S5-02. Uncovering the causes of math anxiety

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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.
 
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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!

Survey

We’re interested in learning more about you. Please fill out this survey!

Program overview

Boost Lectura is a high-quality, personalized Spanish literacy foundational skills program that complements Amplify Reading to build reading proficiency in both English and Spanish for grades K–2.

Student field study experience

Note: This is an early subset of the program experience. Some content may be appropriate for some students, but difficult for others. This is feedback we want to hear. The designs are also still in progress, with many aspects yet to be featured. Please email Aya Bukres with all suggestions!

Field study books and games

Below is a list of books and games (with associated skills) by grade level. Students will access these games and books through Quests.

Note: Books do not include voice-over at this time.

Kindergarten Books

¿Qué pasa con la gallina Tina?¿Qué puedes hacer con los 5 sentidos?¿Por qué croan las ranas?
Un festín de saboresUn ¡pop! en tiempoLos aluxes
El efecto mariposaLas estaciones del año

Kindergarten Games

Game NameBig IdeaSkill that will be practiced
Son sabrosónPhonological AwarenessRhyming
Alfa y betoPhonological AwarenessBlending
Jugando andoPhonological AwarenessSegmentation
Tragaletras exigentesPhonicsLetter-sound correspondences
Tragaletras gruñonesPhonicsLetter combinations
Tragaletras comelonesPhonicsReview of letter-sound correspondences and letter combinations
Investiga la escenaComprehension ProcessesGap-filling Inferences

Grade 1 Books

La leyenda de la colibríLa capibara: Un animal amigableMi ruidoso cuerpo
El zorro y el huaychaoDeseos al sol

Grade 1 Games

Game NameBig IdeaSkill that will be practiced
Alfa y betoPhonological AwarenessBlending
Jugando andoPhonological AwarenessSegmentation
Tragaletras exigentesPhonicsLetter-sound correspondences
Tragaletras gruñonesPhonicsLetter combinations
Tragaletras comelonesPhonicsReview of letter-sound correspondences and letter combinations
Silabalón: la copaPhonicsSyllable decoding
¿Aquí o alla?Phonics & Word RecognitionDecoding words with
y, g, and c
¿Esta o aquella?Phonics & Word RecognitionDecoding words with different graphemes to represent the same phoneme
¡Abra palabra!Phonics & Word RecognitionDecoding – syllable manipulation
Quita y ponPhonics & Word RecognitionDecoding – syllable manipulation
¡Conéctalo!Comprehension ProcessesUsing connectives
Investiga la escenaComprehension ProcessesGap-filling inferences

Grade 2 Books

La despedidaLa verdadera fortunaLa fascinante Ruta de la Seda
Bernardo de GálvezHormigas amigas

Grade 2 Games

Game NameBig IdeaSkill that will be practiced
¿Aquí o alla?Phonics & Word RecognitionDecoding words with y, g, and c
¿Esta o aquella?Phonics & Word RecognitionDecoding words with different graphemes to represent the same phoneme
¡Abra palabra!Phonics & Word RecognitionDecoding – syllable manipulation
Quita y ponPhonics & Word RecognitionDecoding – syllable manipulation
¡Conéctalo!Comprehension ProcessesUsing connectives
Investiga la escenaComprehension ProcessesGap-filling inferences

Consider using Boost Lectura during the following times:

  • Small group or center time
  • Choice time
  • During intervention blocks
  • After school
  • At home
  • Remote learning

Getting your students online

Amplify login page with options to log in using Google, Clever, Amplify, QR code, District SSO, or get help; a rocket illustration is on the left.

Instruct students to navigate to learning.amplify.com, and log in using the method you typically use when logging into Boost Reading.

A screen displays the question "Where are you headed?" with options "Reading" and "Lectura," and a purple "Go!" button at the bottom.

Find and click on the icon for Boost Lectura, as shown above.

At this time, students can begin playing games or reading books by clicking on “Iniciar.”

A large button labeled "INICIAR" is displayed in the center of a colorful, illustrated town map background.

Having students play games in Quests

Select a game from the list to play!

A woman smiles in a café with a blue creature beside her, a barista behind the counter, pastries on display, and three app icons with Spanish text on the right.

Students can play games in Quests by selecting the curioso icon.

A cartoon map shows various buildings, trees, and winding paths with a "Detour" sign and a blue character in the center marked by a location pin.

Students should hear quest narratives in Spanish.

The Automatic Placement Tool (APT)

The Automatic Placement Tool will be served when students first log in and choose the Lectura product. The Experience should take about 15–20 minutes total.

Students are greeted with a comical animation explaining we need their help with answering a few questions.

A concerned scientist stands in a control room surrounded by green goblin-like creatures, some using tools and wearing glasses, with a background of technological equipment.

Students are guided through a few short activities measuring different skills domains.

A digital quiz in Spanish asks, "¿Qué sílaba hace este sonido?" with a sound icon and three answer choices: "al," "en," and "ir.

Students receive closure to their experience via another short animation.

A scientist in a lab coat stands in a futuristic control room, surrounded by four small green creatures also wearing lab coats.

    Troubleshooting guide

    Please check to ensure “cookies” are accepted on your device.
    If you still receive an error message or blank screen when accessing an Amplify page, please email Aya Bukres.

    Please email Aya Bukres to confirm your login credentials.

    Language comprehension: Building mental models

    ©Alexander Huth / The Regents of the University of California

    Throughout this five-part series, we will cover the main components of the Science of Reading (SoR) and provide additional resources and research to guide your exploration and implementation of this important movement.

    Say you’re given a passage of text to read. This particular paragraph describes half an inning of a made-up baseball game.

    After you read the passage, you are asked to reenact the scene.

    Which is more likely to aid your success?

    A. Your ability to read

    B. Your knowledge of baseball

    C. It makes no difference

    Would you be surprised to know the answer is actually B?

    In part one of our series, “What is the Science of Reading anyway?,” we discussed the two main components of the Science of Reading: decoding (converting written words into speech) and language comprehension (understanding that speech). We also provided in-depth coverage of both learning and teaching how to decode the symbols of the English alphabet and strengthen the reading muscle.

    LANGUAGE COMPREHENSION

    In 1988, two young researchers and 64 students took part in an experiment that has forever changed how we think about reading and comprehension. One by one, the students were handed the same story covering half an inning of a made-up baseball game and asked to reenact it.

    To the researchers’ surprise, they found that reading ability had little impact on how well kids understood the story—but knowledge of baseball did. In fact, students who were weak readers did as well as strong readers if they had knowledge of baseball.

    Teaching knowledge explicitly improves reading comprehension. As Willingham has said, “Reading tests are knowledge tests in disguise.”

    Researchers at the Haskins Lab at Yale tested this theory and found an extraordinarily high correlation between how well a 7-to-9-year-old child can recognize words and how well they comprehend text.

    Common teaching mistake — Strategy instruction

    So if reading comprehension is driven by a student’s vocabulary and knowledge, are widely taught strategies like finding the main idea equally critical?

    Many strategies make intuitive sense: Stopping and re-reading when comprehension breaks down, for instance, is helpful for many children. But teaching the main idea strategy over and over is less helpful.

    It is hard to find the main idea of a piece of writing if you don’t really understand any of the ideas in it. And even if you know a strategy — like re-reading when stuck — you also need to be well-versed in when to apply the strategy. You need to notice that you didn’t understand the text.

