote again. And then you end up having grade level winners and then an overall winner, which shout out to my boy in fourth grade, who was our overall winner, Eli, super proud of him.

Shad Lacefield (19:07):
He, he made this really, really space saving system, which was hidden stairs that ran off of Redstone and used motion, energy. And again, in his video, he talks about like how motion energy has changed to electrical energy and then back into motion through the process of how this hidden staircase would be in the wall. And then you’d be able to use this lever to then release that staircase. So you could go up and down but it was just, and again, when you, when you let kids talk about energy conversions and you let them build all of a sudden, you have kids making security systems for banks. Another kid that made a feeding system for kids for animals at the zoo, and it was just like, oh my gosh, I had no idea that this was what you guys could run out and do. When I, when I taught you how energy conversions work, that this is what you could produce and come over, like this is mind blowing. I love it,

Eric Cross (19:56):
What our kids can do and what they can create always kind of blows us away when we give them an opportunity to kind of have that freedom to, to create and take their knowledge and actually do something with it versus channel it into what, show me what, you know, but only do it like this. This is, this is the lane that you have to stay in. How do you get these ideas and, and stay, stay relevant? Like so many of the things like you’re touching, like pop culture, you, you have this hand in education technology, you have you’re, you’re doing video editing. Like where are you drawing from? Cause I’m just thinking like, as a teacher listening to this, that might be newer. And they go to the side like, oh my gosh, this, this guy is doing these so many things like where are you drawing from for inspiration or ideas?

Shad Lacefield (20:39):
I think a lot of it is like you say, when, when you stay relevant, it’s being engaged with your students and figuring out, or what are, what are they liking? And every year it’s gonna be different. And that helps you stay relevant. When you have conversations and you build relationships with your kids to figure out, you know, what’s going on. Because I was not a big Minecraft person. It was the group that came in that really challenged me to do Minecraft because it, it showed up on their Chromebooks one day and all of a sudden it’s like, oh, we can play Minecraft all the time. And I said, no, you can’t play Minecraft until that I’ve had training. And I know what’s going on because I’m super nervous about this new thing. And I wanna make sure you guys aren’t doing something that you’re not supposed to.

Shad Lacefield (21:13):
And like, they hounded me hardcore about you better do you need to do that training, Mr. Lacefield, you need to, we wanna play Minecraft. You better be doing this. Right. And so I was like, all right, man, I’ll, I’ll invest. I’ll, I’ll put some time into this training. And I’m so glad that I did yeah, again, that’s it just like building relationships and having those conversations help you realize like, what’s, what’s what are they interested in? What what’s going on and what would be really funny, even connecting that back to the costumes. What would it be really funny if I showed up in you know, today, princess Jasmine.

Eric Cross (21:42):
Yeah.

Shad Lacefield (21:43):
Been yes. Done that. That’s a great one. I,

Eric Cross (21:45):
I, I just went to the social studies page. I, and I stop laughing while you were talking. Cause I saw the princess Jasmine.

Shad Lacefield (21:52):
Oh yeah. Folks.

Eric Cross (21:53):
I’m telling you, you have to go, you have to go to his videos and see what he’s done. I mean, they’re just, they’re just amazing with my middle school students. They, I, I find myself having to be into things that I’m not normally into. And we have these intergenerational relationships, right? Like I think teachers are unique in this I aspect where I can connect with a 12 year old with what 12 year olds are in no matter where this 12 year old’s from. Cuz I get 12 year old culture. But sometimes when I go back into my adult world, like I forget that like, Hey yeah, haven’t watched a new anime you know, or, or whatever, you know, up

Shad Lacefield (22:26):
That. Yeah. No said too. And a kid will show up wearing a, a shirt to school and I’m like, I wasn’t the world’s that like, I’ve never even seen that before. And you’re like, okay, I’m gonna have to learn what that is cuz that yeah.

Eric Cross (22:38):
And then the next student asks you about, Hey, do you like, do you like these this game? I’m like, yeah, yeah, let me go Google that game real quick. Yeah, I’m totally into it. I’m downloading on my phone real quick. And, and now I’m connected to all kinds of obscure random interests, but to your, to what you said, it like, it helps keep us fresh, right? With I, with ideas, there, there is something that is super practical that you’ve done that you’ve created that I’ve encouraged teachers to do. And I think you really nailed it. On your site, you have these video tutorials. When I look at those, I, I think about how much time you must have saved yourself of not having to explain the same exact thing multiple times. Because you’ve created this virtual help section that allows students to log in amplify earth, check, Flipgrid, whatever. Like do you, when you’re, when you’re teaching students, do you, do you use those in direct students there so they can kind of support themselves? Or is that, what, how did that come to be when you, when you made these, these virtual tools? Because I could just imagine these are time savers for you.

Shad Lacefield (23:49):
Absolutely. Cuz again, like you said, it’s it saves on time. So a lot of when you have kids that are already visual learners as well, and they love watching YouTube and they learn stuff from YouTube, why not? I mean, make the video and then attach it to my Google classroom, keeping everything online. Everyone always has access. And by still having those videos, it allows kids to hear the directions multiple time, but on their time and at their pace. So then it’s posted on the assignment. So even though I probably still will give those directions verbally out loud if a kid forgets and maybe they feel a little nervous about asking in front of their peers, like, oh, how do I do this again? Or, oh, I don’t remember how to do that. That video is linked on there. So that way they can go back and watch it.

Eric Cross (24:28):
It’s almost like a little co-teacher that you have like a little aide that’s like, but it’s you, but it’s like a mini you who’s helping you out. I found that putting sometimes those tutorial videos on ed puzzle, where at different points in time, you can set it up so that at a certain timestamp, it asks a question and you can control it. So they can’t move faster past it until they respond to the question and you have the question be about whatever you just said. And then it, it syncs with Google classroom. So you can import all the grades and you can see how far through the video they got. But that was one other layer that I was able to do. So I can have some accountability and make sure that okay, everybody watched it and they answered all five questions of like, how do you do this?

Shad Lacefield (25:07):
Oh, see, now you’re sharing stuff with me, Eric, because I, I’m not as familiar with ed puzzle. I’ve used like near pod and per deck, but I mean just you saying that I’m like, okay, I need to check out ed puzzle and, and see what, what this is all about. Cause that sounds awesome.

Eric Cross (25:20):
Hey, I shared something with Chad and it it’s useful. I’m I’m feeling good right now. I’m feel I’m feeling good. So as we, as we kind of wind down one, couple questions I wanna ask. One of ’em is you’ve been in teaching for, for 15 years and I, I talk to you like right now and I get this energy and this vibe that’s just so upbeat, so positive. How do you stay fresh, fresh. And how did you stay fresh during a time when things have been so hard, you know, and it, and still is for so many educators, how do you stay encouraged? Like what, what have you done and, and to stay in, in education for, for this long,

Shad Lacefield (26:00):
I think it, it even goes back to like when I made my initial decision to switch my major to education, like I, I really felt like I found so thing that I thoroughly loved and enjoyed, and I always feel like you go through seasons. Like, and I definitely, when, when COVID hit, like you went through a season of where you start to feel again, that pressure like do I really like doing this as much as I thought that I like doing this and am I ready for this next thing? And then I just go back to just the, well, why did I do this to begin with? And, and it gets me, you know, excited to be like, I did it for the kids, like, and it’s about the kids. And I get joy when they’re laughing and smiling. So again, with the videos, it’s like, how can I make ’em laugh and smile because if they’re laughing and smiling and having a good time, I’m gonna get, you know, jacked and ready to start teaching again.

Eric Cross (26:48):
And I just hear that so much in what you’re saying is you’re serving your kids is, is being more than that building the relationship, that connection. And then through all that, the learning happens. The last question I wanna ask you is who’s one teacher that created a memorable experience for you or inspired you. Is it someone that you remember when you were in school or learn experience that just, that stands out to you to this day? Cuz as teachers, we remember thi like our kids remember us and it’s weird to be in that position to think that we’re gonna be that person. So is there anybody or anything that stands out to you that you remember from a, a teacher and experience?

Shad Lacefield (27:27):
Gosh, I have, I have a lot that you know, from my fifth grade science teacher, Mr. Goodman, who we did the ecology meet and the ecology team, and we went to OT Creek park and we competed against other schools about science, connected materials to my physics teacher in high school that let us build boats out of cardboard and take it to the only hotel in our town and the pool. And we had like boat races with the cardboard boats that we did. But really I, I go back to Squire boon and Claudia my manager and I remember not only was, she’s such a, a pivotal like getting me into teaching. But I remember the, the curriculum that we were using at the time that I was. And again, it goes back to what if I was to teach that curriculum, I would not still be a teacher because again, as sometimes you experience with curriculum, it can be boring and not engaging. And I was already putting my own flare on it at SQUI boon during the scout lessons. And I said, what if I just completely rewrote this curriculum? What if I made it really fun and put my own, spin on it? And, and she was like, absolutely, absolutely do that. And I feel like that encouragement as teachers, when we encourage kids to be creative when we encourage kids to, to take risk and to try new things we end up getting such amazing results that we didn’t even expect

Eric Cross (28:45):
Thought I out to Mr. Goodman for the ecology meet the physics teacher for the, the boat races, which are hilarious, by the way, if you’ve ever been able to watch students, did you make ’em at a cardboard?

Shad Lacefield (28:53):
We did. Yep.

Eric Cross (28:54):
Yeah. Those are hilarious to watch. And Claudia for giving the freedom to let you be a educational DJ and remix things to make it fun. Thanks for being on the podcast. Thanks for your inspiration and for sharing your stuff like publicly and letting other people see it and, and get ideas. It’s, I’m sure there’s more people than, you know, and more teachers than, you know, that are looking at that and getting their own ideas and coming up with their own. It might not be star wars, but coming up with their own inspiration, maybe it’s like Harry Potter or Lord of the rings or some like that.

Shad Lacefield (29:26):
Yeah. Whatever. You’re passionate about. Pull that in.

Eric Cross (29:31):
Thanks so much for joining me and Shad today. We want to hear more about you. If you have any great lessons or ways to keep student engagement high, please email us at stem@amplify.com. That’s STEM@amplify.com and make sure to click, subscribe wherever you listen to podcasts until next time.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Shad Lacefield says about science

“It’s about being engaged with your students and figuring out what are they liking. Every year it’s going to be different…when you have conversations and you build relationships with your kids.”

– Shad Lacefield

4th Grade Science Teacher, District Elementary Science

Meet the guest

Shad Lacefield is a teacher at Garden Springs Elementary and part-time professor at Asbury University in Kentucky. Mr. Lacefield leads professional development in his district, and has been a guest speaker for Eastern Kentucky University, Campbellsville University, and Amplify Education. His topics include classroom managment, integrating techology, and student engagement. He earned his bachelor’s degree in elementary education from Campbellsville University in 2007, and his master’s in science from Southwest Baptist University in 2011. Shad has either taught or coached every grade K-12, and in his 14 years in education he has served as a lead teacher in literacy, math, science, and social studies. He currently coordiantes with the FCPS Office of Instructional Technology to plan Minecraft build challenges for elementary students, and is working on setting up a science field trip that turns a golf course into a STEM lab. During the first year of the pandemic, Shad dressed up in over 100 costumes to create a unique and engaging online learning experience for his students. He also created Vader Visits where he visited students at their homes dressed as Darth Vader to celebrate their online successes, and keep them encouraged during a challenging time. His creative teaching style, and over 50 “Vader Visits” with students, have been featured on WKYT-TV, LEX-18, Spectrum 1 News, and several local and college news publications. Shad lives in Lexington Kentucky with his wife Whitney Lacefield and their three children.

Check out his websiteYouTube channel, and Facebook account!

A person with glasses smiling against a blue background, surrounded by a circular design.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. Listen here!

Grade 6

Chapter 1: Numerical Expressions and Factors

Big IdeasDesmos Math 6–A1
Lesson 1: Powers and ExponentsUnit 6
Lesson 10: Powers
Lesson 11: Exponent Expressions (Print available)
Practice Day 2 (Print available)
Lesson 2: Order of OperationsUnit 6
Lesson 11: Exponent Expressions (Print available)
Lesson 3: Prime Factorization
Lesson 4: Greatest Common FactorUnit 5
Lesson 15: Common factors
Lesson 5: Least Common MultipleUnit 5
Lesson 14: Common Multiples
Practice Day 2 (Print available)

Chapter 2: Fractions and Decimals

Lesson 1: Multiplying FractionsUnit 4
Lesson 12: Puzzling Areas (Print available) [Free lesson]
Lesson 13: Volume Challenges
Lesson 14: Planter Planner (Print available)
Lesson 2: Dividing FractionsUnit 4
Lesson 1: Cookie Cutter
Lesson 2: Making Connections (Print available)
Lesson 3: Flour Planner [Free lesson]
Lesson 4: Flower Planters
Practice Day (Print available)
Lesson 3: Dividing Mixed NumbersUnit 4
Lesson 5: Garden Bricks (Print available)
Lesson 7: Break It Down
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 14: Planter Planner (Print available)
Practice Day
Lesson 4: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Lesson 2: Decimal Diagrams [Free lesson]
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 5: Decimal Multiplication
Lesson 12: Budget Vehicles (Print available)
Lesson 5: Multiplying DecimalsUnit 5
Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Lesson 2: Decimal Diagrams 
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 5: Decimal Multiplication
Lesson 12: Budget Vehicles (Print available)
Practice Day 1 (Print available)
Practice Day 2 (Print available)
Lesson 6: Dividing Whole NumbersUnit 5
Lesson 8: Division Diagrams
Lesson 9: Long Division Launch
Lesson 10: Return of the Long Division (Print available)
Lesson 11: Movie Time [Free lesson] 
Lesson 12: Budget Vehicles (Print available)
Lesson 7: Dividing DecimalsUnit 5
Lesson 8: Division Diagrams
Lesson 9: Long Division Launch
Lesson 10: Return of the Long Division (Print available)
Lesson 11: Movie Time [Free lesson] 
Lesson 12:(Print available) Budget Vehicles 
Practice Day 1 (Print available)
Practice Day 2 (Print available)

Chapter 3: Ratios and Rates

Chapter 4: Percents

Chapter 5: Algebraic Expressions and Properties

Chapter 6: Equations

Chapter 7: Area, Surface Area, and Volume

Chapter 8: Integers, Number Lines, and the Coordinate Plane

Chapter 9: Statistical Measures

Chapter 10: Data Displays

Grade 7

Chapter 1: Adding and Subtracting Rational Numbers

Chapter 2: Multiplying and Dividing Rational Numbers

Lesson 1: Multiplying IntegersUnit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Practice Day 2 (Print available)
Lesson 2: Dividing IntegersUnit 5
Lesson 8: Speeding Turtles
Lesson 3: Converting Between Fractions and DecimalsUnit 4
Lesson 13: Decimal Deep Dive (Print available)
Lesson 4: Multiplying Rational NumbersUnit 5
Lesson 7: Back in Time
Lesson 5: Dividing Rational NumbersUnit 5
Lesson 8: Speeding Turtles

Chapter 3: Expressions

Chapter 4: Equations and Inequalities

Chapter 5: Ratios and Proportions

Chapter 6: Percents

Chapter 7: Probability

Chapter 8: Statistics

Chapter 9: Geometric Shapes and Angles

Chapter 10: Surface Area and Volume

Lesson 1: Surface Area of Prisms
Lesson 2: Surface Area of Cylinders
Lesson 3: Surface Area of Pyramids
Unit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 12: Surface Area Strategies (Print available)
Lesson 13: Popcorn Possibilities
Lesson 4: Volumes of Prisms
Lesson 5: Volumes of Pyramids
Unit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 13: Popcorn Possibilities
Practice Day 2 (Print available)
Lesson 6: Cross Sections of Three-Dimensional FiguresUnit 7
Lesson 9: Slicing Solids

Grade 8

Chapter 1: Equations

Chapter 2: Transformations

Chapter 3: Angles and Triangles

Chapter 4: Graphing and Writing Linear Equations

Chapter 5: Systems of Linear Equations

Lesson 1: Solving Systems of Linear Equations by GraphingUnit 4
Lesson 8: When Are They the Same?
Lesson 9: On or Off the Line?
Lesson 10: On Both Lines
Lesson 11: Make Them Balance [Free lesson]
Lesson 12: Line Zapper [Free lesson]
Practice Day 2 (Print available)
Lesson 2: Solving Systems of Linear Equations by Substitution
Lesson 3: Solving Systems of Linear Equations by Elimination 
Lesson 4: Solving Special Systems of Linear Equations 
Lesson 6: Scale Drawings

Chapter 6: Data Analysis and Displays

Chapter 7: Functions

Lesson 1: Relations and FunctionsUnit 5
Lesson 1: Turtle Crossing [Free lesson]
Lesson 2: Guess My Rule [Free lesson]
Lesson 2: Representations of FunctionsUnit 5
Lesson 3: Function or Not?
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 3: Linear FunctionsUnit 5
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 8: Charge! (Print available)
Lesson 4: Comparing Linear and Nonlinear FunctionsUnit 5
Lesson 4: Window Frames
Lesson 5: Analyzing and Sketching GraphsUnit 5  
Lesson 6: Graphing Stories

Chapter 8: Exponents and Scientific Notation

Chapter 9: Real Numbers and the Pythagorean Theorem

Lesson 1: Finding Square RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Lesson 2: The Pythagorean Theorem
Lesson 3: Finding Cube RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Lesson 4: Rational Numbers 
Lesson 5: Irrational NumbersUnit 8
Lesson 14: Hit the Target
Lesson 6: The Converse of the Pythagorean TheoremUnit 8
Lesson 9: Make It Right

Chapter 10: Volume and Similar Solids

S5-03. Cultivating a joy of learning with Sesame Workshop

A blue graphic with text reading "Math Teacher Lounge" in multicolored letters and "Amplify." at the bottom, with abstract geometric shapes and lines as decoration.

Listen as we chat with Dr. Rosemarie Truglio, senior vice president of curriculum and content for Sesame Workshop! Continuing our theme of math anxiety this season, we sat down with Dr. Truglio to chat about Sesame Street and her thoughts on how to spread a growth mindset to young children and put them on course to academic achievement and long-term success.
 
Listen today and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!

Download Transcript

Dr. Rosemarie Truglio (00:00):
Children don’t come with this math anxiety. Math anxiety is learned.

Bethany Lockhart Johnson (00:07):
Welcome back to Math Teacher Lounge. I’m Bethany Lockhart Johnson.

Dan Meyer (00:11):
And I’m Dan Meyer.

Bethany Lockhart Johnson (00:12):
Hello, Dan Meyer.

Dan Meyer (00:14):
Great to see you, Bethany. We are on episode three. Can you believe it?

Bethany Lockhart Johnson (00:18):
So, I feel like we’ve just started scratching the surface about math anxiety. We’ve talked to two amazing researchers. We’ve talked about what math anxiety is, how it’s often screened for some of the causes, some of the consequences … I mean, we’ve had some good conversations. Dan, what do you think?

Dan Meyer (00:38):
Definitely, I think that the consequences have only grown more dire in my head. I’m not sure how you feel about the consequences. But, you know, it is enough for me that we ask students to take mathematics for much of their childhoods, to worry about their anxiety, taking that. But to hear about from these researchers about all the different things that correlate with math achievement and math anxiety—talking about future careers, certainly, but even some other, more serious lifelong concerns? That gives me a lot of motivation to continue this study of math anxiety here with you on the show.

Bethany Lockhart Johnson (01:14):
It is really widespread. It has a big impact, not only on students, but on parents, on educators. You know, it’s—

Dan Meyer (01:23):
Multi-generational.

Bethany Lockhart Johnson (01:25):
Yes. And you know, so often when folks think of math anxiety, what I hear them say is, “Oh, yeah, in high school is when math really ramps up. That’s when anxiety starts.” But we know that it starts in our youngest learners. And our research has already backed that up. We know it. I’ve seen it in my classroom. You may have seen it with some students you work with. And let me tell you, it starts young.

Dan Meyer (01:52):
It does start early. Right now, I have a son that’s just started kindergarten, and he seems relatively math-positive, but we’ve known from our interviews on this show and other kinds of experiences that oftentimes, that feeling —that math is for me, and I am for math, and we are all friends — can turn on a single moment. It seems like one teacher says a thing that changes a student’s perception of themselves as a mathematician or of math itself. So I keep waiting with bated breath, hoping not to find that one moment that changes our current open posture towards mathematics. So now it’s time to really dive into some strategies for combating math anxiety.

Bethany Lockhart Johnson (02:34):
To help us out, we’ve called on a pretty exciting guest. I am so excited, Dan Meyer! We are being joined by Dr. Rosemarie Truglio. She is Senior Vice President of Curriculum and Content at Sesame Workshop. Sesame Workshop! As in, “Tell me how to get to Sesame Street.” Dan, I have to tell you, I spent many, many hours of my childhood watching Sesame Street. I have to ask, do you have happy Sesame Street memories? Is this part of your formation, Dan Meyer?

Dan Meyer (03:08):
At this point? In my advancing years, and the brain cells that I have left, Sesame Street is really kind of just a vibe in my head. But that vibe is such a pleasant one. One in which like nothing bad could happen. One in which learning is common and normalized and fun. And you just kind of feel at home, constantly.

Bethany Lockhart Johnson (03:33):
I don’t know about the “just the vibe” part, because for me, it is visceral. I’m there. I am actually … I mean, I might still be there.

Dan Meyer (03:42):
You could reenact some of the skits?

Bethany Lockhart Johnson (03:44):
. You didn’t watch Sesame Street with your kiddos when they were younger?

Dan Meyer (03:49):
We watched a lot of Elmo. A lot of Elmo. Yeah.

Bethany Lockhart Johnson (03:52):
Next-generation Sesame Street. Well, I think it’s so perfect that we’re gonna be talking about what Sesame Workshop does to help combat math anxiety and create a positive connection and relationship with mathematics. So I’m really excited to hear what Dr. Truglio and her team have been working on. And here’s our conversation with Dr. Truglio.

Dan Meyer (04:15):
Welcome to the show, Dr. Truglio. It is an honor.

Dr. Rosemarie Truglio (04:18):
Great to be here. Thank you for inviting me.

Dan Meyer (04:20):
You are Senior Vice President of Curriculum and Content at Sesame Workshop, which definitely sounds like the coolest job in the world to both four-year-old me and also Now me. Would you just help us help us with some backstory of how you ended up here, and what you do at Sesame Workshop?

Dr. Rosemarie Truglio (04:38):
Sure. It is a pretty cool job. And I am very fortunate that I’ve been in this position for the past 26 years. So, I am a developmental psychologist, and my job is to help Sesame Workshop identify curriculum needs, so that we could address them in the content that we create on the show and across our various platforms. So, Sesame Street is currently in its 53rd season. And we just, wrapped production for the 54th season, which we’ll debut next fall. And Sesame Street began with an experiment: Can television actually teach children school readiness skills, to have them better prepared for school? Especially those children who did not have access to formal education during the preschool years? And it is what we call a whole-child curriculum, because we’re dealing with all of the school readiness needs. So that that includes the academic needs, their social-emotional needs, and their health needs, as well as what we call these cognitive processing skills—how children learn content. Right? So it’s not just content skills, but how you approach learning and how you actually learn content. So as a grad student, I was fortunate to work at the Center for Research on the Influences of Television on Children. Very special center. It was at the University of Kansas. And my advisors, developmental psychologists, they studied the effects of television on children, both the positive effects and the negative effects. And so part of their research was to actually look at the longterm educational effects of Sesame Street. So I was working with Sesame Street content as a grad student, and then came to New York City. My first job was Assistant Professor at Teachers College, Columbia University. And when this position became available, Director of Research at the time, it was called, I took that job. And so my job was to oversee both the curriculum and the implementation of the curriculum, as well as the research. Because what we know, our co-founder, Joan Ganz Cooney has always said, for Sesame Street to be a successful educational program, production has to work closely with early childhood educators. They are the ones who know the curriculum and, and develop the curriculum goals, as well as the developmental psychologists who actually study how children are paying attention to the content. But more importantly, what are they comprehending from the content? And we all have to work together. Because even though we are the experts, the real experts are the children themselves. So nothing is deemed final until we actually show the children and see what they are learning from the content that we are producing.

Dan Meyer (07:54):
Are you referring to like, test audiences of kids then?

Dr. Rosemarie Truglio (07:57):
Yeah, I guess you could call it test audiences. I mean, I don’t. I don’t like to call it that because I see them as co-collaborators. I don’t see them as a test audience. Because, as I said, they’re the experts. It’s a collaboration. I mean, they’re the experts. And so I wanna know—

Dan Meyer (08:12):
As collaborators. I got it now. Yeah.

Dr. Rosemarie Truglio (08:14):
They help us. So that’s exactly what we tell the children too. So it’s called formative research. You know, we, we do what we call, um, storybook testing, an animated version of a storybook to have some little movement and see are they finding the story engaging, but more importantly, are they picking up on the intended educational lesson that we’re trying to teach in the story. So they are co-collaborators. they’re the ones who are helping us get the story just right for them.

Dan Meyer (08:46):
That’s really exciting, and makes me think about what classes might be like if students were regarded in that kind of lens as well. I just wanna say that my four-year-old self is on this interview as well, and is re-contextualizing all the stuff I saw as a kid. And it just felt like, at the time, you folks turned the camera on and went down to the street and we just had this real natural time. And it’s great to hear about all the intense preparation and co-construction at work and work that went into that time. Yeah,

Dr. Rosemarie Truglio (09:12):
It’s about a year preparation from start to finish. From the start of identifying, “What is the educational need? Is it an academic need? Is it a social-emotional need? Is it a health need? Is it a cognitive-processing need?” And then once we have the need identified, we have what we call a curriculum seminar. We bring in the experts who are studying this topic with preschoolers, because we wanna get it, we wanna get it right.

Bethany Lockhart Johnson (09:41):
Which, by the way, little behind the scenes: How often do you get to go to set?

Dr. Rosemarie Truglio (09:46):
So we’re in a production probably about six weeks out of the year. Covid really messed things up. ‘Cause we have to be really—we have very strict Covid protocols, but there is someone on my team—and sometimes we have to, you know, rotate for availability—but there’s always an educator on set.

Bethany Lockhart Johnson (10:06):
Awesome.

Dr. Rosemarie Truglio (10:07):
Because even though you stick to the script, questions arise; they wanna make changes; sometimes they have to cut; things are running too long and they have to cut and we gotta figure out where to cut. So there’s always an educator on set.

Bethany Lockhart Johnson (10:19):
But sometimes you go and have lunch, like—.

Dr. Rosemarie Truglio (10:21):
Oh, I go, yes. Sometimes I go—

Bethany Lockhart Johnson (10:23):
And just hang out with Big Bird, right?

Dr. Rosemarie Truglio (10:24):
Sometimes I go hang out with Big Bird. No, those are my friends!

Bethany Lockhart Johnson (10:27):
They are!

Dr. Rosemarie Truglio (10:28):
No, no, I go hang out with them. They’re my friends. Yes.

Bethany Lockhart Johnson (10:32):
When I think about Sesame Street and I think about … like, I can’t help but smile. Because I think I have such fond memories of the characters. I mean, we invited them, my mom invited them, into our home, right? And, you know, now I have a two-year-old and there’s no doubt that I’m gonna introduce him to Sesame Street. And I see how it really does feel like the folks who are doing this work, you and your team, you have a deep respect for children. So it makes sense that you call your test collaborators “collaborators,” right? They’re a part of it. And you know, I love that. And Sesame Street makes me smile. However, I’m like, we’re talking about math anxiety. And it’s so interesting, because as Dan and I were talking about our memories of Sesame Street … you know, it’s like Sesame Street feels like there’s not much anxiety. I mean, there are problems, and there’s problem solving, and it’s not like everything is perfect. But we figure it out. And it’s OK to make mistakes and it’s OK to try again. And a lot of times, we don’t see that in the math classroom—or at least, how folks talk about math. So, how do you all think about anxiety, about how to prevent it? Like, when you’re doing your work, you know that math anxiety is a real thing. But then that’s not translated in these experiences and the relationships with math that you’re building with your viewers.

Dr. Rosemarie Truglio (12:07):
Yeah, that’s a really good question, because it’s really easy, because our core audience are two- to four-year-olds and they love math. And what’s not to love, right? Because they are figuring the world out as they’re exploring the world. So you said something really interesting, that when you turn on the TV—when you turned on the TV when you were a child, and now you’re a mom of a two-year-old, we wanna make sure that the show represents content that is relevant and meaningful to our target audience. And that comes through with the characters. So all of our characters have very specific personalities, as all children do. And our characters represent all children, in terms of not only personality, but interest and learning styles, ’cause we wanna see—we wanna make sure that children see themselves in these characters. And we have a character who actually loves math. And he’s The Count.

Bethany Lockhart Johnson (13:12):
I’m like, “I know! I know who it is!” I will save you my impression. Although I have done it for my child. But I’ll save our listeners .

Dr. Rosemarie Truglio (13:20):
And you know, he’s an adult character. Some of our characters are preschoolers, like Elmo and Abby—they’re preschoolers—and Zoe. But The Count is an adult. He lives in the castle and he just loves numbers. But what’s really important is while we have The Count to explain—not explain to, but to portray to children, cause we don’t explain anything; we show children that math is more than number, right? Math is a pretty wide concept. Which is what I love about math. And the other thing about math is math language. The language of math. ‘Cause when we’re teaching children vocabulary words, we’re also teaching children the concept. Be it a math concept or a science concept or a social-emotional concept. So children don’t come with this math anxiety. Math anxiety is learned and it’s unfortunate. It’s picked up by their observations of the adults in their lives, who sometimes say out loud, “I don’t like math,” or “Math is hard,” or even worse, “I’m not good at math.” Or may even label it as math anxiety. That word won’t mean anything to a young child. But it then provides a, whaddya call it, like a negative valence for something that they never felt negative about. Because as they’re growing and interacting with the world, math is all around them. And there’s that sense of awe and wonder and joy, especially as they’re learning and they’re figuring it out. So I think we have to reframe math. Instead of saying “math anxiety,” we have to talk about the joy of math and all the wonderful joys that come with the exploration of these math concepts. Number is great. We know kids love numbers. We know that they love to count and use a big word here: enumerate . Because so many parents don’t make this distinction. They’ll say, “Oh, my child is counting!” Well, there’s rote counting, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, which is important. But then it’s like there’s an item for each number. So it’s one Cheerio, two Cheerios. And then as you point to each number, you are then figuring out what the set is, of the number of objects that you have. And then you get at what I love to call the meaningfulness of math. Right? Number has meaning. And as I said, it’s all part of your everyday activities. It’s part of—it’s in your kitchen; you’re following recipes; you’re measuring; you’re weighing. It’s at bath time, right? You could have the sorting of nested cups and you could, you know, and once again, the math language: big, bigger, biggest. These are relational concepts. You could then count what sinks and what floats, if you’re doing science. And then you could put them in two different buckets, and count. These are the items that sunk and these are the items that float. So math and bath time could be a lot of fun. And then there’s math and music. Music is so rich with math, as you talk about rhythm and tempo and dynamics and pitch and duration. That’s all math.

Bethany Lockhart Johnson (16:57):
The way that you talk about it, it is so rich, right? It is so multi-layered. And you know, I’ve shared on the podcast before: I’ve actually had parents in parent-teacher conferences say that, “Well, I wasn’t good at math either,” or “Math’s really not my thing.” And it’s really—it is, it’s rooted in that fear. And so I do see the way that you’re talking about it; I see that come through in Sesame Street. That, in a lot of ways, it’s reeducating parents, right? Because we hope that our caregivers are sitting next to their kiddo and enjoying it together and having conversations about it later. And there’s a way that parents then are also getting their own sense of what math can be, expanded. And I think there’s such a beauty in that. And I love the way that you talk about that, that you really are looking at, “Well, we wanna celebrate counting and the joyfulness of that. And let’s use math talk, you know, and let’s use these words and try out these ideas.” And it’s not because you’re trying to check some list. But you’re really exploring it and having fun together.

Dr. Rosemarie Truglio (18:03):
And you’re embracing it. And you mentioned the word “mistake.” So often when it comes to math, if you make a mistake—you make a mistake in counting or, you know, we’re not doing a lot of math equations on Sesame Street, but that’s when people feel like they can’t do math. ‘Cause they made a mistake. And that’s something that we are trying to address on Sesame Street, that it’s OK to make mistakes and you learn through mistakes. But you have to have—and I’m gonna come up with this other phrase now—you have to have what we call a growth mindset. What that means is that I may not be able to do this yet. Like, it’s called “the power of yet.” So we know that learning any concept, it takes time and practice. And how do we have children embrace the process, right? So often we focus on right and wrong. Now, there is right and wrong with math, of course. You know, there’s a right answer and there’s a wrong answer. But how do we focus, not on the end product, but the process through which you are engaging in? So let’s talk about measurement. Let’s talk about measuring the length and the width or the height of something. You might make some mistakes along the way, but you’re processing it. My son used to make all of these little structures for all his little play animals. Well, you know, he would measure and think he got it right. And then when he put the animals in, of course, you know, either the animal was too wide or it was too tall. And he would have to redo it. But you’re not redoing it from scratch, you’re redoing it now from experience. “I realize that if I’m gonna put the giraffe in with the elephant, I’m gonna need something wide as well as high.” Right? For the length, tall. And that’s process. And then, for children, when they figure it out, that “oops” and “aha”—the “aha” was like, “I did it!” And it’s so empowering, you know, giving them agency—not swooping in and saying, “All right, I’ll fix it for you. You know, we got the wide elephant and the tall giraffe and I’ll you know…”. NO! Having them do it. And another fun activity is in what we call informal measurement. And that’s like getting something of an equal size. It could be paper clips or it could be same-size blocks, and then measuring how long something is. So if it’s measured by blocks versus paperclips, you’re gonna have a lot more paperclips than you are blocks. And that kind of comparison is so fascinating for children. And so that’s measurement. And now we have counting. Like, how many paperclips long is something versus how many blocks long is something.

Dan Meyer (21:02):
So checking my understanding here, you’ve talked about how caregivers and other adults can transmit math anxiety by naming it and claiming it for themselves. And you’ve talked about, some really exciting ways that adults can involve students and kids in different kinds of math. I’d love to go upstream with you a little bit and wonder out loud, where does this anxiety come from initially? It’s gotta be more than adult one to kid two talking about anxiety, and transmitting it from human to human. What is the original spring from which all this anxiety flows?

Dr. Rosemarie Truglio (21:36):
Yeah. I do think it does—a lot of it does come from the adults in their lives. It’s unfortunate, because there is a lot of math talk about it, right? I can’t do math; I’m not good at math. Even when you’re at a restaurant and you get the bill and someone’s figuring out the tip, I can’t tell you how often it’s like, “Pass the bill, because I can’t do math.” Or if you actually then bring gender into it, you know, “Oh, girls aren’t good at math,” and that’s not true. There’s no evidence of that whatsoever, right? So in the younger grades, there’s no gender difference in terms of math ability. What’s also interesting about even socioeconomic status differences, you don’t see a lot of differences between low-income and middle-income children when it comes to math skills. Where you see differences is children’s ability to talk about their mathematical thinking. So if a child doing a math problem is asked, “How did you solve the problem?”, low-income children don’t often have the language to explain their thinking. So that’s something that we did on Sesame Street, where we focused a lot on what we call math talk. So, not just show number and show doing math, but actually narrate and giving the language. Because math literacy is one of the predictors of overall school achievement. So there’s that. They’re getting it from the adults in their lives. They’re getting it, unfortunately, sometimes from their teachers. But I think the anxiety comes from the fear of making mistakes. Because math, there is right and wrong, and always wanting to get the right answer. So that’s why this whole idea of reframing, and saying, “But really, it’s in the process.” So, you know, my son, math is not his strong suit. And I’ve been doing a lot of growth mindset with him as well. And there was a teacher that he had—I think in like 10th or 11th grade—who said, “In a test, I don’t wanna—I’m not even gonna look at the answer. I wanna see the process through which you GOT to this answer. And I’m going to grade the process. So the process could yield a right answer; it could yield a wrong answer. But you’re gonna get graded on the process. Because I wanna see how you are approaching the problem and how you’re thinking it through.” And I think that is a great example of, maybe, to try to reduce math anxiety. Because if you can get people excited about the process through which you’re learning—and that applies to all subjects, it’s not just math!

Bethany Lockhart Johnson (24:36):
I’m like, that applies to life! Right?

Dr. Rosemarie Truglio (24:38):
That applies to life!

Bethany Lockhart Johnson (24:39):
That’s so spot on. Wow. Yeah.

Dr. Rosemarie Truglio (24:41):
But I think that there’s so much focus on right and wrong, and not really understanding the value of the process. So on Sesame, we’ve been doing a lot of “oops” and “ahas.” You know, we’re gonna make mistakes, but what’s important is what do you DO when you make a mistake? So there’s a great episode with The Count. A couple of years ago. The Count was counting. Something he does every day. A lot of time, every day, ’cause he’s obsessed with counting and numbers. And he was counting an array of items.

Gladys the Cow (25:17):
I need 10 sandwiches all together.

The Count (25:22):
Well, of course.

Dr. Rosemarie Truglio (25:23):
And he made a mistake.

Elmo (25:25):
The Count?

The Count (25:25):
Hmm?

The Count (25:25):
Elmo thinks The Count made a little mistake.

The Count (25:31):
No mistake.

The Count (25:32):
Mm-hmm. Yeah.

Dr. Rosemarie Truglio (25:33):
And first time ever, did he make a mistake. And he fell apart.

The Count (25:38):
I must make sure that that never happens again. So I shall never count again.

Dr. Rosemarie Truglio (25:46):
And that’s an example of showing that, you know, you could get upset when you make a mistake, but what’s important is you gotta come back and you gotta come back to doing what you love. In his case, is counting and letting him know that it was an “oops.” But you learn that mistakes are OK. It’s OK to make a mistake and continue to do what you love.

The Count (26:13):
I must keep trying and you should, too.

Elmo (26:17):
Yeah!

The Count (26:17):
So come, let’s count the carrots together!

Elmo (26:18):
Oh, cool!

Bethany Lockhart Johnson (26:19):
And what a beautiful gift to show kiddos. Show that to kiddos, right? And to the adults. I wanna, you know, really acknowledge it, and say, “Hey look this, it’s OK.” And again, you’re giving them that language. That’s such a gift.

Dr. Rosemarie Truglio (26:34):
Thank you.

Dan Meyer (26:34):
We spend a lot of time wondering why other subjects don’t seem to suffer from this negative perception. And I think you’ve unlocked a lot of that. You’ve mentioned that there are issues that cut across different subject areas, but I think from my own experience and research and interviews, it seems that in ELA and the social sciences, there’s this aspect where you need to come up with a claim and “how are you seeing this?” And there are multiple defensible claims. And I love how you imported that generous pedagogy over into math with this example of a teacher who says, “You know what? It’s about the process here.” Disassociating answer and process.

Dr. Rosemarie Truglio (27:09):
And I think the other thing is like, when children are engaged in a project, for parents to point out: “You’re doing math!” Because they don’t realize that they’re doing math. Once again, math is so often equated solely with numbers and mathematical computations. So it was really interesting—the same is true for science. You know, when we’re talking to parents about the use of everyday—like, going to the supermarket or making dinner or bath time, there’s so much math and science in the everyday. And then when you point it out to them—”you’re doing math”—it’s like, “I’m doing math!” Like, you’re setting the table for a family of six: you’re doing math. That’s called one one-to-one correspondence. “I’m doing math: I’m setting the table.” Yeah, but you’re doing math. You can’t set the table because you have to know how many people are gonna be sitting at the table for dinner. You can’t follow a recipe without doing math. You can’t go shopping without doing math. There’s quantity; you gotta figure out how many peppers you gotta buy, or pounds. “I gotta get a bunch of potatoes and I gotta put ’em in the scale. And I have to get two pounds of potatoes.”

Bethany Lockhart Johnson (28:29):
So your book Ready for School: A Parent’s Guide to Playful Learning for Children Ages Two to Five. First, as a parent of a young toddler, I gotta say it’s such a tool; it’s such a resource. It’s very conversational. And I think about these ideas a lot, both in my work and, you know, just for fun. And yet, even if this wasn’t my chosen field, I still feel like it’s just so accessible. And I wanna flag something.

Dr. Rosemarie Truglio (29:01):
Thank you.

Bethany Lockhart Johnson (29:01):
Yeah, no. Thank YOU. . I wanna flag something that you said in the math chapter You were talking about the joy of math, and you said when it comes to our children, caregivers: “take pleasure in reading stories together, especially at bedtime, which in many households is a regular part of a child’s routine. But somehow the notion of introducing math concepts to our children seems daunting. In fact, some studies have shown that parents harbor a strong belief that while it’s important and pleasurable to support their child’s reading skills, it’s the responsibility of the schools to take care of teaching math.” And that quote, I highlighted it, I starred it! And I would love for you to say a little more about that, because you have given us already, like, a bounty of ideas that as caregivers we can do with our kiddos or the kiddos in our lives. And we’ve seen that even what they’re learning in school, it may not be the freeing, joyful math language that we hope our kiddos have access to.

Dr. Rosemarie Truglio (30:05):
Yeah, I’m glad you brought that up. Because a lot of our focus is on how children learn through playful experiences, and how they learn through play in particular. And there are so many playing, either a game or even playing ideas—like we talked about building, you know, a house for animals or building a fort. It’s just so filled with math. And I wish I could narrate for every young parent how I would hope that they would talk as they are co-engaged in this activity. And I think … we asked about, with the anxiety, the adults have to find the joy in math first. They have to see the math. That’s the problem. That’s why I hope that my book provides that. I want you to know that you are doing math and I want you to know that your child is what we call a mathematician—or in the science chapter, is a STEMist. Your child is already doing science, technology, engineering, and math. STEM is so integrated. So to acknowledge them—because babies are doing math! Babies know, they can distinguish between a small quantity and something that is a of a larger quantity and want the larger. Right? So, it’s natural for them. And they are taking it all in. I mean, the joy of watching a child just early counting: you know, one, two. And trying to then figure out the meaningfulness of two. It’s not three objects. There are actually two. And for a parent to see the joy in that I think is step one. And then to see the richness and how expansive math is, and that power of, oops, “I made a mistake, don’t freak out,” and then [not] say, “See, I’m not good at math,” but say, “Let me try again. I know I could figure this out.” Right? It’s all of that supportive language and supportive experiences that builds this mindset, a positive mindset. So that you hope that when you get into the higher grades, they’re not walking in and saying, “I can’t, I can’t do math.”

Dan Meyer (32:26):
Yeah. Super helpful. I think you point at one of the grownups—great powers in the world of kids, which is to label. To name things. And you know, you’ve talked about how grownups should ideally downplay some of their negative experiences with mathematics for the sake of the kid, but also to play up the positive stuff that they’re doing as mathematics. Like that right there, that’s math. I would love to know … you have an extremely loud megaphone to communicate messages about math and the world and everything through Sesame Street. One of the biggest that there is—and I just wonder if you could step out and imagine you had a magic wand to wave over the world in which students grow up, play and learn—what would you do like to help students have better associations or less math anxiety? And, you know, learn more about math itself?

Dr. Rosemarie Truglio (33:19):
If I had a magic wand, I would give everyone what we call a growth mindset that nothing is fixed and everything can be changed if you put the time and effort into the process, and enjoy the process. The joy of learning. I think, you know, it’s really sad. I don’t wanna be sad on your show. But when we were getting ready for the 50th anniversary, I was wondering, “What is gonna be the curriculum focus?” You know, we just came off of literacy and math literacy and social-emotional development. And we talked about the power of play. Playful learning. And building careers. Give children sophisticated play scenarios so that they could explore what they may wanna be when they grow up. Because there’s a concept: If I can see it, I can play it, I can be it. Right? So where are those portrayals? And it’s like, “What are we gonna do for the 50th?” And I had a convening of experts across all disciplines, and brought them into a room. And I said, you know, “What keeps you up at night? Like, what are you worried about?” Sort of like the State of the Union of Child Development. And this is where the sad part is. They talked about how that sense of joy, that sense of wonder, that sense of curiosity, that sense of flexible thinking and creative thinking, was disappearing in early childhood. Wow. If it’s disappearing in early childhood, we are in big, big trouble . ‘Cause I could see it disappearing later on, you know, as you advance in grade. But what do you mean, it’s disappearing in childhood? And then they talked about the fear of making mistakes. And that goes against—it’s the opposite of a growth mindset. And so we have to bring back that sense of joy, wonder, asking those why questions and embracing them. So it’s another problem parents have. They’re fine with the “why” questions until the “whys” become so difficult they don’t have the answers. And then they don’t want the “why” questions, because now they feel like they’re not smart enough to answer their child’s “why” questions. How do I flip that around to be much more positive and say, “You know, I don’t know! But let’s find out together. Let’s explore together; let’s experiment together.” That’s what I mean about the shift in the mindset, that growth mindset. We should not know all of the answers, but where’s the joy of, “Wow, I don’t know, let’s go find out together”? And that applies to math too. But you have to have that open mindset. You have to—you, as yourself, have to have that growth mindset.

Bethany Lockhart Johnson (36:20):
I love that magic wand. I want that magic wand! And I think what—like Dan said about this megaphone, this opportunity to reach so many young people, so many caregivers—what a gift! And I’m so grateful that you took time to be in the lounge with us, and that you have shared these ideas. Because truly, I think, like you said, it’s really our youngest learners, right? How can we create and cultivate these opportunities for our youngest learners to find the joy in mathematics and just in learning, right?

Dr. Rosemarie Truglio (36:54):
Yeah.

Bethany Lockhart Johnson (36:55):
So thank you. Thank you so much, Dr. Truglio. We are deeply grateful for your insight and for all the work you do. And we continue to invite the world of Sesame Street into our homes.

Dr. Rosemarie Truglio (37:08):
Thank you. Thank you for allowing us to come into your home, and for you to re-learn with your child as you’re watching Sesame Street. Because it’s very much a parenting show, as it is for a child-directed show, because we are blessed to have these wonderful human cast members who are the stand-ins for parents. And so we are often giving you the language for how to talk about and how to problem-solve together. So thank you.

Dan Meyer (37:43):
Thanks so much for listening to our conversation with Dr. Rosemarie Truglio, Senior Vice President of Curriculum and Content at Sesame Workshop.

Bethany Lockhart Johnson (37:51):
Dr. Truglio is also the author of Sesame Street Ready for School, A Parents Guide to Playful Learning for Children Ages Two to Five, and we’re gonna make sure we put a link to that in the show notes because it is really, really a rich resource. I’m diving in. I have so many ideas bookmarked that I wanna try out with my kiddo.

Dan Meyer (38:09):
Yeah, it’s really exciting to see—like, for a classroom educator, I just kinda assumed that a lot of math learning happens in the classroom context. That’s my lens. So yeah, I loved reading the book and seeing all the different opportunities for parents for just out there in the world, in front of your house, at the supermarket. All the different opportunities there are for mathematical thinking, and then to think about how to bring that into some of those routines and ideas into the classroom, into formal schooling.

Bethany Lockhart Johnson (38:35):
Exactly. Exactly. Like Dr. Truglio said, the caregivers’s disposition about mathematics matters so deeply. Your teachers’ dispositions about mathematics, their beliefs, the way that you hear people talking about math, that impacts our learners. That impacts—like, as a student, that impacts what you think is possible for yourself. So I love this, re-educating ourselves about what math can look like out in the world, in everyday conversations. I don’t know. I really, really appreciated this conversation with Dr. Truglio.

Dan Meyer (39:12):
Same. Yeah. We’d love to hear what you folks think about the work. the book, her ideas. Definitely get in touch with us. Subscribe to Math Teacher Lounge, wherever you get podcasts. And keep in touch with us on Facebook at Math Teacher Lounge Community, and on Twitter at MTL show.

Bethany Lockhart Johnson (39:27):
Also, if you haven’t already, please subscribe to Math Teacher Lounge wherever you get your podcast. And if you like what you’re hearing, please leave us a rating and a review. It’ll help more listeners find the show. And while you’re at it, let a friend know about this episode, because you enjoyed it; they might enjoy it. On our next episode, we’re gonna be chatting with Dr. Heidi Sabnani and taking a closer look at best practices for coaching teachers to reduce their own math anxiety.

Dr. Heidi Sabnani (39:56):
One of the teachers that I worked with had done her student teaching with a teacher who had math anxiety and who never taught math. And so she entered her teaching career never having taught math before or seeing it taught.

Dan Meyer (40:10):
Thanks again for listening, folks.

Bethany Lockhart Johnson (40:12):
Bye.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Dr. Rosemarie Truglio says about math

“We all have to work together, because even though we are the experts [on curriculum and education], the real experts are the children themselves.”

– Dr. Rosemarie Truglio

Senior Vice President of Curriculum and Content, Sesame Workshop

Meet the guest

Rosemarie T. Truglio, Ph.D. is the Senior Vice President of Curriculum and Content at Sesame Workshop. Dr. Truglio is responsible for the development of the interdisciplinary curriculum on which Sesame Street is based and oversees content development across platforms (e.g., television, publishing, toys, home video, and theme park activities).  She also oversees the curriculum development for all new show production, including  Bea’s Block, Mecha BuildersEsme & RoyHelpsters, and Ghostwriter. Dr. Truglio has written numerous articles in child and developmental psychology journals and presented her work at national and international conferences. Her current book is Ready for School! A Parent’s Guide to Playful Learning for Children Ages 2 to 5, published by Running Press (2019).

A person with short dark hair, wearing a dark blazer and white top, smiles at the camera against a blue background with graphic elements, evoking the inviting atmosphere of a math teacher lounge and highlighting useful math teacher resources.
A laptop displaying a Facebook group page for "Math Teacher Lounge Community," featuring profile photos, a group banner, and geometric shapes in the image background.

About Math Teacher Lounge

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Grade 6

Unit 1: Area and Surface Area

Amplify MathDesmos Math 6–A1
Unit 1: Area and Surface AreaUnit 1: Area and Surface Area
Unit 7: Positive and Negative Numbers
Lesson 1: The TangramUnit 1
Lesson 1: Shapes on a Plane
Lesson 2: Exploring the TangramUnit 1
Lesson 2: Letters
Sub-Unit 1 : Area of Special Polygons
Lesson 3: Tilting the PlaneUnit 1
Lesson 1: Shapes on a Plane
Lesson 4: Compositing and Rearranging to Determine AreaUnit 1
Lesson 2: Letters
Lesson 5: Reasoning to Determine AreaUnit 1
Lesson 2: Letters
Lesson 6: ParallelogramsUnit 1
Lesson 3: Exploring Parallelograms (Print available)
Lesson 4: Off the Grid
Lesson 7: Bases and Heights of ParallelogramsUnit 1
Lesson 3: Exploring Parallelograms (Print available)
Lesson 4: Off the Grid
Lesson 8: Bases and Heights of ParallelogramsUnit 1
Lesson 3: Exploring Parallelograms (Print available)
Lesson 4: Off the Grid
Lesson 9: From Parallelograms to TrianglesUnit 1
Lesson 3: Exploring Parallelograms (Print available)
Lesson 4: Off the Grid
Lesson 6: Triangles and Parallelograms
Lesson 10: Bases and Heights of TrianglesUnit 1
Lesson 4: Off the Grid
Lesson 6: Triangles and Parallelograms
Lesson 11: Formula for the Area of a TriangleUnit 1
Lesson 5: Exploring Triangles (Print available)
Lesson 12: From Triangles to TrapezoidsUnit 1
Lesson 4: Off the Grid
Lesson 6: Triangles and Parallelograms
Lesson 13: PolygonsUnit 1
Lesson 2: Letters
Lesson 8: Pile of Polygons Practice Day 1 (Print available)

Unit 7
Lesson 11: Polygon Maker
Sub-Unit 2: Nets and Surface Area
Lesson 14: What is Surface Area?Unit 1
Lesson 9: Renata’s Stickers
Lesson 15: Nets and Surface Area of Rectangular PrismsUnit 1
Lesson 10: Plenty of Polyhedra
Lesson 11:Nothing but Nets(Print available)
Lesson 12: Face Value
Lesson 13: Take It To Go (Print available)
Lesson 16: Nets and Surface Area of PrismsUnit 1
Lesson 12: Face Value
Lesson 13: Take It To Go (Print available)
Lesson 17: Constructing a RhombicuboctahedronUnit 1
Lesson 13: Take It To Go (Print available)
Lesson 18: Simplifying Expressions for Squares and CubesUnit 1
Lesson 11: Exponent Expressions (Print available)
Lesson 12: Squares and Cubes
Lesson 19: Simplifying Expressions Even More Using ExponentsUnit 1
Lesson 11: Exponent Expressions (Print available)
Lesson 20: Designing a Suspended Tent 

Unit 2: Introducing Ratios

Amplify MathDesmos Math 6–A1
Unit 2: Introducing RatiosUnit 2: Introducing Ratios
Lesson 1: Fermi Problems 
Sub-Unit 1: What are Ratios?
Lesson 2: Introducing Ratios and Ratio LanguageUnit 2
Lesson 1: Pizza Maker
Lesson 2: Ratio Rounds (Print available)
Lesson 3: Representing Ratios with DiagramsUnit 2
Lesson 1: Pizza Maker
Lesson 2: Ratio Rounds (Print available)
Lesson 3:Rice Ratios (Print available)
Lesson 4: A Recipe for Purple Oobleck 
Lesson 5: Kapa Dyes 
Sub-Unit 2:Equivalent Ratios
Lesson 6: Defining Equivalent RatiosUnit 2
Lesson 3: Rice Ratios (Print available)
Lesson 4: Fruit Lab (Print available)
Lesson 11: Community Life (Print available)
Practice Day 1 (Print available)
Lesson 7: Representing Equivalent Ratios with Tables 
Lesson 8: Reasoning with Multiplication and Division (optional) 
Lesson 9: Common Factors 
Lesson 10: Common Multiples 
Lesson 11: Navigating a Table of Equivalent RatiosUnit 2
Lesson 6: Product Prices (Print available)
Lesson 7: Mixing Paint, Part 1
Lesson 12: Tables and Double Number Line DiagramsUnit 2
Lesson 6: Product Prices (Print available)
Lesson 7: Mixing Paint, Part 1
Lesson 13: Tempo and Double Number LinesUnit 2
Lesson 5: Balancing Act
Lesson 6: Product Prices (Print available)
Sub-Unit 3: Solving Ratio Problems 
Lesson 14: Solving Equivalent RatiosUnit 2
Lesson 6: Product Prices (Print available)
Lesson 7: Mixing Paint, Part 1
Lesson 10: Balloons
Lesson 11: Community Life (Print available)
Lesson 15: Part-Part-Whole RatiosUnit 2
Lesson 12 Mixing Paint, Part 2
Lesson 13: City Planning
Lesson 16: Comparing Ratios 
Lesson 17: More Comparing and Solving 
Lesson 18: Measuring with Different-Sized Units 
Lesson 20: More Fermi Problems 

Unit 3: Rates and Percentages

Amplify MathDesmos Math 6–A1
Unit 3: Rates and PercentagesUnit 2: Introducing Ratios
Unit 3: Unit Rates and percentages
Lesson 1: Choosing Representation for Student CouncilLaunch Lesson
Sub-Unit 1: Rates
Lesson 2: How Much for One?Unit 3
Lesson 4: Model Trains
Lesson 3: Constant Speed  
Lesson 4: Comparing SpeedsUnit 2
Lesson 8: World Records (Print available) 

Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve
Lesson 6: Welcome to the Robot Factory
Lesson 5: Interpreting RatesUnit 3
Lesson 8: World Records (Print available) 

Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve
Lesson 6: Welcome to the Robot Factory
Lesson 6: Comparing Rates 
Lesson 7: Solving Rate ProblemsUnit 3
Lesson 7: More Soft Serve
Sub-Unit 2: Percentages
Lesson 8: What Are percentages?Unit 3
Lesson 8: Lucky Duckies
Lesson 9: Bicycle Goals
Lesson 9: Determining Percentages 
Lesson 10: Benchmark PercentagesUnit 3
Lesson 7: Lucky Duckies
Lesson 11: Finding This Percent of ThatUnit 3
Lesson 10: What’s Missing? (Print available)
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Lesson 13: A Country as a Village
Lesson 12: This Percent of What 
Lesson 13: Solving Percentage ProblemsUnit 3
Lesson: 10: What’s Missing (Print available)
Lesson: 11: Cost Breakdown
Lesson: 12: More Bicycle Goals
Lesson: 13: A Country as a Village
Lesson 14: If Our Class Were the World 
Lesson 15: Voting for a School Mascot 

Unit 4: Dividing Fractions

Amplify MathDesmos Math 6–A1
Lesson 1: Seeing Fractions
Sub-Unit 1: Interpreting Division Scenarios
Lesson 3: Relating Multiplication and Division 
Lesson 4: Size of Divisor and Size of QuotientUnit 4
Lesson 1: Cookie Cutter
Sub-Unit 2: Division with Fractions
Lesson 5: How Many GroupsUnit 4
Lesson 3: Flour Planner
Lesson 4: Flower Planters
Lesson 4: Garden Bricks (Print available) 
Lesson 6: Using Diagrams to Find the Number of GroupsUnit 4
Lesson 5: Garden Bricks (Print available)
Lesson 6: Fill the Gap
Lesson 7: Dividing with Common DenominatorsUnit 4
Lesson 6: Fill the Gap
Lesson 8: How Much in Each Group? (Part 1)Unit 4
Lesson 8: Potting Soil
Lesson 9: How Much in Each Group? (Part 2)Unit 4
Lesson 8: Potting Soil
Lesson 10: Dividing by Unit and Non-Unit FractionsUnit 4
Lesson 7: Break It Down
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 11: Using an Algorithm to Divide FractionsUnit 4
Lesson 9: Division Challenges Practice Day
Lesson 13: Fractional LengthsUnit 4
Lesson 12: Puzzling 
Lesson 14: Area with Fractional LengthsUnit 4
Lesson 9: Puzzling Area (Print available)
Lesson 15: Volume of PrismsUnit 4
Lesson 13: Volume Challenges (Print available)
Lesson 16: Fish Tanks Inside of Fish TanksUnit 4
Lesson 10: Swap Meet
Lesson 17: Now, Where Was That Bus?Unit 4
Lesson 10: Capstone

Unit 5: Arithmetic in Base Ten

Amplify MathDesmos Math 6–A1
Lesson 1: Precision and World Records 
Sub-Unit 1: Adding and Subtracting Decimals 
Lesson 2: Speaking of Decimals…Unit 5
Lesson 1: Dishing Out Decimals (Print available)
Lesson 3: Adding and Subtracting DecimalsUnit 5
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 4: X Games Medal ResultsUnit 5
Lesson 2: Decimal Diagrams
Sub-Unit 2: Multiplying Decimals
Lesson 5: Decimal Points in ProductsUnit 5
Lesson 5: Decimal Multiplication
Lesson 6: Methods for Multiplying DecimalsUnit 5
Lesson 5: Decimal Multiplication
Lesson 6: Multiplying with Areas
Lesson 7: Multiplication Methods (Print available)
Lesson 7: Using Diagrams to Represent MultiplicationUnit 5
Lesson 5: Decimal Multiplication
Lesson 6: Multiplying with Areas
Lesson 8: Calculating Products of DecimalsUnit 5
Lesson 6: Multiplying with Areas
Sub-Unit 3: Dividing Decimals
Lesson 9: Exploring Division 
Lesson 10: Using Long DivisionUnit 5
Lesson 8: Division Diagrams
Lesson 9: Long Division Launch (Print available)
Lesson 10: Return of the Long Division (Print available)
Lesson 11: Dividing Numbers That Result in DecimalsUnit 5
Lesson 9: Long Division Launch (Print available)
Lesson 10: Return of the Long Division (Print available)
Lesson 12: Using Related Expressions to Divide with Decimals 
Lesson 13: Dividing Multi-Digit DecimalsUnit 5
Lesson 9: Long Division Launch (Print available)
Lesson 10: Return of the Long Division (Print available)
Lesson 14: The So-called World’s Littlest Skyscraper

Unit 6: Expressions and Equations

Amplify MathDesmos Math 6–A1
Unit 6: Expressions and EquationsUnit 6: Expressions and Equations
Lesson 1: Detecting Counterfeit Coins
Sub-Unit 1: Expressions and Equations in One Variable
Lesson 2: Write Expressions Where Letters Stand for Numbers 
Lesson 3: Tape Diagrams and Equations 
Lesson 4: Truth and EquationsUnit 6
Lesson 1: Weight for It
Lesson 2: Five Equations (Print available)
Lesson 5: Staying in BalanceUnit 6
Lesson 1: Weight for It
Lesson 2: Five Equations (Print available)
Lesson 3: Hanging Around
Lesson 6: Staying in Balance with Variables 
Lesson 7: Practice Solving EquationsUnit 6
Lesson 3: Hanging Around
Lesson 4: Hanging It Up
Lesson 5: Swap and Solve (Print available)
Lesson 8: A New Way to Interpret a over bUnit 6
Lesson 4: Hanging It Up
Lesson 5: Swap and Solve (Print available)
Lesson 9: Revisiting Percentages
Sub-Unit 2: Equivalent Expressions
Lesson 10: Equal and Equivalent (Part 1)Unit 6
Lesson 1: Weight for It
Lesson 2: Five Equations (Print available)
Lesson 3: Hanging Around
Lesson 6: Vari-apples
Lesson 11: Equal and Equivalent (Part 2)Unit 6
Lesson 1: Weight for It
Lesson 2: Five Equations (Print available)
Lesson 3: Hanging Around
Lesson 6: Vari-apples
Lesson 12: The Distributive Property, Part 1Unit 6
Lesson 8: Products and Sums
Lesson 9: Products, Sums, and Differences (Print available)
Lesson 13: The Distributive Property, Part 2Unit 6
Lesson 8: Products and Sums
Lesson 9: Products, Sums, and Differences (Print available)
Lesson 14: Meaning of ExponentsUnit 6
Lesson 10: Powers
Lesson 11: Exponent Expressions (Print available)
Lesson 15: Evaluating Expressions with ExponentsUnit 6
Lesson 11: Exponent Expressions (Print available)
Lesson 12: Squares and Cubes
Lesson 16: Analyzing Exponential Expressions and EquationsUnit 6
Lesson 11: Exponent Expressions (Print available)
Lesson 12: Squares and Cubes
Sub-Unit 3: Relationships Between Quantities
Lesson 17: Two Related Quantities, Part 1Unit 6
Lesson 13: Turtles All the Way
Lesson 14: Representing Relationships
Lesson 15: Connecting Representations (Print available)
Lesson 18: Two Related Quantitites, Part 2Unit 6
Lesson 13: Turtles All the Way
Lesson 14: Representing Relationships
Lesson 15: Connecting Representations (Print available)
Lesson 19: Creating a Class Mobile 

Unit 7: Rational Numbers

Amplify MathDesmos Math 6–A1
Unit 7: Rational Numbers
Unit 1: Area and Surface Area
Unit 7: Positive and Negative Numbers
Lesson 1: How Far? Which Way?
Sub-unit 1: Negative Numbers and Absolute Value
Lesson 2: Positive and Negative NumbersUnit 7
Lesson 1: Can You Dig In
Lesson 2: Digging Deeper
Lesson 3: Points on the Number LineUnit 7
Lesson 2: Digging Deeper
Lesson 4: Comparing IntegersUnit 7
Lesson 3: Order in the Class (Print available)
Lesson 5: Comparing and Ordering Rational NumbersUnit 7 
Lesson 3: Order in the Class (Print available)
Lesson 6: Using Negative Numbers to Make Sense of Contexts>Unit 7
Lesson 4: Sub-Zero
Lesson 7: Absolute Value of NumbersUnit 7
Lesson 5: Distance on the Number Line
Lesson 8: Comparing Numbers and Distance from ZeroUnit 7
Lesson 5: Distance on the Number Line
Sub-Unit 2: Inequalities
Lesson 9: Writing Inequalities 
Lesson 10: Graphing Inequalities 
Lesson 11: Solutions to One or More InequalitiesUnit 7
Lesson 6: Tunnel Travel
Lesson 7: Comparing Weights
Lesson 8: Shira´s Solutions
Lesson 12: Interpreting InequalitiesUnit 7
Lesson 6: Tunnel Travel
Lesson 7: Comparing Weights
Lesson 8: Shira´s Solutions
Sub-Unit 3: The Coordinate Plane
Lesson 13: Extending the Coordinate Plane 
Lesson 14: Points on the Coordinate PlaneUnit 7
Lesson 9: Sand Dollar Search
Lesson 10: The A-maze-ing Coordinate Plane
Lesson 15: Interpreting Points on a Coordinate PlaneUnit 7
Lesson 9: Sand Dollar Search
Lesson 10: The A-maze-ing Coordinate Plane
Lesson 11: Polygon Maker
Lesson 16: Distances on a Coordinate PlaneUnit 7
Lesson 11: Polygon Maker
Lesson 12: Graph Telephone (Print available)
Lesson 17: Shapes on the Coordinate PlaneUnit 1
Lesson 1: Shapes on a Plane
Lesson 2: Letters
Lesson 5: Exploring Triangles (Print available)
Lesson 6: Triangles and Parallelograms

Unit 7
Lesson 3: Exploring Parallelograms (Print available)
Lesson 11: Polygon Maker
Lesson 12: Graph Telephone (Print available)
Lesson 18: Lost and Found Puzzles 
Lesson 19: Drawing on the Coordinate PlaneUnit 7
Lesson 11: Polygon Maker
Lesson 12: Graph Telephone (Print available)

Unit 8: Data Sets and Distributions

Amplify MathDesmos Math 6–A1
Unit 8: Data Sets and DistributionsUnit 8: Describing Data
Lesson 1: Plausible Variation or New Species?
Sub-Unit 1: Statistical Questions and Representing Data
Lesson 2: Statistical QuestionsUnit 8
Lesson 1: Screen Time
Lesson 2: Dot Plots
Lesson 3: Interpreting Dot PlotsUnit 8
Lesson 2: Dot Plots
Lesson 3: Minimum Wage (Print available)
Lesson 4: Lots More Dots
Lesson 4: USing Dot Plots to Answer Statistical QuestionsUnit 8
Lesson 2: Dot Plots
Lesson 3: Minimum Wage (Print available)
Lesson 4: Lots More Dots
Lesson 5: Interpreting HistogramsUnit 8
Lesson 5: The Plot Thickens
Lesson 6: DIY Histograms (Print available)
Lesson 6: Using Histograms to Answer Statistical QuestionsUnit 8
Lesson 5: The Plot Thickens
Lesson 6: DIY Histograms (Print available)
Lesson 7: Describing Distributions on HistogramsUnit 8
Lesson 5: The Plot Thickens
Lesson 6: DIY Histograms (Print available)
Sub-Unit 2: Measures of Center
Lesson 8: Mean as a Fair ShareUnit 8
Lesson 7: Snack Time
Lesson 9: Mean as a Balance PointUnit 8
Lesson 7: Snack Time
Lesson 10: MedianUnit 8
Lesson 11: Toy Cars
Lesson 12: In the News
Lesson 11: Comparing Mean and MedianUnit 8
Lesson 12: In the News
Sub-Unit 3: Measures of Variability
Lesson 12: Describing Variability 
Lesson 13: Variability and MAD 
Lesson 14: Variability and IQRUnit 8
Lesson 13: Pumpkin Patch
Lesson 15: Box PlotsUnit 8
Lesson 14: Car, Plane, Bus, or Train? (Print available)
Lesson 16: Comparing MAD and IQR 
Lesson 17: Asian Elephant Populations 

Grade 7

Unit 1: Scale Drawings

Amplify MathDesmos Math 6–A1
Unit 1: Scale DrawingsUnit 1: Scale Drawings
Unit 3: Measuring Circles
Unit 4: Proportional Relationships and Percentages
Lesson 1: Scale-y Shapes 
Sub-Unit 1: Scaled Copies 
Lesson 2: What are Scaled Copies?Unit 1
Lesson 1: Scaling Machines
Lesson 3: Corresponding Parts and Scale FactorsUnit 1
Lesson 2: Scaling Robots 
Unit 3
Lesson 1: Toothpicks
Lesson 4: Making Scaled CopiesUnit 1
Lesson 3: Make It Scale 
Unit 4
Lesson 3: Sticker Sizes
Lesson 5: The Size of the Scale FactorUnit 1
Lesson 4: Tiles
Lesson 6: Scaling and AreaUnit 1
Lesson 5: Tiles Practice Day 1 (Print available)
Sub-Unit 2: Scale Drawings 
Lesson 7: Scale DrawingsUnit 1
Lesson 6: Introducing Scale
Lesson 7: Will It Fit? (Print available)
Lesson 8: Creating Scale DrawingsUnit 1
Lesson 8: Scaling States
Lesson 9: Scaling Buildings
Lesson 10: Room Redesign (Print available)
Lesson 9: Scale Drawings and Maps 
Lesson 10: Changing Scale in Scale DrawingsUnit 1
Lesson 8: Scaling States
Lesson 9: Scaling Buildings
Lesson 10: Room Redesign (Print available)
Lesson 11: Scales without Units 
Lesson 12: Units in Scale DrawingsUnit 1
Lesson 8: Scaling States
Lesson 9: Scaling Buildings
Lesson 10: Room Redesign (Print available)Practice Day (Print available)
Lesson 13: Build Your Brand 

Unit 2: Introducing Proportional Relationships

Amplify MathDesmos Math 6–A1
Unit 2: Introducing Proportional RelationshipsUnit 2: Introducing Proportional Relationships
Unit 4: Proportional Relationships and Percentages
Lesson 1: Making Music 
Sub-Unit 1: Representing Proportional Relationships with Tables and Equations
Lesson 2: Introducing Proportional Relationships with TablesUnit 2
Lesson 2: Balloon Float
Lesson 3: Sugary Drinks (Print available)
Lesson 4: Robot Factory
Lesson 3: More About Constant of ProportionalityUnit 2
Lesson 3: Sugary Drinks (Print available)

Unit 4
Lesson 3: Sticker Sizes
Lesson 4: Comparing Relationships with TablesUnit 2
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available)
Lesson 7: All Kinds of Equations
Lesson 5: Proportional Relationships and EquationsUnit 2
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available)
Lesson 7: All Kinds of Equations
Lesson 6: Speed and Equations 
Lesson 7: Two Equations for Each RelationshipUnit 2
Lesson 4: Two and Two (Print available)
Lesson 5: Lesson 7: All Kinds of Equations
Lesson 8: Using Equations to Solve ProblemsUnit 2
Lesson 6: Two and Two (Print available)
Lesson 7: All Kinds of Equations
Lesson 9: Comparing Relationships with EquationsUnit 2
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available)
Lesson 7: All Kinds of Equations
Lesson 11: Four Representations (Print available)
Lesson 12: Water Efficiency
Lesson 10: Solving Problems About Proportional RelationshipsUnit 2
Lesson 12: Water Efficiency
Sub-Unit 2: Representing Proportional Relationships with Graphs 
Lesson 11: Introducing Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations
Lesson 12: Water Efficiency
Lesson 12: Interpreting Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations
Lesson 12: Water Efficiency
Lesson 13: Using Graphs to Compare RelationshipsUnit 2
Lesson 8: Dino Pops
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations
Lesson 12: Water Efficiency
Lesson 14: Two Graphs for Each RelationshipUnit 2
Lesson 8: Dino Pops
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations
Lesson 12: Water Efficiency
Lesson 15: Four Ways to Tell One Story (Part 1) 
Lesson 16: Four Ways to Tell One Story (Part 2) 
Lesson 17: Welcoming Committee 

Unit 3: Measuring Circles

Amplify MathDesmos Math 6–A1
Unit 3: Measuring CirclesUnit 3: Measuring Circles
Lesson 1: The Wandering Goat 
Sub-unit 1: Circumference of a Circle 
Lesson 2: Exploring CirclesUnit 3
Lesson 2: Is it a Circle?
Lesson 3: Measuring Around
Lesson 3: How Well Can You Measure? 
Lesson 4: Exploring CircumferenceUnit 3
Lesson 2: Is It a Circle?
Lesson 3: Measuring Around
Lesson 5: Understanding π 
Lesson 6: Applying CircumferenceUnit 3
Lesson 2: Is It a Circle?
Lesson 3: Measuring Around
Lesson 7: Circumference and Wheels 
Sub-Unit 2: Area of a Circle
Lesson 8: Exploring the Area of a CircleUnit 3
Lesson 5: Area Strategies
Lesson 6: Radius Squares (Print available)
Lesson 7: Why Pi?
Lesson 8: Area Challenges
Lesson 9: Circle vs. Square
Practice Day 2 (Print available)
Lesson 9: Relating Area to CircumferenceUnit 3
Lesson 5: Area Strategies
Lesson 6: Radius Squares (Print available)
Lesson 7: Why Pi?
Lesson 8: Area Challenges
Lesson 9: Circle vs. Square
Practice Day 2 (Print available)
Lesson 10: Applying Area to CirclesUnit 3
Lesson 6:Radius Squares (Print available)
Lesson 11: Distinguishing Circumference and AreaUnit 3
Lesson 7: Why Pi?
Lesson 12: Capturing Space 

Unit 4: Proportional Relationships and Percentages

Amplify MathDesmos Math 6–A1
Unit 4: PercentagesUnit 4: Proportional Relationships and Percentages
Lesson 1: (Re)Presenting the United States 
Lesson 2: Understanding Percentages and Decimals 
Lesson 3: Percent Increase and DecreaseUnit 4Lesson 4: More or Less
Lesson 4: Determining 100%Unit 4Lesson 6: 100% (Print available)
Lesson 5: Determining Percent ChangeUnit 4Lesson 7: Percent Machines
Lesson 6: Percent Increase and Decrease With EquationsUnit 4Lesson 5: All the Equations
Lesson 7: Using Equations to Solve Percent ProblemsUnit 4Lesson 5: All the Equations
Sub-Unit 2: Applying Percentages 
Lesson 8: Tax and TipUnit 4
Lesson 8: Tax and Tip
Lesson 9: Minimum Wage (Print available)
Lesson 10: Cost of College (Print available)
Lesson 11: Bookcase Builder
Lesson 12: Posing Percent Problems
Lesson 9: Percent ContextsUnit 4
Lesson 8: Tax and Tip
Lesson 9: Minimum Wage (Print available)
Lesson 10: Cost of College (Print available)
Lesson 11: Bookcase Builder
Lesson 12: Posing Percent Problems
Lesson 10: Determining the PercentageUnit 4
Lesson 4: More and Less
Lesson 11: Measurement ErrorUnit 4
Lesson 11: Bookcase Builder
Lesson 12: Error IntervalsUnit 4
Lesson 11: Bookcase Builder
Lesson 13: Writing Better Headlines 

Unit 5: Rational Number Arithmetic

Amplify MathDesmos Math 6–A1
Unit 5: Rational Number ArithmeticUnit 5: Rational Number Artithmetics
Lesson 1: Target: Zero 
Sub-Unit 1: Adding and Subtracting Rational Numbers 
Lesson 2: Interpreting Negative Numbers
Lesson 3: Changing TemperaturesUnit 5
Lesson 2: More Floats and Anchors
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available)
Lesson 4: Adding Rational Numbers 
Lesson 5: Money and Debts 
Lesson 6: Representing SubtractionUnit 5
Lesson 5: Number Puzzles
Lesson 7: Subtracting Rational Numbers (Part 1)Unit 5
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available)
Lesson 5: Number Puzzles
Lesson 10: Integer Puzzles
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)
Lesson 8: Subtracting Rational Numbers (Part 2)Unit 5
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available)
Lesson 5: Number Puzzles
Lesson 10: Integer Puzzles
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)
Lesson 9: Adding and Subtracting Rational NumbersUnit 5
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available)
Lesson 5: Number Puzzles
Lesson 10: Integer Puzzles
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)Practice Day 1 (Print available)
Sub-Unit 2: Multiplying and Dividing Rational Numbers 
Lesson 10: Position, Speed, and TimeUnit 5
Lesson 7: Back in Time
Lesson 11: Multiplying Rational NumbersUnit 5
Lesson 7: Back in Time
Lesson 12: Multiply!Unit 5
Lesson 7: Back in Time
Lesson 13: Dividing Rational NumbersUnit 5
Lesson 7: Speeding Turtles
Lesson 14: Negative Rates 
Sub-Unit 3: Four Operations with Rational Numbers 
Lesson 15: Expressions with Rational NumbersUnit 5
Lesson 9: Expressions (Print available)
Lesson 16: Say It With Decimals 
Lesson 17: Solving Problems with Rational NumbersLesson 11: Changing Temperatures
Lesson 12: Arctic Ice Sea (Print available)
Lesson 13: Solar Panels and More (Print available)
Lesson 18: Solving Equations With Rational Numbers 
Lesson 19: Representing Contexts With Equations 
Lesson 20: Summiting Everest 

Unit 6: Expressions, Equations, and Inequalities

Amplify MathDesmos Math 6–A1
Unit 6: Expressions, Equations, and InequalitiesUnit 2: Introducing Proportional Relationships
Unit 4: Proportional Relationships and Percentages
Unit 6: Expressions, Equations, and Inequalities
Lesson 1: Keeping the Balance 
Lesson 2: Balanced and UnbalancedUnit 6
Lesson 1: Toothpicks and Tiles
Lesson 2: Balanced and UnbalancedUnit 6
Lesson 1: Toothpicks and Tiles
Lesson 3: Reasoning About Solving Equations (Part 1)Unit 6
Lesson 2: Smudged Receipts
Lesson 4: Reasoning About Solving Equations (Part 2)Unit 6
Lesson 2: Smudged Receipts
Lesson 3: Equations
Lesson 4: Seeing Structure (Print available)
Lesson 5: Dealing with Negative NumbersUnit 6
Lesson 2: Smudged Receipts
Lesson 3: Equations
Lesson 4: Seeing Structure (Print available)
Lesson 5: Dealing with Negative NumbersUnit 6
Lesson 8: Factoring and Expanding (Print available)
Lesson 16: Shira the Sheep
Lesson 6: Two Ways to Solve One EquationUnit 6
Lesson 4: Seeing Struction (Print available)
Lesson 7: Practice Solving EquationsUnit 6
Lesson 2: Smudged Receipts
Lesson 3: Equations
Lesson 4: Seeing Structure (Print available)
Sub-Unit 2: Solving Real-World Problems Using Two-Step Equations 
Lesson 8: Reasoning With Tape DiagramsUnit 6
Lesson 2: Smudged Receipts
Lesson 9: Reasoning About Equations and Tape Diagrams (Part 1)Unit 6
Lesson 2: Smudged Receipts
Lesson 10: Reasoning About Equations and Tape Diagrams (Part 2)Unit 6
Lesson 2: Smudged Receipts
Lesson 11: Using Equations to Solve ProblemsUnit 6
Lesson 2: Smudged Receipts
Lesson 3: Equations
Lesson 4: Seeing Structure (Print available) 
Lesson 12: Solving Percent Problems in New WaysUnit 6
Lesson 4: Seeing Structure (Print available)

Unit 4
Lesson 7: Percent MachinesPractice Day 1 (Print available)
Practice Day 2 (Print available)
Sub-Unit 3: Inequalities 
Lesson 13: Reintroducing InequalitiesUnit 6
Lesson 1: Toothpicks and Tiles
Lesson 14: Solving InequalitiesUnit 6
Lesson 5: Balancing Moves
Lesson 6: Balancing Equations
Lesson 13: I Saw the Signs
Lesson 15: Finding Solutions to Inequalities in ContextUnit 6
Lesson 13: I Saw the Signs
Practice Day 1 (Print available)
Lesson 16: Efficiently Solving InequalitiesUnit 6
Lesson 10: Collect the Squares
Lesson 17: Interpreting InequalitiesUnit 6
Lesson 13: I Saw the Signs
Lesson 14: Unbalanced Hangers
Lesson 15: Budgeting (Print available)
Lesson 18: Modeling With Inequalities 
Sub-Unit 4: Equivalent Expressions 
Lesson 19: Subtraction in Equivalent Expressions 

Unit 7: Angles, Triangles, and Prisms

Amplify MathDesmos Math 6–A1
Unit 7: Angles, Triangles, and PrismsUnit 7: Angles, Triangles, and Prisms
Lesson 1: Shaping Up 
Sub-Unit 1: Angle Relationships 
Lesson 2: Relationships of AnglesUnit 7
Lesson 1: Pinwheels
Lesson 2: Friendly Angles
Lesson 3: Angle Diagrams
Lesson 3: Supplementary and Complementary Angles (Part 1) 
Lesson 4: Supplementary and Complementary Angles (Part 2) 
Lesson 5: Vertical AnglesUnit 7
Lesson 2: Friendly Angles
Lesson 3: Angle Diagrams
Lesson 4: Missing Measures (Print available) [Free lesson]
Lesson 6: Using Equations to Solve for Unknown AnglesUnit 7
Lesson 3: Angle Diagrams
Lesson 4: Missing Measures (Print available) [Free lesson]
Lesson 7: Like Clockwork 
Sub-Unit 2: Drawing Polygons with Given Conditions 
Lesson 8: Building Polygons (Part 1)Unit 7
Lesson 6: Is It Enough?
Lesson 9: Building Polygons (Part 2)Unit 7
Lesson 6: Is It Enough?
Lesson 10: Triangles with Three Common MeasuresUnit 7
Lesson 13: Popcorn Possibilities
Lesson 11: Drawing Triangles (Part 1)Unit 7
Lesson 5: Can You Build It? [Free lesson]
Lesson 6: Is It Enough?
Lesson 7: More Than One
Lesson 8: Can You Draw It? (Print available)
Practice Day 1 (Print available)
Lesson 12: Drawing Triangles (Part 2)Unit 7
Lesson 5: Can You Build It? [Free lesson]
Lesson 6: Is It Enough?
Lesson 7: More Than One
Lesson 8: Can You Draw It? (Print available)
Practice Day 1 (Print available)
Sub-Unit 3: Solid Geometry
Lesson 13: Slicing SolidsUnit 7
Lesson 9: Slicing Solids
Lesson 14: Volume of Right PrismsUnit 7
Lesson 10: Simple Prisms
Lesson 15: Decomposing Bases for AreasUnit 7
Lesson 11: More Complicated Prisms
Lesson 16: Surface Area of Right PrismsUnit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 12: Surface Area Strategies (Print available)
Lesson 17: Distinguishing Volume and Surface Area
Lesson 18: Applying Volume and Surface AreaUnit 7
Lesson 13: Popcorn Possibilities

Unit 8: Probability and Sampling

Amplify MathDesmos Math 6–A1
Unit 8: Probability and SamplingUnit 8: Probability and Sampling
Lesson 1: The Invention of Fairness 
Lesson 2: Chance Experiments 
Lesson 3: What are Probabilities?Unit 8
Lesson 1: How Likely? (Print available)
Lesson 2: Prob-bear-bilities [Free lesson
Lesson 3: Mystery Bag
Lesson 4: Estimating Probabilities Through Repeated ExperimentsUnit 8
Lesson 4: Spin Class
Lesson 5: Is It Fair?
Lesson 6: Fair Games
Lesson 5: Code Breaking (Part 1)
Lesson 6: Code Breaking (Part 2)
Sub-Unit 2: Probabilities of Multi-Step Events
Lesson 7: Keeping Track of All Possible OutcomesUnit 8
Lesson 4: Spin Class
Lesson 5: Is it Fair?
Lesson 6: Fair Games
Lesson 8: Experiments With Multi-Step Events  
Lesson 9: Simulating Multi-Step Events 
Lesson 10: Designing Simulations 
Sub-Unit 3:Sampling
Lesson 11: Comparing Two PopulationsUnit 8
Lesson 10: Crab Island
Lesson 11: Headlines
Lesson 12: Larger PopulationsUnit 8
Lesson 10: Crab Island
Lesson 11: Headlines
Lesson 13: What Makes a Good Sample?Unit 8
Lesson 10: Crab Island
Lesson 11: Headlines
Lesson 14: Sampling in a Fair WayUnit 8
Lesson 10: Crab Island
Lesson 11: Headlines
Lesson 15: Estimating Population Measures of CenterUnit 8
Lesson 9: Car, Bike, or Train?
Lesson 10: Crab Island
Lesson 11: Headlines
Lesson 12: Flower Power
Lesson 16: Estimating Population ProportionsUnit 8
Lesson 9: Car, Bike, or Train?
Lesson 10: Crab Island
Lesson 11: Headlines
Lesson 12: Flower Power
Lesson 17: Presentation of Findings 

Grade 8

Unit 1: Rigid Transformations and Congruence

Amplify MathDesmos Math 6–A1
Unit 1: Rigid Transformations and CongruenceUnit 1: Rigid Transformations and Congruence
Unit 3: Proportional and Linear Relationships
Lesson 1: Tessellations 
Sub-Unit 1: Rigid Transformations 
Lesson 2: Moving in the PlaneUnit 1
Lesson 1: Transformers
Lesson 3: Symmetry and Reflection 
Lesson 4: Grid MovesUnit 1
Lesson 3: Transformation Golf
Lesson 4: Moving Day (Print available)
Lesson 5: Getting Coordinated

Unit 3
Lesson 6: Translations
Lesson 5: Making the MovesUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day (Print available)
Lesson 5: Getting Coordinated
Lesson 6: Coordinate Moves (Part 1)Unit 1
Lesson 4: Moving Day (Print available)
Lesson 5: Getting Coordinated
Lesson 7: Coordinate Moves (Part 2)Unit 1
Lesson 4: Moving Day (Print available)
Lesson 5: Getting Coordinated
Lesson 6: Describing TransformationsUnit 1
Lesson 5: Getting Coordinated
Lesson 6: Connecting the Dots
Sub-Unit 2: Rigid Transformations and Congruence 
Lesson 9: No Bending or StretchingUnit 1
Lesson 7: No Bending, No Stretching
Lesson 10: What is the Same?Unit 1
Lesson 7: Are They the Same?
Lesson 9: Are They Congruent?
Lesson 11: Congruent PolygonsUnit 1
Lesson 7: Are They the Same?
Lesson 9: Are They Congruent?
Sub-Unit 4: Angles in a Triangle 
Lesson 13: Line Moves 
Lesson 14: Rotation Patterns 
Lesson 15: Alternate Interior AnglesUnit 1 
Lesson 11: Tearing It Up (Print available)
Lesson 16: Adding the Angles in a TriangleUnit 1
Lesson 11: Tearing It Up (Print available)
Lesson 17: Parallel Lines and the Angles in a TriangleUnit 1 
Lesson 10: Transforming Angles
Lesson 18: Creating a Border Pattern Using Transformations 

Unit 2: Dilations, Similarity, and Introducing Slope

Amplify MathDesmos Math 6–A1
Unit 2: Dilations and SimilarityUnit 2: Dilations and Similarity
Lesson 1: Projecting and Scaling 
Sub-Unit 1: Dilations
Lesson 2: Circular GridUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 3: Match My Dilation
Lesson 4: Dilations on a Plane
Lesson 3: Dilations on a Plane 
Lesson 4: Dilations on a Square GridUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 3: Match My Dilation
Lesson 4: Dilations on a Plane
Lesson 5: Dilations with CoordinatesUnit 2
Lesson 4: Dilations on a Plane
Sub-Unit 2: Similiarity
Lesson 6: SimilarityUnit 2
Lesson 5: Transformations Golf with Dilations
Lesson 6: Social Scavenger Hunt (Print available)
Lesson 7: Similar PolygonsUnit 2
Lesson 6: Social Scavenger Hunt (Print available)
Lesson 8: Similar TrianglesUnit 2
Lesson 7: Are Angles Enough?
Lesson 8: Shadows
Lesson 9: Ratios of Side Lengths in Similar Triangles
Lesson 12: Optical Illusions 

Unit 3: Linear Relationships

Amplify MathDesmos Math 6–A1
Unit 3: Proportional and Linear RelationshipsUnit 3: Proportional and Linear Relationships
Unit 4: Linear Equations and Linear Systems
Unit 5: Functions and Volume
Lesson 1: Visual Patterns 
Sub-Unit 1: Proportional Relationships 
Lesson 2: Proportional Relationships 
Lesson 3: Understanding Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Graphs of Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 2: Water Tank 

Unit 5
Lesson 4: Window Frames
Lesson 5: Representing Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials 
Unit 5
Lesson 4: Window Frames
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available)
Lesson 8: Charge! (Print available)
Lesson 6: Comparing Proportional RelationshipsUnit 3
Lesson 3: Posters
Sub-Unit 2: Linear Relationships
Lesson 7: Introduction to Linear RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Stacking Cups

Unit 5
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available)
Lesson 8: Charge! (Print available)
Lesson 8: Comparing Linear Relationships 
Lesson 9: More Linear RelationshipsUnit 5
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available)
Lesson 8: Charge! (Print available)
Lesson 10: Representations of Linear RelationshipsUnit 3
Lesson 5: Flags
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available)
Lesson 8: Charge! (Print available)
Lesson 11: Writing Equations for Lines Using Two Points 
Lesson 12: Translating mx + bUnit 3
Lesson 3: Posters
Lesson 6: Translations
Lesson 13: Slopes Don’t Have to be PositiveUnit 3
Lesson 5: Flags
Lesson 6: Translations
Lesson 7: Water Cooler
Lesson 8: Landing Planes
Lesson 10: Calculating SlopeUnit 3
Lesson 7: Water Cooler
Lesson 8: Landing Planes
Lesson 14: Writing Equations for Lines Using Two Points, Revisited 
Lesson 11: Equations of All Kinds of LinesUnit 3
Lesson 3: Posters
Lesson 4: Stacking Cups
Lesson 5: Flags
Lesson 6: Translations
Sub-Unit 3: Linear Equations 
Lesson 16: Solutions to Linear EquationsUnit 3
Lesson 3: Posters
Lesson 6: Translations
Lesson 10: Solutions

 Unit 4
Lesson 3: Balanced Moves
Lesson 4: More Balanced Moves (Print available)
Lesson 17: More Solutions to Linear EquationsUnit 3 
Lesson 4: Stacking Cups
Lesson 5: Flags
Lesson 6: Translations
Lesson 7: Water Cooler
Lesson 10: Solutions
Lesson 18: Coordinating Linear Relationships 
Lesson 19: Rogue Planes 

Unit 4: Linear Equations and Linear Systems

Amplify MathDesmos Math 6–A1
Unit 4: Linear Equations and Systems of Linear EquationsUnit 4: Linear Equations and Systems of Linear Equations
Lesson 1: Number PuzzlesUnit 4
Lesson 1: Number machines
Sub-Unit 1: Linear Equations in One Variable 
Lesson 2: Writing Expressions and Equations
Lesson 3: Keeping the BalanceUnit 4
Lesson 2: Keep It Balanced
Lesson 4: Balanced Moves (Part 1)Unit 4
Lesson 3: Balanced Moves
Lesson 5: Balanced Moves (Part 2)Unit 4
Lesson 4: More Balanced Moves (Print available)
Lesson 6: Solving Any Linear EquationsUnit 4
Lesson 4: More Balanced Moves (Print available)
Lesson 5: Equation Roundtable (Print available)
Lesson 6: Strategic Solving (Print available)
Lesson 7: How Many Solutions? (Part 1)Unit 4
Lesson 5: Equation Roundtable (Print available)
Lesson 8: How Many Solutions? (Part 2)Unit 4
Lesson 5: Equation Roundtable (Print available)
Lesson 9: Strategic Solving 
Lesson 10: When Are They the SameUnit 4
Lesson 8: When Are They the Same?
Sub-Unit 2: Systems of Linear Equations
Lesson 11: On or Off the Line?Unit 4
Lesson 9: On or Off the Line?
Lesson 12: On Both of the LinesUnit 4
Lesson 10: On Both Lines
Lesson 13: Systems of Linear EquationsUnit 4
Lesson 11: Make Them Balance
Lesson 14: Solving Systems of Equations (Part 1)Unit 4
Lesson 14: All, Some, or None? Part 2
Lesson 15: Solving Systems of Equations (Part 2)Unit 4
Lesson 12: All, Some, or None? Part 2
Lesson 16: Writing Systems of Linear EquationsUnit 4
Lesson 14: Strategic Solving, Part 2 (Print available)
Lesson 17: Pay Gaps 

Unit 5: Functions and Volume

Amplify MathDesmos Math 6–A1
Unit 5: Functions and VolumeUnit 2: Dilations, Similarity, and Introducing Slope
Unit 3:
Proportional and Linear Relationships
Unit 5:
Functions and Volume
Lesson 1: Pick a Pitch 
Sub-Unit 1: Representing and Interpreting Functions 
Lesson 2: Introduction to FunctionsUnit 5
Lesson 2: Guess My Rule
Lesson 3: Equations of FunctionsUnit 3
Lesson 4: Window Frames
Lesson 4: Graphs of Functions (Part 1)Unit 5
Lesson 3: Function or Not?
Lesson 5: Graphs of Functions (Part 2)Unit 5
Lesson 5: The Tortoise and the Hare
Lesson 6: Graphs of Functions (Part 3)Unit 5
Lesson 6: Graphing Stories
Lesson 7: Connecting Representations of FunctionsUnit 5
Lesson 7: Feel the Burn (Print available)Lesson 8: Charge! (Print available)
Lesson 8: Comparing Linear Functions 
Lesson 9: Modeling with Linear Functions 
Lesson 10: Piecewise Linear FunctionsUnit 5
Lesson 9: Piecing It Together
Sub-Unit 2: Cylinder, Cones, and Spheres 
Lesson 11: Filling Containers 
Lesson 12: The Volume of a CylinderUnit 5
Lesson 10: Volume LabLesson 11: Cylinders
Lesson 12: Scaling Cylinders
Lesson 13: Determining Dimensions of CylindersUnit 5
Lesson 14: Missing Dimensions (Print available)
Lesson 14: The Volume of a ConeUnit 5
Lesson 10: Volume LabLesson 13: Cones
Lesson 15: Determining Dimensions of ConesUnit 5
Lesson 12: Scaling Cylinders
Lesson 13: Cones
Lesson 14: Missing Dimensions (Print available)
Lesson 16: Estimating a Hemisphere 
Lesson 17: The Volume of a SphereUnit 5
Lesson 15: Spheres
Lesson 18: Cylinders, Cones and SpheresUnit 5
Lesson 15: Practice Day 2 (Print available)
Lesson 19: Scaling One Dimension 
Lesson 20: Scaling Two Dimensions 
Lesson 21: Packing Spheres 

Unit 6: Exponents and Scientific Notation

Amplify MathDesmos Math 6–A1
Unit 6: Exponents and Scientific NotationUnit 7: Exponents and Scienctific Notation
Lesson 1: Create a Sierpinski Triangle 
Sub-Unit 1: Exponent Rules 
Lesson 2: Reviewing ExponentsUnit 7
 Lesson 1: Circles
Lesson 2: Combining Exponents
Lesson 3: Multiplying PowersUnit 7 
Lesson 3: Power Pairs (Print available)
Lesson 4: Rewriting Powers
Lesson 4: Dividing PowersUnit 7 
Lesson 3: Power Pairs (Print available)
Lesson 4: Rewriting Powers
Lesson 5: Negative ExponentsUnit 7 
Lesson 5: Zero and Negative Exponents
Lesson 6: Powers of PowersUnit 7 
Lesson 3: Power Pairs (Print available)
Lesson 7: Different Bases, Same Exponent 
Lesson 8: Practice with Rational BasesUnit 7
Practice Day 1 (Print available)
Sub-Unit 2: Scientific Notation 
Lesson 9: Representing Large Numbers on the Number LineUnit 7
Lesson 8: Point Zapper
Lesson 10: Representing Small Numbers on the Number LineUnit 7
Lesson 8: Point Zapper
Lesson 11: Applications of Arthithmetic with Powers of 10Unit 7
Lesson 8: Point Zapper
Lesson 9: Use Your Powers
Lesson 12: Definition of Scientific NotationUnit 7
Lesson 10: Solar System
Lesson 11: Balance the Scale
Lesson 13: Star Power
Lesson 13: Multiplying, Dividing, and Estimating with Scientific NotationUnit 7
Lesson 11: Balance the Scale
Lesson 13: Star Power
Lesson 14: Adding and Subtracting with Scientific NotationUnit 7
Lesson 11: Balance the Scale
Lesson 12: City Lights
Lesson 13: Star Power
Lesson 15: Is a Smartphone Smart Enough to Go to the Moon? 

