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

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.

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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!