    Often, strategy instruction neglects to offer students practice with identifying the situations in which they should use the strategy.

    In the 1940s, a skills shift began to take place in education systems throughout the world. Its effects can be traced in the U.K., Sweden, Germany, and, most recently, France. This shift brought an emphasis on reading and math, squeezing out the broader knowledge taught in the sciences and social sciences. Some have linked the decline in standardized test scores—the SAT in the U.S. and the DEPP national exam in France—to this shift.

    The National Survey of Science and Mathematics Education reported that today, classes in grades K–3 spend just 19 minutes per day on science and 16 minutes per day on social science.

    To counter this loss of broader knowledge in our students, research suggests that we teach comprehension strategies in moderation and use the freed-up time to build knowledge (and vocabulary).

    But simply exposing students to everyday speech doesn’t build a strong vocabulary. In a typical conversation, there are around 20 unusual words—such as dismayed or zeal—per 1000 words. Newspapers and books contain more than twice as many. Rich vocabulary, then, is gained not solely through speech, but through reading. Rich vocabulary, then, is gained not solely through speech, but through reading—especially when reading a variety of text types.

    Mental models

    Some readers with good word recognition, vocabulary, and knowledge are still weak comprehenders. Why might this be the case?

    After students read a passage, they aren’t likely to recall the precise wording, but they will probably remember the ideas. Researchers use the term mental model to describe the structure you create in your mind to perform this feat of comprehension. Think of the process of building a mental model as a sort of micro-comprehension. Weak comprehenders build poor models. Hence, when asked prediction or mapping character development questions, they answer poorly.

    There are four critical skills students need to improve their mental modeling:

    1. Decoding the usage of anaphoras (she, they, him). Some early readers can’t reliably figure out who the pronoun is referring to, especially in ambiguous text.
    2. Understanding the use of markers to signal ways that the text fits together — connectives, (like so, though, whenever) structure cues, and directions. Inexperienced readers may not know that but, though, yet, and however signal that something opposite follows.
    3. Writers make assumptions about what can be left unstated. For instance, when they read “Carla forgot her umbrella and got very wet today,” good readers will use their prior knowledge to conclude that it rained. Weaker readers who fail to make these gap-filling inferences wind up with gaps in their mental model.
    4. When something doesn’t make sense, you stop, re-read, and try to figure it out. Weaker readers just keep going—not because they’ve failed to figure it out, but because they’ve failed to notice that they don’t understand. They need explicit instruction in monitoring comprehension as they read.

    Overview

    Think of reading as a suitcase that you need two keys to open. The first key is word-level decoding, a skill that becomes automatic and fluent. The second key is language, vocabulary, and domain-specific knowledge. The more words you can decode, the more new words — and their meanings — you can learn. Similarly, the more knowledge you have on a topic, the more you can soak up on the same topic — and on related topics.

    These two keys make up the Science of Reading. When schools focus heavily on one key or the other, the suitcase doesn’t open. So now the greater task of applying this knowledge in the classroom awaits us.

    For more in-depth examples, brain scans, and information about the Science of Reading, download our free primer:

    Science of Reading – Make the Shift Today

    Daily math routines that spark student curiosity

    It’s the educator’s eternal question: How do I keep students engaged?

    When designing daily math practice, teachers are always working to make real-world math problems fresh and relevant, find new entrance points for concepts, or simply come up with surprises. All of these approaches can be very effective.

    And though it may seem counter-intuitive, so can routines.

    The power of instructional routine

    The word routine can connote a sense of doing something mechanically, even without thinking. But teachers know that well-placed classroom routines can open opportunities for creative thought.

    Routines provide a way for you and your students to build and maintain a sense of familiarity and structure throughout the school year. They also free up time teachers would otherwise spend giving directions. When students know exactly how a certain activity should run, and understand all instructions and expectations, everything goes more smoothly.

    That’s why a core set of shared routines can be a powerful, practical force for establishing an effective classroom learning community..

    Bringing math routine into the classroom

    We know routines can be effective in any classroom. Now, we also have research offering direct evidence that certain routines are particularly effective in math classrooms.

    Think-pair-share

    Do you want your students to have more time to think before solving and sharing about a problem? 

    GOAL: Provides opportunities to identify, compare, and contrast multiple strategies

    TIP: During partnered discussion, consider displaying sentence frames such as, “ First they… Next they…” “Their strategy was to…” or “I see a/an… in both strategies.”.

    How to do it:

    • Invite students to solve a problem that can be solved with multiple strategies. Then, display two or more different responses representing different strategies.
    • Give students time to analyze the strategies on their own and then invite them to discuss them with a partner.
    • Facilitate a class discussion to describe, compare, contrast, and connect the different strategies. Utilize open-ended questions like, “Why did different strategies lead to the same outcome?” or, “What was helpful about each strategy?”

    Where to learn more

    We worked with our curriculum team to develop routine cards for math teachers, so you can implement routines that are part of our math program in your classroom. Most of the routines you’ll find throughout Amplify Desmos Math have been specifically proven effective in math classrooms. All of them have been adapted from established teaching practices.

    We invite you to access a sample set of some of our most popular routines and decide which ones to try out in your classroom!

    Resources

    Download free math instructional routine cards.

    Explore Desmos Classroom.

    Learn more about Amplify Desmos Math.

    S2-03: Building meaningful student connections in the science classroom

    Promotional image for a podcast episode titled "Sharita Ware: Building meaningful student connections," featuring Sharita Ware and "Science Connections" branding.

    In this episode, Eric Cross sits down with Indiana State Teacher of the Year, Sharita Ware, to talk about how to successfully build meaningful student connections in the science classroom. Sharita shares her journey from a corporate career to becoming Indiana’s 2022 Teacher of the Year, and her passion for creating project-based lessons for her students. Together, Eric and Sharita discuss how educators can teach students to love science content by building strong relationships, adding in other content areas, and supporting students’ imagination. Explore more from Science Connections by visiting our main page.

    Download Transcript

    Sharita Ware (00:00):
    I try to create that equal playing field where there’s nobody’s voice, that’s more important than anyone else’s and try to make them all feel that what they have to say is important.

    Eric Cross (00:14):
    Welcome to science connections. I’m your host Eric. My guest today is Sheta where Sheta is the 2022 Indiana state teacher of the year. And in her 10 year career, as an engineering and technology teacher, she has dedicated herself to helping students build knowledge and skills for high school and life. Beyond. In this episode, we discuss how she inspires her seventh and eighth grade students to build problem solving and critical thinking skills through hands on real world and collaborative projects. She is as humble as she is knowledgeable and through our conversation, it was easy for me to see why her students feel successful under her guidance. And now please enjoy my conversation with Sharita Ware.

    Eric Cross (00:59):
    Can I start off by saying congratulations on teacher of the year. Thank you for the state of Indiana. Um, that’s amazing. So I, I, I did watch, uh, your videos, uh, short interviews, and then you spoke, was it Purdue? Yes. You were there. And so, uh, to see if fellow seventh grade, eighth grade science teacher out there being celebrated, like I was so excited, so yeah, I wanted to congratulate you on that and, and just kind of talk to you about like your teaching journey and ask you, uh, maybe just kind of start off with your story about what brought you into, into the classroom, especially the middle school.