Unit 7: Irrationals and the Pythagorean Theorem

Practice Day 2 (Print available)

Amplify MathDesmos Math 6–A1
Unit 7: Irrationals and the Pythagorean TheoremUnit 8: The Pythagorean Theorem and Irrational Numbers
Lesson 1: Sliced Bread
Sub-Unit 1: Rational and Irrational Numbers
Lesson 2: The Square RootUnit 8
Lesson 2: From Squares to Roots
Lesson 3: The Ares of Squares and Their Side LengthsUnit 8
Lesson 1: Tilted Squares
Lesson 3: Between Squares
Lesson 4: Estimating Square RootsUnit 8
Lesson 3: Between Squares
Lesson 4: Root Down
Lesson 5: The Cube RootUnit 8
Lesson 5: Filling Cubes
Lesson 6: Rational and Irrational NumbersUnit 8
Lesson 14: Hit the Target
Lesson 7: Decimal Representations of Rational NumbersUnit 8
Lesson 12: Fractions to Decimals
Lesson 8: Converting Repeating Decimals Into FractionsUnit 8
Lesson 13: Decimals to Fractions
Sub-Unit 2: The Pythagorean Theorem
Lesson 9: Observing the Pythagorean TheoremUnit 8
Lesson 6: The Pythagorean Theorem
Lesson 10: Proving the Pythagorean TheoremUnit 8
Lesson 7: Pictures to Prove It
Lesson 11: Determining Unknown Side LengthsUnit 8
Lesson 8: Triangle-Tracing Turtle
Lesson 12: Converse of the Pythagorean TheoremUnit 8
Lesson 9: Make it Right
Lesson 13: Distances on the Coordinate Plane (Part 1)Unit 8
Lesson 11: Pond Hopper
Lesson 13: Distances on the Coordinate Plane (Part 1)Unit 8
Lesson 11: Pond Hopper
Lesson 14: Distances on the Coordinate Plane (Part 2)Unit 8
Lesson 11: Pond Hopper
Lesson 15: Applications of the Pythagorean TheoremUnit 8
Lesson 8: Triangle-Tracing Turtle
Lesson 10: Taco Truck
Lesson 16: Pythagorean Triples

Unit 8: Pythagorean Theorem and Irrational Numbers

Amplify MathDesmos Math 6–A1
Unit 8: Associations in DataUnit 6: Associations in Data
Lesson 1: Creating a Scatter PlotUnit 6
Lesson 1: Click Battle
Sub-Unit 1: Associations in Data
Lesson 2: Interpreting Points on a Scatter PlotUnit 6
Lesson 3: Robots
Lesson 3: Observing Patterns in a Scatter PlotUnit 6
Lesson 7: Scatter Plot City
Lesson 4: Fitting a Line to DataUnit 6
Lesson 4: Dapper Cats
Lesson 5: Fit Fights
Lesson 5: Using a Linear ModelUnit 6
Lesson 6: Interpreting Slopes
Lesson 6: Interpreting Slope and y-interceptUnit 6
Lesson 6: Interpreting Slopes
Lesson 7: Analyzing Bivariate DataUnit 6
Lesson 8: Animal Brains
Lesson 8: Looking for AssociationsUnit 6
Lesson 9: Tasty Fruit
Lesson 9: Using Data Displays to Find AssociationsUnit 6
Lesson 10: Finding Associations
Lesson 11: Federal Budgets

Grade 6

Unit 1: Numbers

GO Math!Desmos Math 6–A1
Module 4: Operations with Fractions
Lesson 4.1: Applying GCF and LCM to Fraction OperationsUnit 4
Lesson 6: Fill the Gap [Free lesson]
Lesson 7: Break It Down
Lesson 4.2: Dividing FractionsUnit 4
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 10: Swap Meet (Print available)
Practice Day
Lesson 4.3: Dividing Mixed NumbersUnit 4
Lesson 8: Potting Soil
Lesson 10: Swap Meet
Practice Day
Lesson 4.4: Solving Multistep Problems with Fractions and Mixed NumbersUnit 4
Lesson 11: Classroom Comparisons
Lesson 12: Puzzling Areas [Free lesson]
Lesson 13: Volume Challenges
Lesson 14: Planter Planner
Module 5: Operations with Decimals
Lesson 5.1: Dividing Whole NumbersUnit 5
Lesson 9: Long Division Launch
Lesson 10: Return of Long Division
Lesson 5.2: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals [Free lesson]
Lesson 2: Decimal Diagrams [Free lesson]
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 5.3: Multiplying DecimalsUnit 5
Lesson 5: Decimal Multiplication
Lesson 6: Multiplying With Areas
Lesson 7: Multiplication Methods
Lesson 5.4: Dividing DecimalsUnit 5
Lesson 8: Division Diagrams
Lesson 10: Return of Long Division
Lesson 11: Movie Time [Free lesson]
Lesson 5.5: Applying Operations with Rational NumbersUnit 5
Practice Day 1
Lesson 12: Budget Vehicles
Lesson 13: Grocery Prices

Unit 2: Number Operations

Module 4: Operations with Fractions
Lesson 4.1: Applying GCF and LCM to Fraction OperationsUnit 4
Lesson 6: Fill the Gap [Free lesson]
Lesson 7: Break It Down
Lesson 4.2: Dividing FractionsUnit 4
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 10: Swap Meet (Print available)
Practice Day (Print available)
Lesson 4.3: Dividing Mixed NumbersUnit 4
Lesson 8: Potting Soil
Lesson 10: Swap Meet (Print available)
Practice Day
Lesson 4.4: Solving Multistep Problems with Fractions and Mixed NumbersUnit 4
Lesson 11: Classroom Comparisons
Lesson 12: Puzzling Areas (Print available) [Free lesson]
Lesson 13: Volume Challenges
Lesson 14: Planter Planner (Print available)
Module 5: Operations with Decimals
Lesson 5.1: Dividing Whole NumbersUnit 5
Lesson 9: Long Division Launch (Print available)
Lesson 10: Return of Long Division
Lesson 5.2: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Lesson 2: Decimal Diagrams [Free lesson]
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 5.3: Multiplying DecimalsUnit 5
Lesson 5: Decimal Multiplication
Lesson 6: Multiplying With Areas
Lesson 7: Multiplication Methods (Print available)
Lesson 5.4: Dividing DecimalsUnit 5
Lesson 8: Division Diagrams
Lesson 10: Return of Long Division (Print available)
Lesson 11: Movie Time [Free lesson]
Lesson 5.5: Applying Operations with Rational NumbersUnit 5
Practice Day 1 (Print available)
Lesson 12: Budget Vehicles (Print available)
Lesson 13: Grocery Prices (Print available)

Unit 3: Proportionality, Ratios, and Rates

Module 6: Representing Ratios and Rates
Lesson 6.1: RatiosUnit 2
Lesson 1: Pizza Maker [Free lesson]
Lesson 2: Ratio Rounds (Print available)
Lesson 3: Rice Ratios (Print available)
Lesson 7:  Mixing Paint, Part 1
Lesson 12: Mixing Paint, Part 2
Lesson 6.2: Rates Unit 2
Lesson 8: World Records (Print available)
Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]
Lesson 6: Welcome to the Robot Factory (Print available)
Lesson 7: More Soft Serve
Lesson 13: A County as a Village
Lesson 6.3: Using Ratios and Rates to Solve ProblemsUnit 2
Lesson 4: Fruit Lab [Free lesson]
Lesson 5: Balancing Act
Lesson 6: Product Prices (Print available)
Lesson 9: Disaster Preparation [Free lesson]
Lesson 10: Balloons
Lesson 11: Community Life (Print available)
Lesson 13:City Planning
Lesson 14: Lunch Waste (Print available)
Module 7: Applying Ratios and Rates
Lesson 7.1: Ratios, Rates, Tables, and GraphsUnit 2
Lesson 4: Fruit Lab [Free lesson]
Lesson 6: Product Prices (Print available)
Lesson 9: Disaster Preparation [Free lesson]
Unit 3
Lesson 5: Soft Serve [Free lesson]
Lesson 6: Welcome to the Robot Factory
Lesson 7.2: Solving Problems with Proportions
Lesson 7.3: Converting Within Measurement SystemsUnit 3
Lesson 2: Counting Classrooms
Lesson 7.4: Converting Between Measurement SystemsUnit 3
Lesson 3: Pen Pals
Module 8:  Percents
Lesson 8.1 Understanding Percent.Unit 3
Lesson 8: Lucky Duckies [Free lesson]
Lesson 9: Bicycle Goals
Lesson 8.2: Percents, Fractions, and Decimals.Unit 3
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Lesson 13: A Country as a Village
Lesson 8.3: Solving Percent ProblemsUnit 3
Lesson 9: Bicycle Goals
Lesson 10: What’s Missing? (Print available)
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Lesson 13: A Country as a Village

Unit 4: Equivalent Expressions

Module 9: Generating Equivalent Numerical Expressions
Lesson 9.1: ExponentsUnit 6
Lesson 10: Powers
Lesson 11: Exponent Expressions (Print available)
Lesson 12: Squares and Cubes
Lesson 9.2: Prime Factorization
Lesson 9.3: Order of Operations
Module 10: Generating Equivalent Algebraic Expressions
Lesson 10.1: Modeling and Writing Expressions
Lesson 10.2: Evaluating Expressions
Unit 6
Lesson 6: Vari-apples
Lesson 8: Products and Sums [Free lesson]
Lesson 9: Products, Sums, and Differences (Print available)
Lesson 10.3: Generating Equivalent ExpressionsUnit 6
Lesson 7: Border Tiles
Lesson 8: Products and Sums [Free lesson]
Lesson 9: Products, Sums, and Differences (Print available)

Unit 5: Equations and Inequalities

Unit 6: Relationships in Geometry

Unit 7: Measurement and Data

Grade 7

Unit 1: The Number System

GO Math!Desmos Math 6–A1
Module 1:  Adding and Subtracting Integers
Lesson 1.1: Adding Integers With the Same Sign
Lesson 1.2: Adding Integers With Different Signs
Lesson 1.3: Subtracting Integers
Unit 5
Lesson 1: Floats and Anchors [Free lesson]
Lesson 2: More Floats and Anchors
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 5: Number Puzzles
Lesson 9: Expressions (Print available)
Lesson 10: Integer Puzzles [Free lesson]
Lesson 1.4:  Applying Addition and Subtraction of IntegersUnit 5
Lesson 11: Changing Temperatures
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)
Module 2: Multiplying and Dividing Integers
Lesson 2.1: Multiplying Integers Unit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 10: Integer Puzzles [Free lesson]
Lesson 2.2: Dividing IntegersUnit 5
Lesson 6: Floating in Groups
Lesson 10: Integer Puzzles [Free lesson]
Lesson 2.3: Applying Integer OperationsUnit 5
Lesson 8: Speeding Turtles
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)
Module 3:  Rational Numbers
Lesson 3.1: Rational Numbers and Decimals
Lesson 3.2: Adding Rational Numbers
Lesson 3.3: Subtracting Rational Numbers
Unit 5
Lesson 2: More Floats and Anchors
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 5: Number Puzzles
Lesson 3.4: Multiplying Rational NumbersUnit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 3.5: Dividing Rational Numbers Unit 5
Lesson 6: Floating in Groups
Lesson 3.6: Applying Rational Number OperationsUnit 5
Lesson 8: Speeding Turtles
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)

Unit 2: Ratios and Proportional Relationships

Module 4:  Rates and Proportionality
Lesson 4.1: Unit RatesUnit 2
Lesson 3: Sugary Drinks (Print available)
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available) [Free lesson]
Lesson 9: Gallon Challenge
Unit 4
Lesson 2: Peach Cobbler (Print available)
Lesson 3: Sticker Sizes
Lesson 4.2: Constant Rates of ChangeUnit 2
Lesson 1: Paint [Free lesson]
Lesson 2: Balloon Float
Lesson 3: Sugary Drinks (Print available)
Lesson 4:  Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available) [Free lesson]
Lesson 7: All Kinds of Equations
Lesson 4.3:  Proportional Relationships and GraphsUnit 2
Lesson 1: Paint [Free lesson]
Lesson 2: Balloon Float
Lesson 3: Sugary Drinks (Print available)
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available) [Free lesson]
Lesson 7: All Kinds of Equations
Lesson 8: DinoPops [Free lesson]
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations (Print available)
Lesson 12: Water Efficiency
Unit 4
Lesson 3: Sticker Sizes
Module 5:  Proportions and Percent
Lesson 5.1: Percent Increase and DecreaseUnit 4
Lesson 1: Mosaics [Free lesson]
Lesson 4: More and Less
Lesson 5: All the Equations
Lesson 7: Percent Machines [Free lesson]
Lesson 9: Minimum Wage (Print available)
Lesson 13: Decimal Deep Dive (Print available)
Lesson 5.2: Rewriting Percent ExpressionsUnit 4
Lesson 9: Minimum Wage
Lesson 5.3: Applications of PercentUnit 4
Lesson 6: 100% (Print available)
Lesson 8: Tax and Tip
Lesson 9: Minimum Wage (Print available)
Lesson 10: Cost of College (Print available)
Lesson 11: Bookcase Builder
Lesson 12: Posing Percent Problems [Free lesson]

Unit 3: Expressions, Equations, and Inequalities

Unit 4: Geometry

Module 8: Modeling Geometric Figures
Lesson 8.1: Similar Shapes and Scale DrawingsUnit 1
Lesson 1: Scaling Machines [Free lesson]
Lesson 2: Scaling Robots
Lesson 3: Make It Scale
Lesson 4: Scale Factor Challenges
Lesson 5: Tiles
Lesson 6: Introducing Scale
Lesson 7: Will It Fit? (Print available) [Free lesson]
Lesson 8: Scaling States (Print available)
Lesson 9: Scaling Buildings
Lesson 10: Room Redesign (Print available)
Unit 7
Lesson 5: Can You Build It? [Free lesson]
Lesson 6: Is It Enough?
Lesson 7: More Than One?
Lesson 8.2: Geometric DrawingsUnit 1
Lesson 6: Introducing Scale
Lesson 7: Will It Fit? (Print available) [Free lesson]
Lesson 8: Scaling States (Print available)
Lesson 9: Scaling Buildings
Lesson 10: Room Redesign (Print available)
Unit 7
Lesson 8:  Can You Draw It? (Print available)
Lesson 8.3: Cross SectionsUnit 7
Lesson 9: Slicing Solids
Lesson 8.4Angle RelationshipsUnit 7
Lesson 1: Pinwheels
Lesson 2: Friendly Angles [Free lesson]
Lesson 3: Angle Diagrams
Lesson 4: Missing Measures (Print available) [Free lesson]
Module 9:  Circumference, Area, and Volume
Lesson 9.1: CircumferenceUnit 3
Lesson 3: Measuring Around [Free lesson]
Lesson 9.2: Area of CirclesUnit 3
Lesson 5: Area Strategies
Lesson 6: Radius Squares (Print available)
Lesson 7: Why Pi?
Lesson 8: Area Challenges [Free lesson]
Lesson 9: Circle vs. Square
Lesson 9.3: Area of Composite FiguresUnit 3
Lesson 5: Area Strategies
Lesson 8: Area Challenges [Free lesson]
Lesson 9.4: Solving Surface Area ProblemsUnit 7
Lesson 12: Surface Area Strategies (Print available)
Lesson 13: Popcorn Possibilities
Lesson 9.5: Solving Volume ProblemsUnit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 13: Popcorn Possibilities

Unit 5: Statistics

Module 10: Random Samples and
Populations
Lesson 10.1: Populations and SamplesUnit 8
Lesson 10: Crab Island [Free lesson]
Lesson 11: Headlines
Lesson 12: Flower Power
Lesson 13: Plots and Samples
Lesson 14: School Newspaper (Print available)
Lesson 15: Asthma Rates (Print available)
Lesson 10.2: Making Inferences from a Random Sample
Lesson 10.3: Generating Random Samples
Unit 8
Lesson 13: Plots and Samples
Lesson 15: Asthma Rate (Print available)
Module 11: Analyzing and Comparing Data
Lesson 11.1: Comparing Data Displayed in Dot PlotsUnit 8
Lesson 14: School Newspaper (Print available)
Lesson 15: Asthma Rates (Print available)
Lesson 11.2: Comparing Data Displayed in Box PlotsUnit 8
Lesson 13: Plots and Samples
Lesson 15: Asthma Rates (Print available)
Lesson 11.3: Using Statistical Measures to Compare PopulationsUnit 8
Lesson 9: Car, Bike, or Train? (Print available)
Lesson 10: Crab Island [Free lesson]
Lesson 15: Asthma Rates (Print available)

Unit 6: Probability

Module 12: Experimental Probability
Lesson 12.1: ProbabilityUnit 8
Lesson 1: How Likely? (Print available) [Free lesson]
Lesson 2: Prob-bear-bilities [Free lesson]
Lesson 12.2: Experimental Probability of Simple EventsUnit 8
Lesson 3: Mystery Bag
Lesson 4: Spin Class
Lesson 5: Is It Fair?
Lesson 12.3: Experimental Probability of Compound EventsUnit 8
Lesson 7: Weather or Not
Lesson 12.4: Making Predictions with Experimental ProbabilityUnit 8
Lesson 3: Mystery Bag
Lesson 5: Is It Fair?
Module 13: Theoretical Probability and
Simulations
Lesson 13.1: Theoretical Probability of Simple EventsUnit 8
Lesson 1: How Likely? (Print available) [Free lesson]
Lesson 2: Prob-bear-bilities [Free lesson]
Lesson 13.2: Theoretical Probability of Compound EventsUnit 8
Lesson 6: Fair Games
Lesson 13.3: Making Predictions with Theoretical ProbabilityUnit 8
Lesson 8: Simulate It! (Print available)
Lesson 13.4: Using Technology to Conduct a SimulationUnit 8
Lesson 7: Weather or Not
Lesson 8: Simulate It! (Print available)

Grade 8

Unit 1: Real Numbers, Exponents, and Scientific Notation

GO Math!Desmos Math 6–A1
Module 1: Real Numbers
Lesson 1.1: Rational and Irrational Numbers
Lesson 1.2: Sets of Real Numbers
Unit 8
Lesson 12: Fractions to Decimals
Lesson 13: Decimals to Fractions
Lesson 14: Hit the Target
Lesson 1.3: Ordering Real NumbersUnit 8
Lesson 4: Root Down [Free lesson]
Module 2: Exponents and Scientific
Notation
Lesson 2.1: Integer ExponentsUnit 7
Lesson 1: Circles [Free lesson]
Lesson 2: Combining Exponents
Lesson 3: Power Pairs (Print available) [Free lesson]
Lesson 4: Rewriting Powers
Lesson 5: Zero and Negative Exponents
Lesson 6: Write a Rule (Print available)
Lesson 2.2: Scientific Notation with Positive Powers of 10Unit 7
Lesson 7: Scales and Weights
Lesson 8: Point Zapper
Lesson 9: Use Your Powers
Lesson 2.3: Scientific Notation with Negative Powers of 10Unit 7
Lesson 8: Point Zapper
Lesson 9: Use Your Powers
Lesson 2.4: Operations with Scientific NotationUnit 7
Lesson 10: Solar System [Free lesson]
Lesson 11: Balance the Scale [Free lesson]
Lesson 12: City Lights
Lesson 13: Star Power 

Unit 2: Proportional and Nonproportional Relationships and Functions

Module 3: Proportional Relationships
Lesson 3.1: Representing Proportional Relationships.Unit 3
Lesson 1: Turtle Time Trials [Free lesson]
Lesson 2: Water Tank
Lesson 3: Posters
Lesson 3.2: Rate of Change and SlopeUnit 2
Lesson 9: Water Slide
Lesson 10: Points on a Line
Unit 3
Lesson 4: Stacking Cups
Lesson 5: Flags [Free lesson]
Lesson 7: Water Cooler
Lesson 8: Landing Planes
Lesson 9: Coin Capture
Unit 5
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 3.3: Interpreting the Unit Rate as SlopeUnit 3
Lesson 2: Water Tank
Lesson 3: Posters
Module 4: Nonproportional Relationships
Lesson 4.1: Representing Linear Nonproportional RelationshipsUnit 3
Lesson 4: Stacking Cups
Lesson 5: Flags [Free lesson]
Lesson 4.2: Determining Slope and y-interceptUnit 3
Lesson 5: Flags [Free lesson]
Lesson 4.3: Graphing Linear Nonproportional Relationships using Slope and y-intercept.Unit 3
Lesson 4: Stacking Cups
Lesson 5: Flags [Free lesson]
Lesson 6: Translations
Lesson 9: Coin Capture
Lesson 4.4: Proportional and Nonproportional SituationsUnit 3
Lesson 1: Turtle Time Trials [Free lesson]
Module 5: Writing Linear Equations
Lesson 5.1: Writing Linear Equations from Situations and GraphsUnit 3
Lesson 5: Flags [Free lesson]Lesson 9: Coin Capture
Lesson 5.2: Writing Linear Equations from a Table
Lesson 5.3: Linear Relationships and Bivariate DataUnit 6
Lesson 1: Click Bait
Lesson 2: Wing Span
Lesson 3: Robots [Free lesson]
Lesson 4: Dapper Cats [Free lesson]
Lesson 5: Fit Fights [Free lesson]
Lesson 6: Interpreting Slopes
Lesson 7: Scatter Plot City
Lesson 8: Animal Brains
Module 6: Functions
Lesson 6.1: Identifying and Representing FunctionsUnit 5
Lesson 2: Guess My Rule [Free lesson]
Lesson 3: Function or Not?
Lesson 4: Window Frames
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 6.2: Describing FunctionsUnit 5
Lesson 3: Function or Not?
Lesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 8: Charge! (Print available)
Lesson 6.3: Comparing FunctionsUnit 5
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 6.4: Analyzing GraphsUnit 5
Lesson 1: Turtle Crossing [Free lesson]
Lesson 3: Function or Not?
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 8: Charge! (Print available)
Lesson 9: Piecing It Together

Unit 3: Solving Equations and Systems of Equations

Module 7:  Solving Linear Equations
Lesson 7.1: Equations with the Variable on Both SidesUnit 4
Lesson 2: Keep It Balanced
Lesson 3: Balanced Moves
Lesson 4: More Balanced Moves (Print available)
Lesson 5: Equation Roundtable (Print available) [Free lesson]
Lesson 6: Strategic Solving (Print available)
Lesson 7: All, Some, or None?
Lesson 8: When Are They the Same?
Lesson 7.2: Equations with Rational NumbersUnit 4
Lesson 6: Strategic Solving (Print available)
Lesson 7.3: Equations with the Distributive PropertyUnit 4
Lesson 4: More Balanced Moves (Print available)
Lesson 5: Equation Roundtable (Print available) [Free lesson]
Lesson 6: Strategic Solving (Print available)
Lesson 7: All, Some, or None?
Lesson 7.4: Equations with Many Solutions or No SolutionUnit 4
Lesson 7:  All, Some, or None?
Module 8:  Solving Systems of Linear Equations
Lesson 8.1: Solving Systems of Linear Equations by Graphing.Unit 4
Lesson 9: On or Off the Line?
Lesson 10: On Both Lines
Lesson 11: Make Them Balance [Free lesson]
Lesson 12: Line Zapper [Free lesson]
Lesson 8.2: Solving Systems by SubstitutionUnit 4
Lesson 13: All, Some, or None? Part 2
Lesson 14: Strategic Solving, Part 2 (Print available)
Lesson 8.3: Solving Systems by Elimination
Lesson 8.4: Solving Systems by Elimination with Multiplication
Lesson 8.5: Solving Special SystemsUnit 4
Lesson 13: All, Some, or None? Part 2

Unit 4: Transformational Geometry

Unit 5: Measurement Geometry

Module 11: Angle Relationships in Parallel Lines and Triangles
Lesson 11.1: Parallel Lines Cut by a Transversal.Unit 1
Lesson 10: Transforming Angles
Lesson 12: Puzzling It Out [Free lesson]
Lesson 11.2: Angle Theorems for TrianglesUnit 1
Lesson 11: Tearing It Up (Print available)
Lesson 12: Puzzling It Out [Free lesson]
Lesson 11.3: Angle-Angle SimilarityUnit 2
Lesson 3: Match My Dilation
Lesson 6: Social Scavenger Hunt (Print available) [Free lesson]
Lesson 7: Are Angles Enough?
Module 12: Pythagorean Theorem
Lesson 12.1: The Pythagorean TheoremUnit 8
Lesson 6: The Pythagorean Theorem
Lesson 7: Pictures to Prove It
Lesson 8: Triangle-Tracing Turtle [Free lesson]
Lesson 10: Taco Truck [Free lesson]
Lesson 12.2: Converse of the Pythagorean TheoremUnit 8
Lesson 9: Make It Right
Lesson 12.3: Distance Between Two PointsUnit 8
Lesson 11: Pond Hopper
Module 13: Volume
Lesson 13.1: Volume of CylindersUnit 5
Lesson 10: Volume Lab
Lesson 11: Cylinders [Free lesson]
Lesson 12: Scaling Cylinders
Lesson 14: Missing Dimensions (Print available)
Lesson 13.2: Volume of ConesUnit 5
Lesson 10: Volume Lab
Lesson 13: Cones [Free lesson]
Lesson 14: Missing Dimensions (Print available)
Lesson 13.3: Volume of SpheresUnit 5
Lesson 10: Volume Lab
Lesson 15: Spheres

Unit 6: Statistics

Module 14: Scatter Plots
Lesson 14.1: Scatter Plots and AssociationUnit 6
Lesson 1: Click Battle
Lesson 2: Wing Span
Lesson 3: Robots [Free lesson]
Lesson 6: Interpreting Slopes
Lesson 7: Scatter Plot City
Lesson 8: Animal Brains
Lesson 14.2: Trend Lines and PredictionsUnit 6
Lesson 4: Dapper Cats [Free lesson]
Lesson 5: Fit Fights [Free lesson]
Lesson 8: Animal Brains
Module 15: Two-Way Tables
Lesson 15.1: Two-Way Frequency TablesUnit 6
Lesson 9: Tasty Fruit
Lesson 15.2: Two-Way Relative Frequency TablesUnit 6
Lesson 10: Finding Associations [Free lesson]
Lesson 11: Federal Budgets

Strengthening critical thinking with a content-first approach: How Amplify CKLA is closing gaps in an elementary classroom

In my first-grade classroom, we’ve been studying early world civilizations. My students and I have pretended to hop in our time machines and travel back—first to ancient Mesopotamia, then to ancient Egypt. We’ve written our names on clay tablets in cuneiform and learned what it means for a religion to be polytheistic. We’ve compared and contrasted early farming systems and places of worship. As I prepared to read aloud another lesson a few days ago, I mentioned to the class that it was the eleventh lesson in the unit of study, prompting widened eyes and a chorus of “Already!?

I teach eighteen six- and seven-year olds in a Title I school, where half of the students are low-income, 75% are non-white, and over half are multilingual/English learners or speak another language at home. In my job, I’m honored to empower students who schools and society have not always served well. I became a teacher to help end that inequity—to close the knowledge gap and ensure that low-income, non-white, and immigrant children receive the tools they need to build a bright future. A growing body of research tells us that a strong base of content knowledge is essential for student growth and success in literacy. We also know that students who come from low-income backgrounds are less likely to come to school possessing the academic background knowledge of their peers, presumably because they have more limited opportunities to come across this type of knowledge at home. For this reason, I’m grateful that around a year and a half ago, my district adopted the knowledge-based literacy curriculum CKLA.

Scenes from a knowledge-based curriculum

What does knowledge-based learning look like in practice? Here’s one powerful example of how a knowledge-forward lesson helped my students succeed in practicing an important literacy skill. We were reading about Howard Carter, the British archaeologist who wanted to locate Tutenkhaman’s tomb. The lesson lends itself well to one of our state’s curriculum standards for the quarter: to make and confirm predictions about nonfiction text. Part one of the Read-Aloud ends on a cliffhanger: After a years-long search with no success, encountering dead ends and tomb robbers, Carter uncovers a hidden door marked with a royal seal.

“A prediction,” I explained, “is a careful guess about what you think might happen, based on the clues you already know. Think about what you know from the story, and predict what Carter might find behind the door.” We quickly reviewed some of the main points as I scribed on chart paper: Carter had been searching for Tutenkhaman’s tomb for six years, pharaohs were often buried with treasure or gold, the door they found was in the last possible place to look in the Valley of the Kings. I handed out papers I’d prepared with sentence frames for students to record or dictate their ideas. We hadn’t yet spent much time this year explicitly practicing prediction-making—in fact, I wondered how many of my students even knew what the word prediction meant—but I could see the wheels already turning behind most of my students’ eyes as they wiggled with excitement, envisioning gold, ghosts, King Tut’s tomb, or a pile of bones.

“Maybe nothing,” one student—a six-year-old who speaks primarily Spanish at home—told me with a shrug as I helped him write down his ideas. “Maybe the tomb robbers took it all.”

How to improve critical thinking—with knowledge

Even though my students might or might not have been familiar with the literacy skill of making and confirming predictions, the rich and meaty Read-Aloud set them up for success. It was rife with topics of interest to many a six- or seven-year-old—exploration, tomb robbers, golden treasure, mummies—which kept them engaged. And it included plenty of details through which they could actually draw a meaningful inference about what Carter might have found. I had to explain only once that a prediction should be based on information you already have—not a random guess—and every one of my eighteen students successfully generated a plausible idea.

This is the magic of a knowledge-based curriculum. It levels gaps in learning by generating a rich, shared base of content knowledge that supports the development of key literacy skills. My students were successful in plausibly guessing what might happen next in the story because they had a strong grasp of the information about Howard Carter. I might have chosen to teach an entire mini-lesson on prediction-making first and then asked my students to apply the skill to a less thoughtfully selected text, or to an independently selected book on their own, but if they weren’t already familiar with the topics it covered, my guess is that they would have been far less successful.

The curriculum standards for literacy in both the Common Core and Virginia (my school’s state) emphasize critical thinking skills and specific comprehension strategies, such as inferencing, over content knowledge. This is understandable: Students must learn to make meaning of a text in front of them, not just read the words on the page. But as Natalie Wexler puts it, “The ability to think critically…is inextricably linked to how much knowledge you have about the situation at hand” (The Knowledge Gap, 39). How could my students make a prediction about a future event in a text if they didn’t understand the textual clues they were given in the first place? Especially given that students from low-income homes are likely to possess less background knowledge about the curriculum they will encounter in school, a focus on teaching skills in isolation can contribute to a far-from-level playing field.

Teaching “comprehension skills” first and then expecting students to apply them is common practice in the method of literacy instruction frequently referred to as balanced literacy. Though the conversation about literacy is, thankfully, moving toward a research-backed approach focused on the Science of Reading, we still have a long way to go. While student teaching during my education master’s program less than three years ago, I was encouraged to teach mini-lessons on topics such as “finding the main idea” and “using topic headings to understand,” which students would then practice with independently selected texts. This approach is not supported by research as a best practice—and it assumes a shared base of cultural knowledge. In that way, it entrenches inequality by privileging students who may already possess more background knowledge, allowing our most vulnerable learners to fall even further behind.

By contrast, a knowledge-based curriculum creates that base together, giving all students a better chance at success. My own experience confirms the research. CKLA empowers my students to take ownership of their learning, expand their vocabularies, make connections, and passionately engage. I’m grateful to use an evidence-based curriculum designed to ensure that every student—including those too often left behind by our schools and other institutions—can learn to read.

More to explore

S5.E6. Why skepticism is essential to the Science of Reading, with Dr. Claude Goldenberg

To view this protected page, enter the password below:



S2-01: How teachers are really feeling this school year

science connections S02-01 Episode Cover

In this special solo episode, Eric Cross starts the season by sharing his personal journey as an educator, and how the difficulties of the last few years have shaped his mindset going into the upcoming school year. Eric also addresses teacher burnout and what inspires him to continue working as a classroom educator. Explore more from Science Connections by visiting our main page.

Download Transcript

Eric Cross (00:02):

Welcome to Science Connection, Season Two. As we begin the next season, I thought it would be a good time to share my story. As the host, I get to ask people questions about their journey, but I’ve actually never shared much about my own. So I’ve taken some of my most frequently asked questions to guests and asked them to myself. I hope you enjoy.

Eric Cross (00:23):

So the origin story question, I think really gets to the heart of why a person does what they do, because so much of who we are, especially as adults and teachers, is a result of experiences that we had in our lives when we were kids or in school with other teachers. And my life’s no different. I was born to a 19-year-old single mom. And when you’re a young boy growing up, especially with a young single mom, you often look to older men in different positions as kinda like a surrogate or like a mentor. And you may not even tell them that they are that to you. You kind of keep it close to the chest. And that’s what I did growing up. One of the ones that really stood out to me is, in seventh grade, I went to a middle school here in San Diego that was called Keiller Middle School. And we were a magnet program that specialized in science. And they had this program that brought professors from the local universities and they did this high-level enrichment. They would even take us to the college campus and we would work in these labs as seventh graders. It was amazing. And one of the people there, his name was Dr. Tress, and he was a professor. And Dr. Tress took a liking to me. I reminded him of his son. We were doing this great embryology experiment. We would take purple sea urchins. And we would inject them with potassium chloride, which would cause them to spawn. And we would fertilize these eggs, and then we would run different experiments using them. And these were things that I had never done before. I had always loved science. I’d always loved tinkering and building things. But this was my introduction, really, to high-level biology and to higher levels of education. I didn’t—I didn’t have many figures like that in my life growing up. I mean, I’m a first-generation, you know, high school, college graduate. Many of these are first generations for me. So, this was a new experience. And so Dr. Tress really unlocked a core memory and was one of my first mentors, as far as academics are concerned. And during my seventh-grade year, I entered the science fair and won first place, which was a huge deal. They took us out to Balboa Park. We got to miss school for a week. We got to go to all the museums for free. It was the best. And I think at that point in time, it really solidified something in me that would lay dormant until later on in my adult life. High school, I was really fortunate: the high school I went to was Morse High School, not too far from Keiller, and they had an aeronautics program. So I was able to enroll in that aeronautics program. And I learned how to fly before I learned how to drive. And I had this great instructor named Mr. Klon, who was this like 6′ 4″, 250-pound hippie guy. And he—we would get in the plane and we would have these like philosophical conversations. And through that, especially looking back now as a teacher, I realized that he was making connections with me and investing into who I was as a person. And it was something that I so needed at the time. Because at home I didn’t have that. You know, my safe place, a lot of time, was school. It was my only structure. It was where I knew I would get encouragement. It was where I knew things were reliable and consistent. For a lot of people, and a lot of kids, their home life isn’t like that. School was that for me. So Mr. Klon, I mean, he was this authentic, you know, consistent person in my life and made a huge difference at this time.

Eric Cross (03:23):

After I graduated high school, I left home just to get away from a difficult environment. And I was homeless for a little while and that was a huge moment in my life. And around that time, an aunt found out and she said, “You’re gonna come stay with us.” And this was like this three-year process of me living with them in this, like, functional family that ate dinner together. And they went to the zoo. They had family passes. And they took family photos at Christmastime. This was all weird stuff. Like, I didn’t know—I didn’t know who did these things. It was—I felt like a puppy that like lived in a home that was like…it was a home that was just always kind of like violent or like just really toxic. And then it gets put into a healthy home and doesn’t know how to act. That’s how it felt. And this was around like 19, 20 years old. During that time I started putting myself through school. So I went to community college and I was broke as a joke. And so I couldn’t afford the textbooks while I was going. So I would just go to the bookstore, the Barnes and Noble bookstore in Mira Mesa here in San Diego. And I would stay there all night using the textbooks or using the books there for doing my work. And then I would just put the books back on the shelves. Because let’s just face it. Textbooks are expensive, brother wasn’t trying to pay for all that. So I really had to earn that time. So I was working full-time. I was going to school. And, eventually I got a job in working in finance with a really great friend who mentored me during my younger twenties. And I didn’t wanna be broke and finance made sense.

Eric Cross (04:44):

And so I did that for a little while, until I got to a point in my career where I was watching an episode of The Office, the UK version, the Ricky Gervais version, and a character said, “I’d rather be at the bottom of a ladder I want to climb than halfway up one I don’t.” And I realized, working in finance, that I was halfway up a ladder I never wanted to climb. So I wanted to move into something that, if I was gonna spend eight hours a day or 10 hours a day doing something, I wanted it to be something that actually filled me up inside. And this is how I got into teaching. So I had always been working with young people, specifically 12- to 18-year-olds, like a non-profit or volunteering, mentoring, after-school programs. And I’ve always managed to rationalize my job in the finance world as meaningful because it let me do the real work that fulfilled me. So the real work was working with the kids. But my day job, my, like, Clark Kent-type job, was just, you know, doing the finance thing of like helping people that have a lot of money make more money. Which at the end of my life, I look back and I said, “That’s not what I want my legacy to be.”

Eric Cross (05:43):

And when the finance crash happened in 2008, that’s when I think I started looking back on it and said, “If I’m gonna spend all my time doing something and spending 40 or 60 or 80 hours of my day of my week doing things, I want it to matter. And that’s when I decided to pivot and leave that field and go and get my master’s in education and get my teaching credential, teaching science specifically. Now, one of the questions we get asked a lot and I’ve been asked is, is “How has teaching changed as a result of the pandemic?” And I feel like this could be several podcasts in and of itself, and it’s also regional, because everybody’s experienced it differently, And we’re still experiencing it! That’s the crazy thing! It’s like, it’s not over, we’re still in it. And some places have innovated and pivoted and some places just did what they needed to and they are trying to go back to business as usual. But if anything has happened, the pandemic revealed how much more, how much schools are more than places of just content learning. For many students it’s where they have their only community, their structure, their emotional wellness. They get regular meals, access to tech, and adults that care about them that are outside of their family. The schools are so much more than that. I mean, my school, they were a place, like a hub, that was giving out food every single day during the pandemic to families that would kind of drive by. So for a lot of schools, they became places like that. It also…the pandemic revealed the intensity of the educator workload. I mean, being able to manage your family, having the capacity, to be a content expert, you need to be a counselor, a trauma-care specialist, a coach, an encourager, a tech expert.

Eric Cross (07:23):

I mean, the term mental health is now more common and starting to become prioritized. Now we’re focusing so much more on the whole child. And we know from research that how a child feels about themselves and their safety and their security impacts their ability to learn. So the more comfortable and safe a student feels in the classroom with teachers and with friends, the better they’re gonna be able to learn. And ultimately the higher they’re gonna be able to achieve. You can’t, you can’t have one without the other. In addition, I think less teachers, see themselves teaching into retirement. I think that’s a big thing. I read these articles about teacher shortages and I think the reality is it’s actually teacher exodus. It’s teachers leaving. And that’s been really difficult. I’ve had many friends who’ve left for the private sector. And I get it, especially if you’re one that has—if you’re the first in your family to graduate from college, with a STEM degree, to them taking a teaching position can mean walking away from a salary in the private sector that pays two or three times more.

Eric Cross (08:23):

And in many places around the country, in order to be a teacher and maintain a median standard of living, you need either dual income, multiple jobs, or a multi-generational household. For a lot of people it just doesn’t make sense. And even right now, today, as I’m recording this, I’m reading articles and getting text messages…and I received a text message three days ago from a teacher that said, “My goal this year is to just not resign.” And that’s where a lot of teachers are feeling right now: isolated, challenged, and under-appreciated. And Plato said, “What’s honored in a country is cultivated there.” And I’ve been looking at how teachers are honored and one of the ways is just, like, practical. Like, look, I gotta pay my bills. You know, love the Starbucks gift card. Love the CPK, the gift card. The cards, all those other things…but brother got a car payment. And at the end of the day, if we care about our kids, we need to take care of the people that take care of them. And there’s very practical ways for that to happen. And everybody in different sectors around the country is dealing with that in different ways. I think the pandemic also revealed, now the public can see how our kids don’t receive the same quality of education. And once you’re aware of that, you can’t put the genie back in the bottle. So once you see on Zoom or once you see in a meeting, or once you see on the news, that students in different areas, whether it’s the rural South or a suburb in Seattle, are not getting equitable educations, well, ultimately that impacts all of us. Now. It’s not all doom and gloom. Good things have come from, as a result of, the pandemic. Many schools have made progress towards narrowing the technology gap, ’cause they had to! ‘Cause you can’t do Zoom and you can’t do Google Meet and all that stuff with a packet! You gotta get those Chromebooks. And Chromebooks and the internet and access to tech is not a new thing. It’s been out for a long time. The technology gap is not a new thing. It’s been written about extensively, but all of a sudden districts and schools started figuring out how to close that gap. And that’s awesome. We didn’t want a pandemic to be the catalyst for that to happen. But at the end of the day, we started closing it. A lot of schools did an amazing job and districts did an amazing job with deploying the hardware, sending out buses with wifi, putting lessons and videos on USB sticks and dropping them off to parents who live in sparsely populated areas. I mean, there were so many stories that I’ve heard about schools and teachers just doing amazing things, going above and beyond what they needed to on behalf of kids.

Eric Cross (10:51):

I think in addition to that, there’s also been students and families are now having more options to personalize their learning. So we have this in-person model, we have this Zoom or kind of online model, and this hybrid model, and it hasn’t all been perfect, you know, at all. But some families have come out and said, you know what actually doing this hybrid model is better for my son or better for my daughter or better for my student, because they’re able to get the socialization, but also able to focus better at home than they are in a classroom of 36. And that’s legitimate. You know, we talk about personalized learning, but it’s not exactly personalized when everybody has to wake up at the same time, same schedule, go to the same, the same classroom of, you know, up to 40 kids, and do the same lesson. I mean, we have to be honest about our limitations with personalizing learning for students. And when we can provide more options and we give teachers the infrastructure to be able to use different platforms, then we’re able to personalize learning a lot more.

Eric Cross (11:51):

There’s also been an emphasis on the whole-child wellness. I think the spotlight on mental well-being heavily impacts their academic success, but counseling teams, social workers, school psychologists—I think more than ever we’ve realized the value that they bring to the schools. And unfortunately many of them have caseloads of 200 students or more. And they’re seeing students most often that are in crisis. And especially after the pandemic, we’re realizing how valuable they are and how much we need to, one, honor them and give them the support that they need, and also recruit more. Because as we start recognizing how our brains are impacted by the things that we’re dealing with, we’re also gonna see how that’s gonna impact our students’ performance. And we need the specialists in those positions to be able to support our kids. I think, last, I think more innovation and lesson design and how we assess students. And so we’ve been talking about in education just kind of critiquing: how do we assess what a student knows? How do we make what a student actually does at school relevant to real life? I mean, so many times I have students who’ve graduated that are like, “I feel like the things I learned in school, like, they’re not always transferable to real life. It helped me on a test, but like, I don’t know how to do my taxes.” Or “I memorized these facts, but I don’t really apply it in my job.” Or “The facts that I learned I could have actually learned on the fly in my job. I wish I would’ve actually focused on the skills or had an earlier opportunity to get some experience because when I’m trying to apply for a job, <laugh> they ask for experience and I’m 22 years old.”

Eric Cross (13:28):

And so all these things kind of come up. And so I think there’s been some great conversations around “how do we rethink what education looks like?” And there’s different pockets around the country that have been doing that, I think, really well. And I think it’s important for us as teachers to stay connected to those people who are kind of pushing the boundaries and thinking outside the box, because when we get siloed, it’s really easy to get calcified and cynical. I get it. And it impacts me too. But when we’re around those people who have those fresh ideas, who are really pushing the limits, it inspires us. And that’s something I think during the pandemic that I’m grateful that I was intentional about, is staying connected with other teachers. There’s a big question; Why do you continue your work in the classroom and what keeps you motivated? And I was thinking really hard about this question, because depending on <laugh>, depending on my day, I feel like my answer’s gonna be a little bit different. So I’ve had to step back from this 30-foot, thousand-foot perspective and answer the question. And my answer is this: I think because I still feel like I can be effective to influence positive change in my classroom with my students and within the larger education system as a whole. I think if I lost either of those two, then I’d rethink my profession. Look, I’m an innovator. I like asking “why” questions and things like that. And I’m not always the most popular person when you do that. But education is like just a huge ship. It doesn’t pivot on a dime. And asking why questions and pushing for change on behalf of kids isn’t easy, fun, or glamorous, but it’s it’s necessary. And I feel like over the last few years, I’ve been able to see these kind of glimmers of a trajectory change, at least where I am locally. And that’s something that has given me a lot of hope. I’m very fortunate to be connected to educators and people in leadership that are really about making a difference beyond just kind of the cliched platitudes. They actually wanna make systemic change, in a way that’s positive. And that’s been really helpful for me. So as long as I feel like I’m useful in the classroom for students, and as long as I feel like I’m bringing, I think change, on behalf of teachers and students and administrators and our community in a way that moves the ball down the field, that’s what keeps me motivated. And what I like to ask teachers when I close in the podcast is. “What teacher or teachers have inspired you?”

Eric Cross (15:54):

And for me, I think it would start off with the teachers who cared about me when they didn’t have to, in elementary school all the way through college. And there are numerous teachers. My science-teacher community of practice. For the last two years, I’ve been fortunate to spend every month, once a month, meeting with just a core group of science teachers that really care about some of the things that we are impacted by in the classroom. And when the pandemic was going on, we still met regularly. And because we’re not all teaching in the same place, we kind of were able to bring different perspectives to the table. I think the current classroom teachers and former classroom teachers that I have in my community really inspire me. The ones who are dedicated to opening doors for students. The graduate students that I teach at the University of San Diego, they keep me fresh. I love leaving teaching my 12- and 13-year-olds, and then driving down the street to the university and teaching 20somethings who are all about to be in the classroom. They come with new ideas, they’re asking questions, and I get to actually share things that I just did three hours ago. I think that’s one thing that continues to inspire me. And it’s one of the reasons why I love teaching at the University of San Diego. Their energy and enthusiasm is super-refreshing. And then all the teachers that are willing to take risks and fail forward, to try things different, to ask hard questions, to push the envelope. Teaching’s hard. It’s easy to point out the problems in education as a whole. But after we do that, it’s important to figure out the practical ways we can make the changes that we wanna see.

Eric Cross (17:23):

Now, that’s to say that if you have the capacity for it and the resources and the support. Some of us, we don’t. Some of us, we are on an island, and that’s a really, really difficult place to be, especially when you have family and kids to take care of. And you have to make decisions on what’s best for you and for your own students. We do this work on behalf of kids. And it’s one of the most honorable services a person can provide to our community. But one area for growth that I think we have kind of as a society, is teachers spend their lives, daily, on behalf of the future of our country. For other people’s children. They fall asleep at night worrying about other people’s kids. They spend their own money to create opportunities and experiences that students might not otherwise have. And it’s important that we collectively, and I know I’m preaching the choir when I say this, but this is one of my messages, is that we honor them in turn. We create programs that allow them to be able to afford housing. We create opportunities for them to be able to generate wealth. We create ways for them to be able to find rest, to get connection. And then internally we create systems where they can just work on themselves, fill themselves, get trained, and be whole, so they can bring their best self to the kids in front of them. That’s one of my personal platforms. It’s something that I think is vital. We gotta take care of the people that take care of our kids. So there’s a saying that says, “It’s better to light a candle than to curse the darkness.” And it takes one person to blow out a candle, but one candle can light thousands of other candles, without diminishing its own light. And that’s what we have to be. So my encouragement, teachers, as you’re going into this new school year, and you’re thinking about what’s going on, you’re thinking about all the challenges—and they’re there, and they’re real, and trust me, it’s not like some Pollyanna, like, “Hey, just be positive!” mindset and everything’s gonna be great—no, no, no, no, no. It’s not that. But my encouragement…if I can tell you one thing that’s helped me more than anything else, it’s being connected to other people who are candle-lighters. Because there are a lot of places that are gonna blow out the candle. It could be the staff lounge. It could be Twitter, it could be Reddit. It could be Instagram. It could be TikTok. It could be, you know, anybody. Someone next door to you. There’s a lot of folks that are gonna be willing to point out and say, “Look, this is what’s wrong.” But find the helpers. Find the people that are candle-lighters. And stay connected with them. Find that community. I can tell you for me, that’s been the thing that’s been able to help me sojourn through all of this—I couldn’t do this by myself—is being able to share my story with other teachers and knowing that I’m doing this work alongside of other folks who are doing this work, and I can share my story with them and listen to their stories, is something that’s been able to fill my cup. And so I hope I can do the same for you and for other people listening to other people I come in contact with.

Eric Cross (20:08):

Teachers, I wish you a great school year. Hang in there. Be those candle-lighters and bring your best self on behalf of the students. Thanks so much for listening. Now, we wanna hear more about you. If you have any stories you wanna share about the classroom, please email stem@amplify.com. That’s STEM at amplifycom.wpengine.com. And make sure to click subscribe wherever you listen to podcasts. And join our Facebook group, Science Connections: The Community. Until next time.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Eric Cross says about science

“We do this work on behalf of kids, and it’s one of the most honorable services a person can provide to our community.”

– Eric Cross

K–8 Science teacher, Host of Science Connections: The Podcast

Meet the guest

Eric Cross is a 7th grade science/technology teacher, grade level lead, and digital learning innovator for Albert Einstein Academies, International Baccalaureate schools. He is also an adjunct professor of learning and technology at the University of San Diego and a Google certified innovator. Eric earned a bachelor’s degree from Azusa Pacific University and a Master of Education from the University of San Diego. He had 17 years of experience working with at-risk youth and underserved populations before becoming a middle school teacher. By building relationships with students, colleagues, and the community, he has become an empowered leader in and out of the classroom. Through meaningful learning experiences centered around student agency, STEM has become accessible to students through highly engaging lesson design, thoughtful integration of digital tools, and culturally relevant pedagogy.

Smiling person with short hair and a beard, wearing a collared shirt and sweater, against a dark background. Small star icon on the top left of the circular frame.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. Listen here!

S4 – 01. Joyful math teaching with Kanchan Kant

Podcast cover for "Math Teacher Lounge," Season 4, Episode 1, titled "Joyful math teaching," featuring Kanchan Kant, described as a math educator and transformative leader.

This season on the Math Teacher Lounge podcast, we follow the theme “joyful math” and uncover its meaning.

In this episode, Kanchan Kant joins Bethany Lockhart Johnson and Dan Meyer to discuss the key, early investment she makes at the start of the school year to ensure her math teaching will be joyful for herself and for her students for the rest of the year.

Explore more from Math Teacher Lounge by visiting our main page.

Download Transcript

Dan Meyer (00:00):
Okay, we are recording. Hey folks. Welcome back to Math Teacher Lounge. (laugh)

Bethany Lockhart Johnson (00:06):
Hardly off to a rocking start.

Dan Meyer (00:06):
Yeah. Yeah. <laugh> Did you like my energy there? Hey folks. Welcome back to Math Teacher Lounge. It’s a new season with your host Dan Meyer. And…

Bethany Lockhart Johnson (00:15):
I’m Bethany, Lockhart Johnson. How’s your summer Dan?

Dan Meyer (00:22):
Summer for me feels really hectic as we prepare, here at Amplify, for the new school year, and everyone’s starting these new math programs. So I’ve been feeling quite amped up, like usual in the summer. But also, my kids started big kid school. So I’ve been seeing the educational system from the role of a parent and all the anxieties and I worry, will I be my kids’ teacher’s most annoying parent <laugh> … So what kind of math curriculum you using? Oh, have you heard of core counting? Can I lead a math center? What’s this worksheet about? I’m really worried my kids are just overall gonna hate my vibe when I come around their classes. Uh, <laugh> so lots going on with me.

Bethany Lockhart Johnson (01:06):
It’s already happening for me and I have a toddler.

Dan Meyer (01:10):
<laugh> There we go. Anyway, that’s what I’m up to. That’s how I’m feeling. I’m curious how you’re doing. We haven’t chatted in a while. We’re excited about the podcast, but it’s been a bit, you know? Bethany got a break from me and my antics over the summer. So, how are we finding you here, as we ramp up to the new season?

Bethany Lockhart Johnson (01:24):
Uhhhh. Well, let me just tell you, I have a toddler. That’s kind of all I need to say. Except that’s not all I will say. Of course, I’ll say more. I am exploring, I’m dipping my toe into the extracurricular toddler activities; the music classes of the toddler world, the creative movement of the toddler world. And yeah, I have lots of opinions and lots of things to say about the teachers. And I’m like, Ugh, I can’t wait to be room mom. And just like…<laugh>

Dan Meyer (01:55):
Just let it rip, you know?

Bethany Lockhart Johnson (01:57):
I have opinions on everything and just hope I don’t get kicked out of the class.

Bethany Lockhart Johnson (02:05):
It’s been an eventfully recharging summer and we are ready for this new season. And in fact, we’re so ready that we decided that we were gonna mix up this season. Just a, just a tiny bit. Shall I explain Dan?

Dan Meyer (02:21):
Yeah. Let’s do it.

Bethany Lockhart Johnson (02:22):
So we have loved all the different topics that we have explored in the Math Teacher Lounge world, but we kind of feel like we need to do some more deep dives. So for this season and the foreseeable seasons …

Dan Meyer (02:38):
We’ll see how it goes.

Bethany Lockhart Johnson (02:38):
Let’s stick with this season. For this season. We’re going to be exploring a singular theme.

Dan Meyer (02:46):
We’re not bouncing around. Yep. We’re not bouncing around from a guest to guest going on whatever shiny thing in the river bed catches our eye. We’re gonna take one theme and see where it goes. What we working with here this season?

Bethany Lockhart Johnson (02:57):
This season, we are going to be exploring the idea of joyful math, joyful math. And Dan, the question I have for you is, is the term joyful math one that you use on the regular?

Dan Meyer (03:10):
No, it definitely is not. I think that joy and math are very rarely, you know, connected in the popular mind. Number one, and number two, you know, I’m kind of an ornery fellow, so that’s not my natural kind of description of math. But we decided that it feels like an important one at the moment, because a lot of math teaching–a lot of teaching in general, math teaching in particular–math teaching is often not a joyful discipline for students, where, you know, I’ve done some research where you look at what people type into Google. And I looked at like, what they…why am I bad at X? And I looked at that for where X is math, where it’s science, where it’s reading, where it’s history. And it was just wild to see how many more hits there are out there on the Internet for “why am I bad at math?” People don’t really associate math with joy, but also we’re looking at joyful math in terms of joyful math teaching. Math teaching, teaching in general, is a tough field at the moment with a lot of teachers leaving teaching. And those who remain are having a lot of soul searching and thinking about, why am I here and how do I sustain this work? And in an environment that seems hostile to my interests or my talents, or work-life balance. And so that’ll be the theme that we’re gonna kind of uncover over the course of our season, talking to various interesting guests, including one today about, yeah, joyful math teaching and joyful math.

Dan Meyer (04:43):
And to help us think about what joyful math teaching looks like, we figured we’d first look at what UN-joyful math teaching looks like. It happens to be the case that we’ve been in a pandemic as you might be aware, and teaching has been challenging. And the NEA, our National Education Association, surveyed its member teachers and asked them the following question … Gave a list of issues that school employees have experienced and asked, for each one indicate how serious of a problem this is for you. This is a survey where more than half of members said they are more likely to leave or retire sooner than planned because of the pandemic. And this is almost double the numbers from July, 2020. It’s really hard to keep track of teacher departures and unfilled vacancies across states. So I don’t wanna like blow this up out of proportion, but it does indicate some real challenges in teaching. So Bethany, I was curious, what do you think like at the top of the list, like what kinds of factors, issues facing educators would you imagine there are?

Bethany Lockhart Johnson (05:48):
So if I’m to understand you correctly, these are reasons someone is not actively experiencing joy in the profession of teaching. Like why would they leave?

Dan Meyer (05:58):
Exactly.

Bethany Lockhart Johnson (05:59):
Well, the number one thing that came to mind for me, well, okay. Wait, wait, one other caveat I need to ask about, you said specifically pandemic-related or just in general, because if it’s pandemic-related, then I think, well, there’s health issues, right? That people are concerned about, but in general, the thing that came to mind was a lack of support from administration districts, lack of funding, and overcrowding in classrooms. Like, you know, I saw somebody had 40 students in their classroom. So those are the two things that I can imagine like top on someone’s list that would make them experience less than a joyful day.

Dan Meyer (06:44):
Yeah. There’s a bunch of you’re kind of identifying here. So number seven on the list is lack of respect from parents and the public, which is like 76% of teachers call that out as serious for them. Others that you kind of circled around in terms of resources go like, not enough planning or unstructured time in the job kind of ties into resources. Yeah. But there’s others that are on the list that I’m curious, you wanna take on the swing at it, given what I’ve said here,

Bethany Lockhart Johnson (07:15):
I feel like too much being asked of them, like being asked to wear too many hats, like they’re being asked to not only teach their class, but also cover all the vacancies and supervise recess and, you know, make a delicious, nutritious lunch. That’s what came to mind. Am am I close?

Dan Meyer (07:33):
Yeah. Number four on the list, unfilled job openings leading to more work for remaining staff. People covering, you know, not just the kind of external to teaching work like you’re describing, but also just taking on like losing your prep period, to take on a class that has been unfilled for all kinds of reasons. Yeah.

Bethany Lockhart Johnson (07:54):
Yeah. I’ve only gotten the fourth. Give me one clue, one clue about …

Dan Meyer (07:59):
So, I mean like, so number one is general stress from the coronavirus pandemic, you know, which I feel like …

Bethany Lockhart Johnson (08:06):
I mentioned that.

Dan Meyer (08:07):
I’ll give you that one. Yep, yep, sure. And then number two, close behind, is feeling burned out, which I think ties into what you’re describing as well. I’m giving Bethany credit on that one. The third one is very different from the ones you’ve been describing. I think I cannot in good faith give you even partial credit for this one. I’ll just say it. Student…

Bethany Lockhart Johnson (08:28):
Wait! Dan, this is not how you give clues.

Dan Meyer (08:31):
Here’s a clue. It’s student absences due to COVID19. It’s really hard to deal student absences. That’s your clue.

Bethany Lockhart Johnson (08:40):
That wasn’t a clue that you told me.

Dan Meyer (08:43):
Yeah, let’s see. I think that’s largely it. There’s also pay is too low, is on the list; student behavioral issues, on the list. And I think that about covers it. So all of that, that basket of items has led to more than half of teachers in this survey, saying that they’re more likely to leave or retire from education sooner than planned. And I don’t know. I think we all know teachers who have bailed.

Bethany Lockhart Johnson (09:08):
I’ve never played a board game with you, Dan, but if we ever play a board game, we’re gonna work on your clue giving, ’cause I want to keep guessing. And you just told me.

Dan Meyer (09:22):
Yeah. Yeah.

Bethany Lockhart Johnson (09:22):
In all seriousness, the <laugh>. In all seriousness, I think yes, the stress of the pandemic and students being absent, what some folks are calling unfinished learning, all of those pieces do play into it. But a lot of those things that you’re mentioning on the list are things that are not unique to the pandemic, right? Like those are things that I feel like there is some modicum of control that we could have over shifting the way the culture of the teaching profession is going so that we could create a more joyful experience for educators, administrators, and students.

Dan Meyer (10:03):
Yeah. Good call out. That’s exactly right. We could tax the people who are not in the classrooms more and increase the pay to classroom teachers. You know, there we go.

Bethany Lockhart Johnson (10:11):
Oh. Bingo. Why didn’t we ask you sooner Dan, for your wisdom.

Dan Meyer (10:15):
Yeah. I’m … solved by Dan. Yeah, good point though. So I read that and yeah, I think that there’s been some … people have critiqued the NEA for being very alarmist about teacher departures as the year has ramped up. It has not been quite the flood of departing teachers as was predicted and thank heavens for that, but we should still be very bummed if teachers are unhappy and wanting to leave and feel like they can’t leave. That is definitely not good. So we were really excited to bring to the table, someone who is just a very joyful teacher and one in a very intentional way. Someone who has a lot of discipline in how she approaches the job and the students in it and tries to create a joyful environment for herself, Kanchan Kant. Kanchan is a math and computer science teacher at Newton North High School in Newton, Massachusetts. She’s been sharing her love for math with her students for the past four years, while also being instrumental in setting the culture and ethos of the math department at her school in her role as the assistant department head. We welcome you on the show Kanchan to help us understand joy and math teaching. Thanks for being here.

Bethany Lockhart Johnson (11:29):
Welcome!

Kanchan Kant (11:30):
Thank you for having me. I really appreciate it.

Bethany Lockhart Johnson (11:33):
One of my friends, her son was asked as his first math homework assignment to write out his math bio. And I loved that idea because we got to hear a little bit about your bio from like a broader perspective. But if we were to ask about your math bio, I will speak for myself to say like, automatically certain images flash into my mind, right? To think about my relationship, my evolving relationship with math. But I’m so curious if I was to ask you, what’s your math bio? How did you become the person, mathematically speaking, that you are today? Would you mind sharing a bit about that?

Kanchan Kant (12:10):
Of course I would love to. So I was born and raised in India and I belong to a family which considers mathematics to be extremely important to succeed in life. My father used to have me add and subtract license plates since I was four years old, when we were out and about. I loved math in school, it just made like complete sense to me. It was logical and you know, it was my favorite subject. I loved it all through high school. I had a confidence speed breaker in undergrad. When in my second semester I almost failed the engineering math course that I took. That was the first time math felt like too much and not like my best friend, which it was supposed to be. So it was a while before I could summon the courage to take on another math course in college.

Kanchan Kant (12:56):
But once I did that, it was like old times. I realized I had to persevere through the challenging bits. And once I did that, it started to make sense again. And through my journey, as an educator speaking to people from various backgrounds and like coming to the United States, I realized that math is challenging for everyone at one time or another. For some people that is elementary school. And for some others, it is college or even later. Either way does not mean that you are not a math person. When I was in college, I felt I was not a math person. Whereas my sister, my very own sister said the same thing about math in middle school. Both of us use math every day. And we are definitely, definitely math people. So for me to be a math person is to persevere, to approach problem-solving in a logical manner, and to find the joy in the process ,as well as the answer.

Dan Meyer (13:47):
That’s wonderful. Yeah. A lot of people, have a moment where they feel like almost betrayed by what they thought was a close friend of theirs, with math, where it’s like, wait, I thought we were tight. You know, I thought we were cool. You and me. And there’s that moment. And I wonder if that’s been a useful moment for you to, you know, bring back now and then as a teacher with students who might feel that even, you know, in high school or in a secondary school as a kid.

Kanchan Kant (14:15):
Absolutely. Like when I talk to students and tell them, yes, I had difficulty in math too. It has not always been easy for men and there are still things I struggle with sometimes, then it’s like more modeling for them that you have to persevere, you should persevere. And once you do that, it makes sense and you can feel successful. So, almost every year I end up sharing the story with my students.

Bethany Lockhart Johnson (14:38):
There’s so much value in that, right? That you are sharing that vulnerability with students. And to say your relationship with mathematics has not been, you know, smooth sailing the whole way through. There were times when you had to work harder than others.

Dan Meyer (14:55):
Yeah. Really fun to hear about you and your father as well. I tried to ask my five-year-old to do some skip counting the other day, like, okay, cool, you’re hot stuff. You can count, you know, up by ones, but what about by twos? And the moment really fell flat. And I watched myself becoming the kind of parent who is whose enthusiasm for math is one day resented by his children. I feel a lot of, yeah, I felt your anxiety Kanchan, with math itself. And now I feel anxiety as like someone who loves math and loves to teach math and may one day alienate the people closest to him. <laugh>

Kanchan Kant (15:31):
I don’t like that future. I have a three-month-old. I do not like this future of mine. If I have to go through what you’re going through. Uh, oh, <laugh>

Dan Meyer (15:38):
You got this. So Kanchan, you’re going back to the classroom coming up here at the time of this recording. It’s a few weeks out. And we’re thinking about like the kind of ways that math teachers sustain a disposition that is joyful. How are you feeling right now, as far as going back to class after this summer? Are you feeling excited, anxious, some combo, tell us about it.

Kanchan Kant (16:01):
I would say combo, but more excited than anxious. I was on maternity leave, as I mentioned, before the school year ended, and I missed the students dearly. Like, my students are what gives me hope in the darkest times. They are thoughtful. They’re empathetic. They’re so eager to learn. And very soon into my teaching career, I realized that if I take the time to get to know my students and make them feel safe and seen in my class, teaching them math would be so much easier and so much more fun. So I’m a little worried about this being like fourth year into the pandemic, but let’s see. Last year I felt the students were finding it difficult to interact with and work with their classmates because they had not been doing it for so long. So I’m hoping this year would go a little better and I’m really looking forward to working with them and building community and see how it goes.

Dan Meyer (16:53):
So if I’m understanding you correctly, you are feeling very well recharged here. You had basically an extended summer with this maternity leave, basically just like a lot of rest and relaxation over the last, like several months. Um, if I get you here. So anyway, I’m glad for that for you. And, yeah. I also hear you on the difficulties of teaching post pandemic or mid pandemic. Anyway, thanks for sharing that.

Bethany Lockhart Johnson (17:19):
What I love is I hear you being so intentional, like thinking about those relationships and thinking about that community that you want to build, you know? How do you hope that you’re gonna cultivate joy in your teaching this year? I mean like, are there certain routines or disciplines that you specifically call forth or that you think other teachers should think about?

Kanchan Kant (17:41):
So at the start of every school year, I dedicate like about three to four weeks to set up the classroom culture, both social and academic. I call my classroom a learning community. We start with community circles, we do icebreaker activities, group building and all those kinds of things. But most importantly, we do a lot of collective problem solving. So I try to present students with problems, which can be solved using multiple strategies and have multiple entry points, basically they are low floor, high ceiling problems. These could be stretch problems that they have seen before, like concepts that they already know or logical puzzles, or just wrapping their heads around different problems. Then I have students share their strategies. The more strategies they have on the board, the more successful I think the problem was. Every year, inevitably, students come up with strategies that I’ve never ever seen before for the same problems that I do.

Kanchan Kant (18:35):
And so I have students come up to the board, they would share their strategies. If they’re not ready for that, they would walk me through their strategies. And I would write their name on the board with different colored markers and everything. Basically to give them choice and agency. It also shows them that the process of doing the problem is so much more important than just getting the right answer and that it is okay to make mistakes in our learning community. I use a lot of vertical whiteboards, some concepts and problems align so well with the vertical surfaces, especially when students can explore together, learn from each other. So I do a lot of that. As for routines, I would say consistency is the key. I consistently reinforce that I want to hear multiple strategies, that it is okay to make mistakes. I am willing to learn from you as much as you’re willing to learn from me. So all like that consistency in culture more than the routines, is I feel important to bring that joy.

Dan Meyer (19:29):
That’s super interesting. Thanks for that. So I’ve heard, I hear two common objections or two common concerns to using rich tasks or doing problem solving. And I think I heard like answers to those two common reservations within what you described there, but I wonder if we can kind of bring it to the surface. And so one of the reservations is around the time that those problems take and another is that teachers often feel like, well, I might be surprised, you know, I might not know what to do with what a student does. And I thought I was hearing like some very interesting answers to both of those kinds of reservations from you, but would you just surface those up if you have some.

Kanchan Kant (20:09):
So in terms of time, I feel if I spend the time at the beginning of the year, setting up that community and doing those problems, it makes learning the math and learning the concepts much more faster throughout the rest of the year. And even when I am trying, like, even throughout the year, if we are doing a warm up problem, as I call it, which has multiple strategies, that’s gonna clarify so many more concepts when we talk about those five, 10 strategies of doing the same problem, then going through multiple problems to clarify those concepts. So for me, it actually saves time instead of taking more time.

Dan Meyer (20:43):
Hmm. That’s super interesting. It’s an investment I’m hearing from you that, yeah, you might not be hitting the curriculum quite as hard early on, but that all of a sudden you’re in the spring and it’s like, oh wow, we’ve been moving so much faster through territory that has been more challenging. What would you say to you know, comfort concerned educators or to address the concern that I don’t know what I’ll do with these five, 10 different strategies. You say, I always see strategies that I’ve never anticipated. Like, it’s a good thing, you know, like you’re happy about that. I think that’s a very intimidating thing for lots of educators. What would you say to that?

Kanchan Kant (21:19):
I think like, for me, it’s a good kind of discomfort. That means like a student is teaching me something, which is actually doing two things. One modeling for them that I’m willing to learn and that I don’t know everything. And two, also telling them that they’re mathematicians. They know what they’re doing. They’re not just receivers of math, they’re actually creating it. So for me, that is very, very important.

Bethany Lockhart Johnson (21:43):
I love that so much. When you think about your students and you’re about to start this new school year, how do you hope your students will experience math in your classroom?

Kanchan Kant (21:53):
So I hope my students can see the beauty and joy of math. They can see that math is a way to see the world and not as something we have to do to get through school. So my hope for my classroom is that we can learn to problem-solve and persevere through problems and learn from each other and not just get through the curriculum. Because like, I think math is a wonderful way to learn these skills, which are so important when you get out of high school. Most importantly, I just wanna make sure that my students see themselves as mathematicians. And like one of the things that like I have to share with you that, because one of my highlights for the year has to be the Desmos art project. I do it every year for the past three years, I think since I’ve started teaching sophomores. And I do it as a unit assessment for functions and my students design something that is meaningful to them, using all the different kinds of functions and colors and shading and everything that you can think of in Desmos.

Kanchan Kant (22:49):
Thank you so much for that though. It is such a cool way for me to see them do that. Like I have seen such amazing creations. One of my students once made a scaled working model of a solar system wherein the planets were rotating at relative speed. The Saturn had rings and they were like asteroids and everything. And then it was beautifully done. Then there was another one who did a very, very detailed whale scenery, her reasoning. I wanna be a Marine biologist and I wanna study whales. So this is what is meaningful to me. So like that one project is just a culmination of everything that I want students to see in math and in my classroom. And like I do more of those kinds of things, but that is one thing that it’s one of the highlights of my year.

Dan Meyer (23:32):
That’s awesome. I love hearing that. Yeah. Shout out to the team at Desmos Studio for building and continuing to develop a tool list that so good for art and animation, even, in addition to some mathematics with a more computational kind. Yeah, that’s really exciting. What’s interesting to me is that you teach high school, and I think that like students at that age have a very well-defined sense of what math is and who they are as mathematicians. And then along you come, you know, and like offer this really interesting disruption, you know, in their sophomore year of high school that like, oh, this can be totally different, this relationship who I am. And that’s just really exciting. I imagine it’s a very surprising year. I would imagine that first month, I would imagine is a very surprising month for a lot of your sophomores.

Kanchan Kant (24:20):
Yeah, it is. I mean, that’s why I take that time to build that community because then that sets the tone and the relationship that we’re gonna have for the rest of the year. Students get to know how to work with each other. They get to know each other, that whole piece is like super important because of that.

Dan Meyer (24:35):
Yeah. That’s awesome. So here’s the thing, like we’re exploring these ideas about joyful math teaching and what it will take to cultivate restore, reclaim joy in math, teaching this next year. And you’ve offered us these really interesting ideas some, some very, you know, philosophical and some technical about how you spend time in ways that lead to joy in the spring for you and your students. Love that. We don’t want to as hosts, as researchers, investigators of this joyful math teaching idea, we don’t wanna say it’s all up to teachers to change their mindset, to do different technical practices, and that will lead to joy. We also wanna be really attentive to the environment that surrounds you, the people who are around to support you, the policy makers, the social structures that influence your joy in very significant ways. So what we would love to know from you is, how are you supported by the greater educational community in keeping your joy in your work? I’m thinking, especially about administrators, you know, front office, staff, parents, even, can you name a few ways for those sorts of people who listen to this podcast, how they can cultivate a math teacher’s joy this coming year?

Kanchan Kant (25:54):
I would say trust. I think more than anything, educators want administrators, parents, the greater educational community, to trust them to be professionals and experts in what they do. That does not mean that we don’t want to learn, that we don’t want feedback, that we don’t wanna get better. It just means that we keep the wellbeing of our students as our top priority. And we would like to be trusted to do just that. Also just keeping in mind that whether we like it or not, we are still adjusting to the new normal while recovering from the worst of the pandemic times. A lot of us are recovering from trauma, a lot of our students are recovering from trauma, and we need time and space for our social and emotional wellbeing.

Dan Meyer (26:35):
Yeah. I’m really curious, Kanchan, you’ve done a lot of work in your area with your grading team and in thinking about equitable and biased resistant instruction. I’m curious how you see those efforts lining up with creating joyful math learning conditions for all students, not just students from a dominant culture of math doing, let’s say.

Kanchan Kant (26:55):
For me, creating an equitable environment in a classroom is most important because once you have that, that’s when you have the relationships, that’s when you have the culture, that’s when all students actually thrive. So to that end, our school and our department has been doing a lot of work around grading practices. We actually assess how we grade students, where the bias is, what we can do to make them more bias resistant. Should we move to mastery based grading? Like that’s something I’ve been experimenting with for the past two years. Through the pandemic, I started doing mastery based grading so that my students can get more opportunities to show that they have learned the content. And so like just little things which help bridge the opportunity gap. I would say another project that our school undertakes is called the calculus project wherein we have students in Black, Latinx, and low income families sign up for that and are recommended for that. And then we do summer classes and yearlong support to preview the material for next year, not as a remedial class, but to actually set students up for success in AP classes for the coming year. So we have the community buildup. We have the courses we have like math support. It’s a very beautiful thing actually. And I’ve been working with that program for four years now. So yeah, so those are my ways of creating more equity in our school.

Bethany Lockhart Johnson (28:19):
That’s so beautiful and I deeply, deeply wish you had been my high school math teacher. And I have to say that the theme that I kind of keep hearing is this intentionality. How you are so intentional about your work, not just with what your students are learning, but how they’re learning it, how they are engaging with this subject and how they are building their own relationship. You talked a little bit about your relationship over the years with mathematics, but how are your students building that relationship? And so I’m just very appreciative of you sharing that with us and with our listeners. And we are so excited to have learned a little bit about, like, I feel like I got a little mini peek into your classroom.

Kanchan Kant (29:03):
Thank you.

Bethany Lockhart Johnson (29:04):
And can I say that if you are listening to this prior to October at NCTM Los Angeles, you will get to hear Kanchan Kant speak at Shadow Con. Can I give that away, Dan? Is that, is that …

Dan Meyer (29:23):
You can drop that. Yeah, It’s pretty top secret.

Bethany Lockhart Johnson (29:26):
Can I drop it?

Dan Meyer (29:27):
Yeah. Do it. Yeah.

Bethany Lockhart Johnson (29:28):
Dan and I will be in the audience cheering you on. It’s been a joy to learn with and from you, and we are so excited to just, you know, kind of keep marinating on some of these ideas about how we can continue to be intentional about creating joyful math spaces for our students. Thank you so much for joining us today.
Kanchan Kant (29:49):
Thank you so much. It was a real pleasure.

Dan Meyer (29:57):
So Bethany, I loved hearing Kanchan talk about both her, just her joyful personality, but how she cultivates joy through craft and technique through, you know, through the various ways she interacts with students in intentional ways, that those make the job more joyful for her. And I thought it was really interesting to hear her talk about how autonomy is the thing that she needs most in her job environment to feel like she can be joyful in her work. In that context, I saw … something on Twitter popped up for me in my, you know, my many Twitter wanderings. This is a segment we might call, Dan finds something on Twitter and shares it with Bethany. Which we’ll tighten that up a little bit, but I’m sending this over to you right now, and I’d love to know as you check this out, what you’re seeing and what you’re thinking and we’ll chat about how it relates to our interview here in a moment.

Bethany Lockhart Johnson (30:47):
All right. I’m ready, send it over. It’s opening. So this appears to be a document by the way, outlining, maybe it’s a district, maybe it’s administration, they’re outlining expectation type and expectation guidelines. Hmm. Okay. And these are lesson plan expectations. Expectation type. Timeliness. Plans are due no later than 6 p.m.. Friday prior to the week of instruction. Comprehensive, all activities for the week for all subjects taught should be included and complete by due date and time. Plans should have at minimum, the following, see template for detail. Okay. So then it goes through the things that the plans need to have, the topic title, target, the objective, the activities, the sequence, the display agendas to be displayed backward design. Okay. So basically <laugh>, we were just talking about, overwhelm. And when I see this document, listeners, have you ever received something from your administrator or anyone, let’s take it more broadly, that is requesting something of you that would take so much time to complete and be so out of touch with your lived reality that it really genuinely sucks the joy out of the experience.

Bethany Lockhart Johnson (32:25):
So the first thing that I see that this document, and again, the goal of whichever district’s plan this is, is that these expectations will lead–now, mind you, I am a fan of like, you know, looking ahead, I’m not a like, oh, hey, what am I gonna teach in five minutes? No, but the idea that then it lays out all of the things in such detail that you’re gonna be teaching feels like one of those pacing guides where, oh, move on to the next page, whether or not your students have any sort of sense making whatsoever. So my first thought is, oh, sad. I have to stay here. I’ll be there past 6 p.m. But I’m gonna be there trying to make the plans for the next week based on what I think my students have learned. Hmm it’s sounds like a little bit of a bummer. Dan, what did you think when you saw this and did I do a fair description of what it is?

Dan Meyer (33:25):
No, it’s, it’s a tough one to describe, ’cause it’s basically a wall of text and commands from an administrator who like, I just have to imagine has just like acres and acres of teachers trying to beat down their door to teach at this school, if this is how you’re gonna treat your teachers. I mean just, yeah. The idea of having a week… I’m with you, you don’t wanna just like, just jump in by the seat of your pants, but the idea of having a full week of lessons for every section you teach, every prep you teach, planned and submitted with every minute, basically morseled out to different goals. It says down here, you gotta like, for all of these, download a CSV of grades and whatnot and attach those. It’s the sort of thing, like you said, there are some edicts that you get from administration where you just have to laugh or just like, you have definitely missed like what I am willing to do here. It’s so far beyond. Yeah. I can’t imagine it. And it just felt like, yeah, it was a great way to get teachers like Kanchan to feel like a real lack of autonomy. Like it’s this would not work. I don’t think.

Bethany Lockhart Johnson (34:33):
And it’s not even like willing to do. Like, let’s say you’re even willing to produce it. Let’s say that me, the rule follower is like, okay. I’m gonna attempt to meet these demands. One, most teachers were just, you know, they probably would put baloney down there anyway. Not saying that I would, but I’m saying like, it’s clearly just a hoop that they’re having to jump through and two…

Dan Meyer (35:04):
Yeah. Compliance, right?

Bethany Lockhart Johnson (35:05):
Yeah. Compliance, compliance. There you go. And two, yeah, it feels like it’s about control and not trusting the teacher. And I love that. Kanchan said that trust is what she needs. Right? You’re hiring me. Yes. I still have lots to learn, but you’re trusting me and you’re creating an environment where I can continue to learn from and with my students. And if I was being asked to submit this tome every Friday before six, that is predicting, what does it say, anticipating the steps necessary for student mastery? You know, I kind of feel like maybe it’s like that one or two teachers where maybe they feel like, oh, I don’t trust that teacher or that teacher isn’t doing a good job, whatever. We better do this for all of the teachers, but then it’s not gonna change the practices of that one teacher and all the other teachers are gonna be resentful.

Dan Meyer (36:00):
Like if there was like feedback that came back to you on, you know, on lesson plans or there was some like something that was very constructive or productive, like maybe that would be different, but it really just feels like these are gonna go into a digital drawer somewhere and not be looked at, at all.

Bethany Lockhart Johnson (36:15):
Yes. The digital drawer. Like I’m gonna send you this report and then nothing is going to happen with it. Except that four hours of my time. Well, you wouldn’t do it, but <laugh>…

Dan Meyer (36:29):
You’ve worn me down. You’ve worn me down. I’m now putty in your hands and more compliant for the next thing. And I also just wanna shout out the administrator today, who I emailed asking about like a teacher participating in a project and this administrator said, I have a standing policy not to email teachers over summer break, which you know, as administrators out there doing just the good work, you know, trusting teachers, watching out for them, trying to be a force multiplier for teachers, making the road wider, the way easier for teachers. So shout out to y’all doing the out there. Really appreciate that.

Bethany Lockhart Johnson (37:04):
Okay. Wait, wait. About that email thing, quick question. Did you ever check your email over the summer?

Dan Meyer (37:11):
Uh, yeah. That’s one way in which I was the, you know, I just love email, you know? Oh. Someone wanted to reach out. Oh, oh, Banana Republic wants to tell me about new clothes that are on offer. <laugh> I mean like, it’s just, I love those personal emails. So yeah, I did check my email over the summer.

Bethany Lockhart Johnson (37:26):
Somebody emailed me recently and they emailed me at like two in the morning. And because I currently have a toddler, I received the email at four in the morning because you know, the best thing to help myself fall back asleep is to hop on my phone, right? Like I’m already up trying to get my toddler back to sleep. I might as well start scrolling. Anyway, so the person had this little thing at the bottom of their email and it said, I have, something to the effect of, I have really like wonky work hours. I may be sending this outside of the like more standard nine to five. But please don’t feel pressure in any way to respond outside of your time. Would you appreciate that, seeing that or does it make you feel like you should respond? ‘Cause I almost responded at four in the morning, and maybe that says something about …

Dan Meyer (38:15):
They’re telling you not to respond.

Bethany Lockhart Johnson (38:16):
I know it was helpful.

Dan Meyer (38:18):
It says don’t, but you’re like, what if they’re saying that because they really expect me to respond and this is one of many ways that you and I are different. I’m always happy to see that.

Bethany Lockhart Johnson (38:29):
Do you respond? I’ve texted you in the evening because you know I have some wonky hours. Do you respond to things, like where’s your boundary there? Or when you were in the classroom, where was your boundary there? Did parents have your phone number?

Dan Meyer (38:43):
No. I gave kids my cell phone number for a couple years and it was a wobbly experiment. But parents will email, you know, back and forth with you. And I think the best thing to like … I love just like adding some friction, some latency into the kind of the chain, you know, like I hate going like back and forth, like da, da, da, da, and then like respond and then da, da da respond. And it just like goes back and forth. So just like just sitting back for an hour or two hours, you know, not responding, just let someone cool down, calm down. Email just gets you more email. That’s like if you send an email, you are just making it more likely to get more email. It’s a, you know, it’s a problem.

Bethany Lockhart Johnson (39:20):
Are you one of the zero people?

Dan Meyer (39:23):
My inbox is at zero. Most days before work.

Bethany Lockhart Johnson (39:26):
You’re joking!

Dan Meyer (39:28):
I end work every day with inbox, at zero.

Bethany Lockhart Johnson (39:31):
You’re joking!

Dan Meyer (39:32):
That’s just, you know.

Bethany Lockhart Johnson (39:33):
Who are you?

Dan Meyer (39:34):
You know, you should take my life coaching, Bethany. I’ll give you a discount since we’re math teacher, lunch pals. But, um yeah. I can help.

Bethany Lockhart Johnson (39:44):
Thank you for qualifying where our pal-dom lives. I wouldn’t even tell you how many are in my inbox. Point is, if you are actively starting the school year, we celebrate you and we are here and over the next few months, we’re gonna be diving into joyful math and that definition’s gonna keep evolving. But I wanna say something that is making me feel a little joyful, Dan. You ready?

Dan Meyer (40:15):
Tell me.

Bethany Lockhart Johnson (40:16):
You and I, in person, at NCTM, the National Council for Teachers and Mathematics. It’s coming up and we are going to be recording Math Teacher Lounge, live. Live, in person! And I hear there’s gonna be like a t-shirt cannon and there’s gonna be, you know, like musicians marching through the aisles or something.

Dan Meyer (40:46):
A marching band?

Bethany Lockhart Johnson (40:46):
A marching band!

Dan Meyer (40:46):
Trained animals. Yeah.

Bethany Lockhart Johnson (40:48):
But the point is, I’m so excited, Dan. And you know, when I see you, I might just, it’s been so long since I’ve seen you, Dan. I’d love to give you a big old embrace.

Dan Meyer (41:04):
You might just, you might just cry. Yeah. Yeah. It’ll be great. Yeah. It’s gonna be awesome for you folks to see me and Bethany have a real awkward first hug since the pandemic. And, uh, but it’s gonna be a blast to hang with us in person. We’ll have some special guests, probably, some interesting segments. You folks should stop on by at NCTM, if you’re gonna be there. Highly recommended.

Bethany Lockhart Johnson (41:29):
Now, we will be broadcasting that episode. You’re gonna get to hear … we’re gonna record it live. It’s gonna happen. In the meantime, you can find us at MTLshow on Twitter, or you can find us in our Facebook group, Math Teacher Lounge. We can’t wait to hear from you. And we’d love to hear what makes math joyful for you? Where can we add a little bit more joy to you this, this season? So thrilled to be back. Thanks for listening.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Kanchan Kant says about math

“Creating an equitable environment in the classroom is most important because once you have that, that’s when you have the relationships, and that’s when all students actually thrive.”

– Kanchan Kant

Meet the guest

As a math and computer science teacher at Newton North High School, Newton, MA, Kanchan has been sharing her love for math with her students for the past four years. Kanchan is instrumental in setting the culture and ethos of the mathematics department at her school in her role as the Assistant Department Head. Kanchan also leads the Math Department Grading Team and has been instrumental in making grading policies which are more equitable and bias resistant. In her new role as a Transformative Leaders of Massachusetts Fellow in collaboration with Springpoint and Barr Foundation, Kanchan looks forward to making equity and joy of learning the foundation of many more classrooms.

Businesswoman with long dark hair, wearing a dark blazer and blue blouse, poses in a professional portrait against a light background, representing math programs.
A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Grade 6

Chapter 2: Fractions and Decimals

Big IdeasAmplify Classroom
Lesson 2: Dividing FractionsUnit 4
Lesson 3: Flour Planner
Lesson 4: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 2: Decimal Diagrams and Algorithms
Lesson 5: Multiplying DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 6: Dividing Whole NumbersUnit 5
Lesson 13: Movie Time
Lesson 7: Dividing DecimalsUnit 5
Lesson 13: Movie Time

Chapter 3: Ratios and Rates

Lesson 1: RatiosUnit 2
Lesson 1: Pizza Maker
Lesson 4: Fruit Lab
Lesson 8: Products and SumsTake Away (coming soon!)
Lesson 3: Using Ratio TablesUnit 2
Lesson 10: Disaster Preparation
Lesson 4: Graphing Ratio RelationshipsUnit 2
Lesson 10: Disaster Preparation
Lesson 5: Rates and Unit RatesUnit 3
Lesson 6: Soft Serve
Lesson 6: Converting MeasuresUnit 3
Lesson 1: Many Measurements

Chapter 4: Percents

Lesson 1: Percent and FractionsUnit 3
Lesson 9: Lucky Duckies
Lesson 2: Percent and DecimalsUnit 5
Lesson 2: Decimal Diagrams and Algorithms

Chapter 5: Algebraic Expressions and Properties

Lesson 2: Writing ExpressionsUnit 6
Lesson 8: Products and SumsTake Away (coming soon!)
Lesson 3: Properties of Addition and MultiplicationUnit 6
Lesson 8: Products and SumsTake Away (coming soon!)
Lesson 4: The Distributive PropertyUnit 6
Lesson 8: Products and SumsTake Away (coming soon!)

Chapter 6: Equations

Lesson 1: Writing Equations in One VariableUnit 6
Lesson 1: Weight for It

Chapter 7: Area, Surface Area, and Volume

Lesson 1: Areas of ParallelogramsUnit 1
Lesson 3: Exploring Parallelograms
Exploring Parallelograms, Part 2
Lesson 5: Surface Area of prismsUnit 1
Lesson 10: Renata’s Stickers

Chapter 8: Integers, Number Lines, and the Coordinate Plane

Lesson 1: IntegersUnit 7
Lesson 1: Can You Dig It?
Lesson 2: Comparing and Ordering IntegersUnit 7
Lesson 4: Order in the Class
Lesson 3: Rational NumbersUnit 7
Lesson 4: Order in the Class
Lesson 7: Writing and Graphing InequalitiesUnit 7
Lesson 7: Tunnel Travels

Chapter 9: Statistical Measures

Lesson 1: Introduction to StatisticsUnit 8
Lesson 3: Minimum Wage
Lesson 2: MeanUnit 8
Lesson 11: Toy Cars
Lesson 3: Measures of CenterUnit 8
Lesson 11: Toy Cars
Lesson 4: Measures of VariationUnit 8
Lesson 11: Toy Cars

Chapter 10: Data Displays

Lesson 2: HistogramsUnit 8
Lesson 5: The Plot Thickens
Lesson 4: Choosing Appropriate MeasuresUnit 8
Lesson 3: Minimum Wage
Lesson 11: Toy Cars

Grade 7

Chapter 1: Adding and Subtracting Rational Numbers

Big IdeasAmplify Classroom
Lesson 1: Rational NumbersUnit 5
Lesson 1: Floats and Anchors
Lesson 2: Adding Integers
Lesson 4: Subtracting Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 3: Adding Rational Numbers
Lesson 5: Subtracting Rational Numbers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles

Chapter 2: Multiplying and Dividing Rational Numbers

Lesson 1: Multiplying IntegersUnit 5
Lesson 10: Integer Puzzles

Chapter 3: Expressions

Lesson 1: Algebraic ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 2: Adding and Subtracting Linear ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 3: The Distributive PropertyUnit 6
Lesson 10: Collect the Squares

Chapter 4: Equations and Inequalities

Lesson 1: Solving Equations Using Addition or Subtraction
Lesson 2: Solving Equations Using Multiplication or Division
Unit 6
Lesson 16: Shira the Sheep
Lesson 4: Writing and Graphing InequalitiesUnit 6
Lesson 16: Shira the Sheep
Lesson 5: Solving Inequalities Using Addition or Subtraction
Lesson 6: Solving Inequalities Using Multiplication or Division
Unit 6
Lesson 16: Shira the Sheep
Lesson 7: Solving Two-Step InequalitiesUnit 6
Lesson 16: Shira the Sheep

Chapter 5: Ratios and Proportions

Lesson 1: Ratio and Ratio TablesUnit 2
Lesson 1: Paint
Lesson 3: Identifying Proportional RelationshipsUnit 2
Lesson 6: Two and Two
Lesson 3: Measuring Around
Lesson 5: Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops

Chapter 6: Percents

Lesson 1: Fraction, Decimals, and PercentsUnit 4
Lesson 1: Mosaics
 
Lesson 4: Percents of Increase and DecreaseUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Lesson 5: Discounts and MarkupsUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)

Chapter 7: Probability

Chapter 8: Statistics

Lesson 1: Samples and PopulationsUnit 8
Lesson 10: Crab Island
Lesson 2: Using Random Samples to Describe populationsUnit 8 
Lesson 10: Crab Island
Lesson 3: Comparing Populations
Lesson 4: Using Random Samples to Compare Populations
Unit 8
Lesson 10: Crab Island

Chapter 9: Geometric Shapes and Angles

Lesson 1: Circle and CircumferenceUnit 3
Lesson 3: Measuring Around
Lesson 2: Areas of CirclesUnit 3
Lesson 9: Area Challenges
Lesson 5: Finding Unknown Angle MeasuresUnit 7
Lesson 4: Missing Measures

Grade 8

Chapter 1: Equations

Big ideasAmplify Classroom
Lesson 2: Solving Multi-Step EquationsUnit 4
Lesson 5: Equation Roundtable
Lesson 3: Solving Equations with Variables on Both SidesUnit 4
Lesson 5: Equation Roundtable

Chapter 2: Transformations

Chapter 3: Angles and Triangles

Lesson 2: Angles and TrianglesUnit 1
Lesson 12: Puzzling It Out
Lesson 4: Using Similar TrianglesUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf

Chapter 4: Graphing and Writing Linear Equations

Lesson 1: Graphing Linear EquationsUnit 3 Lesson 4: Flags
Lesson 2: Slope of a LineUnit 3 Lesson 4: Flags
Lesson 3: Graphing Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Graphing Linear Equations in Slope-Intercept FormUnit 3
Lesson 4: Flags

Chapter 5: Systems of Linear Equations

Lesson 1: Solving Systems of Linear Equations by GraphingUnit 4
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Chapter 6: Data Analysis and Displays

Lesson 1: Scatter PlotsUnit 6
Lesson 3: Robots
Lesson 2: Lines of FitUnit 6
Lesson 4: Dapper Cats
Lesson 3: Two-Way TablesUnit 6
Lesson 11: Finding Associations

Chapter 7: Functions

Lesson 1: Relations and FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 2: Representations of FunctionsUnit 5
Lesson 5: The Tortoise and the Hare

Chapter 8: Exponents and Scientific Notation

Lesson 1: ExponentsUnit 7
Lesson 3: Power Pairs
Lesson 2: Products of Powers PropertyUnit 7
Lesson 3: Power Pairs
Lesson 6: Scientific Notation
Lesson 7: Operations in Scientific Notation
Unit 7
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Chapter 9: Real Numbers and the Pythagorean Theorem

Lesson 1: Finding Square RootsUnit 8
Lesson 4: Root Down
Lesson 3: Finding Cube RootsUnit 8
Lesson 4: Root Down

Chapter 10: Volume and Similar Solids

Lesson 1: Volumes of CylindersUnit 5
Lesson 11: Cylinders
Lesson 2: Volumes of ConesUnit 5
Lesson 13: Cones

Algebra 1

Chapter 1: Solving Linear Equations

Lesson 1.1: Solving Simple EquationsWorking Backwards
Lesson 1.3: Solving Equations with Variables on Both SidesSolving Strategies
Same Position
Lesson 1.5: Rewriting Equations and FormulasSubway Seats
Various Variables

Chapter 2: Solving Linear Inequalities

Lesson 2.4: Solving Multi-Step InequalitiesPizza Delivery

Chapter 3: Graphing Linear Functions

Lesson 3.2: Linear FunctionsShelley the Snail
Lesson 3.5: Graphing Linear Equations in Slope Intercept FormFive Representations

Chapter 4: Writing Linear Functions

Lesson 4.4: Scatter Plots and Lines of FitCorrelation Coefficient
How Hot Is It?
City Slopes
Lesson 4.5: Analyzing Lines of FitPenguin Populations
Behind the Headlines
City Data
Residual Fruit
Lesson 4.6: Arithmetic SequencesMore Visual Patterns
Sequence Carnival
Lesson 4.7: Piecewise FunctionsPumpkin Prices

Chapter 5: Solving Systems of Linear Equations

Lesson 5.2: Solving Systems of Linear Equations by SubstitutionShape It Up
Lesson 5.4: Solving Special Systems of Linear EquationsLizard Lines
Lesson 5.7: Systems of Linear InequalitiesQuilts
Seeking Solutions

Chapter 6: Exponential Functions and Sequences

Lesson 6.3: Exponential FunctionsCarlos’s Fish
Lesson 6.6: Geometric SequencesMore Visual Patterns
Sequence Carnival

Chapter 8: Graphing Quadratic Functions

Lesson 8.1: Solving Systems of Linear Equations by SubstitutionCraft-a-Graph
Quadratic Visual Patterns
Lesson 8.4: Solving Special Systems of Linear EquationsOn the Fence
Stomp Rockets
Plenty of Parabolas
Robot Launch
Lesson 8.5: Systems of Linear InequalitiesParabola Zapper
Two for One
Shooting Stars
Lesson 8.6: Systems of Linear InequalitiesPlane, Train, and Automobile
Detroit’s Population, Part 1
Detroit’s Population, Part 2
Revisiting Visual Patterns, Part 1
Sorting Relationships

Chapter 9: Solving Quadratic Equations

Lesson 9.4: Solving Quadratic Equations by Completing the SquareSquare Tactic
Lesson 9.5: Solving Quadratic Equations Using the Quadratic FormulaStomp Rockets in Space

Chapter 10: Radical Functions and Equations

Lesson 10.4: Inverse of a FunctionChip the Robot

Chapter 11: Data Analysis and Displays

Lesson 11.1: Measures of Center and VariationFinding Desmo

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Reveal Math

To view this protected page, enter the password below:



S4 – 03: LIVE from NCTM with Bethany and Dan

Hosts Bethany and Dan, both smiling, in a promotional image for the "Math Teacher Lounge" podcast, Season 4 Episode 3, titled "Live from NCTM!" with an

In this episode, co-hosts Bethany Lockhart Johnson and Dan Meyer are LIVE with more than one hundred Math Teacher Lounge listeners at the recent National Council of Teachers of Mathematics conference. Listen in as they answer the pressing question: Who is the best teacher in film or television?

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Presenter (00:00):
Ladies and gentlemen, from Math Teacher Lounge, we have Bethany Lockhart Johnson and Dan Meyer! <cheering>

Bethany Lockhart Johnson (00:08):
Doesn’t go well that the door was locked. Like, I could not get in! <Laugh>

Dan Meyer (00:12):
Yeah. Gotcha. All right. We’re gonna sit a little bit. Let’s see how that works—

Bethany Lockhart Johnson (00:16):
Hi!

Dan Meyer (00:16):
Yeah. I think we’ll stand up? Or whaddaya think, sit…?

Bethany Lockhart Johnson (00:19):
Should we stand? Hi.

Dan Meyer (00:22):
Hello. Great to see you folks. Yeah, I can hear you.

Bethany Lockhart Johnson (00:25):
Can you hear me? That’s—I know YOU can me. Can you hear me OK? OK! We’re here. Hello. Thank you for like, lining up and coming out and being here. Thank you!

Dan Meyer (00:35):
Means so much to me that you could be here for me, on my show, with Bethany Lockhart Johnson, my co-host. <Audience laughs>

Bethany Lockhart Johnson (00:40):
The hour has just started.

Dan Meyer (00:42):
We’re just getting going. Yeah. If you folks have heard the podcast, you don’t know how much gets cut out. And it’s like, mostly me just having, you know, anxious nerves and saying something silly and then we cut it out and we can’t do that here today. So it should be real fun for all of us, I think. Yeah.

Bethany Lockhart Johnson (00:55):
It’s not true. It’s mostly dancing. “Bethany, can you stop talking? Bethany?” Cause it’s mostly—

Dan Meyer (00:59):
“It’s my turn. It’s my turn! Bethany <laugh>! I haven’t been heard for a while.”

Bethany Lockhart Johnson (01:02):
Dan. We’re at an in-person conference.

Dan Meyer (01:05):
In-person BIG conference, I would say. I’d say a big conference. Yeah.

Bethany Lockhart Johnson (01:08):
And have you been to the Amplify booth?

Dan Meyer (01:11):
I have! Have these people? There’s a claw machine with free socks.

Bethany Lockhart Johnson (01:16):
Yeah. You’re saving me socks, right? That’s what you’re saying. <Laugh> I mean, it’s exciting. How has your conference been so far?

Dan Meyer (01:21):
So far it’s been a blast. I feel fed. I feel like the community’s been awesome. How are you feeling about it?

Bethany Lockhart Johnson (01:29):
OK. Let’s talk about me for just a second.

Dan Meyer (01:31):
Yeah. Talk about you.

Bethany Lockhart Johnson (01:31):
Last night, Dan, was the very first night that I was away from my toddler. <Audience: Aw!>

Dan Meyer (01:38):
Big commitment being here. Thank you.

Bethany Lockhart Johnson (01:40):
I got super-emotional walking back to the hotel after dinner, and then I got in my room, <laugh> I put on pajamas, and I turned on music. I slept so good!

Dan Meyer (01:50):
Yeah. <Audience laughs> Give it up for no kids! <Audience laughs> Hey!

Bethany Lockhart Johnson (01:55):
I love him so much. But I slept all the way through the night. Oh, by the way, I ordered room service in the morning.

Dan Meyer (02:01):
On Amplify.

Bethany Lockhart Johnson (02:01):
That bill’s coming. But it’s been a great conference and I’m so delighted to be here in person and to get to share energy…and hopefully that’s all we’re sharing today. Y’all got your tests, right? Yep. Sharing energy and community today. Because we know it’s been hard. Hardness. Hard.

Dan Meyer (02:25):
Yeah.

Bethany Lockhart Johnson (02:26):
Years. Hard. And to be in person, I know conferences reinvigorate me and I go back into my educational spaces feeling revitalized with new connections and new ideas to try. So yeah, I’ve been excited to be here. And thank you all for being here.

Dan Meyer (02:40):
Yep. I don’t care if I get six different strains of Covid here. I’m just thrilled to be here. <Audience laughs> I don’t know if you’ve had the same feeling, though, Bethany, you folks…I’m a little bit confused to some degree about what we’re doing. I just wanna be really transparent. This is my sarcastic voice but I’m being sincere here. It kind of feels like we’re in a little bit of a time capsule. Like we all got in a time capsule in 2019 and, you know, you open it back up and it’s like, OK, so we’re still, you know, talking about X, Y, or Z protocol for establishing classroom routines or whatever. And I’m like, OK! Like, I loved that in 2019! But I do admit, I’m still trying to figure out a little bit like, what are we doing now? What’s our relationship to the world out there? Things are very different. I have had some great sessions that I’ve enjoyed. I’m also like, still waiting for a session to draw a little blood. Do you know what I mean? Like there’s been sessions…no? OK. You’ve been in these sessions where it’s like, “Oh, ow.” Like, and you look down and there’s and there’s blood there. It’s like, I thought I knew what we were up to. Like, I thought I knew what teaching was and how we relate to the world. I dunno, like in any Danny Martin session in 2019, “Take a Knee” was one, where I was like, “Oh, OK. Like, I’m not as hot as I think I am here. Like, I’m part of a system.” That kind of thing for me draws blood. And I haven’t been in one of those yet. Been some great sessions. I’m a little hopeful that today we draw a little blood and think about what we’re doing here, is my hope here, if that’s OK. So Bethany’s gonna moderate that impulse and she’ll be the fun one and I’ll be the blood-drawing one.

Bethany Lockhart Johnson (04:05):
No, I don’t…that metaphor doesn’t speak to me personally. But what I will say is, I get what you’re saying about really wanting to be in that room where there’s like this synergy happening. No promises about that today other than—

Dan Meyer (04:18):
I promise. <Audience laughs> Go on.

Bethany Lockhart Johnson (04:20):
Other than I get what you’re saying. I’ll find my own metaphor that does not involve bloodshed, but.

Dan Meyer (04:25):
Sure. There’s a lot of ways we we could go about this today. And the one that I’m excited about is, you know, we could like, you know, analyze some results from students, and talk about what went into that. Look at classroom video. Lots of possibilities. But here’s what we’re up to today. Hope you’re into it. Which is, we are here in the heart of the entertainment industry. You know, Tinseltown! Um, the Big Apple! Uh…

Bethany Lockhart Johnson (04:47):
No!

Dan Meyer (04:47):
Come on. What do you got here? Um…

Bethany Lockhart Johnson (04:51):
It was daytime at night. Like the lights were so bright.

Dan Meyer (04:54):
The City of Lights.

Bethany Lockhart Johnson (04:55):
There was a movie premiere outside my hotel room, which I was not invited to, unfortunately. But so what are we doing today?

Dan Meyer (05:01):
So here’s what we’re doing. We are gonna settle, once and for all, a question you have not asked yourself yet, perhaps, but will want to know the answer to in a moment. Which is: Who is the best teacher in all of film or television? OK? We’re gonna do that. It’ll be fun. But I hope that in debating this a little bit with a special guest we’ll bring up in a moment, that we will start to uncover some truths about what makes good teaching. How that’s different from teaching as we see it in movies and tv. Why middle-class America wants teachers to look a certain way in movies and tv. What all that means. And it’ll be awesome. I think. I’m hopeful it’ll be awesome. So what we did here is we’ve invited eight people. Eight folks you people may have known. You’ve been in their sessions today, in this conference, perhaps. And asked them: Who’s your fave? Like, we might have our favorites, but we wanted to democratize it a bit. So asked some cool people who you folks like, who are very smart and thoughtful about teaching: Who’s your favorite teacher?

Bethany Lockhart Johnson (05:58):
A few of whom are in this room. Thank you for your submission.

Dan Meyer (06:00):
Thank so much. Yeah. We’ll see what happens here. <laugh>

Bethany Lockhart Johnson (06:03):
As they shrink down.

Dan Meyer (06:03):
Yeah. Might draw some blood that I don’t mean to right now. We’ll see. OK.

Bethany Lockhart Johnson (06:06):
That metaphor, what IS that??

Dan Meyer (06:07):
Yeah. Yeah. I love it. I’m still going with it. <laugh> And you folks will be a huge part of this. THE part of this, really. So what will happen is I’ll share with you our first nominees. A few of us will make a case for our favorites, or least favorites, as the case may be sometimes. And then by applause, by acclamation, you folks will decide who wins and advances to the next round. Start with eight, move to four. You folks know math.You know where this goes. OK.

Bethany Lockhart Johnson (06:34):
No, keep going. Keep going.

Dan Meyer (06:36):
Two, then one.

Bethany Lockhart Johnson (06:36):
Yeah. Got it.

Dan Meyer (06:37):
Then a half of it. No?

Bethany Lockhart Johnson (06:38):
He had to school me on the making of brackets. But we got it. Yeah.

Dan Meyer (06:41):
How brackets work.

Bethany Lockhart Johnson (06:41):
But we got it. March Madness, what?

Dan Meyer (06:44):
Yeah, in order to do this right, we had to bring up—all the folks that you’ll see are also former Math Teacher Lounge guests, or like, just fan favorites. And we’re also bringing up a former Math Teacher Lounge guest to help us decide this and debate this in a respectful manner.

Bethany Lockhart Johnson (06:59):
New dad.

Dan Meyer (07:00):
New dad.

Bethany Lockhart Johnson (07:01):
You see where my brain’s still at? I miss him. <Laughs>

Dan Meyer (07:03):
Friend from San Diego. Really cool teacher.

Bethany Lockhart Johnson (07:06):
Incredible teacher.

Dan Meyer (07:06):
Works at Desmos and Amplify. And I just want you to welcome up your friend and mine. Chris Nho!

Bethany Lockhart Johnson (07:11):
Chris Nho!

Dan Meyer (07:13):
Come up, Chris. Let’s go, buddy. We didn’t talk about it, but did you want to do the cornball stuff too?

Chris Nho (07:22):
Wow. Would I love to do—

Bethany Lockhart Johnson (07:23):
And then the door could be locked! And then you have to wait and like, just—

Chris Nho (07:27):
Yeah, I’ll skip that part.

Bethany Lockhart Johnson (07:28):
Hi. Welcome. You’re here. We’re here in person.

Chris Nho (07:30):
Very glad to be here. Thank you all for having me.

Dan Meyer (07:33):
Tell me who you are.

Chris Nho (07:34):
My name is Chris Nho. I live in San Diego. I’m a new dad. A three month old, just had. Yeah, she’s actually here at the conference with us in the hotel room. And I promise you she is not by herself. She is with…come on. I was like, “Hey, just gimme one hour. I’ll be right back. I have to do very important work.” But yeah, I think I got invited here because I have opinions and I’m willing to draw…some…blood.

Dan Meyer (08:02):
There we go! Two outta three! We’re good on the metaphor now.

Bethany Lockhart Johnson (08:06):
We’re so glad you’re here. If you haven’t listened to the episode where Chris and Molly and some other public math folks share their ideas and ideas of how to take math out into the world, please listen, because we had a blast.

Dan Meyer (08:19):
Inspiring work. Really inspiring work. Very cool. Cool. OK. Right on. OK.

Bethany Lockhart Johnson (08:23):
Let’s do this!

Dan Meyer (08:24):
Let’s get started here. Yeah! <Audience cheers> Yeah. And we might ask you who your favorite teacher is, who’s missing from our list of eight? We might have forgotten some people. Anyway. All right. So here’s our first two. Our first two are nominated by way of, let’s see, um, Mandy Jansen is a professor at the University of Delaware. Got some awesome talks here this week, a Shadow Con talk last night. She’ll be nominating one. And also, um, Lani Horn is a professor at Vanderbilt, also extremely cool, prolific author and speaker, just all-around great human and friend of teachers everywhere. And she’ll nominate another in this bracket, which is the Northeastern Comedy bracket, Northeastern comedy bracket.

Bethany Lockhart Johnson (09:06):
It just worked out that way.

Dan Meyer (09:07):
Yeah. Here it is. Here is Tina Fey in Mean Girls.

Tina Fey in Mean Girls (09:12):
“OK. Everybody close your eyes. All right. I want you to raise your hand if you have ever had a girl say something bad about you behind your back. Open your eyes. Now close your eyes again. And this time I want you to raise your hand if you have ever said anything about a friend behind her back. Open up. It’s been some girl-on-girl crime here.”

Lani Horn (09:52):
I am nominating Sharon Norbury from Mean Girls as the best movie math teacher. She is an awesome teacher who is always there for her kids. She always sees the best in them. She shows that she can forgive even some pretty bad behavior, if she sees that kids are trying. She’s a strong feminist who makes sure that smart girls don’t dumb themselves down just to impress boys.

Tina Fey in Mean Girls (10:22):
“Katie, I know that having a boyfriend may seem like the most important thing in the world right now, but you don’t have to dumb yourself down to get guys to like you.”

Lani Horn (10:30):
She’s also super hard-working. She works three jobs. She’s always there for the kids. She plays piano in the talent show and takes them to Mathlete competitions. And she’s also socially aware. And when things go really badly among the girls, she does some pretty creative things to try to get them to be kinder to each other.

Dan Meyer (10:54):
OK. That’s one.

Bethany Lockhart Johnson (10:55):
Helen Case.

Dan Meyer (10:57):
All right. Settle down. Settle down. Settle down. All right.

Bethany Lockhart Johnson (10:59):
Piano too!

Dan Meyer (11:00):
Bethany’s already trying to bias people here. All right. Chill out. Hold on. So next one is Mandy Jansen with Jack Black from School of Rock. Uh-oh. Uh-oh.

Jack Black in School of Rock (11:09):
“What was your name?”

Kid in School of Rock (11:10):
“Katie.”

Jack Black in School of Rock (11:11):
“Katie. What was that thing you were playing today? The big thing.”

Kid in School of Rock (11:14):
“Cello.”

Jack Black in School of Rock (11:15):
“OK. This is a bass guitar and it’s the exact same thing, but instead of playing like this, you tip it on the side. Chellooooo! You’ve got a bass! <Laugh> Try it on.”

Mandy Jansen (11:25):
And I’m nominating for best teacher in a film Jack Black as Dewey Finn playing Mr. Ned Schneebly in the film School of Rock. So why this portrayal? First of all, playing a longterm sub. Those are so hard to find right now. <Audience laughs> Really hard. And then he teaches using class projects. That’s brilliant. Integrated learning. And then love this. He gives students roles and tasks that are differentiated and align to the specific strengths that each student has.

Kid 2 in School of Rock (12:05):
“I can also play clarinet, you know!”

Jack Black in School of Rock (12:06):
“I’ll find something for you when we get back from lunch. I’ll assign the rest of you killer positions.”

Mandy Jansen (12:13):
And the film culminates in a performance of a collaborative song that they all wrote and performed together. And the students experience that collaboration and teamwork and creating something beautiful is much more important than winning first place. And finally, one of the songs that the character sings in the film is “Math is a Wonderful Thing.” Can’t beat that.

Dan Meyer (12:40):
All right. That’s tough. That’s tough. So here’s the deal. What we have right now is just a quick minute—so Bethany, you ranked, we all ranked our own faves here outta the list of eight. And Bethany put Jack Black in School of Rock a bit higher than Tina Fey in Mean Girls.

Bethany Lockhart Johnson (12:54):
Missed the piano part though.

Dan Meyer (12:55):
And Chris, vice versa here. So Bethany, would you start us off and just make a quick case here for Jack Black versus Tina Fey?

Bethany Lockhart Johnson (13:01):
OK. So here’s what I’m thinking. There’s been rumor that maybe they’re putting less than credentialed people into classrooms to fill teaching gaps. I mean, just rumor. And so here’s this guy who is a rocker. He is not a substitute. He has no teaching training. And yet he goes in there and it turns out that he has the ability to see students’ potential and to recognize their unique abilities. And like Mandy said, he really tapped into, like, he saw them and said, “No, more is possible for you than what you think is possible.” And there’s like real sub anxiety. When you walk in, you can either be like, happy there’s a sub, but I was usually really nervous. Right? And he goes in and he makes that classroom into a home.

Dan Meyer (13:53):
Wow.

Chris Nho (13:54):
Wow.

Dan Meyer (13:56):
Chris, speak on it. Tina Fey needs you. Chris.

Chris Nho (13:59):
Tina Fey. Here we go. I’m gonna argue here that—when was that movie made?

Dan Meyer (14:03):
T is for terrific. I is for Interesting.

Chris Nho (14:06):
Decades ago. And I’m gonna argue that Tina Fey was very progressive for her time. OK, let’s talk about social emotional learning. Hello. <Audience laughs> Love that. Right? Stand up if, I mean, she’s getting people to talk about their emotions. And there’s a curriculum. But let’s just pause, because that’s not what’s really happening in the classroom right now. So social emotional learning, I think she’s, she’s got that a lot. And then number two, you know, if you remember the plot of Mean Girls a little bit, she gets her name written in that Burn Book. Like she sees what they say about her. Restorative justice. Let’s go. <Audience laughs>.

Dan Meyer (14:38):
Whom amongst us. Yes.

Chris Nho (14:40):
You write Mr. Nho in the Burn Book?? Well, your grade book is gonna look like a Burn Book! OK? <Audience laughs> Tina Fey, Tina Fey, she was like, “No, you know, know what? I’m actually gonna spend more time with you. You’re gonna become a mathlete.” And Lindsay Lohan discovers—she drops the most iconic line in all of math education. “The limit does not exist.” Thank you, Tina Fey, for that. For that gift.

Dan Meyer (15:04):
Bless. Bless you. Tina Fey. Wow.

Bethany Lockhart Johnson (15:05):
Oh, man. Wow.

Dan Meyer (15:09):
Let’s see what the people say here. I do wanna just add one quick thing about—it’s interesting to me how often in these movies—just kind of go in a little bit, zoom out just a minute—how often it’s a teacher who has no training as a teacher. <Bethany laughs> I am kind of curious why it is. Like, those are the movies that get hot, that get made. Again, these are all kind of a mirror of the taste of the moviegoing public. You know what I’m saying? Like, these, these are not movies—I wanna believe they are made for me and for us as teachers. But they are not. There’s not enough of us to justify, you know, Jack Black’s, you know, M&M budget or whatever he’s got going on in his trailer or whatever. That needs to be for everybody in middle-class America. So what is it about middle-class America that wants to see teaching as something that anybody can do? Just like, you know, just, just run up there in your van and make it happen.

Bethany Lockhart Johnson (15:54):
Magic magically manifests.

Dan Meyer (15:56):
Yeah. Manifest. Yeah. That’s just interesting to me. I just toss that out there as some red meat. Let’s see what the people say here. All right, OK, so you’re ready. Let’s get the bracket going here. The question is Tina Fey versus Jack Black. You had a moment here. Just whisper to someone real fast who you’re going for here real quick. What are you thinking here? <Crowd murmuring> All right. Crowd’s buzzing. Crowd’s buzzing. Would you folks…? All right. Bring it back. Go ahead and make some noise for Tina Fey. <Crowd cheers> OK. OK. Make some noise for Jack Black! <Crowd cheers> Judges say Tina Fey. Tina Fey moves on. All right. All right.

Chris Nho (16:44):
Stunned. I’m stunned. I’m speechless.

Bethany Lockhart Johnson (16:46):
Tina Fey moves on. Wow.

Dan Meyer (16:48):
This has exceeded my expectations in terms of having some fun, but also getting deep, getting deep and real about teaching. I’m into this right here. Yeah. What’s up?

Bethany Lockhart Johnson (16:54):
That’s the goal. That’s the goal. OK. You wanted blood? Oooh, this next matchup might just be where that blood comes forth! OK. Stretch. Warm up. Dan Meyer, who’s up next?

Dan Meyer (17:11):
We’ve got the animated/animatronic round here in the Southeast. And repping the two contestants here, who do we have? We have Allison Hintz, professor, author outta Washington, as one of the two nominators. And the other nominator is one of my heroes, though we’ll find out very wrong about this nomination, Jenna Laib, who’s in the crowd, and I’m trying not to make eye contact here. <Laugh> And here are the two nominations. A couple minutes each. And then we’ll chat about it. And one of us will probably die. But we’ll see how it goes.

Allison Hintz (17:50):
A long, long time ago, in a galaxy far, far away, MTL, we began learning from the Jedi Master of Teaching. With the Socratic and experiential approach. With unparalleled mindfulness, compassion, and humility. The best teacher in TV and film, Yoda is. <Audience laughs> Yoda lives the values we share as teachers and learners. He humbly comes alongside us as we construct new knowledge.

Yoda (18:29):
“You must unlearn what you have learned.”

Allison Hintz (18:32):
Yoda allows us to struggle and sees mistakes as critical to learning.

Yoda (18:39):
“The greatest teacher, failure is.”

Allison Hintz (18:43):
Yoda values curiosity and reminds us of the beauty and joy of teachers learning from children.

Yoda (18:52):
“Truly wonderful, the mind of a child is.”

Allison Hintz (18:59):
MTL! Join the Resistance! Let the force flow through you in declaring, the best teacher in TV and film, Yoda is.

Dan Meyer (19:18):
Give it up for Allison Hintz! All right! <Audience applauds>

Bethany Lockhart Johnson (19:20):
Alison! And to have that on hand too, which Is kind of perfect.

Bethany Lockhart Johnson (19:26):
Just to be clear, the helmet is not a part of a Zoom background.

Dan Meyer (19:29):
You may evaluate the quality of the nomination based on the costumes of the nominator. That is acceptable. That’s acceptable.

Bethany Lockhart Johnson (19:35):
That is a REAL HELMET.

Dan Meyer (19:35):
All right. The next nominator here, this one is from Jenna Laib, math coach, all-around stellar human. Here we go. This is Ms. Frizzle.

Ms. Frizzle (19:42):
“Single file, class. Our rotten field trip has only just begun.”

Jenna Laib (19:47):
And I think that the best teacher from TV or movies is Ms .Valerie Frizzle from The Magic School Bus. First and foremost, Ms. Frizzle believes in her students. She encourages them to take an active role in their learning, and also to advocate for change in their local community. For example, there’s an episode where there is a logger who’s gonna cut down a rotting log that would benefit the local ecosystem. And the students figure out a way to convince him to leave the log so that all of the animals and the plant life can benefit. She orchestrates really challenging situations for these students, and she allows them the space to ask questions and engage in problem-solving and puzzle their way out of these really, really difficult scenarios. Ms. Frizzle has unmatched pedagogy. She’s bold, she’s innovative, and she’s a major proponent of experiential learning. So these students are heading straight into a storm to learn about weather systems. <Audience laughs> These students are heading into the human body to learn about digestion and disease. They literally get baked into a cake to learn about some chemistry and reactions.

Children in The Magic School Bus (20:54):
“What’s happening?” <Audience laughs> “Why is it suddenly getting so hot?” “Maybe it’s because the floor is on fire!” <Audience laughs>

Jenna Laib (21:02):
This pedagogy is all led by her outstanding catchphrase, which is:

Ms. Frizzle (21:06):
“Take chances; make mistakes; get messy!”

Jenna Laib (21:14):
From her pedagogy to the classroom community that she creates, Ms. Frizzle is an inspiration, and that is why I think that she is the best teacher from TV or film. <Audience applauds>

Dan Meyer (21:25):
Right on! Give it up for Jenna. Give it up for Jenna. All right. I’m gonna take first pass at this. Chris knows my argument already, so I’m gonna take this here. I see some of you are feeling how I’m feeling on this one. OK, so I don’t have tons to say in favor of Yoda. I think it was all true what Allison said. I think the costume was banging. It was awesome. So there’s all that, but I have more to say against Ms. Frizzle than for Yoda.

Bethany Lockhart Johnson (21:48):
No, no, no. Wait a second!

Bethany Lockhart Johnson (21:49):
Let’s let it happen. Bethany, I’ve come prepared.

Dan Meyer (21:54):
I may have made a misstep here, I realize.

Bethany Lockhart Johnson (21:56):
I’ve come prepared.

Dan Meyer (21:56):
So I think Jenna is all correct. I think those clips spoke for themselves. I think that what they add up to, to me, is not “great teacher,” but more “someone who should be locked up.” <Audience laughs> Or at the very minimum, “someone who should be kept away from children.” <Audience laughs> Do not let that woman around children. I mean, check it out. Look, I don’t wanna throw down credentials. I’ve been to grad school, though. I know how this works. When your brain is stressed, you get these—all the cortisol happens. Your working memory shrinks up. You cannot learn when you’re stressed. And those kids, like whatever lesson Ms. Frizzle is teaching by sending them into an oven, I repeat, an oven <audience laughs>, like, they’re not gonna learn anything ’cause their brains are freaking out with stress and fear. OK?

Bethany Lockhart Johnson (22:41):
“What’s happening??”

Dan Meyer (22:43):
“What’s happening? Am I on fire? Well…I’m learning lots, though! Sure is magical!” <Audience laughs> It’s like, “No. Get that woman out of a classroom.” That’s my opening and closing argument. Right? There’s all it is.

Chris Nho (23:01):
All right. All right. All right.

Bethany Lockhart Johnson (23:02):
Chris knows.

Chris Nho (23:03):
I’ve got, I’ve got lots to say. First off, I think Dan was in charge of the editing of those video clips. So let’s let that be—you know, let the record stand. <Audience laughs>

Dan Meyer (23:11):
Where’s the lie though? Where’s the lie?

Chris Nho (23:14):
And, you know, second, I think, um—this is the guy up here saying, “I wanna see blood.” You know? And then he has a teacher who literally takes the students into a blood cell and, and you get a little scared! You get a little worried for the students, you know? So I just don’t get it, Dan. This or that. OK? I think Ms. Frizzle—so I actually went to a project-based learning school. I taught at a project-based learning school. And the best thing about it is like, your learning, it doesn’t just stay in this box of math lesson or writing lesson, history lesson. And I think with Ms. Frizzle, like you can’t help but learn things because you are getting baked in a cake. <Audience laughs> Yeah, it is a little scary. And I imagine there’s cortisol and things happening, but guess what? Probably the next episode, they go into their own brains and explore what’s happening. That kind of thing. You know?

Dan Meyer (24:07):
The kids that survived, just be clear. <Audience laughs>

Chris Nho (24:10):
Yeah. OK. Would I want Nora, my three-month-old, to be babysat by Ms. Frizzle? Maybe not. <Audience laughs> But what I have to say about Yoda is Yoda maybe wins the best tutor award. Give it up for Yoda’s Best Tutor Award.

Bethany Lockhart Johnson (24:24):
Oh, yeah…

Chris Nho (24:25):
That ratio’s looking really nice. I could teach the heck outta Luke Skywalker. OK? But 20 little Luke Skywalkers running around. I’m not sure. OK?

Dan Meyer (24:34):
Luke did survive the training, though. <Audience laughs> So that’s awfully nice to say about it. All right, Great words from Chris here. I’m still not convinced. We’ll see how you’re convinced here. Would you whisper to someone where you’re leaning here? Frizzle or Yoda? <Audience buzzing>

Chris Nho (24:47):
I tried. I tried.

Dan Meyer (24:53):
All right. That’s enough of that. Let’s hear it folks. Give it up for Yoda. <Audience cheers> Give it up. Give it up. You. Give. It. Up.

Chris Nho (25:05):
Hey, next. Next.

Dan Meyer (25:06):
All right. All right, all right. <Mutters> Give it up for Ms. Frizzle. <Audience cheers louder> I dunno, it’s pretty close. Call a tie. Maybe Yoda? Yoda by nose? <Audience laughs> All right. All right. Let’s…let me see who’s it. Let’s get the people advancing here. I’ll keep on moving here.

Chris Nho (25:26):
As you’re doing that. Um, Dan ranked Ms. Frizzle last in his personal ranking. And I ranked Ms. Frizzle very high, so we knew this one would be spicy,

Bethany Lockhart Johnson (25:36):
<laugh> Spicy it was. Are you having a good time so far? <Audience cheers> So while we love seeing these images and we love seeing these video clips, at the core, what are these things about how teachers are portrayed? And how accurate is that to our real lives? I mean, besides the cake part, right? That my chemistry class did often feel like I was on fire. I was so stressed in it. Um, we’re ready?

Dan Meyer (26:05):
Yep. Great. We’re ready, we’re up here. So the next two nominees are coming to you folks from Tracy Zager, who is the editor of my book, forthcoming in 2027 at the earliest and 2032 at the latest. And also your very own Zak Champagne from Florida, here in the room. Hey, Zak. Zak, let’s see who the nominations are. I’m gonna skip past that, didn’t work out so well for me. Here it is. This is Marshall Kane from the TV show Community.

Michael K. Williams in Community (26:32):
“You two complete your case to the class and let them decide your grades.”

Joel McHale in Community (26:37):
“Professor, thank you.”

Michael K. Williams in Community (26:40):
“It’s not a favor, Mr. Winger. Man’s gotta have a code.”

Joel McHale in Community (26:44):
“Awesome.”

Zak Champagne (26:46):
This is a pitch for an underdog. This teacher didn’t stand on desks or encourage his students to follow their musical passions. In fact, this teacher was seen only in a few episodes of my favorite TV show of all time, Community, Community has set at Greendale Community College in Colorado. And in season three, we get to meet Dr. Marshall Kane, a biology professor whose story is an inspiration to anyone who just takes the time to look and listen. Dr. Marshall Kane slowly earned his PhD while in prison, serving a sentence of 25 to life. In his classroom, he inspires students to love biology, question why LEGO has become so complicated, and randomly pairs his students for group projects to ensure no one feels left out. His greatest performance comes when a group of students believe their yam project was intentionally sabotaged. Dr. Kane took this as an opportunity for some trans-disciplinary real-world learning. So yes, at community college, he felt that a middle-school mock trial was the best way to determine who killed the yam. So let’s all pick the underdog and vote for Dr. Marshall Kane. After all, man’s gotta have a code. <Audience goes “oh!” and applauds>

Dan Meyer (27:53):
Thank you, Zak.

Bethany Lockhart Johnson (27:54):
I have a code.

Dan Meyer (27:56):
Next up is Tracy Zager, nominating an unusual nomination, not a single person, but an ensemble performance. A bunch of people from a movie called Searching for Bobby Fisher. Here we go.

Rapid-fire movie dialogue (28:11):
“What’s that?” “Schleimann attack.” “Schleimann attack? Where’d you learn that from, a book?” “No, my teacher taught me.” “Aw, your teacher. Well, forget it. Play like you used to, from the gut. Get your pawns rolling on the queen’s side.”

Tracy Zager (28:26):
Hey, Math Teacher Lounge. This is Tracy Zager. I’m excited to share my nominee for the best movie teacher. But I have to admit that when I first got the email, I thought, oh, who am I gonna nominate? Because most movies about teachers are highly problematic. They usually have like a saviorism thing, usually white saviors. And I just felt like I couldn’t suggest any of those. So rather than nominate a movie about a single teacher, I wanted to nominate a movie that taught me something about teaching. And that movie is a deep cut. It’s Searching for Bobby Fischer. It’s a movie about a chess prodigy. And what I love about it is that all of the different adults in the movie are in teacher roles in some way. And the student, Josh, the chess player, is a fully realized character, not an empty pail, who pulls from the strengths of each one of those adults while also dealing with their flaws and humanity. And there’s just beautiful synergy in the way he gets the best out of everybody, but also has to overcome some of the barriers that they put in front of him. So I feel like it’s a much more authentic and humbling, but also inspiring, movie about the power of teaching. So if you haven’t ever seen it, check it out. And I can’t wait to see who the other nominees are. Thanks so much.

Dan Meyer (29:53):
Right on. Thank you, Tracy. Wherever you are. <Applause> We’ll move a little quicker here. I’m curious, Bethany, you put Marshall Kane pretty high. I put Bobby Fischer pretty high. What do you have to say about Marshall Kane for us here?

Bethany Lockhart Johnson (30:04):
Well, I just wanna say two things. One is that, like Zak said, he has this code of conduct that he brings in. And he stays true to it no matter what happens. If you saw him in in Community, you know that he held himself up to such high esteem, but not just himself, his students as well. And he took accountability when he felt he had done wrong, even though, well, that’s controversy. But first—oh, the other thing, rest in peace, Michael K. Williams. Oh my gosh. The actor who plays Marshall K. And the thing that I wanna say most of all about it is that he brings his whole self to the classroom. He was in prison for decades. He brings his whole self and says, “This is who I was. This is who I am today. And this is how we can work together as a community.”

Dan Meyer (30:58):
That’s big. I love your comments about code of conduct too. It makes me wish that Ms. Frizzle had a code of conduct also.

Bethany Lockhart Johnson (31:05):
I knew that was coming back!

Chris Nho (31:06):
Two slides ago, Dan. That was two slides ago.

Dan Meyer (31:08):
Can’t let it go. So yeah, I love what you said there. I have no strong beef here either way. Bobby Fischer’s a movie I have loved dearly and can’t be objective about it. I love that the kid in that movie, more than any other movie here, the kid teaches the adults so much through his innocence and how he challenges them and how they’re treating him. Dig all that so much. Will not, will not begrudge anyone any vote either way here. I do begrudge many of you your vote in previous rounds. <Audience laughs> So let’s just, let’s hear. We’re not gonna ask you folks at all to chitchat. We’re gonna move on this one. So would you folks make some noise here for Marshall Kane in Community? OK. OK. And would you make some noise here for Bobby Fischer, the kid in Bobby Fischer, the ensemble? <Audience cheers, applauds>

Bethany Lockhart Johnson (31:56):
Marshall Kane.

Dan Meyer (31:57):
Marshall Kane takes it. All right. Good job, Marshall Kane! All right. Zak’s feeling good. Moving on to the final four here, Zak, right on. OK. Our last—the Northwest Division here is also the large urban district division here. We have a couple different teachers in sets of large urban schools. They’re nominated, they’re advanced by a couple people here. One is past president of NCTM, Robert Berry. And another is Fawn Nguyen, Southern California phenom. Great teacher and friend of lots of us. Um, let’s see who they nominated here. First from Robert Berry, let’s see, who is it here? Janine Teagues from Abbott Elementary.

Abbott Elementary dialogue (32:37):
“Hey, you know what? I’m probably probably gonna be Kenny’s second-grade teacher. Why don’t you just let him get a head start with me today?” “That’d be great.” “Yeah? OK. Hey, Kenny, would you like to be in my group today?” “Not really.” “That’s the spirit.”

Robert Berry (32:54):
My nomination is gonna be Quinta Brunson, the Emmy Award-winning Quinta Brunson from Abbott Elementary. Janine Teagues is the character. She exemplifies care not only from an affect way, but she also exemplifies care in the things that she does for her students. While the scenes in the show are entertaining, they do represent the challenges that teachers experience when they’re trying to meet the needs of her students. So she goes, goes all out for her students and finding resources. She accesses other people to get resources for her students. But the care shows up in the way that she is mindful of their needs. And so, for me, when I think about teachers and teaching, sometimes we can talk about pedagogy, but sometimes we also can talk about those kind of intangibles that makes a teacher a great teacher. It is apparent from her students that she cares about them, she supports them, and she goes all out 100% for her students. Janine Teagues, Quinta Brunson is, I think, is my choice of the best teacher on television because of the realism and the representation that she brings to this character of what teaching is about. <Applause>

Dan Meyer (34:28):
Right on. Right on. OK. OK. Next up, we’ve got, Fawn Nguyen is nominating Erin Gruwell from Freedom Writers. Here we go.

Hilary Swank in Freedom Writers movie (34:39):
“Look, you can either sit in your seats reading those workbooks or you can play a game. Either way, you’re in here till the bell rings. OK? This is called the Line Game. I’m gonna ask you a question. If that question applies to you, you step onto the line and then step back away for the next question. Easy, right? The first question. How many of you have the new Snoop Dog album? <kids move around> OK, back away. Next question. How many of you have seen Boys in the Hood?”

Fawn Nguyen (35:26):
We all learn about Miss G and her 150 students in the movie Freedom Writers starring Hilary Swank. All great teachers share a common set of traits. They care deeply about their students, have high expectations of them, and always believing wholeheartedly that they will succeed. Great teachers go above and beyond, not because they extraordinary—as Anne Gruwell would always refer to herself as an ordinary teacher—but because extraordinary things happen to people when we believe in them, give them hope, help them write their own story with a different ending. So what stood out for me with Miss G is the scope of her reach, the ever-expanding sphere of her humanity. The red tape she had placed on the classroom floor for the line game shows just how much we all have in common despite our differences. Her students didn’t just learn from her; they learned from one another. If you’d like to be part of this expanding sphere to give voice and hope, please check out Freedom Writers Foundation dot org.

Dan Meyer (36:38):
OK. This right here is a tough one for us. Thank you, Fawn. We collectively ranked—that’s our number one seed and number eight seed, which I hasten to say does not have to do with Erin Gruwell, a person, but the portrayal and the movie. So we don’t have like a whole lot of…there’s not a lot of defense we have to offer here of our eighth seed. And I heard like a kind of a little bit of a murmur over the crowd on Erin Gruwell. So I’m more interested than having a defense back and forth. I’d be curious what you, Bethany, think about what, like, what both movies have to say about like, what teaching is, especially teaching urban schools with black and brown kids and lower-class kids, for instance. They both have, I think, very different things to say about them. Do you have thoughts about that?

Bethany Lockhart Johnson (37:19):
Well, it’s interesting because there is some overlap in the sense that the arguments that both Fawn and Robert Berry put out, they both care deeply about their students, right? We’re not gonna argue that. They care deeply. And something that I would say about Miss Teagues is there’s something about the way that she sees not only her classroom, her students, but she sees all of the students in the school as her students. And her idea of resource generation is really helping the teachers to generate resources from their community themselves, and to also realize that the students see themselves reflected in the teachers. And I think that—you know, again, this is not about the real person—but the movie portrayal, and we often see kind of this, for Freedom Writers, we often see this like, Great Last Hope whisked in and her personal sacrifices are what makes these students, these brown and black students’ transformation possible. Because of her sacrifices. Including her marriage. Including, you know, three jobs. And it’s just portrayed in a way that I think really celebrates her sacrifices rather than what the students have already brought—they already come into the room bringing so much as they are, already, without her intervention.

Dan Meyer (38:38):
I love the portrayal of the teacher as part of a community of teachers. Versus in so many of these movies, it’s the teacher as the only person who gets it, you know, oftentimes coming from outside of the world of teaching and everyone’s against them and wants ’em just to fall in line and do the thing we always do, and they’re the outlier. But in Abbott Elementary, it’s like we all rise and we fall together. And teachers are investing in each other’s success, especially with Gregory the longterm sub. We’re all rooting for his, you know, his flourishing. I love that. And yeah. That’s bigtime.

Chris Nho (39:09):
Yeah, I think one interesting thing is that Freedom Writers, when it came out, I think it was like a commercial success.

Bethany Lockhart Johnson (39:17):
Oh, big time. Yeah. It was.

Chris Nho (39:18):
It probably influenced a lot of people to try teaching out. So I do wonder what it says about us, right? Like that we want teaching to fit this narrative, and we wanna be those people who could go into a classroom and <puts on “cool voice”> “Y’all listen to Snoop Dog?” and just have that question HIT. <laughter> And you know, I’ve taught in a large urban school district, and I’ve been that person and I’ve seen other people try and be that person. And I think stepping away from it a little bit, just—it’s a reflection of what people want out of teaching and what they think better education looks like.

Dan Meyer (39:57):
Yeah, yeah. This idea that, so I’m a middle-class person, let’s say, and like, there’s this idea, like, “I know what I would do if I was going into circumstances of impoverishment.” Like I have—

Bethany Lockhart Johnson (40:06):
“All they really need is…”

Dan Meyer (40:07):
…for me to give ’em some real talk and tell ’em, you know, pull their pants up or whatever, listen to Snoop Dog, that kind of thing. And that will be the key. And that’s not how it is in, you know, in Jack Black in School of Rock or Tina Fey school, which are, you know, coded as largely like upper-class or largely white schools. And in those movies, it’s interesting, like how it’s about students discovering themselves, oftentimes. And the central figures are often students. And the students need to reject an oppressive parent figure or something and find themselves. But no, in Freedom Writers, it’s like, “You need to become more like the middle-class teachers who are coming in here to give you this wisdom.” It’s just interesting. I do find it—a pet peeve of mine is when movies portray teachers as only successful if you endure, for instance, the failure of your marriage, or even in Stand and Deliver, for instance, like Jaime Escalante, they depict him having a heart attack. And, like, the job oughta be…easier. <Audience laughs>

Chris Nho (41:04):
Truth.

Bethany Lockhart Johnson (41:05):
That’s the barometer for how much….

Dan Meyer (41:09):
Like, no heart attacks and no divorces related to the job, that kind of thing. I do love how in Abbott—one last thing and we’ll vote and Abbott will win <audience laughs>—is like how, like there, there is a lot of degradation in Abbott, but it’s not a divorce or a heart attack—it’s the petty indignities of asking a student, “Do you wanna hang with me?” And a student says, “Nah, not really.” And that just spoke to me like how it’s not cinematic, but teaching, successful teaching, is like a collection of developing an immunity to students saying, “You’re not hot.” <Laugh> You know? And so I love that. I do wish that there was more depiction of students in Abbott Elementary. It’s a lot of adult stuff. Whatever. Give it up for Abbott, if you would, please. Let’s just get this done here. All right. That’s plenty. That’s plenty. Not gonna ask folks about Freedom Writers. OK, let’s move on to— all right, let’s hear it for Freedom Writers! Yeah. OK, cool. We go, yep.

Chris Nho (42:05):
Plot twist!

Bethany Lockhart Johnson (42:07):
OK, let’s see our final four. Cut and paste. Real time. Real time.

Audience member (42:12):
Where’s Dolores Umbridge?

Dan Meyer (42:14):
Oh….

Bethany Lockhart Johnson (42:16):
Hey, did you hear that? He said, “Where’s Dolores Umbridge?”

Dan Meyer (42:20):
All right. OK.

Bethany Lockhart Johnson (42:20):
See, we missed so many. We could…

Dan Meyer (42:21):
So coming up here, we’ve got in the Eastern Conference, Tina Fey and Ms. Frizzle. Y’all know how I feel about that one. Let’s just get this one done. OK, let’s give it up for Tina Fey. Let’s hear it. <Audience cheers> OK. All right. Yes! Let’s give it up for menace to children everywhere, the terror, the Ms. Frizzle. <Audience cheers> One more time for Tina Fey. Let’s hear it. <Audience cheers> One more time for Ms. Frizzle. Let’s hear it. <Audience cheers>

Bethany Lockhart Johnson (42:59):
Yeah. OK.

Dan Meyer (43:00):
It took ’em one round, but they made the right call in the end. <Laugh>

Chris Nho (43:04):
All it took was 10 minutes of constant Ms. Frizzle-bashing. <Laugh>

Dan Meyer (43:09):
Persevering and problem-solving, that’s my game. Yes. All right. So, do either of you want to influence the audience one way or the other?

Bethany Lockhart Johnson (43:16):
That’s not how I play, Dan.

Dan Meyer (43:18):
Oh, OK. Yeah, that’s true. That’s true. You’re good. On Abbott versus Marshall Kane, should we just let ’em have it? All right. All right. Give it up For Abbott Elementary. Not bad. And for Marshall Kane. OK. OK. I hear Zak and five other people. All right, cool. <laugh> Right on. All right. We got our, we got our finals,

Bethany Lockhart Johnson (43:45):
We did it. We made it to two. And we know: We left out a lot of people. Right? And honestly, I kind of wish we could poll like everyone. I mean, think you put it on Twitter, right? Like, who would you pick? But I would say we had a pretty solid eight there. I’m excited to see who… Look at the little crown he put, you guys. Come on.

Dan Meyer (44:05):
I worked hard for you. For you. <Laugh> Yeah. I liked that it was a good bunch that had a lot of different kinds of qualities…and lack of qualities in some cases. And it allowed us that—I shouldn’t knock her while she’s down, and she IS down, it’s true. <Laugh> And I appreciate the conversation we’ve had, what they have revealed overall about teaching and what the world wants teaching to be versus what it actually is or actually should be. I appreciate that. So let’s settle this here. Give it up, if you would, for Abbott Elementary. <Audience cheers> And give it up for Tina Fey in Mean Girls. <Audience cheers>

Bethany Lockhart Johnson (44:49):
Wow.

Dan Meyer (44:51):
That was close. I almost give that to Tina Fey.

Audience member (44:55):
Yeah, we do!

Dan Meyer (44:55):
I don’t know. That was a bracket-buster for me right there. Yeah. I lost money in the office pool off that right there. Maybe let’s just find out one more time here. One more time.

Bethany Lockhart Johnson (45:03):
Last time.

Dan Meyer (45:03):
Time to summon up all your conviction on one or the other here. No half-measures right now. All right.

Bethany Lockhart Johnson (45:07):
Emmy Award-winning Quinta Brunson.

Dan Meyer (45:09):
Yeah, you saw Robert Berry on that, right? He was like, “Oh, I got one more card to play. Emmy Award-winning.” That’s admissible. That’s admissible. We’ll take that. All right. So…give it up for Abbott Elementary, one last time. <Audience cheers> OK. All right. All right. And give it up for Tina Fey in Mean Girls. <Audience cheers>

Bethany Lockhart Johnson (45:30):
Drumroll, please!

Chris Nho (45:33):
Best teacher is….

Dan Meyer (45:34):
Tina Fey in Mean Girls! Yeah. Not a bad pick.

Bethany Lockhart Johnson (45:39):
I love it. And I think, too, I think we’re gonna have a little bit of a more reflective lens than we thought we did when we see depictions of teachers in film and television. And, you know, hopefully we’ll see some new tropes come in, right?

Dan Meyer (45:55):
Yep. Yeah. Every dollar we spend on movies with lousy teachers is just encouraging these people to make more lousy teacher movies, you know? Awesome. Thank you for being here for a live taping—

Bethany Lockhart Johnson (46:06):
Thank you for being here.

Dan Meyer (46:06):
—of our podcast, Math Teacher Lounge, in a hot room. Appreciate that. Yeah, it’s been fun for us to have you here. Um, super-important, super-important final remark: Bethany loves Oprah and Oprah occasionally, in the show—

Bethany Lockhart Johnson (46:18):
Is she coming?! Is she here?!

Dan Meyer (46:19):
Not here! Not here! Calm down. Calm down. Um, but we do have in Oprah fashion, not something—

Bethany Lockhart Johnson (46:24):
Oh. Oh, OK. Oh, that’s, that’s OK. Sorry. I got, had really excited for a second. As if the Amplify playing cards, The Amplify t-shirts being chucked at you at high speed—I did try to get a t-shirt cannon, and that was quickly ruled out <laugh>. They didn’t know about my rocket arm, right?

Dan Meyer (46:46):
Yeah, you got a cannon. <Laugh>

Bethany Lockhart Johnson (46:47):
Yeah. Oh, that’s a compliment. Oh, is that a compliment? Thank you, Dan. Thank you. Look under your seat because we have five winners. We wanna thank you for being here in person. We wanna thank the folks who are listening. We wanna thank Amplify. Oh my God. Somebody just pulled off the chair tag. You get to take that chair home with you.

Dan Meyer (47:08):
Does anybody have a prize?

Bethany Lockhart Johnson (47:10):
OK, stand up if you…stand up if you…Yes! Stand up if you have one!

Dan Meyer (47:16):
Free set of classroom dry-erase boards, right here. Congratulations.

Bethany Lockhart Johnson (47:22):
And for you who pulled off the chair tag, I don’t know. We gotta we gotta find something for you.

Dan Meyer (47:27):
Put that in your backpack.

Bethany Lockhart Johnson (47:30):
Thank you again for being here. Thank you. Amplify. Thank you, Desmos. Thank you. Dan Meyer.

Dan Meyer (47:36):
Thank you folks. Chris, thank you buddy.

Bethany Lockhart Johnson (47:38):
Chris! Chris Nho, everybody!

Dan Meyer (47:40):
We will be, we will be at—Bethany and I will be at the booth, if you wanna chit-chat and hang out, sign some stuff. Whatever. You wanna have Bethany sign you, she’ll do that. Um, come on down to the Amplify booth and we’ll—

Bethany Lockhart Johnson (47:50):
We’ll talk to you more about Ms. Frizzle.

Dan Meyer (47:52):
Fun and prizes. I will share with my real thoughts about Ms. Frizzle down there. I’d love to see you. Thanks for being here, folks.

Bethany Lockhart Johnson (47:57):
Thanks for listening. Bye.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Dan Meyer says about math teaching

“Teaching, more than other professions, is a generational profession. The kinds of joyful experiences we offer—or don’t offer—now affect the experiences students that haven’t even been born yet will have years later.”

– Dan Meyer

Meet the guests

Dan Meyer

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Bethany Lockhart Johnson

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

A woman with curly hair and glasses smiles outdoors; a man with short dark hair smiles indoors in front of a blurred math teacher lounge, highlighting valuable math teacher resources.
A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

S5-02. Uncovering the causes of math anxiety

A blue graphic with text reading "Math Teacher Lounge" in multicolored letters and "Amplify." at the bottom, with abstract geometric shapes and lines as decoration.

We’re continuing our season theme of math anxiety, going beyond the basics, diving deeper into what causes it, and how we can help students move forward. In this episode, we talk to Dr. Erin Maloney from the University of Ottawa to better understand what’s actually happening in the brain when a person experiences math anxiety, and how we can take steps to shift student mindsets in a positive direction.
 
Listen now and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!
 
Enjoy this episode and explore more from Math Teacher Lounge by visiting our main page. 

Download Transcript

Dr. Erin Maloney (00:00):

It’s the anxiety itself in many ways that can cause people to underperform.

Bethany Lockhart Johnson (00:06):

Welcome back to Math Teacher Lounge. I’m Bethany Lockhart Johnson.

Dan Meyer (00:10):

And I’m Dan Meyer.

Bethany Lockhart Johnson (00:11):

This is episode two of our new season, all about math anxiety. Who has it? What is it? What do we do about it?

Dan Meyer (00:20):

I’m learning so much, learning a ton.

Bethany Lockhart Johnson (00:22):

I loved our first conversation with Dr. Gerardo Ramirez, episode one, our first episode of the season. Really, our goal with that conversation was just to—we need to talk about the basics of it, for reals. Like, what is math anxiety?

Dan Meyer (00:36):

What is it? How do you measure it? How’s it defined? Super-helpful stuff.

Bethany Lockhart Johnson (00:40):

There’s not only one way that it’s measured. But it’s like, in active research right now, how are folks making sense of it? And I think Dr. Ramirez did such a fantastic job of sharing that with our listeners. And I learned a lot. You learned a lot, Dan?

Dan Meyer (00:56):

I did. And I’m also super-excited to take that knowledge that we have developed together and go and build on top of it and keep on climbing up up the mountain here, and learn more about math anxiety. Which is why we’re super-excited to have a guest on, Dr. Maloney, who is going to help us learn more—especially about what happens to the brain when it’s experiencing math anxiety. There’s some really complex stuff that happens there, including the role of parents and educators in creating and resolving math anxiety. And I think we’ll also learn that the whole situation is a bit of a hot mess. And we’ll try to make it a little bit less messy together.

Bethany Lockhart Johnson (01:34):

Little bit less messy. Dan, if we do nothing else, can we make it a little less messy?

Dan Meyer (01:41):

I sometimes prefer more mess, but in this case I prefer less. So.

Bethany Lockhart Johnson (01:45):

I have a two-year-old, so everything is a mess.

Dan Meyer (01:47):

Your life is mess. Yes. <laugh> Right. Well, I’m excited for you folks to hear this. It was a delightful conversation, so yeah, tune in. We are joined by Dr. Erin Maloney.

Bethany Lockhart Johnson (01:56):

Let’s go. We are joined by Dr. Erin Maloney, associate professor in the School of Psychology at the University of Ottawa, where she directs the Cognition and Emotion Laboratory, as well as serving as the Canada Research Chair in Academic Achievement and Well-being. Welcome to the show, Dr. Maloney. We’re so excited to have you in the Lounge.

Dr. Erin Maloney (02:20):

Yeah, thank you so much for having me. This is fantastic.

Bethany Lockhart Johnson (02:24):

So our last season was all about math and joy. And even when I read your title, I felt more joyful. Like, somebody is thinking about academic achievement, but with well-being in mind. I love it.

Dr. Erin Maloney (02:39):

Aw, thank you.

Dan Meyer (02:40):

Cognition and emotion!

Bethany Lockhart Johnson (02:42):

E-mo-tion!

Dr. Erin Maloney (02:43):

I don’t think they can be separate. I think that you have to think about them together, ’cause they’re so intricately connected.

Dan Meyer (02:49):

Love that. People try, but we love that. Yeah. That’s our vibe here, too.

Bethany Lockhart Johnson (02:52):

People try. That was a big problem with my math anxiety. They just wanted…there was no room for my emotion. They’re like, stop weeping at your desk—

Dan Meyer (03:00):

It’s rearranging neurons….

Bethany Lockhart Johnson (03:01):

—you’re distracting the other children. So would you mind telling us the story of how you even got interested in this topic? You know, when you tell people that you study math anxiety—or, actually, I don’t know how you describe it to them; I’m hopeful you bring in that well-being part—but how did you get here? What do you, what do you, what do you…yeah, tell us! We love it!

Dr. Erin Maloney (03:23):

<laugh> I feel like what you’re actually asking is, “How did you make life choices that got you to here?” <Laugh>

Bethany Lockhart Johnson (03:29):

Justify your life choices! Ready? Go!

Dr. Erin Maloney (03:32):

<laugh> Whoo. OK. So, all right. So we often, in psychology, we joke that instead of doing research, we do “me-search.” And that’s, that’s admittedly true in my case. I was a student who absolutely loved math up until about eighth grade, and then something changed, and all of a sudden I was terrified of math and I had absolutely no sense of self-efficacy in it. Despite trying really hard, I was extremely anxious about it. And so I initially, I set out…my parents were completely convinced that I was absolutely capable of doing mathematics and that I was getting in my own way. And when I went to university, I decided to prove them wrong. So I set out to prove that some people just can’t do math, and that’s the end of it. And, you know, 20 plus years later, my parents were right. And it turns out that many people—well, I would argue virtually everyone—can do math. And that if you are really anxious about it, it can get in the way. And interestingly, you know, in, in the years that we’ve been doing this research, there’s really good strategies that can be used—that hopefully we get a chance to chat about—that can really help reduce the amount of anxiety that students are experiencing. But I really did set out, like the bold teenager that I was, to prove my parents wrong. And that backfired <laugh>. So I know it’s kind of a strange answer, but it’s the truth. So I was really interested in understanding why it was some people just could not do math.

Dan Meyer (05:10):

That makes two for two so far, on guests for this season who did a version of me-search. And I feel like this is pretty common for a lot of researchers. Like, I wanna figure out…my experience as a teacher, the part where you, I think, diverge from a lot of people I knew in grad school, myself included, is that you actually let counter evidence change your perspective on things. Whereas I feel like a lot of us go in: “I know this is true and I’m gonna gather data!” and lo and behold, I’m true! But only now, with the research TM, you know, trademarked research, attached to it. So that’s, really exciting. Thanks for sharing that.

Dr. Erin Maloney (05:43):

No, you’re welcome.

Bethany Lockhart Johnson (05:44):

But don’t people say that the more personal you get, the more universal it is? Right? So if you go and get your doctorate about something that you think is just your experience or in your brain, then people are gonna be gonna be like, “Wait a second; you think that too?” “Wait, that math anxiety isn’t just you?” I don’t know, it sounds like a pretty great path to me. When you tell folks that you study math anxiety or when you’re speaking to folks about your research, do you find that there is a lot of folks who relate to what you’re studying? Or how does that conversation typically go?

Dr. Erin Maloney (06:20):

Yeah, so it is I think an extremely relatable topic. Not in the sense that everyone experiences anxiety about math, but everyone seems to know somebody who’s really anxious about math. Or everyone’s at least aware of the stereotype that like some people are math people and some people aren’t, and that’s just the way it is. So it feels like everyone has feelings about math and everyone seems very happy to share those feelings. So one thing I’ve always found really interesting, and actually, so I, I know you mentioned that you had Gerardo on recently. Gerardo and I have had really interesting conversations about how people are really quick to tell you that they hate math and they can’t do math, and they’re anxious about math. And I’ve yet to have anyone ever tell me they hate reading, they can’t read, they’re really anxious about reading as an adult. So for some reason math seems really different. And in that sense people always seem to be pretty excited to talk about their feelings towards math.

Dan Meyer (07:23):

Yeah, definitely. Been on an airplane or two myself and had those conversations. You know, people asking to be reseated because they found out that I do math for a living or whatever. Or just unburdening themselves, for sure. I’m super-curious: I think that the fact that you are doing the me-search is reason enough to want to dedicate your life to this study. But I am curious: If you were gonna justify to someone else, why is math anxiety important to study? What are its consequences, even outside of math education? What would you say to that?

Dr. Erin Maloney (07:57):

So I think it’s probably not hard to convince people that success in math is important, right? So we know that children who start elementary school behind in mathematics tend to stay behind in mathematics, unless they have any kind of very targeted intervention. We know that children who do worse in mathematics throughout K to 12 education in general get lower-paying jobs when they’re older. We also know that when they do worse than mathematics relative to their peers, there’s fewer jobs that are open to them, relative to if they excelled in math. Right? And so I think in many ways there are really clear consequences for students who are not comfortable with math and who avoid it. But I think one of the really, really interesting things about math anxiety, and maybe part of why I’ve fallen in love with it as a research topic is that it’s the anxiety itself in many ways that can cause people to underperform. So it’s not just the case that people who are bad at math are anxious about it. It’s actually that the anxiety itself can cause you to do worse in math. And that for me is really exciting, ’cause it means that if we can change your mindset, then we can really set you on a path with several more options available to you career-wise. And I think that is really empowering.

Dan Meyer (09:18):

Hmm. Yeah, definitely. And I’d love for you to explore — your laboratory is the cognition and emotion laboratory, which I love, how you’re creating those linkages between how you feel about a thing and what your opportunities or your aptitude for learning it. I’m really curious, can you say more about the, the relationship there? How does feeling anxiety impair your ability to do mathematics?

Dr. Erin Maloney (09:41):

Yeah, so feeling anxiety, typically what you tend to experience is these negative thoughts and ruminations. So you can imagine, you’re somebody who doesn’t really love math, you’re pretty anxious about it; you know, Bethany, maybe you’ve had this kind of experience before. I’m gonna call you out on it. I’ve had it many times, where you sit down to do a math test and all of a sudden you’re not focusing on the actual math test in front of you. You’re focusing on things like the consequences of not doing well on this. Right? Or “my parents are gonna be really disappointed if I don’t pass this test,” or “my teacher is gonna think negatively negative of me,” or sometimes we see things like, “I’m a girl, girls don’t do math.” These types of stereotypes. And what happens is that those thoughts actually tie up really important cognitive resources, like, really important memory resources, that you need to do the math test. And so if you are trying to essentially do two things at once, right? You’re trying to deal with all these negative thoughts that are distracting you and you’re trying to do the math test, then you’re not going to do as well as someone who’s sitting down and doesn’t have all of these distracting thoughts to deal with. And we actually know that from research that we have in our lab right now, where we just ask people like, “Hey, when you did this math test, what kind of stuff are you thinking about?” what we find is that the people who are really anxious about math report a whole bunch of thoughts that are unrelated really to the math test, per se. It’s more about the consequences of doing poorly. And as a result of those thoughts, they actually end up doing worse.

Dan Meyer (11:14):

This has been really helpful to figure out, how the emotional state of doing math affects the ability to do math. And it’s really interesting how you’re saying that the direction of the causality can go from the emotions to the cognition. And I’m just curious then, what is the source of the bad emotions about math? Where does that come from? Is it nature? Is it nurture? Some combination? How do you see it?

Dr. Erin Maloney (11:39):

Yeah, so one, that’s a fantastic question. And there’s been a whole bunch of people all around the world that have been spending a lot of time really trying to pinpoint that down. And I think the answer is that it’s, you know, it’s complex. So most of what it’s looking like right now is that it is a combination of both. So essentially what we find is that kids who start elementary school who are a little bit behind in math—and for the question of why they’re behind, that’s also complex; it could be genetics, it could be just environmental input, before the child ever entered formal schooling kind of thing—but in essence, what we find is that kids that start school behind in mathematics, those are the children who are most likely to develop anxiety about math by the time they’re finished first grade. OK? But we also know that once they’ve developed the anxiety about math, then that’s when they get these thoughts and ruminations that kind of tie up those memory resources, that then is gonna make it harder for them to succeed in math tests. So you get into this sort of vicious cycle, right? Where maybe you start behind a little bit and then you develop the anxiety, the anxiety causes you to underperform relative to what you should be able to, so now you’re even further behind, you get more anxious because you’re not doing as well as you’d like to…but again, kind of coming back to the “Why are the children starting behind in the first place?” Some of that seems to be the role that parents are playing in the household. So some kids come from a household where parents are playing a lot more math games with them, talking about mathematical concepts on a regular basis. Maybe they have older siblings who are, you know, practicing arithmetic and, and mathematical processing in front of them. And so those kids are exposed to more math before they ever even start formal schooling. Those kids seem to do better. And then we also know that the parents’ attitudes matter a lot too. So what we find is that when parents are high in math anxiety themselves, especially when they help their children a lot with their math homework in really early ages, we find that those kids end up being more anxious about math by the end of the school year, and they also end up doing worse in mathematics. So it really does seem to be, you know, kind of a complex set of factors that have something to do with both maybe genetic predisposition to success in math and genetic predisposition to anxiety, but then also the social attitudes and stereotypes about math to which you’re exposed at home that really seem to be coming together to create this anxiety in young children.

Bethany Lockhart Johnson (14:24):

I feel like everything you’re saying is <laugh>…it makes so much sense and yet it’s so often not talked about, right? Because it’s just more like, it gets boiled down to, “Oh, they’re just not a math person,” instead of all these other factors that are at play. And I completely remember the anxiety I felt, whether it was a test or not, walking into my math classroom when I was in ninth grade. And there’s no way I was set up and ready to learn. Right? <Laugh>. And something with—we mentioned Dr. Ramirez, he was talking about validating that anxiety. If teachers validate that like, “Oh, you know what, sometimes you might feel stumped, or this might feel overwhelming.” Even the power in creating space for that in the classroom, right? And acknowledging that it doesn’t—math doesn’t have to “come easy” to you in order for you to have access or make sense, is such a powerful concept. And I love the way that you are looking at all these different factors and saying, “Hey, it’s both simple and also a lot more complicated than we’re we’re making it.” Right?

Dr. Erin Maloney (15:36):

No, and I agree with that sentiment so much. Like, I think, though—one thing I will sort of caution is that I think when teachers are validating the anxiety, or when parents are validating the anxiety, I think there’s a very fine line that needs to be walked where we need to be able to say, you know, “It’s OK to struggle with something. That’s, that is completely OK.” And as we’re, you know, as we’re working towards something that’s really valuable, right? We can, we can work hard at something and by working hard at it, we’re going to get better. And I think that type of validating is really, really important and valuable. I think what we wanna be careful of is not to say things like, “Oh, it’s OK. I also never loved math.” And, you know, “Oh, I was never a math person either.” And so even though we might be bringing comfort to the the child, I think that that’s sending the wrong message. And so sometimes it’s really well intentioned and really not great—

Bethany Lockhart Johnson (16:37):

A hundred percent.

Dr. Erin Maloney (16:38):

—in terms of the messaging. So that’s the only…so just for people listening, the only sort of caution that I would give there is that I think there’s nuances to the validating of the feelings that are important.

Bethany Lockhart Johnson (16:50):

I am so glad you said that because as a kindergarten teacher, I vividly remember—and this is as early as, you know, the kids are five years old, right?—and I remember in a parent-teacher conference, a parent saying, “Oh, I wasn’t a math person either,” or, “Oh, no, ugh.” And they were so quick, like you said, they wouldn’t say that about reading, but they were so quick to talk about their lack of natural math aptitude, right? And, and it was really interesting because you know that even if they’re not saying that specific thing at home, those attitudes are absolutely carrying over at home. And they’re absolutely carrying over to, to how they interact with their kiddo around math and around what’s happening in the conversations about math. And I felt like a lot of times my work as a teacher was also to help support parents through their own math anxiety, and help give them some new language for how they can talk about math. And that math is more than just getting to an answer quickly. Like, let’s talk about, let’s go on math walks, let’s go on number walks, what numbers are around the home? Or oh, is that bigger than this? Do you have more of this? And even those little things, I, my hope was that it was starting to shift the conversation around what math was possible in the home, particularly when you saw that it was the parents who had palpable math anxiety. Right? And how much you know that that’s gonna impact what’s happening when you sit down to do homework together.

Dr. Erin Maloney (18:22):

Yeah. And I love that you have worked to encourage parents to do that. So we do similarly. Like even from a research perspective, where I will often give talks to parents and teachers and we talk about the idea of trying to mathematize everything, right? So just the idea that math is absolutely everywhere, and you know, whether it’s a matter of playing games in the car with your kids where you’re thinking of a number and it’s “My number is higher than 42, but lower than 80, and what number do you think I might be thinking of?” And, and gradually trying to get the child to that number. Or, you know, asking questions like, “What’s your favorite even number and why?” And just little things like that that, that I think can make math fun for kids, that help—I don’t even know how to explain it, but just that idea of bringing joy into it, so it’s not always this heavy subject that kids have to come to. So we definitely try to talk to parents about the idea of, like I said, mathematizing everything. And usually it’s well-received, ’cause often parents find it empowering, right? They’re like, “Oh, well, I could do that! But like, that’s not math!” And you’re like, “No, but it is.”

Dan Meyer (19:33):

Yep.

Dr. Erin Maloney (19:34):

Like, it is! And sometimes parents will say like, “Well, I don’t know how to do fractions.” And you’re like, “OK, but how do you bake?” “Well, I don’t know! I just, like, I know how to do those fractions!” And you’re like, “OK, but that’s the starting point. Let’s work with that.” Like, let’s, you know. And I think a lot of times, it’s reminding the parents that they’re actually far more capable than what they think they are, despite the fact that maybe they struggled with math when they were younger.

Dan Meyer (19:58):

Yeah. This is so interesting. And I feel like part of the challenge around conversations about anxiety and math and how to, how to resolve it and where it comes from, is that it, like, it presupposes a single definition of math. And so, you know, we’re talking about like how to be more mindful about math. But you know, like if kids were walking every day through a treacherous street, you know, the solution might not be become more mindful about that street. It’s just like, we gotta fix the treacherous nature of the street, really. You know, I love that we’re talking also about redefining what math is, making it more playful. That feels like a super-important component here. I’d love to know more about what you know about the role of gender in all of this. Are there differences in the way boys and girls experience math anxiety and how it relates to achievement in math?

Dr. Erin Maloney (20:48):

Yeah, so, there’s really, really interesting research on gender in math anxiety. So in general, we find that girls tend to experience more anxiety about math than boys do. So one hypothesis is that it has to do with just social stereotypes that, you know, girls are, are good at reading; boys are good at math, kind of thing. So there’s some evidence to suggest that that might be playing a role. There’s other evidence to suggest as well that maybe boys actually do experience as much anxiety, they just don’t really own up to it.

Dan Meyer (21:20):

Ooh, yikes.

Dr. Erin Maloney (21:21):

So thoughts are, you know, there’s a bit of an apprehension for males to admit experiencing the anxiety. But I think one of the things that is extremely interesting about it—at least to me—is that we don’t tend to see gender differences in young children. So in early elementary school, even though we’ll see that kids as young as six years old will experience anxiety about math, and that that anxiety is related to how well they do in math and how much they enjoy math, it doesn’t seem to vary as a function of gender at that young age. It doesn’t seem to be related to gender until kids are at about sixth, seventh grade that we really start to see this gender difference coming online. And so that, to me, suggests that it’s probably something more social than biological at play. It probably has something more to do with these stereotypes and stuff. But another really interesting—or at least, I’m biased, but to me—another really interesting line of research that comes into play—and some of this is stuff out of my own lab—so we know that boys in general tend to do better at spatial processing than girls. And we know that spatial processing is really important for math, right? So math and space are pretty connected. And by spatial processing, I mean things like being able to picture something rotating in your mind or, you know, envisioning how these puzzle pieces might fit together. And so we know that boys tend to do better at that type of processing. And the gender difference there seems to be related to gender differences in math anxiety. So there’s some speculation, too, that it might be that as the math starts to become more reliant on spatial processing, that that’s when we see this separation between boys and girls with respect to how much anxiety they feel about math. So a lot of this is to say, I think the answer to the gender question right now is what I think what we would officially call a bit of a hot mess, <laugh> where I think there’s probably more questions than answers. But I think that there’s definitely something going on. And it really seems to be coming on later in elementary school.

Dan Meyer (23:32):

That’s a refreshingly honest admission from a social scientist, that it’s a hot mess and not perfectly clear, <laugh> so I appreciate that. It’s interesting what you said about the spatial reasoning. In our work creating curriculum at Amplify, I find we lean a lot on trying to tie abstract math towards spatial topics. Like, can you estimate a quantity before you calculate it? Can you identify a pattern and where it breaks before you prove it abstractly? And, I dunno, it’s just interesting to me. I’m just thinking out loud about how I feel like math becomes more abstract rather than more spatial. The farther you venture into secondary math…I’m wondering if I misunderstand what you’re meaning by spatial, and the progression of math from K–12.

Dr. Erin Maloney (24:20):

Yeah, so I think you can still have—you can have math be abstract, but still really relying on spatial processing. Right? And I think part of that is maybe a bit of us having different definitions of when we say “spatial.” So in cognitive science, when we talk about spatial representations or spatial reasoning, it’s really like anything you’re picturing in your mind, any time you’re really picturing these things in your mind and manipulating those images at all. So if you imagine, even like at a simple level, but it’s gonna hold when you’re going more complex as well. So doing like equivalence problems, for example, where you have to balance the equations.

Dan Meyer (24:58):

Yeah.

Dr. Erin Maloney (24:59):

Even just being able to envision things kind of moving around that equal sign and bringing one piece of the equation from this side to the other is actually an extremely spatial kind of reasoning. Right? Or when you’re expanding, that’s actually extremely extremely spatial, despite the fact that it might not feel like it initially. Obviously anything in geometry is going to be very spatial. So I think, in that sense, we would argue that the spatial processing is still playing a pretty important role. But it’s maybe a different type of spatial processing than what we’re seeing at a very early level in elementary school. That said, you can completely disagree with me too. ‘Cause I could also just be wrong, and that’s fair. My kids tell me I’m wrong all the time. So I’m used to <laugh> being told that I’m wrong.

Dan Meyer (25:47):

Well, we’re a bit more deferential on this here show, with our guests. So I would not do that. But it makes sense, what you’re saying about how these are things that you manipulate in your mind, whether they are Xs and Ys or numbers and fractions. These are all things that we manipulate. That ties into differences in this spacial reasoning category, it sounds like, which then contributes to math anxiety. And it does start to feel like there’s a lot going on here, is what it feels like.

Bethany Lockhart Johnson (26:14):

You mean hot mess?

Dan Meyer (26:16):

I meant hot mess.

Dr. Erin Maloney (26:17):

Yeah. <laugh>, I think that’s the technical term, right? I’m pretty sure that’s the technical term for it.

Dan Meyer (26:21):

I didn’t know the citation for it. So I didn’t say it. But I knew who in literature named that. But yeah.

Dr. Erin Maloney (26:28):

I’ll write something at some point.

Dan Meyer (26:30):

We’ll cite Maloney, 2022. Yeah. Yes.

Bethany Lockhart Johnson (26:34):

So I will say that one of my dreams in thinking about this season and last season, but particularly this season, since we’re really getting to talk to some researchers who get to think about this, and have really interesting conversations about it all the time…one of my dreams is that we’re bringing—’cause we do have some folks who are researchers that are listening, right? But then we also have teachers and folks who are in the classroom every day, and parents and caregivers listening. And so I think one of the beautiful things about the way that I hear you talking about it is you’re thinking about the research, but it’s so applicable. Right? And I wonder if there’s anything else you can say around it. I wanna reduce that divide, that gap, between the research that’s happening and then what’s happening with the kiddos and in the classroom and at home. And I don’t know if it’s like a magic wand thing where like <laugh> if there were changes you’d wanna see at a societal level, to try to combat math anxiety, but you see where I’m going. You know, it’s like <laugh>….

Dr. Erin Maloney (27:39):

  1. So I’m gonna answer maybe in two ways. So I think the first thing that I’m hearing from you is that idea of diminishing this divide, right? And so one thing I try to keep in mind, as someone who’s a researcher and working in the lab, I will often be called in to talk to teachers and give professional development sessions. And they often want the sage-on-the-stage academic, that stands up there and tells you the answers to things. And one of the first things that I’m gonna admit when I get up there is, “I am not on the front lines.” So what I do in the lab, for me to tell you that that’s gonna work in a classroom of 30 kids who may or may not have eaten dinner that day, and may or may not have snow pants, and may or not…like it’s–

Bethany Lockhart Johnson (28:23):

Mmm, yes.

Dr. Erin Maloney (28:24):

You know, I think we also need to be a little bit reasonable. So I try really hard in my own program of research to make sure that I’m always talking to teachers and to principals and to curriculum designers to make sure that the ideas that I have make sense. In fact, one of the most recent book chapters that I wrote, I wrote in collaboration with a really good friend of mine who’s a principal, an elementary school principal, and a former math consultant. And we wrote it together, to really say like, “Hey, here’s how we can help each other inform how research can inform practice and how practice can also inform research.” ‘Cause he can come to me and say, “I’m doing this. I can’t find anything in the literature to support this, but I’m sure it works!” And we can design something in the lab to test whether or not it seems like it’s gonna work.

Bethany Lockhart Johnson (29:11):

That’s huge. Yeah.

Dr. Erin Maloney (29:12):

Empirically. And so I think that open communication is massive. One thing that we’re doing in my own lab to try to keep that open communication available. So to anyone listening who’s ever tried to get access to a journal article, they’re held behind paywalls, right? So one, the way it works, my understanding of this anyway, is that the journal owns the formatted version of the paper. So what we do is we put up audio recordings of all of the research papers that we ever publish. So I’m pretty sure I own the words as the author, and the journal owns the prettified version that you can buy. So we audio-record all of our papers, so that if teachers or parents ever want to hear the actual science that’s going into some of these decisions, they have access to at least the stuff that we do in our lab. And we also put up an infographic for every paper, just highlighting kind of the main questions and main findings. And we do that because I think that the only way for the information to actually be useful is if it gets into the hands of the stakeholders that actually need that information.

Bethany Lockhart Johnson (30:21):

And is accessible. That’s huge. That’s huge!

Dr. Erin Maloney (30:24):

Yeah. Yeah. So that’s one way that we try to do it. And like I said, the other thing, we try to always be working with principals and with teachers. I joke that the way that I remedied this in my own life…so my husband’s a teacher; it’s like, I just married one! It’s fine! <laugh> I can grill him on a regular basis, and be like, “I wanna try this experiment. Do you think it’s gonna work?” And he can say, like, “It’s not going to. Here’s why.”

Dan Meyer (30:47):

That’s awesome. Marrying a participant—you know, a research participant—is unethical, of course. Would not clear IRB. But turning your partner into a participant? Like, what are you gonna do? That’s great.

Dr. Erin Maloney (30:57):

Yeah, no, that’s fair game.

Dan Meyer (30:58):

Yep.

Dr. Erin Maloney (30:59):

Yeah. So that’s—I think we we compensate each other <laugh>. So, no…so I do joke a little bit about that. He was a teacher simply ’cause he wanted to be one. Not ’cause I needed him to be one. But, I think that communication part is, is really key. That’s one thing. Then the other part of the question or the other sort of piece of the question that I was hearing is that idea of, how do we fix math anxiety. Right? Like, what’s the great, “I’m glad that there’s a whole bunch of time and effort and energy going into trying to understand this, but what, where are we at?” And I think with that, it’s really, really promising. So there’s been a lot of research coming out looking at how best to help children or even adults manage their own anxiety about math. And there’s a few really interesting strategies that seem to be quite effective. So one, and I don’t know if—um, it feels weird calling him Dr. Ramirez, just ’cause I know him well!—but I don’t know if Dr. Ramirez would’ve talked about this when he chatted with you, but he has some really interesting work on expressive writing. Did he chat about that at all?

Bethany Lockhart Johnson (32:07):

He didn’t, but I’ve read some of his work about it and I think it’s so fascinating.

Dr. Erin Maloney (32:11):

Yeah! So, OK, well, I’ll tell you about his work on it.

Bethany Lockhart Johnson (32:13):

Yes, please. Please.

Dr. Erin Maloney (32:14):

Because it’s super-useful. So when we talked about that idea of how anxiety causes these thoughts and ruminations, and they tie up the memory resources that you need, what Gerardo has found is that when you get students to write about their anxiety for about 10 minutes before they do a test, what ends up happening is they end up doing better on the test, relative to if they would not have written about their anxiety at all. And this is particularly true for students who are really high in anxiety. OK? And the idea is that all of those thoughts that they were going to have about the test or the consequences of the test, et cetera, you just kind of get ’em…it’s like a mind dump where you get ’em all onto the page at first before you even go to do the test. And now when you go to do the test, you’re not having to do two things at once. You’re no longer dealing with these thoughts ’cause you got ’em all out on the paper beforehand. And so Gerardo has some really interesting work showing that that works for math anxiety. And then it also works for just testing anxiety in general. And so that’s a strategy that I love. I also—part of what I really love about it is it’s so low-cost, right? You need a paper and a pencil and it’s great. So those are always my favorite strategies, the ones that don’t really cost us anything. So that’s one way of dealing with like the cognitive part of the anxiety. The other thing you can do is try to deal with the anxiety part of the anxiety. So for that, what we find is that the typical strategies that you’re gonna see for anxiety tend to work for math anxiety. So things like focused breathing. Right? Making sure you’re doing deep inhales and exhales. That really diaphragmatic breathing seems to be quite helpful. We know that what we call progressive desensitization is really key. That’s the idea of doing things, you know, starting with the questions that you know how to handle. And then gradually working up to the more difficult questions. So you’re sort of gradually exposing yourself to the more complex stuff. And how that can play out on an actual test at school is, you sit down, and instead of just starting with question number one, you actually read the whole test, see which questions you feel like you know the best, start with those questions, and that helps build your confidence so that you’re better able to tackle the questions that are maybe a little bit outside of where you’re currently at. So that seems to be really helpful. The other part that I will say, too, that’s extremely helpful: So we know that anxiety really ties up those memory resources. And so the more you can make the math automatic, the more immune it’s going to be to anxiety in the moment. And so I know that this part can be a little bit controversial, because we don’t wanna necessarily demotivate children, and kill the enthusiasm for math that we’re trying to cultivate…but really, you know, really committing your arithmetic facts to memory can be extremely helpful. So really learning those times tables, really learning your addition and subtraction facts. ‘Cause what happens is, then when you’re in a situation where you need that information, even if you’re anxious and you’re working with fewer cognitive resources than what you would normally have, you actually don’t need that many cognitive resources to be able to pull something from memory that you’ve memorized. So it really helps to kind of protect you against some of the negative impacts of the anxiety while you’re doing that test.

Bethany Lockhart Johnson (35:37):

And you’re not using all your cognitive resources to figure out seven times eight, because you can really focus on what you’re trying to do with that. Oh, that’s fascinating. Yeah. Yeah.

Dr. Erin Maloney (35:47):

Yes. No, a hundred percent right. And so I know that’s one that, like I said, I know it can be somewhat controversial because it’s…you know, we’ve talked about—or we haven’t talked about in this conversation, but we often talk about—the idea of drilling and killing. Right? So you drill the facts, you kill the, the enthusiasm. But I think that there are ways that we can drill arithmetic facts, or help make them automatic, but still fun, right? It doesn’t have to always be in a high-pressure kind of way.

Bethany Lockhart Johnson (36:16):

Totally. And we’ve talked about fluency, and I’m sure we’ll talk about it more in the Lounge. And that is interesting, that link between anxiety when the fluency isn’t there, that—or, of course we hear about anxiety with timed tests, but the idea of that IS something you can do to reduce it, because you have those facts just at your ready. Right?

Dr. Erin Maloney (36:37):

Yeah. So I actually, again, I’m gonna be a little bit controversial. So I don’t hate timed tests in the way that a lot of people do. But I love time to practice. So I think once we’ve got to a point where children have a fairly decent understanding of skills, of a skill, once they’ve got a fairly decent grasp on it, then I love the idea of the timed practice. So it can be still in a low-pressure situation, where in many ways it doesn’t matter if you get the answer to the question correct. But we’re practicing doing it in a situation in which you might be feeling a little bit of pressure, but it’s not real pressure, if that makes sense. And I think that can be really, really useful for students. And again, it can be done in a fun way, right? It doesn’t have to be these super-intense ways. It can be fun. But I think that in life there are situations in which the time that it takes you to complete a problem matter. And I think that we have to make sure that we don’t get too far away from that.

Dan Meyer (37:40):

Yeah. It feels like we should do an entire other episode thinking about ways to develop that fluency and automaticity that don’t contribute to anxiety, or create further disparities between people who are high math anxiety and low math anxiety. Not a small question, I’m sure. And I appreciate you alluding to all of that. You know, this whole thing, as you said, is quite the hot mess. And I feel like you, Dr. Maloney, have helped us make this a little less messy, in our heads, and hopefully the listeners’ heads. I really appreciate that. I just love…you’ve mentioned lots of resources that you have. You’ve alluded to them: audiobook-style readings of your research, which I need ’cause I just finished, you know, Harry Potter, the seventh book, so I need a new thing to listen to like that. Also infographics. Can you tell our listeners where they can find this work of yours, and if there are any other kinds of resources that you wanna plug for our listeners here?

Dr. Erin Maloney (38:32):

Yeah, for sure. So all of our resources can be found on my lab website. So the address for that is www.ErinMaloney.ca. So there we have, like you said, the infographics and the audio articles and all that stuff. And then we also have a link to a new kids’ book out, actually, that a colleague of mine and I have published recently, that really walks through some of these strategies on combating math anxiety. The book is written as a children’s book, so it’s Peyton & Charlie Challenge Math. But it secretly is a book that would also work for adults. So if you are a parent that’s a little bit anxious about math, or a teacher that maybe is a little bit anxious, and you wanna see how some of these strategies can play out, in that book—we linked to it on the website, but it is available for purchase on Amazon. And the one thing I will say about the book, ’cause this is something that we were pretty proud of, so Sheri-Lynn Skwarchuk, who is a school psychologist, and I wrote the book. And it’s available for purchase at our cost price, so we don’t actually make any money on the book. It was literally just a way of getting some of the science out to people who might be able to benefit from it.

Bethany Lockhart Johnson (39:45):

Reducing that divide!

Dr. Erin Maloney (39:46):

Yeah, well that’s what we’re trying to do! Right? So I think in the U.S., I think it’s like $6 on Amazon. And then in terms of other resources, we’re in the process right now of creating some informational videos and and stuff like that that hopefully will be useful for parents and for teachers, just in terms of understanding a little bit more about the anxiety and understanding how to deal with the anxiety in the classroom more, at home or wherever it might be coming up.

Dan Meyer (40:15):

Well, thanks so much. I really appreciate—we appreciate!—you coming on, and hearing about how you’re trying to bridge so many different barriers from research to practice, and school to home. It’s just really inspiring. And we’d love to have you back on sometime. So thank you so much for joining us.

Bethany Lockhart Johnson (40:29):

I feel like we’ve just hung out! Don’t you, Dan?

Dan Meyer (40:31):

Are we rolling here? Oh my gosh, we’re rolling. I just thought we’re just hanging. Yeah,

Bethany Lockhart Johnson (40:34):

I thought we were just hanging!

Dr. Erin Maloney (40:36):

I know, I do, I really appreciate that it has a very kind of chill vibe to it.

Dan Meyer (40:41):

Chill vibe. Like a lounge.

Bethany Lockhart Johnson (40:42):

It’s the lounge!

Dan Meyer (40:43):

Thank you. You get us; you get us. <laugh>

Bethany Lockhart Johnson (40:45):

Dan Meyer. I was shopping for children’s books, and there was this book, and it was talking about being at home with Mom. And it’s going through all the things that the child did that day with Mom. It’s like, “We played outside, we ran through the sprinklers, we even did some homework.” And it shows them sitting at the table with the homework, that’s clearly math homework, in front of them. And the mom is like, “Harrumph!” Like a very perplexed, anxious face. And there’s all these question marks above her. And it’s just like,

Dan Meyer (41:24):

“There should not be numbers on that paper!”

Bethany Lockhart Johnson (41:25):

Exactly. And the child is like, “Ohhhh,” you know. And I mean, I have to give credit to the illustrator, because they really did capture the clear message of this interaction, which was sitting down to do math homework or think about math together is a source of angst. Right? According to this author and according to too many people. And so I think what’s really important is that we recognize those images when we see them out there and speak back to them, and say, “Hey, wait a second.” Yeah, it can feel like that, and it doesn’t have to. And what’s going on that that’s just the assumed way that it’s gonna feel, to sit down and math together. You know?

Dan Meyer (42:11):

Yeah. It feels like we all have a lot of work to do on the whole math-anxiety front. Dr. Maloney helped us see how parents play a part, educators play a part, society and how they create people plays its own part in how we all define math as a thing where we evaluate student thought or where students play it with their thoughts, has its own huge part as well. So yeah, it was a really fantastic conversation with Dr. Maloney. I hope you folks will check out the show notes, where you will find links to Dr. Maloney’s website. A lot of her work, which as you heard, is very geared towards practitioners and parents and even directly at kids, especially the new children’s book she co-authored, Peyton & Charlie Challenge Math.

Bethany Lockhart Johnson (42:55):

Next time we’re gonna dive even more into the nitty gritty of combating math anxiety. To do that, we’re actually gonna be joined—I am so excited about this—by Dr. Rosemarie Truglio from Sesame Workshop.

Rosemarie Truglio (43:09):

Our core audience are two- to four-year-olds, and they love math. And what’s not to love? Children don’t come with this math anxiety. Math anxiety is learned.

Dan Meyer (43:23):

So excited.

Dr. Erin Maloney (43:24):

Sesame Street was a huge part of my childhood and my toddler doesn’t know it yet, but Sesame Street is coming. It’s coming. Like, we’re we’re gonna introduce Sesame Street to him. We just haven’t yet.

Dan Meyer (43:37):

Sesame Street straight raised me.

Bethany Lockhart Johnson (43:38):

Right?

Dan Meyer (43:39):

Yeah. Don’t tell my parents. But that’s, yeah, that’s true. I’m excited, too. It’s gonna be a blast.

Bethany Lockhart Johnson (43:45):

I’m really excited. I think that the more we dive into this topic—which, again, we’re gonna look at math anxiety from a lot of different angles—and I’m excited to talk to Dr. Truglio about how we can take this research and these conversations that are happening about math and how it can actually impact what’s happening in homes. ‘Cause we wanna help create positive relationships with mathematics, with kids in math. I’m so excited. And I hope you folks keep listening. We love having you here in the Lounge. And if you haven’t already, please subscribe to Math Teacher Lounge, wherever you get podcasts. And if you like what you’re hearing, please leave us a rating and a review. It helps more listeners to find the show, and let other folks know about this show. Recommendations are great. Thanks so much for listening.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Dr. Erin Maloney says about math

“If we can change their mindset, then we can set students on a path to more opportunities and success.”

–Dr. Erin Maloney

Associate Professor in the School of Psychology, Director of the Cognition and Emotion Laboratory, and the Canada Research Chair (Tier II) in Academic Achievement and Well-Being, all at the University of Ottawa

Meet the guest

Erin Maloney is an Associate Professor and Canada Research Chair at the University of Ottawa. Her research sits at the intersection of Cognitive Psychology, Developmental Psychology, and Education and focuses on cognitive and emotional factors that relate to academic achievement. She is a world-renowned expert on the study of math anxiety, conducting research in the lab, in homes, and in classrooms with children, parents, and their teachers. She is passionate about both knowledge mobilization and equity, diversity, and inclusion within education and science.

A woman with straight, shoulder-length light brown hair smiles at the camera, framed by a circular graphic with geometric accents on a white background—perfect for a math teacher lounge or sharing math teacher resources.
A laptop displaying a Facebook group page for "Math Teacher Lounge Community," featuring profile photos, a group banner, and geometric shapes in the image background.

About Math Teacher Lounge

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Winter Wrap-Up 02: Mathematizing Children’s Literature

Promotional graphic for Math Teacher Lounge podcast, episode 2, featuring Allison Hintz and Antony Smith, discussing how mathematizing children's literature can build math fluency.

While we’re hard at work producing the exciting fifth season of Math Teacher Lounge: The Podcast, we’re continuing to share some of our favorite conversations from our first four seasons. This time around, we’re revisiting our popular episode that connected literacy and math!

In this episode, we sit down with Allison Hintz and Antony Smith, authors of Mathematizing Children’s Literature, to talk about what would happen if we were to approach children’s literature, and life, through a math lens–and how we can apply those same techniques to classroom teaching!

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Bethany Lockhart Johnson (00:02):

Hi, I’m Bethany Lockhart Johnson.

Dan Meyer (00:04):

Hi, I’m Dan Meyer.

Bethany Lockhart Johnson (00:05):

And we are so excited for another episode of Math Teacher Lounge. And as you know, podcast format; you’re listening now. I think one beautiful thing about the podcast format is that it gives us a little bit more time to have these rich conversations. And I promise I won’t do it, but I could talk to our guests for hours, hours! Authors Allison Hintz and Tony Smith have just released Mathematizing Children’s Literature: Sparking Connections, Joy, and Wonder Through Read-Alouds and Discussion. And today we get to talk to the authors. Allison, Tony, welcome. Welcome to the lounge.

Allison Hintz (00:53):

Thank you. We’re so grateful to be here.

Bethany Lockhart Johnson (00:55):

We’re so excited to have you here. And I wanna say that my very first—was it my first math conference? Maybe it was my first math conference—up in Seattle, the CGI conference, and I’m all like, you know, wide-eyed and just like, “Can this be a place for me, this math community?” Re-envisioning my relationship with math and thinking about myself as a math teacher, what? And I went to your session on mathematizing children’s literature, and I was just so fired up. I was so wowed by your ideas, your energy, and your passion for students’ thinking. And I feel like as I read this book, I felt like I was hanging out with you. Like you were just so encouraging all the way through. Of educators, of other folks working with young people, and really guiding us how to listen with joy and with an open curious mind.

Dan Meyer (02:03):

Yeah. I would love to hear a bit about the genesis of this book for you folks. Like, I’m coming at this from a secondary educator lens. I’ve got small kids, so that’s also part of my interest here. But I love any book, any idea that seeks to merge what seems like two disparate worlds. Like it’s often the case that we feel like, well, there’s approaches for ELA and approaches for math, and they’re kind of separate disciplines. And these poor elementary teachers have to learn all of them and be experts at all of them. And here you both come along and say, “Hey, what if they are the same kind of technique?” Can you just speak to how this came about?

Allison Hintz (02:38):

Definitely. Tony, do you wanna take a try? Do you want me to start us off?

Antony Smith (02:42):

I can start. We oftentimes present and talk together and so we kinda switch back and forth. So that’s just how we are. So probably about eight or nine years ago, Allison and I, our offices were next to each other on our small campus. We’re both professors and we just happened to have a few children’s books that we looked at together and we were just thumbing through the pages. We really liked children’s literature. And we noticed that I would stop at certain points wondering about character motive or plot or sequence of events or language use. And Allison would stop at very different points in the book and notice number and concepts or something about mathematics. And that’s when we started to wonder, what would it be like if we were sharing a children’s book with a group of children and we put our ideas together? Where would we stop? What would we talk about? What would we ask children about in terms of their thinking and what they notice?

Allison Hintz (03:42):

And so we started playing with these questions that we had and started approaching stories with multiple lenses to see what kinds of things would children notice and what kinds of things might they say. And we were also on our own journey in trying to understand how to plan for and facilitate lively discussions and classrooms that surface really complex mathematics. And it felt like stories were a place where that might be a fruitful context for hearing children’s thinking. We’ve worked with a lot of teachers and students in our region. We live in the Seattle area and we’ve applied for some funding over time that’s really helped us be in a lot of community-based organizations and educational contexts and libraries and pediatricians’ offices and classrooms, various classrooms, and see what’s interesting about this and what might teachers and children do with stories that would surface complex mathematics to think about together.

Antony Smith (04:41):

Over time, we came to the realization that if we wanted to hear children’s ideas, we had to stop bombarding them with questions. <laugh> Yeah. And at first it made it worse that we were asking them math and literacy questions at the same time. And so we realized that what we needed to do was to back off and to ask children what they noticed and wondered.

Bethany Lockhart Johnson (05:01):

Can you say more about that and how that kind of evolved into mathematizing children’s literature?

Antony Smith (05:07):

We did work with a number of very thoughtful, talented classroom teachers and children’s librarians in public library systems who were just so masterful at asking open-ended prompts and questions, rather than kind of like the de facto reading quiz, that a read-aloud can become, which I’ve always disliked as a literacy educator. And we realized in our observing these read-alouds or interactive read-alouds or shared reading experiences that given the opportunity in the space and an adult who was actually listening, that children came up with all of the ideas we would have asked them about and more. So we didn’t have to be bombarding them with questions. They were already much more thoughtful than what would’ve been sufficient to answer our questions.

Allison Hintz (05:58):

And much like mathematics, it was really an iterative process. You know, we had some clunky read-aloud discussions where we were trying to accomplish so much and toggling multiple chart papers and different colored pens and all sorts of “how do we capture these ideas” and “do we separate ’em? do we keep ’em together?” And so it’s really been over time that with partners, we’ve learned these ways of having multiple reads of the same story that allow us to hear what children notice and wonder, and then to delve more deeply into their questions and their ideas through multiple reads where we might spotlight literary ideas that they notice; we might spotlight mathematical ideas that they notice. We might make purposeful integrations between those. But we found it to be most productive—and Kristin Gray really help us think about this—to have an open Notice and Wonder, get everything out much like an open-strategy share. We welcome here, record all the ideas, and it goes all over everywhere. You know, it can be a really not math-y noticing! And those are amazing! So there’s a lot of, um, yes, there is a ladybug on this page! The grandma is wearing green triangle earrings! Oh, your grandma wears green earrings! I mean, it all comes out.

Bethany Lockhart Johnson (07:27):

Wait, have you been in my classroom? ‘Cause that’s exactly— <laugh>

Allison Hintz (07:29):

<laugh> And then, you know, we think of it a lot like if math teachers might use the 5 Practices for selecting and sequencing, or if you might move from an open-strategy share to a targeted share, how can we get out all the questions that children are asking and then step back from them, take some time to really think about what they’re telling us they’re curious about, and plan some purposeful, intentional subsequent discussions that can delve more deeply into their ideas.

Dan Meyer (08:02):

I’d love to go into that a little bit more if that’s all right. Um, I’m gonna speak from someone who doesn’t have an elementary background and I’m gonna voice some worries that I had, some anxiety. One anxiety I have like in a classroom or a curriculum is when there’s no room for student ideas. Right? When it’s like, oh, there’s just room for the curriculum author or the teacher here. That is a sadness. But I when I see an instructional environment like you’re describing here, where there is openness to all kinds of different student ideas, of different levels of formality, from different kinds of cultural fonts of knowledge or wherever, I also get a little bit nervous because that, like, increases the risk that a student might come to understand that “my ideas are not good enough,” whereas in the class with no room for their ideas from their home or their language or their hobbies, like, they’re not gonna internalize the message that, “that wasn’t good enough.” And so I’m really curious as you move from the open Notice and Wonder where kids share all of themselves with you, and then you move to a targeted focus on some sort of disciplinary objective, how do you navigate that tension and help students feel like their contributions are valuable, even though we aren’t taking them up per se?

Allison Hintz (09:18):

That’s such an important question. I mean, I think we’ve grappled with this broadly in math education. I think any time we’re thinking about which ideas we choose to take up to pursue to consider, we have a responsibility to think carefully about whose ideas are being taken up and heard and considered. And so one of the tensions I hear you naming, I think, Dan, is when we engage in lively discussion where children’s thinking’s at the center, how do we make sure to upend and interrupt kinda status norms that run the risk of being deepened? Um, and I think by paying attention to whose ideas are taken up as much as which ideas are taken up, and what’s the mathematics we wanna explore is one tension. Um, another tension I might hear you naming is, you know, the complications that teachers face with time and pressure and coverage, and which mathematics ends up getting worked on. And, um, you know, it’s something we’ve really had to struggle with in mathematics education, where we move to more discussion-oriented classrooms that are really centered in sense-making to know that it takes a lot of time to do this thoughtful, thoughtful work. Um, does that begin to get at some of the tensions you’re raising? Is there, is there more you’re thinking about?

Dan Meyer (10:53):

I think it’s really helpful that you kind of broadened the scope of the question beyond your book to “this is an issue that we are, you know, really challenged by and focused on broadly in math education.” And, um, I appreciate you bringing the element in of whose idea—not just which idea is taken up, but whose idea is taken up—is an opportunity where, let’s say, multiple people raise an idea that is towards an objective the teacher has, they have the opportunity to disrupt certain kinds of status, like ideas about status, in that moment. From your perspective, like, are there techniques to say, I don’t know, parking-lot certain kinds of questions and say like, “Hey, like these are awesome”? I don’t know. I just know that I see kids at like ninth grade. They are very reticent, often. They’ve internalized totally this sense of like, “I’m not gonna just, like, share about the pants the grandma’s wearing, you know; that will not be received well.” And so I’m just kinda wondering how that happens and like, what are the ways we can disrupt that? That process?

Antony Smith (11:54):

So thinking about that, Dan, from the teacher’s perspective, in those kinds of scenarios where you wanna honor each child’s contribution, a couple of things that come to mind: One is that by, you know, initially by modeling what I as a teacher, something that I notice or wonder about, helps kind of set the expectation for what kind of response would be encouraged. And it’s broad, but it gives an example. And then also we really try to record or to chart all of the ideas that are shared so that we can revisit and honor those together. And then either later or on another day, if we choose one or two of those to explore in some way within a more focused read, then another thing that we do is have the idea investigation afterward that continues that thought, but goes back to being as open-ended as possible, so that those students or children who maybe didn’t have their idea as the one that was focused on by the group could go back to that or explore some other idea of their own, so that the idea investigation isn’t a lockstep extension activity, which is why we don’t call it that. So they could again bring in their own perspective. But I have to say from the teacher’s point of view, there is that moment of potential panic <laugh> because there is that power transfer when you’re asking children to help steer where this is going. And if you really mean it, you have to let them steer a little bit. And that can be terrifying. And, um, I always think of one teacher, Ashley, we worked with who read an adorable book, Stack the Cats, by Susie Ghahremani. And in that book, there’s a point where there are eight cats and they’re kind of trying to be a tower of cats and they fall and they’re sort of in the air on that page. And she asked her first graders—she stopped, and she asked, “How, do you think, how will the cats land?” And for about a minute and a half, the entire <laugh> class, was silent. They had their little papers; they had chart paper; they had clipboards; they had everything they needed. But that unusual phenomenon of a group of six- and seven-year-olds actually just sitting and thinking and not being peppered with activities was really stressful, but amazing. And then, after about the 90 seconds, they started out into their exploration of how the eight cats might land. They just needed a minute to think. And it’s so rare that we’re able to let children have that.

Allison Hintz (14:40):

In that same moment, Ashley, who’s a learning partner to us, she turned to us kind of quietly, like, “Should I pose a different question?” And <laugh>, we’re like, “No, let’s stick with it. Let’s see what happens.” So I think it creates this space too, this thinking culture, right? And this culture of “what does that mean to really pose a rich task?That’s open-ended, where there’s multiple access points?” Those eight cats could land in so many different ways. And there was broad access, there was a wide range of all the cats landing, and one’s on their feet, ’cause cats always land on their feet <laugh>, and there was every combination. And so, um, I think what’s really interesting—and to me, this brings back to your wonder, Dan—is, you know, “What’s the risk in openness?” And there’s always risk in openness. Um, it’s scary as a teacher, right? If I’m not the authority of knowledge and I don’t have control over where we’re gonna go, it might get into places that I didn’t anticipate. Or I don’t really feel as solid in the math as I want to. Or I don’t know what it sounds like to stick with silence and wait time, to know if my students are really in productive struggle or if that question was a flop. And so, um, I think this is some practice space for young mathematicians and teachers of mathematics, and just teachers, to explore with that openness and kind of the risk of the openness required for complex thinking to emerge.

Bethany Lockhart Johnson (16:12):

You know, it feels like the way you’re both describing this, it really is a culture shift, right? I kept feeling like I was given permission to be a beginner as I read this book. Like I was really…I loved how you said, I believe it was you, Allison, when you were in the class, you had a couple index card that you kept on your clipboard and that as you walked around, you were like, “Hey, if I don’t know what to ask, I ask one of these questions.” You know? And just this idea that, that, like Dan was saying, there is that loss of control, but that’s also a way to create this culture where students ideas are valued and we are allowing students to really generate the questions, which I thought was such an important idea to explore.

Allison Hintz (17:00):

We started this work long ago, super-excited about math-y books. And we saw a lot of potential in them and we still do. But the limitation we saw is that math-y books, they, they put forth a certain mathematics to be curious about. In some ways they tell you what mathematics to think about. So we started asking ourselves what would happen if we considered any story a chance to engage as mathematical sense-makers. And we started playing with non-math-y books and we got to a place where we could consider every story an opportunity to engage in mathematical thinking. And so we started noticing things over times, oh, these books tend to be really math-y. We call those text-dependent. We’d have to pay attention to the mathematics to understand the story. Whereas this pile of stories, these, they’re not overtly math-y. You could really enjoy the story and not pay attention to mathematics and have an amazing conversation. But what would happen if we thought of about this story as mathematical sense-makers and how might it deepen our understanding of the story? And then this other teetering pile of books, these are books where, you know, children didn’t tend to engage as overtly as mathematicians in it, but there’s opportunities in this story to go back to something—to a moment, to an illustration, to a comment—and think as mathematicians. And those were more about illustration exploring. And so, as we notice these different kinds of books, we really broaden what we thought about. And I think one of the things we really wanna think about in community through this book is what happens if we approach any story, every story, as mathematical sense-makers, because stories are alive in children’s lives, in homes and communities and in schools. And it’s a broad opportunity that we wanna take up. I was thinking, as I stay in this strait for just a moment about book selection, before we move into that process, um, Bethany in a previous MTL, you talked about representation.

Bethany Lockhart Johnson (19:12):

Mm, yeah.

Allison Hintz (19:14):

And do you remember when you shared the image of hair braiding?

Bethany Lockhart Johnson (19:19):

Yes. Vividly, yes. <laugh>.

Allison Hintz (19:22):

Yeah. And can you say just what that meant to you? What that….

Bethany Lockhart Johnson (19:27):

Yeah. Well, it was from a conference; Sunil Singh had used it and was talking about the artistry in mathematics and beauty in hair braiding. And, um, particularly, he was showing this particular image of this Black woman with her hair braided in profile and looking at the angles and the symmetry. And I shared that, you know, I spent so many hours in the beauty shop with my aunties and my mom and my grandma and continue to, to this day, that it just, it struck me immediately as familiar. And it struck me immediately as seeing an image that was reflective of my lived reality, projected as valuable and worthwhile for consideration in the world of mathematics. Which is not what I felt as a student of mathematics as a young adult or child. So it was this beautiful moment of, for me, the power of when we see images and we allow opportunities for re-envisioning what may be a common practice for that student, or may be something that they see every day.

Allison Hintz (20:44):

And in that same way, that image that was put up, we wanna think really carefully about representation in the stories that we select. And when we think of stories as mirrors or windows, we really wanna be mindful in story selection of whose stories are told and whose stories are heard. And when you said that you would sit down to listen to a story and you felt at ease or that you saw an image and you saw yourself that can be and should be something we really think carefully about when we select the stories that we select.

Dan Meyer (21:21):

It’s a wider path for representation of different kinds of people in literature, because people’s stories seem so much more present and towards the surface of their lives, versus, say, the abstractions and numbers and shapes in mathematics. It feels like more of a struggle to find ways to show people, hey, like you’re here, this, this place belongs to you. So in all these reasons, I think it’s really great you folks are using literature, which has this history of humanities, literally humanities, as a vehicle for mathematics. That seems pretty special here.

Antony Smith (21:56):

We both go to libraries and bookstores and look through books as often as we can, but also our partner, a children’s librarian, Mie-Mie Wu, helped us go through—when we would meet, she would bring three or four hundred books at a time.

Bethany Lockhart Johnson (22:13):

When you described her wheeling in the cart, oh, I wish I been in that room! <Laugh>

Antony Smith (22:18):

And the cart was, you know, probably three or four times bigger than she was sometimes. And we would go through hundreds of books and look at them and listen to her thoughts as a skilled librarian sharing with families, diverse families, and what catches the attention of a three-year-old sitting with her grandfather. And that was really a valuable, helpful experience. And it’s a partnership that continues. So in Last Stop on Market Street—and this is in the book; we talk about this, this children’s book quite a bit—in this story, CJ with his Nana, his grandmother, are riding the bus to the last stop on Market Street in San Francisco, to go, as we will find out, to help serve in a soup kitchen to help the community. And the teacher, Susan Hadreas, had the children record their ideas. She charted them in an open Notice and Wonder read. And one of the ideas that a young boy noticed was that CJ on the bus…a man with a guitar starts playing the guitar on the bus and CJ closes his eyes and it says CJ’s chest grew full. And he was lost in the sound and the sound gave him the feeling of magic. So this boy said, “I wonder, what does that feel like if you’re feeling the magic? What’s that?” And that was one of many ideas in the open Notice and Wonder, and Allison will talk about the math lens read, but first Susan went back and read with them. She had that idea, she circled it on the chart paper, and another day that week, she said, let’s go back and visit this story we really liked. And remember, we wondered what feeling the magic was like. Let’s go back through and let’s keep track of all the feelings and emotions that CJ had across the journey to the soup kitchen in this book. And so they did another read of the story; they were very familiar with it, of course, but they noticed new things and they also, every few pages, stopped and she helped chart all of the emotions that CJ experienced from envy to excitement to sadness. There’s a huge range in this book. And it was fascinating.

Allison Hintz (24:36):

I think one of the things that the children noticed was that CJ’s feelings were shaped by community. And that he shaped and shaped…he was shaped by and helped shape his community. And so the ways that he felt across the story were impacted by the other characters that he comes across. The guitar man on the bus. The bus driver who can pull a coin out from behind someone’s ear. The lady with the butterflies in the jar. Nana helping him to see the rainbow. And the students started, you know, being curious about that. How do we shape and how are we shaped by community? What communities are we a part of? This class is one community. I’m in many communities across my life. And they started to quantify the number of people in the story. So Mrs. Hedreas went back for a math lens read, and she said, let’s just keep track of and pay attention to how many people are in CJ’s life in this day. Because I can hear you starting to think about quantity. This class at the same time in other areas of the day had been working on counting collections, how to keep track, so they got out their tools. Some people pulled out ten frames, some people pulled out clipboards. They had a wide range of things they could use to help them keep track. They developed their own strategy, keep track however you want. She did a quicker read through it, flipping the pages, and then they get into these debates: <laugh> “We already counted that person!” “But they took their hat off and put it down to collect money!

Antony Smith (26:10):

“What about the dog?”

Allison Hintz (26:11):

“That’s the same person!” “Yeah, there’s a dog pound in his community!” <laugh> “Do animals count in our community?”

Bethany Lockhart Johnson (26:17):

I love it!

Allison Hintz (26:17):

“Yes, they count!” Uh, and so we went through and quantified and there was really this understanding as you saw these people throughout the story that communities can be of different sizes, but community has impact. And you have responsibility in your community to show up and to lean in and to know that bringing your full, authentic, vulnerable self, you shape people and they shape you. And what communities are people a part of. And it turned into this really interesting discussion about quantity and helped us think more about quantity and community. I think a really important moment for us and for that class was the transition from being people who almost did mathematics to a story, like counted things on a page, um, count acorns on a page in an autumn book, to being mathematicians who thought within the story.

Antony Smith (27:17):

And then two idea investigations that came from that —not at the same time, of course, but with the same group of children—one was they identified an emotion of their own and wrote and drew about that. And also, who helped them address or get out of or acknowledge that emotion. And then the other idea investigation was that all of the children drew or kind of mapped out a community that they were part of. Whether it was their neighborhood or their classroom or their soccer team or whatever it was. And so then those investigations strengthened the connections of those concepts to the lives of those children.

Bethany Lockhart Johnson (28:05):

Well, I, actually wanted to ask you about idea investigations. Because I feel like that was such an important invitation in your book. And the way I understood the idea investigation is you’re really paying attention to what’s coming up in your other reads. Right? And then these are opportunities to extend the thinking, or like you said, to extend a particular aspect: What’s your community? Can we map your community? Or what’s a particular emotion? And it was in such contrast to what I think I have probably done in my classroom more than once, which was like, “Oh, we read this story about seals. So now my story problem is gonna be about seals, right? <laugh> Like in the story, you know, Jojo, the seal had five balls. <laugh> So if Jojo still had five balls and two of them bounced away…” You know, or whatever. Right? But that’s not what an idea investigation is. Right?

Allison Hintz (29:03):

Yeah. I think this is where we also had some stumbles and can totally relate to what you’re saying as previous classroom teachers as well. We have come to a place where we are pretty in favor of a super open-ended idea investigation that takes up the things that have surfaced in the multiple reads and making sure it’s a rich task with many, many ways children can engage with that. There’s many, many, many right answers or ways to engage. Less is more there. So we moved way away from, like, even a worksheet that might have an idea from it to blank paper and math tools and places to get into some productive struggle around some of the complex things that were raised.

Antony Smith (29:59):

A challenge with worksheets is that they put a frame around children’s ideas. So either there are only three lines to write on, or there’s only a small box to draw in. Whereas a blank page really opens up the possibility. Um, and so—is it Ann Jonas who wrote Splash!? sorry, I don’t have it in front of me—the book Splash!, about animals that end up in and out of the pond, including a cat that is not happy about ending up in the pond, an idea investigation after that for very young children was, with the list of the different creatures displayed at the front of the room: On blank paper, hey, draw your own pond and decide how many of which and each type of animal you want in your pond and then write about it. Just on blank paper. And so that allowed some children to draw, like, three giant goldfish. But other children drew 17 frogs and three cats. And, and just, it lets children follow—

Bethany Lockhart Johnson (31:02):

It was theirs, right? It was theirs.

Antony Smith (31:04):

Their idea. <laugh> And that comes partly from, I think, as Allison mentioned, we both were classroom teachers before moving into academia. And I remember giving children worksheets, particularly math worksheets, where they weren’t necessarily bad, but right at the bottom, it says like, explain your strategy. And it gives two lines.

Bethany Lockhart Johnson (31:23):

Right! <laugh>

Antony Smith (31:25):

The only thing a seven-year-old can write there is “I thought.” Or “I solved it.” <laugh> And that’s not where we need to go.

Dan Meyer (31:34):

Yeah. If I could just ask the indulgence of the primary crowd here, like, I’m trying to make sense of all this. And I just wanna like, offer my perspective. My summary statement of what’s going on here. I’m trying to—I love how you both came here—

Bethany Lockhart Johnson (31:45):

<laughs> How ya doin’, Dan? How ya doin’?

Dan Meyer (31:47):

<laughs> I’m, ah, A, I’m loving this a lot. Um, B, I came in here loving how you folks are broadening the work of primary education to kind of find commonalities between these sometimes seemingly disparate kinds of teaching in ELA and math. Love that, I wanna say. But I think you folks are describing, with all these teachers you observed and your own work, is the work of attaching meaning to what students might not realize yet has meaning. Or they might think it only has one kind of meaning. But you, the teacher, with their knowledge, realizes that there are many more dimensions of meaning that can be attached to those thoughts. And I’m hearing that from you folks, when you describe A, what math is and the power of a teacher to name a thing as mathematical. Like, “Oh, you didn’t think math was that, but math is noticing; math is wondering; math is asking questions,” for one. But also this work you’re describing of how, like, first the task has to invite lots of student thoughts and then to say like, “Oh, I see that there’s a similarity to these two.” And to raise those up for a conversation or to ask a question like to extend one person’s, one student’s question a little bit more. But it’s always…I’m just hearing you folks attaching more meaning than the student might have originally thought. I appreciate the conversation. That’s really interesting.

Bethany Lockhart Johnson (33:03):

Well, and now that the book is out, I think it’s gonna keep evolving, right? Now that it’s gonna be in the hands of teachers and librarians and educators and caregivers, it’s exciting to see kind of where it goes next. Which actually brings us to our MTL challenge. Dan Meyer, do you wanna share?

Dan Meyer (33:22):

Math Teacher Lounge, we have a challenge for the folks who listen and we’d love for them to hop into the Facebook group Math Teacher Lounge, or hit us up on Twitter at @MTLShow and just, like, kind of exercise beyond listening, exercise the ideas you folks are talking about, some kind of a challenge that can help us dive deeper into your ideas. So what would you folks suggest for our crowd, for our listeners?

Allison Hintz (33:42):

I would love to invite people to playfully experiment with a favorite story, with a story that’s new to you. I would love to invite listeners to sit with a story maybe on your own, and just ask yourself as a mathematician: What do you notice and wonder in this story? Don’t feel any pressure. Maybe sit with a child or some children and listen to what they notice and wonder. Like, really listen! Don’t ask questions! But hear their questions and place children at the center and consider multiple reads. Consider continuing to pursue their questions. And we have a planning template that might support people in kind of sketching out some ideas if you’re open to playing with that too.

Bethany Lockhart Johnson (34:34):

And we will post—

Dan Meyer (34:36):

That’s awesome.

Bethany Lockhart Johnson (34:36):

—a link for that planning template in our Facebook group and on Twitter as well. So thank you so much for that resource, because I think it’ll definitely help. It could help you, like you said, it could help you kind of organize your thoughts or help you think about this work in a new way. So thank you for that resource and thank you for the amazing resource that is Mathematizing Children’s Literature. I am so excited to continue to engage with you both and with listeners as they dive into this book. If folks want to engage with you more, where can they find you? How can they reach you?

Allison Hintz (35:12):

Well, we’re on Twitter.

Bethany Lockhart Johnson (35:14):

Great.

Dan Meyer (35:15):

What’s your home address? <laugh>

Bethany Lockhart Johnson (35:24):

Wait, let me try that again. <laugh> ‘Cause it does sound like I’m like, <fake ominous voice> “Where can they find you?”

Allison Hintz (35:29):

4-2-5…. <laughs>

Antony Smith (35:32):

At the bookstore!

Bethany Lockhart Johnson (35:34):

Y’all, if folks want to continue this conversation or share these ideas or the math challenge, how can they tag you? How can they, they reach you on the World Wide Web, besides the Math Teacher Lounge Facebook group?

Antony Smith (35:50):

Yeah. Well, we are both on Twitter, and we’ve been trying to promote the hashtag #MathematizingChildrensLiterature. It’s very long, but once you type it once, your phone or computer…

Bethany Lockhart Johnson (36:01):

Easy. Yeah, those click, right? Is that what it is now?

Antony Smith (36:03):

<laugh> The other is that we do for our project, we have an Instagram account that is @MathematizeChildren’sLiterature.

Allison Hintz (36:11):

We care really deeply about hearing from people. You know, we think our ideas are constantly evolving and that there’s such exciting room to grow. And we just felt compelled to share what we were learning now so that together we could learn and build vibrant experiences for young children and teachers and families through stories. So we want to hear from people! We wanna learn about stories that are important in your lives and what children say, and grow these ideas together.

Bethany Lockhart Johnson (36:42):

And credit to Dan, you told me you went and ordered a bunch of the books they have on the suggested read list.

Dan Meyer (36:48):

Oh my gosh.

Bethany Lockhart Johnson (36:49):

You read ’em to your son.

Dan Meyer (36:50):

I got such a side-eye from my significant others around here for what I dropped on Amazon in one night! <laugh> Uh, all these books I didn’t have. Some of them I did. We are not fully illiterate around here! We do love the written word at the Meyer household! But there were a bunch that that I grabbed. I’m morseling them out day by day.

Bethany Lockhart Johnson (37:09):

Wait, at bedtime I read my one-year-old One Is a Snail, Ten Is a Crab. <laugh> And let me tell you, he had vigorous pointing and “Da? Da da da da?”

Allison Hintz (37:22):

<laugh> Aww, da da!

Bethany Lockhart Johnson (37:22):

So hey, we’re on the road. <laugh> <music> Deeply grateful, not only for your work and your beautiful book and your work, but also for the invitation to dive into the world of children’s literature in a way that many of us have not before. And it’s fun! Thank you, Tony. And thank you, Allison. And thanks for hanging out in the lounge.

Allison Hintz (37:48):

Thanks for having the lounge!

Antony Smith (37:49):

It’s been fun!

Allison Hintz (37:52):

Thank you both.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Allison Hintz says about math

“We started asking ourselves, “what would happen if we considered any story a chance to engage as mathematical sensemakers”.”

– Allison Hintz

Author and Associate Professor, University of Washington Bothell

Meet the guest

Allison B. Hintz: Dr. Hintz’s research and teaching are in the area of mathematics education. Her focus on mathematics came about during her years as a fifth grade teacher – it was alongside her students that she developed her own positive identity as a mathematician! Today she studies teaching and learning, specifically facilitating engaging discussion. Her research and teaching happen in partnership with educators and children in formal and informal settings and focuses on beliefs and practices that support all children in lively mathematics learning. She is a co-author, with Elham Kazemi, of Intentional Talk: How to Structure and Lead Productive Mathematical Discussions.

Twitter: @allisonhintz124

Antony T. Smith: Antony T. Smith is an associate professor of literacy education at the University of Washington, Bothell. He works alongside teachers to create engaging literacy-mathematics learning experiences through exploring and discussing children’s literature. He is committed to the concepts of motivation, engagement, challenge, and creativity in literacy teaching and learning.

 Twitter: @smithant  Instagram: mathematizechildrensliterature

Two people appear in separate circular frames; the woman is smiling and wearing headphones, while the man stands in front of bookshelves, perhaps discussing Mathematizing Children’s Literature.
Podcast cover for "Math Teacher Lounge" with Bethany Lockhart Johnson and Dan Meyer; bold text on orange and teal semicircle background.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Reveal Math

Grade 6

Module 1: Ratios and Rates

Reveal MathDesmos Classroom
Lesson 1: Understand ratiosUnit 2
Lesson 1: Pizza Maker
Lesson 2: Tables of Equivalent RatiosUnit 2
Lesson 10: Disaster Preparation
Lesson 4: Compare Ratio RelationshipsUnit 2
Lesson 4: Fruit Lab
Lesson 6: Convert Customary Measurement UnitsUnit 3
Lesson 1: Many Measurements
Lesson 7: Understand Rates and Unit RatesUnit 3
Lesson 6: Soft Serve

Module 2: Fractions, Decimals, and Percents

Lesson 1: Understand PercentsUnit 3
Lesson 9: Lucky Duckies
Lesson 3: Relate Fractions, Decimals, and PercentsUnit 5
Lesson 2: Decimal Diagrams and Algorithms

Module 3: Compute with Multi-Digit Numbers and Fractions

Lesson 1: Divide Multi-Digit Whole NumbersUnit 5
Lesson 13: Movie Time
Lesson 3: Divide Whole Numbers by FractionsUnit 4
Lesson 3: Flour Planner
Lesson 4: Divide Fractions by FractionsUnit 4
Lesson 6: Fill the Gap
Lesson 5: Divide with Whole and Mixed NumbersUnit 4
Lesson 6: Fill the Gap

Module 4: Integers, Rational Numbers, and the Coordinate Plane

Lesson 1: Represent IntegersUnit 7
Lesson 1: Can You Dig It?
Lesson 3: Compare and Order IntegersUnit 7
Lesson 4: Order in the Class

Module 5: Numerical and Algebraic Expressions

Lesson 3: Write Algebraic Expressions
Lesson 4: Evaluate Algebraic Expressions
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 6: Use the Distributive PropertyUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 7: Equivalent Algebraic ExpressionsUnit 6
Lesson 1: Weight for It

Module 6: Relationships in Geometry

Lesson 2: One-Step Addition Equations
Lesson 3: One-Step Subtraction Equations
Unit 6
Lesson 1: Weight for It
Lesson 6: InequalitiesUnit 7
Lesson 7: Tunnel Travels

Module 7: Relationships Between Two Variables

Lesson 4: Multiple RepresentationsUnit 6
Lesson 16: Subway Fares
Take Away (coming soon!)

Module 8: Area

Module 9: Volume and Surface Area

Lesson 2: Surface Area of Rectangular PrismsUnit 1
Lesson 10: Renata’s Stickers

Module 10: Statistical Measures and Displays

Lesson 1: Statistical QuestionsUnit 8
Lesson 3: Minimum Wage
Lesson 2: Dot Plots and HistogramsUnit 8
Lesson 5: The Plot Thickens
Lesson 3: Measures of CenterUnit 8
Lesson 11: Toy Cars
Lesson 7: Interpret Graphical DisplaysUnit 8
Lesson 3: Minimum Wage

Grade 7

Module 1: Proportional Relationships

Reveal MathDesmos Classroom
Lesson 1: Unit Rates Involving Ratios of FractionsUnit 2
Lesson 1: Paint
Lesson 3: Tables of Proportional ReasoningUnit 2
Lesson 1: Paint
Lesson 4: Graphs of Proportional ReasoningUnit 2
Lesson 8: Dino Pops
Lesson 5: Equations of Proportional ReasoningUnit 2
Lesson 6: Two and Two

Module 2: Solve Percent Problems

Lesson 1: Percent of ChangeUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Lesson 3: Tips and MarkupsUnit 4
Lesson 5: Percent Machines
Lesson 4: DiscountsUnit 4
Lesson 5: Percent Machines

Module 3: Operations with Integers

Lesson 1: Add Integers
Lesson 2: Subtract Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 3: Multiply IntegersUnit 5
Lesson 10: Integer Puzzles
Lesson 5: Apply Integers OperationsUnit 5
Lesson 10: Integer Puzzles

Module 4: Operations with Rational Numbers

Lesson 1: Add Integers
Lesson 2: Subtract Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 3: Multiply IntegersUnit 5
Lesson 10: Integer Puzzles
Lesson 5: Apply Integers OperationsUnit 5
Lesson 10: Integer Puzzles

Module 5: Simplify Algebraic Expressions

Lesson 2: Add Linear Expressions
Lesson 3: Subtract Linear Expressions
Unit 6
Lesson 10: Collect the Squares
Lesson 4: Solve Inequalities Using Addition or SubtractionUnit 6
Lesson 16: Shira the Sheep

Module 6: Write and Solve Equations

Lesson 1: Write and Solve One-Step EquationsUnit 6
Lesson 16: Shira the Sheep

Module 7: Write and Solve Inequalities

Lesson 6: Wirte and Solve Two-Step InequalitiesUnit 6
Lesson 16: Shira the Sheep

Module 8: Geometric Figures

Lesson 1: Vertical and Adjacent AnglesUnit 7
Lesson 4: Missing Measures
Lesson 2: Complementary and Supplementary AnglesUnit 7
Lesson 2: Friendly Angles
Lesson 3: TrianglesUnit 7
Lesson 5: Can You Build It?
Lesson 4: Scale DrawingsUnit 1
Lesson 1: Scaling Machines
Lesson 7: Will It Fit?

Module 9: Measure Figures

Lesson 1: Circumference of CirclesUnit 3
Lesson 3: Measuring Around
Lesson 2: Area of CirclesUnit 3
Lesson 9: Area Challenges

Module 10: Probability

Lesson 1: Find Likelihoods
Lesson 2: Relative Frequency of Simple Events
Lesson 3: Theoretical Probability of Events
Unit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities

Module 11: Sampling and Statistics

Lesson 1: Biased and Unbiased SamplesUnit 8
Lesson 10: Crab Island
Lesson 2: Make Predictions
Lesson 3: Generate Multiple Samples
Unit 8 
Lesson 10: Crab Island
Lesson 4: Compare Two PopulationsUnit 8
Lesson 10: Crab Island

Grade 8

Module 1: Exponents and Scientific Notation

Reveal MathDesmos Classroom
Lesson 1: Powers and ExponentsUnit 7 
Lesson 1: Circles
Lesson 2: Multiply and Divide MonomialsUnit 7 
Lesson 3: Power Pairs
Lesson 3: Power of MonomialsUnit 7 
Lesson 3: Power Pairs
Lesson 5: Scientific NotationUnit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale
Lesson 6: Compute with Scientific NotationUnit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Module 2: Real Numbers

Lesson 2: RootsUnit 8
Lesson 4: Root Down

Module 3: Solve Equations with Variables on Each Side

Lesson 1: Solve Equations with Variables on Each SideUnit 4
Lesson 5: Equation Roundtable
Lesson 2: Write and Solve Equations with Variables on Each SideUnit 4
Lesson 5: Equation Roundtable
Lesson 5: Determine the Number of Solutions

Module 4: Linear Relationships and Slope

Lesson 1: Proportional Relationships and SlopeUnit 3
Lesson 1: Turtle Time Trials
Lesson 2: Slope of a LineUnit 3
Lesson 4: Flags
Lesson 5: Slope-Intercept FormUnit 4
Lesson 5: Equation Roundtable
Lesson 6: Graph Linear EquationsUnit 3
Lesson 4: Flags
Unit 5
Lesson 5: The Tortoise and the Hare

Module 5: Functions

Lesson 1: Identify FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 6: Qualitative GraphsUnit 5
Lesson 5: The Tortoise and the Hare

Module 6: Systems of Linear Equations

Lesson 1: Solve Systems of Equations by GraphingUnit 4 
Lesson 11: Make Them Balance

Module 7: Triangles and the Pythagorean Theorem

Lesson 2: Angle Relationships and TrianglesUnit 1 
Lesson 12: Puzzling It Out

Module 8: Transformations

Lesson 1: Translations
Lesson 2: Reflections
Lesson 3: Rotations
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Lesson 4: DilationsUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf

Module 9: Congruence and Similarity

Lesson 3: Similarity and TransformationsUnit 2
Lesson 6: Social Scavenger Hunt

Module 10: Volume

Lesson 1: Volume of CylindersUnit 5
Lesson 11: Cylinders
Lesson 2: Volume of ConesUnit 5
Lesson 13: Cones

Module 11: Scatter Plots and Two-Way Tables

Lesson 1: Scatter PlotsUnit 6 
Lesson 3: Robots
Lesson 2: Draw Lines of FitUnit 6 
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Lesson 4: Two-Way TablesUnit 6
Lesson 11: Finding Associations
Lesson 5: Associations in Two-Way TablesUnit 6
Lesson 11: Finding Associations

Grade K

Unit 1: Math Is…

Lesson 1-2: Math is Exploring and ThinkingConnecting Cubes

Unit 4: Sort, Classify and Count Objects

Lesson 4-1: Alike and DifferentSo Much Sorting
Lesson 4-2: Sort Objects into GroupsSo Much Sorting
Lesson 4-3: Count Objects in GroupsWhat’s that Shape called?
Another Shape

Unit 5: 2-Dimensional Shapes

Lesson 5-1: TrianglesWhat’s that Shape called?
Lesson 5-2: Squares and RectanglesAnother Shape
Lesson 5-4: CirclesWhat’s that Shape called?

Unit 6: Understand Addition

Lesson 6-1: Represent and Solve Add To ProblemsHow Many Objects?
Lesson 6-2: Represent and Solve More Add to ProblemsWhat does it mean to add?
Lesson 6-3: Represent and Solve Put Together ProblemsWhat does it mean to add?

Unit 7: Understand Subtraction

Lesson 7-1: Represent Take Apart ProblemsWhat does it mean to subtract?
Lesson 7-2: Represent and Take From ProblemsWhat does it mean to subtract?

Unit 8: Addition and Subtraction Strategies

Lesson 8-4: Ways to Decompose 6 and 7Harry Explores the Ocean
Lesson 8-6: Ways to Decompose 8 and 9Harry Explores the Ocean
Lesson 8-7: Ways to Make 10Harry Explores Space
Lesson 8-8: Ways to Decompose 10Showing What We Know About 10

Unit 13: Analyze, Compare and Compose Shapes

Lesson 13-1: Compare and Contrast 2-Dimensional ShapesWhat’s that Shape called?

Unit 14: Compare Measurable Attributes

Lesson 14-1: Describe Attributes of ObjectsAnother Shape

Grade 1

Unit 2: Number Patterns

Lesson 2-5: Patterns when Representing Objects in a GroupMeeting Yara

Unit 3: Place Value

Lesson 3-1: Numbers 11 to 19Same Number, Different Ways
Lesson 3-2: Understand 10sBoris’s Thimbles
Lesson 3-4: Represent 2-DigitsSame Number, Different Ways
Lesson 3-5: Represent 2-Digits in Different WaysSame Number, Different Ways

Unit 4: Addition within 20: Facts and Strategies

Lesson 4-1: Relate Counting to AdditionInvestigate: Game Points
Meeting Yara
Lesson 4-5: Make a Ten to AddMaking 10
Lesson 4-9: Find an Unknown Number in an Addition EquationA Community Working Together
Lesson 4-10: Understand The Equal SignKitten Coaster
Lesson 4-11: True Addition EquationsKitten Coaster
Replanting Huli

Unit 5: Subtraction within 20: Facts and Strategies

Lesson 5-1: Relate Counting to SubtractionPacking a Picnic

Unit 7: Meanings of Addition

Lesson 7-1: Represent and Solve Add to ProblemsThe Kalo Plants
Tutu’s Garden in Maui
Lesson 7-2: Represent and Solve More Add to ProblemsHelping Others

Unit 8: Meanings of Subtraction

Lesson 8-1: Represent and Solve Take From ProblemsThe Kalo Plants
Tutu’s Garden in Maui
Lesson 8-2: Represent and Solve More Take From ProblemsHelping Others

Unit 13: Equal Shares

Lesson 13-1: Understand Equal SharesA Bigger Part
Lesson 13-2: Partition Shapes into HalvesFair and Square
Lesson 13-3: Partition Shapes into FourthsFair and Square
Lesson 13-4: Describe the WholeOne of the Parts, All of the Parts
Lesson 13-5: Describe the Halves and Fourths of ShapesOne of the Parts, All of the Parts

Grade 2

Unit 2: Place Value to 1,000

Lesson 2-1: Understand HundredsWhat Makes a Hundred?
Lesson 2-2: Understand 3-digit numbersWhat’s the Value?
Lesson 2-3: Read and Write Numbers to 1000All the Ways!
Lesson 2-4: Decompose 3-digit numbersA New Representation

Unit 3: Patterns within Numbers

Lesson 3-1: Counting PatternsInvestigate: A Mistake in Mom’s Office
Lesson 3-2: Patterns when Skip Counting by 5?What’s that Number?
Lesson 3-3: Patterns when Skip Counting by 10s and 100sLooking for Patterns

Unit 4: Meanings of Addition and Subtraction

Lesson 4-7: Represent and Solve Compare ProblemsAwesome Aquariums

Unit 5: Strategies to Add Fluently Within 100

Lesson 5-9: Add More Than Two NumbersHow Much Money?