    Sharita Ware (01:29):
    Classroom. So what happened is when I was working in industry as an engineer and when my husband and I got married, we decided that I was gonna, um, stay home with the kids because, you know, we wanted, um, our influence to be greater on our kids than, you know, the people that would be watching them, you know, because they would ultimately spend more time with them than they would with us. And, and so, um, I stayed home and when my youngest was going to be going to kindergarten the next year, I was like, okay, what am I going to do? Cuz I really don’t necessarily feel like I need to stay at home. Mm-hmm <affirmative> but um, I knew going back to industry would be a challenge just because in my field, I, I was traveling a lot before I got married and had kids.

    Sharita Ware (02:14):
    And so I knew that that wouldn’t really be conducive to again, raising children. So I, I get this email, my inbox for Woodrow Wilson, teaching fellowship at Purdue. And they were just looking for people in stem fields to go into teaching. And I was like, okay. And it was a national search, you know, I filled out the application, we had to go in and do some sample teaching mm-hmm <affirmative>. And I was picked as, as one of the, the teachers to go through the program. And I started off thinking I wanted high school. And the really cool thing about this, uh, program is that we had long observation periods at high school and at middle schools. And so we would go to a school and we’d stay there two or three weeks. And so it, it kind of gave you right. A little bit more insight to what happened on a daily basis. And after those observations, I was like, I like middle school better than I, uh, like high school. And so I just kind of went that direction and you know, the rest is history. So

    Eric Cross (03:19):
    I feel like our stories are similar because I went into teaching thinking I wanted to do high school because I like the maturity and you a little bit more sophistication, advanced things, but yes, middle school, I felt like I can, I could get them more upstream before and kind of help shape mm-hmm <affirmative> that experience for them? Because I feel like at middle school is really where they kind of decide like what they can do based on their experiences.

    Sharita Ware (03:39):
    I found in the middle school that the kids, I mean, they just, they clamor around you and they’re like, what are we doing today? You know? And they get so excited and, um, they’re, they’re just, I don’t know, I guess in some ways, just more hungry in the sense of like they’re willingness to, um, now sometimes they’re a little reluctant, but you know, their willingness just to try new things. And I think, um, my students really what I have found over the years that they have found a safe space and I hear the kids, you know, say to me so many times that, you know, it it’s safe. I feel, I feel safe in here. And, and it’s not something that in my mind I’m thinking about, oh, I need to make this a safe place. It’s just, I guess part of just who I am as a person has created this environment of, of safety and, and the kids recognize that, you know, I don’t play favorites. You know, everybody starts out mm-hmm, <affirmative> on equal footing. I, I don’t care what your backstory is. I don’t care how many times I see you in the hallway when I’m walking during my prep. You know, when you hit my room, I’m, I’m gonna treat you the same way on day one, that I treat everybody else.

    Eric Cross (04:54):
    You really understand how to build culture with, in, with your classroom, with your students. And, and you said they feel safe, but is there anything that you do that someone could like apply? And like you found that you’ve gotten a lot of just relational capital through doing these things, or is it just your personality? Like how, how do you build those connections?

    Sharita Ware (05:12):
    You know, growing up being a, a very quiet person. I, I think a lot of times my voice was ignored because I was the quiet kid in the back of the room. And oftentimes I became seen or heard because of my work, you know, in the beginning it was kind of like, oh, she’s just this quiet girl in the back of the room. And then, you know, the first essay was due or the first project was due. And then it was like, oh, you know, then you’re the person to be on, you know, people’s teams. And, and that, I don’t know, that always kind of bothered me because, you know, I’m thinking just because you’re not the loudest person in the room doesn’t mean that you don’t have something to say, mm-hmm <affirmative>, you just might not be talking all the time. You know? And, and so for my students, I just, I try to create that equal playing field where there’s, nobody’s voice, that’s more important than anyone else’s and try to make them all feel like that what they have to say, or what they have to contribute is, is enough, is good.

    Sharita Ware (06:14):
    Enough is important as…

    Eric Cross (06:16):
    It is, as it is. And there’s probably a lot of things that you do. But in addition to building these relationships, what do you do? Like how do you make your learning fun for students?

    Sharita Ware (06:25):
    I think, um, I’m also a little bit on the silly side. Um, we do a, a Barbie prosthetic leg project, and this was after trial and error of having the kids make full size prosthetic legs. And I try to make it as real world as possible, but with none of the children being amputee or, you know, having access to someone, it was really hard for them to really visualize what needed to happen. Mm-hmm <affirmative>. And so, um, I found this Barbie that had a prosthetic leg and I was like, well, LA, so I just started collecting Barbies and chopping their legs off <laugh>. And so I have this jar of Barbie legs. And so, and I said, you’re gonna make prosthetic legs. And I lay this jar of legs on the counter and the kids are like, like they gasp and then they crack up and then they’re like, okay, this lady’s crazy. So…

    Eric Cross (07:22):
    That’s when you take off your scarf and there’s this necklace of just Barbie legs that are just around and you’re like, I’m a middle school teacher and they go, oh, okay. I understand. Yeah. Yeah. It’s totally fine. Is this a lesson that someone that you made up or is it something that you’ve re remixed? Is it something that someone could do if they looked it up anywhere?

    Sharita Ware (07:38):
    Um, so I think teach engineering has the, the full size leg that the kids make. And that’s where I initially got it from.

    Eric Cross (07:47):
    Is that the website teach engineering?

    Sharita Ware (07:49):
    Yes. And, um, I, in fact, I get lots of ideals from there. Um, and I, I always usually tweak them, but it’s, it’s one of those things that kind of gets your brain going. And so it was kind of a mixture of, uh, project lead the way gateway to technology and the teach engineering. And I think the project lead the way had us making like braces, uh, for, um, kids with, um, like cerebral palsy or, or something like that. And the kids did okay with that project. Uh, but I wanted to go just a little bit, uh, deeper with it because part of what I was wanting them to do is that context and that connection, that human connection, because for me, it’s not just enough for them to make a project. Uh, before we start this prosthetic leg, I read them a story out of a Scholastic magazine, and it’s a, a teenage girl that lost her leg in a boating accident.

    Sharita Ware (08:42):
    And she was super active, um, playing sports and running. And, and so I was, you know, trying to get the kids to, you know, make that connection, someone close to their age. Um, and then how it’s not, it’s, it’s more than about her physical healing. It’s also about her mental healing and how she had to, you know, talk to herself to say that she could, you know, recover and, and come back from this and still go on to do all of the things that she was doing before. Um, and in some ways it’s kind of cool because, um, you know, she has a running prosthetic, she has a, a swimming prosthetic, and she has her every day with the pain and toils prosthetic. So just trying to, you know, help them to see that it’s more than just the, you know, the biomedical mechanical engineering aspect of the project.

    Sharita Ware (09:30):
    And so they have to design for comfort. They have to design for, um, swelling. And then, um, they also can, if they, if they want to, they don’t have to, if they want to, they can create their own backstory. So when they get there, um, we have a day where they are introduced to their client, so they get to meet their Barbie and, and then they get to decide if they want a backstory and, and then do their research based off of that. So if it’s someone that was a runner, then they can design a prosthetic running blade. So just, they have lots of, uh, flexibility.