Unit 7: Measure and Compare Lengths

Lesson 7-10: Solve Problems using LengthLengths of Jungle Animals

Unit 8: Measurement, Time and Money

Lesson 8-1: Understand the Value of CoinsDiscovering Coins (Part I)
Discovering Coins (Part 2)
Lesson 8-2: Solving Money Problems Using CoinsHow Much Money?

Unit 9: Strategies to Add 3-Digit Numbers

9-2: Represent Addition with 3-Digit NumbersThere’s Something About Berries
9-3: Represent Addition with 3-Digit Numbers With RegroupingBaking with Skunk

Unit 11: Data Analysis

Lesson 11-5: Understand Line PlotsMessy Measurements
Lesson 11-6: Show Data on a Line PlotBracelets and Wristbands

Grade 3

Unit 2: Use Place Value Fluently to Add and Subtract within 1001

Lesson 2-3: Estimate Sums and DifferencesAdding Strategically
Lesson 2-6: Use Partial Sums to AddWhat is an Algorithm
Lesson 2-10: Fluently Add Within 1,000How Would You Solve It?
Determining the Sum of 2 or More Addends

Unit 3: Multiplication and Division

Lesson 3-1: Understand Equal GroupsEqual Groups
Lesson 3-3: Understand the Commutative PropertyArrays of Flavor
Lesson 3-7: Find the UnknownIt’s Chilli In Here!

Unit 4: Use Patterns to Multiply by 0,1, 2, 5 and 11

Lesson 4-6: Solve Problems Using Equal GroupsDivision and Multiplication Equations

Unit 6: Connect Area and Multiplication

Lesson 6-1: Understand AreaTiling Figures
Lesson 6-2: Count Unit Squares to Determine AreaRectangles and Arrays
Unit 2: Lesson 4: Area Hunt

Unit 7: Fractions

Lesson 7-5: Represent Whole Numbers as FractionsCat Crossing
Lesson 7-6: Represent a Greater Than One on a Number LineFractions on the Number Line

Unit 9: Use Multiplication to Divide

Lesson 9-1: Use Multiplication to Solve Division ProblemsRelating Quotients to Familar Products

Unit 12: Measurement and Data

Lesson 12-10: Measure to Halves or Fourths of an InchHow Long Is It?
More Precise Measurements
Lesson 12-11: Show Measurement Data on a Line PlotThe Plot Chickens

Unit 13: Describe and Analyze 2-Dimensional Shapes

Lesson 13-1: Describe and Classify PolygonsPiho’s Shapes
Lesson 13-2: Classify QuadrilateralsRectangles, Squares and Rhombuses

Grade 4

Unit 4: Multiplication as Comparison

Lesson 4-1: Understanding Comparing with MultiplicationRepresenting “Times as Many”
Lesson 4-2: Represent Comparison ProblemsSticker Mania
Lesson 4-3: Solve Comparison Problems Using MultiplicationGoing Swimming

Unit 5: Numbers and Number Patterns

Lesson 5-1: Understand Factors of a NumberHamster Homes
Lesson 5-3: Understand MultiplesFactor or Multiple
Lesson 5-4: Number or Shape PatterrnsHow Does it Grow?
Lesson 5-5: Generate a PatternHow Does it Grow?

Unit 6: Multiplication Strategies with Multi-Digit Numbers

Lesson 6-2: Estimate ProductsA Reasonable Answer
Lesson 6-4: Multiply 2-Digit by 1-Digit FactorsCounting Flowers for Lei
Lesson 6-5: Multiply Multi-Digit 1-Digit FactorsA Lei Making Workshop
Lesson 6-7: Multiply 2-Digit FactorsDouble Decomposition

Unit 9: Addition and Subtractions Meanings and Strategies with Fractions

Lesson 9-2: Represent Adding FractionsPizza Problems
Lesson 9-3: Add Fractions with Like DenominatorsPizza Problems
Lesson 9-4: Represent Subtracting FractionsPizza Problems
Lesson 9-5: Subtract Fractions with Like DenominatorsPizza Problems
Lesson 9-6: Solve Problems Using FractionsPizza Problems

Unit 10: Addition and Subtraction Strategies with Mixed Numbers

Lesson 10-1: Understand Decomposing Mixed NumbersMath Pizzeria

Unit 11: Multiply Fractions by Whole Numbers

Lesson 11-1: Represent Multiplication of a Unit Fraction by a Whole NumberEqual Groups of Fractions

Unit 12: Decimal Fractions

Lesson 12-2: Understand Decimal NotationA New Way to Write Tenths
A New Way to Write Hundredths
Lesson 12-3: Compare DecimalsCan You Compare?

Grade 5

Unit 2: Volume

Lesson 2-2: Use Unit Cubes to Determine VolumePutting It Together
Lesson 2-3: Use Formula to Determine VolumePutting It Together
Lesson 2-4: Determine the Volume of Composite FiguresFigures Made of Prisms

Unit 3: Place Value and Number Relationships

Lesson 3-1: Generalize Place ValuePlace Value Patterns
Lesson 3-4: Compare DecimalsSelling Collectibles
Lesson 3-5: Use Place Value to Round DecimalsWhich Way Down the Mountain?

Unit 5: Multiply Multi-Digit Whole Numbers

Lesson 5-1: Understand Powers and ExponentsMonarch Butterflies
Lesson 5-2: Patterns When Multiplying a Whole Number by Powers of 10All About that Base
Lesson 5-5: Use Partial Products to Multiply Multi-Digit FactorsHow Do They Compare?
Lesson 5-6: Relate Partial Products to an AlgorithmPatrial Products Everywhere
Lesson 5-7: Multiply Multi-Digit Factors FluentlyPatrial Products Everywhere

Unit 6: Multiply Decimals

Lesson 6-1: Patterns when Multiplying Decimals by Powers of 10Powers of 10 Parade

Unit 7: Divide Whole Numbers

Lesson 7-5: Use Partial Quotients to DivideEmptying the Water Tank

Unit 8: Divide Decimals

Lesson 8-1: Division Patterns with Decimals and Patterns of 10Powers of 10 Parade

Unit 10: Multiply Fractions

Lesson 10-3: Represent Multiplication of a Fraction By A FractionMaking Food
Lesson 10-4: Multiply a Fraction By A FractionMaking Food
Lesson 10-5: Determine the Area of Rectanges with Fractional Side LengthsInstalling Turf
Lesson 10-6: Represent Multiplication of Mixed NumbersInstalling Turf
Lesson 10-7: Multiply Mixed NumbersInstalling Turf

Unit 13: Geometry

Lesson 13-2: Plot Ordered Pairs on the Coordinate PlaneBullseye!

Grade 6

Module 1: Ratios and Rates

Reveal MathAmplify Classroom
Lesson 1: Understand ratiosUnit 2
Lesson 1: Pizza Maker
Lesson 2: Tables of Equivalent RatiosUnit 2
Lesson 10: Disaster Preparation
Lesson 4: Compare Ratio RelationshipsUnit 2
Lesson 4: Fruit Lab
Lesson 6: Convert Customary Measurement UnitsUnit 3
Lesson 1: Many Measurements
Lesson 7: Understand Rates and Unit RatesUnit 3
Lesson 6: Soft Serve

Module 2: Fractions, Decimals, and Percents

Lesson 1: Understand PercentsUnit 3
Lesson 9: Lucky Duckies
Lesson 3: Relate Fractions, Decimals, and PercentsUnit 5
Lesson 2: Decimal Diagrams and Algorithms

Module 3: Compute with Multi-Digit Numbers and Fractions

Lesson 1: Divide Multi-Digit Whole NumbersUnit 5
Lesson 13: Movie Time
Lesson 3: Divide Whole Numbers by FractionsUnit 4
Lesson 3: Flour Planner
Lesson 4: Divide Fractions by FractionsUnit 4
Lesson 6: Fill the Gap
Lesson 5: Divide with Whole and Mixed NumbersUnit 4
Lesson 6: Fill the Gap

Module 4: Integers, Rational Numbers, and the Coordinate Plane

Lesson 1: Represent IntegersUnit 7
Lesson 1: Can You Dig It?
Lesson 3: Compare and Order IntegersUnit 7
Lesson 4: Order in the Class

Module 5: Numerical and Algebraic Expressions

Lesson 3: Write Algebraic Expressions
Lesson 4: Evaluate Algebraic Expressions
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 6: Use the Distributive PropertyUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 7: Equivalent Algebraic ExpressionsUnit 6
Lesson 1: Weight for It

Module 6: Relationships in Geometry

Lesson 2: One-Step Addition Equations
Lesson 3: One-Step Subtraction Equations
Unit 6
Lesson 1: Weight for It
Lesson 6: InequalitiesUnit 7
Lesson 7: Tunnel Travels

Module 7: Relationships Between Two Variables

Lesson 4: Multiple RepresentationsUnit 6
Lesson 16: Subway Fares
Take Away (coming soon!)

Module 8: Area

Module 9: Volume and Surface Area

Lesson 2: Surface Area of Rectangular PrismsUnit 1
Lesson 10: Renata’s Stickers

Module 10: Statistical Measures and Displays

Lesson 1: Statistical QuestionsUnit 8
Lesson 3: Minimum Wage
Lesson 2: Dot Plots and HistogramsUnit 8
Lesson 5: The Plot Thickens
Lesson 3: Measures of CenterUnit 8
Lesson 11: Toy Cars
Lesson 7: Interpret Graphical DisplaysUnit 8
Lesson 3: Minimum Wage

Grade 7

Module 1: Proportional Relationships

Reveal MathAmplify Classroom
Lesson 1: Unit Rates Involving Ratios of FractionsUnit 2
Lesson 1: Paint
Lesson 3: Tables of Proportional ReasoningUnit 2
Lesson 1: Paint
Lesson 4: Graphs of Proportional ReasoningUnit 2
Lesson 8: Dino Pops
Lesson 5: Equations of Proportional ReasoningUnit 2
Lesson 6: Two and Two

Module 2: Solve Percent Problems

Lesson 1: Percent of ChangeUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Lesson 3: Tips and MarkupsUnit 4
Lesson 5: Percent Machines
Lesson 4: DiscountsUnit 4
Lesson 5: Percent Machines

Module 3: Operations with Integers

Lesson 1: Add Integers
Lesson 2: Subtract Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 3: Multiply IntegersUnit 5
Lesson 10: Integer Puzzles
Lesson 5: Apply Integers OperationsUnit 5
Lesson 10: Integer Puzzles

Module 4: Operations with Rational Numbers

Lesson 1: Add Integers
Lesson 2: Subtract Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 3: Multiply IntegersUnit 5
Lesson 10: Integer Puzzles
Lesson 5: Apply Integers OperationsUnit 5
Lesson 10: Integer Puzzles

Module 5: Simplify Algebraic Expressions

Lesson 2: Add Linear Expressions
Lesson 3: Subtract Linear Expressions
Unit 6
Lesson 10: Collect the Squares
Lesson 4: Solve Inequalities Using Addition or SubtractionUnit 6
Lesson 16: Shira the Sheep

Module 6: Write and Solve Equations

Lesson 1: Write and Solve One-Step EquationsUnit 6
Lesson 16: Shira the Sheep

Module 7: Write and Solve Inequalities

Lesson 6: Wirte and Solve Two-Step InequalitiesUnit 6
Lesson 16: Shira the Sheep

Module 8: Geometric Figures

Lesson 1: Vertical and Adjacent AnglesUnit 7
Lesson 4: Missing Measures
Lesson 2: Complementary and Supplementary AnglesUnit 7
Lesson 2: Friendly Angles
Lesson 3: TrianglesUnit 7
Lesson 5: Can You Build It?
Lesson 4: Scale DrawingsUnit 1
Lesson 1: Scaling Machines
Lesson 7: Will It Fit?

Module 9: Measure Figures

Lesson 1: Circumference of CirclesUnit 3
Lesson 3: Measuring Around
Lesson 2: Area of CirclesUnit 3
Lesson 9: Area Challenges

Module 10: Probability

Lesson 1: Find Likelihoods
Lesson 2: Relative Frequency of Simple Events
Lesson 3: Theoretical Probability of Events
Unit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities

Module 11: Sampling and Statistics

Lesson 1: Biased and Unbiased SamplesUnit 8
Lesson 10: Crab Island
Lesson 2: Make Predictions
Lesson 3: Generate Multiple Samples
Unit 8 
Lesson 10: Crab Island
Lesson 4: Compare Two PopulationsUnit 8
Lesson 10: Crab Island

Grade 8

Module 1: Exponents and Scientific Notation

Reveal MathAmplify Classroom
Lesson 1: Powers and ExponentsUnit 7 
Lesson 1: Circles
Lesson 2: Multiply and Divide MonomialsUnit 7 
Lesson 3: Power Pairs
Lesson 3: Power of MonomialsUnit 7 
Lesson 3: Power Pairs
Lesson 5: Scientific NotationUnit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale
Lesson 6: Compute with Scientific NotationUnit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Module 2: Real Numbers

Lesson 2: RootsUnit 8
Lesson 4: Root Down

Module 3: Solve Equations with Variables on Each Side

Lesson 1: Solve Equations with Variables on Each SideUnit 4
Lesson 5: Equation Roundtable
Lesson 2: Write and Solve Equations with Variables on Each SideUnit 4
Lesson 5: Equation Roundtable
Lesson 5: Determine the Number of Solutions

Module 4: Linear Relationships and Slope

Lesson 1: Proportional Relationships and SlopeUnit 3
Lesson 1: Turtle Time Trials
Lesson 2: Slope of a LineUnit 3
Lesson 4: Flags
Lesson 5: Slope-Intercept FormUnit 4
Lesson 5: Equation Roundtable
Lesson 6: Graph Linear EquationsUnit 3
Lesson 4: Flags
Unit 5
Lesson 5: The Tortoise and the Hare

Module 5: Functions

Lesson 1: Identify FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 6: Qualitative GraphsUnit 5
Lesson 5: The Tortoise and the Hare

Module 6: Systems of Linear Equations

Lesson 1: Solve Systems of Equations by GraphingUnit 4 
Lesson 11: Make Them Balance

Module 7: Triangles and the Pythagorean Theorem

Lesson 2: Angle Relationships and TrianglesUnit 1 
Lesson 12: Puzzling It Out

Module 8: Transformations

Lesson 1: Translations
Lesson 2: Reflections
Lesson 3: Rotations
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Lesson 4: DilationsUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf

Module 9: Congruence and Similarity

Lesson 3: Similarity and TransformationsUnit 2
Lesson 6: Social Scavenger Hunt

Module 10: Volume

Lesson 1: Volume of CylindersUnit 5
Lesson 11: Cylinders
Lesson 2: Volume of ConesUnit 5
Lesson 13: Cones

Module 11: Scatter Plots and Two-Way Tables

Lesson 1: Scatter PlotsUnit 6 
Lesson 3: Robots
Lesson 2: Draw Lines of FitUnit 6 
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Lesson 4: Two-Way TablesUnit 6
Lesson 11: Finding Associations
Lesson 5: Associations in Two-Way TablesUnit 6
Lesson 11: Finding Associations

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Grade 6

Unit 1: Numbers

GO Math!Amplify Classroom
Module 4: Operations with Fractions
Lesson 4.1: Applying GCF and LCM to Fraction OperationsUnit 4
Lesson 6: Fill the Gap
Module 5: Operations with Decimals
Lesson 5.2: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 2: Decimal Diagrams and Algorithms
Lesson 5.4: Dividing DecimalsUnit 5
Lesson 13: Movie Time

Unit 2: Number Operations

Module 4: Operations with Fractions
Lesson 4.1: Applying GCF and LCM to Fraction OperationsUnit 4
Lesson 6: Fill the Gap
Module 5: Operations with Decimals
Lesson 5.2: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 2: Decimal Diagrams and Algorithms
Lesson 5.4: Dividing DecimalsUnit 5
Lesson 13: Movie Time

Unit 3: Proportionality, Ratios, and Rates

Module 6: Representing Ratios and Rates
Lesson 6.1: RatiosUnit 2
Lesson 1: Pizza Maker
Lesson 6.2: Rates Unit 3
Lesson 6: Soft Serve
Lesson 6.3: Using Ratios and Rates to Solve ProblemsUnit 2
Lesson 4: Fruit Lab
Lesson 10: Disaster Preparation
Module 7: Applying Ratios and Rates
Lesson 7.1: Ratios, Rates, Tables, and GraphsUnit 2
Lesson 4: Fruit Lab
Lesson 10: Disaster Preparation
Unit 3
Lesson 6: Soft Serve
Module 8:  Percents
Lesson 8.1 Understanding Percent.Unit 3
Lesson 9: Lucky Duckies

Unit 4: Equivalent Expressions

Module 10: Generating Equivalent Algebraic Expressions
Lesson 10.1: Modeling and Writing Expressions
Lesson 10.2: Evaluating Expressions
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 10.3: Generating Equivalent ExpressionsUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)

Unit 5: Equations and Inequalities

Module 11:  Equations and Relationships
Lesson 11.1:  Writing Equations to Represent Situations
Lesson 11.2:  Addition and Subtraction Equations
Lesson 11.3:  Multiplication and Division Equations
Unit 6
Lesson 1:  Weight For It
Lesson 11.4: Writing InequalitiesUnit 7
Lesson 7:  Tunnel Travels
Module 12:  Relationships in Two Variables
Lesson 12.2:  Independent and Dependent Variables in Tables and GraphsUnit 6
Lesson 16: Subway Fares
Take Away (coming soon!)
Lesson 12.3:  Writing Equations from Tables.Unit 6
Lesson 16: Subway Fares
Take Away (coming soon!)
Lesson 12.4:  Representing Algebraic Relationships in Tables and GraphsUnit 6
Lesson 16: Subway Fares
Take Away (coming soon!)

Unit 6: Relationships in Geometry

GO Math!Amplify Classroom
Module 13: Area and Polygons
Lesson 13.1: Area of QuadrilateralsUnit 1
Lesson 1: Shapes on a Plane
Lesson 3: Exploring Parallelograms
Exploring Parallelograms, Part 2
Lesson 13.2: Area of TrianglesUnit 1
Lesson 1: Shapes on a Plane
Lesson 13.4: Area of PolygonsUnit 1
Lesson 1: Shapes on a Plane
Module 14:  Distance and Area in the Coordinate Plane
Lesson 14.1: Distance in the Coordinate Plane
Lesson 14.2: Polygons in the Coordinate Plane
Unit 1
Lesson 1: Shapes on a Plane

Unit 7: Measurement and Data

Module 16: Displaying, Analyzing, and
Summarizing Data
Lesson 16.1: Measures of CenterUnit 8
Lesson 11: Toy Cars
Lesson 16.4: Dot Plots and Data DistributionUnit 8
Lesson 3: Minimum Wage
Lesson 16.5: HistogramsUnit 8
Lesson 5: The Plot Thickens

Grade 7

Unit 1: The Number System

GO Math!Amplify Classroom
Module 1:  Adding and Subtracting Integers
Lesson 1.2: Adding Integers With Different Signs
Lesson 1.3: Subtracting Integers
Unit 5
Lesson 1: Floats and Anchors
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Module 2: Multiplying and Dividing Integers
Lesson 2.1: Multiplying Integers Unit 5
Lesson 10: Integer Puzzles
Lesson 2.2: Dividing IntegersUnit 5
Lesson 10: Integer Puzzles
Module 3:  Rational Numbers
Lesson 3.2: Adding Rational Numbers
Lesson 3.3: Subtracting Rational Numbers
Unit 5
Lesson 4: Draw Your Own

Unit 2: Ratios and Proportional Relationships

Module 4:  Rates and Proportionality
Lesson 4.1: Unit RatesUnit 2
Lesson 6: Two and Two
Lesson 4.2: Constant Rates of ChangeUnit 2
Lesson 1: Paint
Lesson 6: Two and Two
Lesson 4.3:  Proportional Relationships and GraphsUnit 2
Lesson 1: Paint
Lesson 6: Two and Two
Module 5:  Proportions and Percent
Lesson 5.1: Percent Increase and DecreaseUnit 4
Lesson 1: Mosaics
Lesson 5: Percent Machines
Lesson 5.3: Applications of PercentUnit 4
Lesson 12: Posing Percent Problems(coming soon!)

Unit 3: Expressions, Equations, and Inequalities

Module 6: Expressions and Equations
Lesson 6.3: Writing Two-Step EquationsUnit 6
Lesson 10: Collect the Squares
Module 6: Expressions and Equations
Lesson 7.2: Writing Two-Step InequalitiesUnit 6
Lesson 16: Shira the Sheep
Lesson 7.3: Solving Two-Step InequalitiesUnit 6
Lesson 16: Shira the Sheep

Unit 4: Geometry

Module 8: Modeling Geometric Figures
Lesson 8.1: Similar Shapes and Scale DrawingsUnit 1
Lesson 1: Scaling Machines
Lesson 7: Will It Fit?
Unit 7
Lesson 5: Can You Build It?
Lesson 8.2: Geometric DrawingsUnit 1
Lesson 7: Will It Fit?
Lesson 8.4: Angle RelationshipsUnit 7
Lesson 2: Friendly Angles
Lesson 4: Missing Measures
Module 9:  Circumference, Area, and Volume
Lesson 9.1: CircumferenceUnit 3
Lesson 3: Measuring Around
Lesson 9.2: Area of CirclesUnit 3
Lesson 8: Area Challenges
Lesson 9.3: Area of Composite FiguresUnit 3
Lesson 8: Area Challenges

Unit 5: Statistics

Module 10: Random Samples and
Populations
Lesson 10.1: Populations and SamplesUnit 8
Lesson 10: Crab Island
Module 11: Analyzing and Comparing Data
Lesson 11.3: Using Statistical Measures to Compare PopulationsUnit 8
Lesson 10: Crab Island

Unit 6: Probability

Module 13: Theoretical Probability and
Simulations
Lesson 13.1: Theoretical Probability of Simple EventsUnit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities

Grade 8

Unit 1: Real Numbers, Exponents, and Scientific Notation

GO Math!Amplify Classroom
Module 1: Real Numbers
Lesson 1.3: Ordering Real NumbersUnit 8
Lesson 4: Root Down
Module 2: Exponents and Scientific
Notation
Lesson 2.1: Integer ExponentsUnit 7
Lesson 1: Circles
Lesson 3: Power Pairs
Lesson 2.4: Operations with Scientific NotationUnit 7
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Unit 2: Proportional and Nonproportional Relationships and Functions

Module 3: Proportional Relationships
Lesson 3.1: Representing Proportional Relationships.Unit 3
Lesson 1: Turtle Time Trials
Lesson 3.2: Rate of Change and SlopeUnit 3
Lesson 4: Flags
Lesson 5: The Tortoise and the Hare
Module 4: Nonproportional Relationships
Lesson 4.1: Representing Linear Nonproportional RelationshipsUnit 3
Lesson 4: Flags
Lesson 4.2: Determining Slope and y-interceptUnit 3
Lesson 4: Flags
Lesson 4.3: Graphing Linear Nonproportional Relationships using Slope and y-intercept.Unit 3
Lesson 4: Flags
Lesson 4.4: Proportional and Nonproportional SituationsUnit 3
Lesson 1: Turtle Time Trials
Module 5: Writing Linear Equations
Lesson 5.1: Writing Linear Equations from Situations and GraphsUnit 3
Lesson 4: Flags
Lesson 5.3: Linear Relationships and Bivariate DataUnit 6
Lesson 3: Robots
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Module 6: Functions
Lesson 6.1: Identifying and Representing FunctionsUnit 5
Lesson 2: Guess My Rule
Lesson 5: The Tortoise and the Hare
Lesson 6.3: Comparing FunctionsUnit 5
Lesson 5: The Tortoise and the Hare
Lesson 6.4: Analyzing GraphsUnit 5
Lesson 1: Turtle Crossing
Lesson 5: The Tortoise and the Hare

Unit 3: Solving Equations and Systems of Equations

Module 7:  Solving Linear Equations
Lesson 7.1: Equations with the Variable on Both SidesUnit 4
Lesson 5: Equation Roundtable
Lesson 7.2: Equations with Rational Numbers
Lesson 7.3: Equations with the Distributive PropertyUnit 4
Lesson 5: Equation Roundtable
Module 8:  Solving Systems of Linear Equations
Lesson 8.1: Solving Systems of Linear Equations by Graphing.Unit 4
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Unit 4: Transformational Geometry

Module 9:  Transformations and Congruence
Lesson 9.1: Properties of Translations
Lesson 9.2: Properties of Reflections
Lesson 9.3:  Properties of Rotations
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Module 10: Transformations and Similarity
Lesson 10.1: Properties of DilationsUnit 2
Lesson 2: Dilation Mini Golf
Lesson 6: Social Scavenger Hunt
Lesson 10.3: Similar FiguresUnit 2
Lesson 1: Sketchy Dilations
Lesson 6: Social Scavenger Hunt

Unit 5: Measurement Geometry

Module 11: Angle Relationships in Parallel Lines and Triangles
Lesson 11.1: Parallel Lines Cut by a Transversal.Unit 1
Lesson 12: Puzzling It Out
Lesson 11.2: Angle Theorems for TrianglesUnit 1
Lesson 12: Puzzling It Out
Lesson 11.3: Angle-Angle SimilarityUnit 2
Lesson 6: Social Scavenger Hunt
Module 12: Pythagorean Theorem
Lesson 12.1: The Pythagorean TheoremUnit 8
Lesson 8: Triangle-Tracing Turtle
Lesson 10: Taco Truck
Module 13: Volume
Lesson 13.1: Volume of CylindersUnit 5
Lesson 11: Cylinders
Lesson 13.2: Volume of ConesUnit 5
Lesson 13: Cones

Unit 6: Statistics

Module 14: Scatter Plots
Lesson 14.1: Scatter Plots and AssociationUnit 6
Lesson 3: Robots
Lesson 14.2: Trend Lines and PredictionsUnit 6
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Module 15: Two-Way Tables
Lesson 15.2: Two-Way Relative Frequency TablesUnit 6
Lesson 11: Finding Associations

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

S4 – 02. Bethany and Dan share their math biographies

Promotional graphic for "math teacher lounge," season 4 episode 2, featuring photos and names of math teaching guests Bethany Lockhart and Dan Meyer.

In this episode, co-hosts Bethany Lockhart Johnson and Dan Meyer get personal and share their “math bios”—their early experiences with math and how those experiences turned them into the educators they are today.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:00):

We’re recording. What’s up, everybody. This is Dan Meyer with Math Teacher Lounge.

Bethany Lockhart Johnson (00:08):

And I’m Bethany Lockhart Johnson. We are so excited to be back. Season Four, Episode Two. Hi, Dan.

Dan Meyer (00:16):

Hey, Bethany, how are you doing today?

Bethany Lockhart Johnson (00:18):

I’m so excited to be talking with you! You know, as we record this, our reunion at NCTM is getting closer and closer.

Dan Meyer (00:28):

The NCTM live show is gonna be bonkers. I don’t think people are ready for it. You think you know what we’re about on MTL from listening to us, but the live show is gonna be outta control. You cannot imagine how many clowns and elephants Bethany wants to have at the live show. We’re still—we’re trying to talk her down from like three to one, but we’ll see.

Bethany Lockhart Johnson (00:44):

All I want is the t-shirt cannon. Because I used to go to these baseball games and they would have a t-shirt cannon. And I thought, I wanna operate a t-shirt cannon! So like, if I could be standing on stage aiming t-shirts at people who are jumping up and down requesting a t-shirt? I don’t know. Doesn’t that sound fun?

Dan Meyer (01:01):

Sounds awesome. High point of my college education was catching a t-shirt. No, it was—it was a burrito. It was a burrito cannon. But I think it was just a t-shirt cannon, but it was a burrito cannon. And I caught a burrito at a game and it was probably the most memorable moment of all of college education for me.

Bethany Lockhart Johnson (01:16):

Was the burrito still warm?

Dan Meyer (01:18):

Oh yeah. I think it got—like, I think it might’ve been warm at one point and then it got warmed back up through the muzzle velocity of the cannon. So it was a pretty great system they had going on there. <Laugh> Yeah. <Laugh> Anyway, I’m off topic, but, we’re thrilled to—I’m thrilled to chat with you and we’re thrilled to be listened to by you folks out there in MTL land. In the lounge itself. We got a fun show today.

Bethany Lockhart Johnson (01:40):

So if you listen to Episode One—which if you haven’t, hope you go back and listen to it—if you listen to Season Four, Episode One, you’re gonna hear—we asked Huon, KT, who is this delight of a joyful teacher. We asked her to talk to us about what’s her math bio. And we want to ask all of our guests—like, I wanna go back and ask every single guest we’ve ever had to tell us their math bio.

Dan Meyer (02:06):

Yep.

Bethany Lockhart Johnson (02:06):

Because, while seemingly simple in nature, our students enter our math classroom already having had this relationship with math and these notions about their role in math or what they think about math. And it impacts our school year with them if we’re a teacher. And it impacts our relationship with math as we move through our education and beyond. Right? And I I’m so excited about this question, ’cause I think it also ties into this theme for Season Four, which is joyful math, and diving into “When has math felt joyful? When has it not? Does it feel like—how do we think about how our math bio, our relationship with math, has evolved into a joyful or less joyful place?”

Dan Meyer (02:54):

I get it. And what’s really key here, I think, is that teaching more than other professions is a generational profession. You know what I’m saying? Like, no one is like, “Well, you know, I sold insurance to you and now you’re selling insurance to, you know, my grandkids; that’s amazing!” But people are always posting photos when, like, you teach someone who then becomes a teacher later. Teaching is a generational sort of thing. So the kinds of joyful experiences that we offer or don’t offer students now affect the experiences that students who haven’t even been born yet will have, you know, some 20, 30 years later. That, to me, is a trip. And well-worth exploring, you know, how we got here, mathematically speaking.

Bethany Lockhart Johnson (03:39):

I remember a friend had sent me this image of an assignment that her son got that was asking for their Mathography. They wanted to know about their history of mathematics. And this was their first assignment. And this teacher, I would like to imagine, read them all and used it to inform conversations about students’ relationship with math. And, you know, some of the questions they asked were thinking about whether you consider yourself, quote, unquote, “good at math.” Like “what kind of experiences have you had? What do you like or dislike about math? What is, you know—what do you expect to learn in math this year?” Just asking students to actually pause and examine and reflect on their relationship and then also looking forward to, like, what kind of a classroom community do we wanna create? And I loved that assignment. And yeah, so today’s episode Dan, guess what?

Dan Meyer (04:32):

What’s going on? What’s happening?

Bethany Lockhart Johnson (04:33):

I figured we should ask each other about our math bio.

Dan Meyer (04:39):

I think the people out there would love to know this about us. ‘Cause you know, we’re both awesome. But also what’s really cool here is that like, I don’t know this about you. Like not, not a lot. You know, the folks at Amplify, they kind of assembled me and Bethany together in the same way that record labels assembled pop boy bands, girl bands, that kind of thing, back in the day. You know, grabbing some stars from screen or film and just like throwing ’em together and saying, “All right, now you’re here to perform together.” And so it’s just a really good moment for us to, like, settle back and just know who we’ve been working with for the last three seasons and change here. I love it.

Bethany Lockhart Johnson (05:15):

Well, I don’t know. I don’t actually agree with that, Dan. Because don’t you remember? We knew each other beforehand. And while I would like to think of us as…oh, I’ll say One Direction—well, no, One Direction is now defunct. Who’s another band that got formed by one of those shows and is still together and still—

Dan Meyer (05:33):

BTS! K-Pop, you know! Let’s go!

Bethany Lockhart Johnson (05:35):

K-pop. BTS.

Dan Meyer (05:38):

Let’s go, Bethany <laugh>.

Bethany Lockhart Johnson (05:39):

So can we incorporate some K-pop into the NCTM Math Teacher Lounge live episode? Don’t answer now. Don’t answer now. OK. So not only are we gonna share our math bios, but we want to encourage you listeners to share your math bio with somebody in your life. It could be a child in your life, maybe talking to your kiddo about what was it like. What was math like for you? It could be a student that you have. It could be a partner, a friend, a parent. I mean, the sky’s the limit. Share your math bio. And most of all, share with us. We wanna hear about your math bio and you can share it with us at Twitter, at MTLShow, or in our Facebook group, Math Teacher Lounge.

Dan Meyer (06:26):

Stop on by, please. All right. I’m gonna just share like, just a couple of quick, signposts. Not the full bio. Gotta leave them wondering about something here. But here’s a few quick highlights and lowlights of my math bio and how, maybe, it made me the teacher that I was and the educator I am. Is that cool?

Bethany Lockhart Johnson (06:44):

Wait, I didn’t even, I didn’t ask you yet.

Dan Meyer (06:46):

Ask me what?

Bethany Lockhart Johnson (06:47):

Hey, Dan!

Dan Meyer (06:49):

Is there like a magical word? Like, what’s your math bio? <Laugh> Oh, go for it. No, no, that’s right. They won’t know what I’m talking about. Why is he talking about his math bio? Bethany—

Bethany Lockhart Johnson (06:57):

That whole lead-in that we just gave? They might not know.

Dan Meyer (07:00):

Yeah. We just talked about math bios for the last 20 minutes. But yeah, they might not know what we’re—

Bethany Lockhart Johnson (07:04):

<laugh> So Dan, why don’t you go first? ‘Cause I know you were gonna ask me to go first, but why don’t you go first? Dan? What’s your math bio?

Dan Meyer (07:12):

Oh, wow. Well, thank you for the formal invitation to share my math bio, Bethany Lockhart Johnson. So, I’ll just share—I just wanna share a couple items here, not the full history. Gotta leave ’em—leave a little mystery in there, you know what I’m saying? But here’s a few highlights and lowlights, and I think what it means for me as an educator. So, I was homeschooled for eight years. That was big—did a lot of math learning on my own. Couple of lowlights from that, a lot of highlights, in terms of just like being able to, like, learn at my own rate and just jump on ahead and pursue different wacky things. But I tried to switch into public school in fourth grade and I lasted, um, four hours. I didn’t even go to class. I enrolled and then it was like, boom, I was out of there. Because we went to the school; we met the teacher, saw the room, very nice person and place. But I got the homework assignment and the homework assignment was gibberish. I had no idea what to do and such was this feeling of just, like, despair and hopelessness, I was like, I cannot be a part of this. I remember the assignment. It was about identifying scalene, isosceles, and equilateral triangles. I’ll tell you this: I am quite good at that now. But at the time, like, I didn’t know what those words meant. And you know, at that moment we had Encyclopedia Britannica, could not Google this or even Ask Jeeves or AltaVista this so well back then. It just—it was an entry moment of failure and realizing that so much of math is like a, kind of a social kind of construct. And if you’re not part of that social circle, what can you do? So that was a bummer. Another bummer was eighth-grade math, learned it all by way of videotape. You know, put in the tape and watch—not gonna say the person’s name and not this person’s fault—but it was just like watching someone work on a whiteboard. Kind of a precursor to Khan Academy, kind of a drag. Went to high school—

Bethany Lockhart Johnson (09:02):

Wait, wait, wait, wait. We were—I’m not ready to jump to high school. Wait. Can you pause for just a second?

Dan Meyer (09:06):

Yeah. Rock on.

Bethany Lockhart Johnson (09:07):

I just need you to go back to the triangle thing. So in that moment, what did that mean for you that you had had all these experiences with math and then you encounter math in a completely different sphere, a public school, and it did not have a connection or meaning to you because prior to that, it sounds like it was pretty positive. Right? Explore these things you’re curious about; there’s not, like, a level you need to stick with…

Dan Meyer (09:33):

Yep, yep. Yeah. I think that’s right. Maybe it was a little bit of a classic, like, “Oh, I didn’t have a growth mindset; my mindset was like, ‘Oh, I’m good at math because I am, you know, born that way,’” and all of a sudden, that identity was, you know, thrown into question. And, you know, my foundation was all of a sudden quite shaky. And yeah, that’s—you know, I think I taught a lesson recently where I was like, “Hey, this whole thing with a less-than or equal-to sign and a greater-than or equal-to sign, like what those signs are: it’s just, it’s language. And if it’s confusing to you, it’s not because you’re bad at math; it’s ’cause language is oftentimes confusing ’cause people have to agree on it.” So I dunno, that sort of thing is kind of filtered in, filtered back in periodically, some sympathy for like how a lot of math is like just socially agreed upon ways of working with, you know, numbers, shapes, patterns, that kind of thing.

Bethany Lockhart Johnson (10:20):

OK.

Dan Meyer (10:21):

Anyway.

Bethany Lockhart Johnson (10:21):

  1. And in this home school—I have a lot of questions about that, but I’ll stick to one—were you in a community of people that you talked about these math ideas with? Were you homeschooled solo? You have a sibling, so I think you were together, right?

Dan Meyer (10:39):

Yeah. Yeah. I’ve got a twin sister. So we were, you know, like, right on with each other the whole way through there. And yeah, so we had—but it wasn’t, it wasn’t like a—it was a lot of individual work, with my flavor of homeschooling.

Bethany Lockhart Johnson (10:54):

  1. Got it. And the tapes—wait, before you go to high school, the tapes, the VHS tapes, which I’m just loving this image—

Dan Meyer (11:02):

Yeah.

Bethany Lockhart Johnson (11:02):

Was that a positive experience? Was that because that was an area of math that whoever was homeschooling you wasn’t that comfortable with? Why was it that route for the tapes, and what was that? Was that joyful for you?

Dan Meyer (11:15):

Yeah, definitely not joyful. Yeah, it was like, if you had questions, you couldn’t really ask them of the VHS tape. It didn’t work out so well in that way. And it was a lot of operational-type math. It was, you know—there was no give and take; it was all kind of take. From the video teacher. And yeah, I was doing that because my homeschool teacher, my mom, who is very smart in lots of areas, did not have the math knowledge or confidence, especially to help with math at eighth grade. And that was a big reason why, flash-forward to the next year, went to high school.

Bethany Lockhart Johnson (11:48):

Nice segue. OK.

Dan Meyer (11:50):

<laugh> You caught up to high school…I encountered just like four years of just crazy-good, just bonkers-good math teachers who just really changed a lot for me. Especially, Mr. Bishop and Mr. Cavender, very cool folks who did a lot. And especially, I think Mr. Bishop and Cavender both modeled for me what curiosity from a knowledgeable adult looks like. Like someone who, you know, now I can say to myself, “Oh, they were kind of like putting on an act of being very curious about answers they were hearing for the 2000th time from a student,” let’s say, but what a powerful experience that was for me to feel like, “Oh, wow, my thoughts are interesting to someone besides myself.” I got like, maybe it’s two real highlights that I’ll just point to, from my math bio that made me the math teacher and person that I am. Let’s see here. Maybe three, if you you’ll indulge me. One is just like the idea that you could do math wherever you have your brain, a pencil and a paper. And so I remember like in high school, I was in church with my family and kind of a little bit bored of whatever’s going on. And I just had the Bolton and I like drew a pentagon, a regular one, then a hexagon, a regular one, and kept on drawing, like adding sides to the shape. And it was like, it was becoming a circle. And, you know, I was able to take the area of each of those shapes and say, you know, “What happens as you send the number of sides to infinity?” And watch as the formula for area of a circle, Pi R squared, popped out. And it was kind of a literal religious experience, in that moment, just like, “Wow, like my brain’s so cool and math is so cool and paper and pencil’s so cool.” And so there’s that. Just that kind of experience was pretty awesome. And then I would just say like, I’ve had some really fantastic experiences with math in the world itself. Stuff like—let’s see, this is gonna invite more questions from Bethany, probably, maybe I should avoid—I got, I have a Guinness—I have a Guinness world record that’s almost 20 years old. This Guinness world record is—it’s old enough to drive basically at this point. And almost old enough to drink. But like it was—it was a record for chaining the longest paper clip chain together in 24 hours. And the only way I was able to break that record was through mathematics. Where, like, I would be finishing a box of clips. And I would say to my buddy who was there, “I just finished a box of clips.” And that person would type in the number of clips that I had just done. And then a mathematical formula that I had created would tell me how many—how long the chain was at that point. It was being rolled around a spool. And like, it’s just like, wow. So math just made this possible. You know, math revealed that the record I was trying to beat was beatable, because I did the math on it. It was, like, thousands of feet long in 24 hours. And other folks might be like, “Oh, like, that’s that’s huge!” But me, I was like, “All right, let’s divide this out. You know, divide by 24 hours in a day, divide by 60 minutes an hour, 60 seconds in a minute. Oh, that’s like one clip every four seconds. That’s really slow.” You know, think about that <counts aloud>, “Clip, two, three, four. Clip two, three…” It was just slow. So math helped me, you know, wreck that record. Which to my knowledge still still stands. Don’t get any ideas, Math Teacher Lounge Folks! Is this news to you, Bethany? You haven’t blinked in the last, like, five minutes. I’m curious if this is new.

Bethany Lockhart Johnson (15:20):

It is news to me. And I have so many questions. Because OK, if four seconds was slow, so then what was your like—so then I’m assuming a hundred clips per box? Like, what was the rate, you know, per box? How long did it take you to complete a box? What did this friend like? Did this friend stick with you for the whole 24 hours? Did you really do it for 24 hours? Or once you beat the record, did you rest? How did you account for biological function? Like, needs? Like a restroom?

Dan Meyer (15:51):

<Interrupting> Like what?

Bethany Lockhart Johnson (15:51):

Eating.

Dan Meyer (15:51):

Like what, Bethany? OK.

Bethany Lockhart Johnson (15:52):

Um, Sleep.

Dan Meyer (15:55):

So yeah, maybe we dive into some of the specifics in a different time.

Bethany Lockhart Johnson (15:59):

Just tell me one of ’em. Tell me one.

Dan Meyer (15:59):

I’ll just say. So as to discourage other Math Teacher Lounge listeners from taking this on—back off of the record, folks!—this was back in college, so I was a little more limber back then. But I did one—I think it was 1.8 seconds per clip. For an entire 24 hours. Just like, so just like think about it, would you? If you’re gonna step to me on this one, just think about that, OK? And then, and then, you know, make an informed decision.

Bethany Lockhart Johnson (16:28):

Wait. Wait, wait, I just wanna tell you one thing. I’m picturing somebody with a straw, and like, giving you water as you keep clipping. I’m picturing, like, music, I…

Dan Meyer (16:37):

That’s not far. That’s not far. That’s not far from—yeah.

Bethany Lockhart Johnson (16:40):

So many questions! OK. Go on. Sorry, sorry, sorry. Go on. This is your bio.

Dan Meyer (16:44):

We gotta, I gotta wrap this up. I wanna hear your bio. But, like, I would just say like this move to this sense that math is actually a thing that’s useful for more than just a grade; it’s useful for more than just, you know, the societal, you know, adulation that comes from being a math nerd. That kind of thing. And so that, I think that affected a lot of math teaching for me. And, if I gotta, like, summarize math teaching itself in a journey, it went from like, “Hey kids, aren’t I awesome?” to, “Hey kids, isn’t math awesome?” to “Hey kids, aren’t you awesome?” And like that journey was facilitated by lots and lots of people, you know, a lot of personal growth, but at this point, at one point I was like, “Hey, math can help you get records and whatnot. It’s really useful.” And now I’m like, “Wow, your brain’s just doing just really interesting things. I can help you understand how interesting those things are, and maybe make them more interesting, or interesting in a different way, with some help here.” Let’s put a pin in that. That’s the math bio.

Bethany Lockhart Johnson (17:50):

  1. So I have no doubt that if you ask someone in your life, listeners, for their math bio, that you will discover things about them that you never knew. Literally the questions that I have…I have so many question. And Dan is very good at, you know, bringing me back. Bring me back, like, come on, come on. But I just wanna say, overall, your journey seems pretty joyful. It seems pretty joyful. It seems pretty full of confidence. I don’t wanna say “ego” in a negative way, but I wanna say you were buoyed by these experiences that allowed you to feel like math was a place for you to thrive.

Dan Meyer (18:36):

Right.

Bethany Lockhart Johnson (18:36):

Where you could try out things. You could try it out and just, “I could do that!” Right? Like…your relationship just felt very, like…you felt like you had autonomy, agency, perhaps much like you, you operate in this world. Dan, is that, is that right <laugh>?

Dan Meyer (18:54):

Yeah, I think it’s fair to say. And without telling too much of her story, my twin sister with whom I share most things, including genetics, you know—she had a very different experience in math early on. She’s brilliant. She’s a doctor. And not, you know, the book kind of doctor that I am, but like a real, you know, medical doctor. She’s brilliant. But we were—we encountered different messages about who math was made for, early on in, you know, in our entire math learning. And she—we both digested the messages that we were sent, and took, you know, different, different paths because of them, for sure.

Bethany Lockhart Johnson (19:31):

Funny how that works. I thank you, Dan. I do. For in all sincerity, I appreciate you sharing that. And I think that it’s exciting to hear how it influenced your teaching. It feels like you want to cultivate those experiences for your students. And I’ve been in the room when you’ve presented; I was in a room where you taught a class live. It felt like you were making space for the students to have these aha moments. And it feels like in your work at Desmos, and now Amplify, you’re trying to create these products that allow folks to recreate these amazing math moments. Right? And that it’s for everyone and that it’s accessible and it can be very positive. I feel like I have this new perspective on kind of the energy you bring to your teaching. So thank you for sharing that.

Dan Meyer (20:24):

Yeah. Been a pleasure. Thanks for your questions here, Bethany. And it’s been—it’s been fun to reflect on it. And I do—I do feel very lucky in lots of ways. Privileged. Lucky. I know, like—I think the world has been set up for my success in lots of ways, as who I am. But I do just…yeah, I feel—I want more people to experience what it’s like when you walk into a math classroom and it’s like, “Hey, this place is for you. You have interesting thoughts about this. Let’s get ’em out.” So that’s awesome. I would love to hear about you and how you…I mean, we have taught different kinds of kids. You know, I taught kids who I think were somewhat set in, they’re a little bit more solid at secondary in who they are as a math learner. Like “I know who math is and who I am with math.” And I’m really excited to hear what your math bio allowed you to do with students who were perhaps open to the idea that they are very mathematical or at least not yet closed off to those possibilities. So, yeah. What are some of the high, the, you know, the high and low water marks of the making of Bethany Lockhart Johnson, math teacher? <Laugh>

Bethany Lockhart Johnson (21:24):

Thanks for asking, Dan. <Laugh> I’ve shared aspects of my math bio because I think it really informs the way that I talk to people about math and think about math. And I like to share it because I want folks to consider their own journey with math, as we like engage with problem-solving and sense-making and thinking about the students in our classroom. My dad is a math and computer science major. So he had a computer very early on. I wish he had invested in Apple early on when he had like one of the first Apple computers ever. And, sorry, dad, but it’s true. I do wish you had done that.

Dan Meyer (22:10):

I’m sure he does too.

Bethany Lockhart Johnson (22:11):

Oh, he does. So math and computers and conversations about counting, you know, it felt like it was kind of just normal. Like it was around me. And I went to Montessori, which is a private school that—oh, they have some public Montessori—but it’s very self-directed. And so we would have these kind of charts, these goals for the day that you explored. And so we would explore math in very, I don’t know, very organic ways, with these natural materials. And I feel like I excelled at math, but it wasn’t something that I was conscious of. It was just like, “Oh, well, yeah. Math, it’s, you know, something we do.” And then when I went to—when I left Montessori in fourth grade, I remember that year being a lot of like repetition. I was like, well, we did this. We covered this. And except for the mission project that we hadn’t done, that was all new. And that’s it. For another time I’ll share about that. But <laugh> then, they actually, I was moved with a group of students to the fifth grade math class, ’cause we had already done the work that we were doing. And so, it wasn’t that it felt like it came easily, but it did make sense. What we were doing made sense. And then it all kind of changed. There was a lot of change in my family. There was, like, missed school time. And we moved and I went to a new middle school and I was in this environment with students who—it was like an accelerated program. And so I was in this environment with students who were pretty competitive with each other. And I remember going—and I was not from of a competitive environment; like Montessori is not competitive. It’s not about that.

Dan Meyer (24:02):

Right. Right.

Bethany Lockhart Johnson (24:02):

It’s—it was very strange to me that I would be competing against anyone, even competing against myself. And I, you know, knew how to set goals. But it was a different level of energy. And I felt like, because I wasn’t competitive in that nature, I felt like that kind—I felt on the outside of a lot of the energy. Besides the regular, like, middle-school feeling outside of things. And I remember the first friend that I made. Hi, Susan! She had said to me, this was like maybe our second week of school, she’s like, “Oh, at lunchtime, come with me to math club.” And I was like, “OK.” And I remember walking into that room and I had no idea what was going on. And so that was one of the first times where I was just like, “Whoa, I have absolutely no concept of what they’re talking about or what.” These are my peers. I felt very—it was very—it was strange. It was strange. I was like, “This doesn’t feel like a space for me at all.” When I think ordinarily I was kind of excited about the idea of going to math club at lunch, you know? And over middle school, I kind of just got progressively more and more behind. It started with missing some work and then missing more and then checking out. And, you know, the problem was that I really made it about myself. That, like, it wasn’t something that I was then good at or could do. When really it was that well, pre-algebra, I was having a really hard time in like the rest of my life. And so I wasn’t real present in that class. And so when I got to algebra, it didn’t make a whole lot of sense. And then if I missed Monday, Tuesday, and Wednesday, well, Thursday is gonna be hard, you know? And, it just got progressively harder and harder. So I had this great idea that between eighth grade and ninth grade, I was going to take this accelerated geometry class. ‘Cause that was the ninth grade class, it was geometry. And I would take it. It was like geometry in three weeks or something. So then when I entered high school, I would’ve gotten this like jumpstart. But I wish I had said, “Oh, I’ll take this, and then in ninth grade I’ll take geometry.” So like I’ve already kind of gotten a preview of the material. But instead I went to the 10th grade math, which was like intermediate algebra, trigonometry. I had absolutely no clue what was going on. And I had a very, very difficult time and I wasn’t ready for that class. But it was exacerbated by the fact that this teacher felt very free to let the freshmen in that class know that they shouldn’t be in that class. That this class was for 10th graders.

Dan Meyer (26:49):

Oh wow. Oh, wow.

Bethany Lockhart Johnson (26:51):

And we had a rather contentious relationship. And I will never forget that we were in the hallway, and he says to me, “You don’t belong here.” And I’ve talked to—I’ve talked to a girlfriend of mine about her experiences with this teacher and she has the fondest memories.

Dan Meyer (27:13):

Wow.

Bethany Lockhart Johnson (27:14):

She—in fact, almost everyone I’ve spoken with, you know, if we are talking about past teachers or, “Oh, what was that class like?” I mean, they just have these wonderful memories! And for me, my sense of like belonging was already so on a tight rope anyway, that to have this adult, this teacher, tell me, “You do not belong here,” just crushed me. And in hindsight, I think he was saying like, “This class is too hard for you.” I mean, maybe. <Laugh> But all I heard was “You don’t belong here.” And I extrapolated it to connect to math and to anything having to do with math in general. And it just got worse and worse through high school in the world of math. My next math class was even—I had to repeat that class, and still didn’t understand what was going on, and felt more out of place, and, you know, it’s one of those things that I just kind of had started to accept that, I guess, math isn’t for me. I guess I’m just not a math person. Or whatever these stories are that I started to create and build and find evidence for around me that was informing that this wasn’t for me. And I had always done well in school. I was in, you know, accelerated classes. I felt like I was capable of problem solving. And yet in math, I just felt like I had all of this evidence saying that I didn’t belong there. And so when I went to college, I took whatever two math classes were—you know, I was in performing arts and then I did ethnic studies as well. And I remember you had to take two math classes that were GEs. There were these classes that if you don’t wanna deal with math, you go take those classes. And I was like, “Oh yeah, I’ll take that. I’ll take that.” The gulf widened, you know? <Laugh> And I didn’t feel like anxiety when I had to do things like balance my checkbook or navigate math in everyday spaces. It was just, it would never occur to me that I would like seek out opportunities to engage with math or think about it or talk about it.

Dan Meyer (29:35):

That is—yeah, that’s just so wild, how, I don’t know, like it’s often, from the student’s perspective, it is them in a vacuum with math, and the two of them interact and decide if, you know, if they’re right for each other. But from the grown-up perspective, it’s just, you know, it’s a little bit clearer that your story with math was not just you in math, but you with, you know, various external things happening. With family, various teachers playing their different roles—sometimes, you know, really tragic and horrible roles—and then like the compounding mathematical debt that it feels like you were kind of building up, as challenges in one year didn’t get resolved and moved into the next year and so on. And all that makes me wonder—it makes me, like really, really scared, first of all, because I would bet that your teacher might not even remember that moment, that for you is part of just a pivotal moment in your math story, and how many kids have I played—have I been a part of their story in that way and wouldn’t even recall? You know what I’m saying? So that’s a scary part. And then also I’m just wondering, like, how can we, how can we help kids who are in those moments recognize that, “Oh, this kid is like absent a bunch,” and give them more resources to be successful rather than say, “Well, you just gotta try harder now.” Those are things I’m wondering, hearing your story. Thank you for sharing that. I’d love to know more about how you then became a teacher and what all that did for you as you helped students.

Bethany Lockhart Johnson (31:06):

Well, but to answer what you were saying, it wasn’t that I wasn’t—I was always absent physically, but at least like mentally at that point, because it had become so difficult. It didn’t make sense to me. So I was just really checked out in math class, you know? So in hindsight, you know, as a teacher, for sure I can look back, and especially hearing these stories and these experiences my friend had with this teacher and just like chalks up as one of like her most favorite teachers ever! And you know, he clearly did a great job for so many students. But for me, and I think for some people, they would’ve taken those challenges and, you know, it would have fortified them in a different way or something. But for me, I took it upon myself to mean certain things about myself and about my ability and what I was capable of. And so I think, I think in some ways, you know, yeah, it’s all, it’s all interconnected. You know, when your students walk in the door, they’re not this—the things that are impacting them in their life are coming into the room with them. And I don’t think we can take that for granted and think, “Well, if they just focus hard enough…”

Dan Meyer (32:21):

Yeah.

Bethany Lockhart Johnson (32:23):

So let’s go back to my love of Oprah. You know, Oprah talks about living your best life. And something I really appreciate about Oprah is that she encourages you to examine, like, sticking points, right? Like she doesn’t just say, “Well, this…just pretend nothing ever happened, and everything’s fine!” You know, she really talks about making time for reflection. And I kind of got mad that anytime I thought about math, or math schooling came up. Or, you know, whatever, any time that came up that I just felt UGH about it. And I felt like a failure. And I’m like, “You know what, what if I took a math class? And I’m an adult at this point. I’ve graduated. I have—I’ve left college. I have my degrees. But I said, “What if I took a math class?” So I went down to, the city college and I found out that you have to take this exam, like a placement exam. And I went and took the placement exam. And I remember it’s one of the responsive tests where if you get it right, the next question’s a little harder. And so I’m taking it, panicking, because it’s getting more like…I just, you know. And I remember it placed me in like, whatever, Algebra Something, this class that was far more advanced than I thought I should be in. And I was like, there’s been a mistake! You know, and I went to the counselor and said, you know, “I got these results, but I couldn’t answer a lot of the questions on the test.” She’s like, “No, no, no, that’s how it works.” So I go take this class and the class was hard. And I decided that I was just gonna keep showing up. And every day before class, I kid you not, they had a little math…it was like a math center where you could go in and they had a bunch of tables and you’d sit at the table and you could sit and do your work or whatever. If you had a question, you walked up and put your name on a clipboard and then somebody would come and help you. So I did that, every single—like before every single class I would go in. I’d sit there. I’d do the work. I’d go. And I’d get help. Like somebody would walk over and you know, some kid for whom they’re like this…you know, they’re math—it might be you, Dan! It could be you! It could have been you! You know, would walk over and be like—

Dan Meyer (34:38):

Yeah, I was in Help like that. Naw, it’s awesome. Love, love those people. Yeah.

Bethany Lockhart Johnson (34:42):

And you know, I did it. And I did so well in the class. I did exceedingly well in the class. And I said—

Dan Meyer (34:50):

Take that! Take that, everything! Every other math experience!

Bethany Lockhart Johnson (34:53):

I said, what?

Dan Meyer (34:55):

Yeah!

Bethany Lockhart Johnson (34:55):

Wait a second.

Dan Meyer (34:56):

Yeah.

Bethany Lockhart Johnson (34:57):

And it was that I was present. I was not afraid to look at what didn’t make sense. And if something didn’t make sense, it didn’t mean there was something wrong with me. Whaaaaat?

Dan Meyer (35:10):

Yeah. Yeah.

Bethany Lockhart Johnson (35:10):

So I was just in such a different space. And then I took another math class and that class was even harder. And I did the same thing where I went to the little lab and, you know, and it just buoyed me. And it made me realize that, like, this story, that my experience with it was very powerful and that was a real lived experience, but that it didn’t have to define my relationship with math. But then! I decided I wanted to go back to school to become a classroom teacher. And I totally—this was a couple years after that math class experience. So now, you know, I’m healing my relationship with math through basic positive experiences, da, da, da, you know, doing other work. But fast-forward, for a whole number of reasons, decided to become a classroom teacher. And I freaked out. All of my—like, I’m studying for the GRE and the CSET and all the things you have to the hoops you have to jump through to apply to the masters program and the credential program. And I freaked out. I was so close to quitting, Dan. Because I was convinced that the reason I couldn’t be a classroom teacher is because I wasn’t capable in math. Like I was—it was all that resurfaced. And even though I now had evidence to say something different, to the contrary, it was still so visceral. And I was so scared. But I passed that Math CSET.

Dan Meyer (36:47):

Get it.

Bethany Lockhart Johnson (36:47):

I did well enough on the GRE—

Bethany Lockhart Johnson (36:50):

Yes!

Bethany Lockhart Johnson (36:50):

You know, I finished my credential. I worked really, really hard. I had to work so hard in my student placement, when I was student teaching for a fifth-grade class, ’cause I felt like, “Oh my God!” I mean, now I could do the mathematics, but I couldn’t TEACH it to someone, you know? But I had amazing professors at UCI, and my math professors really like just—and my mentor teacher! shout out to Jennifer! shout out to Phil!—these amazing mentor teachers who just loved teaching and who loved—like you said, you have these teachers in your life who you got to see the way that they listened to students. They taught me about that love of listening to students. And then I fell in love with, you know, CGI, cognitively guided instruction, and started learning all about all of these educators who just wanna learn from students’ thinking. And it was just so powerful. And I realize as a kindergarten teacher that I have this really special role in helping to create space for a positive school experience. Like we get to talk about—I talk about my students as mathematicians; they’re writers; they’re thinkers; they’re problem-solvers. And I also want to make space for parents. Some of them, this is their first kid in kindergarten, and they brought all of their experiences, a lot of it negative, that they had had with mathematics. So I felt like it was such an exciting opportunity to help show parents how they could have conversations about math with their students. That also, I hope helped heal their own anxiety with mathematics.

Dan Meyer (38:41):

Right, right.

Bethany Lockhart Johnson (38:42):

Like, I’ve not even scratched the surface of math learning. But I just have such a changed perspective and relationship with math. And I just fell in love with the sense-making. And I fell in love with the journey of it. I still experience math anxiety about a wide variety of things, but I do love it. And I feel like there’s a space for me in relationship with math. And that really excites me.

Dan Meyer (39:09):

Yeah. Wow. Listen to that folks. We, we don’t deserve her! Bethany Lockhart Johnson! She got some math game and could have gone off there and, you know, become an accountant or something. And she chose to hang with kids and their parents. That’s so wild that you’re like rehabbing parents and their self-conception about mathematics at the same time. I think that is so cool.

Bethany Lockhart Johnson (39:32):

Well, thanks Dan Meyer. I gotta tell you, I don’t know when or if I’ve ever shared that much of my math story. So there is a certain amount of vulnerability there. But thanks for listening. And I’m glad that, you know—I think there’s space for us to talk about these things that we care deeply about, but that can be really complicated.

Dan Meyer (39:56):

Yes. Yes. And I love how you you’ve really sharpened the point on what I feel like I know in my brain, but not my body all the time: That individual teachers are huge. Like, individual teachers, and individual moments of teaching, are just not something to play with. You know, like that kid that’s in fifth grade having a tough time, like there could be a month or a day-long period where all of a sudden, like, you’re just like, “Oh yeah, I’m back in the mix; like, me and math are still buddies.” And there’s also like moments that you had, where like one casual word from a teacher can just really put a huge wedge between you and a discipline that needs and wants you and your intellect in it.That’s a really powerful testimonial. Not just for math, but for teaching, your teaching bio.

Bethany Lockhart Johnson (40:43):

I agree with you. And I also, I also…you know, I think we can’t put this—we are human. Teachers are human. And so I’m sure there’s things I’ve said to students. Twenty-second story: a student stapled his finger in my class. <Laugh> And I remember holding his hand and saying, “Why did you do that?” And I wasn’t yelling at him, but it was like, I am sure the panic in my face…like, that’s what he’s gonna remember about kindergarten. Right? <Laugh>.

Dan Meyer (41:19):

Yeah.

Bethany Lockhart Johnson (41:20):

That. He will remember that. He won’t remember the really cool city project we did. He’s gonna remember his teacher holding his hand, in his face: “Why did you do that?”

Dan Meyer (41:30):

Yeah. Yeah.

Bethany Lockhart Johnson (41:30):

You know, so we’re human. And yes, it was awful that that teacher said that to me. There were a thousand other ways that he could have said whatever it was he was thinking. And that did deeply wound me. But despite his influence—because teachers do have a lot of power and I think they need to examine that power, ongoing—it still doesn’t have to define us. So I don’t wanna put this pressure, like—

Bethany Lockhart Johnson (41:55):

Sure.

Bethany Lockhart Johnson (41:56):

“So never ever say anything negative!” You know, we’re human.

Dan Meyer (42:00):

I feel like that kid is currently on some office-supply podcast talking about “your office-supply bio” and saying, “Let me tell you how I first got really freaked out by staples. Here’s the deal: I only use paper clips. And here’s why.”

Bethany Lockhart Johnson (42:15):

“Here’s why.” But then—callback!—he’s going to stumble upon THIS podcast and think, “And because I’m so adept with paper clips, I can beat that record!”

Dan Meyer (42:30):

Though—aaay! whoa! Settle down!

Bethany Lockhart Johnson (42:31):

BOOM.

Dan Meyer (42:31):

Don’t get any ideas, kid. No way. Uh-uh. I don’t like that at all. That’s not what—that’s not what I want to have happen here. No, thank you.

Bethany Lockhart Johnson (42:41):

Well, I’m spent, Dan. I need a nap.

Dan Meyer (42:45):

Yeah. I need a box of Kleenex. I need a nap. I need a—yeah, for sure, a baba. Uh-huh. Definitely. Hey, so look, I’m not expecting you folks out there in the lounge to kind of give us the same depth or breadth. You know, we are here, of course, for your entertainment. Feast on our stories and dramas. But I would love to know at some point, like, what are a few, a few moments that really came to define you mathematically? Came to influence you as a teacher? I think we would do really well for each other to understand that about all of our processes. So yeah, I would just toss in a plug in for Twitter, @MTLShow, or Facebook, Math Teacher Lounge; it would be fantastic to hear from you.

Bethany Lockhart Johnson (43:24):

Thanks so much for listening.

Dan Meyer (43:25):

Thanks, folks. Bye now.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Dan Meyer says about math teaching

“Teaching, more than other professions, is a generational profession. The kinds of joyful experiences we offer, or don’t offer, now affect the experiences students that haven’t even been born yet will have years later.”

– Dan Meyer

Meet the guests

Dan Meyer

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Bethany Lockhart Johnson

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

A woman with curly hair and glasses smiles outdoors; a man with short dark hair smiles indoors in front of a blurred math teacher lounge, highlighting valuable math teacher resources.
A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

What’s included

Along with compelling print materials, powerful digital resources, and more hands-on materials than any other program, Amplify Science California also includes engaging and realistic experiences, access to diverse role models, countless a-ha moments, and the inspiration and confidence to consider a future as a scientist or engineer.

Choose level

Year at a glance

Amplify Science California is organized around units where students explore compelling phenomena and real-world problems, develop and strengthen claims by collecting evidence and testing assumptions, and apply their learning in new contexts.

Educational curriculum chart showcasing a progression of amplify science lessons from kindergarten to grade 5, categorized by grade and subject areas like plants, animals, weather, and energy.

Units at a glance

In each Amplify Science California unit, students are asked to inhabit the role of a scientist or engineer in order to investigate a real-world problem. These problems provide relevant, 21st-century contexts through which students investigate different scientific phenomena.

An illustration from Needs of Plants and Animals unit

1

Needs of Plants and Animals

Students take on the role of scientists in order to figure out why there have been no monarch caterpillars in the community garden since vegetables were planted. They investigate how plants and animals get what they need to live and grow, and make a new plan for the community garden that provides for the needs of the monarch caterpillars in addition to producing vegetables for humans.

An illustration from the Pushes and Pulls unit

2

Pushes and Pulls

Students take on the role of pinball machine engineers as they investigate the effects of forces on the motion of an object. They conduct tests in their own prototypes (models) of a pinball machine and use what they learn to contribute to the design of a class pinball machine. Over the course of the unit, students construct a foundational understanding of why things move in different ways.

Silueta de una estructura de parque infantil contra un cielo azul con nubes y tres soles amarillos.

3

Sunlight and Weather

The principals of Woodland Elementary and Carver Elementary need student weather scientists to help them explain why Woodland’s playground is warmer than Carver’s at recess. Students gather data from models of the sun and Earth’s surface and observe their own playgrounds to figure out how sunlight causes changes in the temperatures of different surfaces. Students then use models to figure out why Woodland’s playground sometimes floods.

Illustration of sea turtles swimming among seaweed in the ocean, with a large shark in the background.

1

Animal and Plant Defenses

Students play the role of marine scientists. In their role, students apply their understanding of plant and animal defense structures to explain to aquarium visitors how a sea turtle and her offspring can defend themselves from ocean predators when they are released into the wild.

Dos manos sosteniendo un papel con un dibujo de pirámide y árbol, iluminado por una linterna, proyectando otra sombra de la imagen en la pared.

2

Light and Sound

Students take on the role of light and sound engineers for a puppet show company as they investigate cause and effect relationships to learn about the nature of light and sound. They apply what they learn to design shadow scenery and sound effects for a puppet show.

An illustration from the Spinning Earth unit

3

Spinning Earth

As sky scientists, students explain why a boy living in a place near them sees different things in the sky than his grandma does when he talks to her on the phone. Students record, organize, and analyze observations of the sun and other sky objects as they look for patterns and make sense of the cycle of daytime and nighttime.

An elephant standing next to a tree uses its trunk to pick a fruit from a branch while more fruit hangs above.

1

Plant and Animal Relationships

In their role as plant scientists, students work to figure out why there are no new chalta trees growing in the Bengal Tiger Reserve, which is part of a broadleaf forest. Students investigate what the chalta tree needs to survive, then collect and analyze qualitative and quantitative data to solve the mystery.

A hand holds a red bean on a table, while a wooden stick spreads white glue and scattered beans. Also on the table are a white cup and a yellow pen.

2

Properties of Materials

As glue engineers, students are challenged to create a glue for use at their school that meets a set of design goals. Students present an evidence-based argument for why their glue mixture will be good for their school to use.

Ilustración de una costa con acantilados, un edificio de centro recreativo con un techo rojo y un letrero, árboles de hoja perenne, una bandera azul y una playa de arena debajo.

3

Changing Landforms

The director of the Oceanside Recreation Center gets a scare when a nearby cliff collapses overnight. Research reveals that the distance between the Recreation Center’s flagpole and the edge of the cliff have changed over time. Students play the role of geologists and work to figure out why the cliff has changed over time. Based on what they learn about erosion, they advise on whether it is safe to keep the center open even though the cliff is changing.

An illustration from the Balancing Forces unit

1

Balancing Forces

People in Faraday are excited to hear that a new train service will be built for their city, but concerned when they hear that it will be a floating train. Students are challenged to figure out how a floating train works in order to explain it to the citizens of Faraday. They develop models of how the train rises, floats, and then falls back to the track, and then write an explanation of how the train works.

An illustration from the Inheritance and Traits unit

2

Inheritance and Traits

Students play the role of wildlife biologists working in Greystone National Park. They study two wolf packs and are challenged to figure out why an adopted wolf (“Wolf 44”) in one of the packs has certain traits. Students observe variation between and within different species, investigate inherited traits and those that result from the environment, and explain the origin of several of the adopted wolf’s traits.

An illustration from the Environments and Survival unit

3

Environments and Survival

In their role as biomimicry engineers, students work to figure out how the traits of grove snails affect their survival in different environments. They then explore how the traits of different organisms make them more likely or less likely to survive, collecting and interpreting data to understand how organisms’ traits affect their survival in different environments. Students then apply their understanding to a new challenge: designing effective solutions for the removal of invasive plants.

An illustration from the Weather and Climate unit

4

Weather and Climate

In their role as meteorologists, students gather evidence to decide where to build an orangutan reserve by analyzing patterns in weather data. After choosing the strongest evidence, students use data to make arguments about which of three fictional islands has weather most like that of orangutans’ existing habitats, Borneo and Sumatra. They then discern patterns in the locations of natural hazards in order to figure out which ones the Wildlife Protection Organization must prepare for.

An illustration from the Energy Conversions unit

1

Energy Conversions

Students take on the role of systems engineers for Ergstown, a fictional town that experiences frequent blackouts, and explore reasons why an electrical system can fail. Students apply what they learned as they choose new energy sources and energy converters for the town, then write arguments for why their design choices will make the town’s electrical system more reliable.

An illustration from the Vision and Light unit

2

Inheritance and Traits

As conservation biologists, students work to figure out why a population of Tokay geckos has decreased since the installation of new highway lights in the rainforest. Students use their understanding of vision, light, and information processing to figure out why an increase in light in the geckos’ habitat is affecting the population.

An illustration from the Earth's Features unit

3

Environments and Survival

Playing the role of geologists, students help the director of Desert Rocks National Park explain how and when a particular fossil formed and how it came to be in its current location. Students figure out what the environment of the park was like in the past and why it has so many visible rock layers.

An illustration from the Waves, Energy, and Information unit

4

Weather and Climate

In their role as marine scientists, students work to figure out how mother dolphins communicate with their calves. They write a series of scientific explanations with diagrams to demonstrate their growing understanding of how sound waves travel. Then they apply what they’ve learned about waves, energy, and patterns in communication to figure out how to create patterns that can communicate information over distances.

An illustration from the Patterns of Earth and Sky unit

1

Patterns of Earth and Sky

Playing the role of astronomers, students help a team of archaeologists figure out what the missing piece of a recently discovered artifact might have depicted. As they learn about the sun and other stars and the movement of Earth, students can explain what is shown on the artifact and what might be on the missing piece.

An illustration from the Modeling Matter unit

2

Modeling Matter

In their role as food scientists at a fictional company, students are introduced to the idea that all matter is made of particles too small to see, and that each different substance is made of particles (molecules) that are unique. They are then challenged to solve two problems: one requires them to separate a mixture, and the other requires them to make unmixable substances mix. Students are challenged to use the particulate model of matter to explain their work to the CEO of the company.

An illustration from the Earth System unit

3

The Earth System

The cities of East Ferris and West Ferris are located on different sides of a mountain on the fictional Ferris Island. East Ferris is having a water shortage while West Ferris is not. As water resource engineers, students learn about the Earth system to help figure out what is causing the water shortage problem and design possible solutions, including freshwater collection systems and proposals for using chemical reactions to treat wastewater.

An illustration from the Ecosystem Restoration unit

4

Ecosystem Restoration

As ecologists, students work to figure out why the organisms in a part of a Costa Rican rainforest ecosystem aren’t growing and thriving. As they solve this problem, students learn more generally how organisms in an ecosystem get the matter and energy they need to survive, and then write a series of restoration plans that include arguments about why the rainforest ecosystem is not thriving and recommend actions to restore its health.

Print & digital components

Amplify Science California includes instructional guidance and student materials in English and Spanish for a year of instruction, with lessons and activities that keep students engaged every day.

Component

FORMAT

NEW! Classroom Slides

Meet your new hands-free TG! These lesson-specific PowerPoints make delivering daily instruction a snap with embedded links to related resources and suggested teacher talk in the Notes section of each slide.

Digital

Most adopted curriculum for the NGSS California

Teacher’s Reference Guide

Available digitally and in print, this unit-specific reference guide includes scientific background knowledge, planning information and resources, color-coded 3-D Statements, detailed lesson plans, and tips for delivering instruction and differentiating learning.

Print and digital

Two digital devices displaying educational content, one a tablet showing a green-themed start page, and the other a laptop depicting various science chapters.

Hands-on materials kits

Each unit-specific kit contains consumable and nonconsumable materials for use during hands-on investigations. In each kit you will find:

  • Hands-on materials
  • 18 copies of each of the Student Books
  • Big books (grades K–1)
  • Classroom display materials
  • One Student Investigation Notebook

Kit

Amplify Science California supports 3-D learning with more materials than any other program.

NGSS Benchmark Assessments

Delivered four times per year in grades 3–5 and three times per year in grades 6–8, our benchmark assessments report on students’ facility with each of the grade-level appropriate DCIs, SEPs, CCCs, and performance expectations of the California NGSS.

And now, Amplify Science California users can choose to administer the NGSS Benchmark Assessments (grades 3–8) through their Illuminate assessment platform.

*Also available in Spanish

Digital

An open laptop displaying a website with a quiz question about geographical changes over time, featuring a series of island maps from different years.

Component

FORMAT

Student Investigation Notebooks

Available for every unit, the Student Investigation Notebooks contain instructions for activities and space for students to record data, reflect on ideas from texts and investigations, and construct explanations and arguments.

*Also available in Spanish

Print and digital

Two educational books titled "amplifyscience," one in spanish and one in english, featuring illustrations of desert canyon landscapes on the covers.

Big books (grades K–1)

Amplify Science California never asks our youngest readers to read alone. Rather, we provide scaffolded literacy experiences every step of the way. With our large-format big books, introducing and revisiting concepts though read-aloud and shared reading experiences is a breeze.

*Also available in Spanish

Print

Two hardcover books titled "maravillas rocas" and "rocky wonders" by amplify science, lying open, showing a continuous desert rock formation across both covers.

Simulations and practice tools (grades 2+)

Developed exclusively for the Amplify Science California program, these serve as venues for exploration and data collection, allowing students to explore scientific concepts that might otherwise be invisible or impossible to see with the naked eye.

*Spanish versions coming soon

Digital

A computer screen displays an educational website titled "Earth's Features" with chapters and illustrations of canyons; a printed teacher’s guide is shown beside it.

Explore more programs

Our programs are designed to support and complement one another. Learn more about our related programs.

What’s included in our Grades 3–5 language arts curriculum

Grounded in the science of reading, Amplify CKLA for grades 3–5 integrates foundational skills students have learned in grades K–2 while continuing to build rich content knowledge. With Amplify CKLA, you’ll have the instruction and guidance of proven, evidence-based practices to help all of your students become strong readers, writers, and thinkers.

Year at a glance

The Amplify CKLA curriculum is modeled after proven research in early literacy that supports a two-strand approach to literacy instruction in the early years. With this approach, students in Grades K–2 complete one full lesson per day that builds foundational reading skills in the Skills Strand, as well as one full lesson that builds background knowledge in the Knowledge Strand. The deep content knowledge is sequenced together with research-based foundational skills in Grades K–2 so that students develop the early literacy skills necessary to help them become confident readers, as well as build the context to understand what they’re reading. 

In Grades 3–5, lessons combine skills and knowledge with increasingly complex texts, close reading, and a greater emphasis on writing. Students start to use their skills to go on their own independent reading adventures, further opening up their worlds.

Diagram illustrating how language comprehension and word recognition components integrate to lead to skilled reading, as described in the Simple View of Reading model, aligned with the 3-5 CKLA curriculum and Amplify CKLA digital experience.

Units at a glance

Students move fluidly between reading, writing, speaking and listening, and language activities, with increasingly complex texts, close reading, and a greater writing emphasis.

Classic Tales: The Wind in the Willows

Students explore international classic tales, including The Wind in the WillowsAlice in Wonderland, and “Aladdin and the Wonderful Lamp.”

Number of Lessons: 15

Animal Classification

Students learn how scientists use animals’ characteristics to classify and study them; students apply knowledge through text-based discussions and writing exercises.

Number of Lessons: 15

The Human Body: Systems and Senses

This unit involves the study of the human body, building students’ understanding of its senses and skeletal, muscular, and nervous systems.

Number of Lessons: 14

The Ancient Roman Civilization

Students dive into ancient Rome, studying its history, culture, and myths about Roman gods and goddesses.

Number of Lessons: 15

Light and Sound

Students learn the science behind light and sound, read biographies of Alexander Graham Bell and Thomas Edison, and write newspaper articles.

Number of Lessons: 17

The Viking Age (with Core Quest)

This unit’s informational and literary texts convey information about the Vikings, their culture, and their exploration.

Number of Lessons: 11

Astronomy: Our Solar System and Beyond

Students learn about astronomy, the universe, and important figures in the history of space exploration, including Nicolaus Copernicus and Mae Jemison.

Number of Lessons: 20

Native Americans: Regions and Cultures

Students compare, contrast, assemble information, and reflect on what they have learned about Native Americans and their ways of life.

Number of Lessons: 13

Early Explorations of North America

Students explore reasons for European exploration, what exploration was like, and who went exploring; then students write opinion pieces using this information.

Number of Lessons: 14

Colonial America

Students learn about colonies in early America, including how colonies were started and the progress colonists made after settling.

Number of Lessons: 16

Ecology

Students learn about different aspects of ecology, including food chains, the balance of nature, changes to the environment, and protecting the environment.

Number of Lessons: 12

Personal Narratives

This unit examines the genre of personal narratives, including nonfiction works written by a first-person narrator involved in the events being described.

Number of Lessons: 15

Empires in the Middle Ages

This unit covers the history of various empires and geographical regions throughout the Middle Ages.

Number of Lessons: 25

Poetry

Students explore poetry, training in methods and devices poets use and learning to read, write, and interpret formal and free verse poems.

Number of Lessons: 15

Eureka! Student Inventor

This Core Quest, a narrative-driven unit, immerses students in close-reading adventures and scientific and historical content about inventions. Students write and read opinion, informational, and narrative texts.

Number of Lessons: 10

Geology

This unit focuses on the composition of Earth and the forces that change its surface.

Number of Lessons: 15

Contemporary Fiction with excerpts from The House on Mango Street

This unit explores narrative literature and writing, using excerpts from The House on Mango Street as its anchor text.

Number of Lessons: 13

American Revolution

Students learn that disagreements about principles of government led colonists in North America to seek independence from Great Britain.

Number of Lessons: 17

Treasure Island

Students focus on character development, setting, plot, and literary devices while reading an abridged version of a classic novel, Treasure Island.

Number of Lessons: 19

Writing Quest (supplemental): The Contraption

In this supplemental Quest, students interact with a mysterious machine fueled by their writing and solve the machine’s puzzles. This Quest features a digital environment controlled by the teacher.

Personal Narratives

This unit examines the genre of personal narratives, including nonfiction works written by a first-person narrator involved in the events being described.

Number of Lessons: 15

Early American Civilizations

Students study the geography, climate, flora, and fauna of the Americas and the rise and fall of the Maya, Aztec, and Inca civilizations.

Number of Lessons: 15

Poetry

Students explore poetry, training in methods and devices poets use and learning to read, write, and interpret formal and free verse poems.

Number of Lessons: 13

Adventures of Don Quixote

In this unit students trace the development of plot, characters, and literary elements while reading a full-length, adapted version of Don Quixote.

Number of Lessons: 15

The Renaissance

This unit provides students with a broad exposure to the art and literature of the Renaissance through the works of renowned masters.

Number of Lessons: 19

The Reformation

This unit teaches students about the Reformation, a movement involving religious and political upheaval that shifted the political power in Europe.

Number of Lessons: 10

A Midsummer Night’s Dream (Core Quest)

This unit is an immersive Quest that treats Shakespeare’s comedy as both literature and a living text for interpretation and performance.

Number of Lessons: 15

Native Americans

Students learn how settlers, explorers, and the American government in the 1800s affected Native American cultures and their relationship with the land.

Number of Lessons: 15

Chemical Matter

Students learn about chemistry and close-reading through a literary and informational work, The Badlands Sleuth, in which the protagonist uses chemistry to solve mysteries.

Number of Lessons: 15

Writing Quest (supplemental): The Robot

Students interact with a classroom pet that learns and grows with their writing. This Quest features a digital environment controlled by the teacher.

Program components

The program includes instructional guidance and student materials for a year of instruction, with lessons and activities that keep students engaged every day.

Component

FORMAT

Teacher Guides

Teacher Guides for each unit provide engaging lessons with standards-based objectives and formative assessments that empower teachers with proven strategies and research-based tools.

Print or digital

Differentiation resources

The online Assessment and Remediation Guide (Grade 3) and the Decoding and Encoding Supplement (Grades 4–5) provide thousands of pages of targeted activities in decoding, spelling, and other core literacy skills. Supplemental Guides provide opportunities for enrichment.

Digital

Writing Studio

A riveting connected writing program for more time, practice, and challenge in writing, with a focus on informative, narrative, and opinion modes of writing.

Print or digital

Digital experience

The Amplify CKLA digital experience delivers ready-made, customizable, slides-based lesson presentations to enhance instruction and save time. Everything needed to plan and present high-quality, engaging early literacy instruction is in one convenient place.

Digital

Component

FORMAT

Student Readers

Amplify CKLA’s Student Readers anchor each of the content-based units, providing a close-reading experience fueled by rich background knowledge that inspires students to dig deeper.

Print

Activity Books

In addition to providing daily opportunities for students to respond to text and apply skills and knowledge, Activity Books feature formative assessments for each day’s objectives.

Print

Digital experience

The Amplify CKLA digital experience delivers ready-made, customizable, slides-based lesson presentations to enhance instruction and save time. Everything needed to plan and present high-quality, engaging early literacy instruction is in one convenient place.

Digital

Explore more programs

Our programs are designed to support and complement one another. Learn more about our related programs.

Winter Wrap-Up 03: Ideas to build math fluency

Promotional graphic for "Math Teacher Lounge" episode featuring Valerie Henry, Ed.D., on ideas to build math fluency, with a photo of Valerie Henry in the bottom right corner.

Join us for the third episode in our Winter Wrap-Up! In this episode from season 3 of Math Teacher Lounge: The Podcast, we sit down with Dr. Valerie Henry to talk about math fluency and what that means for students. Listen as we dig into the research, hear Val’s three-part definition of fluency, and explore her five principles for developing it.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:03)

Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.

Dan Meyer (00:11):

Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.

Bethany Lockhart Johnson (00:26):

I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.

Dan Meyer (00:30):

I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?

Bethany Lockhart Johnson (01:05):

Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?

Dan Meyer (02:08):

I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.

Bethany Lockhart Johnson (02:38):

Wait, did you pass the first time? Your test?

Dan Meyer (02:40):

Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.

Bethany Lockhart Johnson (03:32):

So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.

Valerie Henry (04:36):

Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.

Dan Meyer (04:41):

Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.

Valerie Henry (05:12):

The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,

Bethany Lockhart Johnson (07:12):

You mean without having to kind of muscle through it? Or say more about you mean.

Valerie Henry (07:16):

Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”

Bethany Lockhart Johnson (08:53):

That’s such an important distinction. My brain literally just did that actually!

Valerie Henry (08:58):

<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.

Bethany Lockhart Johnson (09:05):

Right.

Valerie Henry (09:07):

So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.

Dan Meyer (09:55):

I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.

Valerie Henry (10:21):

And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.

Bethany Lockhart Johnson (10:30):

Mm, yeah.

Valerie Henry (10:30):

So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.

Bethany Lockhart Johnson (11:18):

I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?

Valerie Henry (11:30):

I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.

Bethany Lockhart Johnson (12:06):

And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.

Valerie Henry (12:15):

Yes.

Bethany Lockhart Johnson (12:16):

Some of us might remember quite vividly.

Valerie Henry (12:18):

<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.

Bethany Lockhart Johnson (13:10):

If I put it in front of you enough times, you’ll become fluent.

Valerie Henry (13:14):

Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.

Dan Meyer (14:01):

It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.

Valerie Henry (14:35):

My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”

Dan Meyer (15:38):

There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?

Valerie Henry (15:57):

I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.

Bethany Lockhart Johnson (17:09):

So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.

Valerie Henry (17:22):

Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—

Bethany Lockhart Johnson (17:33):

Not waiting until you’ve gotten all the way through addition. But making “Ooh!”

Valerie Henry (17:38):

Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.

Bethany Lockhart Johnson (18:11):

What are the other principles?

Valerie Henry (18:13):

The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.

Bethany Lockhart Johnson (18:27):

Don’t put away those manipulatives. Don’t put away those tools.

Valerie Henry (18:31):

Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.

Bethany Lockhart Johnson (19:07):

I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—

Dan Meyer (19:35):

Thank you, Dr. Henry.

Valerie Henry (19:37):

You’re welcome!

Dan Meyer (19:41):

With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.

Bethany Lockhart Johnson (20:49):

Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”

Dan Meyer (20:55):

Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?

Tracy Zager (21:00):

I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!

Bethany Lockhart Johnson (21:10):

Ooh!

Dan Meyer (21:13):

A language fluency, perhaps. All right, Graham. How about you?

Graham Fletcher (21:16):

For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.

Dan Meyer (21:33):

Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?

Tracy Zager (21:40):

I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.

Graham Fletcher (23:53):

And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.

Bethany Lockhart Johnson (24:10):

So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?

Graham Fletcher (24:41):

What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.

Tracy Zager (25:22):

When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—

Bethany Lockhart Johnson (26:18):

Crayons, markers.

Tracy Zager (26:18):

Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.

Bethany Lockhart Johnson (27:03):

I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.

Tracy Zager (27:14):

Yay!

Bethany Lockhart Johnson (27:14):

And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.

Tracy Zager (27:41):

That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”

Bethany Lockhart Johnson (28:37):

That’s kinda true. Knowing you both, it’s kinda true.

Tracy Zager (28:42):

Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—

Bethany Lockhart Johnson (28:58):

But they’re making sense of numbers!

Tracy Zager (28:59):

Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.

Bethany Lockhart Johnson (29:45):

That’s huge.

Dan Meyer (29:46):

That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.

Graham Fletcher (30:47):

Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”

Tracy Zager (32:44):

I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.

Bethany Lockhart Johnson (34:41):

They’re invested!

Tracy Zager (34:45):

They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.

Graham Fletcher (35:47):

It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.

Tracy Zager (35:55):

I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.

Dan Meyer (37:20):

I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?

Graham Fletcher (37:57):

You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.

Bethany Lockhart Johnson (38:19):

If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?

Graham Fletcher (38:35):

Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.

Dan Meyer (39:25):

Bethany and I will be working the same challenge with people in our life.

Bethany Lockhart Johnson (39:29):

Yes.

Dan Meyer (39:29):

Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.

Bethany Lockhart Johnson (39:42):

I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Valerie Henry says about math

“A lot of very fluent adults don’t always have every fact memorized. ”

– Val Henry

Meet the guest

Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops  fluency,  number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.

An older person with short gray hair and glasses, wearing a blue sweater, is outdoors with greenery and a fence in the background.
Podcast cover for "Math Teacher Lounge" with Bethany Lockhart Johnson and Dan Meyer; bold text on orange and teal semicircle background.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

enVision-NEW

To view this protected page, enter the password below:



Desmos Math 6–A1 correlations with Carnegie Math Texas

To view this protected page, enter the password below:



Grade 6

Chapter 1: Use Positive Rational Numbers

enVision MathDesmos Classroom
Lesson 1: Fluently Add, Subtract, and Multiply DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 2: Decimal Diagrams and Algorithms
Lesson 2: Fluently Divide Whole Numbers and DecimalsUnit 5
Lesson 13: Movie Time
Lesson 4: Understand Division with FractionsUnit 4
Lesson 13: Movie Time
Lesson 6: Divide Mixed NumbersUnit 4
Lesson 6 Fill the Gap
Lesson 7: Solve Problems with Rational NumbersUnit 4
Lesson 3: Flour Planner

Chapter 2: Integers and Rational Numbers

Lesson 1: Understand IntegersUnit 7
Lesson 1: Can You Dig It?
Lesson 2: Represent Rational Numbers on the Number LineUnit 7
Lesson 4: Order in the Class

Chapter 3: Numeric and Algebraic Expressions

Lesson 4: Write Algebraic ExpressionsUnit 6
Lesson 8: Products and SumsTake Away (coming soon!)
Lesson 6: Generate Equivalent Expressions Unit 6
Lesson 8: Products and SumsTake Away (coming soon!)

Chapter 4: Represent and Solve Equations and Inequalities

Lesson 1: Understand Equations and SolutionsUnit 6
Lesson 1: Weight for It
Lesson 6: Understand and Write InequalitiesUnit 7
Lesson 7: Tunnel Travels
Lesson 9: Use Patterns to Write and Solve Equations
Lesson 10: Relate Tables, Graphs, and Equations
Unit 6
Lesson 16: Subway FaresTake Away (coming soon!)

Chapter 5: Understand and Use Ratio and Rate

Lesson 1: Understand RatiosUnit 2
Lesson 1: Pizza Maker
Lesson 2: Generate Equivalent RatiosUnit 2
Lesson 4: Fruit Lab
Lesson 4: Represent and Graph RatiosUnit 2
Lesson 10: Disaster Preparation
Lesson 5: Understand Rates and Unit RatesUnit 3
Lesson 6: Soft Serve
Lesson 6: Compare Unit RatesUnit 3
Lesson 6: Soft Serve

Chapter 6: Understand and Use Percent

Lesson 1: Understand PercentUnit 3
Lesson 9: Lucky Duckies

Chapter 7: Solve Area, Surface Area, and Volume Problems

Lesson 1: Find Areas of Parallelograms and RhombusesUnit 1
Lesson 3: Exploring Parallelograms, Part 1
Exploring Parallelograms, Part 2
Lesson 5: Represent Solid Figures Using NetsUnit 1
Lesson 10: Renata’s Stickers

Chapter 8: Display, Describe, and Summarize data

Lesson 2: Summarize data Using Mean, Median, and ModeUnit 8 
Lesson 11: Toy Cars
Lesson 4: Display Data in Frequency Tables and HistogramsUnit 8 
Lesson 5: The Plot Thickens
Lesson 7: Summarize Data DistributionsUnit 8 
Lesson 3: Minimum Wage

Grade 7

Chapter 1: Rational Number Operations

enVision MathDesmos Classroom
Lesson 1: Relate Integers and Their OppositesUnit 5
Lesson 1: Floats and Anchors
Lesson 3: Add Integers
Lesson 4: Subtract Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 5: Add and Subtract Rational NumbersUnit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 6: Multiply IntegersUnit 5
Lesson 10: Integer Puzzles
Lesson 7: Multiply Rational NumbersUnit 5
Lesson 10: Integer Puzzles
Lesson 9: Divide Rational NumbersUnit 5
Lesson 10: Integer Puzzles

Chapter 2: Analyze and Use Proportional Relationships

Lesson 3: Understand Proportional Relationships: Equivalent RatiosUnit 2
Lesson 1: Paint
Lesson 4: Describe Proportional Relationships: Constant of ProportionalityUnit 2
Lesson 6: Two and Two
Lesson 5: Graph Proportional RelationshipsUnit 2
Lesson 8: Dino Pops

Chapter 3: Analyze and Solve Percent Problems

Lesson 1: Analyze Percents of Numbers
Lesson 2: Connect Percent and Proportion
Unit 4
Lesson 1: Mosaics
Lesson 4: Solve Percent Change and Percent Error ProblemsUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Lesson 5: Solve Markup and Markdown ProblemsUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)

Chapter 4: Generate Equivalent Expressions

Lesson 3: Simplify ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 4: Expand ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 6: Add Expressions
Lesson 7: Subtract Expressions
Unit 6
Lesson 10: Collect the Squares

Chapter 5: Solve Problems Using Equations and Inequalities

Lesson 4: Solve Inequalities Using Addition or Subtraction
Lesson 5: Solve Inequalities Using Multiplication or Division
Unit 6
Lesson 16: Shira the Sheep
Lesson 6: Solve Two-Step Inequalities
Lesson 7: Solve Multi-Step Problems
Unit 6
Lesson 16: Shira the Sheep

Chapter 6: Use Sampling to Draw Inferences About Populations

Lesson 1: Populations and SamplesUnit 8
Lesson 10: Crab Island
Lesson 2: Draw Inferences from DataUnit 8 
Lesson 10: Crab Island
Lesson 3: Make Comparative Inferences About Populations
Lesson 4: Make More Comparative Inferences About Populations
Unit 8
Lesson 10: Crab Island

Chapter 7: Probability

Lesson 1: Understand Likelihood and ProbabilityUnit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities

Chapter 8: Solve Problems Involving Geometry

Lesson 1: Solve Problems Involving Scale DrawingsUnit 1 Lesson 1: Scaling Machines Lesson 7: Will It Fit?
Lesson 3: Draw Triangles with Given ConditionsUnit 7
Lesson 5: Can You Build It?
Lesson 4: Solve Problems Using Angle RelationshipsUnit 7
Lesson 2: Friendly Angles
Lesson 4: Missing Measures
Lesson 5: Solve Problems Involving Circumference of a CircleUnit 7
Lesson 3: Measuring Around
Lesson 6: Solve Problems Involving Area of a CircleUnit 3
Lesson 9: Area Challenges

Grade 8

Chapter 1: Real Numbers

enVision MathDesmos Classroom
Lesson 4: Evaluate Square Roots and Cube RootsUnit 8
Lesson 4: Root Down
Lesson 6: Use Properties of Integer ExponentsUnit 7  
Lesson 3: Power Pairs
Lesson 9: Understand Scientific NotationUnit 7  
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Chapter 2: Analyze and Solve Linear Equations

Lesson 3: Solve Multi-Step EquationsUnit 4
Lesson 5: Equation Roundtable
Lesson 5: Compare Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 6: Connect proportional Relationships and SlopeUnit 3
Lesson 4: Flags
Lesson 8: Understand the y-intercept of a LineUnit 3
Lesson 4: Flags

Chapter 3: Use Functions to Model Relationships

Lesson 1: Understand Relations and FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 2: Connect Representations of FunctionsUnit 5
Lesson 5: The Tortoise and the Hare
Lesson 5: Intervals of Increase and DecreaseUnit 5
Lesson 1: Turtle Crossing

Chapter 4: Investigate Bivariate Data

Lesson 1: Construct and Interpret Scatter PlotsUnit 6  
Lesson 3: Robots
Lesson 2: Analyze Linear AssociationUnit 6  
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Lesson 5: Interpret Two-Way Relative Frequency TablesUnit 6  
Lesson 11: Finding Associations

Chapter 5: Analyze and Solve Systems of Linear Equations

Lesson 2: Solve Systems by GraphingUnit 4  
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Chapter 6: Congruence and Similarity

Lesson 1: Analyze TranslationsUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Lesson 2: Analyze Reflections
Lesson 3: Analyze Rotations
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Lesson 6: Describe DilationsUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 7: Understand Similar FiguresUnit 2
Lesson 6: Social Scavenger Hunt
Lesson 9: Interior and Exterior Angles of TrianglesUnit 1
Lesson 12: Puzzling It Out

Chapter 7: Understand and Apply the Pythagorean Theorem

Lesson 1: Understand the Pythagorean TheoremUnit 8
Lesson 8: Triangle-Tracing Turtle
Lesson 3: Apply the Pythagorean Theorem to Solve ProblemsUnit 8
Lesson 10: Taco Truck

Chapter 8: Solve Problems Involving Surface Area and Volume

Lesson 2: Find Volume of CylindersUnit 5
Lesson 11: Cylinders
Lesson 3: Find Volume of ConesUnit 5
Lesson 13: Cones

Algebra 1

Topic 1: Solving Equations and Inequalities

Lesson 1-2: Solving Linear EquationsWorking Backwards
Lesson 1-3: Solving Equations with Variables on Both SidesSolving Strategies
Same Position
Lesson 1-4: Literal Equations and FormulasSubway Seats
Various Variables
Lesson 1-5: Solving Inequalities in One VariablePizza Delivery

Topic 2: Linear Functions

Lessons 2-1 to 2-3 Forms of Linear EquationsSubway Seats
Five Representations

Topic 3: Linear Functions

Topic 4: Systems of Linear Equations and Inequalities

Lesson 4-1: Solving Systems of Equations by GraphingLizard Lines
Lesson 4-2: Solving Systems of Equations by SubstitutionShape It Up
Lesson 4-5: Systems of Linear InequalitiesQuilts
Seeking Solutions

Topic 5: Piecewise Functions

Lesson 5-2: Piecewise-Defined FunctionsPumpkin Prices

Topic 6: Exponents and Exponential Functions

Lesson 6-2: Exponential FunctionsCarlos’s Fish
Revisiting Visual Patterns, Part 1
Lesson 6-4: Geometric SequencesSequence Carnival
More Visual Patterns

Topic 8: Quadratic Functions

Lesson 8-1: Key Features of a Quadratic FunctionQuadratic Visual Patterns
Lesson 8-2: Quadratic Functions in Vertex FormOn the Fence
Plenty of Parabolas
Lesson 8-5: Linear, Exponential and Quadratic ModelsDetroit’s Population, Part 1
Detroit’s Population, Part 2
Sorting Relationships
Lesson 8-3: Quadratic Functions in Standard FormRobot Launch
Lesson 8-4: Modeling with Quadratic FunctionsStomp Rockets

Topic 9: Solving Quadratic Equations

Lesson 9-2: Solving Quadratic Equations by FactoringTwo for One
Parabola Zapper
Shooting Stars
Lesson 9-5: Completing the SquareSquare Tactic
Lesson 9-6: The Quadratic Formula and the DiscriminantStomp Rockets in Space

Topic 10: Working with Functions

Lesson 10-1: The Square Root functionPlane, Train, and Automobile
Lesson 10-3: Analyzing Functions GraphicallyCraft-a-Graph
Lesson 10-7: Inverse FunctionsChip the Robot

Topic 11: Statistics

Lesson 11-4: Standard DeviationFinding Desmo

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Grade 6

Unit 1: Expressions and Equations: Area, Algebraic Expressions, and Exponents

iReady ClassroomDesmos Math 6–A1
Lesson 1: Find the Area of a ParallelogramUnit 1
Lesson 3: Exploring Parallelograms (Print available) [Free lesson]
Lesson 4: Off the Grid
Lesson 2: Find the Area of Triangles and Other PolygonsUnit 1
Lesson 7: Off the Grid, Part 2
Practice Day 1 (Print available)
Lesson 3: Use Nets to Find Surface AreaUnit 1
Lesson 11: Nothing But Nets (Print available)
Practice Day 2 (Print available)
Lesson 4: Work with Algebraic ExpressionsUnit 6
Lesson 6: Vari-apples
Lesson 5: Write and Evaluate Expressions with ExponentsUnit 6
Lesson 4: Hanging it Up
Lesson 5: Swap and Solve (Print available)
Practice Day 2 (Print available)
Lesson 6: Find Greatest Common Factor and Least Common MultipleUnit 5
Lesson 14: Common Multiples
Lesson 15: Common Factors
Practice Day 2 (Print available)

Unit 2: Decimals and Fractions: Base-Ten Operations, Division with Fractions, and Volume

Unit 3: Ratio Reasoning: Ratio Concepts and Equivalent Ratios

Unit 4: Ratio Reasoning: Unit Rates and Percent

Unit 5: Algebraic Thinking: Equivalent Expressions and Equations with Variables

Unit 6: Positive and Negative Numbers: Absolute Value, Inequalities, and the Coordinate Plane

Lesson 23: Understand Positive and Negative NumbersUnit 7
Lesson 1: Can You Dig It [Free lesson]
Lesson 4: Sub-Zero
Lesson 24: Order Positive and Negative NumbersUnit 7
Lesson 2: Digging Deeper
Lesson 3: Order in the Class (Print available) [Free lesson]
Lesson 25: Understand Absolute ValueUnit 7
Lesson 5: Distance on the Number Line
Practice Day 1 (Print available)
Lesson 26: Write and Graph One-Variable InequalitiesUnit 7
Lesson 6: Tunnel Travels [Free lesson]
Lesson 7: Comparing Weights
Lesson 8: Shira’s Solutions
Lesson 27: Understand the Four-Quadrant Coordinate PlaneUnit 7
Lesson 9: Sand Dollar Search
Lesson 10: The A-maze-ing Coordinate Plane
Lesson 11: Polygon Maker
Practice Day 2 (Print available)
Lesson 28: Solve Problems in the Coordinate PlaneUnit 7
Lesson 12: Graph Telephone
Practice Day 2 (Print available)

Unit 7: Statistical Thinking: Data Distributions and Measures of Center and Variability

Grade 7

Unit 1: Proportional Relationships: Ratios, Rates, and Circles

Unit 2: Numbers and Operations: Add and Subtract Rational Numbers

Unit 3: Numbers and Operations: Multiply and Divide Rational Numbers

Lesson 11: Understand Multiplication with Negative IntegersUnit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 12: Multiply and Divide with Negative NumbersUnit 5
Lesson 8: Speeding Turtles
Lesson 13: Express Rational Numbers as Terminating or Repeating DecimalsUnit 4
Lesson 13: Decimal Deep Dive (Print available)
Lesson 14: Use the Four Operations with Negative NumbersUnit 5
Lesson 10: Integer Puzzles [Free lesson]
Lesson 13: Solar Panels and More (Print available)
Practice Day 2  (Print available)

Unit 4: Algebraic Thinking: Expressions, Equations, and Inequalities

Unit 5: Proportional Reasoning: Percents and Statistical Samples

Unit 6: Geometry: Solids, Triangles, and Angles

Lesson 25: Solve Problems Involving Area and Surface AreaUnit 7
Lesson 12: Surface Area Strategies (Print available)
Lesson 26: Solve Problems Involving VolumeUnit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Practice Day 2 (Print available)
Lesson 27: Describe Plane Sections of Three-Dimensional FiguresUnit 7
Lesson 9: Slicing Solids
Lesson 28: Find Unknown Angle MeasuresUnit 7
Lesson 1: Pinwheels
Lesson 2: Friendly Angles [Free lesson]
Lesson 4: Missing Measures (Print available) [Free lesson]
Lesson 29: Draw Plane Figures with Given ConditionsUnit 7
Lesson 6: Is It Enough
Lesson 7: More Than One?
Lesson 8: Can You Draw It? (Print available)
Practice Day 1 (Print available)

Unit 7: Probability: Theoretical Probability, Experimental Probability, and Compound Events

Lesson 30: Understand ProbabilityUnit 8
Lesson 1: How Likely? (Print available) [Free lesson]
Lesson 2: Prob-bear-bilities [Free lesson]
Lesson 31: Solve Problems Involving Experimental ProbabilityUnit 8
Lesson 4: Spin Class
Lesson 5: Is It Fair?
Lesson 32: Solve Problems Involving Probability ModelsUnit 8
Lesson 6: Fair Games
Lesson 33: Solve Problems Involving Compound EventsUnit 8
Lesson 7: Weather or Not
Lesson 8: Simulate It! (Print available)
Practice Day 1 (Print available)

Grade 8

Unit 1: Geometric Figures: Rigid Transformations and Congruence

iReady ClassroomDesmos Math 6–A1
Lesson 1: Understand Rigid Transformations and Their PropertiesUnit 1
Lesson 1: Transformers [Free lesson]
Lesson 2: Spinning, Flipping, Sliding [Free lesson]
Lesson 3: Transformation Golf
Lesson 2: Work with Single Rigid Transformations in the Coordinate PlaneUnit 1
Lesson 4: Moving Day (Print available) [Free lesson]
Lesson 8: No Bending, No Stretching
Lesson 9: Are They Congruent?
Practice Day (Print available)
Lesson 3: Work with Sequences of Transformations and CongruenceUnit 1
Lesson 3: Transformation Golf

Unit 2: Geometric Figures: Transformations, Similarity, and Angle Relationships

Unit 3: Linear Relationships: Slope, Linear Equations, and Systems

Lesson 8: Graph Proportional Relationships and Define SlopeUnit 2
Lesson 9: Water Slide

Unit 3
Lesson 1: Turtle Time Trials [Free lesson]
Lesson 2: Water Tank
Lesson 3: Posters
Lesson 7: Water Cooler
Lesson 8: Landing Planes
Lesson 9: Derive and Graph Linear Equations of the Form y = mx + bUnit 3
Lesson 6: Translations
Lesson 9: Coin Capture
Lesson 10: Solve Linear Equations in One VariableUnit 4
Lesson 1: Number Machines
Lesson 2: Keep It Balanced
Lesson 11: Determine the Number of Solutions to One-Variable EquationsUnit 4
Lesson 7: All, Some, or None
Lesson 8: When Are They the Same?
Lesson 12: Understand Systems of Linear Equations in Two VariablesUnit 4
Lesson 9: On or Off the Line?
Lesson 10: On Both Lines
Lesson 13: Solve Systems of Linear Equations AlgebraicallyUnit 4
Lesson 11: Make Them Balance [Free lesson]
Lesson 12: Line Zapper [Free lesson]
Lesson 14: Represent and Solve Problems with Systems of Linear EquationsUnit 4
Lesson 13: All, Some, or None? Part 2
Lesson 14: Strategic Solving, Part 2 (Print available)
Practice Day 2 (Print available)

Unit 4: Functions: Linear and Nonlinear Relationships

Lesson 15: Understand FunctionsUnit 5
Lesson 1: Turtle Crossing [Free lesson]
Lesson 2: Guess My Rule [Free lesson]
Lesson 3: Function or Not?
Lesson 16: Use Functions to Model Linear RelationshipsUnit 5
Lesson 4: Window Frames
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 6: Graphing Stories
Lesson 17: Compare Different Representations of Functions
Lesson 18: Analyze Functional Relationships Qualitatively
Unit 5
Lesson 7: Feel the Burn (Print available) [Free lesson]

Unit 5: Integer Exponents: Properties and Scientific Notation

Unit 6: Real Numbers: Rational Numbers, Irrational Numbers, and the Pythagorean Theorem

Lesson 23: Find Square Roots and Cube Roots to Solve ProblemsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Lesson 5: Filling Cubes
Lesson 24: Express Rational Numbers as Fractions and DecimalsUnit 8
Lesson 12: Fractions to Decimals
Lesson 13: Decimals to Fractions
Lesson 25: Find Rational Approximations of Irrational NumbersUnit 8
Lesson 10: Taco Truck [Free lesson]
Lesson 26: Understand the Pythagorean Theorem and its ConverseUnit 8
Lesson 6: The Pythagorean Theorem
Lesson 27: Apply the Pythagorean TheoremUnit 8
Lesson 7: Pictures to Prove It
Lesson 8: Triangle-Tracing Turtle [Free lesson]
Lesson 9: Make It Right
Lesson 11: Pond Hopper
Practice Day 2 (Print available)
Lesson 28: Solve Problems with Volumes of Cylinders, Cones, and SpheresLesson 10: Volume Lab
Lesson 11: Cylinders [Free lesson]
Lesson 12: Scaling Cylinders
Lesson 13: Cones [Free lesson]
Lesson 14: Missing Dimensions (Print available)
Lesson 15: Spheres

Unit 7: Statistics: Two-Variable Data and Fitting a Linear Model

Lesson 29: Analyze Scatter Plots and Fit a Linear Model to DataUnit 6
Lesson 3: Robots [Free lesson]
Lesson 4: Dapper Cats [Free lesson]
Practice Day 1 (Print available) [Free lesson]
Lesson 5: Fit Fight [Free lesson]
Lesson 30: Write and Analyze an Equation for Fitting a Linear Model to DataUnit 6
Lesson 6: Interpreting Slopes
Lesson 7: Scatter Plot CityLesson 8: Animal Brains
Practice Day 2 (Print available)
Lesson 31: Understand Two-Way TablesUnit 6
Lesson 9: Tasty Fruit
Lesson 10: Finding Associations [Free lesson]
Lesson 32: Construct and Interpret Two-Way TablesUnit 6
Lesson 11: Federal Budgets
Practice Day 3

S3 – 04. Ideas to build math fluency with Valerie Henry, Graham Fletcher, and Tracy Zager

Promotional image for "Math Teacher Lounge" Season 3, Episode 4 titled "Ideas to Build Math Fluency," featuring Valerie Henry, Tracy J. Zager, and Graham Fletcher.

Fluency in math can oftentimes be associated with negative experiences with its development— timed worksheets, for example. Bethany and Dan are joined by three guests to better understand fluency and how to make its approach fun. Dr. Val Henry shares her three-part definition of fluency and her five principles for developing it. Additionally, Tracy Zager and Graham Fletcher join Bethany and Dan to better understand fluency through a lens of equity and using multimedia as a tool.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:03)

Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.

Dan Meyer (00:11):

Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.

Bethany Lockhart Johnson (00:26):

I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.

Dan Meyer (00:30):

I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?

Bethany Lockhart Johnson (01:05):

Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?

Dan Meyer (02:08):

I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.

Bethany Lockhart Johnson (02:38):

Wait, did you pass the first time? Your test?

Dan Meyer (02:40):

Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.

Bethany Lockhart Johnson (03:32):

So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.

Valerie Henry (04:36):

Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.

Dan Meyer (04:41):

Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.

Valerie Henry (05:12):

The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,

Bethany Lockhart Johnson (07:12):

You mean without having to kind of muscle through it? Or say more about you mean.

Valerie Henry (07:16):

Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”

Bethany Lockhart Johnson (08:53):

That’s such an important distinction. My brain literally just did that actually!

Valerie Henry (08:58):

<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.

Bethany Lockhart Johnson (09:05):

Right.

Valerie Henry (09:07):

So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.

Dan Meyer (09:55):

I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.

Valerie Henry (10:21):

And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.

Bethany Lockhart Johnson (10:30):

Mm, yeah.

Valerie Henry (10:30):

So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.

Bethany Lockhart Johnson (11:18):

I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?

Valerie Henry (11:30):

I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.

Bethany Lockhart Johnson (12:06):

And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.

Valerie Henry (12:15):

Yes.

Bethany Lockhart Johnson (12:16):

Some of us might remember quite vividly.

Valerie Henry (12:18):

<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.

Bethany Lockhart Johnson (13:10):

If I put it in front of you enough times, you’ll become fluent.

Valerie Henry (13:14):

Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.

Dan Meyer (14:01):

It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.

Valerie Henry (14:35):

My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”

Dan Meyer (15:38):

There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?

Valerie Henry (15:57):

I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.

Bethany Lockhart Johnson (17:09):

So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.

Valerie Henry (17:22):

Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—

Bethany Lockhart Johnson (17:33):

Not waiting until you’ve gotten all the way through addition. But making “Ooh!”

Valerie Henry (17:38):

Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.

Bethany Lockhart Johnson (18:11):

What are the other principles?

Valerie Henry (18:13):

The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.

Bethany Lockhart Johnson (18:27):

Don’t put away those manipulatives. Don’t put away those tools.

Valerie Henry (18:31):

Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.

Bethany Lockhart Johnson (19:07):

I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—

Dan Meyer (19:35):

Thank you, Dr. Henry.

Valerie Henry (19:37):

You’re welcome!

Dan Meyer (19:41):

With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.

Bethany Lockhart Johnson (20:49):

Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”

Dan Meyer (20:55):

Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?

Tracy Zager (21:00):

I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!

Bethany Lockhart Johnson (21:10):

Ooh!

Dan Meyer (21:13):

A language fluency, perhaps. All right, Graham. How about you?

Graham Fletcher (21:16):

For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.

Dan Meyer (21:33):

Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?

Tracy Zager (21:40):

I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.

Graham Fletcher (23:53):

And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.

Bethany Lockhart Johnson (24:10):

So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?

Graham Fletcher (24:41):

What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.

Tracy Zager (25:22):

When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—

Bethany Lockhart Johnson (26:18):

Crayons, markers.

Tracy Zager (26:18):

Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.

Bethany Lockhart Johnson (27:03):

I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.

Tracy Zager (27:14):

Yay!

Bethany Lockhart Johnson (27:14):

And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.

Tracy Zager (27:41):

That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”

Bethany Lockhart Johnson (28:37):

That’s kinda true. Knowing you both, it’s kinda true.

Tracy Zager (28:42):

Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—

Bethany Lockhart Johnson (28:58):

But they’re making sense of numbers!

Tracy Zager (28:59):

Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.

Bethany Lockhart Johnson (29:45):

That’s huge.

Dan Meyer (29:46):

That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.

Graham Fletcher (30:47):

Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”

Tracy Zager (32:44):

I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.

Bethany Lockhart Johnson (34:41):

They’re invested!

Tracy Zager (34:45):

They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.

Graham Fletcher (35:47):

It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.

Tracy Zager (35:55):

I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.

Dan Meyer (37:20):

I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier for their inclusion in mathematics. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?

Graham Fletcher (37:57):

You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.

Bethany Lockhart Johnson (38:19):

If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?

Graham Fletcher (38:35):

Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.

Dan Meyer (39:25):

Bethany and I will be working the same challenge with people in our life.

Bethany Lockhart Johnson (39:29):

Yes.

Dan Meyer (39:29):

Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.

Bethany Lockhart Johnson (39:42):

I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Valerie Henry says about math

“A lot of very fluent adults don’t always have every fact memorized. ”

– Val Henry

Meet the guests

Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops  fluency,  number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.

Graham Fletcher has served in education as a classroom teacher, a math coach, and currently as a math specialist. He is continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary mathematics. He is the author of Building Fact Fluency and openly shares many of his resources at gfletchy.com. Follow him on Twitter.

Tracy Johnston Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of the Building Fact Fluency toolkits and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books by teachers, for teachers at Stenhouse Publishers. Follow her on Facebook.

A collage of three headshots: an older woman with glasses, a man with a beard in a blue shirt, and a woman with dark hair smiling in front of greenery.
A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

S1-10: Empowering the science educator: Jessica Kesler

Promotional graphic for "science connections podcast" season 1, episode 10, featuring a smiling black woman named Jessica Kesler, with educational icons like a globe and magnifying glass around her.

In the final episode of the season, Eric sits down with his friend and professional development facilitator, Jessica Kesler. Jessica describes her passion for sharing free, high-quality, empathy-centered professional development for K12 educators. Jessica also shares her experience jumping into leadership positions while teaching in Philadelphia. Eric also chats with Jessica about how students often lean on teachers for more than delivering content. Explore more from Science Connections by visiting our main page.

Download Transcript

Jessica Kesler (00:01):

One student at a time, isn’t gonna bring a million students through the door. But if we focus on their teachers, then they can implement it in their classroom and have this multiplicative effect that can continue on and help us to reach those millions of kids and helping them be prepared for future careers.

Eric Cross (00:19):

Welcome to science connections. I’m your host. Eric Cross. My guest today is Jessica Kessler. Jessica’s director of professional learning at TGR foundation, which is a tiger woods charity. There she creates and leads free stem, professional learning opportunities for educators across the country. Prior to working at TGR, Jessica worked as an elementary, middle and high school science teacher while fulfilling several leadership roles, including science department, chair and principal intern. In this episode, Jessica shares some of her classroom experiences while working in Philadelphia, where she was in classrooms, where her students needed her to be more than just her content. She also addresses how designing professional learning with empathy for teachers in mind creates better experiences for teachers. And now please enjoy my discussion with Jessica Kessler. So let’s, let’s start off with St. Joseph’s chemistry college to the classroom, like your origin story. What led you to ultimately get into the classroom and being successful, even just looking at, at your kinda like your resume or your CV of all of the things that you’ve done. You definitely weren’t idle, but start off with chem. Yeah. Like where did that passion come from?

Jessica Kesler (01:27):

Yeah. So when I was younger, I just had this burning passion to help people. Right. And when you’re young and you think about helping people, you think about doctors, doctors help people. Right. So I had this idea that I wanna be a surgeon. I wanna be a black surgeon. I wanna be a young girl, female Charles drew, and I just wanna go out there and do it. And so my mom is actually an alum of St Joe’s. So I spent a lot of time on campus cuz as she was getting her mini master’s degrees I will visit campus with her often. And so when I applied, I had the scholarships, had everything and I went in ready to be bio ready to be a surgeon. I took my first bio class and I was like, yes, let’s talk about the human body. And let’s get into dissections and sections. And they were like, okay, so a plant so has this. And I was like, Ooh <laugh> I was like, this is not what I was expecting at all. It just felt so detached from the trajectory that I wanted to take. And it just did not feed that passion of helping people in the immediate moment.

Eric Cross (02:31):

Did it, did it feel too abstract?

Jessica Kesler (02:33):

It felt abstract. It felt boring. Okay. And one thing I didn’t want was to be like stuck, bored. Like if I’m not being stimulated in a good way, mm-hmm <affirmative> then it’s not gonna last, but I love science. So I switched over to chemistry cuz I’m like this chemistry is exciting. I’m mixing things together. I’m producing new things. I’m doing extractions. I’m being introduced to machinery that I haven’t seen before. I’m loving it. I’m doing a math. The math is awesome. And so I switched over to chem and I started doing research in the summers and things like that. My research was around water quality in Philadelphia and looking at different natural water sources and comparing them and all those great things. But I was in a lab and the lab had no windows and I was stuck talking to this atomic absorption specter every day.

Jessica Kesler (03:24):

And I hit that, that wall again, where it was like, is this the rest of my life? Like talking to these machines and not having windows and not being able to interact with people. What is this? This can’t be life. And so I was seeking out some new opportunities that said, Hey, I need more money. First of all. So I’m like, I call the financial aid office like every week, like, Hey, what’s out today. What new scholarships do you have? I’m applying for everything. Like it was my goal to not have to pay for much of my education. And so I was talking to them and they’re like, Hey, you’re in science. There’s this awesome opportunity called a noise scholarship where they’ll pay for your last year and your master’s degree. If you go into education mm-hmm <affirmative> and I sat on it and I was like, this makes so much sense to me.

Jessica Kesler (04:12):

I was like, I’ve been literally tutoring my peers and teaching in churches and all this other kind of stuff. My whole life. It makes so much sense. How come nobody ever said this before? <Laugh> and so I applied for the noise scholarship, got in and started, you know, mm-hmm, <affirmative> doing practicums in the classroom as I went through my last year as a chemistry major and my first year for my masters and it just felt so right. And I was like, I can do this. And of course there were a lot of people who told me, no, Josh, you can’t do that. Like these kids will eat you alive. And I’m like I don’t think so. <Laugh> but, but that’s give it a go. And I stepped into the classroom and it, it just felt like, felt like it was always meant to be there.

Eric Cross (04:57):

So you were able to, you were able to make that connection between, I mean, if you’re, if you’re studying chemistry and bio and going into stem, I mean, there’s, there’s an aptitude there, but then you realize that this there’s a road that you could take that leads you into a room with no windows. And you’re just hanging out with machines all day

Jessica Kesler (05:14):

And I’m not helping people. Right. Right. And that was, my passion was like, I’m not helping people sitting in this room. I need to be a person that’s outside telling people about what happens in the room. Right. And how they can get involved and like what’s going on in here. Like that’s, that’s where I can be useful.

Eric Cross (05:28):

When you were, you were in Philly when you were teaching, what were you teaching when you were there?

Jessica Kesler (05:33):

So I started off teaching eighth grade science first job in north Philadelphia, teaching eighth grade science and just a, a funding tangent that first day a student called me a B

Eric Cross (05:44):

Trial by fire

Jessica Kesler (05:45):

Trial by fire called me out in front of like the whole floor. We were outside doing line drills and just was like, I hate you miss Kusa your B. And I was like, oh, this is it. This is it. This is where you stand your ground and you take it or you, you bail out <laugh> and you go back into the lab mm-hmm <affirmative>. And of course at the end of that, that traumatic experience between all the kids, like two months later, she wanted me to adopt her. So like everything comes full circles. Right.

Eric Cross (06:10):

That’s how it is. Right.

Jessica Kesler (06:11):

But I started teaching eighth grade science. There’s not a lot of science teachers at that level who actually have a science background. Most of them have elementary school background. So I’m the only scientist walking into the science classroom and saying, this is how science actually works. And so I ended up taking a lot of onus of science while I was there. Ended up building out the K through eight curriculum for science. I ended up doing like a science strategic plan to submit to the district. I ended up leading out our first couple stem nights and like really leading the stem department and kind of our science department. And this was as like a second, third year teacher <laugh> know, but nobody else had the science mm-hmm, <affirmative> the way that I had the science and the education. So it really opened up a door for me to be able to, to run full steam with all those things.

Eric Cross (07:04):

So MI was it primarily middle school during those, those years that you were there?

Jessica Kesler (07:07):

So there, I started with middle school and I did that purposefully because I was still young and I wanted there to be a good age gap between me and the students. And then I moved up to high school and taught high school chemistry, also taught a couple other different subjects while I was at that school. But primarily high school chemistry. Then I actually took a big leap down and I said, okay. I was going for my second master’s degree in educational leadership. And I was going for my principal cert. And I said, if I’m gonna be a principal of a school, then I need to understand all the levels of education and how they operate, cuz they operate really differently. So I said, I started in middle school, went to high school. I don’t have elementary school experience. In fact, I’d spent a day in a kindergarten classroom and I was like this never again, but I was like, I need to go back down there and I need to figure out how this system works because you know, I never know where I’m gonna land as far as principalship.

Jessica Kesler (08:01):

So I went and taught fourth grade.

Eric Cross (08:03):

How was that experience?

Jessica Kesler (08:05):

So imagine me going from teaching high school, seniors and juniors Uhhuh and like they’re self-sufficient and you know, they’re independent, they’re driving to school and all these things. And then I immediately drop down and go into fourth grade where these kids are crying every five seconds. They still have like a lot of bodily fluids, like there’s noses running and things. And like <laugh>, I was like a fish outta water. I was like, what is this? What’s going on down here. But those kids pour out so much love. And they, you, you become another parent to them. Mm-Hmm <affirmative> your high schoolers know who their parents are. They kind of are finding their place in society, but the little ones, they only know big people as parents, small people as equal. So they see you as another parent. So it taught me a lot about, you know, patience and breaking information down, even smaller. I had to figure out new and inventive ways to teach science and bring it down so far that they would be able to grab onto it and achieve it. And it was a challenge, but at the end it paid off, we were running, we were hitting like great markers for all of our PSSA goals that year. I mean, we were really knocking it out the park

Eric Cross (09:17):

And this backstory leads into how we met and adds to the picture as to why I really want to have you on, because your involvement with TGR, which is where I want to go next for the folks listening. I bet a lot of them have no idea what it’s about, just like I did. And now me learning about TGR foundation and meeting you I would love to make sure that everyone knows about it and what they offer.

Jessica Kesler (09:39):

Absolutely. So TGR foundation, a tiger woods charity was founded by tiger woods and his father with a mission to really introduced them education to students in low income minority populations and prepare them for success in their world and their future careers moving forward. And so was founded in 1996 and went through several changes in iterations since 1996. But eventually opened up its first learning lab, which is in Anaheim, California. And through the learning lab, they opened up these satellite sites. So they basically partner with schools to provide after school education and robotics and wearable electronics and things like that. And they would partner with schools to teach these courses after school, they would pay the teacher, pay for the materials and stuff like that to provide more opportunity for students in different areas. And so that’s how I was introduced to the foundation because while I was teaching high school my good friend and previous manager, Jason Porter shout out to JP Jason Porter used to lead the tiger woods foundation when it was the tiger woods foundation.

Jessica Kesler (10:52):

He used to lead the afterschool program. And when I joined that high school, he said, Jess, you got all this great content, knowledge, all this great enthusiasm, and we wanna get more women into this robotics. We wanna get them engaged in this process of, of stuff. And you will be a great role model to start bringing in more of our female students. And I was like, great, sign me up. And that’s where I started working with the TGR foundation, right after school programs, getting my students into robotics, competitions and clubs, doing different challenges and design challenges. And then after some time, a few years, they actually needed someone to come to the DC area and support the development of professional learning and partnerships here in DC, as they were continuing to expand. And really it came out of the idea that tiger gave this big mission to the organization that he wanted to reach millions of kids.

Jessica Kesler (11:48):

He said millions and everybody said, what millions, what M <laugh>. So the foundation was like, okay, well we can’t reach millions by just tackling one student at a time, right? Not one student at a time, isn’t gonna bring a million people or students through the door. But if we focus on their teachers, mm-hmm <affirmative>, then those teachers not only spend most of their day with these students and learn the basics of their skills with these students. But each one of those teachers has 30 to 150 200 students that they see every day. And that’s how we multiply this effect. So we train the teachers on all the stem competencies and the pedagogical tools and strategies to implement the stem that we’re doing in our learning labs. And then they can implement it in our classroom and have this multiplicative effect that can continue on and help us to reach those millions of kids and helping them be prepared for future careers.

Eric Cross (12:44):

And so D divide the effort, multiply the effects. Exactly. And then when I was exposed to it, this was over zoom. Now, how long has it been going on? Has it always been virtualized or did you do the, were you all doing this before? We all went online

Jessica Kesler (12:57):

Before the pandemic man, the glory days, right before pandemic, it feels like I’m talking about prehistoric times, right? Like back in the dinosaur, like era, like, I don’t know, pre we actually did these workshops in a person. So we would invite people to come to DC, invite teachers in Philadelphia to do a Philly one. We were in New Mexico. We were in Florida. We were, I mean, we were everywhere and this would be a extremely hands on engaging workshops. So not only do we focus on this is the theory and the philosophy behind the pedagogy, but we would also focus on like creating a student experience for the teacher, having the teacher flip into student mode and put on that student hat and actually go through sample lessons, model lessons and activities as the student so that they can feel it. So you can feel if, if you feel confused, your students are gonna feel confused.

Jessica Kesler (13:52):

If you feel like this is challenging, you, your students are gonna feel the challenge. If you are, don’t understand the instructions, your students will understand the instructions. So it gives us a different perspective and it puts us in their shoes. So we can better empathize with them and create more responsive lesson planning. So we flipped them into that student role for that purpose. When COVID hit, we went virtual, but virtual allowed us to reach teachers that we probably would’ve never hit. So it was kind of that blessing and disguise, right? It was like we didn’t keep people as long cuz obviously virtually you’re not, you don’t wanna stare at a screen for eight hours. So we cut it down. We revised it a little bit, but we kept the hands on philosophy and feel of it going by, you know, using materials that they could find at home really modeling what education could look like.

Jessica Kesler (14:41):

Mm-Hmm <affirmative> if you used your Z zoom room to capacity, or if you had these materials and resources or rethought your lesson plans and structures. So we went virtual and not only were we able to hit so many more thirst that first year thirsty educators ready to get, dive into it, ready for some comradery with fellow educators. But we were also able to expand our international network. We were able to get so many international educators through our global work that it was, it was beyond what we had when we were in person. So it really had this skyrocketing effect.

Eric Cross (15:20):

There’s professional learning pathways and then virtual stem studio. Is that right for professional development for like teachers who are listening, are those the two kind of main prongs?

Jessica Kesler (15:30):

Yeah. So a stem studio is basically just one, right? And a pathway is a collection. So we now offer four stem studios, four separate stem studios. The first one is on inquiry mindset. You attended that one area. And it’s really about for teachers who are changing their perspective on what the classroom should look and feel like, especially administrators too. It’s about developing that inquiry mindset. So you understand and you feel, and you practice and you learn the tools that are necessary for inquiry to happen in your classroom. We never promote overhauling your classroom. We’re just saying, add a little bit here and there and see how it impacts your students. The second one is on making inquiry, visible, making inquiry visible is all about making students thinking visible in the moment. What are tools and strategies that you use so that students can illuminate their thinking for themselves, but for you and their peers as well and how we benefit from that.

Jessica Kesler (16:28):

So not only do the students get to see their own thinking as they progress and you get to tell the story of how their minds have evolved, but you, as the teacher get to see, oh, this is where everyone is making the mistake, or this is how this misconception came about. Or this is where I need to target for my next lesson. So it makes you more responsive in the moment. And then the third and fourth one where we’re actually launching for a small group this summer, it won’t be available to the masses until maybe a year or two down the line. We have one small group that we’re just going to test it out with. The third one is about developing your inquiry environment. So thinking not just about your physical space, but thinking about your intellectual space too. So what are the things that you can embed into your physical space and develop in a student’s intellectual space that will help you create a holistic inquiry environment?

Eric Cross (17:22):

So this is this inquiry space, not just physical, but then also the intellectual environment

Jessica Kesler (17:26):

Intellectual. Exactly. And it focuses in on the design process and how we design spaces. Because as a teacher, we take a lot of background in the background onus of de creating these spaces. If you take someone out of an old habit or space and tell them, oh, we are gonna change in your minds and teach inquiry, but put them back in the same environment, they’re gonna be conflicted, right? Their bodies wanna do one thing, their minds wanna do another thing. And they don’t know how to bridge the gap between the two. So this is a really illuminating, like how do you change all the spaces? How do you design a flow in space in your classroom and in your students thinking that allows them to be productive in that inquiry environment. It’s really good stuff

Eric Cross (18:11):

Who creates these experiences for teachers.

Jessica Kesler (18:14):

We do. So me and my teammate, Holly, Dard shout out HD. Holly Dard, we really put our brains together and developed these. So it’s a really a team effort because like Jason Porter, Eric even David Tong when he was with us, really collectively thought about what it is that we wanted educators to experience. And then Holly and I do a lot of the grunt work, but then we really collectively put it all together and make it what it is. So I have a heavy hand and a lot of that. And in fact, inquiry four is all about the entrepreneurial mindset. So oftentimes educators don’t consider themselves entrepreneurs, but if you take a look at what an entrepreneur is and what they do on a regular basis, educators are entrepreneurs, but we are missing an opportunity to use our entrepreneurialship in the classroom to drive for stem competencies in inquiry based practices. And so in, in stem studio, four, we really focus in on how the educator is the entrepreneur of their classroom, but also uses entrepreneurial techniques to tackle issues in their schools, districts, and spheres of influence. So it’s really taking the educator to the next level of their teaching practice through entrepreneurship. This is some deep stuff.

Eric Cross (19:37):

It is, well, this entrepreneurial mindset is, is something that I’ve heard before. And I definitely see the link between even the term teacherpreneur beyond just selling lessons on teachers, pay teachers. <Laugh> it’s way bigger than that,

Jessica Kesler (19:52):

Where entrepreneurs actually in the classroom, not just because we do things on the side to make money. Exactly.

Eric Cross (19:57):

A lot of teachers hear that. They’re like, yeah, I got, you know, I got, got a few jobs going on. Exactly. Yeah. And, and I think one thing we, I should have said this earlier, and I’ll, I’ll say the intro, but these are all free.

Jessica Kesler (20:07):

This is largely sponsored by do OD stem as well. So we have a partnership with D O D stem and they have been driving forth the department of defenses, strategic stem plan for years. And as a part of that, they give us funding in order to provide these opportunities for educators for free. So literally educators don’t have to come with anything. And we are giving you not only the content of our, our lessons and our instruction, but we’re also going give you a chance to earn a free micro credential. So people are spending 12 plus hours with us in a workshop which sounds like a lot of time, but it’s over a series of time and days. But we wanna give you something that means something after that, we wanna give you a micro credential to add to your resume, to show your administrator, to show that you have achieved the next level in your professional learning career.

Jessica Kesler (20:59):

Right? And if you finish the pathway, which is all for, then we give you our TGR foundation certificate that says that you’ve completed so much professional learning in these areas that you are basically a warrior of inquiry that you are ready to go out and really lay inquiry out in new creative ways, not in your CLA just in your classroom, but everywhere you go in your district, in your school. And on top of that, we just offer so many other great free partnership incentives like discovery, education, experience licenses. We’re doing raffles this summer. We’re giving out free a free meal voucher so that you can get some lunch. One of these days we’re offering $50 gift cards so that people can get school supplies. So anything you do with us, and you’re like, man, I really wish I could have this so that I can do that in my classroom. We wanna break down all the barriers that prevent teachers from doing this stuff in their classroom, actively engaging in this stuff. And we give you a free copy of the books that we reference. Again, trying to break down the barriers,

Eric Cross (22:00):

What are some of the things that you’ve noticed kind of being on both sides of science teaching in the classroom, and then in training trends with teachers, things like moments that have been great or, or challenges that you’re noticing teachers experiencing, especially maybe changes in differences from a, from, you know, an outsider’s perspective. Seeing what teachers are experiencing are like, since you’ve been doing PDs for folks.

Jessica Kesler (22:22):

Yeah. So it’s actually really interesting being on both sides of the fence. You know, what I always noticed is that teachers are eager, but they’re tired. They’re wanting to learn, but they can’t take advantage of every opportunity to learn. And especially during COVID time, if you take a look at even all the professional learning that’s happening across the world right now, attendance is going down because teachers are so burnt out this hybrid space, this either we’re in person, but we’re still wearing masks and still social distancing and all this other stuff, or I’m still virtual or I’m virtual some days and I’m in person other days, it’s just wearing our teachers out. And I think we notice that as we see a large numbers of friends and family just start to retire, right? Like people are just like, I don’t know if I can adapt to another change in education.

Jessica Kesler (23:14):

Like education goes through these waves of big changes and it’s hard for everybody to adapt to, but for those who are willing to stick it out and those who are able to stick it out and, and still have that energy and enthusiasm to learn, they come in so hungry for more resources, so hungry to learn more and they still have their why at the top of their minds, as they think about why they do this it’s for the kids it’s to drive this mission is to get more kids excited about this. And they just come in so passionate. So once they come in, once we can get them to come in they stick with us for a really long time. They’re like, what else do you have? What else do you have? What else do you have? But we hear, still hear the common threads of like, do I have time for this?

Jessica Kesler (23:58):

Do I have the funding for this? Do I have the energy for this? Do, will my students understand this? And we are constantly facing that challenge of trying to address those things by, but keeping the excitement going, like we know you don’t have enough time. We’re gonna call it out from the start. I know you don’t have enough time to try to do 29 extra things. Mm-Hmm <affirmative>. But my advice is always, but do one thing at a time, start with something small, asking your students a few questions rather than lecturing to them. Doesn’t take a whole lot of extra time, but it gives you so much extra insight. So let’s not work, you know, harder, let’s work smarter. Let’s embed this into our, our work together. And I always say that we’re not asking you to add to your plate. You know, it’s not Thanksgiving where you just pile, keep piling on a plate.

Jessica Kesler (24:47):

It’s it’s a time where you organize the plate. It’s allowing inquiry to restructure your plate so that everything has its place and its time mm-hmm <affirmative> do you wanna leave room so that the educator feels comfortable trying some new initiative? That’s why we encourage admin. We have librarians attend elementary school teachers, administrators, we, and we encourage it because everyone can support the classroom. And if administrators are more in touch with these new practices and tools and strategies, then they can help facilitate the learning. As the teachers are trying new things and coaching them in specific areas. So we really opened the door for some studios, for any and all who are gonna participate in that child’s education, because us all rallying around them as that three-legged stool helps to create that environment and helps support the teacher. The teachers need support, and we’re trying to do our part by providing the resources and the tools, but they need everyone else to.

Eric Cross (25:42):

We don’t always think about it as a way to support, to get support in our classrooms for ourselves. But I agree with you by, by educating vertically up the chain, you know, vice principal, principal, whoever it is, mm-hmm <affirmative> superintendent getting them on boarding and, and educating them to see what’s ex expected. We’ll open up doors and more freedoms for you because now you just have this vertical alignment of folks kind of on the same wave length. Exactly.

Jessica Kesler (26:07):

Yep. And that’s why we love districts. Anaheim union school district is actually one of our partners this year, where they have invited their teachers to participate in the whole pathway because they know how important it is that we practice these tools and strategies. And they want as many educators in the same space going through this at the same time as possible so that we can support each other through it. And so that we don’t feel like islands, oftentimes as educators, we feel like islands we’re in our classroom day in and day out. And we don’t feel like there’s anybody else who’s doing the same things we’re doing and supporting the work that we’re doing. So when we get administrators who support it, it’s magical. It can be magical.

Eric Cross (26:47):

What are some opportunities that are coming up if somebody’s listening and they, they wanna sign up for something, are there things coming up this month or next month or in the summer that they can participate in?

Jessica Kesler (26:55):

Yeah, for sure. So we’ve been doing our monthly workshops. And if you go to our website, so if you actually go to TGR foundation.org and slash stem studio you’ll actually see our summer events already posted, already live for everybody to start engaging in. And again, everything is free. So registration is open and available for everybody to participate. We are offering that first inquiry stem studio inquiry mindset twice the week of June 21st and the week of June 28th, two opportunities for educators to join us for inquiry mindset for the first one. And then also in July, we’re offering the second one making inquiry visible, and that’s the week of July 12th. So again, all free stuff, raffle prizes are available for those who register early and get in there and reserve their seat. It is limited seating. And so, yeah, a bunch of opportunities coming up this summer and guess what all you have to do is sign up and then you get all these free things coming your way. You get to look forward to all this exciting stuff. So TGR foundation.org/studio.

Eric Cross (28:01):

And if folks wanna follow you in your career, your journey.

Jessica Kesler (28:05):

Yeah. I’m on Twitter and LinkedIn, for sure. And it’s Jessica Kessler, K E S L E R one S

Eric Cross (28:12):

I wanna honor your time. And as we close, you’ve been an educator of impact in, in your own classroom. And I know you’re still teaching actively now, and you’ve also made an impact on me and other educators through your professional development. And, and the last question I’d like to end with is who’s the most memorable teacher or learning experience that you had during K eight. When you think about you, your time in school, who was a memorable teacher or a moment that kind of stands out to you and what was it that they did that made them memorable?

Jessica Kesler (28:44):

It was that one teacher who brought me my first T I, 84. You remember when a new calculators came out, I had a teacher give me one amazing, but I think in high school, there was really a turn about where I had miss Caroline and Mr. Canello math and Spanish teacher. So two opposite wings of the, the education spectrum there. But most of all, they listened. They listened to me. I felt seen with those teachers, they supported me. They listened to me, they saw my potential. And they just rallied around me and continued to support me thereafter. Even afterwards, I continued to reach out to those educators. And I think that’s what drives me to be that force for, for my students. And I remember my most memorable heart touching education experience was probably, I had a high school student get interviewed by the newspaper.

Jessica Kesler (29:38):

And they were like, oh, what’s your favorite classes? And what’s your favorite this, and what’s your favorite of that? And he was like, well, I love chemistry, which is what I was teaching. It was like, and I love my after school robotics team. I was leading and I love this and this and this. And he basically listed all the stuff that I was doing that I was teaching and that I was leading in the school. And I was like this one student, literally out of all the classes and experiences he’s experiencing is really just calling out everything that I’m doing. And I feel like it’s because he felt seen, he felt heard. He was like, this person is listening to me. And no matter what space we’re in this teacher is, is there for me. And so I try to be that wherever I go, <laugh>,

Eric Cross (30:16):

It’s amazing how making someone feel seen and, and making them feel important and heard, and, and being present for them. All of a sudden opens up their interests into the subjects that you’re teaching. Thank you for, for making time for serving our kids for serving teachers during a hard time, and for making PD one, being part of an organization that made it free and serve teachers, but also making PD fun and enthusiastic. I think that was one of the things in addition to the empathy that you led with, but also your enthusiasm and passion was something that really resonated with me. And it made our time together. Feel like something that was, was making me a better teacher for my kids. And so, thanks for making time for us tonight. Oh,

Jessica Kesler (30:53):

Bless face.

Eric Cross (30:57):

Thanks so much for joining me and Jessica today. If you have any great lessons or ways that you connect with students, please email us@stemamplifycom.wpengine.com. That’s S TM amplifycom.wpengine.com. And please remember to support the podcast by clicking subscribe, wherever you listen to podcasts, you can also hear more about the podcast in our Facebook group, science connections, the community until next time.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Jessica Kesler says about science

“One student at a time isn’t gonna bring a million students through the door. But if we focus on their teachers, then they can reach those millions of kids and help them be prepared for future careers. ”

– Jessica Kesler

Director of Professional Learning, TGR Foundation

Meet the guest

In the final episode of the season, Eric sits down with his friend and professional development facilitator, Jessica Kesler. Jessica describes her passion for sharing free, high-quality, empathy-centered professional development for K12 educators. Jessica also shares her experience jumping into leadership positions while teaching in Philadelphia. Eric also chats with Jessica about how students often lean on teachers for more than delivering content.

Person with glasses smiling, wearing a black headwrap and earrings, outdoors with trees and sunlight in the background.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. Listen here!

What’s included in our phenomena-based science curriculum

Amplify Science is a phenomena-based science curriculum for grades K-8. This program is designed to give students engaging, realistic experiences that mirror how scientists and engineers actually work. To do this, the Lawrence Hall of Science and Amplify created compelling print and digital resources that work seamlessly together to enable students’ investigations and explorations.

Year at a glance

Amplify Science is organized around units where students are introduced to compelling phenomena and real-world problems, develop and strengthen claims by collecting evidence and testing assumptions, and apply their learning in new contexts.

Un gráfico que muestra secuencias de lecciones de ciencias desde jardín de infantes hasta quinto grado, detallando temas, números de lecciones, días de evaluación y duración de las lecciones para cada grado.

Units at a glance

In each Amplify Science unit, students are asked to inhabit the role of a scientist or engineer in order to investigate a real-world problem. These problems provide relevant, 21st-century contexts through which students investigate different scientific phenomena.

1

Needs of Plants and Animals

Students take on the role of scientists in order to figure out why there have been no monarch caterpillars in the community garden since vegetables were planted. They investigate how plants and animals get what they need to live and grow, and make a new plan for the community garden that provides for the needs of the monarch caterpillars in addition to producing vegetables for humans.

2

Pushes and Pulls

Students take on the role of pinball machine engineers as they investigate the effects of forces on the motion of an object. They conduct tests in their own prototypes (models) of a pinball machine and use what they learn to contribute to the design of a class pinball machine. Over the course of the unit, students construct a foundational understanding of why things move in different ways

Silueta de una estructura de parque infantil contra un cielo azul con nubes y tres soles amarillos.

3

Sunlight and Weather

The principals of Woodland Elementary and Carver Elementary need student weather scientists to help them explain why Woodland’s playground is warmer than Carver’s at recess. Students gather data from models of the sun and Earth’s surface and observe their own playgrounds to figure out how sunlight causes changes in the temperatures of different surfaces. Students then use models to figure out why Woodland’s playground sometimes floods.

1

Animal and Plant Defenses

Students play the role of marine scientists. In their role, students apply their understanding of plant and animal defense structures to explain to aquarium visitors how a sea turtle and her offspring can defend themselves from ocean predators when they are released into the wild.

Dos manos sosteniendo un papel con un dibujo de pirámide y árbol, iluminado por una linterna, proyectando otra sombra de la imagen en la pared.

2

Light and Sound

Students take on the role of light and sound engineers for a puppet show company as they investigate cause and effect relationships to learn about the nature of light and sound. They apply what they learn to design shadow scenery and sound effects for a puppet show.

Ilustración que muestra un paisaje urbano dividido en noche a la izquierda con una luna y estrellas, y día a la derecha con un sol, nubes y un avión.

3

Spinning Earth

As sky scientists, students explain why a boy living in a place near them sees different things in the sky than his grandma does when he talks to her on the phone. Students record, organize, and analyze observations of the sun and other sky objects as they look for patterns and make sense of the cycle of daytime and nighttime.

1

Plant and Animal Relationships

In their role as plant scientists, students work to figure out why there are no new chalta trees growing in the Bengal Tiger Reserve, which is part of a broadleaf forest. Students investigate what the chalta tree needs to survive, then collect and analyze qualitative and quantitative data to solve the mystery.

Una mano sostiene un frijol rojo sobre una mesa, mientras un palo de madera esparce pegamento blanco y frijoles esparcidos. Sobre la mesa también hay una taza blanca y una pluma amarilla.

2

Properties of Materials

As glue engineers, students are challenged to create a glue for use at their school that meets a set of design goals. Students present an evidence-based argument for why their glue mixture will be good for their school to use.

Ilustración de una costa con acantilados, un edificio de centro recreativo con un techo rojo y un letrero, árboles de hoja perenne, una bandera azul y una playa de arena debajo.

3

Changing Landforms

The director of the Oceanside Recreation Center gets a scare when a nearby cliff collapses overnight. Research reveals that the distance between the Recreation Center’s flagpole and the edge of the cliff have changed over time. Students play the role of geologists and work to figure out why the cliff has changed over time. Based on what they learn about erosion, they advise on whether it is safe to keep the center open even though the cliff is changing.

Una ilustración de un tren de alta velocidad moderno y aerodinámico que viaja por una vía elevada con un paisaje verde de fondo.

1

Balancing Forces

People in Faraday are excited to hear that a new train service will be built for their city, but concerned when they hear that it will be a floating train. Students are challenged to figure out how a floating train works in order to explain it to the citizens of Faraday. They develop models of how the train rises, floats, and then falls back to the track, and then write an explanation of how the train works.

Ilustración de una escena de bosque con un oso, un alce, pájaros en una rama y un grupo de lobos en primer plano. Las colinas y los árboles están al fondo bajo un cielo despejado.

2

Inheritance and Traits

Students play the role of wildlife biologists working in Greystone National Park. They study two wolf packs and are challenged to figure out why an adopted wolf (“Wolf 44”) in one of the packs has certain traits. Students observe variation between and within different species, investigate inherited traits and those that result from the environment, and explain the origin of several of the adopted wolf’s traits.

Ilustración de un pájaro mirando un caracol en el suelo, con hojas verdes en el lado izquierdo y un fondo de cielo azul.

3

Environments and Survival

In their role as biomimicry engineers, students work to figure out how the traits of grove snails affect their survival in different environments. They then explore how the traits of different organisms make them more likely or less likely to survive, collecting and interpreting data to understand how organisms’ traits affect their survival in different environments. Students then apply their understanding to a new challenge: designing effective solutions for the removal of invasive plants.

4

Weather and Climate

In their role as meteorologists, students gather evidence to decide where to build an orangutan reserve by analyzing patterns in weather data. After choosing the strongest evidence, students use data to make arguments about which of three fictional islands has weather most like that of orangutans’ existing habitats, Borneo and Sumatra. They then discern patterns in the locations of natural hazards in order to figure out which ones the Wildlife Protection Organization must prepare for.

Ilustración de un paisaje urbano nocturno con ventanas iluminadas y farolas, una luna visible y estrellas en el cielo. Una figura solitaria se recorta en una de las ventanas.

1

Energy Conversions

Students take on the role of systems engineers for Ergstown, a fictional town that experiences frequent blackouts, and explore reasons why an electrical system can fail. Students apply what they learned as they choose new energy sources and energy converters for the town, then write arguments for why their design choices will make the town’s electrical system more reliable.

Un gecko se prepara para atrapar un grillo bajo una farola por la noche. Las flechas amarillas ilustran la luz de la lámpara que golpea al grillo y se refleja en los ojos del gecko.

2

Vision and Light

As conservation biologists, students work to figure out why a population of Tokay geckos has decreased since the installation of new highway lights in the rainforest. Students use their understanding of vision, light, and information processing to figure out why an increase in light in the geckos’ habitat is affecting the population.

3

Earth’s Features

Playing the role of geologists, students help the director of Desert Rocks National Park explain how and when a particular fossil formed and how it came to be in its current location. Students figure out what the environment of the park was like in the past and why it has so many visible rock layers.

Dos delfines nadan bajo el agua en un ambiente teñido de azul, uno frente al otro, y uno parece abrir ligeramente la boca.

4

Waves, Energy, and Information

In their role as marine scientists, students work to figure out how mother dolphins communicate with their calves. They write a series of scientific explanations with diagrams to demonstrate their growing understanding of how sound waves travel. Then they apply what they’ve learned about waves, energy, and patterns in communication to figure out how to create patterns that can communicate information over distances.

1

Patterns of Earth and Sky

Playing the role of astronomers, students help a team of archaeologists figure out what the missing piece of a recently discovered artifact might have depicted. As they learn about the sun and other stars and the movement of Earth, students can explain what is shown on the artifact and what might be on the missing piece.

2

Modeling Matter

In their role as food scientists at a fictional company, students are introduced to the idea that all matter is made of particles too small to see, and that each different substance is made of particles (molecules) that are unique. They are then challenged to solve two problems: one requires them to separate a mixture, and the other requires them to make unmixable substances mix. Students are challenged to use the particulate model of matter to explain their work to the CEO of the company.

Ilustración de un paisaje costero con una montaña y flechas que representan el flujo del viento sobre y alrededor de la montaña, lo que indica la dinámica del flujo de aire.

3

The Earth System

The cities of East Ferris and West Ferris are located on different sides of a mountain on the fictional Ferris Island. East Ferris is having a water shortage while West Ferris is not. As water resource engineers, students learn about the Earth system to help figure out what is causing the water shortage problem and design possible solutions, including freshwater collection systems and proposals for using chemical reactions to treat wastewater.

Ilustración de una escena de la jungla en la que aparecen un guepardo y un perezoso entre un denso follaje verde y varias plantas coloridas.

4

Ecosystem Restoration

As ecologists, students work to figure out why the organisms in a part of a Costa Rican rainforest ecosystem aren’t growing and thriving. As they solve this problem, students learn more generally how organisms in an ecosystem get the matter and energy they need to survive, and then write a series of restoration plans that include arguments about why the rainforest ecosystem is not thriving and recommend actions to restore its health.

Print & digital components

The program includes instructional guidance and student materials for a year of instruction, with lessons and activities that keep students engaged every day.

Component

Format

Teacher’s Guides

Available digitally and in print, the Teacher’s Guides contain all of the information teachers need to facilitate classroom instruction, including detailed lesson plans, high-level overview documentation, differentiation strategies, standards alignments, materials and preparation steps, teacher support strategies and in-context professional development, possible student responses, and more.

Print and digital

Hands-on materials kits

Hands-on learning is integrated into every unit of Amplify Science. Each hands-on activity is supported through clear instructions for the teacher, as well as easily accessible materials in unit-specific kits. Each kit contains hands-on materials, both consumable and nonconsumable, and various print materials (e.g., Vocabulary and Key Concept cards). With Amplify Science, students can actively participate in science: gathering evidence, thinking critically, making observations, and communicating their claims.

Kit

A collection of gardening supplies including a blue bucket, soil bags, plastic cups, hose, fertilizer pellets, and a black tray on a white background.

Component

Format

Student Investigation Notebooks

Available for every unit, the Student Investigation Notebooks contain instructions for activities and space for students to record data, reflect on ideas from texts and investigations, and construct explanations and arguments.

Print and digital

Student books

The age-appropriate Student Books in Amplify Science allow students to engage with content-rich text, obtain evidence, develop research and close reading skills, and construct arguments and explanations about the ideas they are learning in class.

Print and digital

Simulations and practice tools (grades 2+)

Developed exclusively for the Amplify Science program, these serve as venues for exploration and data collection, allowing students to explore scientific concepts that might otherwise be invisible or impossible to see with the naked eye.

Digital

Laptop screen displaying a geographical simulation of a river system with zones: Upper River, Floodplain, and River Delta, including an elevation chart and controls for speed and time adjustment.

Explore more programs

Our programs are designed to support and complement one another. Learn more about our related programs.

New York

To view this protected page, enter the password below:



Leading in early literacy with science-based practices

A group of adults poses in a hallway, all wearing matching gray shirts with a black design, celebrating their work with early literacy and the Science of Reading curriculum. Most are smiling and kneeling or standing in two rows.

Bruin Point Elementary sits at the base of Utah’s Book Cliff Mountain Range in the small mining town of Sunnyside, 30 miles from the nearest district hub. With just 107 students, and one teacher per grade, it’s Carbon School District’s smallest school—and now one of its brightest early literacy success stories.

All of Bruin Point’s students face significant systemic barriers, with 100% qualifying for free lunch. Yet when it comes to literacy development, the school’s educators have achieved something remarkable.

In just one year, their student literacy proficiency rates jumped 19 percentage points—from 39% at the beginning of the year to 58% by mid-year.

That’s why Bruin Point Elementary has been named a Literacy Legend in our 2025 Science of Reading Star Awards. These awards honor educators, schools, and districts that have transformed classrooms and empowered students through the Science of Reading.

Teaching early literacy skills in a community with challenges

Sunnyside tells the story of many rural American communities. “Since the closing of the local mines, there has been an increase in the number of unemployed family members,” says Cindy Garcia, Bruin Point’s principal.

As a result, an already high poverty rate has risen still further, along with levels of substance abuse, neglect, behavioral issues, and more. Parent involvement in school is extremely low, according to Garcia. “Basic needs take priority.”

Yet Garcia and her six-teacher team saw potential where others might have seen obstacles. They understood that their students deserved the strongest possible foundation in early literacy skills. And they knew they had to make a change.

The importance of relying on data

“Many of us had been trained in methods that didn’t fully meet the needs of all students, and shifting the mindset required trust, training, and time,” says fifth-grade teacher Tyler Grundy. “Our biggest challenge wasn’t just learning a new approach. It was unlearning old ones. But we stayed the course.”

Four of the six teachers completed LETRS training, with two more currently working through it. Teachers began to trade guesswork for systematic, explicit classroom instruction, using data to guide their early literacy program.

“We equipped our teachers with the knowledge and tools to teach reading explicitly and systematically,” Grundy says. “We relied on data, not assumptions, to guide our instruction and interventions.”

Building literacy and knowledge together

The school implemented Amplify Core Knowledge Language Arts (CKLA), providing systematic phonics instruction and rich content knowledge that builds comprehension.

“CKLA weaves literacy skills together to help make my students proficient readers and writers,” says first-grade teacher Chelsea Timothy. “They’re making connections between the Greek myth of Arachne and spiders being arachnids. They put together a web of knowledge.”

Just having a wealth of content at their fingertips made a huge difference, too, and the instructors learned quickly how to leverage it.

“I didn’t have to spend countless hours looking for content,” said Julia Sanders, a first-year kindergarten teacher. “It saved me time, so I could focus on making it more encouraging for the kids.”

For second-grade teacher Francie Aufdemorte, having comprehensive materials meant being able to focus on instruction. “It reduced the stress of creating lesson plans from scratch,” she says. “I was nervous about the rigor, but my students have excelled with it.”

Building a culture in which “success is expected”

The 19-point proficiency jump speaks to real student growth, but Garcia knows the impact goes beyond test scores.

“Struggling students who once guessed at words began to decode with confidence,” she said. “We built a culture where reading success is expected and not left to chance.”

Bruin Point’s success rests on ongoing commitment to evidence-based practices. Garcia and her team continue meeting regularly for data discussions, sustaining the mindset shift that began their journey to improved student outcomes.

“Our interventions and extensions are like a well-oiled machine,” Garcia said. “We can see that the young ones are off to a much better start.”

She adds: “We didn’t just change our curriculum, we changed lives. And that is a legacy worth celebrating.”

More to explore

What’s included in our Spanish language arts curriculum

Amplify Core Knowledge Language Arts® (CKLA) is available in both English and Spanish. Amplify Caminos al Conocimiento Esencial, our robust Spanish language arts companion for grades K–5, supports multiple teaching models, including dual language immersion and transitional classrooms.

A laptop screen displays a kindergarten instructional webpage in Spanish, showing lesson categories with illustrated thumbnails and navigation options.

Year at a glance

The program’s intentional Knowledge Sequence from K–5 connects knowledge and vocabulary within a grade level and across grade levels, for deeper reading comprehension and preparation for college, career, and life. Instead of “activating prior knowledge,” Amplify Caminos helps you build it in the classroom from day one, for every child, expanding each student’s knowledge base long before they transition to reading to learn.

Curriculum flowchart showing reading themes and activities from Kindergarten to Grade 5, organized by grade level and literary theme, with interconnected boxes for each topic.

Units & domains at a glance

Each Knowledge Domain in grades K–2 and Unit in grades 3–5 varies in the number of days based on instructional purpose. Just as with our top-rated Amplify CKLA program, the Amplify Caminos materials engage and delight young learners with resources that are both appealing and original.

Una mujer rubia con un vestido azul cuida ovejas blancas y negras, sosteniendo un bastón de pastor. Un cerdo vestido de azul corre y un hombre de negro toca el violín en una valla. Al fondo hay una casa.

Domain

Nursery Rhymes and Fables/Rimas y fábulas infantiles

Start learning about literature with these classic Mother Goose rhymes.

Ilustración de tres personas en un paisaje cubierto de hierba, una tratando de atrapar mariposas con una red, otra escondiéndose detrás de una escultura alta y frondosa de una mano y otra con binoculares.

Domain

The Five Senses/Los cinco sentidos

Learning about the body starts with learning about how we experience the world.

Una ilustración que representa a un gran lobo con sombrero de copa liderando un desfile de animales y personas con instrumentos musicales a través de un paisaje montañoso.

Domain

Stories/Cuentos

Learn about the parts of a book and some of the stories that go in one.

Una ilustración vibrante de una escena rural con colinas, una granja, una mariposa, un sol brillante, varias verduras como tomates y lechugas, y un gusano en el suelo.

Domain

Plants/Plantas

Discover the lifecycle of plants and the history of George Washington Carver.

Ilustración de una escena de granja que muestra un camión rojo que transporta verduras, campos de cultivo, vacas pastando en una colina, un granero y un molino de viento contra un cielo azul.

Domain

Farms/Granjas

Now we know how plants make their food… but what about animals?

Ilustración de un nativo remando en una canoa en un río con búfalos pastando en un campo, tipis al fondo y pájaros volando en el cielo bajo un sol brillante.

Domain

Native Americans/Los nativos americanos

Who were the first people in America? A look at the Lenape, Wampanoag, and Lakota Sioux.

Una ilustración muestra un rey y una reina en tronos, un castillo en un acantilado y una mujer con enanos cerca de un árbol. Cortinas rojas enmarcan la escena.

Domain

Kings and Queens/Reyes y reinas

To understand fairy tales, it’s best to first understand royalty.

Ilustración que muestra las cuatro estaciones: primavera con flores, verano con árboles verdes, otoño con hojas que caen e invierno con nieve y gente en trineo. Un niño lee debajo de un árbol.

Domain

Seasons and Weather/Las estaciones y el tiempo

The study of natural cycles continues with the weather and why it happens.

Un velero de madera con símbolos de cruz roja en sus velas navega cerca de una isla tropical con exuberante vegetación y palmeras. A lo lejos se ven otros dos barcos en el agua.

Domain

Columbus and the Pilgrims/Colón y los peregrinos

A look at the first contact between Europe and the Americas, and some of its results.

Una escena histórica muestra gente afuera de una gran mansión de estilo colonial con dos chimeneas. En primer plano se ve un carruaje tirado por caballos y a la izquierda se ve una casa más pequeña.

Domain

Colonial Towns and Townspeople/Las colonias y sus habitantes

Before the War for Independence, how did the town and country depend on one another?

Ilustración de personas clasificando materiales reciclables en un parque cerca de un río contaminado. Las fábricas emiten humo al fondo, mientras que las mariposas, las flores y los árboles están presentes en el primer plano.

Domain

Taking Care of the Earth/Cuidar el planeta Tierra

We only have one Earth—here are some ways to help care for it.

Ilustración del Monte Rushmore con los rostros tallados de cuatro presidentes de Estados Unidos. Un águila vuela en primer plano.

Domain

Presidents and American Symbols/Presidentes y símbolos de los Estados Unidos

Start learning about government through the lives of five presidents.

Una ilustración caprichosa que muestra animales de granja alrededor de una casa en un árbol junto a un río. Un zorro, un conejo y una oveja interactúan mientras la gente acampa junto a una fogata al fondo. Una araña cuelga del árbol.

Domain

Fables and Stories/Fábulas y cuentos

Learn some of the key elements of a story through classic fables.

Ilustración que presenta anatomía humana, actividades de estilo de vida saludable, profesionales médicos, símbolos dietéticos, una ambulancia y microorganismos, destacando la conexión entre salud, nutrición y ejercicio.

Domain

The Human Body/El cuerpo humano

What are germs? What are the organs? And what does it all have to do with health?

Una ilustración que presenta varias escenas de cuentos de hadas y folclore, incluida una calabaza grande, un tigre, Caperucita Roja, personas con atuendos tradicionales y una pagoda roja con una montaña de fondo.

Domain

Different Lands, Similar Stories/Tierras diferentes, cuentos similares

A world tour of storytelling, and the stories that stay the same across the world.

Ilustración que muestra el antiguo Egipto con pirámides, la Esfinge, agricultores arando un campo con bueyes y ganado pastando bajo un cielo soleado.

Domain

Early World Civilizations/Antiguas civilizaciones del mundo

Rivers, farming, writing, and laws: just what does it take to build a civilization?

Escena ilustrada de la antigua Mesoamérica con maíz, un río, agricultores y pirámides al fondo. En primer plano se ve a una persona con traje tradicional.

Domain

Early American Civilizations/Antiguas civilizaciones de América

What will we find in the great temples of the Aztec, Maya, and Inca civilizations?

Ilustración de la exploración espacial: se lanza un cohete, un astronauta se para cerca de un módulo de aterrizaje, una persona usa un telescopio y aparece un planeta distante con anillos sobre un fondo estrellado.

Domain

Astronomy/Astronomía

How the Earth relates to the moon, the sun, and the rest of the planets.

Dos paleontólogos en un paisaje volcánico examinan fósiles en primer plano, mientras un volcán emite humo y lava al fondo.

Domain

The History of the Earth/La historia de la Tierra

Just what lies beneath the Earth’s surface, and what can it teach us about the past?

Una escena de vida silvestre diversa que presenta un cactus del desierto con un pájaro, un conejo, elefantes, un león, un oso polar sobre el hielo y montañas distantes bajo un cielo nublado.

Domain

Animals and Habitats/Los animales y sus hábitats

A look at the connection between how animals live and where they make their homes.

Una princesa con un vestido rosa sostiene una rana junto a un arroyo con un castillo, árboles y gente al fondo. En primer plano camina un zorro con un sombrero con una pluma roja.

Domain

Fairy Tales/Cuentos de hadas

What do fairy tales have to teach us about how stories are told?

Ilustración que muestra una escena histórica con soldados, veleros y hombres con atuendo colonial discutiendo en el interior.

Domain

A New Nation: American Independence/Una nueva nación: la independencia de los Estados Unidos

The story of the birth of the United States out of the 13 Colonies.

Los pioneros con carros cubiertos y caballos señalan hacia un valle con tipis nativos, fogatas y humo elevándose. Un oso se encuentra sobre una roca y se ven montañas al fondo.

Domain

Frontier Explorers/Exploradores de la Frontera

The story of the journey west from the newborn U.S.A. to find the Pacific Ocean.

Un hombre con un hacha se encuentra entre paisajes exagerados con un castillo, un tren con humo, un buey azul y una persona con un mono observando la escena.

Domain

Fairy Tales and Tall Tales/Cuentos de hadas y cuentos exagerados

Learn about exaggeration and characterization on the frontier.

Ilustración de un paisaje vibrante que presenta diversos monumentos culturales, incluidos templos, palacios, pirámides, una escena de elefantes, montañas distantes y fuegos artificiales en el cielo.

Domain

Early Asian Civilizations/Antiguas civilizaciones de Asia

Tour the world of classical civilization, starting with India and China.

Ilustración que muestra la antigua Grecia con un anfiteatro, estatuas, soldados con armadura, un barco y un templo en una colina rodeada de vegetación.

Domain

Ancient Greek Civilization/La civilización griega antigua

The tour continues with the philosophy and politics of Greece.

Illustration of various mythological scenes including greek gods, a flying horse, and roman architecture under a sunny sky.

Domain

Greek Myths/Mitos griegos

Dive deep into the characters and storytelling of classic myths.

Ilustración de una batalla entre barcos británicos y estadounidenses cerca de un fuerte. El barco británico está a la izquierda con soldados, mientras que el barco estadounidense está a la derecha. La gente porta una gran bandera estadounidense en primer plano.

Domain

The War of 1812/La guerra de 1812

Learn about America’s “Second War for Independence.”

Un paisaje nevado con un zorro durmiendo en una madriguera, gente corriendo y andando en bicicleta por un sendero y árboles que muestran los cambios estacionales.

Domain

Cycles in Nature/Los ciclos de la naturaleza

Introducing the natural cycles that make our lives possible.

Ilustración de carros cubiertos tirados por caballos a lo largo de un sendero en el desierto, con un coyote aullando sobre una alta formación rocosa y un tren de vapor al fondo.

Domain

Westward Expansion/La expansión hacia el oeste

Why did pioneers go west? What happened to the people who were there?

Ilustración de un jardín vibrante con flores, abejas, mariposas, una oruga en una hoja, una crisálida y un apicultor que maneja una colmena junto a un estanque.

Domain

Insects/Los insectos

Lay the grounds for animal classification by looking at solitary and social insects.

Ilustración de una escena histórica con gente escuchando el discurso de un hombre en una plataforma. Al fondo se ve un río y una procesión de personas. En primer plano hay un documento de proclamación.

Domain

The U.S. Civil War/La Guerra Civil de los Estados Unidos

Begin to grapple with U.S. history’s central crisis over slavery.

Una escena en la que aparece una persona explicando un diagrama anatómico humano, otra persona haciendo ejercicio, una cadena de ADN, campos y un microscopio de fondo.

Domain

Human Body: Building Blocks and Nutrition/El cuerpo humano: componentes básicos y nutrición

A deeper dive into the digestive system and the nutrition process.

Un grupo diverso de personas se encuentra en un muelle con vistas a un bullicioso puerto con barcos y un gran barco, un avión volando por encima y la Estatua de la Libertad al fondo.

Domain

Immigration/La inmigración

Why did people immigrate to the United States, and what did they find here?

Women in early 20th-century clothing march with signs for voting rights and justice in front of a yellow bus labeled "Cleveland Ave.," making history that can inspire lessons in a K–2 language arts curriculum.

Domain

Fighting for a Cause/Luchar por una causa

How people can do extraordinary things to make the world better for everyone.

Dos ratones antropomórficos en un bote de remos, uno de ellos remando, navegan por un río tranquilo rodeado de exuberante vegetación y árboles. El ratón que rema lleva una chaqueta azul y el otro ratón parece conversar.

Unit 1

Classic Tales: The Wind in the Willows/Cuentos Clásicos: El viento en los sauces

A deep dive into character, theme, and POV in classic stories from around the world.

Ilustración de un jaguar, una garza, una rana roja, una tortuga y un pez en un paisaje vibrante con montañas y vegetación bajo un cielo soleado.

Unit 2

Animal Classification/La clasificación de los animales

How do we classify different animals by their appearance and behavior?

Ilustración de una figura humana que muestra la anatomía interna, incluidos el cerebro, los pulmones, el corazón, el sistema digestivo y una articulación de la cadera resaltada sobre un fondo degradado.

Unit 3

The Human Body: Systems and Senses/El cuerpo humano: sistemas y sentidos

Let’s take a closer look at how the skeleton, muscles, and nervous system all work.

Un ángel se arrodilla ante una mujer sentada en un sofá dorado encima de un templo en una noche estrellada. Unas escaleras conducen al templo en un paisaje montañoso.

Unit 4

The Ancient Roman Civilization/La civilización romana antigua

What is Rome’s greatest cultural contribution? In this unit, your students decide.

Ilustración de un perro saltando bajo un árbol, persiguiendo una abeja, con una mesa en primer plano sosteniendo una jarra y vasos de limonada. El sol brilla intensamente en el cielo.

Unit 5

Light and Sound/La luz y el sonido

The science behind all the ways we see and hear the world.

Un barco vikingo con una proa en forma de dragón navega en el océano bajo un cielo azul con nubes. El barco tiene una sola vela grande y varios escudos recubren sus costados.

Unit 6

The Viking Age/La era vikinga

An immersive narrative experience about what life was like in Viking communities.

Ilustración de una escena espacial con varios planetas y anillos sobre un fondo de estrellas. Dos planetas grandes dominan el primer plano y se ven planetas más pequeños al fondo.

Unit 7

Astronomy: Our Solar System and Beyond/Astronomía: nuestro sistema solar y más allá

More about our universe, including a writing project about daily life on a space station.

Una persona sentada en el borde de un acantilado con vistas a un vasto paisaje desértico con nubes arremolinadas en el cielo.

Unit 8

Native Americans: Regions and Cultures/Los nativos americanos: regiones y culturas

How did Native American nations change their way of life in different parts of the world?

Ilustración de un velero en el océano con la costa este de América del Norte visible a la izquierda.

Unit 9

Early Explorations of North America/La exploración europea de América del Norte

What was it like to sail to North America with the early European explorers?

Una pintura representa una escena del siglo XVII con colonos, un velero al fondo y un hombre conduciendo un carro tirado por caballos cargado de mercancías. Se ve a otras personas descargando y trabajando cerca.

Unit 10

Colonial America/La época colonial en los Estados Unidos

A study of the very different ways of life in the different pre-U.S. colonies.

Ilustración que muestra el ciclo de la vida: un esqueleto en el suelo, un pájaro posado en una cerca, otro pájaro en una planta y un ave rapaz más grande arriba, todos conectados por flechas circulares.

Unit 11

Ecology/Ecología

Students keep ecologist’s journals to learn about our world and how best to protect it.

Una mano alcanza una manzana verde en una rama. Cerca hay una brújula, un termómetro, un lápiz, notas musicales y un granero rojo sobre un paisaje cubierto de hierba.

Unit 1

Personal Narratives/Narrativas personales

Read stories of personal experience… and learn to reflect on your own.

Ilustración medieval que representa un grupo de figuras con armadura a la entrada de un alto castillo gris con puente levadizo, adornado con banderas y rodeado por un paisaje decorado y fondos ornamentados.

Unit 2

Empires in the Middle Ages/Los imperios en la Edad Media, parte 1 & Los imperios en la Edad Media, parte 2

Explore the medieval history of Europe and the Middle East.

Ilustración dorada de un dragón con alas sobre fondo beige, rodeado de diversos elementos decorativos como estrellas, hojas y estampados abstractos.

Unit 3

Poetry/Poesía

Study the poetry of many nations using licensed text anthologies, and begin to write your own.

Vintage styled illustrations of a microscope, an old telephone, and a clock on textured background with geometric patterns.

Unit 4

Eureka! Student Inventor/¡Eureka! Estudiante inventor

Transform the class into a lab for students to build and present inventions.

Formaciones rocosas en un paisaje desértico con capas vibrantes y arremolinadas de arenisca roja, naranja y amarilla bajo un cielo parcialmente nublado.

Unit 5

Geology/Geología

Plate tectonics, volcanoes, erosion: all the forces that shape the Earth.

Una imagen abstracta y colorida que representa varias formas geométricas de edificios sobre un fondo azul estampado.

Unit 6

Contemporary Fiction with excerpts from The House on Mango Street/Ficción Contemporánea con Fragmentos de La Casa en Mango Street

Explore The House on Mango Street… and write a book while doing it.

Cuadro que representa a un hombre y un niño tocando una gran campana en una torre, con espectadores al fondo y un cartel de "LIBERTAD" visible.

Unit 7

American Revolution/La Revolución estadounidense

Why did America seek independence? Let’s investigate the causes and effects.

Un pequeño bote de remos con tres personas navega por mares agitados mientras dos grandes barcos luchan al fondo, con humo y fuego visibles.

Unit 8

Treasure Island/La Isla del Tesoro

How dSeek the treasure of plot in this detailed study of a classic fiction adventure.

Unit 1

Personal Narratives/Narrativas personales

Through writing and sharing their writing, students begin to identify themselves as writers.

Unit 2

Early American Civilizations/Las primeras civilizaciones americanas

Students craft a codex to explain the rise and fall of the Maya, Aztec, and Inca people.

Dos jinetes medievales a caballo, uno de ellos con la espada en alto, avanzan por un terreno rocoso. El fondo presenta un paisaje brumoso bajo un tono violeta.

Unit 3

Poetry/Poesía

Students close read many forms of poetry… and learn to write them.

Collage ilustrado con un paraguas, un cuervo, un sextante náutico, estrellas, una luna creciente y una brújula sobre un fondo beige texturizado.

Unit 4

Adventures of Don Quixote/Las Aventuras de Don Quijote

Was Don Quixote right to fight the windmill? In this full-length novel study, students decide.

Unit 5

The Renaissance/El Renacimiento

Exploring the art and literature of the Renaissance through the works of its masters.

Tres hombres vestidos con ropa de época examinan una gran hoja de papel dentro de una imprenta. Un hombre parece llevar un delantal, mientras que otro señala el papel y el tercero observa de cerca.

Unit 6

The Reformation/La Reforma

How did the printing press transform the religion and society of Europe?

Patrón botánico morado y lila con hojas, plantas y formas abstractas, incluida una luna creciente y estrellas, sobre un fondo violeta oscuro.

Unit 7

William Shakespeare’s A Midsummer Night’s Dream/Sueño de Una Noche de Verano de William Shakespeare

Students enter the world of Shakespeare by reading, designing, and acting out his work.

Retrato en tonos sepia de una joven de pelo largo, con un collar de pedrería y un chal drapeado.

Unit 8

Native Americans/Los nativos americanos

How did the policies of the U.S. government impact Native American culture and lives?

Una lupa sobre documentos que contienen una pintura de paisaje de montañas, un dibujo con la etiqueta "Raptor Claw" y una nota adhesiva con la "Pista n.° 2". También se ven un sobre y una insignia exterior.

Unit 9

Chemical Matter/Química

Students use knowledge of chemistry to solve a mystery.

Print & digital components

The program includes instructional guidance and student materials for a year of instruction, with lessons and activities that keep students engaged every day.

Component

FORMAT

Knowledge (Conocimientos) Teacher Guides (K–2)

Knowledge Strand Teacher Guides contain Amplify CKLA’s cross-curricular read-alouds and application activities, all of which are standards-based to build mastery of content knowledge and literacy skills. There is one Teacher Guide per Knowledge Domain.

Print and digital

Knowledge Image Cards (K–2)

Amplify Caminos includes Image Cards for each Knowledge Domain to bring each topic to life through vivid visuals.

Print and digital

Knowledge Flip Books (K–2)

Projectable Flip Books are provided to accompany the read-alouds in each Knowledge Domain.

Digital

Teacher Guides (3–5)

Teacher Guides for grades 3–5 units are based on content-rich topics and incorporate reading, writing, speaking, and listening skills in the context of background knowledge. There is one Teacher Guide per unit.

Print or digital

Teacher Resource Site (K–5)

The program includes a one-stop-shop website for lesson projections, digital versions of all Amplify Caminos materials, lesson planning resources, multimedia (such as eBooks), and more.

Digital

Professional Learning Site (K–5)

The Professional Learning site includes training materials, best practices, and other resources to develop program expertise. Access professional development anywhere, anytime.

Digital

Component

FORMAT

Knowledge (Conocimiento) Activity Books (K–2)

Activity Books provide students with the opportunity to deepen world and word knowledge by responding to text in a diversity of ways.

Print

Student Readers (3–5)

Student Readers serve as content-rich anchor texts for each unit. Units such as Poetry and Contemporary Fiction feature authentic texts originally written in Spanish.

Activity Books (3–5)

Activity Books in grades 3–5 provide daily opportunities for students to hone reading and writing skills within the context of each unit.

Print and digital

Explore more programs

Our programs are designed to support and complement one another. Learn more about our related programs.

An Aussie teaching American phonemes

A woman smiles in a portrait overlaid on an illustrated open book with a ladybug, web, and green landscape, reflecting an interactive teaching style; a speech bubble shows "/u/".

Ever heard of bidialectalism? It means the ability to fluently switch between two dialects.
It was a new word for me when I first started teaching in the U.S.—but I figured it out fast, just by opening my mouth in the classroom.

Bringing my own Australian dialect to teaching six-year-olds deepened my capacity to help struggling readers and multilingual readers. It has also strengthened our classroom community and provided surprising, even amusing opportunities to learn—for all of us.

“What if they get an Australian accent?”

When I first entered an American classroom, I was nervous about teaching phonemes to kids. I kept wondering, “What if they get an Australian accent?” (That never happened.)

I remember my first year teaching Amplify CKLA, standing in front of my students and trying to figure out why the word “from” seemed tricky. For me, it sounded exactly how it was spelled. I kept saying “from,” but my students said: “/f/ /r/ /u/ /m/.”

That was the first of many times I realized how different my dialect really was.

The next one came during our Animals and Habitats unit. We were deep into the lesson when I casually said what sounded like “Pythin,” and a student turned and said, “Don’t you mean PythOn?”

Then came the r-controlled vowels. (R-controlled vowels, also called r-influenced vowels, are vowels that change their sound when followed by an “r” in the same syllable. Instead of sounding short or long, the vowel is “controlled” by the “r”—like in “car,” “bird,” “corn,” “turn,” and “her.”)

Because of my accent, when I said those sounds, they almost always came out as “uh.” (I think that’s why I’ve been told Aussies were responsible for the schwa!) While that got a good laugh—and gave students lots of chances to mimic my accent—it drove home the real importance of phonological awareness.

Learning together: Teaching phonemes and pronunciation

I spent the rest of that first year going over the phoneme videos on the Amplify resources hub, practicing my r-controlled vowels. I did my best to learn to switch between the Australian and American dialects. I even started challenging my students to correct me more often. (“Wait, did I say that right?”)

That led to more intentional practice when teaching grade-level spelling patterns for those individual sounds. I started adding silly actions to go with each one. For example, we’d say, “‘e’ and ‘r’ are friends and together they go ‘errrrr,’” and we’d pretend to turn a key into either side of our cheeks.

Those small quirks helped my students remember the sounds—and they helped me just as much.

Don’t dread it—use it!

So, to any teacher who’s dreading teaching phonemes or teaching kids to read because of their speech or dialect—don’t!

Learning with your students, blending Amplify’s tools with your own quirks and personality, builds classroom memories and creates powerful literacy instruction.

You don’t have to erase your accent to be effective. In fact, embracing your uniqueness might just make you a better teacher.

From one teacher to another: Don’t be afraid of the greatness you already have.

To close out, here’s my favorite use of what I believe is the greatest phoneme/diphthong of all time: Aussie! Aussie! Aussie! Oi! Oi! Oi!

Amplify CKLA 1st Edition resources

Coming March 13, Amplify will be providing links below so that you can easily access and print Student Workbook pages, which students complete as part of the daily lessons. In addition to providing daily opportunities for students to respond to text and apply skills and knowledge, Workbooks feature formative assessments for each day’s objectives.

In the meantime, Student Workbook pages are accessible and printable from the Teacher Resource site by following these steps:

  1. Log in to the 1st Edition Teacher Resource site. The 1st Edition resource site can be accessed by following this link or navigating to ckla.amplify.com. (Note: If you don’t have a login, click “Register” to create a login using access code CKLA01)
  2. Open the Digital Planning Guide.
  3. Navigate to a grade, lesson, and lesson activity—you will find the workbook page hyperlinked in the lesson activity at point of use.
  4. Click on the hyperlinked workbook page to open it up in your browser.
  5. Print the workbook page directly from your browser or save the page to your computer.
Illustration of a mesoamerican scene, featuring a large pyramid and a foreground portrait of an indigenous woman, with people harvesting crops in the background.

Illustrative Mathematics-NEW

To view this protected page, enter the password below:



GO Math!-NEW

To view this protected page, enter the password below:



Big Ideas

Grade 6

Chapter 2: Fractions and Decimals

Big IdeasDesmos Classroom
Lesson 2: Dividing FractionsUnit 4
Lesson 3: Flour Planner
Lesson 4: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 2: Decimal Diagrams and Algorithms
Lesson 5: Multiplying DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 6: Dividing Whole NumbersUnit 5
Lesson 13: Movie Time
Lesson 7: Dividing DecimalsUnit 5
Lesson 13: Movie Time

Chapter 3: Ratios and Rates

Lesson 1: RatiosUnit 2
Lesson 1: Pizza Maker
Lesson 4: Fruit Lab
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 3: Using Ratio TablesUnit 2
Lesson 10: Disaster Preparation
Lesson 4: Graphing Ratio RelationshipsUnit 2
Lesson 10: Disaster Preparation
Lesson 5: Rates and Unit RatesUnit 3
Lesson 6: Soft Serve
Lesson 6: Converting MeasuresUnit 3
Lesson 1: Many Measurements

Chapter 4: Percents

Lesson 1: Percent and FractionsUnit 3
Lesson 9: Lucky Duckies
Lesson 2: Percent and DecimalsUnit 5
Lesson 2: Decimal Diagrams and Algorithms

Chapter 5: Algebraic Expressions and Properties

Lesson 2: Writing ExpressionsUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 3: Properties of Addition and MultiplicationUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 4: The Distributive PropertyUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)

Chapter 6: Equations

Lesson 1: Writing Equations in One VariableUnit 6
Lesson 1: Weight for It

Chapter 7: Area, Surface Area, and Volume

Lesson 1: Areas of ParallelogramsUnit 1
Lesson 3: Exploring Parallelograms
Exploring Parallelograms, Part 2
Lesson 5: Surface Area of prismsUnit 1
Lesson 10: Renata’s Stickers

Chapter 8: Integers, Number Lines, and the Coordinate Plane

Lesson 1: IntegersUnit 7
Lesson 1: Can You Dig It?
Lesson 2: Comparing and Ordering IntegersUnit 7
Lesson 4: Order in the Class
Lesson 3: Rational NumbersUnit 7
Lesson 4: Order in the Class
Lesson 7: Writing and Graphing InequalitiesUnit 7
Lesson 7: Tunnel Travels

Chapter 9: Statistical Measures

Lesson 1: Introduction to StatisticsUnit 8
Lesson 3: Minimum Wage
Lesson 2: MeanUnit 8
Lesson 11: Toy Cars
Lesson 3: Measures of CenterUnit 8
Lesson 11: Toy Cars
Lesson 4: Measures of VariationUnit 8
Lesson 11: Toy Cars

Chapter 10: Data Displays

Lesson 2: HistogramsUnit 8
Lesson 5: The Plot Thickens
Lesson 4: Choosing Appropriate MeasuresUnit 8
Lesson 3: Minimum Wage
Lesson 11: Toy Cars

Grade 7

Chapter 1: Adding and Subtracting Rational Numbers

Big IdeasDesmos Classroom
Lesson 1: Rational NumbersUnit 5
Lesson 1: Floats and Anchors
Lesson 2: Adding Integers
Lesson 4: Subtracting Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 3: Adding Rational Numbers
Lesson 5: Subtracting Rational Numbers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles

Chapter 2: Multiplying and Dividing Rational Numbers

Lesson 1: Multiplying IntegersUnit 5
Lesson 10: Integer Puzzles

Chapter 3: Expressions

Lesson 1: Algebraic ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 2: Adding and Subtracting Linear ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 3: The Distributive PropertyUnit 6
Lesson 10: Collect the Squares

Chapter 4: Equations and Inequalities

Lesson 1: Solving Equations Using Addition or Subtraction
Lesson 2: Solving Equations Using Multiplication or Division
Unit 6
Lesson 16: Shira the Sheep
Lesson 4: Writing and Graphing InequalitiesUnit 6
Lesson 16: Shira the Sheep
Lesson 5: Solving Inequalities Using Addition or Subtraction
Lesson 6: Solving Inequalities Using Multiplication or Division
Unit 6
Lesson 16: Shira the Sheep
Lesson 7: Solving Two-Step InequalitiesUnit 6
Lesson 16: Shira the Sheep

Chapter 5: Ratios and Proportions

Lesson 1: Ratio and Ratio TablesUnit 2
Lesson 1: Paint
Lesson 3: Identifying Proportional RelationshipsUnit 2
Lesson 6: Two and Two
Lesson 3: Measuring Around
Lesson 5: Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops

Chapter 6: Percents

Lesson 1: Fraction, Decimals, and PercentsUnit 4
Lesson 1: Mosaics
 
Lesson 4: Percents of Increase and DecreaseUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Lesson 5: Discounts and MarkupsUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)

Chapter 7: Probability

Chapter 8: Statistics

Lesson 1: Samples and PopulationsUnit 8
Lesson 10: Crab Island
Lesson 2: Using Random Samples to Describe populationsUnit 8 
Lesson 10: Crab Island
Lesson 3: Comparing Populations
Lesson 4: Using Random Samples to Compare Populations
Unit 8
Lesson 10: Crab Island

Chapter 9: Geometric Shapes and Angles

Lesson 1: Circle and CircumferenceUnit 3
Lesson 3: Measuring Around
Lesson 2: Areas of CirclesUnit 3
Lesson 9: Area Challenges
Lesson 5: Finding Unknown Angle MeasuresUnit 7
Lesson 4: Missing Measures

Grade 8

Chapter 1: Equations

Big ideasDesmos Classroom
Lesson 2: Solving Multi-Step EquationsUnit 4
Lesson 5: Equation Roundtable
Lesson 3: Solving Equations with Variables on Both SidesUnit 4
Lesson 5: Equation Roundtable

Chapter 2: Transformations

Chapter 3: Angles and Triangles

Lesson 2: Angles and TrianglesUnit 1
Lesson 12: Puzzling It Out
Lesson 4: Using Similar TrianglesUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf

Chapter 4: Graphing and Writing Linear Equations

Lesson 1: Graphing Linear EquationsUnit 3 Lesson 4: Flags
Lesson 2: Slope of a LineUnit 3 Lesson 4: Flags
Lesson 3: Graphing Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Graphing Linear Equations in Slope-Intercept FormUnit 3
Lesson 4: Flags

Chapter 5: Systems of Linear Equations

Lesson 1: Solving Systems of Linear Equations by GraphingUnit 4
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Chapter 6: Data Analysis and Displays

Lesson 1: Scatter PlotsUnit 6
Lesson 3: Robots
Lesson 2: Lines of FitUnit 6
Lesson 4: Dapper Cats
Lesson 3: Two-Way TablesUnit 6
Lesson 11: Finding Associations

Chapter 7: Functions

Lesson 1: Relations and FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 2: Representations of FunctionsUnit 5
Lesson 5: The Tortoise and the Hare

Chapter 8: Exponents and Scientific Notation

Lesson 1: ExponentsUnit 7
Lesson 3: Power Pairs
Lesson 2: Products of Powers PropertyUnit 7
Lesson 3: Power Pairs
Lesson 6: Scientific Notation
Lesson 7: Operations in Scientific Notation
Unit 7
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Chapter 9: Real Numbers and the Pythagorean Theorem

Lesson 1: Finding Square RootsUnit 8
Lesson 4: Root Down
Lesson 3: Finding Cube RootsUnit 8
Lesson 4: Root Down

Chapter 10: Volume and Similar Solids

Lesson 1: Volumes of CylindersUnit 5
Lesson 11: Cylinders
Lesson 2: Volumes of ConesUnit 5
Lesson 13: Cones

Grade K

Unit 1: Count Sequence and Numbers to 5

Module 1: Represent Numbers to 5 with Objects

Lesson 1: Represent 1 and 2Connecting Cubes
Lesson 2: Represent 3 and 4Skye’s Style
Matching Groups
Designing Shoes With Skye

Unit 2: Count Sequence and Numbers to 10

Module 7: Represent Numbers 6 to 10 with Objects

Module 10: Compare Numbers to 10

Lesson 4: Compare Groups Within 10 by CountingMore, Fewer, or the Same
Fingers and Counters
Lesson 5: Compare Groups Within 10 by MatchingComparing Words
Forest Friends

Module 11: Add To and Take From Within 10

Module 12: Put Together and Take Apart Within 10

Lesson 3: Solve Put Together Problems Within 10How Many Objects in Pictures?
How Will You Count?
What Does It Mean to Add?
Lesson 4: Solve Take Apart Problems Within 10What Does It Mean to Subtract?
Lesson 5: Solve Word Problems Within 10The Bus Depot

Module 13: Ways to Make Numbers to 10

Lesson 4: Ways to Make 10Harry’s Hamster Wheel
Harry Explores Space
Lesson 5: Make 10 From a Given NumberShowing What We Know About 10
Lesson 1: Ways to Make 6 and 7Harry Explores the Ocean

Unit 3: Geometry

Module 14: Analyze and Compare Three-Dimensional Shapes

Module OpenerWhat’s That Shape?
Lesson 5: Build ShapesBuilding Solid Shapes

Module 15: Describe Position of Objects

Module 16: Analyze and Compare Two-Dimensional Shapes

Lesson 7: Compare Two-Dimensional and Three-Dimensional ShapesSo Much Sorting
What’s That Shape Called?
Another Shape

Unit 4: Number and Operations in Base Ten

Module 17: Place Value Foundations-Represent Numbers to 20

Lesson 3: Compose Ten Ones and Some More Ones to 19Investigate: Packing Snacks
Lesson 4: Represent Numbers to 20Getting Ready for the Game
How Many on the Field?
Pass, Shoot, Score

Module 18: Place Value Foundations-Represent Number to 20 with a Written Numeral

Lesson 1: Count and Write 11 to 14Jersey Jam!
Lesson 3: Count and Write 16-19People at the Park

Grade 1

Unit 1: Ways to Add and Subtract

Module 2: Subtraction Strategies

Lesson 2.1: Represent SubtractionPacking a Picnic
Lesson 2.2: Count BackWhat’s the Difference?
Lesson 2.3: Count on to SubtractLeaping Lily Pads!

Module 3: Properties of Operations

Lesson 3.6: Determin Equatl and Not EqualReplanting Huli

Module 4: Apply Addition and Subtraction Relationships

Lesson 4.2: Represent Related FactsSame Number, Different Ways
Lesson 4.3: Identify Related FactsKitten Coaster
Lesson 4.6: Solve for Unknow AddendTutu’s Garden in Maui

Module 5: Understand Add to and Take From Problems

Lesson 5.4: Solve Add To and Take From ProblemsA Community Working Together
Helping Others
Making 10

Module 6: Understand Put Together and Take Apart Problems

Lesson 6.3: Represent Addend and Unknown Problems with Objects and DrawingInvestigate: Let’s Grow!

Module 8: Data

Lesson: 8.2 Represent Data with Picture GraphsShapes Ying Saw

Unit 3: Numbers to 120

Module 10: Count and Represent Numbers

Lesson 10.4: Decompose Numbers in Different WaysInvestigate: Game Points
Lesson 10.5: Represent, Read, and Write Numbers from 100 to 110From Head to Claw
From Wing Tip to Wing Tip
Measuring More Wingspans
Lesson 10.5: Represent, Read, and Write Numbers from 110 to 120From Head to Claw
From Wing Tip to Wing Tip
Measuring More Wingspans

Unit 4: Addition and Subtractoin in Base Ten

Module 12: Understand Addition and Subtraction with Tens and Ones

Lesson 12.1: Representing Adding TensMeeting Yara
It’s a Match
From Park to Table
Lesson 12.3: Add and Subtract TensHow Many Cubes?
Boris’s Thimbles
How Many Tens?

Module 13: Two-Digita Addition and Subtraction

Lesson 13.1: Use Hundred Charts to Show Two-Digit Addtion and Subtraction.Investigate: Squashes at the Playground
Lesson 13.2: Understand and Explain Place Value AdditionTown Helpers
Making Squash Butter

Unit 6: Measurment

Module 16: Fraction Foundations

Lesson 16.1: TAke Apart Two-Dimensional ShapesFair and Square
Lesson 16.2: Identify Equal or Unequal PartsOne of the Parts, All of the Parts
Lesson 16.4: Partition Shapes into FourthsA Bigger Part

Grade 2

Unit 1: Numbers and Data

Module 1: Fluency for Addition and Subtraction Within 20

Lesson 1.5: Use the Make a Ten Strategy to AddExploring Within 10
Ways to Make 10

Module 1: Fluency for Addition and Subtraction Within 21

Lesson 1.6: Use a Tens Fact to SubtractExploring Within 10
Ways to Make 10

Module 2: Equal Groups

Lesson 2.1: Identify Even and Odd NumbersCan You Share?
Is It Even or Odd?
Lesson 2.2: Write Equations to Represent Even NumbersEverybody, Find A Partner!

Module 3: Data

Lesson 3.5: Draw bar graphs to Represent DataAwesome Aquariums

Unit 2: Place Value

Module 4: Understand Place Value

Lesson 4.1: Group Tens as HundredsWhat Makes a Hundred?
Lesson 4.2: Understand Three-Digit NumbersWhat’s the Value?
Lesson 4.4: Represent Numbers with Hundreds, Tens, and OnesMail Call!
What’s Your Name?

Module 5: Read, Write, and Show Numbers to 1000

Lesson 5.3: Different Ways to Write NumbersA New Representation
Lesson 5.4: Different Ways to Show NumbersAll the Ways!

Module 6: Use Place Value

Lesson 6.1: Count Within 1000Investigate
Turtle Hurdle
Lesson 6.5: Use Symbols to Compare NumbersTime to Line Up!

Unit 3: Money and Time

Module 7: Coins

Lesson 7.1: Relate Place Value to CoinsInvestigate
Lesson 7.2 Identify and Find Value of CoinsDiscovering Coins (Part 1)
Lesson 7.3: Compute the Value of Coin CombinationsHow Much Money?
Lesson 7.4: Show Amounts in Different WaysDiscovering Coins (Part 2)
The Toy Stand

Module 8: Dollar Amounts

Lesson 8.3: Solve Problems Involving MoneyThe Craft Stand at the Block Party

Unit 5: Three-Digita Addition and Subtraction

Module 16: Three-Digit Addition

Lesson 16.1: Use Drawing to Represent Three-Digit AdditionThere’s Something About Berries
Lesson 16.2: Decomposte Three-Digit AddendsBaking With Skunk

Unit 6: Measurement

Module 18: Lengths in Inches, Feet, and Yards

Lesson 18.4: Make Line Ploits to Show Measurement DataMessy Measurements
Bracelets and Wristbands

Module 20: Relate Addition and Subtraction to Length

Lesson 20.1: Relate Inches to a Number LineInvestigate
Time to Line Up!
What’s That Number?
Lesson 20.2: Add and Subtract Lengths in InchesLengths of Jungle Animals
Lesson 20.3: Relate Centimeters to a Number LineInvestigate
Time to Line Up!
In Full Bloom

Unit 7: Geometry and Fractions

Module 21: Two- and Three- Dimensional Shapes

Lesson 21.2 Identify and Draw Three-Dimensional ShapesMore to Measure
Lesson 21.2: Identify and Draw Two-Dimensional ShapesFrame It!
Measure It, Draw It

Grade 3

Unit 1: Understand Multiplication and Area

Module 1: Understand Multiplication

Lesson 1.1: Count Equal GroupsEqual Groups
Lesson 1.3: Represent Multiplication with ArraysArrays of Flavor
Lesson 1.4: Understand the Commutative Property of MultiplicationArrays of Flavor

Module 2: Relate Multiplication and Area

Lesson 2.1 Understand Area by Counting Unit SquareInvestigate: Comparing Rugs
Which Covers More Space?
Lesson 2.2: Measuring Area by Counting Unit SquaresTiling Figures
Area Hunt
Lesson 2.3: Relate Area to Addition and MultiplicationRectangles and Arrays

Unit 2: Multiplication and Division

Module 7: Relate Multiplication and Division

Lesson 7.7: Build Fluency with Multiplication and DivisionRelating Quotients to Familiar Products

Module 8: Apply Multiplication and Division

Lesson 8.3: Use Multiplication and Division to Solve Problem SituationsIt’s Chili in Here!
Lesson 8.4: Solve Two-Step ProblemsDivision and Multiplication Equations

Unit 3: Addition and Subtraction Strategies

Module 9: Addition and Subtraction Strategies

Lesson 9.3: Use Properties to AddHow Would You Solve It?
Lesson 9.4: Use Mental Math to Assess ReasonablenessAdding Strategically

Module 10: Addition and Subtraction Within 1000

Lesson 10.1: Use Expanded Form to AddWhat Is an Algorithm?
Lesson 10.2: Use Place Value to AddAdding Your Way
Using Fewer Digits
Lesson 10.5: Choose a Strategy to Add or SubtractDetermining Sums of 2 or More Addends

Unit 4: Fractions

Module 13: Understand Fractions as Numbers

Lesson 13.4: Represent and Name Fractions on a Number LineFractions on the Number Line
Lesson 13.5: Express Whole Numbers as FractionsCat Crossing
Lesson 13.6: Represent and Name Fractions Greater Than 1Location, Location, Location

Unit 5: Measurement and Data

Module 18: Represent and Interpret Data

Lesson 18.4: Make a Bar GraphPuppy Pile
2, 5, or 10?
Egg-cellent Pick
Lesson 18.5: Use Line Plots to Display Measurement DataHow Long Is It?
More Precise Measurements
Same Lengths, Different Names
Lesson 18.6: Make Line Plots to Display Measurement DataThe Plot Chickens
Let’s Make a Line Plot

Unit 6: Geometry

Module 19: Define Two-Dimensional Shapes

Lesson 19.1: Describe ShapesPiho’s Shapes
Lesson 19.4: Define QuadrilateralsRectangles, Squares, and Rhombuses

Module 20: Categorize Two-Dimensional Shapes

Lesson 20.1: Draw QuadrilateralsMore Quadrilaterals

Grade 4

Unit 1: Place Value and Whole Number Operations

Module 3: Interpret and Solve Problem Situations

Lesson 3.1: Explore Multiplicative ComparisonsSticker Mania
Lesson 3.4: Use Comparison to Solve Problem SituationsRepresenting “Times as Many”
Going Swimming

Unit 2: Multiplication and Division Problems

Module 4: Mental Math and Estimation Strategies

Lesson 4.3: Estimate Products by 1-Digit NumbersA Reasonable Answer

Module 5: Multiply by 1-Digit Numbers

Lesson 5.1: Represent MultiplicationInvestigate: Packing Lei
Lesson 5.2: Use Area Models and the Distributive Property to MultiplyCounting Flowers for Lei
Lesson 5.4: Multiplying Using Partial ProductsThree of a Kind
Lesson 5.6: Multiplying 3-Digit and 4-Digit NumbersA Lei Making Workshop

Unit 3: Extend and Apply Multiplication

Module 8: Extend and Apply Multiplication

Lesson 8.1: Multiply with TensGrowing Flowers for the Lei
Lesson 8.3: Relate Area Model and Partial ProductsDouble Decomposition
Lesson 8.4: Multiplying Using Partial ProductsRevisiting Strategies
Lesson 8.7: Solve Multi-step Problems and Assess ReasonablenessHow Many Supplies?

Unit 4: Fractions and Decimals

Module 10: Algebraic Thinking and Number Theory

Lesson 10.1: Investigate FactorsHamster Homes
Lesson 10.2: Identify FactorsFactor or Multiple?
Lesson 10.4: Identify Prime and Composite NumbersA Number Game
Lesson 10.5 Generate and Analyze Number PatternsHow Does It Grow?

Module 11: Fraction Equivalence and Comparison

Lesson 11.1: Compare Fractions Using Viaula ModelsInvestigate: Building Your Own Number Line
Lesson 11.2: Compare Fractions Using BenchmarksFraction Strips
Lesson 11.6: Compare Fractions Using Common DenominatorsChop It
Lesson 11.7: Use Comparison to Order FractionsAll Kinds of Fractions

Module 12: Relate Fractions and Decimals

Lesson 12.1: Represent Tenths as Fractions and DecimalsA New Way to Write Tenths
Lesson 12.2 Represent Hundredths as Fractions and DecimalsA New Way to Write Hundredths
Lesson 12.3: Identify Equivalent Fractions and DecimalsAre They Equivalent?
Lesson 12.4: Compare DecimalsHow Can You Compare?
Robot Factory
What’s the Order

Module 13: Use Fractions to Understand Angles

Lesson 13.2: Explore AnglesAngle Adventures
Lesson 13.3: Relate Angles to Fraction Part of a CircleThe Spin on Angles
Lesson 13.6: Join and Separate AnglesAngles in Motion

Module 14: Understand Addition and Subtraction of Fractions with Like Denominators

Lesson 14.2: Joining Parts of the Same WholePizza Problems

Module 15: Add and Subtract Fractions and Mixed Numbers with Like Denominators

Lesson 15.1: Add and Subtract Fractions to Solve ProblemsMath Pizzeria

Unit 6: Two-Dimensional Figures and Symmetry

Module 18: Symmetry and Patterns

Lesson 18.3: Generate and Identify Shape PattersHow Does It Grow?

Grade 5

Unit 1: Whole Numbers, Expressions, and Volume

Module 1: Whole Number Place Value and Multiplication

Lesson 1.3: Use a Pattern to Multiply by Multiplies of 10, 100, and 1000Partial Products Everywhere
Monarch Butterflies
All About That Base
Lesson 1.5: Multiply Multi-Digit NumbersHow Do They Compare?

Module 2: Understand Division of Whole Numbers

Lesson 2.4: Use Partial QuotientsEmptying the Water Tank

Module 5: Volume

Lesson 5.2: Understand VolumeWhich is Largest
Lesson 5.3: Estimate VolumePacking the Barge
Lesson 5.6: Find Volume of Composed FiguresPutting it Together
Figures Made of Prisms

Unit 3: Multiplying Fractions and Mixed Numbers

Module 8: Understand Multiplication of Fractions

Lesson 8.1: Explore Groups of Equal Shares to Show MultiplicationInvestigate: Sharing Sandwiches
Investigate: Folding Paper
Lesson 8.2: Represent Multiplication of Whole Numbers by FractionsSharing More Sandwiches
Lesson 8.3: Represent Multiplication with Unit FractionOne Part of One Part
Lesson 8.4: Represent Multiplication of FractionsDance Breaks
Parts of Parts
Making Food
Lesson 8.5: Use Representations of Area to Develop ProceduresOne Part of One Part
Installing Turf
Rows and Columns
Lesson 8.6: Interpret Fraction Multiplication as ScalingChores at Animal Haven
The Re-size-inator
Lesson 8.7: Multiplying FractionsMessy Multiplication

Module 9: Understand and Apply Multiplication of Mixed Numbers

Lesson 9.3: Practice Multiplication with Fractions and Mixed NumbersMessy Multiplication
Applying Fraction Multiplication

Unit 4: Divide Fractions and Convert Customary Units

Module 10: Understand Division with Whole Numbers and Unit Fractions

Lesson 10.1: Interpret a Fraction as DivisionDivision Story Problems
Making Generalizations

Unit 5: Add and Subtract Decimals

Module 13: Decimal Place Value

Lesson 13.1: Understand ThousandthsWhat Is One Thousandth?
Lesson 13.2: Read and Write Decimals to ThousandthsSay What?
Lesson 13.3: Round DecimalsWhich Way Down the Mountain?
Rounding Races
Lesson 13.4: Compare and Order DecimalsInvestigate: Numbers Between Numbers
The Claw
Selling Collectibles

Unit 6: Multiply Decimals

Module 15: Multiply Decimals and Whole Numbers

Lesson 15.1: Understand Decimal Multiplication PatternsPlace Value Patterns
Powers of 10 Parade

Unit 7: Divide Decimals and Convert Customary Units

Module 17: Understand Decimal Division Patterns

Lesson 17.1: Understand Decimal Division PatternsPowers of 10 Parade

Unit 8: Graphs, Patterns, and Geometry

Module 19: Graphs and Patterns

Lesson 19.1: Describe a Coordinate SystemCreating a Coordinate System
Lesson 19.2: Understand Ordered PairsBullseye!
Lesson19.4: Generate and Identify Numerical PattermsCoordinating Satellite Repairs

Grade 6

Unit 1: Number Systems and Operations

Module 1: Integer Concepts

Lesson 1: Identify and Interpret IntegersCan You Dig It?
Lesson 2: Compare and Order Integers on a Number LineOrder in the Class

Module 3: Fraction Division

Lesson 1: Understand Fraction DivisionFlour Planner
Fill the Gap

Module 4: Fluency with Multi-Digit Decimal Operations

Lesson 1: Add and Subtract Multi-Digit DecimalsDishing Out Decimals
Decimal Diagrams and Algorithms
Lesson 4: Divide Multi-Digit DecimalsMovie Time

Unit 2: Ratio and Rate Reasoning

Module 5: Ratio and Rates

Lesson 1: Understand the Concept and Language of RatiosPizza Maker
Lesson 2: Represent Ratios and Rates with Tables and GraphsFruit Lab
Disaster Preparation
Lesson 3: Compare Ratios and RatesModel Trains
Lesson 4: Find and Apply Unit RatesWorld Records
Lesson 5: Solve Ratio and Rate Problems Using Proportional ReasoningWelcome to the Robot Factory
More Soft Serve

Module 6: Apply Ratios and Rates to Measurement

Lesson 2: Use Rate Reasoning to Convert withing Measurement SystemsSoft Serve
Many Measurements

Module 7: Understand, Express, and Compare Percent Ratios

Lesson 1: Understand, Express, and Compare Percent RatiosLucky Duckies

Unit 3: Expressions, Equations, and Inequalities

Module 8: Numerical and Algebraic Expressions

Lesson 3: Write Algebraic Expressions to Model SituationsProducts and Sums

Module 9: Solve Problems Using Equations and Inequalities

Lesson 1: Write Equations to Represent SituationsWeight for It
Five Equations
Lesson 2: USe Additions and Subtraction Equations to Solve ProblemsHanging Around
Hanging It Up
Lesson 3: Use Multiplication and Division Equations to Solve ProblemsHanging Around
Hanging It Up
Lesson 4: Use One-Step Equations to Solve a Variety of ProblemsSwap and Solve
Lesson 5: Write and Graph InequalitiesTunnel Travels

Module 10: Real-World Relationships Between Variables

Lesson 1: Represent Equations in Tables and GraphsSubway Fares
Lesson 2: Write Equations from Verbal DescriptionsSubway Fares

Unit 4: Relationships in Geometry

Module 11: Polygons on the Coordinate Plane

Lesson 4: Find the Perimeter and Area on the Coordinate PlaneShapes on a Plane

Module 12: Area of Triangles and Special Quadrilaterals

Lesson 1: Develop and Use the Formula for Area of ParallelogramsExploring Parallelograms, Part 1
Exploring Parallelograms, Part 2
Off the Grid, Part 1
Lesson 2: Develop and Use the Formula for Area of TrianglesExploring Triangles
Triangles and Parallelograms
Off the Grid, Part 2
Lesson 3: Develop and Use the Formula for Area of TrapezoidsPile of Polygons
Lesson 4: Find Area of Composite FiguresPuzzling Areas
Letters

Module 13: Surface Area and Volume

Lesson 1: Explore Nets and Surface AreaRenata’s Stickers

Unit 5: Data Collection and Analysis

Module 14: Data Collection and Displays

Lesson 2: Display Data in Dot PlotsMinimum Wage
Lesson 3: Make Histograms and Frequency TablesThe Plot Thickens

Module 15: Measure of Center

Lesson 2: Find Measures of CenterToy Cars
Lesson 3: Choose a Measure of CenterHoops

Grade 7

Unit 1: Proportional Relationships

Module 1: Identify and Represent Proportional Relationships

Lesson 1: Explore RelationshipsPaint
Lesson 2: Recognize Proportional Relationships in TablesTwo and Two
Lesson 3: Compute Unit Rates Involving FractionsDinoPops
Lesson 4: Recognize Proportional Relationships in GraphsScale Factor Challenges
Lesson 5: Use Proportional Relationships to Solve Rate ProblemsScaling Robots
Lesson 6: Practice Proportional Reasoning with Scale DrawingsScaling Machines
Make it Scale
Tiles
Will It Fit

Module 2: Proportional Reasoning with Percents

Lesson 1: Percent ChangeMosaics
Percent Machines
Lesson 2: Markups and DiscountsMore and Less
All the Equations
Lesson 3: Taxes and Gratuities100%
Lesson 5: Simple InterestBack in My Day

Unit 2: Rational Number Operations

Module 3: Understand Addition and Subtraction of Rational Numbers

Lesson 1: Add or Subtract a Positive Integer on a Number lineFloats and Anchors
Lesson 3: Use a Number Line to Add and Subtract Rational NumbersDraw Your Own

Module 4: Add and Subtract Rational Numbers

Lesson 1: Compute Sums of IntegersMore Floats and Anchors
Lesson 2: Compute Differences of IntegersMore Floats and Anchors
Lesson 4: Apply Properties to Multi-step Addition and Subtraction ProblemsInteger Puzzles

Unit 3: Model with Expressions, Equations, and Inequalities

Module 7: Solve Problems Using Expressions and Equations

Lesson 1: Write Linear Expressions in Different Forms for Different SituationsCollect the Squares
Lesson 3: Write Two-Step Equations for SituationsKeeping it True
Lesson 5: Apply Two-Step Equations fo Find Angle MeasuresFriendly Angles
Missing Measures

Module 8: Solve Problems Using Inequalities

Lesson 1: Understand and Apply Properties to Solve One-Step InequalitiesI Saw the Signs
Lesson 2: Write Two-Step Inequalities for SituationsUnbalanced Hangers
Shira the Sheep
Lesson 3: Apply Two-Step Inequalities to Solve ProblemsBudgeting
Write Them and Solve Them

Unit 4: Geometry

Module 9: Draw and Analyze Two-Dimensional Figures

Lesson 2: Draw Circles and Other FiguresCan You Build It

Module 10: Analyze Figures to Find Circumference and Area

Lesson 1: Derive and Apply Formulas for CircumferenceMeasuring Around
Lesson 2: Derive and Apply a Formula for the Area of a CircleWhy Pi?
Lesson 4: Areas of Composite FiguresArea Challenges

Unit 5: Sampling and Data Analysis

Module 13: Use Statistics and Graphs to Compare Data

Lesson 3: Compare Means Using MAD and Repeated SamplingCrab Island

Module 14: Understand and Apply Experimental Probability

Lesson 1: Understand Probability of an EventHow Likely
Lesson 2: Find Experimental Probability of Simple EventsProb-bear-bilities

Module 15: Find Theoretical Probability of Simple Events

Lesson 1: Find Theoretical Probability of Simple EventsIs It Fair?