    Eric Cross (10:04):
    The, that aspect of adding the narrative. It does so much for like listening to it on the outside. It one, it adds this humanity to, you know, what can sometimes just feel like it may be cold, logical stem. We’re just, we’re just doing things. We’re fixing things. We’re, you know, we’re discovering things, but really the stem has value when we’re actually applying it to, to, to serve humanity or our ecosystem or whatever it is. There was a, a coding, uh, class I was doing with my students and I showed them this app called be my eyes. And it’s for people who are visually impaired and it pairs them with a volunteer. And when they call, and there’s a whole huge pool of volunteers and I’m one of them. And when my, when it happens in class, I answer and it uses the FaceTime. So the person who’s visually impaired is holding up their phone and you see what they see and you tell them and real time what’s happening.

    Sharita Ware (10:54):
    Oh, wow. That’s so cool.

    Eric Cross (10:56):
    These are, these were the things I think for students that the story, the, the human part of it, mm-hmm, <affirmative>, it must bring in so many more students into engagement.

    Sharita Ware (11:05):
    Yeah. I, I feel like it does because I, I think, um, and, you know, along the journey, they kind of lose, um, they lose sight a little bit because, you know, they get out in the lab and they have access to all of these different materials. And I think, you know, truly making it, you know, project based for me is I try not to control the materials too much. Um, I try not to make it so wide that they just get lost, but I try to throw a few curve balls in there, you know, of, of materials that really don’t make sense to use, but they kind of think they make sense to use. Um, because the, the, the meat of it is that the prosthetic leg is a similar size of the original leg and that the, the knee functions. And so I don’t limit, and I grade them off of efficient use of materials.

    Sharita Ware (11:59):
    So, and that just throws them off because I think, well, how many Popsicle sticks can I use? And I’m like, you can use as many as you like, but remember, this is a prosthetic leg that, um, your Barbie, which is one six scale, um, is going to be wearing all day. So you could think that a Popsicle stick, if you chose to use a Popsicle stick is kind of like dragging around a two by four <laugh>, you know? So do, is that what you really want to use as your material? And some of the kids really think about it and saying, okay, I’m, I’ve got this aluminum rod, okay. This is probably what I would use for my bone structure, because it’s lightweight, but yet it is supportive. And then sometimes they come up with their own ideas in terms of materials, like one student brought in his, um, 3d doodle pin mm-hmm <affirmative> and he made joints and everything with this pin.

    Sharita Ware (12:54):
    And I’m, and I had delayed buying one, cause I’m like, I, how do you have control over that thing? Mm-hmm <affirmative> he brought that in and he did probably two or three iterations of it and, and got it to work where even the knee where it bit back 90 degrees, but it stopped. He made like, so that it didn’t bend forward. It blows my mind. I’m like so many UN unexpected things have, have happened just from my, um, teaching style. Now I did have, my first few years, I had a, a teaching coach, um, come in and, um, I asked her to come into my room because I just wanted to make sure because I was not a traditional teacher. She said, this classroom is amazing. And, and I think the one thing that she helped me with was, was purpose and consistency and the sense of making sure that with the standards that all of these cool things and ways of being, um, that I was doing in my classroom, that, that I kept it purposeful and intentional. So many times as educators, I know in having student teachers again, ask yourself the question, what is the big picture I want the kids to take away. And once you ask that question, then everything that you have them do will lead to that big picture. Well, it should lead to that big picture.

    Eric Cross (14:22):
    So it sounds like they’re, you’re starting with this end goal in mind and then kind of backwards planning to get there. Yeah. Do you think you would’ve been the same type of teacher if you would’ve gone straight from college into the classroom? No. And if, if, no, as you’re shaking your head, what do you think it is about? Cause I’ve been asking myself these questions, like just over the years, what is it about coming from industry and going into the classroom? Do you feel like, is how has that impacted you in how you teach?

    Sharita Ware (14:45):
    Well, I think it’s twofold cuz I was older. I already had three children. I think the combination for me, I think is I was already a mom and I had worked in industry. So the behavior aspect of kids and, and then having that real world experience. And I, I just feel like whether it’s in the classroom, um, marriage, kids, to me, it’s 90% relationship, you know, and the rest will work itself out. That’s, that’s just my, my take on it. But I, I feel like having kids, so some of the behavioral things I kind of was aware of, you know, and just learned many times just not to react to some of the things that they did.

    Eric Cross (15:31):
    Which is huge. Right. Especially in middle school is controlling your reactions.

    Sharita Ware (15:35):
    Yes. Cuz that’s what they want. You know? And, and I had this student last year as well. She’s brilliant. And so if she cannot wrap her mind around the purpose of what you’re doing and, and you’re pushing her to do something that she doesn’t think is necessary, mm-hmm <affirmative>, she kind of has these meltdowns. And, and so we just had this, you know, I don’t know, we just came to this understanding and it, and it works to control the meltdowns. I tried to make sure. And, and I used her as a gauge because I knew she wasn’t, she wasn’t getting upset because she didn’t understand. She didn’t understand the why mm-hmm <affirmative>. And so I felt like if she got the why then so would everyone else. So when she, if she was okay with it, then I was like, okay, then I must have explained it well enough.

    Sharita Ware (16:25):
    And so in my mind that I really need to make sure they understand the, again, going back to that purpose <laugh> and intention, making sure that that is clear. And then I think that’s what gets lost. Sometimes mm-hmm <affirmative> uh, with us as teachers, we, we know where we want the kids to go and we want us to trust the process, you know, just do it because I said so, but sometimes, you know, empowering your children to under to understand the why, because that again is what allows them to be able to do bigger and greater things on their own. So on that next project comes along. They’re starting to tell you, well, first we need to make sure we understand what, um, we’re being asked to do to do. So we have to define the question. We have to make our driving question that will help us stay focused. And, and you’re just standing up there going, okay, now you don’t need me. I’ll go here and sit down. <laugh> so it’s, uh, it is really cool.

    Eric Cross (17:28):
    Now I’m thinking about my own kids. Like, do my students know the why behind the lesson we did today? It’s one area of growth that I wanna make sure I do this year with my students. And so I really appreciate that. So the, and you just hit on something that is, has been in the forefront of my mind lately and math and English as you know, tend to be prioritized in schools everywhere because it’s what state tested. And it’s what, you know, this is a whole other conversation, but I’ve been talking to math teachers frequently about one of the challenges that they experience or they’ve been telling me is that math is kind of taught. Like it’s just computational, you’re solving these problems, but it’s really separated from any real life application. A lot of times, you know, it’s pizza or gumballs or, or just fictional scenarios and students don’t perform well many times. And some of the reasons why is cuz just no connection. I don’t want to solve puzzles. Like it’s not my jam. Do you have any just inside or, or perspective on how math is, is taught in maybe a way that you think it would students would benefit more?

    Sharita Ware (18:32):
    You know how kids learn in elementary school, you’ve got this, the same teacher teaching all of the subjects. And so wouldn’t that be an awesome opportunity for you to have like these, these projects where I feel like you could, a class could legit work on the same project for a whole entire year. And so couldn’t the English be writing your persuasive letter to the mayor, asking him to do this or do that. And the process of doing that they’re, they’re, they’re writing with a purpose with a true purpose. Um, and then when they’re doing math, you know, they want, they want a new neighborhood park. So, you know, well how much is this gonna cost? Well, math, what size is it gonna be math? Let’s see what it looks like, art, you know, you just, you have all of this things. And then of course then science.