Grade 8

Unit 1: Transformational Geometry

Module 1: Transformations and Congruence

Module 2: Transformations and Similarity

Lesson 1: Investigate Reductions and EnlargementsSketchy Dilations
Lesson 2: Explore DilationsDilation Mini Golf
Lesson 3: Understand and Recognize Similar FiguresSocial Scavenger Hunt

Unit 2: Linear Equations and Applications

Module 3: Solve Linear Equations

Lesson 1: Solve Multi-Step Linear EquationsEquation Roundtable
Lesson 3: Apply Linear Equations

Module 4: Angle Relationships

Lesson 1: Develop Angle Relationships for TrianglesPuzzling It Out
Lesson 3: Explore Prarallel Lines Cut by a TransversalPuzzling It Out

Unit 3: Relationships and Functions

Module 5: Proportional Relationships

Lesson 2: Derive y = mxTurtle Time Trials
Lesson 3: Interpret and Graph Proportional RelationshipsTurtle Time Trials
Lesson 4: Compare Proportional RelationshipsTurtle Time Trials

Module 6: Understand and Analyze Functions

Lesson 1: Understand and Graph FunctionsGuess My Rule
Lesson 2: Derive and Interpret y = mx + bFlags
Translations
Lesson 3: Interpret Rat of Change and Initial ValueStacking Cups (Optional)
Lesson 4: Construct FunctionsWater Cooler
Lesson 5: Compare FunctionsUps and Downs
Lesson 6: Describe and Sketch Nonlinear FunctionsTurtle Crossing
The Tortoise and the Hare

Module 7: Systems of Linear Equations

Lesson 1: Represent Systems by GraphingMake Them Balance
Lesson 2: Solve Systems by GraphingLine Zapper

Unit 4: Statistics and Probability

Module 8: Scatter Plots

Lesson 1: Construct Scatter Plots and Examine AssociationRobots
Dapper Cats
Lesson 2: Draw and Analyze Trend LinesInterpreting Scatter Plots
Find the Fit (called Fit Fights in Desmos Math)
Lesson 3: Interpret Linear Data in ContextInterpreting Slopes
Scatter Plot City
Animal Brains

Module 9: Two-Way Tables

Lesson 1: Construct and Interpret Two-Way Frequency TablesFinding Associations
Lesson 3: Interpret Two-Way Relative Freqency TablesFinding Associations

Unit 5: Real Numbers and the Pythagorean Theorem

Module 10: Real Numbers

Lesson 2: Investigate RootsRoot Down

Module 11: The Pythagorean Theorem

Lesson 1: Prove the Pythagorean TheoremTriangle Tracing Turtle
Lesson 3: Apply the Pythagorean TheoremTaco Truck

Unit 6: Exponents, Scientific Notation, and Volume

Module 12: Exponents and Scientific Notation

Lesson 1: Know and Apply Properties of ExponentsCircles
Power Pairs
Lesson 2: Understand Scientific NotationSpecific and Scientific (formerly Solar System)
Lesson 3: Compute with Scientific NotationBalance the Scale

Module 13: Volume

Lesson 1: Find Volume of CylindersCylinders
Lesson 2: Find Volumes of ConesCones

Algebra 1

Intro/Launch

Unit 1: Real Numbers and Connections to Algebra

Module 2: Linear Equations and Inequalities in One Variable

Lesson 2.2: Write and Solve EquationsWorking Backwards
Solving Strategies
Same Position
Lesson 2.3: Rewrite Formulas and Solve Literal EquationsVarious Variables
Lesson 2.4: Write and Solve InequalitiesPizza Delivery

Unit 2: Linear Functions and Equations

Module 3: Linear Equations in Two Variables

Lesson 3.1: Linear Equations in Standard FormShelley the Snail
Five Representations
Lesson 3.2: Slopes of Lines and Rates of ChangePlane, Train, and Automobile

Module 4: Linear Functions and Models

Lesson 4.3: Characteristics of Linear FunctionsCraft-a-Graph

Module 5: Relationships Among Linear Functions

Lesson 5.3: Compare Linear FunctionsSubway Seats
Lesson 5.4: Inverses of Linear FunctionsChip the Robot

Unit 3: Build Linear Functions and Models

Module 6: Fit Linear Functions to Data

Lesson 6.1: Scatter Plots, Correlation, and Fitted LinesCorrelation Coefficient
How Hot Is It?
City Slopes
Behind the Headlines
City Data
Lesson 6.2: Residualts and Best-Fit LinesResidual Fruit
Penguin Populations

Module 7: Discrete Linear Functions

Lesson 7.1: Arithmetic Sequences Defined RecursivelySequence Carnival
Lesson 7.2: Arithmetic Sequences Defined ExplicitlyMore Visual Patterns

Module 8: Piecewise-Defined Functions

Lesson 8.1: Graph Piecewise-Defined FunctionsPumpkin Prices

Unit 4: Linear Systems

Module 9: Systems of Linear Equations

Lesson 9.1: Solve Linear Systems by GraphingLizard Lines
Lesson 9.2: Solve Linear Systems by SubstitutionShape It Up

Module 10: Linear Inequalities

Lesson 10.2: Graph Systems of Linear InequalitiesQuilts
Seeking Solutions

Unit 5: Exponential Functions and Equations

Module 11: Exponential Functions and Models

Lesson 11.1: Exponential Growth FunctionsCarlos’s Fish

Unit 6: Build Exponential Functions and Models

Module 13: Fit Exponential Functions to Data

Lesson 13.1: Scatter Plots and Fitted Exponential CurvesDetroit’s Population, Part 1
Detroit’s Population, Part 2

Module 14: Discrete Exponential Functions

Lesson 14.1: Geometric Sequences Defined RecursivelySequence Carnival
Lesson 14.2: Geometric Sequences Defined ExplicitlyMore Visual Patterns

Unit 8: Quadratic Functions and Equations

Module 17: Use Graphing and Factoring to Solve Quadratic Equations

Lesson 17.1: Solve Quadratic Equations by Graphing Quadratic FunctionsRevisiting Visual Patterns, Part 1
Quadratic Visual Patterns
On the Fence
Plenty of Parabolas
Lesson 17.3: Solve Quadratic Equations by Factoring ax^2+bx+cStomp Rockets
Two for One
Robot Launch
Lesson 17.4: Use Special Factoring Patterns to Solve Quadratic EquationsParabola Zapper
Shooting Stars

Module 18: Use Square Roots to Solve Quadratic Equations

Lesson 18.2: Solve Quadratic Equations by Completing the SquareSquare Tactic
Lesson 18.3: Use the Quadratic Formula to Solve EquationsStomp Rockets in Space

Unit 9: Function Analysis

Module 20: Function Analysis

Lesson 20.1: Choose Among Linear, Exponential, and Quadratic ModelsSorting Relationships

Unit 10: Data Analysis

Module 22: Numerical Data

Lesson 22.1: Data Distributions and Appropriate StatisticsFinding Desmo

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Grade 6

Unit 1: Area and Surface Area

Lesson 2: Finding Area by Decomposing and RearrangingShapes on a Plane
Lesson 3: Reasoning to Find AreaLetters
Lesson 4: ParallelogramsExploring Parallelograms, Part 2
Lesson 5: Bases and Heights of ParallelogramsExploring Parallelograms, Part 1
Lesson 6: Areas of ParallelogramsOff the Grid, Part 1
Lesson 7: From Parallelograms to TrianglesTriangles and Parallelograms
Lesson 8: Areas of TrianlgeExploring Triangles
Lesson 10: Bases and Heights of TrianglesOff the Grid, Part 2
Lesson 11: PolygonsPile of Polygons
Lesson 15: More Nets, More Surface AreaRenata’s Stickers

Unit 2: Introducing Rations

Lesson 3: RecipesPizza Maker
Lesson 5: Defining Equivalent RatiosFruit Lab
Lesson 12: Navagating a Table of Equivalent RationsDisaster Preparation

Unit 3: Unit Rates and Percentages

Lesson 1: Anchoring Units of MeasureMany Measurements
Lesson 4: Comparing Speeds and PriceWorld Records
Lesson 5: Interpreting RatesSoft Serve
Lesson 6: Equivalent Ratios Have the Same Unit RatesWelcome to the Robot Factory
Lesson 8: Solving Rate ProblemsMore Soft Serve
Lesson 9: More about Constant SpeedModel Trains
Lesson 11: Representing Percentages with Double Number Line DiagramsLucky Duckies

Unit 4: Dividing Fractions

Lesson 4: How Many Groups? (Part 1)Flour Planner
Lesson 6: Using Diagrams to Find the Number of GroupsFill the Gap
Lesson 13: Rectangles with Fractional Side LengthsPuzzling Areas

Unit 5: Arithmetic in Base 10

Lesson 1: Using Decimals in Shopping ContextDishing Out Decimals

Unit 5: Arithmetic in Base 11

Lesson 2: Using Diagrams to Represent Addition and SubtractionDecimal Diagrams and Algorithms

Unit 5: Arithmetic in Base 12

Lesson 15: Making and Measuring BoxesMovie Time

Unit 6: Expressions and Equations

Lesson 1: Tape Diagrams and EquationsFive Equations
Weight for It
Lesson 3: Staying in BalanceHanging Around
Lesson 4: Practice Solving EquationsHanging It Up
Lesson 5: Represent Situations with EquationsSwap and Solve
Lesson 9: The Distributive Property: Part 1Products and Sums
Lesson 17: Two Related Quantaties, Part 2Subway Fares

Unit 7: Rational Numbers

Lesson 3: Comparing Positive and Negative NumbersOrder in the Class
Lesson 5: Using Negative Numbers to Make Sense in ContextMinimum Wage
Lesson 8: Writing and Graphing InequalitiesTunnel Travels

Unit 8: Data Sets and Distributions

Lesson 5: Using Dot Plots to Answer Statistical QuestionsMinimum Wage
Lesson 6: Interpreting HistogramsThe Plot Thickens
Lesson 11: Variability and MADHoops
Lesson 13: MedianToy Cars

Grade 7

Unit 1: Scale Drawing

Lesson 1: What are scaled copies?Scaling Machines
Lesson 2: Correspond Parts and Scale FactorsMake it Scale
Lesson 3: Making Scaled CopiesScaling Robots
Lesson 5: The Size of the Scale FactorScale Factor Challenges
Lesson 6: Scaling AreaTiles
Lesson 6: Scaling AreaWill It Fit

Unit 2: Introducing Proportional Relationships

Lesson 1: One of These Things is Not Like the OtherPaint
Lesson 5: Two Equations for Each RelationshipTwo and Two
Lesson 10: Introducing Graphs of Proportional RelationshipsDinoPops

Unit 3: Measuring Circles

Lesson 2: Exploring CirclesMeasuring Around
Lesson 7: Exploring the Area of a CircleWhy Pi?
Lesson 9: Applying Area of a CircleArea Challenges

Unit 4: Proportional Relationships and Percentages

Lesson 6: Increasing and DecreasingMosaics
100%
Lesson 7: One Hundred PercentMore and Less
Back in My Day
Lesson 8: Percent Increase and Decrease with EquationsAll the Equations
Lesson 11: Percentage ContextsPercent Machines

Unit 5: Rational Number Arithmetic

Lesson 3: Changing ElevationFloats and Anchors
Lesson 5: Representing SubtractionMore Floats and Anchors
Lesson 6: Finding DifferencesDraw Your Own
Lesson 13: Expressions with Rational NumbersInteger Puzzles

Unit 6: Expressions, Equations, and Inequalities

Lesson 9: Dealing with Negative NumbersKeeping it True
Lesson 13: Reintroducing InequalitiesI Saw the Signs
Lesson 14: Finding Solutions to Inequalities in ContextUnbalanced Hangers
Lesson 15: Efficiently Solving InequalitiesShira the Sheep
Lesson 16: Interpreting InequalitiesBudgeting
Lesson 17: Modeling with InequalitiesWrite Them and Solve Them
Lesson 20: Combining Like Terms (Part 1)Collect the Squares

Unit 7: Angles, Triangles, and Prisms

Lesson 2: Adjacent AnglesFriendly Angles
Lesson 5: Using Equations to Solve For Unknown AnglesMissing Measures
Lesson 7: Building Polygons (Part 2)Can You Build It

Unit 8: Probability and Sampling

Lesson 1: Mystery BagsHow Likely
Lesson 3: What are Probabilities?Prob-bear-bilities
Lesson 4: Estimating Probabilities through Repeated ExperimentsIs It Fair?
Lesson 13: What Make a Good Sample?Crab Island

Grade 8

Unit 1: Rigid Transformations and Congruence

Lesson 1: Moving the PlaneTransformers
Lesson 2: Naming the MovesSpinning, Flipping, Sliding
Lesson 3: Grid MovesMoving Day
Lesson 4: Making MovesTransformation Golf
Lesson 5: Coordinate MovesGetting Coordinated, Part 1
Lesson 6: Describing TransformationsGetting Coordinated, Part 2
Lesson 16: Parallel Lines and Angles in a TrianglePuzzling It Out
Lesson 17: Rotate and TesselateTessellate

Unit 2: Dilations, Similarity, and Introducing Slope

Lesson 1: Projecting and ScalingSketchy Dilations
Lesson 3: Dilations with No GridDilation Mini Golf
Lesson 7: Similar PolygonsSocial Scavenger Hunt

Unit 3: Linear Relationships

Lesson 1: Understanding Proportional RelationshipsTurtle Time Trials
Lesson 5: Introductions to Linear RelationshipsFlags
Lesson 6: More Linear RelationshipsStacking Cups (Optional)
Lesson 8: Translating y=mx+bTranslations
Lesson 9: Slopes Don’t Have to Be PositiveWater Cooler
Lesson 10: Calculating SlopeUps and Downs

Unit 4: Linear Equations and Systems

Lesson 5: Solve Any Linear EquationEquation Roundtable
Lesson 12: Systems of EquationsMake Them Balance
Lesson 13: Solving Systems of EquationsLine Zapper

Unit 5: Functions and Volume

Lesson 1: Inputs and OutputsGuess My Rule
Lesson 5: More graphs of FunctionsTurtle Crossing
Lesson 6: Even More Graphs of FunctionsThe Tortoise and the Hare
Lesson 13: The Volume of a CylinderCylinders
Lesson 15: The Volume of a ConeCones

Unit 6: Associations and Data

Lesson 3: What a Point on a Scatter Plot MeansRobots
Lesson 4: Fitting a Line to DataDapper Cats
Lesson 5: Describing Trends in Scatter PlotsInterpreting Scatter Plots
Lesson 6: Slope of a Fitted LineFind the FIt (called Fit Fights in Desmos Math)
Lesson 7: Observing More Patterns in Scatter PlotsScatter Plot City
Lesson 8: Analyzing Bivariate DataInterpreting Slopes
Lesson 9: Looking for AssociationAnimal Brains
Lesson 10: Using Data Displays to Find AssociationFinding Associations

Unit 7: Exponents and Scientific Notation

Lesson 1: Exponent ReviewCircles
Lesson 6: What about Other Bases?Power Pairs
Lesson 12: Applicatios of Arithmetic with Powers of 10Balance the Scale
Lesson 13: Definition of Scientific NotationSpecific and Scientific (formerly Solar System)

Unit 8: Pythagorean Theorem and Irrational Numbers

Lesson 5: Square Roots on the Number LineRoot Down
Lesson 7: Finding Side Lengths of TrianglesTriangle Tracing Turtle
Lesson 11: Applications of the Pythagorean TheoremTaco Truck

Algebra 1

Intro/Launch

Unit 1: One Variable Statistics

Lesson 12: Standard DeviationFinding Desmo

Unit 2: Linear Equations and Systems

Lesson 4: Equations and Their SolutionsWorking Backwards
Solving Strategies
Same Position
Lesson 5: Equations and Their GraphsShelley the Snail
Five Representations
Lesson 6: Equivalent EquationsSubway Seats
Lesson 7: Explaining Steps for Rewriting EquationsVarious Variables
Lesson 12: Writing and Graphing Systems of Linear EquationsLizard Lines
Lesson 13: Solving Systems by SubstitutionShape It Up

Unit 3: Two Variable Statistics

Lesson 5: Fitting LinesCity Slopes
Penguin Populations
Lesson 6: ResidualsResidual Fruit
Lesson 7: Correlation CoefficientCorrelation Coefficient
City Data
Lesson 8: Using the Correlation CoefficientHow Hot Is It?
Lesson 9: Causal RelationshipsBehind the Headlines

Unit 4: Linear Inequalities and Systems

Lessons 4-6: Graphing Linear Inequalities in Two VariablesPizza Delivery
Lesson 7: Solutions to Systems of Linear Inequalities in Two VariablesQuilts
Seeking Solutions
Lesson 8: Solving Problems with Systems of Linear Inequalities in Two VariablesCarlos’s Fish

Unit 5: Functions

Lesson 1: Describing and Graphing SituationsCraft-a-Graph
Lesson 7: Using Graphs to Find Average Rate of ChangePlane, Train, and Automobile
Lesson 12: Piecewise FunctionsPumpkin Prices
Lesson 15: Inverse FunctionsChip the Robot

Unit 6: Introduction to Exponential Functions

Unit 7: Introduction to Quadratic Functions

Lesson 1: A Different Kind of ChangeRevisiting Visual Patterns, Part 1
Quadratic Visual Patterns
Lesson 10: Graphs of Quadratic Functions in Standard and Factored FormsOn the Fence
Stomp Rockets
Plenty of Parabolas
Two for One
Lesson 11: Graphing Quadratics from the Factored FormParabola Zapper
Shooting Stars
Lesson 14: Quadratic Graphs that Represent SituationsRobot Launch

Unit 8: Quadratic Equations

Lesson 2: When and Why Do We Write Quadratic Equations?Sorting Relationships
Lesson 12-14: Completing the SquareSquare Tactic
Lesson 24: Using Quadratic Equations to Model Situation and Solve ProblemsStomp Rockets in Space

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Grade 6

Unit 1: Area and Surface Area

Illustrative MathematicsAmplify Classroom
Topic A: Reasoning to Find Area 
Lesson 1: Tiling the PlaneUnit 1
Lesson 1: Shapes on a Plane
Lesson 4: Parallelograms
Lesson 5: Bases and Heights of Parallelograms
Lesson 6: Area of Parallelograms
Unit 1
Lesson 3: Exploring Parallelograms
Topic 3: Triangles
Lesson 7: From Parallelograms to TrianglesUnit 1
Lesson 3: Exploring Parallelograms
Topic 5: Surface Area
Lesson 12: What is Surface Area?Unit 1
Lesson 10: Renata’s Stickers

Unit 2: Introducing Ratios

Topic 1: Introducing Ratios
Lesson 1: Introducing Ratios and Ratio LanguageUnit 2
Lesson 1: Pizza Maker
Lesson 2: Representing Ratios with DiagramsUnit 2
Lesson 1: Pizza Maker
Topic 2: Equivalent Ratios
Lesson 3: RecipesUnit 2
Lesson 4: Fruit Lab
Lesson 5: Defining Equivalent RatiosUnit 2
Lesson 1: Pizza Maker
Topic 4: Solving Ratio and Rate Problems
Lesson 11: Representing Ratios with TablesUnit 2
Lesson 10: Disaster Preparation

Unit 3: Rates and Percentages

Topic 2: Unit Conversion
Lesson 2: Anchoring Units of MeasurementUnit 3
Lesson 1: Many Measurements
Topic 3: Rates
Lesson 5: Comparing Speeds and PricesUnit 3
Lesson 6: Soft Serve
Lesson 6: Interpreting Rates
Lesson 7: Equivalent Ratios Have the Same Unit Rates
Unit 3
Lesson 6: Soft Serve
Topic 4: Percentages
Lesson 10: What Are percentagesUnit 3
Lesson 9: Lucky Duckies
Lesson 13: Benchmark percentagesUnit 3
Lesson 9: Lucky Duckies
Topic 5: Let’s Put It to Work 
Lesson 7: Equivalent Ratios Have the Same Unit RatesUnit 3
Lesson 6: Soft Serve

Unit 4: Dividing Fractions

Topic 2: Meanings of Fraction Division
Lesson 4: How Many Groups (Part 1)Unit 4
Lesson 3: Flour Planner 
Lesson 6: Using Diagrams to Find the Number of GroupsUnit 4
Lesson 6: Fill the Gap

Unit 5: Arithmetic in Base Ten

Topic 1: Warming Up to Decimals 
Lesson 1: Using Decimals in a Shopping ContextUnit 5
Lesson 1: Dishing Out Decimals
Topic 5: Let’s Put It to Work
Lesson 14: Using Operations on Decimals to Solve ProblemsUnit 5
Lesson 13: Movie Time

Unit 6: Expressions and Equations

Lesson 1: Tape Diagrams and Equations
Lesson 2: Truth and Equations
Unit 6
Lesson 1: Weight for It
Lesson 3: Staying in BalanceUnit 6
Lesson 1: Weight for It
Topic 2: Equal and Equivalent
Lesson 8: Equal and EquivalentUnit 6
Lesson 1: Weight for It
Topic 9: The Distributive Property, Part 1Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 10: The Distributive Property, Part 2
Lesson 11: The Distributive Property, Part 3
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Topic 5: Let’s Put It to Work
Lesson 19: Tables, Equations, and Graphs, Oh My!Unit 6
Lesson 16: Subway Fares
Take Away (coming soon!)

Unit 7: Rational Numbers

Lesson 1: Positive and Negative NumbersUnit 7
Lesson 1: Can You Dig It?
Lesson 3: Comparing Positive and Negative Numbers
Lesson 4: Ordering Rational Numbers
Unit 7
Lesson 4: Order in the Class
Topic 2: Inequalities
Lesson 9: Solutions of Inequalities
Lesson 10: Interpreting Inequalities
Unit 7
Lesson 7: Tunnel Travels
Topic 3: The Coordinate Plane
Lesson 15: Shapes on the Coordinate PlaneUnit 1
Lesson 1: Shapes on a Plane

Unit 8: Data Sets and Distributions

Topic 2: Dot Plots and Distributions
Lesson 3: Representing Data Graphically
Lesson 4: Dot Plots
Lesson 5: Using Dot Plots to Answer Statistical Questions
Unit 8
Lesson 3: Minimum Wage
Lesson 6: Interpreting Histograms
Lesson 7: Using Histograms to Answer Statistical Questions
Lesson 8: Describing Distributions on Histograms
Unit 8
Lesson 5: The Plot Thickens
Topic 4: Median and IQR
Lesson 13: MedianUnit 8
Lesson 11: Toy Cars

Grade 7

Unit 1: Scale Drawings

Illustrative MathematicsAmplify Classroom
Topic 1: Scaled Copies 
Lesson 1: What are Scaled Copies?Unit 1
Lesson 1: Scaling Machines
Topic 2: Scale Drawings 
Lesson 7: Scale DrawingsUnit 1
Lesson 7: Will It Fit?

Unit 2: Introducing Proportional Relationships

Topic 1: Representing Proportional Relationships with Tables
Lesson 1: One of These Things Is Not Like the OthersUnit 2
Lesson 1: Paint 
Topic 2: Representing Proportional Relationships with Equations 
Lesson 4: Proportional Relationships with EquationsUnit 2
Lesson 6: Two and Two
Lesson 5: Two Equations for Each Relationship
Lesson 6: Using Equations to Solve Problems
Unit 2
Lesson 6: Two and Two
Topic 3: Comparing Proportional and Nonproportional Relationships 
Lesson 8: Comparing Relationships with EquationsUnit 2
Lesson 6: Two and Two
Topic 4: Representing Proportional Relationships with Graphs
Lesson 10: Introducing Graphs of Proportional Relationships
Lesson 11: Interpreting Graphs of Proportional Relationships
Lesson 12: Using Graphs to Compare Relationships
Lesson 13: Two Graphs for Each Relationship
Unit 2
Lesson 8: Dino Pops

Unit 3: Measuring Circles

Topic 1: Circumference of a Circle 
Lesson 1: How Well Can You Measure?Unit 3
Lesson 8: Toothpicks (coming soon!)
Lesson 2: Exploring Circles
Lesson 3: Exploring Circumference
Lesson 4: Applying Circumference
Unit 3
Lesson 3: Measuring Around
Take Away (coming soon!)
Topic 2: Area of a Circle
Lesson 7: Exploring the Area of a Circle
Lesson 8: Relating Area to Circumference
Unit 3
Lesson 9: Area Challenges
Take Away (coming soon!)

Unit 4: Proportional Relationships and Percentages

Topic 1: Proportional Relationships with Fractions 
Lesson 1: Lots of Flags
Lesson 2: Ratios and Rates with Fractions
Lesson 3: Revisiting Proportional Relationships
Lesson 4: Half as Much Again
Unit 4
Lesson 1: Mosaics
Topic 2: Percent Increase and Decrease 
Lesson 6: Increasing and DecreasingUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Topic 3: Applying Percentages
Lesson 10: Tax and Tip
Lesson 11: Percentage Contexts
Unit 4
Lesson 12: Posing Percent Problems (coming soon!)
Topic 4: Let’s Put It to Work 
Lesson 16: Posing Percent ProblemsUnit 4
Lesson 12: Posing Percent Problems (coming soon!)

Unit 5: Rational Number Arithmetic

Topic 1: Interpreting Negative Numbers 
Lesson 1: Interpreting Negative NumbersUnit 5
Lesson 1: Floats and Anchors
Topic 2: Adding and Subtracting Rational Numbers
Lesson 2: Changing Temperatures
Lesson 3: Changing Elevation
Unit 5
Lesson 4: Draw Your Own
Lesson 6: Subtracting Rational Numbers
Lesson 7: Adding and Subtracting to Solve Problems
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles

Unit 6: Expressions, Equations, and Inequalities

Topic 1: Representing Situations of the Form px + q and p(+ q) = r 
Lesson 1: Relationships Between QuantitiesUnit 2
Lesson 1: Paint
Unit 4
Lesson 1: Mosaics
Topic 9 Dealing with Negative Numbers 
Lesson 10: Different Options for Solving One EquationUnit 6
Lesson 10: Collect the Squares
Topic 3: Inequalities 
Lesson 13: Reintroducing InequalitiesUnit 6
Lesson 16: Shira the Sheep
Lesson 14: Finding Solutions to Inequalities in Context
Lesson 15: Efficiency Solving Inequalities
Unit 6
Lesson 16: Shira the Sheep
Lesson 16: Interpreting Inequalities
Lesson 17: Modeling with Inequalities
Unit 6
Lesson 16: Shira the Sheep
Topic 4: Writing Equivalent Expressions 
Lesson 18: Subtraction in Equivalent ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 20: Combining Like Terms (Part 1)
Lesson 21: Combining Like Terms (Part 2)
Lesson 22: Combining Like Terms (Part 3)
Unit 6
Lesson 10: Collect the Squares

Unit 7: Angles, Triangles, and Prisms

Lesson 2: Adjacent Angles
Lesson 3: Nonadjacent Angles
Unit 7
Lesson 2: Friendly Angles
Lesson 4: Solving for Unknown AnglesUnit 7
Lesson 2: Friendly Angles
Lesson 5: Using Equations to Solve for Unknown AnglesUnit 7
Lesson 4: Missing Measures
Topic 2: Drawing Polygons with Given Conditions 
Lesson 9: Drawing Triangles (Part 1)
Lesson 10: Drawing Triangles (Part 2)
Unit 7
Lesson 5: Can You Build It?

Unit 8: Probability and Sampling

Topic 1: Probabilities of Single Step Events
Lesson 1: Mystery Bags
Lesson 2: Chance Experiments
Lesson 3: What Are Probabilities?
Unit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities
Topic 3: Sampling
Lesson 11: Comparing Groups
Lesson 12: Larger Populations
Lesson 13: What Makes a Good Sample?
Lesson 14: Sampling in a Fair Way
Unit 8
Lesson 10: Crab Island
Topic 4: Using Samples
Lesson 15: Estimating Population Measures of Center
Lesson 16: Estimating Population Proportions
Unit 8 
Lesson 10: Crab Island
Lesson 17: More about Sampling Variability
Lesson 18: Comparing Populations Using Samples
Lesson 19: Comparing Populations with Friends
Unit 8
Lesson 10: Crab Island

Grade 8

Unit 1: Rigid Transformations and Congruence

Illustrative MathematicsAmplify Classroom
Topic 1: Rigid Transformations 
Lesson 1: Moving in the PlaneUnit 1
Lesson 1: Transformers
Lesson 2: Naming the MovesUnit 1
Lesson 2: Spinning, Flipping, Sliding
Lesson 3: Grid MovesUnit 1
Lesson 4: Moving Day
Lesson 4: Making the MovesUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Lesson 5: Coordinate MovesUnit 1
Lesson 4: Moving Day
Lesson 6: Describing TransformationsUnit 1
Lesson 6: Connecting the Dots (coming soon!)
Topic 2: Properties of Rigid Transformations 
Lesson 8: Rotation PatternsUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Topic 5: Let’s Put It to Work
Lesson 17: Rotate and TessellateLesson 13: Tessellate

Unit 2: Dilations, Similarity, and Introducing Slope

Topic 1: Dilations
Lesson 1: Projecting and ScalingUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 2: Circular Grid
Lesson 3: Dilations with No Grid
Lesson 4: Dilations on a Square Grid
Lesson 5: More Dilations
Unit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Topic 2: Similarity 
Lesson 6: SimilarityUnit 2
Lesson 6: Social Scavenger Hunt
Topic 3: Slope
Lesson 10: Meet SlopeUnit 3
Lesson 4: Flags

Unit 3: Linear Relationships

Topic 1: Proportional Relationships 
Lesson 1: Understanding Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 2: Graphs of Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 3: Representing Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials 
Topic 2: Representing Linear Relationships
Lesson 5: Introduction to Linear RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 7: Representations of Linear RelationshipsUnit 3
Lesson 4: Flags
Topic 3: Finding Slopes 
Lesson 9: Slopes Don’t Have to be PositiveUnit 3
Lesson 4: Flags
Lesson 11: Equations of All Kinds of LinesUnit 3
Lesson 4: Flags
Topic 4: Linear Equations 
Lesson 13: More Solutions to Linear EquationsUnit 3 
Lesson 4: Flags

Unit 4: Linear Equations and Linear Systems

Topic 2: Linear Equation in One Variable 
Lesson 5: Solving Any Linear EquationUnit 4
Lesson 5: Equation Roundtable
Lesson 6: Strategic SolvingUnit 4
Lesson 5: Equation Roundtable
Topic 3: Systems of Linear Equations
Lesson 11: On Both of the Lines
Lesson 12: Systems of Equations
Lesson 13: Solving Systems of Equations
Unit 4
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Unit 5: Functions and Volume

Topic 1: Inputs and Outputs 
Lesson 1: Inputs and OutputsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 2: Introduction to FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Topic 2: Representing and Interpreting Functions 
Lesson 3: Equations of FunctionsUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Tables, Equations, and Graphs of Functions
Lesson 5: More Graphs of Functions
Unit 5
Lesson 5: The Tortoise and the Hare
Topic 3: Linear Functions and Rates of Change
Lesson 8: Linear FunctionsUnit 3
Lesson 4: Flags
Lesson 9: Linear ModelsUnit 5
Lesson 5: The Tortoise and the Hare
Topic 4: Cylinder and Cones 
Lesson 13: The Volume of a CylinderUnit 5
Lesson 11: Cylinders
Lesson 14: Finding Cylinder DimensionsUnit 5
Lesson 11: Cylinders
Lesson 15: The Volume of a ConeUnit 5
Lesson 13: Cones
Lesson 16: Finding Cone DimensionsUnit 5
Lesson 13: Cones

Unit 6: Associations in Data

Topic 2: Associations in Numerical Data 
Lesson 3: What a Point in a Scatter Plot MeansUnit 6 
Lesson 3: Robots
Lesson 4: Fitting a LineUnit 6 
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Lesson 5: Describing Trends in Scatter PlotsUnit 6 
Lesson 3: Robots
Lesson 7: Observing More patterns in Scatter PlotsUnit 6 
Lesson 3: Robots
Topic 3: Associations in Categorical data 
Lesson 9: Looking for AssociationsUnit 6
Lesson 11: Finding Associations
Lesson 10: Using Data Displays to Find associationsUnit 6
Lesson 11: Finding Associations

Unit 7: Exponents and Scientific Notation

Topic 1: Exponent Review 
Lesson 1: Exponent ReviewUnit 7 
Lesson 1: Circles
Lesson 2: Multiplying Powers of 10
Lesson 3: Powers of Powers of 10
Lesson 4: Dividing Powers of 10
Unit 7 
Lesson 3: Power Pairs
Topic 3: Scientific Notation 
Lesson 13: Defining Scientific Notation
Lesson 14: Multiplying, Dividing, and Estimating with Scientific Notation
Unit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale
Lesson 15: Adding and Subtracting with Scientific NotationUnit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Unit 8: Pythagorean Theorem and Irrational Numbers

Topic 1: Side Lengths and Areas of Squares
Lesson 5: Reasoning about Square RootsUnit 8
Lesson 4: Root Down
Topic 2: The Pythagorean Theorem
Lesson 6: Finding Side Lengths of TrianglesUnit 8
Lesson 8: Triangle-Tracing Turtle
Lesson 10: Applications of the Pythagorean TheoremUnit 8
Lesson 10: Taco Truck
Topic 5: Let’s Put It to Work
Lesson 16: When Is the Same Size Not the Same Size?Unit 8
Lesson 10: Taco Truck

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Eureka Math²

Level K

Module 1: Counting and Cardinality

Topic A: Classify to Make Categories and Count

Lesson 1: Compare objects based on their attributes.Connecting Cubes
Lesson 3: Classify objects into two categories and count.Skye’s Style

Topic B: Answer How Many Questions with Up to 5 Objects

Lesson 3: Sort by Same ColorMatching Groups

Topic C: Write Numerals and Create Sets of Up to 5 Objects

Lesson 10: Count out a group of objects to match a numeral.Designing Shoes with Skye

Topic E: Answer How Many Questions with Up to 10 Objects

Lesson 19: Organize, count, and represent a collection of objects.Investigate: Cafeteria Math
Lesson 20: Count objects in 5-group and array configurations and match to a numeral.Fingers as Math Tools
Lesson 23: Conserve number regardless of the order in which objects are counted.Moving and Grooving

Module 2: Two- and Three- Dimensional Shapes

Topic A: Analyze and Name Two-Dimensional Shapes

Lesson 1: Find and describe attributes of flat shapes.So Much Sorting
Lesson 2: Classify shapes as triangles or nontriangles.What’s That Shape Called?
Lesson 3: Classify shapes as circles, hexagons, or neither.What’s That Shape Called?
Lesson 4: Classify shapes as rectangles or nonrectangles, with square rectangles as a special case.Another Shape

Module 3: Comparison

Topic C: Compare Sets Within 10

Lesson 12: Relate more and fewer to length.More, Fewer, or the Same
Forest Friends
Lesson 13: Compare sets by using more than, fewer than, and the same number as.Fingers and Counters
Comparing Words

Module 4: Composition and Decomposition

Topic A: Explore Composition and Decomposition

Lesson 1: Compose flat shapes and count the parts.Investigate: Casey’s Town
Lesson 2: Decompose flat shapes and count the parts.How Many Objects?
Lesson 3: Decompose a group to identify parts and total.How Many Objects in Pictures?

Topic B: Record Composition and Decomposition

Lesson 5: Sort to decompose a number in more than one way.How Will You Count?
Lesson 6: Decompose a number in more than one way and record.Harry Explores the Ocean

Module 5: Addition and Subtraction

Topic A: Represent Addition

Lesson 1: Represent add to with result unknown story problems by using drawings and numbers.What Does It Mean to Add?

Topic B: Represent Subtraction

Lesson 8: Understand taking away as a type of subtraction.What Does It Mean to Subtract?

Topic C: Make Sense of Problems

Lesson 15: Identify the action in a problem to represent and solve it.The Bus Depot

Level 1

Module 1: Counting, Comparison, and Addition

Topic A: Count and Compare with Data

Lesson 2: Organize and represent data to compare two categories.Shapes Ying Saw

Module 2: Addition and Subtraction Relationships

Topic A: Reason About Take From Situations

Lesson 1: Represent result unknown problems and record as addition or subtraction number sentences.Packing for a Picnic
Lesson 3: Subtract 1 or subtract 1 less than the total.What’s the Difference?
Leaping Lily Pads!

Topic B: Relate and Distinguish Addition and Subtraction

Lesson 5: Use the Read–Draw–Write process to solve result unknown problems.Investigate: Let’s Grow!
Lesson 6: Represent and solve related addition and subtraction result unknown problems.Tutu’s Garden in Maui
Lesson 7: Count on or count back to solve related addition and subtraction problems.The Kalo Plants

Topic C: Find an Unknown Part in Change Unknown Problems

Lesson 8: Interpret and find an unknown change.Replanting Huli
Lesson 11: Represent and solve take from with change unknown problems.Helping Others
A Community Working Together

Module 3: Properties of Operations to Make Easier Problems

Topic B: Make Easier Problems to Add

Lesson 9: Make ten with either addend.Making 10
Kitten Coaster

Topic D: Reason about Ten as a Unit to Add or Subtract

Lesson 16: Identify ten as a unit.Same Number, Different Ways

Module 5: Place Value Concepts to Compare, Add, and Subtract

Topic A: Grouping Units in Tens and Ones

Lesson 2: Count a collection and record the total in units of tens and ones.Investigate: Game Points
Meeting Yara
Lesson 4: Represent a number in multiple ways by trading 10 ones for a ten.It’s a Match
Lesson 6: Add 10 or take 10 from a two-digit number.How Many Cubes?

Topic D: Addition and Subtraction of Tens

Lesson 15: Count on and back by tens to add and subtract.Boris’s Thimbles
Lesson 16: Use related single-digit facts to add and subtract multiples of ten.How Many Tens?

Level 2

Module 1: Place Value Concepts Through Metric Measurement and Data · Place Value, Counting, and Comparing Within 1,000

Topic A: Representing Data to Solve Problems

Lesson 3: Use information presented in a bar graph to solve put together and take apart problems.Exploring Within 10
Ways to Make 10
Lesson 4: Use information presented in a bar graph to solve compare problems.Awesome Aquariums

Topic C: Estimate, Measure, and Compare Lengths

Lesson 12: Model and reason about the difference in length.Lengths of Jungle Animals

Topic D: Solve Compare Problems by Using the Ruler as a Number Line

Lesson 15: Use a measuring tape as a number line to add efficiently.Investigate: Where Am I?
Time to Line Up!
What’s That Number?
Lesson 17: Represent and solve comparison problems by using measurement contexts.Greater Than, Less Than, or Equal to

Module 2: Addition and Subtraction Within 200

Topic A: Simplifying Strategies for Addition

Lesson 1: Reason about addition with four addends.Investigate: Activities at the Block Party

Module 5: Money, Data, and Customary Measurement

Topic A: Problem Solving with Coins and Bills

Lesson 1: Organize, count, and represent a collection of coins.Discovering Coins (Part 1)
Discovering Coins (Part 2)
Lesson 2: Use the fewest number of coins to make a given value.How Much Money?
Lesson 5: Use different strategies to make 1 dollar or to make change from 1 dollar.The Toy Stand
Lesson 3: Solve one- and two-step word problems to find the total value of a group of coins.The Craft Stand at the Block Party

Topic B: Use Customary Units to Measure and Estimate Length

Lesson 12: Identify unknown numbers on a number line by using the interval as a reference point.In Full Bloom

Topic C: Use Measurement and Data to Solve Problems

Lesson 15: Use measurement data to create a line plot.Messy Measurements
“Lesson 16: Create a line plot to represent data and ask and answer questions.
60 min
Bracelets and Wristbands

Level 3

Module 1: Multiplication and Division with Units of 2, 3, 4, 5, and 10

Topic A: Conceptual Understanding of Multiplication

Lesson 2: Interpret equal groups as multiplication.Equal Groups

Topic C: Properties of Multiplication

Lesson 10: Demonstrate the commutative property of multiplication using a unit of 2 and the array model.Arrays of Flavor

Topic D: Two Interpretations of Division

Lesson 15: Model division as an unknown factor problem.It’s Chili in Here

Module 2: Place Value Concepts Through Metric Measurement

Topic A: Understanding Place Value Concepts Through Metric Measurement

Lesson 1: Connect the composition of 1 kilogram to the composition of 1 thousand.Investigate: Create a Photo Gallery

Topic C: Simplifying Strategies to Find Sums and Differences

Lesson 13: Collect and represent data in a scaled bar graph and solve related problems.Puppy Pile
Lesson 14: Use place value understanding to add and subtract like units.Adding Your Way
Lesson 15: Use the associative property to make the next ten to add.Panda Patterns
Lesson 16: Use compensation to add.How Would You Solve It?

Topic D: Two- and Three-Digit Measurement Addition and Subtraction

Lesson 20: Add measurements using the standard algorithm to compose larger units once.What is an Algorithm?
Using Fewer Digits
Lesson 21: Add measurements using the standard algorithm to compose larger units twice.Determining Sums of 2 or More Addends
Adding Strategically

Module 3: Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9

Topic B: Multiplication and Division Concepts with an Emphasis on the Unit of 7

Lesson 11: Use the break apart and distribute strategy to divide with units of 7.Relating Quotients to Familiar Products
Lesson 12: Solve one-step word problems involving multiplication and division.Division and Multiplication Equations

Module 4: Multiplication and Area

Topic A: Foundations for Understanding Area

Lesson 2: Recognize area as an attribute of polygons.Investigate: Comparing Rugs
Which Covers More Space?
Lesson 3: Tile polygons to find their areas.Tiling Figures
Area Hunt

Topic B: Concepts of Area Measurement

Lesson 6: Tile rectangles with squares to make arrays and relate the side lengths to area.Rectangles and Arrays
Lesson 7: Draw rows and columns to complete a rectangular array and determine its area.Area Hunt

Module 6: Geometry, Measurement, and Data

Topic D: Collecting and Displaying Dat

Lesson 23: Solve problems by creating scaled picture graphs and scaled bar graphs.2, 5, or 10?

Level 4

Module 1: Place Value Concepts for Addition and Subtraction

Topic A: Multiplication as Multiplicative Comparison

Lesson 1: Interpret multiplication as multiplicative comparison.How Does It Grow?

Module 2: Place Value Concepts for Multiplication and Division

Topic E: Factors and Multiples

Lesson 24: Recognize that a number is a multiple of each of its factors.Hamster Homes
Factor or Multiple?
Lesson 25: Explore properties of prime and composite numbers up to 100 by using multiples.A Number Game

Module 4: Foundations for Fraction Operations

Lesson 1: Decompose whole numbers into a sum of unit fractions.

Lesson 1: Decompose whole numbers into a sum of unit fractions.Investigate: Building Your Own Number Line
Lesson 3: Decompose fractions into a sum of fractions.Math Pizzeria
Lesson 4: Represent fractions by using various fraction models.Fraction Strips
Chop It
Lesson 5: Rename fractions greater than 1 as mixed numbers.All Kinds of Fractions

Topic D: Add and Subtract Fractions

Lesson 21: Solve addition and subtraction word problems and estimate the reasonableness of the answers.Pizza Problems

Topic F: Repeated Addition of Fractions as Multiplication

Lesson 32: Multiply a fraction by a whole number by using the associative property.Equal Groups of Fractions

Module 5: Place Value Concepts for Decimal Fractions

Topic A: Exploration of Tenths

Lesson 1: Organize, count, and represent a collection of money.Investigate: Different Units
Lesson 3: Represent tenths as a place value unit.A New Way to Write Tenths
Lesson 4: Write mixed numbers in decimal form with tenths.A New Way to Write Tenths

Topic B: Tenths and Hundredths

Lesson 5: Decompose 1 one and express hundredths in fraction form and decimal form.Are They Equivalent?
Lesson 6: Represent hundredths as a place value unit.A New Way to Write Hundredths
Lesson 7: Write mixed numbers in decimal form with hundredths.A New Way to Write Hundredths

Topic C: Comparison of Decimal Numbers

Lesson 10: Use pictorial representations to compare decimal numbers.How Can You Compare?
Lesson 11: Compare and order decimal numbers.Robot Factory
What’s the Order?

Level 5

Module 1: Place Value Concepts for Multiplication and Division with Whole Numbers

Topic B: Multiplication of Whole Numbers

Lesson 8: Multiply two- and three-digit numbers by two-digit numbers by using the distributive property.Partial Products Everywhere
Lesson 9: Multiply two- and three-digit numbers by two-digit numbers by using the standard algorithm.How Do They Compare?

Topic C: Division of Whole Numbers

Lesson 15: Divide three-digit numbers by two-digit numbers in problems that result in two-digit quotients.Emptying the Water Tank

Module 2: Addition and Subtraction with Fractions

Topic A: Fractions and Division

Lesson 1: Interpret a fraction as division.Investigate: Sharing Sandwiches
Sharing More Sandwiches
Dance Breaks
Lesson 3: Represent fractions as division by using models.Making Generalizations
Lesson 4: Solve word problems involving division and fractions.Division Story Problems

Module 3: Multiplication and Division with Fractions

Topic B: Multiplication of Fractions

Lesson 7: Multiply fractions less than 1 by unit fractions pictorially.Investigate: Folding Paper
Lesson 8: Multiply fractions less than 1 pictorially.Parts of Parts
One Part of One Part
Rows and Columns
Lesson 9: Multiply fractions by unit fractions by making simpler problems.Messy Multiplication
Lesson 10: Multiply fractions greater than 1 by fractions.Making Food
Installing Turf
Lesson 11: Multiply fractions.Applying Fraction Multiplication
Chores at Animal Haven
The Re-size-inator

Module 5: Addition and Multiplication with Area and Volume

Topic C: Volume Concepts

Lesson 17: Find the volume of right rectangular prisms by packing with unit cubes and counting.Which is Largest
Lesson 18: Find the volume of right rectangular prisms by packing with improvised units.Packing the Barge

Topic D: Volume and the Operations of Multiplication and Addition

Lesson 25: Find the volumes of solid figures composed of right rectangular prisms.Putting It Together
Figures Made of Prisms

Level 6

Module 1: Ratios, Rates, and Percents

Topic A: Ratios

Lesson 2: Introduction to RatiosPizza Maker

Topic B: Collections of Equivalent Ratios

Lesson 6: Ratios Tables and Double Number LinesFruit Lab
Lesson 9: Multiplication Patterns in Ratio RelationshipsDisaster Preparation

Topic D: Rates

Lesson 16: SpeedWorld Records
Lesson 17: RatesMany Measurements
Soft Serve
Lesson 18: Comparing RatesWelcome to the Robot Factory
Lesson 19: Unit Rates to Convert UnitsModel Trains
More Soft Serve
Lesson 20: Solving Rate ProblemsLucky Duckies

Module 2: Operations with Fractions and Multi-Digit Numbers

Topic B: Dividing Fractions

Lesson 6: Dividing a Whole Number by a FractionFlour Planner
Lesson 8: Dividing Fractions by Making Common DenominatorsFill the Gap

Topic C: Dividing Fractions Fluently

Lesson 9: Dividing Fractions by Using Tape DiagramsPuzzling Areas

Topic D: Decimal Addition, Subtraction, and Multiplication

Lesson 13: Decimal Addition and SubtractionDishing Out Decimals
Lesson 16: Applications of Decimal OperationsDecimal Diagrams and Algorithms

Topic F: Decimal Division

Lesson 21: Dividing a Decimals by a Whole NumberMovie Time
Lesson 22: Dividing a Decimal by a Decimal Greater than 1Movie Time
Lesson 23: Dividing a Decimal by a Decimal Less than 1Movie Time

Module 3: Rational Numbers

Topic A: Integers and Rational Numbers

Lesson 1: Positive and Negative NumbersCan You Dig It?
Lesson 3: Rational NumbersOrder in the Class

Module 4: Expressions and One-Step Equations

Topic B: Expressions and Real-World Problems

Lesson 9: Addition and Subtraction Expressions from the Real-WorldSubway Fares

Topic C: Equivalent Expressions Using the Properties of Operations

Lesson 13: The Distributive PropertyProducts and Sums

Topic D: Equations and Inequalities

Lesson 17: Equations and SolutionsFive Equations
Lesson 18: Inequalities and SolutionsHanging It Up
Tunnel Travels
Lesson 19: Solving Equations with Addition and SubtractionWeight for It
Lesson 20: Solving Equations with Multiplication and DivisionHanging Around
Lesson 21: Solving Problems with EquationsSwap and Solve

Module 5: Area, Surface Area, and Volume

Topic A: Areas of Polygons

Lesson 1: The Area of a ParallelogramExploring Parallelograms, Part 1
Lesson 2: The Area of a Right TriangleOff the Grid, Part 2
Lesson 3: The Area of a TriangleExploring Parallelograms, Part 2
Off the Grid, Part 1
Lesson 4: Areas of Triangles in Real-World SituationsExploring Triangles

Topic B: Problem Solving with Area

Lesson 5: Perimeter and Area in the Coordinate PlaneShapes on a Plane
Lesson 6: Problem Solving with Area in the Coordinate PlaneLetters
Lesson 7: Areas of Trapezoids and Other PolygonsTriangles and Parallelograms
Lesson 8: Areas of Composite Rigures in Real-World SituationsPile of Polygons

Topic C: Nets and Surface Area

Lesson 12: From Nets to Surface AreaRenata’s Stickers

Module 6: Statistics

Topic A: Understanding Distributions

Lesson 2: Describing a Data DistributionHoops
Lesson 3: Creating a Dot PlotMinimum Wage
Lesson 4: Creating a HistogramThe Plot Thickens

Topic B: Mean and Mean Absolute Deviation

Lesson 7: Using the Mean to Describe CenterToy Cars

Level 7

Module 1: Ratios and Proportional Relationships

Topic A: Understanding Proportional Relationships

Lesson 1: An Experiment with Ratios and RatesPaint
Lesson 2: Exploring Tables and Proportional RelationshipsTwo and Two
Lesson 4: Exploring Graphs of Proportional RelationshipsDinoPops

Topic C: Scale Drawing and Proportional Relationships

Lesson 14: Extreme BicyclesScaling Machines
Lesson 15: Scale DrawingScaling Robots
Lesson 16: Using Scale FactorScale Factor Challenges
Lesson 17: Finding Actual Distances from ScaleMake it Scale
Lesson 18: Relating Areas of Scale DrawingTiles
Will It Fit

Module 2: Operations with Rational Numbers

Topic A: Adding Rational Numbers

Lesson 2: Adding IntegersFloats and Anchors

Topic B: Subtracting Rational Numbers

Lesson 8: Subtracting Integers, Part 1More Floats and Anchors
Lesson 10: Subtracting Rational Numbers, Part 1Draw Your Own

Topic E: Numberical Expressions with Rational Numbers

Lesson 25: Writing and Evaluating Expressions with Rational NumbersInteger Puzzles

Module 3: Expressions, Equations, and Inequalities

Topic A: Equivalent Expressions

Lesson 1: Equivalent ExpressionsCollect the Squares

Topic B: Unknown Angle Measurements

Lesson 7: Angle Relationships and Unknown Angle MeasuresFriendly Angles

Topic C: Solving Equations

Lesson 11: Dominoes and DominoesKeeping it True

Topic D: Inequalities

Lesson 18: Understanding Inequalities and Their SolutionsI Saw the Signs
Lesson 19: Using Equations to Solve InequalitiesUnbalanced Hangers
Lesson 20: Preserving and ReversingShira the Sheep
Lesson 21: Solving Two-Step InequalitiesBudgeting
Lesson 22: Solving Problems Involving InequalitiesWrite Them and Solve Them

Module 4: Geometry

Topic A: Constructing Geometric Figures

Lesson 3: Side Lengths of a TriangleCan You Build It
Lesson 4: Angles of a TriangleFriendly Angles

Topic C: Circumference and Areas of Circles

Lesson 10: The Outside of a CicleMeasuring Around
Lesson 11: The Inside of a CircleWhy Pi?
Lesson 14: Composite Figures with Circular RegionsArea Challenges

Module 5: Percent and Applications of Percent

Topic A: Proportion and Percent

Lesson 3: Percent as a Rate per 100Mosaics
Lesson 4: Proportion and PercentMore and Less

Topic C: More of Less Than 100%

Lesson 10: Percent IncreaseAll the Equations

Topic D: Applications of Percent

Lesson 16: Markups and Discount100%
Lesson 18: Simple Interest – Solving for Unknown ValuesPercent Machines

Topic E: Problems Involving Percent

Lesson 20: Making Money, Day 1Back in My Day

Module 6: Probability and Populations

Topic A: Calculating and Interpreting Probabilities

Lesson 2: Empirical ProbabilityHow Likely
Lesson 4: Theoretical ProbabilityProb-bear-bilities

Topic B: Estimating Probabilities

Lesson 7: The Law of Large NumbersIs It Fair?

Topic C: Random Sampling

Lesson 11: Populations and SamplesCrab Island

Level 8

Module 1: Scientific Notation, Exponents, and Irrational Numbers

Topic A: Introduction to Scientific Notation

Lesson 2: Comparing Large NumbersSpecific and Scientific (formerly Solar System)
Lesson 4: Adding and Subtracting Numbers Written in Scientific NotationBalance the Scale

Topic B: Properties and Definitions of Exponents

Lesson 6: More Properties of ExponentsCircles
Lesson 7: Making Sense of the Exponent 0Power Pairs

Topic D: Perfect Squares, Perfect Cubes, and the Pythagorean Theorem

Lesson 18: The Pythagorean TheoremTriangle Tracing Turtle
Lesson 19: Using the Pythagorean TheoremTaco Truck
Lesson 23: Ordering Irrational NumbersRoot Down

Module 2: Rigid Motions and Congruent Figures

Topic A: Rigid Motion and Their Properties

Lesson 1: Motions in the PlaneTransformers
Moving Day
Lesson 2: TranslationsSpinning, Flipping, Sliding
Moving Day
Lesson 4: Translations and Reflections on the Coordinate PlaneGetting Coordinated, Part 1
Lesson 6: Rotations on the Coordinate PlaneGetting Coordinated, Part 2

Topic B: Rigid Motions and Congruent Figures

Lesson 8: Sequencing the Rigid MotionsTransformation Golf

Topic C: Angle Relationships

Lesson 12: Lines Cut by a TransversalPuzzling It Out

Module 3: Dilations and Similar Figures

Topic A: Dilations

Lesson 1: Exploring DilationsSketchy Dilations
Lesson 3: Reductions and More EnlargmentsDilation Mini Golf

Topic B: Properties of Dilations

Lesson 5: Figures and DilationsSocial Scavenger Hunt

Module 4: Linear Equations in One and Two Variables

Topic A: Linear Equations in One Variable

Lesson 3: Solving Linear Equations with Rational CoefficientsEquation Roundtable

Topic D: Slope of a Line

Lesson 16: Proportional Relationships and SlopeTurtle Time Trials
Lesson 17: Slopes of Rising LinesFlags
Ups and Downs
Lesson 18: Slopes of Falling LinesFlags
Water Cooler
Ups and Downs

Topic E: Different Forms of a Linear Equation

Lesson 20: Slope-Intercept form of the Equation of a LineStacking Cups (Optional)
Lesson 21: Slopes and Parallel LinesTranslations

Module 5: Systems of Linear Equations

Topic A: Solving Systems of Linear Equations Graphically

Lesson 1: Solving Problems with Equations and Their GraphsMake Them Balance

Topic B: Solving Systems of Linear Equations Algebraically

Lesson 6: Solving Systems of Linear Equations without GraphingLine Zapper

Module 6: Functions and Bivariate Statistics

Topic A: Functions

Lesson 1: Motion and SpeedTurtle Crossing
Lesson 2: Definition of a FunctionGuess My Rule

Topic B: Linear and Nonlinear Functions

Lesson 9: Increasing and Decreasing FunctionsThe Tortoise and the Hare

Topic C: Bivariate Numerical Data

Lesson 11: Scatter PlotsRobots
Dapper Cats
Lesson 12: Patterns in Scatter PlotsInterpreting Scatter Plots
Lesson 13: Informally Fitting a Line to DataFind the Fit (called Fit Fights in Desmos Math)
Lesson 14: Determining an Equation of a Line Fit to DataInterpreting Slopes
Lesson 15: Linear ModelAnimal Brains
Lesson 16: Using the Investigative ProcessScatter Plot City
Lesson 17: Analyzing the ModleScatter Plot City

Topic D: Bivariate Categorical Data

Lesson 18: Bivariate Categorical DataFinding Associations

Topic E: Volume

Lesson 22: Volume of a CylinderCylinders
Lesson 23: Volume of ConesCones

Algebra 1

Module 1: Expressions, Equations and Inequalities in One Variable

Lesson 1: The Growing Pattern of DucksMore Visual Patterns
Lesson 8: Solution Sets for Equations and Inequalities in One VariableSame Position
Lesson 9: Solving Linear Equations in One VariableWorking Backwards
Solving Strategies
Lesson 12: Rearranging FormulasSubway Seats
Various Variables
Shelley the Snail
Five Representations
Lesson 13: Solving Linear Inequalities in One VariablePizza Delivery
Lesson 21: Describing Variability in a Univariate Distribution with Standard DeviationFinding Desmo

Module 2: Equations and Inequalities in Two Variables

Lesson 1: Solution Sets of Linear Equations in Two VariablesSubway Seats
Various Variables
Shelley the Snail
Five Representations
Lesson 6: Applications of Linear Equations and InequalitiesSubway Seats
Various Variables
Shelley the Snail
Five Representations
Pizza Delivery
Lesson 8: Systems of Linear Equations in Two VariablesShape It Up
Lizard Lines
Lesson 12: Solution Sets of Systems of Linear InequalitiesQuilts
Lesson 13: Graphing Solution Sets of Systems of Linear InequalitiesSeeking Solutions
Lesson 16: Using Lines to Model Bivariate Quantitative DataCity Data
Lesson 17: Modeling Relationships with a LinePenguin Populations
Lesson 18: Calculating and Analyzing ResidualsResidual Fruit
Lesson 20: Interpreting CorrelationCorrelation Coefficient
How Hot Is It?
City Slopes
Lesson 21: Analyzing Bivariate Quantitative DataBehind the Headlines

Module 3: Functions and Their Representations

Lesson 7: Exploring Key Features of a Function and Its GraphCraft-a-Graph
Lesson 17: Piecewise Linear Functions in ContextPumpkin Prices

Module 4: Quadratic Functions

Topic A: Quadratic Functions and Their GraphsRobot Launch
Lesson 1: Falling ObjectsQuadratic Visual Patterns
Lesson 2: Projectile MotionStomp Rockets
Lesson 3: Analyzing Functions That Model Projectile MotionStomp Rockets in Space
Lesson 4: Graphs of Quadratic FunctionsOn the Fence
Plenty of Parabolas
Lesson 5: Solving Equations that Contain Factored ExpressionsShooting Stars
Lesson 11: Graphing Quadratic Functions from Factored FormTwo for One
Parabola Zapper
Lesson 14: Solving Quadratic Equations by Completing the SquareSquare Tactic
Lesson 27: Search and Rescue HelicopterCity Data

Module 5: Linear and Exponential Functions

Topic A: Arithmetic and Geometric SequencesMore Visual Patterns
Sequence Carnival
Lesson 8: Exponential FunctionsCarlos’s Fish
Topic A: Arithmetic and Geometric SequencesSequence Carnival
Topic A: Arithmetic and Geometric SequencesRevisiting Visual Patterns, Part 1
Lesson 18: Modeling PopulationsSorting Relationships
Lesson 20: Comparing Growth of FunctionsPlane, Train, and Automobile
Sorting Relationships

Module 6: Modeling with Functions

Topic A: Modeling Bivariate Quantitative DataCity Data
Topic B: Developing Models for ContextsDetroit’s Population, Part 1
Detroit’s Population, Part 2

Grade 6

Module 1: Composing and Decomposing

Topic 1: Factors and Multiples

MATHbookLesson 1: Taking Apart Numbers and ShapesProducts and Sums
MATHbookLesson 5: Yours IS to Reason Why!Fill the Gap

Topic 2: Area, Volume, and Surface Area

MATHbookLesson 1: All About That Base….and HeightExploring Triangles
Triangles and Parallelograms
MATHbookLesson 2: Slicing and Dicing: Composit FigureShapes on a Plane
Letters

Topic 3: Decimals

MATHbookLesson 1: You Have a PointDishing Out Decimals
MATHbookLesson 2: Get In LineDecimal Diagrams and Algorithms
MATHbookLesson 4: Dividend In the HouseMovie Time

Topic 4: Fraction by Fraction Division

MATHiaLesson 1: Representing Fraction DivisionFlour Planner

Topic 5: Area of Triangles and Quadrilaterals

MATHiaLesson 2: Developing Area FormulasExploring Parallelograms,
Part 1
MATHiaLesson 3: Calculating Areas of Various FiguresExploring Parallelograms,
Part 2

Off the Grid, Part 1
Off the Grid, Part 2

Topic 6: Composite Figures

MATHiaLesson 2: Calculating Area of Composite FiguresPile of Polygons

Topic 8: Surface Area of Regulat Prisms and Pyramids

MATHiaLesson 1: Determing Surface Area Using NetsRenata’s Stickers

Module 2: Relating Quantitites

Topic 1: Ratios

MATHbookLesson 2: Going StrongPizza Maker
MATHbookLesson 3: Different but the SamePizza Maker
MATHbookLesson 4: A trip to the MoonFruit Lab

Topic 2: Percents

MATHbookLesson 2: Warming the BenchLucky Duckies

Topic 3: Using Tables to Represent Equivalent Ratios

MATHbookLesson 1: Many ways to MeasureMany Measurements
Model Trains
MATHbookLesson 2: What is the Best Buy?World Records
MATHbookLesson 3: A Trip to the MoonWelcome to the Robot Factory
MATHiaLesson 2: Using Tables to Determine Equivalent RatiosDisaster Preparation
MATHiaLesson 3: Problem Solving with Equivalent Rations and Rates using TablesDisaster Preparation

Topic 9: Introduction to Unit Rate

MATHiaLesson 2: Determining and Comparing RatesSoft Serve
More Soft Serve

Module 3: Determining Unknown Values

Topic 2: Equations

MATHbookLesson 2: Double TalkWeight for It
MATHbookLesson 3: Play It in ReverseWeight for It
MATHbookLesson 4: One, None, or a TonTunnel Travels
MATHbookLesson 5: Getting RealFive Equations
Swap and Solve

Topic 3: Graphing Quantitative Relationships

MATHbookLesson 3: Planes, Trains, and PaychecksSubway Fares

Topic 6: Solving One-Step Addition and Subtraction Equations

MATHiaLesson 1: Exploring One-Step Equations with Double-Number LinesHanging Around

Topic 7: Solving One-Step Multiplication and Division Equations

MATHiaLesson 1: Using Double Number Lines to Solve One-Step Multiplicaiton EquationsHanging Around

Topic 8: Solving One-Step Equations with Decimals and Fractions

MATHiaLessons 1-4:Hanging Around

Module 4: Moving Beyond Positive Quantities

Topic 1: Signed Numbers

MATHbookLesson 1: Signed NumbersCan You Dig It?

Topic 1: Introduction to Negative Numbers

MATHiaLesson 2: Representing Integers on Number LinesOrder in the Class

Module 5: Describing Variability of Quantities

Topic 1: The Statical Process

MATHbookLesson 3: SkyscrapersThe Plot Thickens

Topic 2: Numerical Summaries of Data

MATHbookLesson 1: In the MiddleToy Cars
MATHbookLesson 3: March MADnessHoops

Topic 2: Analyzing Numeric Data Displays

MATHiaLesson 1: Creating Dot PlotsMinimum Wage

Grade 7

Module 1: Thinking Proportionally

Topic 1: Circles and Ratios

MATHbookLesson 1: Pi: The Ultimate RatioMeasuring Around
MATHbookLesson 2: That’s a Spicy Pizza!Why Pi?
MATHbookLesson 2: Circular ReasoningArea Challenges
MATHbook
Lesson 4: Pound for Pount, Inch for Inch
Scaling Machines
Tiles
Scaling Robots

Topic 2: Proportionality

MATHbookLesson 1: Poultry in MotionPaint
MATHbookLesson 6: Minding Your Ps and QsTwo and Two

Topic 3: Proportional Relationships

MATHbookLesson 1: Markups and MarkdownsAll the Equations
100%
MATHbookLesson 4: More Ups and DownsMosaics
More and Less

Topic 3: Scale and Scale Drawing

MATHiaLesson 1: Critical Attributes of Similar FiguresScale Factor Challenges
MATHiaLesson 3: Calculating Measurements Using ScaleMake it Scale
Will It Fit

Topic 4: Ratio Representations

MATHiaLesson 2: Determining Characteristics of Graphs of Proportional RelationshipsDinoPops

Topic 11: Introducing Proportions to Solve Percent Problems

MATHiaLesson 2: Solving Simple Percent ProblemsBack in My Day

Topic 13: Percent Increase and Percent Decrease

MATHiaLesson 1: Calculating Percent Change and Final AmountsPercent Machines

Module 2: Operating with Signed Numbers

Topic 1: Adding and Subtracting Rational Numbers

MATHbookLesson 1: Math FootballFloats and Anchors
MATHbookLesson 2: Walk the LineMore Floats and Anchors
MATHbookLesson 4: What’s the Difference?More Floats and Anchors

Topic 5: Rewriting Expressions

MATHiaLesson 2: Evaluating Simple Numberic Expressions with IntegersInteger Puzzles

Topic 6: Using Number Properties to Interpret Expressions with Signed Numbers

MATHiaLesson 2: Operating with Signed DecimalsDraw Your Own

Module 3: Reasoning Algebraically

Topic 1: Two-Step Expressions and Equations

MATHbookLesson 4: Formally YoursKeeping it True

Topic 2: Multiple Representations of Equations and Inequalities

MATHbookLesson 3: Solving Inequalities with Inverse OperationsUnbalanced Hangers
MATHbook
Lesson 4: Deep Dive
Budgeting
Write Them and Solve Them

Topic 1: Rewriting Algebraic Expressions

MATHiaLesson 2: Rewriting Algebraic Expressions Involving Integer CoefficientsCollect the Squares

Topic 8: Solving Inequalities with Inverse Operations

MATHiaLesson 3: Solving Two-Step InequalitiesI Saw the Signs
Shira the Sheep

Module 4: Analyzing Populations and Probabilities

Topic 1: Introduction to Probability

MATHbookLesson 1: Rolling, Rolling, Rolling…How Likely
Prob-bear-bilities
MATHbookLesson 2: Give the Model a ChanceIs It Fair?

Topic 3: Drawing Inferences

MATHbookLesson 2: Tiles, Gumballs, and PumpkinsCrab Island

Module 5: Constructing and Measuring

Topic 1: Angles and Triangles

MATHbookLesson 2: Special DeliveryFriendly Angles
MATHbookLesson 3: Consider Every SideCan You Build It

Topic 1: Special Angle Relationships

MATHiaLesson 2: Exploring Angle RelationshipsMissing Measures
MATHiaLesson 3: Solving for Angle MeasuresMissing Measures

Grade 8

Module 1: Transforming Geometric Objects

Topic 1: Rigit Motion Transformaitons

MATHbookLesson 1: Patty Paper, Patty PaperTransformers
MATHbookLesson 2: Slides, Flips, and SpinsSpinning, Flipping, Sliding
MATHbookLesson 3: Lateral MovesGetting Coordinated, Part 1
Getting Coordinated, Part 2
MATHbookLesson 4: Mirror, MirrorGetting Coordinated, Part 1
Getting Coordinated, Part 2
MATHbookLasson 5: Half Turnsa and Quarter TurnsGetting Coordinated, Part 1
Getting Coordinated, Part 2
MATHbookLesson 6: Every Which WayTransformation Golf

Topic 2: Dilations

MATHbookLesson 1: Pinch-Zoom GeometrySketchy Dilations
MATHbookLesson 2: Rising, Running, Stepping, ScalingDilation Mini Golf
MATHbookLesson 3: From Here to ThereSocial Scavenger Hunt

Topic 3: Line and Angle Relationships

MATHbookLesson 2: Crisscrsoss ApplesaucePuzzling It Out

Topic 1: Rigid Motion in the Coordinate Plane

MATHiaLesson 1: Experimenting with Rigid MotionMoving Day

Module 2: Modeling Linear Relationships

Topic 1: From Proportions to Linear Relationships

MATHbookLesson 2: Jack and Jill Went Up the HillTurtle Time Trials
MATHbookLesson 4: Up, Down, and All AroundTranslations

Topic 2: Modeling Linear Relationships

MATHbookLesson 2: Been There, Done That, Got the T-shirtWater Cooler
MATHbookLesson 3: Dining, Dancing, DrivingFlags
Ups and Downs
MATHbookLesson 4: Derby DayStacking Cups (Optional)

Topic 3: Systems of Linear Equations

MATHbookLesson 1: Crossing PathsMake Them Balance
MATHbookLesson 2: The Road Less TraveledLine Zapper

Topic 11: Solving Linear Equations with Variables on Both Sides

MATHiaLesson 3: Solving with Variables on Both Sides with RationalsEquation Roundtable

Module 3: Developing Function Foundations

Topic 1: Introduction to Functions

MATHbookLesson 1: Patterns, Sequences, Rules…Guess My Rule
MATHbookLesson 2: Once Upon a GraphTurtle Crossing
MATHbookLesson 4: Over the River and Through the WoodsThe Tortoise and the Hare
Scatter Plot City
Interpreting Slopes

Topic 2: Patterns in Bivariate Data

MATHbookLesson 1: Pass the SqueezeRobots
MATHbookLesson 2: Off the ChainDapper Cats
MATHbookLesson 3: Mia is Growing Like a WeedFind the FIt (called Fit Fights in Desmos Math)
MATHbookLesson 4: The Stroop TestInterpreting Scatter Plots
MATHbookLesson 5: Would You Rather…?Finding Associations

Topic 4: Drawing Lines of Best Fit

MATHiaLesson 1: Estimating Lines of Best FitInterpreting Slopes
MATHiaLesson 2: Using Lines of Best FitAnimal Brains

Module 4: Expanding Number Systems

Topic 2: Pythagorean Theorem

MATHbookLesson 1: The Right ConnectionTriangle Tracing Turtle
MATHbookLesson 4: Catty CornerTaco Truck

Topic 1: The Real Number System

MATHiaLesson 2: Graphing Real Numbers on the Number LineRoot Down

Module 5: Applying Powers

Topic 1: Exponents and Scientific Notation

MATHbookLesson 1: It’s a Generational ThingCircles
MATHbookLesson 2: Show What You KnowPower Pairs
MATHbookLesson 3: The Big and Small of ItSpecific and Scientific (formerly Solar System)
MATHbook
Lesson 4: How Much Larger?
Balance the Scale

Topic 2: Volume of Curved Figures

MATHbookLesson 1: Drum Roll, Please!Cylinders
MATHbookLesson 2: Conse of SilenceCones

Algebra 1

Module 1: Searching for Patterns

Topic 1: Quantities and Relationships

Lesson 3: f of x, Recognizing Functions and Function FamiliesCraft-a-Graph
Pumpkin Prices

Topic 2: Sequences

Lesson 1: Is there a Pattern Here?Visual Patterns
Revisiting Visual Patterns, Part 1
Lesson 2: The Password is Operations!Sequence Carnival
Revisiting Visual Patterns, Part 2
Lesson 3: Did You Mean: Recursion?More Visual Patterns

Topic 3: Linear Regressions

Lesson 1: Like a GlovePenguin Populations
Lesson 2: Gotta Keep It Correlatin’Correlation Coefficient
How Hot Is It?
Behind the Headlines
City Data
Lesson 3: The Residual EffectResidual Fruit
Lesson 4: To Fit or Not To Fit? That Is the Question!City Slopes

Module 2: Exploring Constant Change

Topic 1: Linear Functions

Lesson 1: Connecting the DotsPlane, Train, and Automobile

Topic 2: Solving Linear Equations and Inequalities

Lesson 1: Strike a BalanceWorking Backwards
Solving Strategies
Same Position
Lesson 2: It’s Literally About Literal EquationsSubway Seats
Various Variables
Shelley the Snail
Five Representations
Lesson 3: Not All Statements Are Made EqualPizza Delivery

Topic 3: Systems of Equations and Inequalities

Lesson 1: Double the FunShape It Up
Lizard Lines
Lesson 3: Throwing ShadeSeeking Solutions
Lesson 4: Working with ConstraintsQuilts

Module 3: Investigating Growth and Decay

Topic 1: Introduction to Exponential Functions

Lesson 2: The Power WithinCarlos’s Fish

Topic 2: Using Exponential Equations

Module 4: Describing Distributions

Topic 1: One-Variable Statistics

Lesson 2: A Skewed RealityFinding Desmo

Module 5: Maximizing and Minimizing

Topic 1: Introduction to Quadratic Functions

Lesson 1: Up and Down or Down and UpQuadratic Visual Patterns
On the Fence
Stomp Rockets
Plenty of Parabolas
Robot Launch
Lesson 2: Endless Forms Most BeautifulParabola Zapper
Two for One
Shooting Stars
Lesson 4: You Lose Some, You Lose SomeSorting Relationships

Topic 2: Solving Quadratic Equations

Lesson 4: The Missing LinkSquare Tactic
Lesson 5: The Quadratic FormulaStomp Rockets in Space

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Eureka Math® crosswalk to Amplify Desmos Math free lessons

Grade 6

Module 1: Ratios and Unit Rates

Eureka MathAmplify Classroom
Topic A Representing and Reasoning About Ratios 
Lesson 3: Equivalent Ratios
Lesson 4: Equivalent Ratios
Unit 2
Lesson 4: Fruit Lab
Topic C Unit Rates 
Lesson 16: From Ratio to RatesUnit 3
Lesson 6: Soft Serve
Lesson 18: Finding a Rate by Dividing Two QuantitiesUnit 3
Lesson 6: Soft Serve
Lesson 24: Percent and Rates per 100Unit 3
Lesson 9: Lucky Duckies

Module 2: Arithmetic Operations Including Division of Fractions

Topic A Dividing Fractions by Fractions
Lesson 2: Interpreting Division of a Whole Number by a Fraction —Visual Models.Unit 4
Lesson 3: Flour Planner
Lesson 3: Interpreting and Computing Division of a Fraction by a Fraction—More Models
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—More Models
Unit 4
Lesson 6: Fill the Gap
Lesson 8: Dividing Fractions and Mixed NumbersUnit 4
Lesson 6: Fill the Gap
Topic B Multi-Digit Decimal Operations—Adding, Subtracting, and Multiplying
Lesson 9: Sums and Differences of DecimalsUnit 5
Lesson 2: Decimal Diagrams and Algorithms

Module 3: Rational Numbers

Topic B Order and Absolute Value
Lesson 7: Ordering Integers and Other Rational Numbers
Lesson 8: Ordering Integers and Other Rational Numbers
Lesson 9: Comparing Integers and Other Rational Numbers
Unit 7Lesson 4: Order in the Class

Module 4: Expressions and Equations

Topic D Expanding, Factoring, and Distributing Expressions 
Lesson 9: The Relationship of Addition and SubtractionUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 10: Writing and Expanding Multiplication Expressions
Lesson 11: Factoring Expressions
Lesson 12: Distributing Expressions
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Topic F Writing and Evaluating Expressions and Formulas 
Lesson 18: Writing and Evaluating Expressions—Addition and Subtraction
Lesson 19: Substituting to Evaluate Addition and Subtraction Expressions
Lesson 20: Writing and Evaluating Expressions—Multiplication and Division
Lesson 21: Writing and Evaluating Expressions—Multiplication and Addition
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Topic G Solving Equations 
Lesson 23: True and False Number Sentences
Lesson 24: True and False Number Sentences
Unit 6
Lesson 1: Weight for It
Lesson 25: Finding Solutions to Make Equations TrueUnit 6
Lesson 1: Weight for It
Lesson 26: One-Step Equations—Addition and SubtractionUnit 6
Lesson 1: Weight for It
Topic H Applications of Equations 
Lesson 33: From Equations to Inequalities
Lesson 34: Writing and Graphing Inequalities in Real-World Problems
Unit 7
Lesson 7: Tunnel Travels

Module 5: Area, Surface Area, and Volume Problems

Topic A: Area of Triangles, Quadrilaterals, and Polygons
Lesson 1: The Area of Parallelograms Through Rectangle FactsUnit 1
Lesson 3: Exploring Parallelograms
Exploring Parallelograms, Part 2
Topic D Nets and Surface Area 
Lesson 18: Determining Surface Area of Three-Dimensional FiguresUnit 1
Lesson 10: Renata’s Stickers

Module 6: Statistics

Topic A Understanding Distributions 
Lesson 2: Displaying a Data Distribution
Lesson 3: Creating a Dot Plot
Unit 8
Lesson 3: Minimum Wage
Lesson 4: Creating a Histogram
Lesson 5: Describing a Distribution Displayed in a Histogram
Unit 8
Lesson 5: The Plot Thickens
Topic C Summarizing a Distribution That Is Skewed Using the Median and the Interquartile Range 
Lesson 12: Describing the Center of a Distribution Using the MedianUnit 8
Lesson 11: Toy Cars
Topic D Summarizing and Describing Distributions 
Lesson 18: Connecting Graphical Representations and Numerical SummariesUnit 8
Lesson 5: The Plot Thickens
Lesson 3: Creating a Dot PlotUnit 8
Lesson 3: Minimum Wage

Grade 7

Module 1: Ratios and Proportional Relationships

Eureka MathAmplify Classroom
Topic A Proportional Relationships 
Lesson 1: An Experience in Relationships as Measuring RateUnit 2
Lesson 1: Paint
 
Unit 4
Lesson 1: Mosaics
Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs
Lesson 6: Identifying Proportional and Non-Proportional Relationships in Graphs
Unit 2
Lesson 8: Dino Pops
Topic B Unit Rate and the Constant of Proportionality 
Lesson 8: Representing Proportional Relationships with Equations
Lesson 9: Representing Proportional Relationships with Equations
Unit 2
Lesson 6: Two and Two
Lesson 10: Interpreting Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops
Topic C Ratios and Rates Involving Fractions 
Lesson 11: Ratios of Fractions and Their Unit Rates
Lesson 12: Ratios of Fractions and Their Unit Rates
Unit 2
Lesson 6: Two and Two
Lesson 15: Equations of Graphs of Proportional Relationships Involving FractionsUnit 2
Lesson 8: Dino Pops
Topic D Ratios of Scale Drawings 
Lesson 16: Relating Scale Drawings to Ratios and RatesUnit 1
Lesson 1: Scaling Machines
Lesson 18: Computing Actual Lengths from a Scale DrawingUnit 1
Lesson 7: Will It Fit?
Lesson 19: Computing Actual Areas from a Scale DrawingUnit 1
Lesson 7: Will It Fit?

Module 2: Rational Numbers

Topic A Addition and Subtraction of Integers and Rational Numbers 
Lesson 1: Opposite Quantities Combine to Make ZeroUnit 5
Lesson 1: Floats and Anchors
Lesson 2: Using the Number Line to Model the Addition of Integers
Lesson 3: Understanding Addition of Integers
Lesson 4: Efficiently Adding Integers and Other Rational Numbers
Lesson 5: Understanding Subtraction of Integers and Other Rational Numbers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 7: Addition and Subtraction of Rational NumbersUnit 5
Lesson 4: Draw Your Own
Lesson 10; Integer Puzzles
Topic B Multiplication and Division of Integers and Rational Numbers 
Lesson 10: Understanding Multiplication of Integers
Lesson 11: Develop Rules for Multiplying Signed Numbers
Unit 5
Lesson 10: Integer Puzzles
Lesson 15: Multiplication and Division of Rational NumbersUnit 5
Lesson 10: Integer Puzzles

Module 3: Expressions and Equations

Topic A Use Properties of Operations to Generate Equivalent Expressions 
Lesson 3: Writing Products as Sums and Sums as Products
Lesson 4: Writing Products as Sums and Sums as Products
Unit 6
Lesson 10: Collect the Squares
Topic B Solve Problems Using Expressions, Equations, and Inequalities 
Lesson 8: Using If-Then Moves in Solving Equations
Lesson 9: Using If-Then Moves in Solving Equations
Unit 6Lesson 10: Collect the Squares
Lesson 10: Angle Problems and Solving EquationsUnit 7
Lesson 2: Friendly Angles
Lesson 4: Missing Measures
Lesson 12: Properties of Inequalities
Lesson 13: Inequalities
Lesson 14: Solving Inequalities
Unit 6
Lesson 16: Shira the Sheep
Topic C Use Equations and Inequalities to Solve Geometry Problems 
Lesson 16: The Most Famous Ratio of AllUnit 3
Lesson 3: Measuring Around
Lesson 17: The Area of a CircleUnit 3
Lesson 9: Area Challenges
Lesson 18: More Problems on Area and CircumferenceUnit 3
Lesson 9: Area Challenges

Module 4: Percent and Proportional Relationships

Topic A Finding the Whole 
Lesson 1: PercentUnit 4
Lesson 1: Mosaics
Lesson 2: Part of a Whole as a PercentUnit 4
Lesson 1: Mosaics
Lesson 3: Comparing Quantities with PercentUnit 4
Lesson 1: Mosaics
Lesson 4: Percent Increase and DecreaseUnit 4
Lesson 5: Percent MachinesLesson 12: Posing Percent Problems(coming soon!)
Lesson 5: Finding One Hundred Percent Given Another Percent 
Lesson 6: Fluency with PercentsUnit 4
Lesson 5: Percent MachinesLesson 12: Posing Percent Problems(coming soon!)
Topic B Percent Problems Including More Than One Whole 
Lesson 7: Markup and Markdown ProblemsUnit 4
Lesson 5: Percent MachinesLesson 12: Posing Percent Problems(coming soon!)
Lesson 8: Percent Error Problems
Lesson 9: Problem Solving When the Percent Changes
Unit 4
Lesson 5: Percent MachinesLesson 12: Posing Percent Problems(coming soon!)
Lesson 10: Simple Interest 
Lesson 11: Tax, Commissions, Fees, and Other Real-World Percent ApplicationsUnit 4
Lesson 12: Posing Percent Problems
(coming soon!)
Topic C Scale Drawings 
Lesson 13: Changing ScalesUnit 1
Lesson 1: Scaling Machines
Lesson 7: Will It Fit?
Lesson 14: Computing Actual Lengths from a Scale DrawingUnit 1
Lesson 7: Will It Fit?
Topic D Population, Mixture, and Counting Problems Involving Percents 
Lesson 16: Population ProblemsUnit 8
Lesson 10: Crab Island

Module 5: Statistics and Probability

Topic A Calculating and Interpreting Probabilities 
Lesson 1: Chance ExperimentsUnit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities
Topic C Random Sampling and Estimating Population Characteristics 
Lesson 13: Populations, Samples, and Generalizing from a Sample to a PopulationUnit 8
Lesson 10: Crab Island
Lesson 14: Selecting a Sample
Lesson 15: Random Sampling
Lesson 16: Methods for Selecting a Random Sample
Unit 8
Lesson 10: Crab Island
Topic D Comparing Populations 
Lesson 22: Using Sample Data to Compare the Means of Two or More Populations
Lesson 23: Using Sample Data to Compare the Means of Two or More Populations
Unit 8
Lesson 10: Crab Island

Module 6: Geometry

Topic A Unknown Angles 
Lesson 1: Complementary and Supplementary AnglesUnit 7
Lesson 2: Friendly Angles
Lesson 2: Solving for Unknown Angles Using Equations
Lesson 3: Solving for Unknown Angles Using Equations
Lesson 4: Solving for Unknown Angles Using Equations
Unit 7
Lesson 4: Missing Measures
Topic B Constructing Triangles 
Lesson 8: Drawing TrianglesUnit 7
Lesson 5: Can You Build It?
Lesson 11: Conditions on Measurements That Determine a TriangleUnit 7
Lesson 5: Can You Build It?
Topic D Problems Involving Area and Surface Area 
Lesson 22: Area Problems with Circular RegionsUnit 3
Lesson 9: Area Challenges

Grade 8

Module 1: Integer Exponents and Scientific Notation

Eureka MathAmplify Classroom
Topic A Exponential Notation and Properties of Integer Exponents 
Lesson 1: Exponential NotationUnit 7 
Lesson 1: Circles
Lesson 2: Multiplication of Numbers in Exponential Form
Lesson 3: Numbers in Exponential Form Raised to a Power
Unit 7 
Lesson 3: Power Pairs
Topic B Magnitude and Scientific Notation 
Lesson 9: Scientific Notation
Lesson 10: Operations with Numbers in Scientific Notation
Unit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Module 2: The Concept of Congruence

Topic A Definitions and Properties of the Basic Rigid Motions 
Lesson 1: Why Move Things Around?
Lesson 2: Definition of Translation and Three Basic Properties
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 3: Translating LinesUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Definition of Reflection and Basic Properties
Lesson 5: Definition of Rotation and Basic Properties
Lesson 6: Rotations of 180 Degrees
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Topic B Sequencing the Basic Rigid Motions 
Lesson 9: Sequencing Rotations
Lesson 10: Sequences of Rigid Motions
Unit 1
Lesson 13: Tessellate
Lesson 14: More on the Angles of a TriangleUnit 1 
Lesson 12: Puzzling It Out

Module 3: Similarity

Topic A Dilation 
Lesson 1: What Lies Behind “Same Shape”?Unit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 2: Properties of Dilations
Lesson 3: Examples of Dilations
Unit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 4: Fundamental Theorem of Similarity
Lesson 5: First Consequences of FTS
Unit 2
Lesson 6: Social Scavenger Hunt
Topic B Similar Figures 
Lesson 8: Similarity
Lesson 9: Basic Properties of Similarity
Unit 2
Lesson 6: Social Scavenger Hunt
Topic C The Pythagorean Theorem 
Lesson 13: Proof of the Pythagorean TheoremUnit 8
Lesson 8: Triangle-Tracing Turtle

Module 4: Linear Equations

Topic A Writing and Solving Linear Equations 
Lesson 4: Solving a Linear EquationUnit 4
Lesson 5: Equation Roundtable
Lesson 5: Writing and Solving Linear EquationsUnit 4
Lesson 5: Equation Roundtable
Lesson 6: Solutions of a Linear EquationUnit 4
Lesson 5: Equation Roundtable
Topic B Linear Equations in Two Variables and Their GraphsUnit 3
Lesson 4: Flags
Lesson 10: A Critical Look at Proportional RelationshipsUnit 3
Lesson 1: Turtle Time TrialsLesson 4: Flags
Lesson 11: Constant RateUnit 3
Lesson 4: Flags
Lesson 13: The Graph of a Linear Equation in Two VariablesUnit 3 
Lesson 4: Flags
Topic C Slope and Equations of Lines 
Lesson 15: The Slope of a Non-Vertical LineUnit 3
Lesson 4: Flags
Lesson 18: There Is Only One Line Passing Through a Given Point with a Given SlopeUnit 3
Lesson 4: Flags
Lesson 19: The Graph of a Linear Equation in Two Variables Is a LineUnit 3
Lesson 4: Flags
Lesson 20: Every Line Is a Graph of a Linear EquationUnit 3
Lesson 4: Flags
Lesson 22: Constant Rates RevisitedUnit 3
Lesson 1: Turtle Time Trials
Topic D Systems of Linear Equations and Their Solutions 
Lesson 25: Geometric Interpretation of the Solutions of a Linear SystemUnit 4  
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Module 5: Examples of Functions from Geometry

Topic A Functions 
Lesson 1: The Concept of a FunctionUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 2: Formal Definition of a FunctionUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 3: Linear Functions and ProportionalityUnit 3
Lesson 1: Turtle Time Trials
Lesson 5: Graphs of Functions and EquationsUnit 5
Lesson 5: The Tortoise and the Hare
Lesson 6: Graphs of Linear Functions and Rate of ChangeUnit 3
Lesson 4: Flags
Lesson 7: Comparing Linear Functions and GraphsUnit 5
Lesson 5: The Tortoise and the Hare
Topic B Volume 
Lesson 10: Volumes of Familiar Solids—Cones and CylindersUnit 5
Lesson 11: Cylinders

Module 6: Linear Functions

Topic A Linear Functions 
Lesson 2: Interpreting Rate of Change and Initial ValueUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Increasing and Decreasing Functions
Lesson 5: Increasing and Decreasing Functions
Unit 5
Lesson 1: Turtle CrossingLesson 5: The Tortoise and the Hare
Topic B Bivariate Numerical Data 
Lesson 6: Scatter Plots
Lesson 7: Patterns in Scatter Plots
Unit 6 
Lesson 3: Robots
Lesson 8: Informally Fitting a LineUnit 6
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Lesson 10: Linear Models
Lesson 11: Using Linear Models in a Data Context
Unit 5
Lesson 5: The Tortoise and the Hare
Topic D Bivariate Categorical Data 
Lesson 14: Association Between Categorical VariablesUnit 6
Lesson 11: Finding Associations

Module 7: Introduction to Irrational Numbers Using Geometry

Topic A Square and Cube Roots 
Lesson 2: Square RootsUnit 8
Lesson 4: Root Down
Lesson 4: Simplifying Square RootsUnit 8
Lesson 4: Root Down
Topic C The Pythagorean Theorem 
Lesson 18: Applications of the Pythagorean TheoremUnit 8
Lesson 10: Taco Truck

Algebra 1

Module 1: Relationships Between Quantities and Reasoning with Equations and Their Graphs

Topic A: Introduction to Functions Studied this Year—Graphing Stories

Lesson 1: Graphs of Piecewise FunctionsPumpkin Prices
Lesson 2: Graphs of Quadratic FunctionsRevisiting Visual Patterns, Part 1
Quadratic Visual Patterns

Topic C: Solving Equations and Inequalities

Lesson 10: True and False EquationsSame Position
Lesson 11: Solution Sets for Equations and InequalitiesWorking Backwards
Solving Strategies
Shelley the Snail
Lesson 19: Rearranging FormulasSubway Seats
Various Variables
Lesson 21: Solution Sets to Inequalities with Two VariablesPizza Delivery
Lesson 22 & Lesson 23: Solution Sets to Simultaneous Equations (and Inequalities)Shape It Up
Lizard Lines
Quilts
Seeking Solutions

Module 2: Descriptive Statistics

Topic D: Numerical Data on Two Variables

Lesson 14: Modeling Relationships with a LineCity Slopes
Residual Fruit
Penguin Populations
Lesson 19: Interpreting CorrelationCorrelation Coefficient
How Hot Is It?
Behind the Headlines
City Data

Module 3: Linear and Exponential Functions

Topic A: Linear and Exponential Sequences

Lesson 3: Arithmetic and Geometric SequencesSequence Carnival
More Visual Patterns
Lesson 5: The Power of Exponential GrowthCarlos’s Fish

Topic B: Describing Variability and Comparing Distributions

Lesson 4: Summarizing Deviations from the MeanFinding Desmo
Lesson 13: Interpreting the Graph of a FunctionCraft-a-Graph
Lesson 14: Linear and Exponential Models – Comparing Growth RatesDetroit’s Population, Part 1
Detroit’s Population, Part 2

Topic D: Using Functions and Graphs to Solve Problems

Lesson 21: Comparing Linear and Exponential Models AgainPlane, Train, and Automobile
Lesson 21: Comparing Linear and Exponential Models AgainCarlos’s Fish

Module 4: Polynomial and Quadratic Expressions, Equations, and Functions

Topic A: Quadratic Expressions, Equations, Functions, and Their Connection to Rectangles

Lesson 8: Exploring the Symmetry in Graphs of Quadratic FunctionsOn the Fence
Plenty of Parabolas
Robot Launch
Lesson 9: Graphing Quadratic Functions from Factored Form, 𝑓(𝑥)=𝑎(𝑥−𝑚)(𝑥−𝑛)Two for One
Parabola Zapper
Shooting Stars
Lesson 10: Interpreting Quadratic Functions from Graphs and TablesStomp Rockets

Topic B: Using Different Forms for Quadratic Functions

Lessons 11–12: Completing the SquareSquare Tactic
Lesson 15: Using the Quadratic FormulaStomp Rockets in Space

Topic C: Function Transformations and Modeling

Lesson 18: Graphing Cubic, Square Root, and Cube Root FunctionsSorting Relationships
Lesson 22: Comparing Quadratic, Square Root, and Cube Root Functions Represented in Different WaysSorting Relationships

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

National Reading Month: Making reading in elementary schools fun

Happy National Reading Month!

Of course, every month is reading month—and every day is reading day!

But March makes National Reading Month official, and we’d like to help you celebrate.

  • Brain Builders” is an animated video series you can share with your students to help them understand what the brain does in order to read—placing reading science in the hands (and brains!) of students.

Your kids will join Minh on his journey as his babysitter, Tamara, helps him cultivate a love for reading—while also learning a bit of cognitive science. The series includes 13 episodes that you won’t want to miss!

  • Reading Buddies” makes learning to read fun (with the help of a talking dog, of course). Created by a pair of performers during the COVID-19 quarantine, the show became a smash hit when The Reading League came on to help it grow.

The series is based on the Science of Reading—but that’s not why students like it! They get to follow and practice along with Dusty the Dog as his person, Dott, teaches him to read. All the while, the kids are learning the underlying components of skillful word reading such as phonological awareness, letter names/sounds, and blending sounds.

And for a little good old-fashioned coloring, we’ve also created this literary reference sheet for your students to bring alive with their own imaginations.

We hope you enjoy celebrating your kids’ brains and creativity!

More to read and learn

From Amplify’s Science of Reading: The Podcast:

Find out how “Reading Buddies” came to be (and managed to outpace “Sesame Street”)!

Meet Margaret Goldberg, co-founder of The Right to Read Project, to get her take on Brain Builders and the importance of the comprehension strand of the Science of Reading.

Request a free sample of CKLA.

S3-05: Thinking is power

A graphic with the text "Science Connections" and "Amplify" features colorful circles and curved lines on a dark gray background.

Join us as we sit down with Melanie Trecek-King, college professor and creator of Thinking is Power, to explore how much of an asset science can truly be in developing the skills students need to navigate the real world. You’ll learn about “fooling” students and the importance of developing critical thinking, information literacy, and science literacy in the classroom. We’ll also share real strategies and lesson examples that help build these essential skills and engage students in learning.

And don’t forget to grab your Science Connections study guide to track your learning and find additional resources!

We hope you enjoy this episode and explore more from Science Connections by visiting our main page!

DOWNLOAD TRANSCRIPT

Melanie Trecek-King (00:00):

We say knowledge is power, but it’s not enough to know things. And there’s too much to know. So being able to think and not fall for someone’s bunk is my goal for my students.

Eric Cross (00:12):

Welcome to Science Connections. I’m your host, Eric Cross. On this third season, we’ve been talking about science’s underdog status. And just this past March at the NSTA conference in Atlanta, I had the chance to speak with science educators from around the country about this very topic.

Hermia Simanu (00:28):

Right now, there’s only two teachers in our high school teaching science.

Shane Dongilli (00:32):

I have 45 minutes once a week with each class. The focus is reading and math.

Alexis Tharpe (00:38):

Oftentimes science gets put by the wayside. And you know, I love math and I love my language arts, but I also think science needs to place be placed on that high pedestal as well.

Askia Little (00:46):

In fifth grade, oh, they teach science, because that’s the only grade that it’s tested.

Eric Cross (00:50):

That was Hermia Simanu from American Samoa. Her team flew for three days to make it to the conference. You also heard from Shane Dongilli from North Carolina, Alexis Tharpe from Virginia, and Askia Little from Texas. All of these teachers were excited to be at the conference and had a lot to say about the state of science education in their local schools. Throughout this season, we’ve been trying to make the case for science, showing how science can be utilized more effectively in the classroom. We’ve explored the evidence showing that science supports literacy instruction. We’ve talked about science and the responsible use of technology like AI. My hope is that all of you listeners out there can use some of this evidence to feel empowered to make the case for science in your own communities. And on this episode, we’re going to examine how science can help develop what might be the most important skill that we try to develop in our students: Good thinking. On this episode, I’m joined by a biologist who actually advocated for eliminating the Intro to Bio course at her college. Instead, Professor Trecek-King created a new course focused on critical thinking, information literacy, and science literacy skills. In this conversation, we discuss why the science classroom is such a good environment for helping students become better thinkers. Now, I don’t think that you can make a much stronger argument for science than using it to develop the skills that Melanie describes in this conversation. So, without further ado, I’m thrilled to bring you this conversation with Melanie Trecek-King, Associate Professor of Biology at Massasoit Community College, and creator of Thinking Is Power. Here’s Melanie.

Eric Cross (02:29):

Well, Melanie, thank you for joining us on the show. It’s so good to have you.

Melanie Trecek-King (02:34):

I am so happy to be here.

Eric Cross (02:35):

Now, I went to your session at NSTA in Chicago … I think it was two years ago. A couple years ago. And I was listening to your session, and as I was listening to you, I started Reverse Engineering in my mind what you were doing with your college students. I started reverse engineering the K–8. I was like, “This is amazing.” Where has what you’ve been doing been hiding? We need this not just in the college, higher ed. We need this all the way up and down. Because I hadn’t seen it before. So I think a good place for us to start is gonna be like the story of how and why you as a biologist wound up making the case to actually eliminate the Intro to Biology course at your college. So can you start off and tell us a little bit about that story?

Melanie Trecek-King (03:20):

Sure. So I started teaching at a community college in Massachusetts. And I absolutely love teaching at a community college. And I was teaching the courses that people who don’t wanna be scientists when they grow up have to take to fulfill their science requirement. And that course was Intro Bio. And I tried every way I could figure out to make that class be useful,] relevant to students. I mean, the thing is, our world is based on science and you have to understand science to be a good consumer of information, to make good decisions. And I’m a biologist, so it pains me to say this, but you know, somewhere in the middle of teaching students about the stages of mitosis and protein synthesis, I thought, “Is this really — like, if I have one semester that’s gonna be the last chance that someone’s gonna get a science education, is this really what they need?” And I just decided, “No.” So, to my college’s credit, they were very supportive. I went to them and said, “You know, I think we should assess the non-majors courses. Like, why do we teach non-majors science?” And we all agreed, well, it was for science literacy. OK, great. Do our existing non-majors courses do that? And so we evaluated each of the courses. I made a case that Intro Bio was not doing it. And so we actually replaced it with a course that I call Science for Life. And the whole course is designed to teach science literacy, critical thinking, and information literacy skills.

Eric Cross (04:48):

And so you did this while you were looking at mitosis. And you’re looking at students who may or may not be science majors. And then kind of asking that question. I know every educator asks this, and whether or not it’s welcomed or supported is a different question: “Is what I’m teaching actually gonna be relevant and useful later on down the road for this group of students?” And you actually got to run with it and then create this course, this new course. So, what were the skills that you were hoping to achieve with the new course you developed, and and why were those skills so important?

Melanie Trecek-King (05:21):

Well, if I just go back for a second to what you said, ’cause it, really hit me: I remember the actual moment — it had been building up to that point, but the actual moment that it hit me — I was teaching students the stages of mitosis. And I was applying it to cancer, because the thought is that if we use issues that are relevant to students to teach concepts, that it will be more meaningful to them. They’ll learn it better; they’ll be able to apply it. And they just looked absolutely deflated. They didn’t wanna be there. And I had this moment where I thought, “You know, if, if these students ever have cancer somewhere in their lives, is what I taught them going to be something that they remember? Is it going to be useful to them?” And quite frankly, like, no. <Laugh> They’re not gonna remember proto-oncogenes. And quite frankly, is that really what they need to know at that moment? What they need to know is, “What does this mean? Who is a reliable source of information here? If these treatments are recommended, what is the evidence for them? What are the cost-benefit analyses? Where do I go to find reliable information?” And in that space, cancer in particular, we have this whole field of — I wanna say charlatans, ’cause they may not actually be lying, but they’re pedaling false cures, false hopes. And people need that kind of hope, and so in their time of need, they’re more likely to fall for that kind of thing. Which leads me to the skills that I teach students. I call them this tree of skills. And the order is important. I start — and there’s a lot of overlap to be fair — but critical thinking, and then information literacy, and science literacy. The idea is that students carry in their pockets access to basically all of human’s knowledge at this moment in time. And if they needed to access it, they could. The question is, do they know what they’re looking for? Are they aware of their own biases that are leading them to certain sources, or certain false hopes? Are there certain things that are making them more vulnerable to the people that might prey on them? Are they able to use that information to make good decisions? There’s a great Carl Sagan quote, and it’s something like, “If we teach people only the findings of science, no matter how useful or even inspiring they may be, without communicating the method, then how is anyone to be able to tell the difference between science and pseudoscience?” So yes, the process of science is a process of critical thinking. However, we do tend to present science most of the time. Like, here’s what science has learned. And to be fair, those things that we’ve learned from science are really useful and inspiring. But if we don’t teach the process, so you’ve got somebody now who let’s say has been diagnosed with cancer and is on their phone and they’re scrolling through social media and everything looks the same. And of course the algorithms learn who you are. Next thing you know, there’s all of these like pseudo-treatments popping up. It all looks the same. Somebody who says that acupuncture can be used to cure cancer can feel the same, from someone who doesn’t understand the process of science, as a medical fact. And so the process is the process of critical thinking. My class everything is open note. The quizzes are open note. The exams — and I say open note, they’re also open online, because I know for the rest of their life they’re gonna have resources available to them; I want them to be good consumers with that information, which to me requires metacognition and critical thinking and information literacy and all those skills that I’m trying to teach them.

Eric Cross (08:58):

You’re basically taking what … we’ve taught science for so long. And more recently, it’s changed to more focusing on skills. At least in K through 12. But a lot of it was just memorization of a ton of different things that now we can pull up our phone, go on the internet. You can pull up a lot of those facts. But those facts don’t necessarily translate to actual real-world skills. When I listen to… I kind of make this analogy sometimes: students say … it’s funny, I have 12-year-olds that say this. They go, “How come they don’t teach us how to do our taxes?” And you know they’re regurgitating what they hear from adults, right? “Teach us real-world skills!” And I was like, really, if we taught you right now how to do your taxes, how many of you would really be like, “Oh, this is an awesome lesson! We’re really engaged!” But their point is that “I wanna learn something that I could actually use later on, that’s that I’m gonna carry on.” And in your course, you’re talking about these skills that actually can apply. Like you said, if I had cancer and I’m looking at different types of medical procedures, do I have the skills to really be able to evaluate and make informed decisions on that? And that’s, that’s not something that I’ve seen explicitly taught really anywhere. And I hadn’t heard anybody talk about it, really, until I heard your session, where you’ve kind of unpacked this, and over the last couple of years, have created some programs or resources for educators, where they can take this into their classroom. So what were some of those skills, again? What were were some of the skills that you thought, “I wanna make sure that my students can walk out and they know how to do this and apply it to maybe several different fields”?

Melanie Trecek-King (10:35):

Oh, that’s a really good question. Because the whole thing was a process for me. Like, when I finally let go of Intro Bio, I was so glad to see that class go, by the way. ‘Cause I just felt like I was beating a dead horse. So when I let go of it, I thought, “What do they need instead?” And for me, what I realized was I was trying to make the class I would’ve wanted to take. I realized the things that I personally didn’t know, that my own education maybe let me down a bit. But things that I thought were important. So then I took all of those, synthesized them, tried to figure out the best order. The class is currently in its third iteration. And I hope every iteration is an improvement. But I’m thinking about the students that I taught before the pandemic. It was Intro Bio. Up to just maybe the couple years before the pandemic, and during the pandemic, we had a new virus and we had a new vaccine and we had new treatments. There was hydroxychloroquine and there was ivermectin and then there’s masks. Are masks effective? Well, you know, in what circumstances? What kind of mask? There are all of these questions. And that whole thing was we saw science playing out in real time.

Eric Cross (11:50):

Absolutely.

Melanie Trecek-King (11:51):

And so were my students able to follow that? And then what happened in that process is that science became politicized. And in a time where things are uncertain and we need answers, ’cause it’s scary, people want certainty and science doesn’t tend to provide that. Especially when it’s just starting out. And then when it becomes politicized, people decide that they’re going to — it’s not necessarily a conscious decision — but they retreat into what people in their camps are saying or their groups are saying. Which actually leads me to one of the more important parts of information literacy skills in there, which is most of our knowledge is shared. We tend to have overinflated senses of what we individually know. And studies actually show that with Google, if you have access to Google, you think you’re smarter than if you don’t have access to Google. But we all have access to knowledge in our communities, and that’s one of the reasons humans are so successful, is that we can each specialize in different things and share our expertise and become greater than the sum of our parts. The problem with that, of course, is that we forget what we don’t know, and we assume that we know what the community knows. And so recognizing the limits of your own knowledge and how different communities produce knowledge, like the different epistemic processes that communities use to come to knowledge. When it comes down to it, an important part of knowing is knowing who to trust, right? Knowing where the source of knowledge lives. And in order to do that, you have to understand the processes that they’re using to come to that knowledge and the limits of your own knowledge. And then how to find who has that knowledge so that you can use that to make better decisions.

Eric Cross (13:38):

So, when I hear what you’re doing with your college students, and I think about what I’m doing in the classroom, in the middle school, we are really focusing on literacy as skills. Reading, writing, speaking, listening. And then when I think of the next step of the journey, your information literacy and the literacy you’re teaching is really the application of those things in the real world. And the examples that you gave are very critical examples. Evaluating claims about Covid. Making informed decisions about a medical procedure that you might need. And we all get that applied to us. We’re scrolling through social media and somehow social media is listening. It’s figuring out exactly what I’m doing, because all of a sudden the ads are telling me … how did you know I was alking about KitchenAid mixers now? I just said KitchenAid mixers and it’s gonna show up in my feed! But <laugh> I take that in the same way from the same place that I take in maybe an oncologist. So it’s it’s coming through the same channels. So now I kind of wanna pivot. So we’ve talked about what you’re doing, why you’re doing it, the connection between “am I really teaching the skills that my students need in the science class? Is it really critical thinking explicitly or is it just kind of implied?” Now I wanna ask you how you do it. What’s the annotated, abbreviated kind of syllabus of your course?

Melanie Trecek-King (15:03):

So the course is called Science for Life. And the premise behind it is the kinds of skills and understanding of the process of science that they would need to make good decisions to be empowered in a world based on science. And so the very first lecture, I say, “OK, I’m gonna tell you a story and I just want you to listen to the story. And at the end I’m gonna ask you why I told the story.” And the story that I tell them is some of the history of the witchcraft trials in Europe. And I start with the Malleus Maleficarum, or the Hammer of Witches, from the Pope, and about how people would accuse witches of causing birth defects or storms or crops dying. And, the best evidence that they had to absolutely know somebody was a witch was if somebody accused them, and then if they were accused, if they confessed. OK? But the problem is, to get them to confess, they would torture them. Roasting over coals, or splitting until somebody broke. And so I tell my students, “OK, this was absolute proof that someone was guilty of witchcraft. I don’t know about you; I would confess to anything, right? Make it stop!” So this is where I get to ask students, “Why would I ask you this? Why would I tell you this story? And traumatize you on the very first day of lecture?” And they see the reasoning, right? They thought they had evidence. The question was, is that good evidence? And so, you know, I’m getting students to have a basic understanding of epistemology, right? Without calling it that, or without going into all of the philosophical background of epistemology. Apply this to your own reasoning. What are you wrong about? Well, you probably wouldn’t know. OK, how would you know if you were wrong? Like what kinds of things do you feel that you’re so right about? How good is your evidence for that? So what I want them to do is internalize the thinking about thinking, and analyzing how they come to conclusions, and proportioning how strongly they believe. Their confidence in how right they are. So I think starting with that kind of misinformation, and getting students to internalize that process is important. But I think the example is really useful, because most of my students don’t believe in witchcraft. Right? So it’s not an issue that would immediately threaten them in some way. So when, when a belief is tied to identity or how we see ourselves or is really important to us, then it’s very difficult to be objective about that belief. And so by starting with witchcraft, it’s not triggering. I get them to think about thinking and practice that muscle so that when we get to those more important issues, they have the skills they need to evaluate them.

Eric Cross (17:55):

So would it be fair to say that your Science for Life class is really applied scientific thinking for the real world?

Melanie Trecek-King (18:01):

Absolutely. That’s the idea. I mean, science is too good to keep to ourselves, right? And it’s everywhere. So how can you understand the world through a scientific lens?

Eric Cross (18:10):

What are the nuts and bolts of how you teach your students these strategies? What do you do? What are some strategies and techniques that we can maybe share with listeners? And then where I want to go after that is I wanna ask you, how early do you think this can be started? So lemme start off first with, what do you do?

Melanie Trecek-King (18:28):

So I use three different strategies. One is, I provide students with a toolkit. And the toolkit is one that I created and it is like my one toolkit to rule them all. It is trying to apply critical thinking and science reasoning all together in one place. So that if students are met with a claim, they’ve got the toolkit with an acronym. They can now start and have somewhere to go. In that if I gave you a claim and said, “Just critically think through this claim,” I mean, that’s a mighty task. But if you have a structured toolkit, then it’s hopefully a systemic way that’s helpful. The toolkit is summarized by FLOATER. I have published it on Skeptical Inquirer. It’s free. So it’s Falsifiability, Logical, Objectivity, Alternative Explanations, Tentative Conclusions, Evidence, and Reproducibility. So I provide students with a toolkit. The next thing I do is I use a lot of misinformation in class. Back to what Carl Sagan says: What I heard was we should use pseudoscience to teach students the difference between a pseudo-scientific process and a scientific process. So, I use science denial, conspiracy theories, and give my students a lot of opportunities to practice evaluating claims with the toolkit. And the other thing I do is, I use inoculation activities. So inoculation theory is based on William McGuire’s original research in the ’60s, which is basically like a vaccine analogy. Where you can inject a small amount of a virus or bacterium into the body, so that it creates an immune response, so that it can learn the real thing. And so in the real world, it can fight it off. Inoculation theory does the same thing, but with misinformation. So, what we can do is, in controlled environments, expose students to little bits of misinformation so that they can recognize it in the real world. There’s different kinds of inoculation, but I’m a big fan of what’s called active and technique-based inoculation. So technique-based means that students are learning not the facts of misinformation, not factually why this thing is wrong, but about the technique used to deceive. So maybe the use of fake experts. Or maybe the use of anecdotes. Or the use of logical fallacies. The other part of that is active, which is where students create the misinformation. So for example, my students, just now, we finished covering pseudoscience. And I teach students the characteristics of pseudoscience. And basically we have fun with it. Where they pretend to be grifters and they sell a pseudoscience product. And so they have to make an ad like they’d see on social media, using the different techniques. And the point there is that it’s supposed to be funny, right? And lighthearted. But in a real way, by using the techniques used to sell something like pseudoscience, it’s opening their eyes. You can’t unsee how every alternative product has, “it’s an all-natural and used for centuries and millions use it and look at this person who says, ‘Wow, it worked for me!’ And it’s certified by some society that doesn’t exist, but this doctor behind it says that it’s really great!” I mean, it’s all the same stuff. So they create the misinformation using their own techniques.

Eric Cross (22:02):

That’s one of my favorite things that you’ve talked about, and I want to dive in that a little bit more. But when you’re teaching the toolkit, FLOATER, what does that look like in the classroom, when you’re actually breaking all of those things down? What does it look like as you’re walking your students through this, and you’re kind of coaching them on all of those different things? ‘Cause I feel like some things might be like, “Oh yeah, I got that.” And then some of them might be, “Oh, what is that?”

Melanie Trecek-King (22:24):

Yeah, it takes me probably a good solid lecture to get through the basis of the toolkit. But then over the rest of the semester, I’ll spend more time going into different parts, different rules, a bit more in-depth. So, for example, logical fallacies and objectivity. So the rule of objectivity basically states that you need to be honest with yourself. I’m gonna quote Feynman here, so: “The first principle is that you must not fool yourself — and you are the easiest person to fool.” We don’t tend to think that we can be fooled. But of course we can. So actually, if you wanna talk about it, I start class by fooling my students.

Eric Cross (23:03):

Wait, what do you do? What do you do for that?

Melanie Trecek-King (23:05):

Oh, so this is really fun. Day 1 of class, after the syllabus, I tell my … so you’re in my class now, Eric. “So I have a friend, and she’s a psychic. She’s an astrologer and she’s pretty good at what she does. I mean, she’s got books and she’s been on TV and stuff. She knows I teach this course about skepticism. And so she’s agreed to test how effective she is by providing personality assessments to students in class. So if you wanna participate, what I need from you is your birthday, your full name, answer a few questions. Like, if your house was on fire and you could take one thing, what would it be? Or if you could get paid for anything to do anything for a living, what would it be? Um, there’s a third one. Oh! If you could have any superpower, what would it be?” So the next class, it’s usually over a weekend. The next class I say, “OK, I’ve got your personality assessments back, but remember, we wanna test how effective she is. So in order to do that, I need you to read your profile as quietly as possible. And then I’m gonna have you rate her accuracy on a scale of 1 to 5. OK? So close your eyes; rate her.” Over the years doing this, it’s about a 4.3 to 4.5 out of 5. They think she’s pretty accurate. OK? “So now, if you feel comfortable, get with a person next to you. And I want you to talk about what parts of the personality assessment really spoke to you and, and why, and why you thought she was accurate or not.” And it takes them 5, 10 minutes before they realize they all got the same one. So, this is not my original experiment. It was first done by Bertram Forer in … I think it was the ’50s. And it’s done in psychology classrooms. James Randi made it famous. But the personality assessment itself is full of what are called Barnum statements. So, named after P.T. Barnum. These are statements that are very generic. So, “You have a need to be liked and admired by people. You are often quiet and reserved, but there are times where you can be the life of the party.”

Eric Cross (25:13):

How do you know this about me, by the way? This is a — I feel like you know me right now.

Melanie Trecek-King (25:17):

“There are times where you’ve wondered whether you’ve done the right thing.”

Eric Cross (25:19):

This is getting weird.

Melanie Trecek-King (25:21):

I’m just on fire, right? So these are Barnum statements. They’re the basis of personality assessment.

Eric Cross (25:29):

Mel, can I pause you right there? You said Barnum. Is that the same Barnum, like Barnum & Bailey Circus?