    Sharita Ware (19:32):
    So if it’s on a heel, how can we, you know, deal with erosion? And you know, you can just pull so many different things into that. And so not only are they learning, but they’re narrowed in and focused on a project, they’re, they’re able to dive deep into, you know, learning more of learning, how to express themselves and communicate with real people. So it’s more of taking these compartmentalized learning that we do in middle school and high school. Mm-hmm, <affirmative> where you’re almost learning apprenticeship style. Mm-hmm <affirmative>, you know, you have these master educators and it’s not about them being the best at math or being the best at this or that. Cuz there’s so many tools now that could help you through that. But you’re, you’re giving, you’re teaching them so many life skills and so many ways to think and problem solve that, that we’re just that the kids just don’t have.

    Eric Cross (20:27):

    I think that that is amazing. And I think that in that situation, what I’m hearing is we’re going deeper, not wider because there are a lot of different concepts that kids are expected to learn. Or I should say there are several concepts that teachers are expected to teach doesn’t necessarily mean that our kids are learning, but we’re teaching them. And this way you’re embedded it into an authentic context. Students are able to go through this cycle just like real life. And then they’re also able to build these kind of really transdisciplinary skills. Not only am I learning the math, the English, the the, but I’m also learning the interpersonal skills of being able to sell myself and present myself in a way that’s winsome. And it’s especially powerful coming from someone from industry. Last question, even just listening to you, I know you, you are this for a lot of people, but I wanted to ask you who inspires you?

    Sharita Ware (21:14):
    I think there have been lots of people over the years. Like I’m thinking of my shop teacher who has since, uh, the last few years passed away. Um, he was one of those people, I think similar personality to me, super quiet person, but he was always in the background on my journey and his name was Joe Mo and we called her Madam Carol was my 10th grade English lit teacher. And she was the one that started reading my work out in front of the class. And you know, and that just gave me courage, not so much to be seen. Uh, but that the work I was doing was, was good. And, and I think I needed that kind of encouragement. Lastly, my students inspire me because when I look at their faces and see the excitement, I think of those students for the first time and, and, and think about this seventh and eighth graders for the first time feeling like they really have something to say, they really have something to contribute of value. And, and I do it for them. You know, the reason why I am here in this moment is because of them. Um, without them, you wouldn’t be talking to me <laugh>

    Eric Cross (22:37):
    This is, this is true. This is, this is true. You would probably never say this about yourself, but you just exude a humility and a service in how you talk about your students and yourself. And I just wanna thank you for using your gifts, but I don’t wanna just call them gifts because it makes it sound like you didn’t earn ’em and your skills that you’ve earned and worked very hard to acquire over the years to go back into the classroom and leave industry, cuz you, you could have gone back to industry too, but you decided not to. And you could have worked in the industry and your hours were a little different pay is a little different, but you came back to serve the kids of Indiana and because of you and because of that choice, those students have a brighter future and believe in themselves and they’re finding their voice. And I want to thank you for that and for representing all of us stem teachers who are in middle school and being that leader. So thank you for that and thank you for being on the podcast.

    Sharita Ware (23:24):
    You’re welcome. Thank you for having me.

    Eric Cross (23:28):
    Thank so much for listening. Now we wanna hear more about you in the amazing work you’re doing for students. Do you have any educators who inspire you? You can nominate them as a future guest on science connections by emailing stem, amplifycom.wpengine.com. That’s ST E M amplifycom.wpengine.com. Make sure to click, subscribe wherever you listen to podcasts and join our Facebook group science connections, the community until next time.

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    What Sharita Ware says about science

    “Sometimes, empowering your students to understand the why is what allows them to be able to do bigger and greater things on their own.”

    – Sharita Ware

    Engineer and Technology Teacher, 2020 Indiana Teacher of the Year

    Meet the guest

    Sharita Ware, a Purdue University graduate, is in her 10th year of teaching engineering and technology education to middle school students in the Tippecanoe School Corporation. Ware challenges her students with real-world, problem-based design scenarios that will help them contribute to global technology and integrated STEM. Follow her on Twitter and Instagram.

    A woman with curly black hair, glasses, and a white turtleneck smiles at the camera.

    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 Amplify Desmos Math California!

    California educators, welcome to math that motivates. Introducing Amplify Desmos Math California, a curiosity-driven TK–12 program that builds lifelong math proficiency. Each lesson poses problems that invite a variety of approaches before guiding students to synthesize their understanding of the learning goals. Students encounter math problems they’re eager to solve, while teachers spend more time where it’s most impactful—creating a collaborative classroom of learners.

    Keep reading to learn more about the program and explore sample materials.

    About the program

    Amplify Desmos Math California is a TK–12 core math program designed to meet the CA Math Framework and the Common Core State Standards for Mathematics. Amplify Desmos Math California thoughtfully combines conceptual understanding, procedural fluency, and application through a structured approach to problem-based learning. Through engaging activities, Amplify Desmos Math California invites curiosity and math discourse into the classroom to create lifelong math proficiency.

    Continue reading to learn more about the K–8, Algebra 1, and Math 1 programs and to explore sample materials. (Spanish, TK and high school materials are in development and will be available in the 2026–27 school year. Geometry and Algebra 2 beta pilots will be available in the 2025–26 school year.)

    A powerful math suite

    Amplify Desmos Math California combines the best of assessment, problem-based core lessons, personalized practice, and intervention into a coherent and engaging experience for both students and teachers.

    Laptop displaying a math problem interface with student assessment reports in the background.

    Screening and progress monitoring

    mCLASS Math benchmark assessments, along with the embedded program assessments, measure not just what students know, but how they think. The asset-based assessment system provides teachers with targeted, actionable insights, linked to core instruction and intervention resources. Unit- and lesson-level core assessments give teachers data at their fingertips to guide and differentiate instruction. In grades 3–8, core assessments and performance tasks are designed to prepare students for success on the Smarter Balanced Assessment Consortium (SBAC) testing.

    Core instruction

    Amplify Desmos Math California core lessons pair problems students are eager to solve with clear instructional moves for teachers. 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. With built-in differentiation and multilingual/English learner support, Amplify Desmos Math California enables every student to find success in the math classroom.

    A digital math activity asks users to choose a block that makes 10 with a given number; a worksheet shows a similar "make 10" math exercise with blank spaces to fill in.
    A digital educational screen showing a math problem about converting meters to centimeters. It involves a diving toy sinking 5 meters into a pool. Text prompts users to input the conversion.

    Personalized Learning

    Boost Personalized Learning activities help students access grade-level math through engaging, independent digital practice. Responsive Feedback adjusts to students’ work, providing item-level adaptivity to further support their learning.

    Differentiation and intervention

    Amplify Desmos Math views differentiation as an ongoing process where teachers are both reactive and proactive to student needs, ensuring that all students have clear pathways to proficiency. Through rich data and teacher support, Amplify Desmos Math uses flexible categories of intervention and enrichment that adjust daily according to student thinking.

    In-the-moment differentiation supports are available for every lesson, both digitally and in the print Teacher Edition.

    Two pages of a math worksheet and teacher’s guide about determining coordinates after a rotation, featuring diagrams, tables, and step-by-step problem-solving instructions.

    An approach that supports teachers

    Clear, step-by-step instructional moves help teachers plan and teach student-centered lessons that use
    student thinking to differentiate instruction and guide to grade-level understanding. They include:

    • Guidance on what to listen for and how
      to respond.
    • Clear learning objectives to keep learning on
      track for each activity and lesson.
    • Daily reinforcement activities to provide direct
      instruction when needed.
    A woman writes on a whiteboard using math teaching resources while a man sits at a desk, smiling. There are books and papers on the desk.
    Network diagram with interconnected nodes labeled: Measure and Compare Objects, Represent Data, Dollars and Cents, Problem Solving with Measure, Skip Counting to 100, Number Strategies, Squares in an Array, Seeing Fraction in Shapes.

    Big Ideas

    The CA Mathematics Framework encourages a shift from power standards to thinking about math as a series of connected Big Ideas. Each Amplify Desmos Math California lesson supports one or more Big Ideas and the connections between them. The grade-level diagram changes through the course based on the math concepts addressed within.

    Please refer to the following Keeping the Big Ideas at the Center documents to review specific lesson designs and alignments with the Big Ideas for each grade level.

    Click here to see how the Big Ideas are represented within the K–8 core lessons.

    Focus, coherence, and rigor

    Amplify Desmos Math California incorporates the Drivers of Investigation (DIs) and Content Connection (CCs) throughout the program. Throughout the year, students engage with open and authentic tasks of varying durations—from lesson activities to unit-level Explore lessons and longer course-level Investigations. Every lesson and investigation opportunity is grounded in the why, how, and what of the learning experience, and helps teachers bring mathematical concepts to life.

    An educational slide on addition story problems, detailing goals for solving problems, language goals, and strategies using equal expressions, tens and ones, and number sense.

    Please refer to the following Amplify Desmos Math California alignments to the Standards for Mathematical Practice, provided by grade level.

    A screen titled "Match the Score" with a 2D target graph showing various scores. Instructions request four ordered pairs to total 400. Four pairs are listed: (4, 2), (7, 4), (7, 6), (10, 6). A "Try again" button is shown.

    Built-in authentic tasks

    Mathematics is not learning in isolation. Students are connected to each other’s thinking and can use math to understand the world. With accessible invitations to authentic tasks, all students can experience mathematical success. Amplify Desmos Math California provides these authentic invitations in a variety of ways:

    Each unit begins with an “Explore” lesson, which allows students to engage with authentic exploration in low-floor, high-ceiling tasks. These tasks are designed to promote an inclusive and differentiated learning environment—allowing all students to access basic mathematical concepts, while offering advanced exploration and problem-solving for those ready for more complex work.

    Our innovative course-level investigations are designed to facilitate multi-part exploration. Students grapple with Big Ideas, diving deep into key concepts that encourage comprehensive understanding. Data science is infused into the approach, giving students a solid foundation from which to interpret and apply data-driven solutions. They’re also encouraged to understand and appreciate the interrelatedness of Earth’s environmental systems via our lesson’s focus on the Environmental Principles and Concepts (EP&Cs).

    Explicit support for multilingual/English learners

    Three overlapping educational worksheets for first grade math, including a cover page, a list of learning goals, and a lesson plan with bilingual English and Spanish text.

    Amplify partnered with the English Learner Success Forum (ELSF), a national nonprofit organization that advocates for high-quality instructional materials that are inclusive of multilingual/English learners (ML/ELs). ELSF reviewed Amplify Desmos Math California, and provided directional guidance and feedback to ensure that the program reflects their research-based instructional strategies for multilingual/English learners.

    Amplify Desmos Math California recognizes the diverse language needs of our students and is designed to be inclusive. Each lesson in the program features a parallel language activity, designed to be available to all students, in the form of teacher guidance and student activities. The activities in the Math Language Development Resources have level ELD differentiation to support all levels of ML/ELs. This approach ensures that all students, regardless of their language skills, can participate fully, grasp the material, and excel in their mathematical journey.

    Our Multilingual Glossary includes, in addition to Spanish, nine languages: Simplified Mandarin, Tagalog, Vietnamese, Arabic, European French, Russian, Brazilian-Portuguese, Haitian-Creole, and Urdu.

    Amplify Desmos Math California will include Spanish student-facing materials beginning in the 2026–27 school year.

    Assessments

    By starting with what students already know, Amplify Desmos Math helps build a strong foundation for success to guide and support future learning. Teachers are empowered to transform every classroom into an engaged math community that invites, values, and develops student thinking. With explicit guidance on what to look for and how to respond, teachers can effectively support students as they develop their understanding.

    Open math workbook showing an End-of-Unit Assessment with multiple-choice and written response questions on fractions and equivalent values.

    Program assessments

    A variety of performance data in Amplify Desmos Math provides evidence of student learning while helping students bolster their skills and understanding.

    Unit-Level Assessments

    Our embedded unit assessments offer key insights into students’ conceptual understanding of math. These assessments provide regular, actionable information about how students are thinking about and processing math, with both auto-scoring and in-depth rubrics that help teachers anticipate and respond to students’ learning needs.

    Lesson-Level Assessments

    Amplify Desmos Math lessons are centered around sense-making and in-the-moment feedback. Daily moments of assessment provide valuable evidence of learning for both the teacher and student.

    Data and reporting

    Amplify Desmos Math provides teachers and administrators with unified reporting and insights so that educators have visibility into what students know about grade-level math—and can plan instruction accordingly for the whole class, small groups, and individual students.

    A table displays students' performance levels across various items, with a detailed score distribution for a specific assessment shown in a separate overlay. Geometric design elements accented the background, providing an engaging visual touch ideal for any math classroom using Amplify Desmos Math.

    Assessment reports

    Reporting functionality integrates unit assessments, lesson assessments, personalized learning, Benchmark assessments, and Progress Monitoring for a comprehensive look at student learning.

    Our reports show proficiency and growth by domain, cluster, standard, and priority concept using performance data from unit assessments. Then our reports highlight areas of potential student need to allow teachers to modify their instruction and target differentiated support.

    At-a-glance views of unit-level assessment results inform your instructional planning, and you can also drill down to item-level analysis.

    Standards reports

    Our standards report allows you to monitor proficiency at the class and individual student levels. Proficiency and growth are shown by domain, cluster, standard, and priority concepts. Areas of potential student need are highlighted to allow teachers to modify their instruction and target differentiated support.

    Administrator reports

    Amplify Desmos Math provides a complete picture of student, class, and district performance, allowing administrators to implement instructional and intervention plans.

    • Track student, class, and district performance with usage, completion, and assessment data.
    • Accurately group students and classes with the Benchmark and Progress Monitoring data of mCLASS Assessments and allow teachers to reliably implement and track the progress of Tier 2 and Tier 3 intervention.
    • Provide one data-driven solution that educators can rely on for high-quality math instruction.

    Elementary review resources

    To learn about the elementary program, please start by watching the Amplify Desmos Math California Elementary Program Overview video.

    For additional program information and helpful navigation tips, download the Amplify Desmos Math California Elementary Program Guide.

    View the Elementary Program Components Guide here. 

    View the Hands-on manipulatives brochure here.

    Middle School review resources

    To learn about the middle school program, please start by watching the Amplify Desmos Math California Middle School Program Overview video.

    For additional program information and helpful navigation tips, download the Amplify Desmos Math California Middle School Program Guide.

    View the Middle School Program Components Guide here.

    View the middle school manipulative kit components here.

    The digital experience

    In Amplify Desmos Math, embedded interactions and animations allow students to test predictions, get feedback, share ideas, and connect representations.