Melanie Trecek-King (25:34):

Yeah. P.T. Barnum, who didn’t actually say “There’s a sucker born every minute,” but we attribute him with that kind of ethos. These statements though, if you read a horoscope or even like personality indicators, like the MBTI, it is basically pseudo-scientific. And it ends up with lots of these Barnum statements. They produce what’s called the Barnum Effect, which is, “Wow, that’s so me! How did you know me?” I could even do more. Like, you have a box of photos in your house that need to be sorted. Or unused prescriptions. And these can apply to nearly everyone, but they produce this effect where we go, “Wow, that is so me!” Right? So by fooling them this way, I get to … well, so the next thing is, “Yes, I lied to you. And I’d like to tell you I won’t do that again. But I’m not going to, ’cause I might. So be on your guard.” But I did it for free. And why did I do it? “I did it because I could tell you ‘I could fool you,’ but you wouldn’t necessarily believe me. So I fooled you, so that you would learn what it feels like to be fooled.” It’s not fun. But we’re gonna make a joke outta this. And students are almost never upset about this ’cause it’s a fun process and they’re all fooled. And again, the point is, I didn’t disprove psychic powers. I didn’t just disprove psychics with this exercise. But I did show you how easy it was to fake. So if somebody is gonna tell you that they can know these things about you through some way, hopefully the evidence they provide should be stronger than something that’s easily faked. Right? Extraordinary claims require extraordinary evidence. If you claim to be able to read my personality based on my birthdate, then I need more than something that you can be taught to do in 15 minutes. So, I fool them to convince them that they could be fooled.

Eric Cross (27:27):

You’re giving them a practice scenario for thinking. And I was thinking about basketball. I grew up playing basketball. And my coach would have our own team be the defenders of the next team we were gonna play, so that we can be prepared for the defense. We were gonna see. Now, when I’m thinking about education, and what you just said reminded me of this, it’s like we’re often just teaching offense. We’re always teaching the plays. We’re always teaching what to do. But we rarely teach defense. What happens when someone comes towards you and, and they challenge you or they come at you with claims? How do we evaluate this? And I think in pockets we do it. We do claim-evidence-reasoning. We present claims and evidence and reasoning. But we don’t always have practice defending them. And I think there’s great resources. There’s Argumentation Toolkit and there’s all these awesome resources that do this. But does that fit? You’re kind of having them practice defense?

Melanie Trecek-King (28:26):

Yeah. You know, that’s brilliant. I never considered that analogy. But, yeah, in the real world, you don’t just get to always try to score all the time. Someone’s gonna challenge you and give you a claim that maybe you haven’t heard before. So how do you think through it?

Eric Cross (28:41):

Yeah. And you become better. So now I’m thinking about how early could we start doing this? For one, I love the idea of lying to your students, because I do that. And it’s just such a fun scenario. How early could we start implementing these strategies or these ideas or these toolkits? In your mind, what do you imagine? How early could we start this with young people?

Melanie Trecek-King (29:07):

Yeah. I’m so glad you asked that question, ’cause honestly, by the time they get to me, it’s almost too late. And I don’t wanna say it’s too late, ’cause it’s never too late. But, oh, we need to start so much earlier! That example that I gave about the selling pseudoscience argument? I have a wonderful colleague, Bertha Vasquez, who’s a middle school teacher in Miami and the director of TIES at CFI. She did this with her middle school students. And quite frankly, their examples were just as good, or in some cases better, than my college students. And they had so much fun with it, too. And she just said that, you know, <laugh>, they actually are more savvy with the kinds of things that they see online than we — I don’t wanna say give them credit for. But almost that we want to believe. My students give me examples of things that are from corners of the internet that I didn’t know existed. And quite frankly, that’s probably a good thing for my own mental health. But students are on there too, like middle school students, and we need to prepare them for the kinds of things that they see in the wild.

Eric Cross (30:13):

So in middle school, definitely. Now, you’ve also done some work in high school as well, right? In Oklahoma? Did you do some. …?

Melanie Trecek-King (30:17):

Yeah.

Eric Cross (30:18):

…some work with high schoolers? What was that like? Did you see any impact there?

Melanie Trecek-King (30:21):

So I didn’t actually do it in Oklahoma. I have taught the course … actually, you were talking about younger kids. I’ve taught the course to high schoolers in my area that are parts of dual enrollment. And they absolutely ate up the curriculum. And they were wonderful, wonderful students. And it was completely appropriate for … they were juniors, actually. But the course has also been taught in Oklahoma, through a dual enrollment program as well. And it was a small sample size. But we have pre-post testing that showed that it improved their critical thinking, their acceptance of science. But anecdotally the head of the program there said that in his years doing this, he’d never seen a course that helped them improve in their other courses so well. So, I felt very rewarded by hearing this. But apparently their critical thinking skills and information literacy skills helped them succeed in their other courses that they were taking. And I love that the students were transferring those skills to other classes. That’s the whole point.

Eric Cross (31:23):

And that’s a big … I think that what you just said is really the core, especially of what we’ve been talking about this season: What you’re talking about and what you’re teaching can transfer and supports literacy. And this is an example of science doing that across all other content areas. So I think that that’s huge, that that was said. What do people say about this course? I know I went on your website, and I looked at some of the comments that some folks were saying, and I know it’s just a snippet, but what do you hear from the education world about this? Because I don’t see it in many places. I see it kind of embedded, sprinkled into different content areas. But you’re actually teaching it explicitly. Do you tend to find positive feedback, overwhelmingly? Or do you get pushback on on some of this? What’s it been like for you?

Melanie Trecek-King (32:16):

I think the biggest pushback — and it’s good pushback, and I would agree entirely — is with inoculation activities, you do need to be careful to, when you debrief students, you wanna tell them why you did what you did and to use their powers for good and not for fooling other people. And I think importantly, for not putting misinformation out into the wild without having context around it. So if you do these kinds of inoculation activities, like if you have your students create pseudoscience ads, don’t just let them put them on social media. Obviously, you can’t control everything that they’re doing. But explain to them why you wouldn’t wanna do that. As far as everything else, I’ve heard really great feedback. You’re referencing my website. So, when I put together the course, I was trying to find resources for students to read. Textbooks are ridiculously expensive and I couldn’t find anything that I really wanted students to buy. So I just started writing, and I put it on my site. I have a site that’s basically the core of the curriculum. More in progress. And then I’ve got some of the topics that we explore and those are all assigned readings. My students are captive, in that I know they want a grade, and for four months they have to sit with me for the entire semester, in that I’ve specifically ordered the content in a way that would be most conducive to them learning these things. On the internet, though, and on social media, ’cause I post on there as well, people come in from all kinds of entry points, and so the goal would be to have them start at the beginning and go to the end. But people … I’m pleasantly surprised that there is an audience for critical thinking and science literacy content out there. And so that really warms my heart. But I am doing more and more for educators. And so I have a section for educators. I put content on there. I put assignments, the assignments that we’ve talked about and more, are on there. And the educators that I’ve had use it have just been really wonderful. Like, I hear great things. If I might, the biggest issue that I’m having is actually reaching educators. I’ve gone to — I met you at NSCA, actually, that was only last summer.

Eric Cross (34:30):

Oh, wow. Wow.

Melanie Trecek-King (34:32):

Right?

Eric Cross (34:32):

Yeah, you’re right. It wasn’t even a year.

Melanie Trecek-King (34:35):

Yeah, I think it was like July last year. So, um, you’ve been to the conferences. And I just went to the last one as well. But I have yet to figure out a way to really get in front of enough educators to share the content. So if anybody’s listening and is interested in learning more, please let me know! <Laugh>

Eric Cross (34:52):

Yes. And we talked about your website, but I didn’t say what the website was. So it’s ThinkingIsPower.com.

Melanie Trecek-King (34:57):

Yes.

Eric Cross (34:58):

And on there, there’s tons of resources. There is the toolkit. And it’s all free.

Melanie Trecek-King (35:06):

Yes.

Eric Cross (35:07):

And there’s a dope t-shirt on there that I just bought today, that Melanie’s actually wearing right now. It says, “Be curious, be skeptical, and be humble.” And I love that. Because I think one of the things that we can’t forget about teaching people how to think and critically evaluating information, sometimes those conversations can become very dehumanizing. And what I mean by that is it sometimes can become, like, intellectual sport, where we forget that there’s a human being on the other other side. And we lose that empathy and compassion. We can kind of see that. It just becomes this intellectual jousting and arguing. And one of the things I know about you, and when you talk about this or you talk about the work that you do, and even the shirt that you’re wearing, there’s this, “be humble.” There’s this human that is never lost in this. And you said it, too: When you’re teaching your students and you’re equipping them with all of these intellectual skills and all of these tools, to use it for good. So to maintain your humanity, to maintain your character, and then to use it to edify and lift people up, not to go out and do harm. That balance, I think, is so, so important. So it’s something that I really appreciate about you and how you teach.

Melanie Trecek-King (36:19):

I appreciate those kind words. Actually—

Eric Cross (36:21):

Oh, of course!

Melanie Trecek-King (36:22):

—and if I might, I sometimes see people using critical thinking like a weapon. It’s like, “I have learned fallacies and I’m just gonna use the tools of critical thinking to tell you why you’re stupid, or why you’re wrong, and why my position is right!” But real critical thinking involves applying those same standards to your own thought processes. And even something like argumentation: the goal of our argumentation is not to BE right; it’s to GET it right. And so we’re on the same team. If we’re arguing about something, if the idea is in scientific argumentation we’re trying to find the truth, which one of us is making a better argument based on the evidence? Can your perspective help me see my own blind spots and vice versa? And the more different perspectives that we have, the more able we are to find whatever reality is. But we are in this together. And so, yeah, I think … I’m glad to hear that that’s coming through. But if you don’t have the kind of humility that says, “You know, I could be wrong,” then you’re never gonna change your mind anyway. So having the humility to say, I’m wrong. <Laugh>

Eric Cross (37:33):

Yeah. You end up just seeing people just defend turf, as opposed to support “look for truth.” And I know for me, my own education journey, I end up with more questions than answers anyways. So I go in trying to find an answer for something and I end up with 10 more questions. And I go, “OK, this is kind of how it is.” You go down this rabbit hole and you just end up with all these different questions. And it forces the humility, because you’re like, “I don’t know! I think this is what it could be, but it could also be these other answers or explanations. So this is just where I’m at, based on what we know right now, at this present time, which might shift.”

Melanie Trecek-King (38:07):

And that sounds reasonable. Yes. Which might shift. Yes.

Eric Cross (38:11):

And especially for us as life-science biology teachers, our content is something that definitely shifts. I know some of the things I teach now are not things that I learned when I was even in middle school. Just because things evolve. They change. We learn, we get new data. That’s just the way it is.

Melanie Trecek-King (38:24):

<Sighs> And Pluto is no longer a planet.

Eric Cross (38:26):

I know. Rest in — well, no, Pluto’s still there. Yeah. It’s no longer a planet. But that was one part of my kindergarten memorizations <laugh> is Pluto being in there.

Melanie Trecek-King (38:36):

Gotta change your mind.

Eric Cross (38:38):

I know. Any words of advice for science educators out there who want to focus more on honing these critical thinking skills and strategies with their own students, but they don’t know where to start? Where would you point them? Or what advice would you give them?

Melanie Trecek-King (38:52):

I think start with what you want the students to know. And not necessarily the FACTS that you want students to know, but start with the skills that you want them to know. And then really be honest with your process. When I designed Science for Life, I started with, “these are the skills that I want students to know.” And everything was in service of that. So this sort of backwards design, I think, helped me follow a path that was more likely to be useful, if that makes any sense. But it really required doing it all over again. So don’t be afraid to question the things that you’re currently doing, even if that’s all you’ve been taught or all you know.

Eric Cross (39:41):

What I’m hearing is, don’t be afraid to question your own assumptions about what you’re doing. And don’t be afraid to adapt or change or modify. Kinda, pivot. Be flexible.

Melanie Trecek-King (39:51):

Yes, be flexible and pivot. And this is where I’m in a different position than middle school and high school educators. Because I have complete freedom over what I teach in my class.

Eric Cross (40:01):

Sure.

Melanie Trecek-King (40:01):

At the end of the semester, I always joke with non-majors that there’s nothing they have to know, which actually gives me a lot of flexibility, because I could teach ’em a lot of different things. So if there are things that you have to teach students, obviously that’s one thing. But I personally think that the way that we’ve been teaching science needs a refresher. A rethinking. And so I would say, “If you want your students to learn science literacy, honestly ask, what does that mean to you? And what would that look like to get to that point?” For me, though, it was also keeping in mind that maybe I didn’t already know the best way to do that.

Eric Cross (40:43):

One of the things you mentioned earlier is trying to reach out to educators. And I know that when we work together, it’s a force multiplier. And what you’re doing is developing skills. And there’s these skills that are happening right now in academia that you’re doing. And then how do we transfer that into middle and high school. Or, I’m sorry, middle and elementary school, high school. We need to get more people into this conversation to kind of brainstorm and figure that out. We have a Facebook group, Science Connections: The Community, where we have educators that gather. That can be one place we start the conversation. And again, I know on your website you’ve been super active on social media; you’ve grown your presence on Twitter and all these different places, engaging with folks. Which is awesome. ‘Cause I know I see your posts and I’m saving the things that you’re posting and I’m thinking of ways that I can do it in my classroom. I’m gonna take that product. By the way, is that on your website, the lesson that you do with the product?

Melanie Trecek-King (41:43):

No, actually. So the article, “How to Sell Pseudoscience” is … I know Bertha Vasquez wrote up a version of it.

Eric Cross (41:50):

Maybe we can grab that. ‘Cause we might be able to put that into the show notes for folks, because she’s a middle school educator. If there’s already something that’s been done for teachers like us, we’re like, “Yeah, let me get that and let me remix it and make it my own!” if there’s already a exemplar out there.

Melanie Trecek-King (42:04):

Yeah, she’s done it. And so I will absolutely share that with you.

Eric Cross (42:08):

So, all season long, we’ve been talking about science as the underdog. We kind of framed it, you know, science oftentimes takes a back seat to math and English. It’s kinda the first thing to go. Or the first area where time can get cut. Because of what gets tested gets focused on, oftentimes. And then in addition to that, when you’re a multi-subject teacher, elementary science isn’t just one thing — it’s every field. You know, you’re a biologist, which is different than a geologist. And when you’re teaching every subject, that’s a lot. And you might not have had a science class for years. And the realities that we’re seeing over and over with different researchers and practitioners is that science could actually enhance literacy, and building those skills. And I think you really talked about it with the critical thinking skills. Those can transfer. Or the administrator that said, “This is one of the only courses I’ve seen where it transfers to other areas.” Could you share maybe with our listeners, just any advice for advocating for science in their own world?

Melanie Trecek-King (43:13):

Wow, I’m not sure I’m qualified to answer that question! One of the things that comes to mind though — because I was listening to your last episode and educators … I honestly didn’t realize how little time they had for science. And how often science was then the first to go, to allow room for other subjects. But science overlaps with a lot of other issues. And so I feel like there could be a way to bring in science when teaching these other subjects. So, for example, argumentation and logical fallacies are easy to apply to reading and writing. Information literacy, and being able to find good information online, teaching students how to laterally read, to be able to check a source, or how to use Google effectively, to put in neutral search terms to find sources, or teaching students how to recognize the characteristics of conspiratorial thinking: All of these things can overlap with so many other subjects. So the scientist in me is a little biased towards science being important enough to do this. But try to bring it into the other subjects. It doesn’t have to be completely separate.

Eric Cross (44:43):

So integrating science into other things. And I … big believer. And a hundred percent agree with you. Now I’m gonna ask a question that kinda like takes us backwards. You shared an app with me when we first met that I thought was really cool. And I know it’s a friend or colleague of yours. But as a middle school teacher, I thought it was great, because it was something that my students could download and practice some of the skills that you’re talking about. Would you talk a little bit about the cranky uncle? Is it the Cranky Uncle app?

Melanie Trecek-King (45:17):

Cranky Uncle.

Eric Cross (45:18):

Could you share a little bit about that?

Melanie Trecek-King (45:20):

Yeah. Cranky Uncle is awesome. So, Cranky Uncle is the brainchild of John Cook, who is the founder of Skeptical Science and the author of the 97% Consensus study on climate change. Cranky Uncle … so he’s also a cartoonist. And Cranky Uncle is a cartoon game where … I don’t even have to explain who Cranky Uncle is to my students. Everybody inherently gets the, the character, right? So he’s like the guy at Thanksgiving that you don’t wanna talk to because he denies climate change and he’s just really cranky. But Cranky Uncle uses the techniques of science denial, which are summarized by the acronym FLICC: So it’s Fake experts, Logical fallacies, Impossible expectations, Cherry-picking, and Conspiratorial thinking. So he uses those techniques. Again, this is technique-based inoculation. So they recognize the techniques in the game, and you earn cranky points. And as you make Cranky crankier and crankier because you’re recognizing his techniques, you learn the techniques of science denial, and level up and open up other techniques. This is another one of those examples where climate change has a lot of science behind it, right? And if you wanted to get to the science behind climate change for any particular issue … so let’s say it’s cold today, so I’m gonna say there’s no climate change. OK? If I’m gonna unpack that at a factual level, and with science, we could be here for a while. But if I told you, “That’s like saying, ‘I just ate a sandwich so there’s no global hunger.’” OK? So that’s a parallel argument. Humorous. Love to use this kind of argumentation, ’cause it makes for some … I mean, it’s funny, but you get the point. It’s an anecdote. And anecdotes aren’t good evidence. So just like that, you could teach the technique of using an anecdotal fallacy for climate-change denial. So, I have my students play this game. You could do it when you’re studying argumentation. You could do it for science denial. I use an inoculation extension with that, where I have my students pretend that … um, actually, back up for a second. So I teach a class on critical thinking. And at the end of semesters I would get emails from students on, well, they’re failing the class, but they really shouldn’t, for all of these reasons. And reading these emails, I’m like, “If you think that’s a good argument, you clearly didn’t learn what I was hoping you would learn.” So I now have my students, early in the semester, after they play Cranky, pretend that it is the end of the semester and you’re failing the class and you’re failing because you didn’t do the work. Use at least four of the fallacies from class to argue for why you should pass. So they have to put it on a discussion forum, and they’ll say things like, “Well, if you fail me, then I won’t get into graduate school and then people will die and it will all be your fault.” Or, “My dog died, and so I was really sad.” Or, um, “You’re just a terrible teacher. And you’re short. So I don’t like you.” Or that kind of thing. So, oh, they love to attack my character. It’s really funny. But it’s supposed to be funny. And the point is, the students are using those arguments, they’re using the fallacies, to argue for something. And so by creating that misinformation themselves, they learn how those fallacies work. But taken together, I mean, everything that we just talked about there, Cranky Uncle, and the fallacy assignment, or whatever iteration you want that to be in, that doesn’t have to be in a purely science unit. Right? That could be sociology. It could be argumentation. It could be English.

Eric Cross (49:01):

Absolutely. That could be totally a prompt in an English class. And practiced in there. And then this could be an interdisciplinary thing, going back and forth between English and and science. Just having these discussions and looking at it from different angles. And you’re practicing the skills in two different contexts. So you get into argumentation. And then that app, I know I had fun with it. And the questions on there definitely resonate with people in my own family. I’m like, “I feel like I’m talking to exactly somebody that I’m related to right now.” <Laugh> Melanie, anything else that you wanna share, or discuss or highlight, before we wrap up?

Melanie Trecek-King (49:39):

So we could talk about lateral reading, if you like. ‘Cause I know a lot of educators use the crap test.

Eric Cross (49:45):

Please, please, please talk about that.

Melanie Trecek-King (49:47):

So, when evaluating sources, a lot of educators teach what’s called the CRAP test. And I wish I remembered what it stood for. But basically what you do, a lot of us have been taught when you go to a website, to figure out if it’s reliable, you wanna go to the about page. Read the mission; see who they are; maybe read some of the content; evaluate the language. So is it inflammatory? Are they making logical arguments? Are the links to reputable sources as well? And the problem is that if a site wants to mislead you, they’re not going to tell you that it’s a bunk site, right? They’re just gonna do a good job of misleading you. And so, what you wanna do instead … the CRAP test basically is an evaluation of a site. And that’s what’s called vertical reading. So you’re looking through a site to determine if it’s reliable. Uh, I think his name’s Sam Wineberg at Stanford, proposed something called lateral reading. Where, instead of on the site, what you wanna do is literally open a new tab and into the search engine type the source. You could do the claim, too. And then something like Reliability or FactCheck or whatever it’s that you’re checking, and then see what other reputable sites have to say about it. So, in their study, actually, they did a really interesting study where they compared professional fact checkers to PhD historians to Stanford undergrads. And they evaluated — I wish you could … um, there’s two pediatrician organizations. One’s like the American Association of Pediatrics and the American Academy of Pediatricians, something like that. They’re very similar sounding. So you give them to students. I do this with my students as well, the same study. So I give my students those two websites. And I say, “Which one of these is more reliable?” And they do exactly what most of us do, which is spend time on the site looking around. And most of the time, if not nearly all the time, they come to the wrong conclusion. And so then I tell them what lateral reading is: “OK, instead of looking through the site, open a new tab, search the organization and reliability.” Something like that. And it takes probably 30 seconds before they realize one of them has been dubbed by the Southern Poverty Law Center as a hate group. As opposed to the other one, which is like a hundred year old huge pediatrician organization that produces their own journals and so on. But nearly all my students are fooled. And in the study, none of the fact checkers were fooled. I’m gonna get the number right. It’s something like 50% of the historians and 20% of the Stanford undergraduates got the correct answer. And they spent a lot more time on it. So it’s a great way to teach students how to use the power of the internet to evaluate sources much more quickly and, effectively. And yes, use Wikipedia, right? Wikipedia is not a final answer, but Wikipedia is actually pretty accurate. So if Wikipedia is the first place you stop, then yes, go there, see what Wikipedia says, and then follow some of their sources.

Eric Cross (52:47):

What popped in my head was like, Yelp reviews for websites. That almost sounds like what it was. It’s like when I search for a product, I don’t go and read the product description marketing. ‘Cause that’s all designed to sell me on something. But I’ll go and look in Reliability, if it’s like a car, or just other sites to cross-reference. And that sounds like what you were talking about is like cross-referencing. Seeing what FactChecker [sic] said about this site, versus seeing what a site says about itself.

Melanie Trecek-King (53:14):

Well, that’s a great analogy. Because if I wanted to know if a product was effective, what the manufacturer says about the product, clearly there’s a strong chance of bias. Right? They’re going to be on their best, um, put their best foot forward. Versus, what do independent reviewers say about this product?

Eric Cross (53:35):

Yep. And I am known to research something to death. And I get something called “paralysis by analysis.”

Melanie Trecek-King (53:42):

Ohhhh, yeah.

Eric Cross (53:44):

And it’s so bad that even if I’m trying to buy, like, towels, I need to find the best-bang-for-the-buck towel. I have to defer some of these decisions out, because I’m on the internet for three hours now. I’ll be a pseudo-expert in towels, and thread count, and all of that stuff. But yeah, that maybe that’s just the science person.

Melanie Trecek-King (54:03):

I mean, I feel your pain. I do the same thing. <Laugh> It’s annoying. Like, it’s just towels. What does it really matter? But yeah.

Eric Cross (54:10):

Coffee! It doesn’t matter what it is. I just need to go, “OK, I have to use these powers for good. Otherwise I’m gonna be researching forever.”

Melanie Trecek-King (54:16):

I wanna say one other thing. So, again, this is a college class and I have a lot of freedom. But one of the driving philosophies behind the class is a wonderful quote in a book, Schick and Vaughn, How to Think about Weird Things. And they said, “The quality of your life is determined by the quality of your decisions, and the quality of your decisions is determined by the quality of your thinking.” And I know my students want a grade. But I’m really trying to teach them how to be empowered through better thinking. That’s where the name “Thinking is Power” came from. I mean, we say “Knowledge is Power,” but it’s not enough to know things. And there’s too much to know. So being able to think and be empowered to have your own agency and not fall for someone’s bunk is my goal for my students.

Eric Cross (55:07):

And doing that is gonna help them through the rest of their lives. Not be swindled, not be taken advantage of, be able to make better decisions. There’s so many benefits to building that skill. And I know your students have definitely grown and benefited. I’m sure you’ve heard, long after you’ve taught them, heard back from them and how they’ve applied that course to their lives. Melanie, thank you so much for being here. For a few things. One, for providing and filling this space where there’s such a need. Again, the critical thinking resources, the tools that you used, are so, so important. If we ever lived in a time where they were critical, it was really what we experienced during the pandemic in the last few years. We watched people’s information literacy and science literacy play out in real time. And we literally saw life-and-death decisions being made based off those skills. That highlighted, I think how important this is. And then, taking the time to generate resources for educators like myself, that we can take and adapt and put into our classroom and start teaching our students. ‘Cause like you said, by the time they get to you, they’re, they’re so far downstream or so far in a system that, depending on the teachers that they’ve had and the education system they’ve been in, may or may not have even touched on these things. They might have learned a lot of facts, but they may not have built their muscle to be able to critically analyze and interpret the world around them. And you’ve just — even the last year, it hasn’t even been a year since we talked the first time — I’ve watched your resources continue to grow, and you share them. And so I, on behalf of those of us in K–12, thank you. And thank you for being here.

Melanie Trecek-King (56:49):

Oh, well, thank you so much for this opportunity. Thank you for everything that you do, reaching out to other educators and for giving me a platform to hopefully reach other educators.

Eric Cross (57:00):

Thanks so much for listening to my conversation with Melanie Trecek-King, Associate Professor of Biology at Massasoit Community College and creator of Thinking Is Power. Make sure you don’t miss any new episodes of Science Connections by subscribing to the show, wherever you get podcasts. And while you’re there, we’d really appreciate it if you can leave us a review. It’ll help more listeners to find the show. You can find more information on all of Amplify shows at our podcast hub, Amplify.com/Hub. Thanks again for listening.

Stay connected!

Join our community and get new episodes every other Wednesday!

We’ll also share new and exciting free resources for your classroom every month!

What Melanie Trecek-King says about science

“Students carry in their pocket access to basically all of humanity’s knowledge at this moment in time. The question is: do they know what they’re looking for?”

– Melanie Trecek-King

Associate Professor of Biology at Massasoit Community College and creator of Thinking is Power

Meet the guest

Melanie Trecek-King is the creator of Thinking is Power, an online resource that provides critical thinking education to the general public. She is currently an associate professor of biology at Massasoit Community College, where she teaches a general-education science course designed to equip students with empowering critical thinking, information literacy, and science literacy skills. An active speaker and consultant, Trecek-King loves to share her “teach skills, not facts” approach with other science educators, and help schools and organizations meet their goals through better thinking. Trecek-King is also the education director for the Mental Immunity Project and CIRCE (Cognitive Immunology Research Collaborative), which aim to advance and apply the science of mental immunity to inoculate minds against misinformation.

A woman with long blonde hair and a black top is shown in front of a blue background, framed by a circular graphic with an illustrated flask in the corner.
A laptop screen displays the “Science Connections: The Community” private group page, with science-themed icons decorating the background and edges.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. 

S2-05: Moving students forward with project-based learning

A promotional image for the podcast "Science Connections" featuring guest Janis Lodge and the topic "Moving students forward with project-based learning." Season 2, Episode 5.

In this episode, Eric Cross sits with K–5 educator Janis Lodge to chat about building on her own science curriculum to create meaningful project-based learning experiences. Janis shares her work teaching Gifted and Talented Education (GATE), and how to use those practices to help accelerate the learning of all students. Eric and Janis also talk about making time for science within K–5 classrooms. Explore more from Science Connections by visiting our main page.

DOWNLOAD TRANSCRIPT

Janis Lodge (00:00):
To me, the reward of having those kids feel like they accomplished something and the way that they can take ownership of it and go in so many different directions, I cannot take that away from them. That’s such an opportunity that if I have the means to do it, I have to just take it and run with it.

Eric Cross (00:18):
Welcome to Science Connections. I’m your host, Eric Cross. My guest today is Janis Lodge. Janis is a third-grade teacher in Orange County, California, with a specialization in gifted and talented education. Recently, Janis was awarded the Orange County Council for the Gifted and Talented Education Classroom grant. This grant funds a project that provides an extension to her third-grade science unit about environments and survival. Through this project, students will think like a biomimicry engineer as they design a robot that is inspired by an innovation found in nature. In this episode, we discuss how she uses interdisciplinary teaching practices to make time for science learning; why gifted and talented education strategies can benefit all students; and her process for creating a problem-based lesson that ultimately earned her a grant for her classroom. And now, please enjoy my conversation with Janis Lodge. One, welcome! Thanks for being here.

Janis Lodge (01:14):
Of course, I am happy to do it. I’m excited for the opportunity.

Eric Cross (01:17):
Of course! Yeah. Elementary school teachers in science, I feel like there’s so many things to have conversations about. And some of the things that you’ve really focused on, I think, are, really, really important. But I wanna start off with your journey of you becoming a teacher in the classroom. And so, would you kind of give your background, your origin story? How did you end up as a third-grade teacher?

Janis Lodge (01:37):
Well, my story is definitely not a traditional story. Before I was a teacher, I was actually living in Maui, Hawaii. I moved there right after college. I went to Chico State in Northern California. And I got a degree in graphic design. And after I graduated, well, I should give a little bit of a backstory. My last summer before graduating, I spent the whole summer in Maui and I just fell in love with it. So when I graduated, I decided instead of applying for jobs in Northern California, I’m just gonna put some resumes out in Maui and see if I can get a job. And I did. I ended up getting a job doing graphic design and marketing for a kite surf company out there. And I ended up just staying for seven years on the island. And after about seven years, I kind of got a little bit of island fever and decided I wanted to come back to California. I wasn’t sure exactly what I wanted to do, but I just had this calling that I need to do something a little more fulfilling with my life. And I started thinking about different ideas and dreams I had. And I actually started thinking about when I was younger, right? I had this dream. If you were to ask me when I was 10 years old what I wanted to be when I grow up, it would be elementary school teacher.

Eric Cross (02:48):
Really?

Janis Lodge (02:48):
Believe it or not. When I was younger, I transformed my bedroom into a classroom. My stuffed animals were my students. I just thought I’m gonna be the next best teacher ever. And you know, as I went through life and kind of went in different directions, I kind of lost sight of that dream a little bit. But for some reason, when I decided to change careers, I just remembered that. And so I just decided to go get my teaching credential and see if it worked out. And it was probably the best decision I made. I feel like everything just fell perfectly into place. I ended up getting a job at an amazing school, and now, five years later, I’m a third grade teacher.

Eric Cross (03:28):
So one of the questions I have to ask, and talking to elementary school teachers, this comes up a lot: How do you make time for science as an elementary school teacher who’s teaching everything? And let me kind of premise this with, at least for those of us in California, and I’m sure the rest of the states too, but we know this; There’s kind of this pressure with pacing and then even, depending on what school you’re at, math and English tend to get the bulk of things. And maybe there’s this perception also of like, well, I gotta teach math and English, and sometimes science gets put to the back burner for different reasons.

Janis Lodge (03:57):
Well, you’re exactly right. The beginning of the year, we were provided with a pacing from the district. And you know, they try to keep us on track, saying, “You should be starting Unit 2 at this time.” But other than that, there’s really no specific guidelines of how many days we’re supposed to be teaching or for how long. But one kind of secret that I’ve discovered is that I can weave science into the other subjects, specifically with language arts. So quite often what I do is I take a look at the language arts standard, and if it’s identifying the key details and the main idea, well I can do that with the science books used from the curriculum. So I’ll just pull those readers and we’ll do the exact same skill, start with the same standard, but we’ll use the content from science. By doing that, we call that kind of like interdisciplinary study. And the students really enjoy that more, too, because they’re using the same skills but they’re diving deeper into the content.

Eric Cross (04:54):
Right.

Janis Lodge (04:55):
And so also that helps build the background knowledge. So then when it comes to time where, if I want to do a science lab or a science investigation, now they already have that background knowledge ’cause we already dove deep into the reading and they can apply that pretty quickly right away into their lab or whatever activity they’re doing.

Eric Cross (05:12):
Can you give an example maybe of how you might pull out something that might be a skill that you’re trying to develop, maybe in an English content, but you would pull that out in a science lesson, maybe? What would you do?

Janis Lodge (05:25):
We’re actually doing that right now. So we’re in our second unit of science and they’re studying inheritance and traits and they’re looking at different organisms to see how they have adaptations to help them survive in their environment. So coincidentally part of the literacy skills is to look at multiple sources, do research, and summarize and make analysis of what they’re reading. And so we have different varied resources. I have websites; I have books, ebooks, videos, and pictures. And they’re choosing which four sources they want to use. And then, then they’re coming up with a summary at the end and then putting together a Google Slides presentation based on whatever organism that they chose.

Eric Cross (06:05):
Did you have a science background before becoming an elementary school teacher?

Janis Lodge (06:11):
Um, none. Besides what I, you know, took in high school and college.

Eric Cross (06:16):
Did you find it easy to kind of lean into the science, or was it something you just kind of jumped into and said, “All right, I’m gonna get after it”?

Janis Lodge (06:23):
What’s interesting is if, you know, throughout my education, my favorite subjects were English and reading and writing and art. And quite honestly, science wasn’t my favorite subject. But I think because of that, that inspires me to come up with creative ways of presenting the information to them and making it exciting and engaging for them, because I don’t want them to feel that way. I want them to be excited about all subjects. And I think that’s the beauty of combining the different subjects like I mentioned before. Like I say, you know, “What would a scholar do? Think like a wildlife biologist. And like with my project, think like a biomimicry engineer.” And so it kind of shifts their thinking. Like, it’s not just, “Oh, we have to study science.” It’s like, “No, you are the scientist; you are a meteorologist; or you are an author. How would an author write about this? How would an illustrator capture this in a photo or a comic strip?” And so, when you really combine those disciplines, you can take it to another level. So even if science isn’t their favorite subject, like maybe it wasn’t for me growing up, they can still take something they’re passionate about and apply the science content to it and they really resonate with them.

Eric Cross (07:37):
You leaned into your strengths. Which are more like, coming into it, you had all these kind of creative strengths. You have that background as a graphics designer. You were into the arts. But then with those strengths, did that kinda give you more confidence to dive into the science work, because you approached it from your assets that you were already coming to the table with?

Janis Lodge (07:55):
Yeah.You said it perfectly. If you look at it from a different lens, there’s all these different ways you can approach science.

Eric Cross (07:59):
I find it in my own science class, too. We’re all teaching the same standards. But how I approach it is through Eric Cross’s kind of personality and understanding and my angle, and another teacher might do it a different way. But we’re all leading to the same destination.

Janis Lodge (08:14):
Exactly.

Eric Cross (08:15):
That kind of leads me to my next question, and this is having to do with the project that you just alluded to. The biomimicry project. So you did a biomimicry project. Would you consider that like a project based-learning assignment?

Janis Lodge (08:26):
Well, this will be the third year that I’ve taught this unit. And when I wrapped it up last year, it’s through the Amplify Science program, and they do a wonderful job of having a lot of investigations and really thinking like a biomimicry engineer. But the final part of the unit was to design a robot inspired by a giraffe, to eliminate invasive plants in a particular environment. And the project part of it at the end was to create a model using Popsicle sticks and pipe cleaners. And then the other part of it was a digital simulation where they would put in different shape structures of teeth, and kind of reconfigure the shape of the mouth. And then they’d put in what they think is effective, and then the computer would say, oh, you’re 98% successful or 70% successful. And I remember at the end of it the students were like, “OK, well when do we make the robots?” And I thought, “Well, we’re just doing the simulation, or we’re just doing this model out of Popsicle sticks; we’re not actually gonna make a robot.” And they just seemed so disappointed. And that’s kind of how the wheels started turning my head like, “Well, what if they actually could make a robot? The only thing stopping me is I don’t have the materials to do it.” So, shortly after that unit wrapped up, coincidentally I saw the email about this grant opportunity that was being offered through the Orange County Council for Gifted Education. And they said, If you have a project that you wanna get funded that would promote GATE strategies within the classroom, then you can submit this proposal. So that’s how the ball got rolling for that proposal. And I researched different robotics kits and different companies and I found one that was really user-friendly for third graders, and not so difficult for me to learn as well.

Eric Cross (10:10):
You’re a risk taker. Like, I’m already seeing this as I’m talking to you. Is that just who you are or do you have a network? Like what keeps you taking these risks?

Janis Lodge (10:18):
I don’t really consider it a risk, because it’s exciting for me. Like I said, I don’t know that much about robotics, but the idea of learning more and then teaching that to my students is exciting. And you know, there was a little bit of risk ’cause I’m deviating a little bit from the curriculum, from the standard lesson, but to me, the reward of having those kids feel like they accomplished something, and the way that they can take ownership of it and go in so many different directions, and on top of that, develop coding skills and computer science skills and robotic skills, to me it was just like I cannot take that away from them. That’s such an opportunity that if I have the means to do it, I have to just take it and run with it. So I think just being inspired by the potential outcomes of what could happen is what made me take that risk.

Eric Cross (11:05):
Did you just kind of create this from scratch? Did you work with a team of people? How did you come to the point where you were ready to present this for the grant?

Janis Lodge (11:12):
Pretty much from scratch. Like I said, the Amplify unit, it does teach them about robotics that were inspired by nature. So some of the materials that they read, and there’s some videos that show really great examples. There’s like a robotic arm that was inspired by an elephant trunk. There’s a book that shows what this field is, biomimicry engineer, they actually show like what they do in that field. And I thought this is a perfect way to apply it because the curriculum’s already pretty much set it up for me; now I just have to add this one final component to it. And essentially it becomes project-based learning at that point, because they’re taking their knowledge and their skills that they’ve learned up to that point. Even the unit that we’re doing doing right now is building up to it. So it’s kind of that final—instead of giving them a test at the end and saying, “OK, tell me what you learned about inheritance and traits and environments,” they can actually take that knowledge and apply it to an innovation or creation that comes out of their own mind, which is so much more powerful.

Eric Cross (12:11):
Do they connect to any other learning goals as they’re doing these projects?

Janis Lodge (12:15):
Well, I think first and foremost, the 21st century skills that from day one I tell them, the four Cs: collaboration, creativity, communication, and critical thinking. All of those are woven in through this lesson. From the beginning, we talked about the whole engineering design process. So from the beginning, they start with a question and oftentimes that actually can be the hardest for them to think about, “What’s a scientific question or a problem that I wanna solve?” If they’re passionate about, maybe, a sport or the environment or something within their school, I go, “There it is. OK, that’s the problem. How can you design something inspired by nature to solve that problem?” And then, from there they go into the planning and the designing and the testing and then the improving. So going through that engineering design process, I think, is what really makes them feel like they are the engineer going through this. And they can make mistakes. They can take risks. A lot of my students I’ve found are afraid to take risks. They wanna make sure they succeed. And they need that challenge to know that if they do fail, that’s OK. We can just revisit this. We can test it. We can look at it in a different way.

Eric Cross (13:27):
You maybe wonder about, how do you assess something like this?

Janis Lodge (13:30):
I think that’s where all those stages along the way are important. Because I wanna make sure that they have a plan and that it’s based on the knowledge that they’ve gained in the unit. I think one of the other things about project-based learning is the final product of how they demonstrate their mastery. And in my classroom I oftentimes give them a choice of how they’re gonna present that to me. So maybe they’re going to write it out like an essay. Maybe they’re gonna create a Google slide. Maybe they’re gonna make a video. Maybe they’re going to—obviously in this part they will have the model, but they’ll have to have some way to explain it to me. And I think giving them that choice gives them the opportunity to show it in the way that’s meaningful to them.

Eric Cross (14:14):
And are you using like a rubric when you’re grading these assignments? Or, how do you actually grade it?

Janis Lodge (14:20):
Yes. So we have a rubric that’s provided to us for the written component that all the students will do at the end. But I can take that same rubric and see if they’ve applied that to the project. So even the verbiage wouldn’t really need to change. I think it’s still important that the students are able to demonstrate this in written form and so all of them will still complete that written component, but to also give them the opportunity to show that in the modality of their choice. I think is really important too.

Eric Cross (14:48):
Right. And you have some students that feel much more comfortable being able to present orally versus—

Janis Lodge (14:53):
Exactly.

Eric Cross (14:53):
—versus writing versus maybe doing a video. I mean, we see that in middle school and in high school too. Students show their knowledge or their understanding of a topic depending on the medium in different ways, and some better than others. Some may find that they can communicate it a lot better orally, but when pen goes to paper or fingers go to keyboard, you might grade it completely different, ’cause they’re not able to transfer what’s in their mind into writing. And the way you’re doing it, and giving that student choice, they probably have so much more buy-in, I’d imagine, because they get to pick what they get to do.

Janis Lodge (15:21):
Right.

Eric Cross (15:22):
You said something earlier and I wanna come back to it. So you mentioned GATE, and GATE is not something that I hear a lot in my world, but it was something I heard a lot when I was in school. There were kind of all of these perceptions and ideas about GATE. You’re a GATE teacher, correct?

Janis Lodge (15:38):
Right.

Eric Cross (15:39):
What is GATE, and what is it like being a GATE teacher? What are the misconceptions, if any, that you might have heard or come across?

Janis Lodge (15:46):
Well, so GATE stands for Gifted and Talented Education. And first and foremost, I think a misconception is that we’re just kind of doing whatever we want; we come up with our own lessons and teach a totally different curriculum. Which is definitely a myth. Because we start with the exact same standards as any other third grade class that you’d walk into. That’s definitely where we start. But I think in addition to the standards, we also implement what are called GATE standards: So they’re Depth, Complexity, Acceleration, and Novelty. And there’s a lot of tools that we use in the classroom, different strategies. You’ll see things like the prompts of Depth and Complexity. We’ll use things like “think like a disciplinarian”; I’m doing “think like a biomimicry engineer.” But really, all they are are just thinking tools and strategies to elevate students thinking and kind of go below that surface level of the content to dive deeper. It also provides opportunities for acceleration. So for example, our last science unit, it was on magnetic force, and there was a handful of students that just grasped the concepts right away, and they’re ready for something else. They’re ready for more rigor. They need some challenge. And so at that point I can kind of pull that group aside and provide some differentiation for them. And I said, “OK, well, you understand the concept of magnetic force, balanced forces. So now what I want you to do is think about something that you’re really passionate about, and how could you use magnetic force somewhere in that field—again to solve a problem, problem-based learning—and present it to me?” So they create this form, it’s like a “think like a disciplinarian” frame, and one of them was “think like a hockey player.” And he’s trying to think of a way that he can incorporate magnetic force. Anyway, I could go on and on. But basically it’s finding what these students’ passions are. And I do that with all my students. And I should probably preface this by saying that even though these are standards that I implement in my classroom because it’s a GATE classroom, these are practices and tools that can be applied to any learner, at any age. And they really just enrich the education for all students.

Eric Cross (18:02):
So your classroom is, is a mixed classroom. There’s GATE students and then general—

Janis Lodge (18:05):
Right.

Eric Cross (18:07):
—students, non-GATE students, in the same class. It’s interesting because I imagine GATE is kind of scaffolding up to a higher level, but then, you also said something that I’ve noticed when I’m creating scaffolds for my students to support them, who may not be at a grade level, maybe in reading or literacy or math, those same scaffolds can help all students.

Janis Lodge (18:27):
So yeah, I don’t just go, “OK, you’re my GATE students; I’m gonna use these practices on you.” I use it for the whole class. But I’m also surprised by having that mix of these different learning styles. A lot of times students are inspired by other students, or, you know, we have this big thing about one of the prompts is Multiple Perspectives. I try to do that as much as I can, because students are inspired by the ideas of their peers. And quite often, if they hear it from a peer, it could be exactly what I just said, but they heard their student say it in a different way and it just clicks and they’re like, “Wow, I get that.”

Eric Cross (19:00):
I think a lot of teachers struggle or, or maybe feel ill-equipped, to support higher-level students. Did you get trained to be a GATE teacher? First lemme ask that question: Did you get special training for this?

Janis Lodge (19:13):
Yes. I went through a course, I think it was like a six-week certification course, through my district.

Eric Cross (19:19):
OK, so you got a special training, which—I’ve been in the classroom for nine years; I teach at a university as an adjunct professor; but I’ve never been trained on teaching gifted or accelerated students. And I’m kind of wondering now, like, do you feel like it made you a better teacher?

Janis Lodge (19:33):
Absolutely.

Eric Cross (19:34):
And if so, how do I get to do this?

Janis Lodge (19:36):
Well, it’s through the county. I mean, anybody can get trained and certified how to teach this way. But, just like you said, I think coming out of that, my eyes were just open, and my biggest takeaway is that these practices, even though they are designed for gifted and talented, it really kind of reshaped my thinking about how I, number one, present material to the students, that I’m doing it in an engaging way, and I’m not just lecturing at them; there’s opportunities for them to collaborate and communicate and use multiple resources. So, you know, how I’m teaching has changed. And then also, how I’m providing opportunities for them to demonstrate their learning. And a lot of that is project-based learning, because once they have the knowledge and skills they need to do something with it. I mean, that’s really the true definition of innovation, is taking the skills or taking something that you’ve learned, and now go with it. Run with it.

Eric Cross (20:32):
How can we take what you’ve learned and then kind of spread it, so teachers have this in their toolkit, too? Like for me, I have multiple ways to be able to support reading and literacy and math and tools and sentence frames. And my students who have special learning plans, I have a have a lot of tool sets for that. I wanna build my tool sets for this other area for my students who want to continue, who wanna run, or go beyond, or even stretch themselves. I think we need to take some of the things that you’re doing and not make them kind of like this exclusive group, but also let’s share it with everyone, ’cause if everybody can access it—

Janis Lodge (21:03):
I agree.

Eric Cross (21:03):
—we might see a lot more potential or a lot more opportunities for students who might not otherwise have them.

Janis Lodge (21:08):
And one thing: My school, I’m really proud to say that my principal has seen that. You know, he’s like, “Well why are we just keeping this in the GATE classroom?” So he’s working on getting all of our teachers certified.

Eric Cross (21:19):
No, I love what you’re doing and your principal sounds, sounds awesome for doing that and recognizing that this can benefit more students than just the ones who, you know, pass the Raisin Test, I think it’s what it was called when I was taking it, or whatever it is back then.

Janis Lodge (21:31):
Exactly.

Eric Cross (21:32):
We’ve talked about project-based learning, the GATE classroom…I kind of wanna come back to you as we wrap up. Thinking about, like, the jobs that you and I do, and the people that listen to this podcast, we have one of the few jobs that people remember us for a lifetime. And I wanna ask you, who was someone that was maybe inspirational in your educational career, that inspired you, or is maybe one of the most memorable? You might have several…but who is someone that was memorable to you in your career, and why? Why were they memorable to you?

Janis Lodge (22:02):
Yeah. Well, obviously, when I was younger, I was definitely inspired by all my teachers. The fact that I turned my bedroom into a classroom…I just was just in awe of this profession. But I think one that really resonated with me was my junior year in high school. I was taking a newspaper class and the teacher was Mrs. Kavanaugh, and she really taught us everything from writing the articles to the editing, to putting the pages together. And I remember in that class I was working on this program called QuarkXPress. I don’t even know if it exists anymore. But I was just fascinated with putting all these pieces together that we’d worked on for so long and getting the articles, picking the pictures, the illustrations and the titles. And I remember her looking at me saying, “You really enjoy this, don’t you?” And I said, “Yeah.” And she said, “Well, I have a computer graphics elective class that you should take next year.” And I thought, “OK, I’d love to do this, this opportunity to expand my knowledge and my skills.” So because of that, I took the computer graphics class the next year and I just remember throughout the whole time, she was just constantly encouraging me and acknowledging my skills. And I find myself doing that as a teacher as well. ‘Cause that really resonated with me. And it’s funny, this summer I was going through some boxes of some old stuff from high school, and I found this handout that I had made, because I remember my senior year of high school, she said, “Janis, you know what? You’re doing such a great job; we have these new, incoming students coming into the newspaper class, and I’d love for you to actually teach them how to do this pagination on this QuarkXPress program. I want you to put something together and actually teach it to them.” I thought, “Wow, she believes in me that much that she’s gonna let me teach this to the incoming students.” But I think my takeaway from that was that she gave me the opportunity to take those skills and actually do something with them, to apply them right away.

Eric Cross (23:53):
Mrs. Kavanaugh. Miss Kavanaugh. Shout-out to Miss Kavanaugh. As you told that story, I heard you as a teacher because I’m hearing she’s applying these GATE strategies in that situation. That’s what that’s what I heard.

Janis Lodge (24:08):
Yeah, absolutely.

Eric Cross (24:09):
She personalized this learning. She created a specialized opportunity. You presented to a real audience that was authentic. It had this personalization in it and this rigor and this challenge and it made a huge impact. And it’s just amazing to listen to you and hear this come full-circle, and now you’re doing this with little ones. And I just wanna thank you for your time in doing the interview, sharing your story with how you became a teacher, your students, the projects that you do. And just like so many teachers, going the extra mile for your kids and bringing in these really important 21st century skills; they’re gonna be so much better off for it. And I know it makes my job easier when I get them in the classroom, so thank you.

Janis Lodge (24:49):
Yeah. Well, thank you for the opportunity.

Eric Cross (24:51):
My pleasure. Thanks so much for listening and we wanna hear more about you and the educators who inspire you. You can nominate them as a future guest on Science Connections by emailing STEM@amplify.com. That’s S -T-E-M at amplify dot com. And be sure to click subscribe, wherever you listen to podcasts, and join our Facebook group, Science Connections: The Community. Until next time.

Stay connected!

Join our community and get new episodes every other Wednesday!

We’ll also share new and exciting free resources for your classroom every month!

What Janis Lodge says about science

“The reward of having kids feel like they accomplished something and take ownership is such an opportunity [with project-based learning] that I have to run with it. Being inspired by the potential outcomes of what could happen is what made me take that risk.”

– Janice Lodge

3rd Grade Teacher, De Portola Elementary

Meet the guest

Janis Lodge is a third grade teacher in Orange County, California. Her career in education started six years ago when she decided to follow her passion of making a positive difference in the lives of young scholars. Prior to teaching, Janis lived in Maui, Hawaii for seven years, working in the field of graphic design, marketing, and hospitality. She has found that her interest in innovation, project-based learning, and inquiry-driven exploration has helped shape her into the educator she is today. STEAM is integrated regularly into her classroom, and her students continually develop 21st century skills through a variety of unique projects. ​​Janis is also a PAL (Peer Assistance Leadership) Advisor for her school, where she helps young leaders (4th-6th graders) cultivate their leadership skills and empowers them to make a positive difference in their school and community. Janis was recently awarded the Orange County Council for the Gifted & Talented Education Classroom Grant, which will provide an extension to the third grade Amplify Science Unit: Environments and Survival.

A woman with long blonde hair smiles at the camera; she is inside a circular frame with a small decorative star in the corner.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. Listen here!

Welcome to Grade K

BACK TO MAIN TK–5 PAGE

Amplify Science California is so effective you can cover 100% of the NGSS in half the time of other programs.

You can breathe a sigh of relief knowing all you need is:

  • 66 days per year
  • 2 lessons per week
  • 45 minutes per lesson
Four images of children engaged in science experiments: growing plants, using liquids, a girl in safety goggles mixing substances, and playing with a physics kit.

What students learn

When you’re ready:

  • Find a summary of each unit below including each unit’s student role and anchor phenomenon.
  • Click on the orange “See how the unit works” link to download a helpful Unit Guide. These guides make great companions to busy reviewers looking for a big-picture understanding of how each unit works.
An illustration from Needs of Plants and Animals unit

Unit 1

Needs of Plants and Animals

Student role: Scientists

Phenomenon: There are no monarch caterpillars in the Mariposa Grove community garden ever since vegetables were planted.

See how this unit works

An illustration from the Pushes and Pulls unit

Unit 2

Pushes and Pulls

Student role: Pinball engineers

Phenomenon: Pinball machines allow people to control the direction and strength of forces on a ball.

See how this unit works

An illustration from the Sunlight and Weather unit

Unit 3

Sunlight and Weather

Student role: Weather scientists

Phenomenon: Students at one school are too cold during morning recess, while students at another are too hot during afternoon recess.

See how this unit works

How teachers teach

When you’re ready:

  • Scroll down and take a closer look at your classroom resources.
  • Click on the orange links below each component to see grade-specific samples.
Most adopted curriculum for the NGSS California

Classroom Slides

These customizable PowerPoints are available for every lesson of the program and make delivering instruction a snap with visual prompts, colorful activity instructions, investigation set-up videos and animations, and suggested teacher talk in the notes section of each slide.

Video introduction to Classroom Slides

Sample Classroom Slides

Sample Classroom Slides (Spanish)

Teacher’s guide and digital screen displaying the needs of plants and animals: milkweed monarchs educational material with illustrations of insects.

Teacher’s Reference Guide

Available digitally and in print, our unit-specific reference guides are chock full of helpful resources, including scientific background knowledge, planning information and resources, color-coded 3-D Statements, detailed lesson plans, tips for delivering instruction, and differentiation strategies.

Login to platform below to access

Amplify Science California supports 3-D learning with more materials than any other program.

Materials Kits

Our kits include enough non-consumable materials to support a class of 36 students and enough consumable items to support 72 students. In other words, each kit can last two years! Plus, our unit-specific kits mean you just grab the tub you need and then put it all back with ease.

List of investigations by unit

List of materials by unit

Illustrations of two children’s book covers displayed on a tablet, titled Un día ocupado en Villa Empuja and A Busy Day in Pushville, showing a street scene.

Big Books and Student Books

Students are never asked to read alone. Rather, books are read to, with, and by students with ample scaffolding and support provided by the teacher. Big Books are read aloud or together with the class to introduce ideas. Student Books allow for small-group reading and reading in pairs.

Sample Student Book (Spanish)

List of Student Books by unit

Sample Student Book

Two amplify science textbooks, one in spanish and one in english, displaying pinball machine diagrams on their covers.

Consumable Notebooks

Available for every unit, our Student Investigation Notebooks contain instructions for activities and space for students to record data and observations, reflect on ideas from texts and investigations, and construct explanations and arguments.

Sample Student Investigation Notebook

Sample Student Investigation Notebook (Spanish)

Amplify Science California and Mystery Science work together to help you transition to the California NGSS.

Mystery Science

Our exclusive partnership with Mystery Science means you get our NGSS core curriculum plus two years of free access to Mystery Doug and his extensive library of captivating videos that deepen students’ understanding of each unit’s phenomenon.

Mystery Science lesson alignment

Line drawing of a person using a laptop, with headphones and a line illustration of a rocket launching above their head, symbolizing creativity or inspiration in Boost Reading.

Coming Soon

Unlike other publishers, we don’t make you wait until your next adoption to get the latest and greatest from Amplify. We’re always launching new and exciting features. What’s more, we’ll push them out to you even after you adopt us!

See what’s coming for 2020-2021

Health benefits

Amplify offers a comprehensive benefits package that meets the health needs of our diverse population and their families. Preventative care, mental health services, fertility benefits, flexible spending and health savings accounts, life insurance, and robust dental and vision coverage are just some of the benefits accessible to all eligible employees. The Transparency in Coverage Final Rule requires health plans and issuers to publicly disclose pricing information via machine readable files (MRFs). 

Time off

Our employees and their well-being are our top priority. For that reason, Amplify offers unlimited paid time off to all permanent (salaried) employees. Hourly employees receive a generous PTO bank. This can be used for vacation, sick days, or personal time—whether you need to take your pet to the vet, or care for a sick friend or family member. Paid parental leave, short-term and long-term disability benefits, and paid holidays are also common employee benefits offered at Amplify.

Voluntary benefits

Looking to protect your spouse, partner, children, or pet? Our comprehensive selection of voluntary benefits makes it easier and more affordable to cover those that you care about the most. Supplemental life insurance, pet insurance, and critical illness are just some of the voluntary benefits our employees can take advantage of at any time during their employment with Amplify.

Financial benefits

If saving for retirement is a priority to you, you’re at the right place. Amplify offers traditional (pre-tax) and Roth-based retirement account options with an employer-match benefit, giving you the flexibility and freedom to set and save for your retirement goals. Also, all members of our full-time staff have the opportunity to take advantage of our equity incentive plan, which demonstrates our commitment to our employees and the success of our organization.

Remote work

Remote work isn’t a new trend at Amplify. With more than half our staff based in cities outside the Amplify headquarters, we believe our employees can be productive and make valuable contributions regardless of where they’re located. Fun is also part of the remote work experience at Amplify—from happy hours to talent shows, yoga, and meditation sessions, Amplifiers can enjoy the many virtual employee engagement events that take place all year round.

At Amplify, we believe Pennsylvania students and teachers deserve high quality instructional materials.

That’s why we partner with schools across the Keystone State to meet their core curriculum, assessment, and intervention goals. With solutions grounded in research and evidence-based practices, Amplify is leading the way with rigorous and relevant learning experiences.

Select a program below to learn more.

Illustration of Pennsylvania featuring cows, a barn, city skyline, groundhog, pretzel, chocolate bar, Liberty Bell, and a train on a green landscape.
Group of diverse middle school students working on laptops and discussing in classroom.

Amplify Desmos Math (K–12)

Amplify Desmos Math is a comprehensive K–12 math suite that has everything in one place: benchmark and progress monitoring, core instruction, integrated personal learning, embedded intervention, and more. This structured, problem-based approach builds on students’ curiosity while strategically developing math fluency and lasting grade-level understanding. The program delivers:

  • Engaging, discourse-rich math lessons that fuel classroom conversations and drive the learning process.
  • Comprehensive integrated resources, including print and digital, along with manipulatives and Centers Kits in K–5.
  • Real-time insights, data, and reporting that inform instruction and celebrate student thinking.

Flexible, social problem-solving experiences

Digital lessons should be able to bring student thinking to the surface and spark productive discussions. We bring this vision to life with interactive social, collaborative lessons powered by Desmos technology.

A teacher using a tablet interacts with a young student in a classroom, with educational posters in the background.

mCLASS early literacy assessment and intervention (K–8)

Effective universal screening and progress monitoring means that every student is an individual and targeted instruction should become a reality, not a dream. 

mCLASS® is the gold-standard K–8 assessment and intervention suite for early literacy that helps every child learn to read confidently.

  • Universal screening presented in one-minute measures shows where your students are, who is at risk, and where to target instruction.
  • Dyslexia screening identifies students who are at risk for reading difficulties without needing an additional assessment system
  • Elimination of manual assessment process gives you instant results and clear next steps for each student.
  • Progress monitoring allows you to quickly adjust to student needs, based on how they are responding to instruction.

The power of mCLASS

Based on decades of leading literacy research, mCLASS lets you know exactly which part of a skill a student is struggling with, then gives you effective next steps and lesson plans.

Watch how mCLASS can help teachers:

  • Save hours of time.
  • Catch at-risk students earlier.
  • Connect data to personalized learning.
Several students listening attentively

Amplify Core Knowledge Language Arts (PreK–5)

High-quality, content-rich instruction should combine multisensory phonics instruction with knowledge-rich texts and interactive multimedia resources.

Built on the Science of Reading, Amplify Core Knowledge Language Arts® (CKLA) sequences deep content knowledge with research-based foundational skills.

  • Explicit, systematic foundational skills lessons are easy to teach and exciting to learn.
  • Deep knowledge-building across units and grades helps access complex text, so real comprehension can happen.
  • Rich, authentic texts with engaging topics and immersive learning support students wherever they are.

Students love CKLA. But don’t just take our word for it.

Amplify CKLA is impactful for teachers, administrators, families, and most of all—students! Hear what students think about Amplify CKLA.

A young girl focuses on a laptop with a stack of books, a colorful creature, and autumn leaves in a stylized graphic.

Boost Reading (K–5)

Authentic personalized learning should be developmentally appropriate, grounded in research, and truly adaptive.

Boost Reading is a personalized, digital supplemental reading tool for grades K–5 featuring:

  • Research-based approach to critical literacy skill development that is proven to accelerate reading growth in just 30 minutes per week.
  • Captivating storylines and games with powerful individualized reading instruction and practice to bridge learning gaps while learning independently.
  • Actionable data that offers deeper insights into student performance and needs.

Boost Reading keeps all students playing and motivated to learn.

Boost Reading includes age-appropriate storylines that excite students’ curiosity. Regardless of their reading ability, students are placed in a year-long storyline that is developmentally appropriate for them. As students grow, so do the immersive worlds around them.

A student reading "Summer of the Mariposas"

Amplify ELA (6–8)

Amplify ELA is the only program truly designed to support middle school students at this critical developmental moment. We ensure that skills are taught, standards are covered, and the test is prepped – all while bringing texts to life and differentiating instruction.

  • Rich, complex text and research-based instruction at the center of every lesson to build the vocabulary, knowledge, and skills needed in middle school, high school, and beyond.
  • Multiple points of entry and differentiated support allow every student, regardless of fluency or ability, to engage deeply in the same curriculum.
  • Immersive digital apps that offer engaging interactive experiences where students work with key skills in brand new ways.

We are the program for middle schoolers.

Let’s face it– middle school students are different from high school students. That’s why they deserve a program of their own.

A futuristic cityscape with a figure in a red hood looking at a large digital billboard displaying a "wanted for unlawful reading" alert.

Boost Close Reading (6–8)

Middle school students need to exercise their close reading skills in order to deeply comprehend across the curriculum. Based on a riveting storyline designed especially for middle schoolers, Boost Close Reading helps students find deeper meaning in a digital journey like no other.

  • Inspire engagement via high-interest storytelling, choose-your-own adventure experiences, and skill-building features.
  • Explore topics like claim, evidence, reasoning, word choice, and tone in both literary and informational texts.
  • Detailed teacher dashboards display student progress, performance, and usage information, offering easy-to-access insights on areas of strength and weakness.

Fight the machines and save the world.

Before the machines took over, humans could fend for themselves. Now humanity is trapped. And their only hope? You.

A badge for EdReports Review Year 2023, two students at a computer, two students discussing with a tablet, and an educational diagram of a spider on a screen.

Amplify Science Pennsylvania (K–8)

Amplify Science Pennsylvania is a proven K–8 curriculum that develops critical thinkers who are prepared to solve problems in their communities and beyond. It features:

  • Phenomena-based exploration and three-dimensional learning where students take on the roles of scientists and engineers to solve real-world problems.
  • Immersive hands-on activities that teach students how to gather evidence, ask questions, and develop and defend claims.
  • Literacy-rich science instruction that enables young scientists to become excellent readers, writers, and speakers.
  • Custom lessons specifically designed to meet Pennsylvania’s STEELS standards.
Bar chart comparing science content knowledge: Do-Talk-Read-Write approach at 51.5% and Business-as-usual approach at 36.6%.

Do, Talk, Read, Write students outperform their peers.

Bar graph comparing middle school science vocabulary, showing 48.6% for the Do-Talk-Read-Write approach with Amplify Science and 22.5% for the Business-as-usual approach.

English language learners who use Do, Talk, Read, Write outperform their ELL peers.

Bar chart compares middle school science learning progression outcomes before and after a unit, showing similar distributions with the highest value at category 3 in both cases, illustrating the impact of Amplify Science instruction.

Do, Talk, Read, Write increases learning outcomes.

Get Support

Get support

Do you use already use an Amplify program in Pennsylvania? Our support team is here to provide technical and instructional support by phone, live chat, or email.

Get help now

Contact us

A woman with long brown hair and glasses wearing a light blue sweater, smiling at the camera against a gray background.

Julie Couch

District Enrollment <1800 students

A woman with long blonde hair and blue eyes is smiling at the camera, wearing a black top, in a well-lit indoor setting.

Jen Mee

Western PA

A smiling person with shoulder-length gray hair, wearing a peach-colored scarf and a gray sweater, stands against a plain white background. This image captures the essence of Pennsylvania teachers who are dedicated to enriching Science programs for elementary students.

Monica Vincent

Southeast PA

A man with curly brown hair and a beard, smiling broadly, wearing a suit, dress shirt, and floral tie, standing outdoors with trees and grass in the background.

Keenan Zambelli

Northeast & Central PA

Acceptable Use Policy

Amplify Education, Inc. (“Amplify”) products support classroom instruction and learning and include Amplify CKLA, Amplify ELA, Amplify Science, Amplify Desmos Math, Desmos Math, Boost Reading, Boost Math, mCLASS, Mathigon, services at classroom.amplify.com (for creating and assigning activities) and student.amplify.com (for use of the activities or curricula as directed by an instructor), and any other product or service that links to this Acceptable Use Policy (together, the “Products”). This Acceptable Use Policy (the “AUP”) provides the general terms and conditions applicable to your use of the Products. By accessing, downloading, or using the Products, you agree to be bound by the terms of this AUP. 

Notwithstanding the foregoing, nothing in this AUP supersedes or limits your rights under the terms of any other agreement you or your institution have entered into with Amplify regarding the use of Products. In the event of any conflict between the AUP and the terms and conditions of an applicable agreement that you or your institution have entered into with Amplify, the terms and conditions of such agreement shall control.

Our Products are geared towards K–12 students, educators, and staff who use the Products as authorized by their School District or State Agency (each as defined in the Privacy Policy (defined below), and together, “School”) (“Authorized School Users”). Student Data (defined below) is owned and controlled by the School, and Amplify receives Student Data as a “school official” under Section 99.31 of the Family Educational Rights and Privacy Act of 1974 (“FERPA”) for the purpose of providing the Products hereunder. In addition, we rely on the School acknowledging that it is acting as the parent’s agent and consenting on the parent’s behalf to process personal information of students under the age of 13 (“Child Users”) in accordance with the Children’s Online Privacy Protection Act (“COPPA”). 

Schools may provide authorization in two ways: 

(1) by the School agreeing to our Customer Terms and Conditions located at amplify.com/customer-terms or another agreement between Amplify and the School, as applicable; or 

(2) by an educator, staff member, or agent of a School (“Educator”) agreeing to this AUP. If you are an Educator and wish to use the Products in your classroom, you represent and warrant that the use of the Products in your classroom has been authorized by your School, and that you are authorized to accept this AUP on behalf of the School.

In each case, we provide these Products solely for the benefit of the School and for no other commercial purpose. We require all Schools to review our Privacy Policy, available at amplify.com/customer-privacy (“Privacy Policy”), and to make a copy of the Privacy Policy available to the parents or guardians of Child Users.

We also provide limited opportunities for individual users to sign up for a restricted account for at-home use of our Products (together, with Authorized School Users, “Authorized Users”). Please see Additional terms for Mathigon and Amplify Classroom accounts (Section 18) for additional information.

1. License

Subject to compliance with this AUP, you are granted a non-transferable, non-exclusive, non-sublicensable license to access and use the Products. You understand that your use of the Products does not confer to you any intellectual property rights held by Amplify or its licensors. Unless otherwise indicated, any future release, update, or other addition to functionality or content of the Products will be subject to this AUP. 

2. Restrictions

You may access and use the Products solely for non-commercial instructional and administrative purposes. Guidelines for such purposes may be set forth at http://amplify.com/amplify-program-usage-guidelines and additional guidelines may be detailed in materials associated with the Product You are accessing. Further, You may not, except as expressly authorized by Amplify: (a) copy, modify, translate, distribute, disclose, or create derivative works based on the contents of, sell, or otherwise exploit, the Products, or any part thereof; (b) decompile, disassemble, reverse engineer the Products, or otherwise use the Products to develop functionally similar products or services; (c) modify, alter, or delete any of the copyright, trademark, or other proprietary notices in or on the Products; (d) rent, lease, or lend the Products or use the Products for the benefit of any third party; (e) avoid, circumvent, or disable any security or digital rights management device, procedure, protocol, or mechanism in the Products; (f) use any content from the Products, including but not limited to text, images, videos, assessments, lesson plans, or code, as input or training material for any machine learning or artificial intelligence system, including large language models, neural networks, or other algorithmic models, for any purposes, commercial or non-commercial; or (g) permit any Authorized User or third party to do any of the foregoing. You also agree that any works created in violation of this section are derivative works, and, as such, You agree to assign, and hereby assign, all right, title, and interest in such works to Amplify. The Products and derivatives thereof may be subject to export control laws, restrictions, regulations, and orders of the U.S. and other jurisdictions (together, “Export Laws”). You agree to comply with all applicable Export Laws, and will not, and will not permit Authorized Users to, export, or transfer for the purpose of re-export, any Product to any prohibited or embargoed country in violation of any U.S. export law or regulation. Further, You represent that You are not located in a country that is subject to a U.S. Government embargo, subject to sanctions by the U.S. Office of Foreign Assets Control, or included on any restricted party list maintained by the U.S. Bureau of Industry and Security. The software and associated documentation portions of the Products are “commercial items” (as defined at 48 CFR 2.101), comprising “commercial computer software” and “commercial computer software documentation,” as those terms are used in 48 CFR 12.212. Accordingly, if You are associated with the U.S. Government or its contractor, You will receive only those rights set forth in this Agreement in accordance with 48 CFR 227.7201-227.7204 (for Department of Defense and their contractors) or 48 CFR 12.212 (for other U.S. Government licensees and their contractors).

3. Use of the products

In connection with your access to and use of the Products, you agree not to: (a) post, upload, or otherwise transmit or link to content that is: unlawful; threatening; harmful; abusive; pornographic or includes nudity; offensive; harassing; excessively violent; tortious; defamatory; false or misleading; obscene; vulgar; libelous; hateful; or discriminatory; (b) violate the rights of others, including patent, trademark, trade secret, copyright, privacy, publicity, contract, or other proprietary rights; (c) harass or harm another person; (d) exploit or endanger a minor; (e) impersonate any person or entity; (f) introduce or engage in activity that involves the use of viruses, bots, worms, Trojan horses, time bombs, spyware, or any other computer code, files, or programs that interrupt, destroy, or limit the functionality of any computer software or hardware or telecommunications equipment, or otherwise permit the unauthorized access to or use of a computer or a computer network; (g) interfere with, damage, disable, disrupt, impair, create an undue burden on, or gain unauthorized access to the Products or any account (as defined below), or Amplify’s servers or networks; (h) restrict or inhibit any other person from using the Products (including by hacking or defacing the Products); (i) remove, disable, block, or obscure any portion of the Products; (j) use technology or any automated system, such as scripts or bots, to collect user names, passwords, email addresses, or any other data from or through the Products, or to circumvent or modify any security technology or software that is part of the Products; (k) send or cause to send (directly or indirectly) unsolicited bulk messages or other unsolicited bulk communications of any kind through the Products; (l) solicit, collect, or request any information for commercial or unlawful purposes; (m) post, upload, or otherwise transmit an image, audio recording, or video of another person without that person’s consent; (n) use the Products to advertise, promote, or engage in any commercial activity (including engaging in advertising, sales, contests, sweepstakes, or other promotions) without Amplify’s prior written consent; (o) frame or mirror the Products without Amplify’s express prior written consent; (p) use the Products in a manner inconsistent with any applicable law, rule, or regulation; (q) use any robot, spider, search/retrieval application, or other manual or automatic device to retrieve, index, “scrape,” “data mine,” or in any way gather content of the Products or reproduce or circumvent the navigational structure or presentation of the Products; (r) attempt, facilitate, or encourage others to do any of the foregoing. In addition to the foregoing restrictions, your use of the Products may also be subject to an additional acceptable use policy provided to you by your School, as applicable. You are responsible for meeting the hardware, software, telecommunications, and other requirements listed at amplify.com/customer-requirements.

4. Intellectual property

The Products and any Product logo, and certain other of the names, logos, and materials displayed in the Products, may constitute trademarks, trade names, or service marks (“Marks”) of Amplify or other entities. You are not authorized to use any such Marks. Ownership of all such Marks and the goodwill associated therewith remains with Amplify or those other entities. The content provided to you in the Products, including the software, graphs, text, and graphics, is protected under copyright laws, is subject to other intellectual property and proprietary rights and laws, and is owned by Amplify or its licensors. Your access to the Products does not transfer to you or any third party any rights, title, or interest in or to such intellectual property rights. You may not use the content of the Products, in whole or in part, to train or fine-tune any machine learning or artificial intelligence model or system, including for research, product development, commercial services, or any other purpose, commercial or non-commercial. Such use constitutes unauthorized derivative work and a violation of Amplify’s intellectual property rights. Your rights to make use of the Products are limited to those provided under this AUP, any additional terms as may be agreed upon between your School and Amplify, and any available exceptions under applicable intellectual property laws. Amplify Products are protected by patents (see amplify.com/virtual-patent-marking).

5. Account information

Your authentication to enable your access and use of these Products is based in part upon information supplied by you. You are required to (a) provide accurate information to Amplify and promptly report any changes to such information, (b) not share or allow others to use your account, (c) maintain the confidentiality and security of your account information, and (d) use the Products solely via such authorized accounts. You may not share your credentials (i.e., username and password) to access the Products with anyone except the person for whom that account was created. You agree to notify Amplify immediately of any unauthorized use of your account or related authentication information. Amplify will not be responsible for any losses arising out of the unauthorized use of your account.

6. Student data

The parties acknowledge and agree that in the course of providing the Products, Amplify may collect, receive, or generate information that directly relates to an identifiable current or former student of a School (“Student Data”). Student Data may include personal information from a student’s “educational records,” as defined by FERPA. Student Data is owned and controlled by the School and Amplify receives Student Data as a “school official” under Section 99.31 of FERPA for the purpose of providing the Products hereunder. Individually and collectively, Amplify and School agree to uphold our obligations, as applicable, under FERPA, COPPA, the Protection of Pupil Rights Amendment (“PPRA”), and applicable state laws relating to Student Data privacy. Amplify’s Privacy Policy governs the collection, use, and disclosure of Student Data collected or stored on behalf of the School under this AUP. The School is responsible for providing notice or obtaining appropriate consents under applicable laws to authorize Authorized School Users’ use of the Products, including making a copy of the Privacy Policy available to the parents or guardians of Child Users. Please see Additional Terms for Mathigon and Amplify Classroom accounts (Section 18) for additional information.

7. Confidentiality

You acknowledge that in connection with these terms, Amplify may provide you with certain sensitive or proprietary information (“Confidential Information”), including software, source code, assessment instruments, research, designs, methods, processes, customer lists, training materials, product documentation, know-how, or trade secrets, in whatever form. You agree (a) not to use Confidential Information for any purpose other than use of the Products in accordance with the AUP, and (b) to take all steps reasonably necessary to maintain and protect the Confidential Information of Amplify in strict confidence. Confidential Information shall not include information that, as evidenced by your contemporaneous written records: (i) is or becomes publicly available through no fault of your own; (ii) is rightfully known to you prior to the time of its disclosure; (iii) has been independently developed by you without any use of the Confidential Information; or (iv) is subsequently learned from a third party not under any confidentiality obligation.  

8. User materials

You represent, warrant, and covenant that you have all the necessary rights, including consents and intellectual property rights, in connection with any data, information, content, and other materials provided to or collected by Amplify from you or on your behalf in connection with your use of the Products, including materials and content that you post, upload, transmit, email, or otherwise make available on, through, or in connection with the Products (“User Materials”), and that except as otherwise agreed by your School and Amplify, you retain any ownership rights that you have in your User Materials. You hereby grant to Amplify and its affiliates, licensees, and authorized users, a perpetual, non-exclusive, fully paid-up, royalty-free, sublicensable (through multiple tiers), transferable (in whole or in part), worldwide license to use, modify, excerpt, adapt, create derivative works and compilations based upon, publicly perform, publicly display, reproduce, and distribute such User Materials in connection with the Products, subject to Amplify’s Privacy Policy. You and your School are responsible for the accuracy, integrity, completeness, quality, legality, and safety of such User Materials. You further represent and warrant that the posting of such User Materials through or in connection with the Products does not violate the privacy rights, publicity rights, copyrights, contract rights, or any other rights of any person or entity. Amplify and your School reserve the right (but have no obligation) to monitor the Products, including for inappropriate content or conduct, and to remove any content in their discretion without liability to you or any third party. Further, Amplify reserves the right to investigate and take appropriate legal action against anyone who, in Amplify’s discretion, violates this AUP or attempts to do so, including terminating or suspending a user’s account or access to or use of the Products, or reporting any content or conduct to law enforcement authorities. You are solely responsible for creating and maintaining your own backup copies of your User Materials. Amplify is not responsible for any loss, theft, or damage of any kind to any User Materials. 

9. Feedback

If you provide us with any ideas, proposals, or suggestions related to the Products (“Feedback”), you hereby acknowledge and agree that your provision of any Feedback is gratuitous, unsolicited, and without restriction, and does not place Amplify under any fiduciary or other obligation. You hereby grant to Amplify a worldwide, royalty-free, fully paid-up, exclusive, perpetual, irrevocable, transferable, and fully sublicensable (through multiple tiers) license to reproduce, distribute, perform and/or display (publicly or otherwise), adapt, modify, and otherwise use such Feedback, in any format or media now known or hereafter developed, and you hereby represent and warrant that you have all necessary rights to grant the foregoing license.

10. Third party links and services

The Products may make available, or third parties may provide, links to websites, software, applications, resources, advertisements, content, or other products or services created, hosted, or made available by third parties (“Third Party Services”). When you access or use a Third-Party Service, you are interacting with the applicable third party, not with Amplify, and you do so at your own risk. Inclusion of any Third-Party Service or a link thereto within the Products does not imply approval or endorsement of such Third-Party Service. Amplify does not control any content that is not Amplify content, and as such, you may be exposed to offensive, indecent, inaccurate, or otherwise objectionable content in the course of accessing or using such Third-Party Services linked from the Products. You are solely responsible for your interactions with other users of the Products, providers of Third-Party Services, and any other third parties with whom you interact on, through, or in connection with the Products. AMPLIFY IS NEITHER RESPONSIBLE NOR LIABLE FOR ANY THIRD-PARTY SERVICES, INCLUDING THE ACCURACY, INTEGRITY, COMPLETENESS, QUALITY, LEGALITY, USEFULNESS, OR SAFETY OF, OR INTELLECTUAL PROPERTY RIGHTS RELATING TO, SUCH THIRD-PARTY SERVICES. ANY ACCESS TO OR USE OF SUCH THIRD-PARTY SERVICES MAY BE SUBJECT TO THE TERMS AND CONDITIONS AND INFORMATION COLLECTION, USAGE, AND DISCLOSURE PRACTICES OF THIRD PARTIES. THIS AUP DOES NOT CREATE ANY RELATIONSHIP BETWEEN YOU AND ANY PROVIDER OF THIRD-PARTY SERVICES, AND NOTHING IN THIS AUP WILL BE DEEMED TO BE A REPRESENTATION OR WARRANTY BY AMPLIFY WITH RESPECT TO ANY THIRD-PARTY SERVICE.

11. Digital Millennium Copyright Act

The Digital Millennium Copyright Act of 1998 (“DMCA”) provides recourse for copyright owners who believe that material appearing on the Internet infringes their rights under U.S. copyright law. If you believe that any material residing on or linked to from the Products infringes your copyright, please send (or have your agent send) to Amplify’s Copyright Agent, by email, fax, or regular mail, a written notification of claimed infringement with all of the following information: (a) identification of the copyrighted work claimed to have been infringed, or, if multiple copyrighted works are covered by a single notification, a representative list of such works; (b) identification of the claimed infringing material and information reasonably sufficient to permit us to locate the material on the Products (such as the URL(s) of the claimed infringing material); (c) information reasonably sufficient to permit us to contact you, such as an address, telephone number, and, if available, an e-mail address; (d) a statement by you that you have a good-faith belief that the disputed use is not authorized by the copyright owner, the copyright owner’s agent or the law; (e) a statement by you that the above information in your notification is accurate, and a statement by you, made under penalty of perjury, that you are the owner of an exclusive right that is allegedly infringed, or that you are authorized to act on such owner’s behalf; and (f) your physical or electronic signature. Amplify’s Copyright Agent for notification of claimed infringement can be reached as follows: Amplify Education, Inc., 55 Washington Street #800, Brooklyn NY 11201; Attn: Copyright Agent. Amplify’s Copyright Agent for notification of claimed infringement can also be reached electronically at legal@amplify.com. Amplify reserves the right to terminate infringers’ and suspected infringers’ accounts or their access to or use of the Products.

12. Changes to the products

Amplify may, without prior notice, change any Product or stop providing any features of any Product. We may permanently or temporarily terminate or suspend your access to any Product features without notice for any reason, including if in our sole determination you violate any provision of this AUP. Upon termination, you continue to be bound by this AUP.

13. Warranty disclaimer

PRODUCTS ARE PROVIDED “AS IS” AND WITHOUT WARRANTY OF ANY KIND BY AMPLIFY. AMPLIFY EXPRESSLY DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING ANY WARRANTY AS TO TITLE, NON-INFRINGEMENT, MERCHANTABILITY, OR FITNESS FOR A PARTICULAR PURPOSE OR USE. YOU ASSUME RESPONSIBILITY FOR SELECTING THE PRODUCTS TO ACHIEVE YOUR INTENDED RESULTS AND FOR THE ACCESS AND USE OF THE PRODUCTS, INCLUDING THE RESULTS OBTAINED FROM THE PRODUCTS. WITHOUT LIMITING THE FOREGOING, AMPLIFY MAKES NO WARRANTY THAT THE PRODUCTS WILL BE ERROR-FREE OR FREE FROM INTERRUPTIONS OR OTHER FAILURES OR WILL MEET YOUR REQUIREMENTS. AMPLIFY IS NEITHER RESPONSIBLE NOR LIABLE FOR ANY THIRD-PARTY CONTENT OR SOFTWARE INCLUDED IN PRODUCTS, INCLUDING THE ACCURACY, INTEGRITY, COMPLETENESS, QUALITY, LEGALITY, USEFULNESS, OR SAFETY OF, OR IP RIGHTS RELATING TO, SUCH THIRD-PARTY CONTENT AND SOFTWARE. ANY ACCESS TO OR USE OF SUCH THIRD-PARTY CONTENT AND SOFTWARE MAY BE SUBJECT TO THE TERMS AND CONDITIONS AND INFORMATION COLLECTION, USAGE, AND DISCLOSURE PRACTICES OF THIRD PARTIES.

14. Limitation of liability

IN NO EVENT WILL AMPLIFY BE LIABLE TO YOU FOR ANY INCIDENTAL, SPECIAL, CONSEQUENTIAL, PUNITIVE, RELIANCE, OR COVER DAMAGES, DAMAGES FOR LOST PROFITS, LOST DATA, LOST BUSINESS, OR ANY OTHER INDIRECT DAMAGES, EVEN IF AMPLIFY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. TO THE EXTENT PERMITTED BY APPLICABLE LAW, AMPLIFY’S ENTIRE LIABILITY TO YOU ARISING OUT OF PERFORMANCE OR NONPERFORMANCE BY AMPLIFY OR IN ANY WAY RELATED TO THE SUBJECT MATTER OF THIS AUP, REGARDLESS OF WHETHER THE CLAIM FOR SUCH DAMAGES IS BASED IN CONTRACT, TORT, STRICT LIABILITY, OR OTHERWISE, WILL NOT EXCEED $100 IN AGGREGATE. UNDER NO CIRCUMSTANCES WILL AMPLIFY BE LIABLE FOR ANY CONSEQUENCES OF ANY UNAUTHORIZED USE OF THE PRODUCTS THAT VIOLATES THIS AUP OR ANY APPLICABLE LAW OR REGULATION.

15. Termination

Amplify may terminate or suspend your access to the Products at any time for any reason, including if Amplify believes that you have violated the AUP or have engaged in conduct that violates applicable law or is otherwise harmful to the interests of Amplify, any other Amplify user, or any third party. Upon termination, you will: cease using the Products and return, purge, or destroy all copies of any Products and, if so requested, certify to Amplify in writing that such surrender or destruction has occurred. Sections 3–13, 16, and 17 will survive the termination of this Agreement.

16. Governing Law

This Agreement will be governed by and construed and enforced in accordance with the laws of the U.S., state of New York, without giving effect to the choice of law rules thereof.

17. Additional terms for iOS apps

By downloading any Products through Apple, Inc.’s App Store (“iOS Products”), you agree that the following additional terms apply to your use of our iOS Products:

  1. This AUP is not a legal agreement with Apple, Inc. (“Apple”). As between Amplify and Apple, Amplify (not Apple) is responsible for the iOS Products and the contents thereof.
  2. The license to use the iOS Products under Section 3 above is limited to use (i) on iOS devices that you or your School owns or controls, separate from and in addition to any specific technical requirements for any iOS Product, and (ii) as permitted by the Usage Rules set forth in Apple Media Services Terms and Conditions.
  3. You must comply with applicable third-party terms of agreement when using the Products.
  4. Without limiting Section 13 above and solely as between Amplify and Apple, you acknowledge that: (i) Apple has no obligation whatsoever to furnish any maintenance and support services with respect to the iOS Products; (ii) Amplify (not Apple) is responsible for addressing any claims of yours or of any third party relating to the iOS Products or your possession and/or use of the iOS products, including but not limited to (1) product liability claims, (2) any claim that the iOS Products fail to conform to any applicable legal or regulatory requirement, and (3) claims arising under consumer protection, privacy, or similar legislation; (iii) in the event of any failure of the iOS Products to conform to any applicable warranty, you may notify Apple, and Apple will refund the purchase price for the iOS Products to you; to the maximum extent permitted by applicable law, Apple will have no other warranty obligation whatsoever with respect to the iOS Products, and any other claims, losses, liabilities, damages, costs, or expenses attributable to any failure to conform to any warranty will be Amplify’s sole responsibility; and (iv) in the event of any third-party claim that the iOS Products or your possession and use of the iOS Products infringes that third party’s intellectual property rights, Amplify (not Apple) will be responsible for any investigation, defense, settlement, and discharge of any such intellectual property infringement claim.
  5. You represent and warrant that: (i) you are not located in a country that is subject to a U.S. Government embargo, or that has been designated by the U.S. Government as a “terrorist supporting” country; and (ii) you are not listed on any U.S. Government list of prohibited or restricted parties.
  6. Apple and Apple’s subsidiaries are third-party beneficiaries of these Terms, and upon your acceptance of these Terms, Apple will have the right (and will be deemed to have accepted the right) to enforce these Terms against you as a third-party beneficiary thereof.
  7.  Any questions, complaints, or claims with respect to the Products should be directed to: 

Email: privacy@amplify.comMail: Amplify Education, Inc., 55 Washington St. #800, Brooklyn, NY, 11201

18. Additional terms for Mathigon and Amplify Classroom accounts.

a. Mathigon updates: Amplify no longer offers accounts for Child Users, but we will continue to allow Child Users to access their active legacy Mathigon accounts where verifiable parental consent was obtained. We will continue to protect personal information in accordance with the Privacy Policy and applicable law.

b. Mathigon and Amplify Classroom:

i. School Use:

  1. Educators: If you are an Educator, you can create a Mathigon or an Amplify Classroom account using any existing email or through an existing third-party account (e.g. Google, Microsoft). Go to https://mathigon.org/signup#teacher  to sign up for Mathigon. Go to classroom.amplify.com to sign up for Amplify Classroom.
  2. Students can also sign up using a unique class code provided by an Educator. Educators are responsible for gaining appropriate authorization or permission from their School to use the Products with students, including Child Users, before providing their unique class code or linking the Products to a third-party service like Google Classroom. For such use in the school context, we do not request additional consent from parents in accordance with the “school official” exception under FERPA and relevant COPPA guidance. For more information, visit our Privacy Policy, which describes how we collect, use, and disclose personal information and data through the provision of our Products in schools. 

ii. Outside of School Use: If you are an individual user using the Products at home or otherwise outside of the school context, you are prohibited from collecting or providing any personal information from students or minors. You are permitted to access the platform for instructional purposes, but you may not enroll or roster minors, create accounts for minors, or input any personal information of minors into the Product.

19. Updates to this policy

We may change this Acceptable Use Policy in the future. For example, we may update it to address changes in our product offerings, or to address changes in the law or best practices. If we make changes that materially impact your legal rights or use of our products, we will provide prominent notification to you (e.g. via the Site or by email).  Otherwise, we will post any updates to the policy with an updated “Last Revised Date” and all changes will become effective immediately. Please check the Last Revised Date to confirm if the policy has been revised.

Last Modified: February 2, 2026

A closer look at grades K–2

Amplify Science California is based on the latest research on teaching and learning and helps teachers deliver age-appropriate, high-quality, literacy-rich instruction that enables students to take on the roles of scientists and engineers to solve real-world phenomena every day.

In the K–2 classroom, this looks like students:

  • Collecting evidence from a variety of sources.
  • Making sense of evidence in a variety of ways.
  • Formulating convincing scientific arguments.
A collage of four images: building a toothpick structure, a boy reading a book to a girl, two children conducting a water experiment, and a light projection setup.
Graphic showing a research process with four steps: spark intrigue with a real-world problem, explore evidence, explain and elaborate, and evaluate claims, connected in a cycle with arrows.

Program structure

Our cyclical lesson design ensures students receive multiple exposures to concepts through a variety of modalities. As they progress through the lessons within a unit, their understanding gradually builds and deepens, ultimately leading to their ability to develop and refine increasingly complex explanations of the unit’s phenomenon.

It’s this proven program structure and lesson design that enables Amplify Science California to teach less, but achieve more. Rather than asking teachers to wade through unnecessary content, we designed our K–2 program to address 100% of the California NGSS in just 66 days.

Scope and sequence

Every year of our K–2 consists of 3 units and 66 total lessons. Said another way, each unit contains 20 lessons plus two dedicated assessment days (a Pre-Unit Assessment and End-of-Unit Assessment).

Lessons at grades K–1 are written for a minimum of 45-minutes, and grade 2 lessons are written for a minimum of 60-minutes—though teachers can expand or contract the timing to meet their needs.

Educational curriculum chart showcasing a progression of amplify science lessons from kindergarten to grade 5, categorized by grade and subject areas like plants, animals, weather, and energy.

Unit types

While every unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, each unit also emphasizes a particular science and engineering practice.

In each grade K–2:

  • One unit emphasizes the practice of investigation.
  • One unit emphasizes the practice of modeling.
  • One unit emphasizes the practice of engineering design.
Investigation Units

Investigation units focus on the process of strategically developing investigations and gathering data to answer questions. Students are first asked to consider questions about what happens in the natural world and why, and are then involved in designing and conducting investigations that produce data to help answer those questions.

Modeling Units

Modeling units provide extra support to students engaging in the practice of modeling. Students use physical models, investigate with computer models, and create their own diagrams to help them visualize what might be happening on the nanoscale.

Engineering Design Units

Engineering design units provide opportunities for students to solve complex problems by applying science principles to the design of functional solutions, and iteratively testing those solutions to determine how well they meet preset criteria.

Units at a glance

An illustration from Needs of Plants and Animals unit
Needs of Plants and Animals

Domains: Life Science, Earth and Space Science, Engineering Design

Unit type: Investigation

Student role: Scientists

Phenomenon: There are no monarch caterpillars in the Mariposa Grove community garden since vegetables were planted. 

Download unit guide

Download lesson planner

An illustration from the Pushes and Pulls unit
Pushes and Pulls

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Pinball engineers

Phenomenon: Pinball machines allow people to control the direction and strength of forces on a ball.  

Download unit guide

Download lesson planner

Silhouette of a playground structure against a blue sky with clouds and three yellow suns.
Sunlight and Weather

Domains: Earth and Space Science, Life Science, Engineering Design

Unit type: Modeling

Student role: Weather scientists

Phenomenon: Students at Carver Elementary School are too cold during morning recess, while students at Woodland Elementary School are too hot during afternoon recess.  

Download unit guide

Download lesson planner

Illustration of sea turtles swimming among seaweed in the ocean, with a large shark in the background.
Animal and Plant Defenses

Domain: Life Science

Unit type: Modeling

Student role: Marine scientists

Phenomenon: Spruce the Sea Turtle lives in an aquarium and will soon be released back into the ocean, where she will survive despite ocean predators.  

Download unit guide

Download lesson planner

Two hands holding a paper with a drawing of a pyramid and a tree, illuminated by a flashlight, projecting another shadow of the image on the wall.
Light and Sound

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Light and sound engineers

Phenomenon: A puppet show company uses light and sound to depict realistic scenes in puppet shows.  

Download unit guide

Download lesson planner

An illustration from the Spinning Earth unit
Spinning Earth

Domain: Earth and Space Science

Unit type: Investigation

Student role: Sky scientists

Phenomenon: The sky looks different to Sai and his grandma when they talk on the phone.  

Download unit guide

Download lesson planner

An elephant standing next to a tree uses its trunk to pick a fruit from a branch while more fruit hangs above.
Plant and Animal Relationships

Domains: Life Science, Engineering Design

Unit type: Investigation

Student role: Plant scientists

Phenomenon: No new chalta trees are growing in the fictional Bengal Tiger Reserve in India.  

Download unit guide

Download lesson planner

A hand holds a red bean on a table, while a wooden stick spreads white glue and scattered beans. Also on the table are a white cup and a yellow pen.
Properties of Materials

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Glue engineers

Phenomenon: Different glue recipes result in glues that have different properties.  

Download unit guide

Download lesson planner

Illustration of a coastline with cliffs, a recreation center building with a red roof and a sign, evergreen trees, a blue flag, and a sandy beach below.
Changing Landforms

Domain: Earth and Space Science

Unit type: Modeling

Student role: Geologists

Phenomenon: The cliff that Oceanside Recreation Center is situated on appears to be receding over time.  

Download unit guide

Download lesson planner

Peoria K–5 Science Review

To view this protected page, enter the password below:



Welcome to Boost Reading (formerly Amplify Reading) for grades K–8!

On this site, you’ll find resources to guide you in your review.

About the program

Boost Reading is a K–8 student-driven literacy program that provides both enrichment and remediation for all students, leveraging the power of compelling storytelling to engage students in personalized reading instruction and practice. 

Excite and engage your class with game-based learning within a literacy program that supports teachers in building their students’ skills in decoding, fluency, comprehension, and close reading.

Hear from educators like you

“Boost Reading has been a great way for me to add differentiation in my classroom. My students love working on it….I also love that I can monitor how they doing and adjust small group instruction to help them.”

Hear from teachers, administrators, and students across the country who are using Boost Reading in their classrooms right now.

Resources to support your review

Download the resources below before you review the program to better understand the program structure, components, digital resources, and more.

Engaging, age-appropriate narratives

Below you’ll find examples of games students will encounter in Boost

Reading K–5 as well as an overview of the Boost Reading 6–8 experience.

K-5 overview

Watch an overview of the many games in Boost Reading’s engaging K-5 game world.

Grade K: Gem and Nye

Students learn to blend sounds into words, by choosing the picture of the word that the “soundbots” say when blended together.

Oral Reading Fluency (ORF)

Students are tasked with verbally repeating what they hear, and thus teachers have deeper diagnostic data about their oral language abilities and errors.

Grade 3: Ink Blott

In Ink Blott, Students help a subterranean dweller repair her underground world by tunneling through dirt and fixing broken sentences using morphology skills.

Grades 6-8: The Last Readers

Boost Reading sets students in a dystopian future world run by Machines, where people are told what to read and what to think. This interactive graphic novel is divided into three books with each chapter focusing on a different skill or concept.

Request a demo

Fill out the form and a sales representative will be in touch!

A closer look at grades K–2

Amplify Science is based on the latest research on teaching and learning and helps teachers deliver age-appropriate, high-quality, literacy-rich instruction that enables students to take on the roles of scientists and engineers to solve real-world phenomena every day.

In the K–2 classroom, this looks like students:

  • Collecting evidence from a variety of sources.
  • Making sense of evidence in a variety of ways.
  • Formulating convincing scientific arguments.
A collage shows science activities: toothpick structure, two kids reading, two kids pouring liquid into cups, and a light experiment with shadows.
A four-step process diagram: Spark, Explore, Explain and elaborate, and Evaluate, connected by arrows, with a summary below about engaging through cohesive storylines.

Program structure

Our cyclical lesson design ensures students receive multiple exposures to concepts through a variety of modalities. As they progress through the lessons within a unit, their understanding gradually builds and deepens, ultimately leading to their ability to develop and refine increasingly complex explanations of the unit’s phenomenon.

It’s this proven program structure and lesson design that enables Amplify Science to teach less, but achieve more. Rather than asking teachers to wade through unnecessary content, we designed our K–2 program to address 100% of the NGSS in just 66 days.

Scope and sequence

Every year of our K–2 consists of 3 units and 66 total lessons. Said another way, each unit contains 20 lessons plus two dedicated assessment days (a Pre-Unit Assessment and End-of-Unit Assessment).

Lessons at grades K–1 are written for a minimum of 45-minutes, and grade 2 lessons are written for a minimum of 60-minutes—though teachers can expand or contract the timing to meet their needs.

Grid of nine educational subject cards for kindergarten, grade 1, and grade 2, each listing curriculum topics like "needs of plants and animals" and "engineering design" with lesson durations.

Unit types

While every unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, each unit also emphasizes a particular science and engineering practice.

In each grade K–2:

  • One unit emphasizes the practice of investigation.
  • One unit emphasizes the practice of modeling.
  • One unit emphasizes the practice of engineering design.
Investigation Units

Investigation units focus on the process of strategically developing investigations and gathering data to answer questions. Students are first asked to consider questions about what happens in the natural world and why, and are then involved in designing and conducting investigations that produce data to help answer those questions.

Modeling Units

Modeling units provide extra support to students engaging in the practice of modeling. Students use physical models, investigate with computer models, and create their own diagrams to help them visualize what might be happening on the nanoscale.

Engineering Design Units

Engineering design units provide opportunities for students to solve complex problems by applying science principles to the design of functional solutions, and iteratively testing those solutions to determine how well they meet preset criteria.

Units at a glance

Needs of Plants and Animals

Domains: Life Science, Earth and Space Science, Engineering Design

Unit type: Investigation

Student role: Scientists

Phenomenon: There are no monarch caterpillars in the Mariposa Grove community garden since vegetables were planted. 

Pushes and Pulls

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Pinball engineers

Phenomenon: Pinball machines allow people to control the direction and strength of forces on a ball.  

Sunlight and Weather

Domains: Earth and Space Science, Life Science, Engineering Design

Unit type: Modeling

Student role: Weather scientists

Phenomenon: Students at Carver Elementary School are too cold during morning recess, while students at Woodland Elementary School are too hot during afternoon recess.  

Animal and Plant Defenses

Domain: Life Science

Unit type: Modeling

Student role: Marine scientists

Phenomenon: Spruce the Sea Turtle lives in an aquarium and will soon be released back into the ocean, where she will survive despite ocean predators.  

Light and Sound

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Light and sound engineers

Phenomenon: A puppet show company uses light and sound to depict realistic scenes in puppet shows.  

Spinning Earth

Domain: Earth and Space Science

Unit type: Investigation

Student role: Sky scientists

Phenomenon: The sky looks different to Sai and his grandma when they talk on the phone.  

Plant and Animal Relationships

Domains: Life Science, Engineering Design

Unit type: Investigation

Student role: Plant scientists

Phenomenon: No new chalta trees are growing in the fictional Bengal Tiger Reserve in India.  

Properties of Materials

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Glue engineers

Phenomenon: Different glue recipes result in glues that have different properties.  

Changing Landforms

Domain: Earth and Space Science

Unit type: Modeling

Student role: Geologists

Phenomenon: The cliff that Oceanside Recreation Center is situated on appears to be receding over time.  

Corona-Norco Unified School District

To view this protected page, enter the password below:



Our new activity page: Inside the renovation

We all love a good before-and-after story—it’s the reason we watch those home improvement shows, right? You see a space that could use some love, a design team works their magic, there’s a grand reveal (often with tears), and the result is breathtaking. Most importantly, if it’s a good reno, the design successfully meets the family’s unique needs. It’s one of the best parts of our work as designers, product managers, and engineers: the opportunity to make something both enjoyable and practical for a group of real people that needed something better in their lives.

That’s just what we’ve done for this coming school year: put on our Joanna Gaines pants and did an overhaul of the Amplify Classroom activity page. 

It’s a big change! So before the official release on June 26, we wanted to share this before-and-after story—what this page is, why it needed some love, how we ran our process, and what renovation moves we made. 

And while we don’t necessarily expect tears of joy, we are very eager to hear your reactions!

Wait, what is the activity page?

It’s the essential page that so many of you use every day to deliver interactive lessons that drive student engagement and success. Our math, literacy, and science teams create so many rich learning resources for educators teaching kindergarten through high school—and this page is where those Amplify Classroom activities come together.

This is what it looks like today:

A screenshot of the Amplify Desmos Math platform shows the "Hamster Homes" lesson page, featuring lesson goals, instructions, and a sidebar menu of math topics—highlighting engaging Amplify classroom activities​.

Within a given activity page, you might find:

  • At-a-glance lesson information, such as timing and device needs.
  • Details about pedagogical approach, such as goals, routines, and standards.
  • Thumbnail previews of screens, organized by section.
  • PDFs, videos, or images to accompany the lesson.
  • Links to related lessons, practices, or assessments.
  • The students and classes to which you’ve assigned the lesson.

Amplify’s curriculum teams spend years ensuring teachers have everything they need to be successful in the classroom, which is evident in our activity pages (and in long lists like the one above). 

Ok…what’s the issue?

With so many resources comes the risk of overwhelm. Imagine buying a small starter home and filling it with all of your treasures. You might get a work-from-home office, perhaps a cat, maybe a kid or two, eventually a woodworking hobby—and suddenly all the goodness is a bit much. You’re wrestling with too much stuff, digging through piles to find the one thing you need.

Our teachers are feeling this overwhelm in the activity page, and they don’t have the luxury of time to dig around for what they need—not when they have 30 impatient students waiting for them to start, or 10 minutes to prepare for tomorrow.

Here’s what we were hearing:

  • “The Assign and Teach buttons are hard to find. I don’t think I would’ve noticed them without someone pointing them out.” —7th- and 8th-grade math teacher
  • “It causes me some anxiety that I can’t see the entire lesson at once. I would prefer knowing how many slides there are because it gives me a whole picture.” —7th- and 11th-grade math teacher
  • “It’s like Amplify took every suggestion and put them all in. We need it to be more streamlined, as in, ‘Here’s what you need to get through the day in one area, here’s extra stuff in another area.’” —2nd-grade CKLA teacher

We want this page to be a useful guide, not a scavenger hunt. Something had to change.

So what did we do?

Talked to you—we connected with nearly 400 teachers (through surveys and live conversations) to understand your needs, to share our ideas, and to test whether these designs made sense for real teachers using this page. 

We dug into the pain points to understand them in more detail. We examined 15 other products to understand how content landing pages are typically laid out, including great ones like Canva, Pear Practice, Notion, YouTube, and more. We talked to our curriculum authors across all subjects to understand their priorities and future plans. We sketched diagrams organizing categories of information on the page, developed them into varied options and clickable prototypes, and refined and iterated and tried again, on repeat.

Throughout these iterations, we heard loud and clear that we needed to:

  • Organize the page elements more intuitively, to make it simpler to find things faster.
  • Clearly emphasize the actions teachers should take, so there’s never any doubt in the moment of teaching.

Here are some of the design options we explored.

Screenshot of an educational webpage titled "Packing Up School Supplies," featuring a video, instructions, and illustrations of a backpack and school supplies to amplify classroom activities for a kindergarten math lesson.

Click to expand each image.

Screenshot of an Amplify Desmos Math lesson page titled "Packing Up School Supplies" for kindergarten, featuring a video player and amplify classroom activities​ along with detailed guidance for teachers.
Screenshot of an online lesson plan for kindergarten math titled "Packing Up School Supplies," designed to amplify classroom activities​, with detailed activities, materials needed, and instructions for teachers.

While you gave us some really excellent critique (as all great teachers do, and for which we are forever grateful), you also gave us encouraging signs that we were on the right track. When we shared our final design concept, you said:

  • “This activity page seems less overwhelming. It’s just easier on my nervous system.” —3rd-grade CKLA teacher
  • It reads a lot cleaner. I don’t feel like I have to scroll around to find what I’m looking for.” —6th-grade science teacher
  • “I love the layout. It’s so easy to see the flow and it got me thinking about pacing and how to chunk student work.” —6th- and 7th-grade math teacher

What does it look like now?

After almost two years of work with your needs at the forefront, we felt confident making three big moves.

  1. We used tabs to drive page organization, so there are no more long scrolls. Each tab has a clear job to do, and answers a key question for lesson planning:
    • What am I teaching? (Screens tab)
    • What context do I need to understand? (About tab)
    • Which students have access to this? (Sessions tab)
    • What additional resources do I need? (Resources tab)
  2. We created a sticky left sidebar for always-present facilitation actions. The sidebar surfaces high-value information that teachers need quick access to, regardless of which tab they are on.
  3. We made the lesson flow clearly visible. We gave maximum real estate to screen thumbnails and organized them into sections to show teachers the flow in just one glance.

And now it’s almost your turn to try it! 

On June 26, 2026, we will cut the ribbon, open the door, and give you your turn to explore. 

If you are a free Amplify Classroom user, you’ll see the new activity page by default. If you’re a paid Amplify customer, you’ll need to opt in to see the new activity page this year. At the end of the upcoming 2026-27 school year, the old page will be retired.

So walk around, live in it for a bit, then tell us what you think! We have more improvements coming, and we are always listening—please contact us here with any thoughts. Thank you to every single educator who joined us on this journey.


Eli and Gretchen are writing on behalf of a huge team of people who delivered this project.

Gretchen Keillor is a Product Design Manager for Amplify Classroom.

Eli Sheldon is a Senior Product Manager for Amplify Classroom.

Amplify ELA – Atlanta Review3

To view this protected page, enter the password below:



Program pg template redesign -AI

To view this protected page, enter the password below:



What’s included in our Spanish language arts curriculum

Amplify Core Knowledge Language Arts® (CKLA) is available in both English and Spanish. Amplify Caminos al Conocimiento Esencial, our robust Spanish language arts companion for grades K–5, supports multiple teaching models, including dual language immersion and transitional classrooms.

A laptop screen displays a kindergarten instructional webpage in Spanish, showing lesson categories with illustrated thumbnails and navigation options.

Year at a glance

The program’s intentional Knowledge Sequence from K–5 connects knowledge and vocabulary within a grade level and across grade levels, for deeper reading comprehension and preparation for college, career, and life. Instead of “activating prior knowledge,” Amplify Caminos helps you build it in the classroom from day one, for every child, expanding each student’s knowledge base long before they transition to reading to learn.

Curriculum flowchart showing reading themes and activities from Kindergarten to Grade 5, organized by grade level and literary theme, with interconnected boxes for each topic.

Units & domains at a glance

Each Knowledge Domain in grades K–2 and Unit in grades 3–5 varies in the number of days based on instructional purpose. Just as with our top-rated Amplify CKLA program, the Amplify Caminos materials engage and delight young learners with resources that are both appealing and original.

Una mujer rubia con un vestido azul cuida ovejas blancas y negras, sosteniendo un bastón de pastor. Un cerdo vestido de azul corre y un hombre de negro toca el violín en una valla. Al fondo hay una casa.

Domain

Nursery Rhymes and Fables/Rimas y fábulas infantiles

Start learning about literature with these classic Mother Goose rhymes.

Ilustración de tres personas en un paisaje cubierto de hierba, una tratando de atrapar mariposas con una red, otra escondiéndose detrás de una escultura alta y frondosa de una mano y otra con binoculares.

Domain

The Five Senses/Los cinco sentidos

Learning about the body starts with learning about how we experience the world.

Una ilustración que representa a un gran lobo con sombrero de copa liderando un desfile de animales y personas con instrumentos musicales a través de un paisaje montañoso.

Domain

Stories/Cuentos

Learn about the parts of a book and some of the stories that go in one.

Una ilustración vibrante de una escena rural con colinas, una granja, una mariposa, un sol brillante, varias verduras como tomates y lechugas, y un gusano en el suelo.

Domain

Plants/Plantas

Discover the lifecycle of plants and the history of George Washington Carver.