    The digital interactions included in lesson activities are designed to elicit student thinking in a way that feels fun and inviting. As students play and explore math concepts, teachers can highlight the ideas that students share, connect those ideas to other students’ ideas, and build on their thinking through productive class discussion.

    Watch the video to preview the digital experience and for helpful platform navigation tips.

    A laptop displays a math activity about platform heights and tube length, while a worksheet titled "Hamster Homes" is visible in the background.

    Explore grade level samples

    All lessons in Amplify Desmos Math California include print materials and rich digital experiences. Every lesson is supported with Student Edition pages, teacher presentation screens, and interactive digital resources for practice and differentiation. Some lessons also enable students to use devices to interact with lesson content.

    You’ll find sample materials by grade level in the following drop-downs. Please refer to your physical samples and the digital platform (accessed through the demo account provided by your account executive) for a comprehensive program review.

    Scope and Sequence

    Math 2–3 is currently being developed and will be available in the 2026–27 school year.

    Cover of "Amplify Desmos Math California Teacher Edition GEO Volume 1" featuring abstract geometric illustrations and people engaged in mathematical activities.
    Scope and Sequence (National Edition)

    The Amplify Desmos Math Geometry Beta National Edition is available for piloting in the 2025–26 school year. Amplify Desmos Math California Geometry will be available in the 2026–27 school year.

    Cover of "Amplify Desmos Math California Geo Volume 1 Student Edition" featuring geometric shapes and small illustrated people interacting with mathematical elements.
    Geometry sampler

    This sampler includes Teacher Edition front matter for program overview information, plus Teacher Edition and Student Edition pages for Units 1–2.

    Cover of "Amplify Desmos Math California A2 Teacher Edition," featuring a Ferris wheel, math graphs, and students interacting with mathematical concepts.
    Scope and sequence (National Edition)

    The Amplify Desmos Math Algebra 2 Beta National Edition is available for piloting in the 2025–26 school year. Amplify Desmos Math California Algebra 2 will be available in the 2026–27 school year.

    Cover of "Amplify Desmos Math California Student Edition A2 Volume 1" featuring mathematical graphs, a Ferris wheel, and students interacting with math concepts.
    Algebra 2 sampler

    This sampler includes Teacher Edition front matter for program overview information, plus Teacher Edition and Student Edition pages for Units 1–2.

    Contact us

    For questions, samples, or more information, please contact your local Amplify account executive:

    Erin King
    Sales Director, CA
    (512) 736-3162
    eking@amplify.com

    Northern CA
    Wendy Garcia
    Senior Account Executive
    (510) 368-7666
    wgarcia@amplify.com

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    Account Executive
    (415) 830-5348
    lburbank@amplify.com

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    Senior Account Executive
    (559) 355-3244
    dgonos@amplify.com

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    (310) 902-1407
    jsorenson@amplify.com

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    (949) 397-5766
    lsherman@amplify.com

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    kvanwagoner@amplify.com

    Under 2300 students in Bay Area, Sacramento Valley, and Northern Counties
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    Lead Account Executive
    (815) 534-0148
    kmauser@amplify.com

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    chsnyder@amplify.com

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    Discovering and exploring mathematics in every story

    Smiling young boy sits at a classroom desk holding an open book, developing reading comprehension, while two other children are seen in the background engaged in activities.

    Every picture book on your classroom shelf holds mathematical treasures waiting to be discovered! What if every read-aloud could go beyond a literacy moment to become a catalyst for mathematical sense-making? This question lies at the heart of Allison Hintz and Antony T. Smith’s delightful and informative book, Mathematizing Children’s Literature: Sparking Connections, Joy, and Wonder Through Read-Alouds and Discussion.

    Many teachers have used traditional counting books and shape-focused stories to support students in connecting mathematics to literature. According to Hintz and Smith, you can challenge readers to extend and expand upon these experiences in ways that provide more space for them to make sense of stories; ask their own questions; see mathematics authentically in the world; and make connections between the stories, the math, and their lives. That’s the promise of mathematizing—approaching any story with a mathematical lens.

    The concept of “mathematizing” goes beyond simply finding numbers in a story. Children are naturally curious and construct meaning by noticing, exploring, explaining, and modeling. The story context becomes a place to play and practice seeing math everywhere in our world. As we read a story aloud and pause to ask, “What do you notice? What do you wonder?,” students are able to surface structure, compare quantities, model situations, and justify their ideas, all while staying rooted in characters, plot, setting, and theme. The result is a classroom where math feels joyful, meaningful, connected, and accessible.

    In this post, we’ll explore simple moves to mathematize your next read-aloud, sample prompts to elevate discussion, and follow-up activities to turn your library into a launchpad for mathematical thinking!

    Mathematizing process and structure

    While there’s no one way to facilitate a mathematical read-aloud, the following steps can help you get started:

    1. Explore books in your current library. There are no hard and fast rules for choosing the right book to mathematize, because a book can spark mathematical ideas in many ways. Look for books that a) are overtly ‘mathy’ where the math is central to the story’s plot, b) have illustrations that provide opportunities to explore the math in them, and/or c) have a story that inspires mathematical thinking, even if the math isn’t central to the story’s plot.
    2. Read the book aloud for the first time. The first read is a wonderful opportunity for students to hear and enjoy the story itself.
    3. Ask students what they noticed and wondered. As students share their responses, record them on a piece of chart paper to revisit later. If no responses pertain to the math in the story, you can follow up with the question, “Where did you see math in the story?”
    4. Reread the book a second time or revisit a specific page in the book. At this point, you want to start to focus on the math the students will explore in the book. You can either reread the entire story and pause on strategic pages that center on the mathematical ideas, or revisit specific pages in the story. (If the story is longer,it will probably be easiest to just flip back to specific pages.)
    5. Elicit student thinking. Ask students what math questions they could ask based on the pages they revisited.
    6. Give students a follow-up math activity. This could be based on a question the students mentioned earlier in this process, or one the teacher has planned.

    Mathematizing examples

    To save you time finding a book to use, we’ve outlined a plan based on some of our favorite books to mathematize (listed by grade band).