Ilustración de una escena de granja que muestra un camión rojo que transporta verduras, campos de cultivo, vacas pastando en una colina, un granero y un molino de viento contra un cielo azul.

Domain

Farms/Granjas

Now we know how plants make their food… but what about animals?

Ilustración de un nativo remando en una canoa en un río con búfalos pastando en un campo, tipis al fondo y pájaros volando en el cielo bajo un sol brillante.

Domain

Native Americans/Los nativos americanos

Who were the first people in America? A look at the Lenape, Wampanoag, and Lakota Sioux.

Una ilustración muestra un rey y una reina en tronos, un castillo en un acantilado y una mujer con enanos cerca de un árbol. Cortinas rojas enmarcan la escena.

Domain

Kings and Queens/Reyes y reinas

To understand fairy tales, it’s best to first understand royalty.

Ilustración que muestra las cuatro estaciones: primavera con flores, verano con árboles verdes, otoño con hojas que caen e invierno con nieve y gente en trineo. Un niño lee debajo de un árbol.

Domain

Seasons and Weather/Las estaciones y el tiempo

The study of natural cycles continues with the weather and why it happens.

Un velero de madera con símbolos de cruz roja en sus velas navega cerca de una isla tropical con exuberante vegetación y palmeras. A lo lejos se ven otros dos barcos en el agua.

Domain

Columbus and the Pilgrims/Colón y los peregrinos

A look at the first contact between Europe and the Americas, and some of its results.

Una escena histórica muestra gente afuera de una gran mansión de estilo colonial con dos chimeneas. En primer plano se ve un carruaje tirado por caballos y a la izquierda se ve una casa más pequeña.

Domain

Colonial Towns and Townspeople/Las colonias y sus habitantes

Before the War for Independence, how did the town and country depend on one another?

Ilustración de personas clasificando materiales reciclables en un parque cerca de un río contaminado. Las fábricas emiten humo al fondo, mientras que las mariposas, las flores y los árboles están presentes en el primer plano.

Domain

Taking Care of the Earth/Cuidar el planeta Tierra

We only have one Earth—here are some ways to help care for it.

Ilustración del Monte Rushmore con los rostros tallados de cuatro presidentes de Estados Unidos. Un águila vuela en primer plano.

Domain

Presidents and American Symbols/Presidentes y símbolos de los Estados Unidos

Start learning about government through the lives of five presidents.

Una ilustración caprichosa que muestra animales de granja alrededor de una casa en un árbol junto a un río. Un zorro, un conejo y una oveja interactúan mientras la gente acampa junto a una fogata al fondo. Una araña cuelga del árbol.

Domain

Fables and Stories/Fábulas y cuentos

Learn some of the key elements of a story through classic fables.

Ilustración que presenta anatomía humana, actividades de estilo de vida saludable, profesionales médicos, símbolos dietéticos, una ambulancia y microorganismos, destacando la conexión entre salud, nutrición y ejercicio.

Domain

The Human Body/El cuerpo humano

What are germs? What are the organs? And what does it all have to do with health?

Una ilustración que presenta varias escenas de cuentos de hadas y folclore, incluida una calabaza grande, un tigre, Caperucita Roja, personas con atuendos tradicionales y una pagoda roja con una montaña de fondo.

Domain

Different Lands, Similar Stories/Tierras diferentes, cuentos similares

A world tour of storytelling, and the stories that stay the same across the world.

Ilustración que muestra el antiguo Egipto con pirámides, la Esfinge, agricultores arando un campo con bueyes y ganado pastando bajo un cielo soleado.

Domain

Early World Civilizations/Antiguas civilizaciones del mundo

Rivers, farming, writing, and laws: just what does it take to build a civilization?

Escena ilustrada de la antigua Mesoamérica con maíz, un río, agricultores y pirámides al fondo. En primer plano se ve a una persona con traje tradicional.

Domain

Early American Civilizations/Antiguas civilizaciones de América

What will we find in the great temples of the Aztec, Maya, and Inca civilizations?

Ilustración de la exploración espacial: se lanza un cohete, un astronauta se para cerca de un módulo de aterrizaje, una persona usa un telescopio y aparece un planeta distante con anillos sobre un fondo estrellado.

Domain

Astronomy/Astronomía

How the Earth relates to the moon, the sun, and the rest of the planets.

Dos paleontólogos en un paisaje volcánico examinan fósiles en primer plano, mientras un volcán emite humo y lava al fondo.

Domain

The History of the Earth/La historia de la Tierra

Just what lies beneath the Earth’s surface, and what can it teach us about the past?

Una escena de vida silvestre diversa que presenta un cactus del desierto con un pájaro, un conejo, elefantes, un león, un oso polar sobre el hielo y montañas distantes bajo un cielo nublado.

Domain

Animals and Habitats/Los animales y sus hábitats

A look at the connection between how animals live and where they make their homes.

Una princesa con un vestido rosa sostiene una rana junto a un arroyo con un castillo, árboles y gente al fondo. En primer plano camina un zorro con un sombrero con una pluma roja.

Domain

Fairy Tales/Cuentos de hadas

What do fairy tales have to teach us about how stories are told?

Ilustración que muestra una escena histórica con soldados, veleros y hombres con atuendo colonial discutiendo en el interior.

Domain

A New Nation: American Independence/Una nueva nación: la independencia de los Estados Unidos

The story of the birth of the United States out of the 13 Colonies.

Los pioneros con carros cubiertos y caballos señalan hacia un valle con tipis nativos, fogatas y humo elevándose. Un oso se encuentra sobre una roca y se ven montañas al fondo.

Domain

Frontier Explorers/Exploradores de la Frontera

The story of the journey west from the newborn U.S.A. to find the Pacific Ocean.

Un hombre con un hacha se encuentra entre paisajes exagerados con un castillo, un tren con humo, un buey azul y una persona con un mono observando la escena.

Domain

Fairy Tales and Tall Tales/Cuentos de hadas y cuentos exagerados

Learn about exaggeration and characterization on the frontier.

Ilustración de un paisaje vibrante que presenta diversos monumentos culturales, incluidos templos, palacios, pirámides, una escena de elefantes, montañas distantes y fuegos artificiales en el cielo.

Domain

Early Asian Civilizations/Antiguas civilizaciones de Asia

Tour the world of classical civilization, starting with India and China.

Ilustración que muestra la antigua Grecia con un anfiteatro, estatuas, soldados con armadura, un barco y un templo en una colina rodeada de vegetación.

Domain

Ancient Greek Civilization/La civilización griega antigua

The tour continues with the philosophy and politics of Greece.

Illustration of various mythological scenes including greek gods, a flying horse, and roman architecture under a sunny sky.

Domain

Greek Myths/Mitos griegos

Dive deep into the characters and storytelling of classic myths.

Ilustración de una batalla entre barcos británicos y estadounidenses cerca de un fuerte. El barco británico está a la izquierda con soldados, mientras que el barco estadounidense está a la derecha. La gente porta una gran bandera estadounidense en primer plano.

Domain

The War of 1812/La guerra de 1812

Learn about America’s “Second War for Independence.”

Un paisaje nevado con un zorro durmiendo en una madriguera, gente corriendo y andando en bicicleta por un sendero y árboles que muestran los cambios estacionales.

Domain

Cycles in Nature/Los ciclos de la naturaleza

Introducing the natural cycles that make our lives possible.

Ilustración de carros cubiertos tirados por caballos a lo largo de un sendero en el desierto, con un coyote aullando sobre una alta formación rocosa y un tren de vapor al fondo.

Domain

Westward Expansion/La expansión hacia el oeste

Why did pioneers go west? What happened to the people who were there?

Ilustración de un jardín vibrante con flores, abejas, mariposas, una oruga en una hoja, una crisálida y un apicultor que maneja una colmena junto a un estanque.

Domain

Insects/Los insectos

Lay the grounds for animal classification by looking at solitary and social insects.

Ilustración de una escena histórica con gente escuchando el discurso de un hombre en una plataforma. Al fondo se ve un río y una procesión de personas. En primer plano hay un documento de proclamación.

Domain

The U.S. Civil War/La Guerra Civil de los Estados Unidos

Begin to grapple with U.S. history’s central crisis over slavery.

Una escena en la que aparece una persona explicando un diagrama anatómico humano, otra persona haciendo ejercicio, una cadena de ADN, campos y un microscopio de fondo.

Domain

Human Body: Building Blocks and Nutrition/El cuerpo humano: componentes básicos y nutrición

A deeper dive into the digestive system and the nutrition process.

Un grupo diverso de personas se encuentra en un muelle con vistas a un bullicioso puerto con barcos y un gran barco, un avión volando por encima y la Estatua de la Libertad al fondo.

Domain

Immigration/La inmigración

Why did people immigrate to the United States, and what did they find here?

Women in early 20th-century clothing march with signs for voting rights and justice in front of a yellow bus labeled "Cleveland Ave.," making history that can inspire lessons in a K–2 language arts curriculum.

Domain

Fighting for a Cause/Luchar por una causa

How people can do extraordinary things to make the world better for everyone.

Dos ratones antropomórficos en un bote de remos, uno de ellos remando, navegan por un río tranquilo rodeado de exuberante vegetación y árboles. El ratón que rema lleva una chaqueta azul y el otro ratón parece conversar.

Unit 1

Classic Tales: The Wind in the Willows/Cuentos Clásicos: El viento en los sauces

A deep dive into character, theme, and POV in classic stories from around the world.

Ilustración de un jaguar, una garza, una rana roja, una tortuga y un pez en un paisaje vibrante con montañas y vegetación bajo un cielo soleado.

Unit 2

Animal Classification/La clasificación de los animales

How do we classify different animals by their appearance and behavior?

Ilustración de una figura humana que muestra la anatomía interna, incluidos el cerebro, los pulmones, el corazón, el sistema digestivo y una articulación de la cadera resaltada sobre un fondo degradado.

Unit 3

The Human Body: Systems and Senses/El cuerpo humano: sistemas y sentidos

Let’s take a closer look at how the skeleton, muscles, and nervous system all work.

Un ángel se arrodilla ante una mujer sentada en un sofá dorado encima de un templo en una noche estrellada. Unas escaleras conducen al templo en un paisaje montañoso.

Unit 4

The Ancient Roman Civilization/La civilización romana antigua

What is Rome’s greatest cultural contribution? In this unit, your students decide.

Ilustración de un perro saltando bajo un árbol, persiguiendo una abeja, con una mesa en primer plano sosteniendo una jarra y vasos de limonada. El sol brilla intensamente en el cielo.

Unit 5

Light and Sound/La luz y el sonido

The science behind all the ways we see and hear the world.

Un barco vikingo con una proa en forma de dragón navega en el océano bajo un cielo azul con nubes. El barco tiene una sola vela grande y varios escudos recubren sus costados.

Unit 6

The Viking Age/La era vikinga

An immersive narrative experience about what life was like in Viking communities.

Ilustración de una escena espacial con varios planetas y anillos sobre un fondo de estrellas. Dos planetas grandes dominan el primer plano y se ven planetas más pequeños al fondo.

Unit 7

Astronomy: Our Solar System and Beyond/Astronomía: nuestro sistema solar y más allá

More about our universe, including a writing project about daily life on a space station.

Una persona sentada en el borde de un acantilado con vistas a un vasto paisaje desértico con nubes arremolinadas en el cielo.

Unit 8

Native Americans: Regions and Cultures/Los nativos americanos: regiones y culturas

How did Native American nations change their way of life in different parts of the world?

Ilustración de un velero en el océano con la costa este de América del Norte visible a la izquierda.

Unit 9

Early Explorations of North America/La exploración europea de América del Norte

What was it like to sail to North America with the early European explorers?

Una pintura representa una escena del siglo XVII con colonos, un velero al fondo y un hombre conduciendo un carro tirado por caballos cargado de mercancías. Se ve a otras personas descargando y trabajando cerca.

Unit 10

Colonial America/La época colonial en los Estados Unidos

A study of the very different ways of life in the different pre-U.S. colonies.

Ilustración que muestra el ciclo de la vida: un esqueleto en el suelo, un pájaro posado en una cerca, otro pájaro en una planta y un ave rapaz más grande arriba, todos conectados por flechas circulares.

Unit 11

Ecology/Ecología

Students keep ecologist’s journals to learn about our world and how best to protect it.

Una mano alcanza una manzana verde en una rama. Cerca hay una brújula, un termómetro, un lápiz, notas musicales y un granero rojo sobre un paisaje cubierto de hierba.

Unit 1

Personal Narratives/Narrativas personales

Read stories of personal experience… and learn to reflect on your own.

Ilustración medieval que representa un grupo de figuras con armadura a la entrada de un alto castillo gris con puente levadizo, adornado con banderas y rodeado por un paisaje decorado y fondos ornamentados.

Unit 2

Empires in the Middle Ages/Los imperios en la Edad Media, parte 1 & Los imperios en la Edad Media, parte 2

Explore the medieval history of Europe and the Middle East.

Ilustración dorada de un dragón con alas sobre fondo beige, rodeado de diversos elementos decorativos como estrellas, hojas y estampados abstractos.

Unit 3

Poetry/Poesía

Study the poetry of many nations using licensed text anthologies, and begin to write your own.

Vintage styled illustrations of a microscope, an old telephone, and a clock on textured background with geometric patterns.

Unit 4

Eureka! Student Inventor/¡Eureka! Estudiante inventor

Transform the class into a lab for students to build and present inventions.

Formaciones rocosas en un paisaje desértico con capas vibrantes y arremolinadas de arenisca roja, naranja y amarilla bajo un cielo parcialmente nublado.

Unit 5

Geology/Geología

Plate tectonics, volcanoes, erosion: all the forces that shape the Earth.

Una imagen abstracta y colorida que representa varias formas geométricas de edificios sobre un fondo azul estampado.

Unit 6

Contemporary Fiction with excerpts from The House on Mango Street/Ficción Contemporánea con Fragmentos de La Casa en Mango Street

Explore The House on Mango Street… and write a book while doing it.

Cuadro que representa a un hombre y un niño tocando una gran campana en una torre, con espectadores al fondo y un cartel de "LIBERTAD" visible.

Unit 7

American Revolution/La Revolución estadounidense

Why did America seek independence? Let’s investigate the causes and effects.

Un pequeño bote de remos con tres personas navega por mares agitados mientras dos grandes barcos luchan al fondo, con humo y fuego visibles.

Unit 8

Treasure Island/La Isla del Tesoro

How dSeek the treasure of plot in this detailed study of a classic fiction adventure.

Unit 1

Personal Narratives/Narrativas personales

Through writing and sharing their writing, students begin to identify themselves as writers.

Unit 2

Early American Civilizations/Las primeras civilizaciones americanas

Students craft a codex to explain the rise and fall of the Maya, Aztec, and Inca people.

Dos jinetes medievales a caballo, uno de ellos con la espada en alto, avanzan por un terreno rocoso. El fondo presenta un paisaje brumoso bajo un tono violeta.

Unit 3

Poetry/Poesía

Students close read many forms of poetry… and learn to write them.

Collage ilustrado con un paraguas, un cuervo, un sextante náutico, estrellas, una luna creciente y una brújula sobre un fondo beige texturizado.

Unit 4

Adventures of Don Quixote/Las Aventuras de Don Quijote

Was Don Quixote right to fight the windmill? In this full-length novel study, students decide.

Unit 5

The Renaissance/El Renacimiento

Exploring the art and literature of the Renaissance through the works of its masters.

Tres hombres vestidos con ropa de época examinan una gran hoja de papel dentro de una imprenta. Un hombre parece llevar un delantal, mientras que otro señala el papel y el tercero observa de cerca.

Unit 6

The Reformation/La Reforma

How did the printing press transform the religion and society of Europe?

Patrón botánico morado y lila con hojas, plantas y formas abstractas, incluida una luna creciente y estrellas, sobre un fondo violeta oscuro.

Unit 7

William Shakespeare’s A Midsummer Night’s Dream/Sueño de Una Noche de Verano de William Shakespeare

Students enter the world of Shakespeare by reading, designing, and acting out his work.

Retrato en tonos sepia de una joven de pelo largo, con un collar de pedrería y un chal drapeado.

Unit 8

Native Americans/Los nativos americanos

How did the policies of the U.S. government impact Native American culture and lives?

Una lupa sobre documentos que contienen una pintura de paisaje de montañas, un dibujo con la etiqueta "Raptor Claw" y una nota adhesiva con la "Pista n.° 2". También se ven un sobre y una insignia exterior.

Unit 9

Chemical Matter/Química

Students use knowledge of chemistry to solve a mystery.

Print & digital components

The program includes instructional guidance and student materials for a year of instruction, with lessons and activities that keep students engaged every day.

Component

FORMAT

Knowledge (Conocimientos) Teacher Guides (K–2)

Knowledge Strand Teacher Guides contain Amplify CKLA’s cross-curricular read-alouds and application activities, all of which are standards-based to build mastery of content knowledge and literacy skills. There is one Teacher Guide per Knowledge Domain.

Print and digital

Knowledge Image Cards (K–2)

Amplify Caminos includes Image Cards for each Knowledge Domain to bring each topic to life through vivid visuals.

Print and digital

Knowledge Flip Books (K–2)

Projectable Flip Books are provided to accompany the read-alouds in each Knowledge Domain.

Digital

Teacher Guides (3–5)

Teacher Guides for grades 3–5 units are based on content-rich topics and incorporate reading, writing, speaking, and listening skills in the context of background knowledge. There is one Teacher Guide per unit.

Print or digital

Teacher Resource Site (K–5)

The program includes a one-stop-shop website for lesson projections, digital versions of all Amplify Caminos materials, lesson planning resources, multimedia (such as eBooks), and more.

Digital

Professional Learning Site (K–5)

The Professional Learning site includes training materials, best practices, and other resources to develop program expertise. Access professional development anywhere, anytime.

Digital

Component

FORMAT

Knowledge (Conocimiento) Activity Books (K–2)

Activity Books provide students with the opportunity to deepen world and word knowledge by responding to text in a diversity of ways.

Print

Student Readers (3–5)

Student Readers serve as content-rich anchor texts for each unit. Units such as Poetry and Contemporary Fiction feature authentic texts originally written in Spanish.

Activity Books (3–5)

Activity Books in grades 3–5 provide daily opportunities for students to hone reading and writing skills within the context of each unit.

Print and digital

Explore more programs

Our programs are designed to support and complement one another. Learn more about our related programs.

S5-01. Investigating math anxiety in the classroom

A blue graphic with text reading "Math Teacher Lounge" in multicolored letters and "Amplify." at the bottom, with abstract geometric shapes and lines as decoration.

Season 5 is here! This season, we’ll be talking all about math anxiety: what it is, what causes it, and what we can do to prevent or ease this anxiety in the math classroom. To launch this very important theme, we sat down with Dr. Gerardo Ramirez, associate professor of educational psychology at Ball State University.
 
As someone who’s been studying math anxiety for more than a decade, he had some interesting research and advice to share on why math anxiety affects so many students (and adults), and tips for how to start reducing it.
 
Listen now and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!
 
Enjoy this episode and explore more from Math Teacher Lounge by visiting our main page.

Download Transcript

Dan Meyer (00:01):
Hey, folks. Welcome back to Math Teacher Lounge. I’m one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:05):
And I am your other host. I’m Bethany Lockhart Johnson. Season five! Hello!

Dan Meyer (00:11):
Bethany, how are you doing? How have you been spending the long break between our recording sessions?

Bethany Lockhart Johnson (00:16):
As much as I loved sharing content from previous seasons, I am so thrilled that we’re back for season five. I have been, you know, chasing a toddler. I think he’s already tired of me saying, “Ooh, can we count that?” He’s like [sighs] “One two, one two.” Like, he’s done already.

Dan Meyer (00:36):
Too much counting. Yeah, I worry about that so much, that my love of mathematics might be perceived by my kids as smothering. Yeah, I worry about the same. We shared with you folks some bangers of reruns, in my humble opinion. Some great guests. But, we’ve been excited—me and Bethany—to hop back on the mics, on the ones and twos, and explore some new ideas together.

Bethany Lockhart Johnson (01:01):
Well, I loved our season talking about joy in mathematics. And personally I could…like, we could turn this whole podcast into joy in mathematics. However, we’re kind of going a different route. Because if you ask folks why they don’t feel joy in mathematics, a lot of times at the root of that is some really intense math anxiety. So this whole season, we’re going to be delving into math anxiety. Exploring what it is, who has it, why do we think it happens, what do we think we can do about it, and how can we navigate through it, so that we can experience that joy in math? These are questions that we’re gonna explore over the course of the season. Dan Meyer, how do you feel about that?

Dan Meyer (01:49):
It feels big and it feels personal. I mean, as we shared in our math stories back from season…whatever it was, math anxiety was a huge part.

Bethany Lockhart Johnson (01:59):
It was last season, Dan.

Dan Meyer (02:00):
Last…? I mean, who can remember? Big part of your journey. I’ve had some very punctuated but intense moments of anxiety in math class. And socially, we have built math up to be this incredibly powerful thing. You know, restricting movement on economic ladders, preventing people from getting into careers they want. Whether or not they have much to do with math class, math anxiety is a really large part of educational but also social life. And yeah, I’m really excited to explore it with you. We’re bringing on some really excellent guests. Some researchers, yes. But not just researchers! Also people who practice in the field and know firsthand what it looks like to resolve issues of anxiety with students.

Bethany Lockhart Johnson (02:45):
Yeah, you’re right, Dan. My math story contained quite a bit of math anxiety, so I am particularly invested in this season. I mean, I still navigate math anxiety. And, you know, many of us do, and let’s talk about it. And let’s—I love that you reminded me. We’re gonna have a lot of great researchers all throughout the season, and a lot of times folks feel like the research happening, there’s sometimes a gap between researchers and what’s actually happening in the classroom. Not in all cases, but a lot of times. Right? And I remember a lot of conversation about the latest research when I was in grad school, but unless you’re actively studying something, sometimes we don’t know what’s happening. Right? We’re really focused on what’s happening right in front of us in our classroom. So let’s take some of that research; let’s break it down; let’s talk to some of the folks who are thinking about this for the bulk of their day, right?

Dan Meyer (03:41):
Yep. So we got our first guest coming up in a moment here.

Bethany Lockhart Johnson (03:45):
So to kick off this season, we’re starting episode one by talking to Dr. Gerardo Ramirez, Associate Professor of Educational Psychology at Ball State University. And he’s been researching math anxiety for more than a decade. He’s worked with so many amazing folks in the field. He’s worked with students, he’s worked with teachers, with educators…I’m just so excited to talk to him. If you look up math anxiety, you see his name as one of the folks who is really thinking about this at so many different angles, and we get to talk to him. So enjoy our conversation with Dr. Gerardo Ramirez.

Dan Meyer (04:29):
We are so excited to have Dr. Gerardo Ramirez on the show with us. Dr. Ramirez is an Associate Professor of Educational Psychology at Ball State University. Thanks so much for joining us.

Dr. Gerardo Ramirez (04:40):
Yeah, thank you for inviting me to talk about math anxiety.

Bethany Lockhart Johnson (04:43):
So with your interview, Dr. Ramirez, we are actually launching the season. We’re gonna be talking about all different aspects of math anxiety, and it feels pretty perfect that you are first guest of the season, because of the sheer breadth of research and conversations you’ve had about math anxiety. Could you start us off kind of telling us a story of how did you get interested in studying math anxiety? Or why, you know, why did you dive into this topic that, you know, I think a lot of folks might…like, if you’re on a plane, and you say, “Oh, I study math anxiety,” what kind of reaction are you gonna get?

Dr. Gerardo Ramirez (05:24):
Oh, sure. Yeah. I think most people are actually very interested because they all have their own story about feeling anxious about math, or just being anxious about evaluation situations that involve math. And, yeah, they wanna share those stories. People feel quite comfortable talking about their anxiety about math, for some reason. But for me, I started off, when I was in undergrad, I was studying to take the GRE quiz. I was hoping to go into a psych program. But I wasn’t exactly sure what direction yet. As I took some of the practice tests, there’s some situations in which I was very nervous about taking the practice test. And I just noticed that I did really poorly on some of these exams. And so I became very interested in issues like choking under pressure, which means when you underperform relative to what you expected to perform. And so, as I was researching these issues, I started to come across this whole field of math anxiety. And I saw that while there are some people who choke under pressure during tests, there are other people who just have a strong general fear of mathematics.

Dan Meyer (06:29):
That’s really helpful. I can imagine you’re doing a lot of free psychology sessions, free therapy for people on airplanes when they bring to you their own stories of math. So let’s thank you for your service in that sense. I’m super-curious. So Bethany and I have both taught math. We both have seen firsthand what it looks like when a student is anxious in math class, though maybe we don’t have kind of the clinical language to describe it. And I’m curious, from a clinical sense, how do we define math anxiety?

Dr. Gerardo Ramirez (06:57):
Sure. So first off, math anxiety is not something that you would find in the DSM, for instance. But we generally define that as a fear or apprehension to situations that involve math. So it doesn’t have to necessarily be educational situations. It could be someone asks you a math-related question during a party, or you have to calculate the tip at a restaurant, for instance. It doesn’t have to be about schooling situations, although that’s obviously where it seems to matter a lot for many people. So it is basically a fear or apprehension to situations that involve math. And I think distinguishing the term “fear” from “anxiety” is really important here. A lot of times people use those terms interchangeably, and the term “fear” is obviously within our definition of math anxiety. But oftentimes what differentiates anxiety from fear is that, anxiety is—think of it like a recipe. Anxiety is fear plus a little bit of unknown. OK? So if, for instance, if you hated snakes, and they threw a snake at you, you’d be in intense fear. Whereas if you hated snakes and they said, “There is a snake in the room, but I’m not gonna tell you where,” that’s gonna cause anxiety. And so the reason why we call it math anxiety is because a lot of times people experience this fear for a possible unknown future that involves math or possible unknown evaluations that people might have about your competence, because of math. And so for a lot of kids, they feel anxious about how they’re gonna do on a test or whether they’re gonna be able to pass a class or whether they’ll be able to understand what you’re saying in your lessons, for instance. And so the anxiety component really gets at fear of something that’s unknown, but related to mathematics situations.

Dan Meyer (08:47):
Math is somewhere in the ceiling right now. Perhaps I might be surprised with a math situation!

Dr. Gerardo Ramirez (08:52):
Yeah. yep.

Dan Meyer (08:52):
So I have this tendency to assume that every other subject that we teach has it better and easier than math does. It’s not true. I know this is not true. But I’m kind of curious here. Is math anxiety, like, part of a general just set of anxiety around schooling itself? Like, is there a reading anxiety, a writing anxiety, and does that all just flow from the same kind of fount of anxiety around schooling or situations about learning? And what makes math special in this regard? If it is its own special anxiety, for instance?

Dr. Gerardo Ramirez (09:27):
There are different…so some people obviously suffer from generalized anxiety. Right? And so they would, you know, feel anxious both for evaluative and non-evaluative situations. But in the research that we’ve done and that other people have done, there are differences between things like reading anxiety, math anxiety; I’ve also studied spatial and creativity anxiety. A lot of times what we’re trying to do in these studies is we measure all of the above, and we try to show that, look, math anxiety predicts math situations above and beyond these other things. So yeah, we definitely distinguish those things. And so what’s special about math is that, well, I think the symbolic nature is a big part of it. The abstract symbolic nature is just not as tangible to students. They can’t touch it. And so it doesn’t allow ’em to use their full cognitive faculties to play with it, as you might see, for instance, in science. Or it doesn’t allow people to relate math to their own interests the way you might see, for instance, in English. So maybe I hate reading novels, but I’m interested in zombies and you give me a book on zombies, well, ok, great, you’ve connected my personal assets to the topic. Whereas with math, either that’s harder to do or instructors don’t do such a good job of setting that connection up.

Bethany Lockhart Johnson (10:46):
Also, I think, you know, I’ve heard of students being really anxious, let’s say, during a reading session, when teachers used to do—hopefully they’re still not doing it—the popcorn reading, where you just randomly call on a student to read out a sentence. Right? But you don’t really hear students or adults talking about, “Oh, no, no, no, I don’t read; I don’t mess with reading.” You know? Whereas with math, you do hear, “Oh, I’m not a math person. Oh no, no, no, don’t ask me any math questions.” And that is such a distinction.

Dr. Gerardo Ramirez (11:18):
Yeah. And I think a lot of that’s because it’s just so common. As an adult, to be nervous about reading is kind of an uncommon thing. So people feel a stigma around admitting that. But math is something that everyone feels like they’re inadequate in. And so there’s a lot of comfort in telling you how they’re just one of the many people who don’t like math. And that, you know, can have a lot of different consequences and outcomes. I think on the one hand, I think for a lot of kids it becomes a normalized message that if you fear math, that’s OK, join the club. Right? But we have to be careful about that, ’cause a lot of math anxiety researchers will oftentimes say, part of what leads to math anxiety is adults normalizing that it’s OK to be scared of math. So I think a lot of times adults, teachers, for instance, math teachers, they’ll tell kids, “You know, if you’re scared, that’s OK.” And so a lot of the math anxiety community says, “No, no, no, you’re not supposed to do that.” But my recent view is different. I view that as a form of validation. Because math is hard. And so telling kids, “Hey, look, it’s actually easy if you just try,” I don’t think that’s true. It’s actually just hard. And I think even if it was easy, to the kid, it feels hard! And I think something that’s not really well-studied right now in our field is the value of validating people’s math negative math experiences. We don’t want to validate that, ’cause we think that we’re gonna reinforce that. But actually, I think the opposite. I think when you validate people’s negative math experiences, it helps ’em to feel that they can handle it. They can start to take control over their own emotions.

Bethany Lockhart Johnson (12:52):
I love that. And I, I actually, I think that’s so powerful, what you’re talking about, that validation. I taught kindergarten, and I vividly remember being in a parent-teacher conference and that parent saying, “Oh, I wasn’t a math person either,” right? Or, you know, their language and their experience with their own math schooling, their anxiety about math was actually impacting their students’ experience of math. Or the conversation that, when I would go to talk about a math assessment, let’s say, you could see the parent actually tensing up. And there was this moment of validation, that I felt like we needed to make space for that in the conversation with the parents, right?

Dr. Gerardo Ramirez (13:38):
Yeah.

Bethany Lockhart Johnson (13:38):
Like, this is a real thing. And we are working on teaching students that math is something that gets to—your experience with math gets to look all sorts of different ways. And it’s OK if we, you know, make a mistake, or if we kind of only get this part, but we’ve really got that part. Or let’s talk about it; let’s write about it. So I really feel like that that validation is something that’s so missing. And instead of the validation, like you said, you see folks being like, “Oh yeah, me neither. I’m not a math person either.” Right?

Dr. Gerardo Ramirez (14:10):
Yeah. I think…part of the reason why people are comfortable sharing this because they’re looking for validation also. When they say, “Oh, I’m not a math person,” you know, I think they’re hoping that, you’ll say like, “Yeah, me neither,” or “Of course not, ’cause math is terrible.” Right? They’re looking for validation, not to reinforce their perspective, but to feel that it’s OK not to be a math person. And I think that’s one of the techniques that I’m trying to work on in my research right now, is to provide evidence that actually people will work harder when you validate their math experience. You don’t have to tell them a positive story per se. If your current story is “Math is hard and I’m very, very anxious; I’m scared,” then we can just validate that and help you work through that. And it actually will strengthen our relationships. Because if you’re a student and you’re struggling with math and I tell you, “Yeah, it’s hard; it’s OK to struggle with math,” that makes you feel seen. And that’s gonna lead you to want to ask me more for help, because I’m someone who understands you. And that’s a great, you know, remediation opportunity.

Dan Meyer (15:14):
A common thread that I think I’m seeing here in several answers is that math sometimes asks students to disassociate part of themselves. Where success in math oftentimes means working from an a level of abstraction with symbols, like you said, that can feel alien. Like, who am I here? And in the same way, I love that you’re proposing we validate and reassociate people with a very deeply felt part of themselves that is anxious about mathematics.

Dr. Gerardo Ramirez (15:44):
Yeah. I mean, I think that’s what validation’s supposed to do, right? So a lot of us, when we feel these strong emotions, we wonder, “Is this even a real thing? Are other people feeling this? Is there something wrong with me?” So we feel the emotions, but we can’t actually deal with them, because we wonder if they’re legitimate. And so when someone says, like, “Yeah, this is hard,” it crystallizes that emotion. And once something is made real, you can actually choose how you want to deal with it. Some kids are gonna deal with it by staying anxious. But some people are gonna choose to deal with it by saying, “Well, there’s nothing I can do about it now; I have to take this math test, so I’m just gonna think positive.” And that’s great. If the kid can end up saying that to themselves, that’s much more effective than me telling the kid, “Hey, you just gotta think positive. You’re gonna start the test anyway.” And so we want the kid to make meaning of their experience, and the way we do that is by crystallizing their emotions through validation.

Dan Meyer (16:36):
Yeah. I love that. And so what you’re proposing there, I think, sounds like, a solution, like a post-talk solution after students are feeling anxiety.

Dr. Gerardo Ramirez (16:43):
Yes.

Dan Meyer (16:43):
To validate and empathize.

Dr. Gerardo Ramirez (16:45):
Yes.

Dan Meyer (16:45):
And over the course of our season, we hope to explore a lot about solutions to math anxiety that are preventative, that reduce the odds of anxiety arising, through instruction and curriculum, before it arises. And I’m just wondering if you’ve seen anything that would hint at either specific or general words of wisdom you wanna share with the educators, about not just addressing it after the fact, but preventing math anxiety before it arises?

Dr. Gerardo Ramirez (17:14):
To be honest, at this point, I haven’t seen enough evidence for me to recommend anything concretely as an intervention for math anxiety, or an intervention to prevent its development. All I can really do here is rely a lot on the more broad cognitive-behavioral research on anxiety, which says that one of the ways we prevent people from developing anxiety is by helping them to make more positive appraisals of challenge situations. So a lot of times, when kids are challenged, they don’t know how to interpret that. “What does it mean that I’m struggling with this thing?” And so that’s where I think a lot of teachers can help students’ interpretations of that. ‘Cause if you leave kids to their own devices, they’re gonna think, “I’m struggling because I’m stupid. I’m struggling because I’m not good enough. I’m struggling because my dad is right; I’m gonna be a failure.” You know? They’re going to impose an interpretation to a challenge situation regardless. And so, as teachers, one thing we can do is we can help shape that interpretation and say, “What does it mean to struggle with math? People will say it means you’re stupid. That’s one interpretation. What’s another one? It means that your brain is working really hard to think through something. That’s another interpretation. What’s better? What do you think is more helpful?” And then, helping students to see how interpretations matter to how you ultimately feel about something. And that’s a very metacognitive way of thinking about things. So yeah, I would say that one way to prevent it is to help students to take more positive interpretations of their experience. But another way, and I think a more successful way, I think, is to give students early experiences where they feel efficacious dealing with math. One of the ways you do that, for instance, is by obviously making sure that the students understand the material—but that’s obvious; people are trying to do that. One of my favorite recommendations is to keep reassigning assignments, the same exact assignment, for, say, three weeks, back-to-back. So if in week one you do the homework assignment, you do OK, you don’t do so great, when week two you do it, you give the exact same assignment, and now the student can see like, “Wow, OK, this was much easier.” And then, week three, you give the exact same assignment; now the kid’s feeling really confident. And the reason why that’s great is because it helps kids to see that they’re growing in confidence. A lot of times kids don’t get to see that because we’re constantly throwing new assessments at them. And so they’re never seeing that growth. All they’re seeing is a new challenge, a new challenge, a new challenge. So I think we need to set up situations where they can feel that they’re growing, when we keep the assessment static. That can be a formative assessment, for instance—doesn’t have to be a summative assessment.

Bethany Lockhart Johnson (19:55):
That feels so powerful and it feels like it really connects to that validation piece, right? We are actually helping to create a culture in our math classroom where we might struggle with something, but we keep revisiting it. And it’s not so much to reach mastery, but as Dr. Megan Franke — we talked to her about this partial understanding and about pulling on those threads of things that you do understand, so that you can build your confidence…build, not just confidence, but build your…I guess, kind of get your footing, right? You’re saying, “Well, I do understand this. I see how this works.” And if I’m revisiting an assignment, I feel like that would give me permission to like, “Hey, I don’t have to have this figured out on the first pass. You know?

Dr. Gerardo Ramirez (20:44):
Yes, yes. Yeah. I mean, I’m gonna give you a silly analogy, but I think it works. You know, a lot of times people will have nightmares, right? And they’ll keep having the same nightmare over and over again, right? And so one reason that we suspect this happens is because they haven’t worked through whatever that nightmare’s supposed to be about. So if, say, I’m scared of driving, I may be having the same dream about driving and crashing over and over. And we keep having these nightmares. And I think math anxiety is kind of like a waking nightmare, where you keep rehashing something because you haven’t had the chance to finally address that dragon. You know? And so if someone was having a lot of fear over driving, then one behavioral approach would be, you know, to work with a therapist to actually get behind the wheel and maybe drive around the same track over and over until you feel comfortable at that, and then the nightmares stop. Well, the same thing is true, I think, about math, math and math anxiety, is that you wanna give people these opportunities to feel confident by going back to that original experience that caused them to feel anxious, and saying, “This one assignment that we did in week three that really freaked you out, let’s try it again now in week five. How was that?” “Yeah, it wasn’t so bad. It was still kind of annoying.” “OK, we’ll we’ll come back to it.” “Now it’s week seven. Now let’s go back to that assignment. How is it now?” “That’s actually…it wasn’t that terrible.” And that gives people the opportunity to reflect on how they’ve grown past that nightmare.

Bethany Lockhart Johnson (22:05):
I have to say, Dan talked about you being like a therapist. I’m like, wait, “How did you know, Dr. Ramirez? I did have this recurring dream! I did! And I had to face it. No, but I had such intense math anxiety in high school and it was debilitating. And the biggest thing for me, I thought I was the only one. I thought there was something wrong with me. I thought, “Why can’t I figure this out?” There wasn’t a conversation about “Here are some tools,” or “Here are some, some, some…”. Like, “This is OK, for you to feel scared about this or overwhelmed!”

Dr. Gerardo Ramirez (22:41):
Mm-hmm. Mm-hmm.

Bethany Lockhart Johnson (22:42):
You know, I think often when we talk about how widespread math anxiety is, I think a lot of folks automatically jump to high schoolers or college students avoiding math courses. But we see this in really young kids.

Dr. Gerardo Ramirez (22:56):
Yeah. So people are…people are just constantly making meaning of themselves, regardless of the age range. And that’s true even with young kids; they are trying to figure out who they are. Right? And so one of the things you see oftentimes with young kids is you ask ’em, “What are you good at?” And they say, “Everything!” And that’s their attempt to, you know, make meaning of themselves. But sometimes they’re not good at everything. Sometimes they actually struggle in math. And I think even early on, they have to make meaning of that. They say, “Well, I’m good at everything except math.” And how do you make sense of that? Well, why not math? “Oh, because math is terrible. It’s not for everybody. You know, it’s not something that I like.” And so, yeah, in a lot of the studies that we did early on, we basically went into these first-grade classrooms with the purpose of trying to assess whether we can actually show variability in kids’ math anxiety, even early on. In other other words, do kids even report feeling anxious about math situations? Or do they tell us that they’re great at everything? And what we found was that in fact, a good chunk of kids are, again, perfectly willing to tell you that “No, certain situations involving math make me very anxious.” Counting or addition, or doing a problem on the board. And the way we do that is by—I think there are probably more sophisticated ways that can be done, but this is the best we have at this point—is we go in there and we ask them, we show them a bunch of smiley faces and anxious faces. And we say, “I want you to tell me how you feel about these different situations that involve math.” And so we say, “If you feel kind of nervous, I want you to point to this face. If you feel very nervous, point to this face.” And we basically will read to them situations. We’ll say, “How would you feel if your teacher asked you to open up your new math textbook and you saw all the numbers inside of it?” And they’ll point to the really nervous face. So right now, those are some of the more reliable assessments for math anxiety among young kids. And that work showed us that even young kids are self-reporting math anxiety.

Dan Meyer (24:51):

Obviously this is worth our study, because we would hope people would not feel anxious in general, and especially if we have a mandated…kids are mandated to be in math classes for their entire childhood. So I see the need for this study, these studies. I’m curious: What are the consequences, though? Like what, what correlates with math anxiety? What are other reasons why we should care about math anxiety and work to remediate it?

Dr. Gerardo Ramirez (25:16):
Oh, sure. So it correlates with their actual math performance. It can correlate when they choose to do homework. Right? So a lot of times, the parents report having to fight with their kids over math homework a lot. And you also oftentimes see a lot of frustration over mathematics specifically. And so it can, you know, not only affect their academic ongoing outcomes, like math tests and math assignments, but it can also affect their relationship with their parents. So if every time you come home, your dad’s screaming at you because you haven’t done your math homework, and when he asks you to solve the problem in front of them, you don’t remember, ’cause you were checked out, ’cause you’re so stressed out, that’s gonna cause a really negative experience. You know, a lot of times people grow up and they still remember their dad screaming at them over the math homework. You know, it’ll affect your relationship with your teacher. So if you’re making me feel incompetent, if you’re stressing me out, you’re not the kind of person I wanna come to for help. So it can predict relational outcomes as well as academic outcomes. And down the line, of course, when it affects students’ opportunities to get into things like AP classes, it affects students standardized test performance and their choice of colleges, as well as scholarship opportunities.

Dan Meyer (26:29):
Once you show that it correlates to performance, then that opens up a whole range of other correlations that are pretty important, it sounds like. Whether that’s career options or, you know, post-secondary education and the like.

Dr. Gerardo Ramirez (26:40):
Yeah. And a lot of times, when people are choosing a career at college, a lot of times students will make a decision specifically based on what career has less math requirements or less math courses. So I think this finding needs to be verified further. But, there’s some studies showing that, for instance, elementary ed teachers, one factor that feeds into the decision to go into elementary ed is the math requirements are very low in elementary ed. So that can…obviously it’s not what we wanna hear, because these are our first formal math teachers, right? For our kids.

Bethany Lockhart Johnson (27:16):
It feels so powerful, the impact that math anxiety can have, not only while you’re in, let’s say, elementary school, high middle school, high school, but then the impacts beyond that in terms of your career. And I shared this last season, when we talked about our personal math story, but I know when I was navigating the deepest part of my math anxiety, I really felt like, maybe this is a reason I can’t be an elementary school teacher. Because I was so worried that I wouldn’t be able…not that I wouldn’t understand the math for fourth grade, fifth grade, but that there was something about my ability to teach it or understand it or develop a love and passion for it that I wouldn’t be able to do. And I really had to reclaim it in my own way. But, you know, something that I think is so powerful about your research is just the applicability — not only to the field of mathematics, but folks’ everyday lives. And the way that you have talked in the past about math being a gatekeeper…I have a family member who, brilliant American Sign Language interpreter. I mean, amazing. Like a dance with her fingers. I could just watch it all day. And she actually didn’t complete the program because she couldn’t complete the math requirements. And I remember talking to her about like, “Well, have you gone to the free tutoring? Have you gone to, you know, this or that?” But it was a paralyzing fear, you know? So Dr. Ramirez, what do you wish educators understood about math anxiety? Or the research about math anxiety? Or maybe even the general public at large, what do you wish folks understood about math anxiety?

Dr. Gerardo Ramirez (28:58):
Oh, I think that a lot of students, they struggle with math. And I think we wanna normalize that struggle as much as possible. We want to create a culture where it’s OK to do math slow; it’s ok to take your time. And I know that’s not possible with a lot of these requirements that a lot of math teachers have to do. But I think if we want to prevent math anxiety, we have to create opportunities to tell better stories. So that’s ultimately what I tell people is, why do people develop math anxiety? Because they had experiences that challenged their competency and they told a negative story. And so making space to reflect in math classrooms about what does it mean to go slow in math, or what does it mean to make mistakes, and then helping kids to tell better stories, I think it’s really the best thing we can do as math educators. ‘Cause you know, your job is not to be a therapist ultimately. You know, there’s only so much math teachers can do. But I think one of the most powerful things we can create is setting up students’ experiences where they feel confident, and they can tell better stories, so they can have better dreams about math.

Dan Meyer (30:06):
Really appreciate this introduction to math anxiety. It’s been a fantastic kickoff to our season. Dr. Ramirez, thank you so much for joining us.

Dr. Gerardo Ramirez (30:14):
Sure. Thank you.

Dan Meyer (30:16):
Thank you folks so much for listening to that conversation with Dr. Gerardo Ramirez, Associate Professor of Educational Psychology at Ball State University.

Bethany Lockhart Johnson (30:25):
Dan, OK, if not for your frantic signaling, I would’ve probably asked another 20 questions. I need to know what you thought .

Dan Meyer (30:34):
I found it interesting at all points. And especially I think I started to understand a little bit better where the anxiety comes from for some students. I got a little bit here, which is that I think math, more than other disciplines, involves alienation. Check that word. You like that? Alienation? I’m into it. I’m feeling it. It’s like…to get good at math, to be successful in math, you gotta, as a kid, lose your attachment to the world you understand. And I mean, “got to” as in like, “you are asked to” — many times, unfortunately, by curriculum and instruction. Which is to say, you’re turning things you can hold onto into numerals. Right? You’re turning the world and its patterns that you can see and touch into Xs and Ys. And I just don’t know that other disciplines deal with that as much. Maybe I’m wrong and just guilty of, you know, “grass is always greener” syndrome here. But I think that’s an experience that kids have in math. And I thought that Dr. Ramirez got at that when he’s talking about the need to validate a student’s experience of anxiety. Like, in treating anxiety, sometimes we alienate people further by just like saying, “Oh, no, no, no, it’s just like, you need to, you know, drill yourself more, practice more,” and kind of invalidate that. So this feeling of alienation, I think permeates a lot of math instruction. I’m looking forward to learning more about that with our future episodes

Bethany Lockhart Johnson (32:00):
Alienation. That’s interesting. I definitely felt, I definitely felt isolated and alone many times in my math journey, when I was having my…you know, in high school, when I was feeling like, “Clearly everyone can look at tan, sign, cosign, and that means something to them.” Right? I think it’s really interesting, because I’m thinking about the other disciplines; I’m running through them, and I’m like, even in science, which can seem abstract, so oftentimes there’s these experiments that accompany these concepts, where you’re like, “Look at this concept made real in front of you.” Right? . And so yeah, that’s really interesting.

Dan Meyer (32:39):
You’re always one step away from blowing something up! Or, you know, dissecting something that’s tangible to you.

Bethany Lockhart Johnson (32:46):
Yeah. That’s really interesting. I did really love how he brought up the abstract. And how, I think, even validating it…he talked so much about validation. Which to me was like, YES. If somebody just said, “Hey, it’s not only possible to have math anxiety, but it also doesn’t mean that you don’t belong here.” If somebody had said that, it would’ve literally changed the trajectory, you know? And I wonder what those conversations could look like in our classrooms, where teachers celebrate that. Like, WHOA, this is a new way to think of this. This is a new way. Asking how many, or what do you notice for this image, through a mathematical lens, or looking…we talked to Alison Hintz and Antony Smith, like mathematizing books, like looking through these lenses — it’s an invitation to step into this other world, right? But there’s not only one way to do it. And I think oftentimes it’s like that anxiety of “Am I gonna say the right thing?” or “Am I gonna notice the right thing?” Right? How do we create that space more, where there’s so many possibilities and we want kiddos to notice what they notice, right?

Dan Meyer (33:54):
You gotta become a certain kind of person to be successful in math class. I feel like is part of the implied deal. Where you’ve gotta—like how you said—say a certain thing or think about a certain thing a certain kind of way. You’re trying to become someone who is not necessarily you. Which I think is fundamentally an experience of alienation, separating you from important parts of yourself.

Bethany Lockhart Johnson (34:19):
I will never, ever dive into mathematics on the scale and level that you have with your PhD. You understand math in a way that my brain just…I won’t get there, right? And yet I’m allowed to call myself a mathematician, with all of my deep dives in elementary math and my love of early numeracy and thinking about how we start thinking about counting and numbers. Right? It’s like, if we make more space for what mathematicians can look like, and what is your personal relationship with math…I mean, that to me feels really exciting. ‘Cause I think we both have something to offer each other.

Dan Meyer (35:03):
I think I have never found early math more interesting than when I talk to early math educators. And learn just like all the different ways that students come to understand a concept that I had thought was simple. Like addition of whole numbers. Whoa! There’s a lot of ways kids do that work, and their brains think those thoughts. And, yeah. That’s a good word there you’re offering us and our listeners.

Bethany Lockhart Johnson (35:27):
Yeah. Yeah. I’m really excited about this season. I think there’s — again, there’s no way we’re gonna cover all facets of math anxiety. But I think having the chance to explore it over the course of a season is going to be really fascinating. And really, I hope, destigmatize it and open up the conversation for our listeners. And, you know, if you listeners…we wanna know what you thought of this episode. Do you have any particular questions? Do you have questions related to math anxiety? Questions related to this episode? We are in development for this season, so we’re gonna do our best to get those questions answered. You can keep in touch with us in our Facebook discussion group, Math Teacher Lounge Community, and on Twitter at MTLshow.

Dan Meyer (36:14):
Next time, we’re gonna go deeper into the causes and consequences of math anxiety.

Dr. Erin Maloney (36:20):
It’s not just the case that people who are bad at math are anxious about it. It’s actually that the anxiety itself can cause you to do worse in math. And that for me is really exciting, ’cause it means that if we can change your mindset, then we can really set you on a path with several more options available to you.

Dan Meyer (36:41):
Til next time folks,

Bethany Lockhart Johnson (36:41):
Bye.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Dr. Gerardo Ramirez says about math

“A lot of students struggle with math, and we want to normalize that struggle as much as possible. We have to find opportunities to tell better stories and reflect on our experiences.”

– Dr. Gerardo Ramirez

Associate Professor of Educational Psychology, Ball State University

Meet the guest

Dr. Gerardo Ramirez obtained his Ph.D. from the University of Chicago, where he studied the  role of teachers and parents in shaping the math attitudes of their students, as well as reappraisal techniques to help students cope with anxiety during testing situations.

Dr. Ramirez is currently an associate professor at Ball State, where he examines the role of frustration, empathy, and cultural capital in shaping students’ success and persistence.

A man with glasses, a beard, and a receding hairline wearing a suit and tie, pictured inside a circular frame with simple graphic accents—perfect for representing math teacher resources or the math teacher lounge.
A laptop displaying a Facebook group page for "Math Teacher Lounge Community," featuring profile photos, a group banner, and geometric shapes in the image background.

About Math Teacher Lounge

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Winter Wrap-Up 01: Problem-solving and facilitating classroom discussions

Promotional graphic for Math Teacher Lounge podcast, episode 1, featuring Fawn Nguyen, Christy Thompson, and Kassia Omohundro Wedekind discussing classroom problem-solving and discussions.

As we prep for an exciting new season of Math Teacher Lounge: The Podcast, hosts Bethany Lockhart Johnson and Dan Meyer are looking back at the amazing speakers and conversations from past episodes and sharing some of their favorites!

First up: A season 2 double feature of the power of problem-solving with Fawn Nguyen and Facilitating Classroom Discussions with authors Christy Hermann Thompson and Kassia Omohundro Wedekind.

Fawn is a specialist on Amplify’s advanced math team and a former math teacher and math coach—so she knows her stuff! You’ll hear about her five criteria for good problem-solving problems, and the power and importance of exposing all students to problem-solving.

Then, we’ll move into Bethany and Dan’s conversation with Christy and Kassia to learn how hands-down conversations allow students to become better listeners and the steps you can take to implement hands-down conversations in your classroom.

Explore more from Math Teacher Lounge by visiting our main page.

Download Transcript

Dan Meyer: (00:01)

Hey folks. Welcome back to Math Teacher Lounge. My name is Dan Meyer.

Bethany Lockhart Johnson: (00:03)

And I’m Bethany Lockhart Johnson. Hello! Happy New Year! Hello, Dan Meyer.

Dan Meyer: (00:09)

HNY, Bethany. HNY to you and to all of the listeners out there in Math Teacher Lounge. HNY is the abbreviation that I use sometimes.

Bethany Lockhart Johnson: (00:18)

Oh, is that what that is? Is that—I wasn’t sure what that was. If on my birthday you send me HBD…no.

Dan Meyer: (00:25)

Yeah.

Bethany Lockhart Johnson: (00:25)

No. Unacceptable.

Dan Meyer: (00:27)

I will. No, you want the full thing. To demonstrate my care for your birthday, I gotta spell the whole thing out. I’m just trying to stay relevant. You know, I’m just trying to stay relevant and youthful. So I’m using The Abreevs.

Bethany Lockhart Johnson: (00:38)

The Brevvies.

Dan Meyer: (00:40)

To the extent of even abbreviating the word “abbreviation.” . So, any New Year’s resolutions you wanna share with the listeners, Bethany? While you think, I’ll just share mine real quick here. This is the year of the perfect Wordle streak for yours truly, Dan Meyer. I’m going the full 365. Watch. Watch me do it, folks. I’m naming it here. Live on air. recorded on air. Perfect Wordle year. What you got for the listeners, Bethany?

Bethany Lockhart Johnson: (01:10)

Let’s see. It’s raining very hard here in Southern California, and my newest resolution is to embrace nature. My child wants nothing more than to go and splash in all the puddles.

Dan Meyer: (01:22)

Nice.

Bethany Lockhart Johnson: (01:23)

And be amongst the mud. And what I’m gonna keep telling myself—and so far, so far, I’ve been doing pretty good with this—thrive, child. Splash. Squish. We can dry you off. You will not melt. So I want to keep finding opportunities. Like, for instance, my response is, “It’s pouring rain. Let’s stay under covers and let’s read this book together!” And his response is like, banging on the windows, like, “Please let me go outside.” So I myself have some rain boots. I’m going to go forth and splash with my child. So hopefully you’ll see me doing that a bit more.

Dan Meyer: (02:08)

Love that.

Bethany Lockhart Johnson: (02:09)

Ask me what I’m doing. I’m outside, splashing in nature.

Dan Meyer: (02:12)

I don’t wanna put words in your mouth, but I have felt a bit like parenting is a means for rounding out aspects of my own personality that I have felt are—or habits or hobbies that are lacking. Like, I’ve never been real outdoorsy or into camping, but I don’t want that to limit my own kids’ aspirations or interests. So let’s do the thing that’s not super natural for me, for their own sake. Which is kind of what I’m hearing a little bit from you, which—that sounds exciting.

Bethany Lockhart Johnson: (02:35)

Do you wanna go camping together? Like, our families?

Dan Meyer: (02:38)

Uhhh. Let’s take this one off the air. I also love something that’s more relevant to a teachers audience that you said, that I think is super interesting, is how there’s ways that we can make the jobs harder for ourselves, that are optional. And what I hear from you is like, “I’m just not gonna freak out. We’re getting wet. We’re getting soggy. And I’m just not gonna freak out.” And I just think that that’s interesting to think about, the things that we take on, you know, that’s optional. Freaking out is optional, sometimes. And there’s other areas, I think, for parenting or for teaching, where it’s like, “Oh, do I really need to choose this particular battle?” And to reconsider that.

Bethany Lockhart Johnson: (03:19)

And in that spirit, our whole Wordle episode that we talked about? Do you remember you talked about how beautiful Wordle mistakes are, and how you keep learning from mistakes? I mean, you obviously want the final correct answer, but just, you know, when you get on a losing streak, Dan, I hope you’ll continue to pat yourself on the back.

Dan Meyer: (03:38)

Well, I will not be taking on a losing streak, or even lose one day. This is what’s gonna happen here. I’m just speaking that and putting it out in the universe.

Bethany Lockhart Johnson: (03:49)

Speak it!

Dan Meyer: (03:50)

But if it happens, I will be taking a long break from all human interaction. And lamenting, as I do.

Bethany Lockhart Johnson: (03:59)

Camping. Dan’s off in the woods, weeping.

Dan Meyer: (04:01)

That’s right. That’s right. Yeah. Well, we wanna share with you folks—an exciting programming note is that we are currently working very hard on producing a special fifth season of this podcast. You thought the other seasons were special? Let me tell you, this fifth season gives new meaning to the word “special.” And we can’t wait to tell you more about that. But in the meantime, Bethany, you wanna tell ’em what we’re up to in the meantime?

Bethany Lockhart Johnson: (04:26)

Well, Dan and I went back and we were having a conversation about some of our most favorite conversations, or the conversations that people bring up to us. Like, when we were at the CMC conference, or NCTM, folks, when we talk about the podcast, they’re like, “Oh, I loved this one.” “Oh, I love this one.” And that, to me, I don’t know, that is exciting. And so, while we’re putting together this new season over these next few weeks, we’re gonna feature a few of our favorite conversations from our first four seasons. Dan, four seasons!

Dan Meyer: (04:59)

We’ve been at this for four seasons! And I do want to just emphasize something you said, Bethany: that all of our conversations are our favorite conversations. They’re all our special children. What we just felt like you, the listeners, did not quite learn enough from some of these, and so we really needed you to hear them again to make sure you got everything that you should get out of them. So, let’s tell ’em who’s up first. And who’s up first is a conversation we had about problem-solving with Fawn Nguyen, who’s an advanced math team specialist here at Amplify. Been a former math coach, math teacher. Just really done the work, is what I’d say about Fawn.

Bethany Lockhart Johnson: (05:38)

If you have been listening to this podcast, you’re like, “Whoa, whoa. Wait, I have not missed an episode. I didn’t hear Fawn’s interview.” That is because we used to be video only, not podcasts. So this conversation with Fawn was from, what, our second season?

Dan Meyer: (05:55)

Yeah.

Bethany Lockhart Johnson: (05:56)

And we were on video. And another thing about it is it was, this is a conversation that, when folks talk about problem-solving, a lot of the responses we’ve gotten are like, “Wait, I’ve never thought of problem-solving this way.” In fact, you’ll hear us say that exact thing . So we really appreciated the time with Fawn. And yeah.

Dan Meyer: (06:17)

Enjoy it, folks. Especially enjoy Fawn’s—I think a four-part?—definition of problem-solving, a word that’s often kind of mushily defined. And Fawn really goes into, I think, precision and depth on it. So hope you folks enjoy it.

Dan Meyer: (06:35)

Give a wave, Fawn, to the camera. Would you? Cool. Fawn has been a teacher for a very long time. She is someone who could have left the classroom at any point and taken any number of jobs in the math-teaching universe. But I’ve always admired that Fawn has taught kids for a very long time, and that has given her, in my view, just a lot of clarity on what is important to her about students. I’ve seen her not get upset or obsessed with certain kinds of small niche issues that a lot of us, like, they get a lot of us down in the classroom, sometimes. And she’s maintained a laser focus on among many other things, problem-solving as a virtue in mathematics classrooms. So, please welcome Fawn to our show. Fawn, thanks so much for being here.

Fawn Nguyen: (07:18)

Hey, thank you so much. Thank you. I am so excited and honored that you guys invited me for this, Bethany and Dan.

Bethany Lockhart Johnson: (07:24)

Thank you for being here.

Fawn Nguyen: (07:26)

I love you, Bethany. Dan, I can tolerate, but I love you.

Dan Meyer: (07:30)

I really worked myself up there on that complimentary opening for you, and that’s how you get me back, here? OK. Problem-solving is fully on the consciousness of math teachers. Every math teacher knows that they need to say, like, “Yeah, oh, problem-solving. Yes. Love it. Do it. I dig it.” But even so, I feel like it’s become kind of a buzzword. Like, it’s not always obvious what that means…or am I doing problem-solving, really? So we’re curious: As someone who is a problem-solving expert, who is asked all over the world to talk about problem-solving: How do I know if I’m doing problem-solving in my classroom?

Fawn Nguyen: (08:12)

This is not my definition of it, but—nor am I an expert, by the way, Dan, thank you! but I try really, really hard and work on it!—my definition—or it’s not my definition, but I like it because it’s short and honest—is “problem-solving is what we do when we don’t know what to do.” And so—

Bethany Lockhart Johnson: (08:32)

Ooh!

Fawn Nguyen: (08:32)

—with that mind-frame, I’m hoping teachers think more about what they task. Because I think it gets mislabeled a lot, as to what is problem-solving. If the kids already know what to do, there’s a solution path. Then it’s not problem-solving.

Dan Meyer: (08:48)

Yeah. So what are examples then? An example of, like, I might call something problem-solving, but it it fails that particular definition that you just proposed there. Very short, very honest definition.

Fawn Nguyen: (08:59)

Just, it needs to have constraint and contradiction to what the kids think naturally. It should come as a surprise. There’s an element of surprise in it. There’s tension.

Dan Meyer: (09:11)

Maybe if there’s harder numbers or, you know, decimals or fractions in the same kind of procedure…I can feel myself thinking, “Yeah, this is hard. This is problem-solving. Problem-solving equals hard. But we already know what to do.”

Fawn Nguyen: (09:27)

Or just word problems. That’s the most common thing. As soon as it just has words attached to the math, it becomes problem-solving. But that’s just coding it to me. That’s just coding it with words, wrapping it around. It doesn’t mean anything until we read through and see if there’s true problem-solving in it.

Bethany Lockhart Johnson: (09:45)

Like, what’s the moment that it becomes problem-solving? In the way that you envision it?

Fawn Nguyen: (09:53)

Well, I think there’s the bigger problem-solving of really bringing a task…I wanna call it left field. It just—we rarely ever, if ever, see it in the regular coursework, but it can also be problem-solving if we just take what we expect the children to do at the end of the unit, how about we front-load that? To me, that’s also problem-solving. And I’m trying to encourage teachers to do that last problem first. The task writers put more thought—not that they don’t do the rest of it!—but you know, this is a special one, because they label it “challenge,” or “enrichment,” or “are you ready for more?” I’ve seen those. And so it is this really special problem. And I would love for us to think about “do that first.” Because my biggest fear is that because it comes at the end, that not all the children are involved. And so that to me is the saddest part. Because we might not get to it, right? In mathematics, we always think, “OK, well, let’s do these problems and then we don’t have time for the rest.” But I think that’s your richest task right there, is at the very end. So why don’t we front-load it, start it, and it’s OK—of course it’s OK!—that we don’t all get it. But the exposure to all students is so important. Talk about, you know, equity. Talk about that, everybody gets the same thing. If everyone dug into that first one with everybody’s collaboration, and we get to share that, and then we leave it, because “Yeah, OK, now we learn more of the other stuff, right? That hopefully support. And then we can go back. And now everybody had a chance to go get into it, and then we can come back to it as, as many problems, we need to go back to it.”

Bethany Lockhart Johnson: (11:37)

And that feels so powerful. Because it feels like—as a teacher, I’m thinking it would also inform my work, how I approach the unit, and how I approach the next steps. Right? Like, what kind of work would we be doing if I let it, if I allow it, to change the way that I approach the unit.

Dan Meyer: (11:58)

Yeah. What you’re describing is so powerful, and really asks a lot of the task designers as well, I think. There are problem-solving tasks that really require, like, abstract knowledge of the way formulas and variables fit together. And what I love about what Amplify is doing with their problem-solving, what you’re helping them do, is that they start with a true low floor that can draw in every student. And they might get stuck at different places; that’s fine. But everyone has a way in. That’s exciting.

Fawn Nguyen: (12:24)

It’s a big deal for me to have this opportunity and this trust, to integrate problem-solving into the curriculum, make it intentional. It’s difficult to implement. It is, to be honest. Because for me, what is a good task? This makes one of my four criteria: One is, it is non-routine. It is simply stated. Simply stated—that’s like your low floor. And then has multiple solutions. And the fourth: This makes it. Because that the teacher enjoys solving it. And so you have to enjoy solving it to bring it. Because so that way I can say to my kids, “This is my gift.” It really is, Because, you know, it has so much fun and joy. And I appreciate the struggle. And I wanna illustrate an example. For example, let’s say Dan and I are classmates. And I know that Dan gets A’s on his tests and the lowest score he ever got was an 89%. I, on the other hand, just sitting right next to him, I average D. I have a D average on everything. While Bethany, our amazing and wonderful teacher, brings in a problem. And when she brings it in, she says, “I worked on this problem. I found this problem; I worked on it; and I struggled with it. And it was amazing. I enjoyed it so much, I’m sharing it with you.” And all of a sudden it’s like, “OK!” And I”m sitting there, right? My teacher loves this problem so much; she’s bringing it in to share with us. And now, all of a sudden, it’s not, you know…and I know she only gives us non-routine. When she talks about problem-solving, it’s non-routine. So it’s not directly tied to the textbook that I’ve been struggling with. So it gives me a chance, it gives me a chance to contribute. To think differently. And now, suddenly I look forward to working with Dan, because in this space, in this problem-solving space, Dan is no longer Mr. Know-It-All. And so that’s what I mean by—I am saying this a hundred times, and I will not stop saying it—problem-solving levels the playing field. Our world is filled with unsolved problems. Are you kidding me? Right? We look around us, we have so many things that are not solvable, or people are working on it, and yet in mathematics, what happens? The bell rings; we start; and we solve everything during that time, and we leave. And that’s…yeah. No! No! We need to wrestle with problems.

Dan Meyer: (15:04)

And that was our conversation with Fawn Nguyen, which we first released way back in November, 2021. You folks can follow Fawn on Twitter at Fawn P Nguyen. Um, that’s @ F A W N P N G U Y E N.

Bethany Lockhart Johnson: (15:18)

So our episode today is a double feature. We are featuring another conversation that we loved from Season Two. This is a conversation with Christy Hermann Thompson and Kassia Omohundro Wedekind. They’re authors of the book, “Hands Down, Speak Out: Listening and Talking Across Literacy and Math.” And I don’t know if you remember, but not only did we have a conversation with them, but we did a whole book study on Facebook, a Facebook Live book study, over the course of several months. And it was one of my most favorite things. And then they did a webinar at the end. So our conversation with them on the podcast for me felt like such a beautiful dive into their book. And you know, I’ve said it before, you think you have something down in the classroom, you’re like, “Oh, hand-raising, I’ve got that down.” You think you have it down, but then somebody says, “OK, but have you ever considered thiiiis?” You know, and it just—

Dan Meyer: (16:17)

NOT that??

Bethany Lockhart Johnson: (16:18)

, Not that? Something totally different? And I loved talking with them. They’re a lot of fun. And I loved the book.

Dan Meyer: (16:23)

Wonderful conversation, great book. Very provocative ideas. Yeah. As someone who’s like, “OK, classroom management, I gotta get the hand-raising going…”. In the classroom before we talked, they offered a really potent challenge to some really standard classroom management ideas. Yeah. Loved it.

Bethany Lockhart Johnson: (16:40)

And this conversation also offers some really practical tips for facilitating student conversations. So we think you’ll enjoy it. Here’s our conversation with Christy and Kassia.

Bethany Lockhart Johnson: (16:53)

So today we are talking about “Hands Down, Speak Out: Listening and Talking Across Literacy and Math, K—5.” And we have the authors here, Kassia Omohundro Wedekind and Christy Hermann Thompson. Before we begin, let’s define what a hands-down conversation is. A hands-down conversation is just another way to structure discourse in your classroom. So in a typical classroom, you might see students raising their hand and waiting on a teacher to call on them before they share their ideas or engage in discussion. But in a hands-down conversation, it’s students’ ideas and voices that are taking the lead, and teachers are stepping back and focusing on listening and facilitating. Hello! Welcome to the Lounge.

Kassia Omohundro Wedekind: (17:44)

Thank you. We’re excited to be here. We’re fans of Season One. So we’re ready to go.

Dan Meyer: (17:50)

I was a secondary teacher but I still found so much to love about the book. I think facilitating conversations is just generally challenging, and perhaps even more so in math, where answers feel so tightly dialed-in, in lots of ways. But I loved it. I would love for you to just explain to our audience, what is a hands-down conversation and how does that contrast with what might be standard practice for some people? For some classes?

Christy Hermann Thompson: (18:13)

We just started using the term hands-down conversation because we wanted to differentiate the fact that there are different times to have different types of dialogue in the math classroom, in the literacy classroom. And we use this as one of our tools. Right? It’s not that every day, all day long, we’re very against hand-raising and should never see that again. We find that having this as one of our tools will be where we make really clear to the students that this is a moment where we’re turning it over to you to negotiate the space and make the decisions about when your voice comes in and who speaks next. You know, carry on kind of like that dinner table or that playground or, you know, whatever is your natural habitat for talk. And bringing that into the classroom and then hoping that it also someday transfers back out of the classroom back into the real world.

Bethany Lockhart Johnson: (19:09)

For the teachers who feel like that’s terrifying to have students just start speaking, and speaking without any sort of control or my little equity sticks, my little popsicle sticks, or my popcorn, or whatever other thing they’re using, what would you say is the first step?

Christy Hermann Thompson: (19:25)

So I think recognizing and naming that fear is part of it. And then saying to yourself, “What’s the worst that could happen here?” You know, I think the worst that could happen is that nobody talks and it’s totally silent. Or on the other hand, everybody talks at the same time. And both of those things will happen! And so what? It’s gonna be messy. And if you just acknowledge that it’s gonna look messy, and that’s part of growing; that every child as they learn—and every adult—is messy as they grow.

Kassia Omohundro Wedekind: (19:59)

And we have to see what kinds of things will happen in a hands-down conversation. Like there’s no prerequisite. You just start and then you see what happens. And those are the signs that tell you, “What can help this community grow as talkers and listeners? If everyone’s talking at the same time, and they’re kind of pushing each other over with their words by saying, “I have something to add!” “I have something to add!” or something like that, that’s a common thing that sometimes happens at the beginning. Then you know that the next step is to do some work about how to hold your thoughts back, how to add, wait for a space in the conversation to talk. And those are all things we need people to know out in the world.

Bethany Lockhart Johnson: (20:41)

So can you give an example of a micro-lesson that…well, first, what do you define as a micro-lesson? And then, what’s an example of one that maybe somebody who wants to dip their toe into the world of hands-down conversations that they could try?

Christy Hermann Thompson: (20:56)

The reason we call them micro-lessons is because we wanted to differentiate from the term mini lesson, which is out there and tends to describe about 10 or 15 minutes that might take place at the beginning of a work period of time. And this is much smaller than that. We usually follow a pretty predictable structure of naming. Here’s this thing that’s so helpful when we’re having conversations, and we love to especially be able to name something that a student had done: “Kaylee did this yesterday and it really helped us.” So what we might call that is, “And then here’s how Kaylee and other people might do that. They might do something like this.” And, you know, having a little anchor chart, so there’s a visual reminder of that skill. “So when we’re having a conversation today, you could try…”. And that’s basically a micro-lesson, just in a nutshell.

Kassia Omohundro Wedekind: (21:51)

When I was doing these hands-down conversations and I had more space for myself to listen as a teacher, I’m like, “Well, look at those kids, like, slumped onto the ground, like, pulling the carpet apart, but they’re having this amazing conversation!” And so I learned that listening is a lot broader. So in this lesson that I’m thinking about, we just talk with kids about what are lots of different ways that listening can look like. Sometimes with younger kids, I’ll take pictures of them listening in different ways and we’ll notice things about them together. And then we invite them to talk with their Turn and Talk partner about like, “How do you like to be listened to?” Or “Tell me about how you listen.” And just kind of broaden that. And really, I like to think that like the micro-lessons are for the kids, but also I’m saying those things to say them for myself. Like, “Remember, you don’t have to insist that kids are staring each other down in the eyes all the time. Like, “It’s OK when they’re doing other things. There’s other ways of listening.” So I think I’ve learned as much from the micro-lessons each time I do them as the kids that I’m trying to help grow as listeners and talkers, as well.

Dan Meyer: (23:00)

You folks have a lot of really eloquent ideals you express, around democratic classrooms and engagement. But you also have just some very tangible, practical…even down to, like, how a teacher positions their body in space and the way they use their eyes to connect. I think it would be really helpful for teachers to hear that it’s not just they’re signing on to a manifesto of sorts, but there’s ways they can act their way into the beliefs that you both expressed here.

Christy Hermann Thompson: (23:26)

When I’m starting hands-down conversation work, if I put myself a little bit outside of the circle and look down, and give myself a clipboard, it, it helps me bite my tongue and it helps me give better wait time and see what the kids are doing before I have that tendency to jump in and teach and do lots of teacher-y things.

Bethany Lockhart Johnson: (23:48)

Kassia and Christy, thank you so much for joining us. We are so excited to have this conversation and to share your work. This is exciting. And I feel like this conversation is just the beginning of a deeper dive into this book.

Kassia Omohundro Wedekind: (24:01)

Thanks for having us.

Christy Hermann Thompson: (24:02)

Thank you.

Dan Meyer: (24:03)

Thank you both.

Bethany Lockhart Johnson: (24:06)

Thanks so much for listening to our conversations with Fawn Nguyen and Christy Hermann Thompson and Kassia Omohundro Wedekind, both of which were released in 2021, part of our second season. And, you know, we hoped you enjoyed listening to it for a first, second, maybe third, fourth time.

Dan Meyer: (24:24)

Let’s be real. There’s some real fans out there.

Bethany Lockhart Johnson: (24:26)

We loved it then. We love it now!

Dan Meyer: (24:28)

Yep, yep, yep. Please keep in touch with the show by following us on Twitter at MTL Show, and join our Facebook group, the Math Teacher Lounge community. We’d love to hear from you there. And please stay tuned for more info on what we’re cooking up here in the Math Teacher Lounge. Thank you folks for listening. Take care, Bethany.

Bethany Lockhart Johnson: (24:47)

Bye now.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Fawn Nguyen says about math teaching

“It’s a big deal for me to have the opportunity and this trust to integrate problem-solving into the curriculum.”

– Fawn Nguyen

Specialist, Math Advance Team, Amplify Desmos Math

Meet the guests

Fawn Nguyen

Fawn began her work with Amplify in 2022 as a Math Advance Team Specialist. She was a math coach for a K-8 school district for three years, and a middle school teacher for 30 years before that. Fawn has also received a number of accolades as an educator.

Christy Thompson

Christy Thompson is a Literacy Coach in Fairfax County Public Schools in Virginia. She has spent her teaching and coaching career particularly focused on listening to and learning from the talk of our youngest students.

Kassia Omohundro Wedekind

Kassia Omohundro Wedekind spent many wonderful years as a classroom teacher and math coach in Fairfax County Public Schools in Virginia and now splits her time between being an independent math coach and an editor at Stenhouse Publishers. Her favorite days are spent in classrooms learning from the many ways children talk, listen and negotiate meaning together.

Three women are pictured separately in circular frames, each smiling and facing the camera, against a white background with overlapping pastel shapes—perfect for highlighting math teacher lounge discussions or sharing essential math teacher resources.
A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Welcome, Flowing Wells, to Amplify Desmos Math!

Amplify Desmos Math thoughtfully combines conceptual understanding, procedural fluency, and application. Each lesson is designed to tell a story by posing problems that invite a variety of approaches before guiding students to synthesize their understanding of the learning goals.

Keep reading to learn more about the program and explore sample materials.

A collage of educational software screens, featuring Desmos Math with vibrant graphs and animations, amplifies mathematical comparisons alongside engaging plant growth simulations. Perfect for educators in New York math classrooms seeking dynamic learning tools.

About the program

Our structured approach to problem-based learning builds on students’ curiosity to develop lasting grade-level understandings for all students.  The program thoughtfully combines conceptual understanding, fluency, and application, motivating students with interesting problems they are eager to solve. Teachers can spend more time where it’s most impactful: creating a collaborative classroom of learners.

Screenshot of an educational activity page using Amplify Desmos Math to present a function machine and a table for calculating outputs of ( h(x) = f(x + 2) ) with given inputs for ( x ), offering an engaging approach to New York math standards.
The geometry activity screen features a circle with intersecting lines and a shaded area. Instructions prompt users to explore Sam's construction and determine if a square was formed, all enhanced by the innovative tools of Amplify Desmos Math.

Structured approach to problem-based learning

  • Easy-to-follow instructional guidance
  • Robust assessments and reports
image of Amplify Desmos Math

Math that motivates

  • Powerful teacher-facilitation supports and tools
  • Students talking and building from each other’s ideas 
  • Every lesson has compatible print and digital materials for a collaborative classroom
Screenshot of a design challenge interface from Amplify Desmos Math, featuring overlapping purple circles. The left shows 3 circles, and the right displays 5. Task: match the two designs as if solving a New York math puzzle.

Student thinking is made evident

  • Curiosity-driven lessons that motivate students with interesting problems they are eager to solve
  • Explicit guidance for teachers on what to look for and how to respond
  • Technology that provides Responsive Feedback and is designed to reveal mathematical thinking
A chart titled "Scope and Sequence" for Algebra 1, Geometry, and Algebra 2, with colorful units and topics, overlaid by an illustration of lab equipment with a gauge and liquid.

Scope and sequence

Click the link below to view the program scope and sequence.

Preview lessons

Check out the links below to explore our interactive digital lessons. Download a navigation guide for tips on navigating the print and digital program components.

A laptop showcases a mathematical graph using Desmos Math, amplifying the learning experience. Behind it lie two papers with printed graphs and text, reflecting a bustling New York math classroom environment.

Looking for help?

We are dedicated to supporting you throughout your review. Get help at any time by getting in touch with your account executive directly:

Tommy Gearhart, Account Executive
tgearhart@amplify.com
(505) 206-7661

Welcome, Amplify Math families and community to Amplify Desmos Math High School (AGA, Integrated 1–3)!

Welcome to Amplify Desmos Math! Below, you’ll find links to sample lessons, scope and sequence, and more information about our AGA and Integrated high school math programs.

Algebra 1, Geometry, Algebra 2, and Integrated 1 are available for Beta implementations and pilots in 2025–26. Integrated 2–3 will be available for the 2026–27 school year.

A collage of educational software screens, featuring Desmos Math with vibrant graphs and animations, amplifies mathematical comparisons alongside engaging plant growth simulations. Perfect for educators in New York math classrooms seeking dynamic learning tools.

About the program

Our structured approach to problem-based learning builds on students’ curiosity to develop lasting grade-level understandings for all students.  The program thoughtfully combines conceptual understanding, fluency, and application, motivating students with interesting problems they are eager to solve. Teachers can spend more time where it’s most impactful: creating a collaborative classroom of learners.

Screenshot of an educational activity page using Amplify Desmos Math to present a function machine and a table for calculating outputs of ( h(x) = f(x + 2) ) with given inputs for ( x ), offering an engaging approach to New York math standards.
The geometry activity screen features a circle with intersecting lines and a shaded area. Instructions prompt users to explore Sam's construction and determine if a square was formed, all enhanced by the innovative tools of Amplify Desmos Math.

Structured approach to problem-based learning

  • Easy-to-follow instructional guidance
  • Robust assessments and reports
  • Spanish student materials (available 2026–27)
A classroom dashboard displays student names and their progress in activities, with checkmarks indicating completed tasks and circles showing ongoing or incomplete tasks.

Math that motivates

  • Powerful teacher-facilitation supports and tools
  • Students talking and building from each other’s ideas 
  • Every lesson has compatible print and digital materials for a collaborative classroom
Screenshot of a design challenge interface from Amplify Desmos Math, featuring overlapping purple circles. The left shows 3 circles, and the right displays 5. Task: match the two designs as if solving a New York math puzzle.

Student thinking is made evident

  • Curiosity-driven lessons that motivate students with interesting problems they are eager to solve
  • Explicit guidance for teachers on what to look for and how to respond
  • Technology that provides Responsive Feedback and is designed to reveal mathematical thinking
A chart titled Scope and Sequence for Algebra 1, Geometry, and Algebra 2, with colorful units and topics, overlaid by an illustration of lab equipment with a gauge and liquid.

Scope and sequence

Click the link below to view the program scope and sequence.

Preview lessons

Check out the links below to explore our interactive digital lessons. Download a navigation guide for tips on navigating the print and digital program components.

A laptop showcases a mathematical graph using Desmos Math, amplifying the learning experience. Behind it lie two papers with printed graphs and text, reflecting a bustling New York math classroom environment.

Looking for help?

Support is always within reach. Our team is dedicated to supporting you throughout your review and can be reached at any time by emailing or calling us directly.

  • Live chat: Click the orange icon while logged in to get immediate help.
  • Phone: Call our toll-free number: (800) 823-1969.
  • Email: Send an email to help@amplify.com. In the message body, please include your name and question. Provide as much detail as possible, so we can more quickly help you find a solution.
A laptop screen displays a curriculum dashboard with a list of core units and colorful thumbnails for a sixth-grade ELA program.

Ready to learn more?

Amplify Desmos Math New York high school

Welcome to Amplify Desmos Math! Below, you’ll find information about the program, login credentials to access the digital curriculum, and additional resources to support your review.

A laptop screen displays a math activity showing a machine representing the function h(x) = f(x + 2) and a table for input and output values.

About the program

Our structured approach to problem-based learning builds on students’ curiosity to develop lasting grade-level understandings for all students.  The program thoughtfully combines conceptual understanding, fluency, and application, motivating students with interesting problems they are eager to solve. Teachers can spend more time where it’s most impactful: creating a collaborative classroom of learners.

A geometry activity shows a circle intersected by several lines, with a shaded quadrilateral inside. Questions and answer options appear on the right.

Structured approach to problem-based learning

  • Easy-to-follow instructional guidance
  • Robust assessments and reports
  • Explicit guidance for teachers on what to look for and how to respond
A classroom activity tracker shows a grid with students’ names in the left column and progress checkmarks or crosses for seven activities across the top.

Math that motivates

  • Powerful teacher-facilitation supports and tools
  • Students talking and building from each other’s ideas 
  • Compatible print and digital materials for every lesson to foster a collaborative classroom
A design challenge interface shows two side-by-side diagrams with interlocking purple circles; the left is editable with 3 objects, the right is the design to match.

Student thinking is made evident

  • Curiosity-driven lessons that motivate students with interesting problems they are eager to solve
  • Technology that provides Responsive Feedback and is designed to reveal mathematical thinking
  • Student Notes pages to prepare students for college-level skills

Scope and sequence and standards alignment

Click the link below to view the program scope and sequence, alignment to standards, and alignment to the NYC DOE Definition of Culturally Responsive-Sustaining Education and the New York State Culturally Responsive-Sustaining Education Framework

A two-page chart outlines the scope and sequence for Algebra 1, Geometry, and Algebra 2 units, with a vector graphic of lab equipment in the lower right corner.
A laptop displays a graph of a diver's path above water, with two printed math worksheets featuring graphs, tables, and practice problems in the background.

Experience Amplify Desmos Math New York.

Explore our digital program to review content from Algebra 1, Geometry, and Algebra 2. To log in, click the orange “Review now” button below, select “Log in with Amplify” and use the following login credentials:

Username: t.math-adm-ny-hs@tryamplify.net

Password: AmplifyNumber1

Resources to support your review

To learn more about Amplify Desmos Math New York, including pedagogical philosophy, origins, implementation examples, and nationally recognized independent reviews, please download the following documents:

A worksheet and two digital screens show math activities involving tables and blocks, focusing on comparing numbers and filling in missing values.

Looking for help?

Support is always within reach. Our team is dedicated to supporting you throughout your review and can be reached at any time by emailing or calling us directly.

  • Live chat: Click the orange icon while logged in to get immediate help.
  • Phone: Call our toll-free number: (800) 823-1969.
  • Email: Send an email to help@amplify.com. In the message body, please include your name and question. Provide as much detail as possible, so we can more quickly help you find a solution.

Your Beyond My Years 2024 recap!

In August of last year, our teaching podcast Beyond My Years took its first steps—and in no time we were exploring a lot of new territory on our journey to soak up teacher advice and wisdom from seasoned educators across the globe. Their experiences became our experiences. So let’s recap some of the top moments of 2024.

In 2024 on Beyond My Years we:

Traveled 3,469 miles to Stasia, Alaska.

We ventured all the way to the northernmost part of Alaska alongside Patti and Rod Lloyd to teach in a rural indigenous community. Joining such a rich and unique culture as outsiders taught Patti and Rod the importance of learning from their students.

“Even though they’re coming to me at five and six years old, they are coming with a lot of rich knowledge that I don’t have. And if I remain open and work with them, I’ve got a lot to learn.” —Rod Lloyd

Went back to school at the age of 80.

When the United Kingdom put out a call in 2020 for retired educators to return to aid a national shortage, Eric Jones knew he still had more left to teach, even at the age of 80! He knows that to stay in the education field as long as he has you need to celebrate and honor all areas of what a teacher does. When you honor every piece of the work you can do, you can make sure every moment stays aligned with your goals and serves your students.

“I like teaching kids things they didn’t know before and now they’re excited about. I love the idea that they will then move on into realms of industry and economic success that I would never dream of.” —Eric Jones

Shared our first Amplify podcast episode entirely in Spanish.

We even had our first bonus episode entirely in Spanish with Luz Selenia Muñoz. She taught us that some things transcend language—like the importance of knowing the “why” behind student behavior. According to Luz, whether your classroom is monolingual or multilingual, it is important to make connections with your students. You will see what they need and know what their triggers are. Behavior improves when you understand what your kids are going through.

“Yo creo que le diría que tenga paciencia. Paciencia. Que respire. Que las cosas van a mejorar cada día.” —Luz Selenia Muñoz

“I think I would tell them to be patient. Be patient. Breathe. Things will change for the better with every passing day.” —Luz Selenia Muñoz

Took time for ourselves.

Kamphet Pease called out the overachiever in all of us educators. An important piece of teacher advocacy: We all took a hard look at our school to-do lists together and recognized that we have to do better at prioritization—including prioritizing self-care.

“Make sure you take care of yourself as well. Take the time to go for a walk, take the time to take a bubble bath, cook for yourself, whatever you find enjoyment in.” —Kamphet Pease

Want even more of the best of the best from season one of Beyond My Years, which is brought to you by the team that produces Science of Reading: The PodcastDownload our key takeaways, a curated collection of invaluable wisdom and practical guidance from our lineup of inspiring educator guests.

More to explore:

Welcome

Elementary Literacy Program – Family Welcome Letter

Lectoescritura en Español – Carta de bienvenida para las familias

Grade K

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Welcome

Elementary Literacy Program – Family Welcome Letter

Lectoescritura en Español – Carta de bienvenida para las familias

Grade K

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

i-Ready Classroom-NEW

To view this protected page, enter the password below:



Welcome!

Amplify Science: California Edition is an immersive and engaging core curriculum authored by UC Berkeley’s Lawrence Hall of Science and built specifically for the NGSS.

K–8 Integrated Course Model

Grades 6–8 Integrated Model

Grades 6–8 Discipline Specific Model

Amplify Science

A new core curriculum designed from the ground up for the NGSS.

Preview the Student Books and Student Investigation Notebooks

Grades 6–8 Integrated Model

Spanish Student Books and Student Investigation Notebooks

Amplify Science

A new core curriculum designed from the ground up for the NGSS.

Preview the Student Books and Student Investigation Notebooks

Spanish Student Books and Student Investigation Notebooks

Amplify Science

A new core curriculum designed from the ground up for the NGSS.

Preview the Student Books and Student Investigation Notebooks

Grades 6–8 Integrated Model

NGSS Benchmark Assessments

The Amplify NGSS Benchmark Assessments were authored by Amplify and were not developed as part of the Amplify Science program or created by the Lawrence Hall of Science.

Grade K

Unit 1: Position, Length, Height, and Sorting

Lesson 2: Describe and Compare Length and Height, Session 3Connecting Cubes

Unit 2: Numbers to 5, Shapes and Weight

Lesson 4: Count, Show and Write Numbers to 5, Session 2Skye’s Style
Lesson 5: Compare Numbers to 5, Session 4Matching Groups
Lesson 5: Compare Numbers to 5, Session 5Designing Shoes With Skye
Lesson 6: Three-Dimensional Shapes and Weight, Session 1What’s That Shape?
Lesson 6: Three-Dimensional Shapes and Weight, Session 2Building Solid Shapes
Lesson 6: Three-Dimensional Shapes and Weight, Session 5Putting Solid Shapes Together

Unit 3: Addition and Subtractions with 5 and Shapes,

Lesson 8: Two-Dimensional Shapes,
Session 1
So Much Sorting
Lesson 8: Two-Dimensional Shapes,
Session 2
What’s That Shape Called?
Another Shape

Unit 4: Numbers to 10 and Shapes

Lesson 11: Count, Show, and Write Numbers to 10, Session 1Investigate: Cafeteria Math
Fingers as Math Tools
Lesson 12: Compare Numbers to 10, Session 1Moving and Grooving
Fingers and Counters
Lesson 12: Compare Numbers to 10, Session 2More, Fewer, or the Same
Comparing Words
Lesson 12: Compare Numbers to 10, Session 5Forest Friends
Lesson 14: Compose and Decompose 10, Session 2Harry’s Hamster Wheel
Lesson 14: Compose and Decompose 10, Session 3Harry Explores Space
Lesson 14: Compose and Decompose 10, Session 4Showing What We Know About 10
Lesson 14: Compose and Decompose 10, Session 5Harry Explores the Ocean

Unit 6: Addition and Subtraction Within 10

Lesson 20: Add Within 10, Session 1Investigate: Casey’s Town
What Does It Mean to Add?
Lesson 20: Add Within 10, Session 2How Many Objects?
Lesson 20: Add Within 10, Session 3How Many Objects in Pictures?
How Will You Count?
Lesson 21: Subtract Within 10, Session 1What Does It Mean to Subtract?
Lesson 22: Add and Subtract to Solve Wold Problems, Session 1The Bus Depot

Unit 7: Teen Numbers and Shapes

Lesson 23: Compose and Decompose Teen Numbers with Tools and Drawings, Session 2Investigate: Packing Snacks
Getting Ready for the Game
Pass, Shoot, Score
Lesson 23: Compose and Decompose Teen Numbers with Tools and Drawings, Session 3How Many on the Field?
Lesson 25: Compose and Decompose Teen Numbers with Symbols, Session 2Jersey Jam!
People at the Park

Grade 1

Unit 1: Relating Addition and Subtraction

Lesson 2: Add and Subtract Within 10, Session 1What’s the Difference?
Leaping Lily Pads!
Investigate: Let’s Grow!
Lesson 2: Add and Subtract Within 10, Session 3Packing a Picnic
Lesson 5: Solve Word Problems to 10, Session 2Tutu’s Garden in Maui
Lesson 5: Solve Word Problems to 10, Session 2Replanting Huli
Lesson 5: Solve Word Problems to 10, Session 3The Kalo Plants
Lesson 5: Solve Word Problems to 10, Session 4A Community Working Together
Lesson 5: Solve Word Problems to 10, Session 5Helping Others

Unit 2: Addition and Subtraction Within 20

Lesson 6: Teen Numbers, Session 2Same Number, Different Ways
Lesson 7: Add Three Numbers, Session 2Making 10
Kitten Coaster

Unit 4: Using Tens and Ones to Organize and Count

Lesson 15: Tens and Ones, Session 1Investigate: Game Points
Lesson 15: Tens and Ones, Session 3Meeting Yara
It’s a Match
Lesson 16: Numbers to 120, Session 1How Many Cubes?
Boris’s Thimbles
Lesson 21: Add Two-Digit Numbers, Session 1How Many Tens?
Investigate: Squashes at the Playground
Lesson 21: Add Two-Digit Numbers,
Session 2
Town Helpers
Lesson 21: Add Two-Digit Numbers,
Session 3
Making Squash Butter

Unit 5: Operations with Tens and Ones

Lesson 19: Addition with Two-Digit Numbers, Session 2From Park to Table

Unit 6: Geometry and Measurement

Lesson 22: Shapes, Session 1Shapes Ying Saw
Lesson 23: Break Shapes Into Equal Parts, Session 2Fair and Square
One of the Parts, All of the Parts
Lesson 23: Break Shapes Into Equal Parts, Session 5A Bigger Part

Grade 1 (ADM G2)

Unit 1: Relating Addition and Subtraction

Lesson 1: Partner Pairs for 10, Session 3Ways to Make 10
Lesson 2: Add and Subtract Within 10, Session 3Exploring Within 10

Grade 2

Unit 1: Numbers Within 20

Lesson 2: Using Mental Math Strategies to Subtract, Session 1Awesome Aquariums

Unit 2: Numbers Within 100

Lesson 10: Solve Word Problems Involving Money, Session 1Investigate
Lesson 10: Solve Word Problems Involving Money, Session 2Discovering Coins (Part 1)
The Toy Stand
Lesson 10: Solve Word Problems Involving Money, Session 3How Much Money?
Discovering Coins (Part 2)
Lesson 10: Solve Word Problems Involving Money, Session 4The Craft Stand at the Block Party

Unit 3: Numbers Within 1000

Lesson 12: Three-Digit Numbers, Session 1Investigate: A Mistake in Mom’s Office
What Makes a Hundred?
Lesson 12: Three-Digit Numbers, Session 2Looking for Patterns
Lesson 13: Read and Write Three-Digit Numbers, Session 1What’s the Value?
Lesson 13: Read and Write Three-Digit Numbers, Session 2Mail Call!
Lesson 13: Read and Write Three-Digit Numbers, Session 3A New Representation
What’s Your Name?
All the Ways!
Lesson 15: Mental Addition and Subtraction, Session 2Turtle Hurdle
Lesson 16: Add Three-Digit Numbers, Session 2There’s Something About Berries
Lesson 18: Using Addition and Subtraction Strategies with Three-Digit Numbers, Session 2Baking With Skunk

Unit 4: Length

Lesson 25: Solving Problems About Length, Session 2Lengths of Jungle Animals
Lesson 27: Sorting and Organizing Data, Session 1Messy Measurements
Lesson 27: Sorting and Organizing Data, Session 3Bracelets and Wristbands
Lesson 26: Add and Subtract on the Number Line, Session 1Investigate
Time to Line Up!
In Full Bloom
Lesson 26: Add and Subtract on the Number Line, Session 2What’s That Number?
Lesson 26: Add and Subtract on the Number Line, Session 3Greater Than, Less Than, or Equal to

Unit 5: Shapes and Arrays

Lesson 28: Recognize and Draw Shapes, Session 2Frame It!
Lesson 28: Recognize and Draw Shapes, Session 3Measure It, Draw It
Lesson 32: Even and Odd Numbers,
Session 1
Can You Share?
Lesson 32: Even and Odd Numbers,
Session 2
Everybody, Find A Partner!
Lesson 32: Even and Odd Numbers,
Session 3
Is It Even or Odd?

Grade 2 (ADM G3)

Unit 2: Numbers Within 100

Lesson 6: Adding Two-Digit Numbers, Session 1Panda Patterns
Lesson 12: Understand Three-Digit Numbers, Session 2Investigate: Creating a Photo Gallery
Lesson 16: Add Three-Digit Numbers, Session 2How Would You Solve It?
Adding Your Way
What Is an Algorithm?
Lesson 16: Add Three-Digit Numbers, Session 3Using Fewer Digits
Determining Sums of 2 or More Addends
Lesson 16: Add Three-Digit Numbers, Session 3Adding Strategically

Unit 4: Length

Lesson 27: Read and Make Line Plots, Session 2The Plot Chickens
Let’s Make a Line Plot

Grade 3

Unit 2: Multiplication and Division

Lesson 4: Understand the Meaning of Multiplication, Session 1Equal Groups
Lesson 6: Multiply with 3, 4, and 6, Session 2Rectangles and Arrays
Lesson 8: Use Order and Grouping to Multiply, Session 2Arrays of Flavor
Lesson 11: Understand How Multiplication and Division Are Connected, Session 1It’s Chili in Here!
Lesson 12: Multiplication and Division Facts, Session 3Relating Quotients to Familiar Products

Unit 3: Multiplication

Lesson 19: Scaled Graphs, Session 1Puppy Pile
Lesson 19: Scaled Graphs, Session 42, 5, or 10?
Lesson 14: Understand Area, Session 1Tiling Figures
Lesson 14: Understand Area, Session 2Which Covers More Space?
Lesson 15: Multiply to Find Area, Session 3Area Hunt
Lesson 17: Solve One-Step Word Problems Using Multiplication and Division, Session 2Division and Multiplication Equations

Unit 4: Fractions

Lesson 21: Understand Fractions on a Number Line, Session 1Cat Crossing
Lesson 21: Understand Fractions on a Number Line, Session 2Fractions on the Number Line
Lesson 21: Understand Fractions on a Number Line, Session 3Location, Location, Location

Unit 6: Shapes

Performance TaskInvestigate: Comparing Rugs
Lesson 30: Understand Categories of Shapes, Session 1Piho’s Shapes
Lesson 31: Classify Quadrilaterals, Session 1Rectangles, Squares, and Rhombuses
Lesson 31: Classify Quadrilaterals, Session 3More Quadrilaterals

Grade 4

Unit 2: Operations

Lesson 6: Understand Multiplication as a Comparison, Session 1Sticker Mania
Lesson 6: Understand Multiplication as a Comparison, Session 2Representing “Times as Many”
Going Swimming
Lesson 8: Multiples and Factors, Session 1Hamster Homes
Lesson 8: Multiples and Factors, Session 3Factor or Multiple?
Lesson 8: Multiples and Factors, Session 4A Number Game
Lesson 9: Number and Shape Patterns, Session 1How Does It Grow?

Unit 3: Multi-Digit Operations and Measurement

Lesson 11: Multiply by One-Digit Numbers, Session 1Investigate: Packing Lei
Counting Flowers for Lei
Lesson 11: Multiply by One-Digit Numbers, Session 3A Lei Making Workshop
A Reasonable Answer
Three of a Kind
Lesson 12: Multiply by Two-Digit Numbers, Session 2Growing Flowers for the Lei
Double Decomposition
Lesson 12: Multiply by Two-Digit Numbers, Session 3Revisiting Strategies
How Many Supplies?

Unit 4: Fractions, Decimals, and Measurement

Lesson 17: Understand Equivalent Fractions, Session 1Investigate: Building Your Own Number Line
Fraction Strips
Lesson 18: Understand Equivalent Fractions, Session 3Chop It
All Kinds of Fractions
Lesson 19: Fraction Addition and Subtraction, Session 1Pizza Problems
Lesson 20: Add and Subtract Fractions, Session 4Math Pizzeria
Lesson 24: Multiply Fractions by Whole Numbers, Session 2Equal Groups of Fractions
Lesson 25: Fractions as Tenths and Hundredths, Session 3Investigate: Different Units
Lesson 26: Relate Decimals and Fractions, Session 2A New Way to Write Tenths
A New Way to Write Hundredths
Lesson 26: Relate Decimals and Fractions, Session 4Are They Equivalent?
Lesson 27: Compare Decimals, Session 2How Can You Compare?
Lesson 27: Compare Decimals, Session 3Robot Factory
Lesson 27: Compare Decimals, Session 4What’s the Order

Unit 5: Geometry and Measurement

Lesson 30: Points, Lines, Rays, and Angles, Session 3Angle Adventures
Lesson 31: Angles, Session 1The Spin on Angles
Lesson 32: Add and Subtract with Angles, Session 3Angles in Motion

Grade 5

Unit 1: Whole Number Operations and Applications

Lesson 2: Find Volume Using Unit Cubes, Session 1Which is Largest
Lesson 2: Find Volume Using Unit Cubes, Session 2Packing the Barge
Lesson 3: Find Volume Using Formulas, Session 3Putting it Together
Figures Made of Prisms
Lesson 4: Multiply Multi-Digit Numbers, Session 1Partial Products Everywhere
Lesson 4: Multiply Multi-Digit Numbers, Session 4How Do They Compare?
Lesson 5: Divide Multi-Digit Numbers, Session 4Emptying the Water Tank

Unit 2: Decimals and Fractions

Lesson 6: Understand Decimal Place Value, Session 1Investigate: Numbers Between Numbers
Lesson 6: Understand Decimal Place Value, Session 2What Is One Thousandth?
Lesson 8: Read and Write Decimals,
Session 1
Say What?
Place Value Patterns
Lesson 9: Compare and Round Decimals, Session 2Selling Collectibles
Lesson 9: Compare and Round Decimals, Session 3The Claw
Which Way Down the Mountain?
Lesson 9: Compare and Round Decimals, Session 4Rounding Races
Lesson 7: Understand Powers of 10, Session 1Monarch Butterflies
All About That Base
Powers of 10 Parade

Unit 3: More Decimals & Fractions

Lesson 18: Fractions as Division, Session 1Investigate: Sharing Sandwiches
Division Story Problems
Making Generalizations
Investigate: Folding Paper
Lesson 18: Fractions as Division, Session 2Sharing More Sandwiches
Dance Breaks
Lesson 19: Multiplication by a Fraction, Session 2Parts of Parts
Lesson 20: Multiply Fractions to Find Area, Session 2One Part of One Part
Lesson 20: Multiply Fractions to Find Area, Session 3Making Food
Lesson 22: Multiply Fractions in Word Problems, Session 3Installing Turf
Rows and Columns
Lesson 22: Multiply Fractions in Word Problems, Session 4Messy Multiplication
Applying Fraction Multiplication
Lesson 21: Exploring Multiplication as Scaling, Session 1Chores at Animal Haven
The Re-size-inator

Unit 5: Algebraic Thinking and the Coordinate Plane

Lesson 31: Understand the Coordinate Plane, Session 1Bullseye!
Lesson 31: Understand the Coordinate Plane, Session 2Creating a Coordinate System
Coordinating Satellite Repairs

Grade 6

Unit 1: Expressions and Equations: Area, Algebraic Expressions, and Exponents

iReady ClassroomAmplify Classroom
Lesson 1: Find the Area of a ParallelogramUnit 1
Lesson 3: Exploring Parallelograms
Exploring Parallelograms, Part 2

Unit 2: Decimals and Fractions: Base-Ten Operations, Division with Fractions, and Volume

Lesson 7: Add, Subtract, and Multiply Multi-Digit DecimalsUnit 4
Lesson 1: Dishing Out Decimals
Lesson 8: Divide Whole Numbers and Multi-Digit DecimalsUnit 5
Lesson 13: Movie Time
Lesson 9: Understand Division with FractionsUnit 4
Lesson 3: Flour Planner
Lesson 10: Divide FractionsUnit 4
Lesson 6: Fill the Gap

Unit 3: Ratio Reasoning: Ratio Concepts and Equivalent Ratios

Lesson 12: Understand Ratio ConceptsUnit 2
Lesson 1: Pizza Maker
Lesson 13: Find Equivalent RatiosUnit 2
Lesson 4: Fruit Lab
Lesson 10: Disaster Preparation

Unit 4: Ratio Reasoning: Unit Rates and Percent

Lesson 15: Understand Rate ConceptsUnit 3
Lesson 1: Many Measurements
Lesson 16: Use Unit Rates to Solve ProblemsUnit 3
Lesson 6: Soft Serve
Lesson 17: Understand PercentsUnit 3
Lesson 9: Lucky Duckies

Unit 5: Algebraic Thinking: Equivalent Expressions and Equations with Variables

Lesson 19: Write and Identify Equivalent ExpressionsUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 22: Analyze Two-Variable RelationshipsUnit 6
Lesson 16: Subway Fares
Take Away (coming soon!)

Unit 6: Positive and Negative Numbers: Absolute Value, Inequalities, and the Coordinate Plane

Lesson 23: Understand Positive and Negative NumbersUnit 7
Lesson 1: Can You Dig It?
Lesson 24: Order Positive and Negative NumbersUnit 7
Lesson 4: Order in the Class
Lesson 26: Write and Graph One-Variable InequalitiesUnit 7
Lesson 7: Tunnel Travels

Unit 7: Statistical Thinking: Data Distributions and Measures of Center and Variability

Lesson 30: Use Dot Plots and Histograms to Describe Data DistributionsUnit 8
Lesson 3: Minimum Wage
Lesson 5: The Plot Thickens
Lesson 31: Interpret Median and Interquartile Range in Box PlotsUnit 8
Lesson 11: Toy Cars

Grade 7

Unit 1: Proportional Relationships: Ratios, Rates, and Circles

iReady ClassroomAmplify Classroom
Lesson 2: Find Unit Rates Involving Ratios and FractionsUnit 2
Lesson 1: Paint
Lesson 4: Represent Proportional RelationshipsUnit 2
Lesson 6: Two and Two
Lesson 5: Solve Proportional Relationship Problems
Lesson 6: Solve Area and Circumference Problems Involving CirclesUnit 3
Lesson 3: Measuring Around
Lesson 9: Area Challenges

Unit 2: Numbers and Operations: Add and Subtract Rational Numbers

Lesson 7: Understand Addition with Negative NumbersUnit 5
Lesson 1: Floats and Anchors
Lesson 8: Add with Negative NumbersUnit 5
Lesson 1: Floats and Anchors
Lesson 9: Understand Subtraction with Negative IntegersUnit 5
Lesson 1: Floats and Anchors
Lesson 10: Add and Subtract Positive and Negative NumbersUnit 5
Lesson 1: Floats and Anchors

Unit 3: Numbers and Operations: Multiply and Divide Rational Numbers

Lesson 14: Use the Four Operations with Negative NumbersUnit 5
Lesson 10: Integer Puzzles

Unit 4: Algebraic Thinking: Expressions, Equations, and Inequalities

Lesson 19: Write and Solve InequalitiesUnit 6
Lesson 16: Shira the Sheep

Unit 5: Proportional Reasoning: Percents and Statistical Samples

Lesson 20: Solve Problems Involving Percents Unit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Lesson 22: Understand Random SamplingUnit 8
Lesson 2: Prob-bear-bilities
Lesson 24: Compare PopulationsUnit 8
Lesson 10: Crab Island

Unit 6: Geometry: Solids, Triangles, and Angles

Lesson 28: Find Unknown Angle MeasuresUnit 7
Lesson 2: Friendly Angles
Lesson 4: Missing Measures

Unit 7: Probability: Theoretical Probability, Experimental Probability, and Compound Events

Lesson 30: Understand ProbabilityUnit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities

Grade 8

Unit 1: Geometric Figures: Rigid Transformations and Congruence

iReady ClassroomAmplify Classroom
Lesson 1: Understand Rigid Transformations and Their PropertiesUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 2: Work with Single Rigid Transformations in the Coordinate PlaneUnit 1
Lesson 4: Moving Day

Unit 2: Geometric Figures: Transformations, Similarity, and Angle Relationships

Lesson 4: Understand Dilations and SimilarityUnit 2
Lesson 2: Dilation Mini Golf
Lesson 6: Describe Angle RelationshipsUnit 2
Lesson 6: Social Scavenger Hunt
Lesson 7: Describe Angle Relationships in TrianglesUnit 1
Lesson 12: Puzzling It Out

Unit 3: Linear Relationships: Slope, Linear Equations, and Systems

Lesson 8: Graph Proportional Relationships and Define SlopeUnit 3
Lesson 1: Turtle Time Trials
Lesson 13: Solve Systems of Linear Equations AlgebraicallyUnit 4
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Unit 4: Functions: Linear and Nonlinear Relationships

Lesson 15: Understand FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 16: Use Functions to Model Linear RelationshipsUnit 5
Lesson 5: The Tortoise and the Hare

Unit 5: Integer Exponents: Properties and Scientific Notation

Lesson 19: Apply Exponent Properties for Positive Integer ExponentsUnit 7
Lesson 1: Circles
Lesson 3: Power Pairs
Lesson 22: Work with Scientific NotationUnit 7
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Unit 6: Real Numbers: Rational Numbers, Irrational Numbers, and the Pythagorean Theorem

Lesson 23: Find Square Roots and Cube Roots to Solve ProblemsUnit 8
Lesson 4: Root Down
Lesson 25: Find Rational Approximations of Irrational NumbersUnit 8
Lesson 10: Taco Truck
Lesson 27: Apply the Pythagorean TheoremUnit 8
Lesson 8: Triangle-Tracing Turtle
Lesson 28: Solve Problems with Volumes of Cylinders, Cones, and SpheresUnit 8
Lesson 11: Cylinders
Lesson 13: Cones

Unit 7: Statistics: Two-Variable Data and Fitting a Linear Model

Lesson 29: Analyze Scatter Plots and Fit a Linear Model to DataUnit 6
Lesson 3: Robots
Lesson 4: Dapper Cats
Lesson 6: Find the Fit

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.