    Grade levelK–1
    Book title and authorBear Says Thanks by Karma Wilson
    Mathematical focusCounting, addition, and mathematical representations
    LaunchRead the story aloud. Ask students, “What do you notice? What do you wonder?” Record their responses on a piece of chart paper. And ask students, “How many friends visited Bear? What different food items did Bear’s friends bring?”
    Pages to revisitAs students describe the different foods, revisit those pages. Identify any foods the students didn’t mention. As you revisit each page, ask students, “How many of that food item did that friend bring? ”Record their responses on a piece of chart paper for each friend. 
    ActivityArrange students in small groups of 3–4 and give them a piece of poster paper. Ask students to show each friend’s food items. They can represent them using pictures, counters, ten-frames, etc. After they’ve correctly represented each friend, ask them to show how many total food items Bear’s friends brought using numbers and equations. When they’ve finished, have them visit one another’s posters to see how others represented and added the food items. 
    Grade level2–3
    Book title and author100 Hungry Ants by Elinor J. Pinczes
    Mathematical focusConnecting arrays to expressions
    LaunchRead the story aloud. Ask students, “What do you notice? What do you wonder?” Record their responses on a piece of chart paper. And ask students, “How did the ants rearrange themselves throughout the book?”
    Pages to revisitAs students describe the different arrangements of ants, revisit those pages so students have a visual of the array. As you revisit each page, ask students, “How many ants are in each row? Each column? What is an equation we can write to represent the array?” Record their responses on a piece of chart paper. 
    ActivityArrange students in small groups of 3–4 and give them a piece of poster paper. Give each group a different number of ants. Suggested numbers are: 12, 24, 36, 20, 18. Ask students to draw all of the different ways their number of ants could rearrange themselves and record an equation to match each. If it’s helpful, you can give each group a set of cubes, counters, or beans to represent the ants so they can manipulate them. Wrap up the activity by having students visit one another’s posters and discussing the similarities and differences between them. 
    Grade level4–5
    Book title and authorDozens of Doughnuts by Carrie Finison
    Mathematical focusMultiplication and division
    LaunchRead the story aloud. Ask students, “What do you notice? What do you wonder?” Record their responses on a piece of chart paper. And ask students, “How many ways did Luanne share her doughnuts as friends arrived at her door?”
    Pages to revisitAs students describe the different ways Luanne shared her doughnuts, revisit those pages. As you revisit each page, ask students, “How many doughnuts were being shared? By how many animals? ”Record their responses on a piece of chart paper. 
    ActivityArrange students in small groups of 3–4 and give them each a piece of poster paper. Ask them to show all of the ways Luanne shared her doughnuts. To enable variation, refrain from specifying the representation they should use. After they’ve finished, ask them to do a Gallery Walk to each other’s posters to get ideas to add to their poster. If none of the groups have a multiplication and division equation for each way, ask students to record those as well. Ask students how Luanne could have shared a dozen doughnuts with the following number of animals showing up at her door: 5, 8, 10, 14, 16, and 18. Encourage students to show their work and record multiplication and division equations. 

    And with all the upcoming holidays and opportunities to gather with friends and family, we were also inspired to use Spaghetti and Meatballs for All! by Marilyn Burns in a mathematizing read-aloud. Follow this link to find K–2 and 3–5 lesson plans for this book that you can use right away!

    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.

    A closer look at grades 6–8

    Amplify Science California is based on the latest research on teaching and learning and helps teachers deliver rigorous and riveting lessons through hands-on investigations, literacy-rich activities, and interactive digital tools that empower students to think, read, write, and argue like real scientists.

    In the 6–8 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.

    Is your school implementing the domain model? Click here.

    Collage of four images showing children engaged in educational activities such as conducting experiments and crafting in a classroom setting.
    A four-step process diagram with icons: spark a real-world problem, explore sources, explain and elaborate, and evaluate claims, all linking to engage with 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, students build and deepen their understanding, increasing their ability to develop and refine 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 6–8 program to address 100% of the California NGSS in fewer lessons than other programs.

    Scope and sequence

    Every year our grades 6–8 sequence consists of 9 units, with each unit containing 10–19 lessons. Lessons are written to last a minimum of 45-minutes, though teachers can expand or contract the timing to meet their needs.

    Chart displaying educational science topics for grades 6 to 8, categorized by grade level, duration in days, and number of classes. Includes subjects like microbiome, geology, and natural selection.

    Unit types

    Each unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, while also serving a unique purpose.

    In grades 6–8, there are three types of units:

    • One unit is a launch unit.
    • Three units are core units.
    • Two units are engineering internships.
    Launch units

    Launch units are the first units taught in each year of Amplify Science California. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

    Core units

    Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

    Engineering Internship units

    Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

    Units at a glance

    Abstract art with vibrant colors featuring a yellow silhouette of a person holding a book against a background of geometric shapes, swirling patterns, and bold textures.
    Microbiome

    Domain: Life Science

    Unit type: Launch

    Student role: Microbiological researchers

    Phenomenon: The presence of 100 trillion microorganisms living on and in the human body may keep the body healthy.  

    Abstract artwork of a person's side profile with geometric shapes and colorful patterns flowing from the head, holding a small sledgehammer. A vision chart is visible in the corner.
    Metabolism

    Domain: Life Science

    Unit type: Core

    Student role: Medical researchers

    Phenomenon: Elisa, a young patient, feels tired all the time.  

    Download unit guide

    Orange abstract background with hexagonal shapes featuring icons of a bar chart, plant, safety vest, test tube, peach, and stethoscope.
    Metabolism Engineering Internship

    Domains: Life Science, Engineering Design

    Unit type: Engineering internship

    Student role: Food engineers

    Phenomenon: Designing health bars with different molecular compositions can effectively meet the metabolic needs of patients or rescue workers.  

    Imagen que muestra un gráfico de arañas de diferentes colores con patrones distintos de patas y cuerpo, incluidas variaciones de color marrón, amarillo y azul. El fondo es una superficie oscura y texturizada.
    Traits and Reproduction

    Domain: Life Science

    Unit type: Core

    Student role: Biomedical students

    Phenomenon: Darwin’s bark spider offspring have different silk flexibility traits, even though they have the same parents.  

    Download unit guide

    Illustration of a person in a red hat and fur-lined coat with eyes closed, surrounded by large orange circles on a dark background.
    Thermal Energy

    Domain: Physical Science

    Unit type: Core

    Student role: Thermal scientists

    Phenomenon: One of two proposed heating systems for Riverdale School will best heat the school. 

    Download unit guide

    Abstract artwork depicting a bright sun with blue and orange swirling patterns next to green hills under a sky with shades of blue, orange, and red.
    Ocean, Atmosphere, and Climate

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.  

    An illustration from the Weather Patterns unit
    Weather Patterns

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Forensic meteorologists

    Phenomenon: In recent years, rainstorms in Galetown have been unusually severe.  

    Download unit guide

    An illustration from the Earth's Changing Climate unit
    Earth’s Changing Climate

    Domains: Earth and Space Science, Life Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.  

    Download unit guide

    Abstract geometric design in shades of blue and purple featuring a hexagon with icons of a building, wrench, molecules, sun, paint can, and screwdriver.
    Earth’s Changing Climate Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.  

    A barren, rocky desert landscape with rover tracks leading to a distant vehicle on a hill under a hazy sky.
    Geology on Mars

    Domain: Earth and Space Science

    Unit type: Launch

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable. 

    Two prehistoric reptiles with long snouts and tails are near the shore, one on land and one in water, with plants, rocks, and an island in the background.
    Plate Motion

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean, even though the Mesosaurus species once lived all together.  

    Download unit guide

    Geometric design featuring a telescope, mountain, sound waves, and cosmic elements on a purple hexagonal background.
    Plate Motion Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.  

    Illustration of a cross-section of Earth showing a volcano near the ocean. Trees, mountains, and clouds are visible above, with subterranean layers below.
    Rock Transformations

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.  

    Download unit guide

    Ilustración que muestra las etapas de fusión de una paleta de naranja: entera, parcialmente derretida, más derretida y casi derretida por completo, con palitos de madera, sobre un fondo morado.
    Phase Change

    Domains: Physical Science, Earth and Space Science

    Unit type: Core

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart

    Download unit guide

    Green geometric background with a hexagonal emblem containing a parachute icon, ruler, bandage, and stacked layers on a gradient pattern.
    Force and Motion Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Designing emergency supply delivery pods with different structures can maintain the integrity of the supply pods and their contents.  

    An illustration from the Chemical Reactions unit
    Chemical Reactions

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Forensic chemists

    Phenomenon: A mysterious brown substance has been detected in the tap water of Westfield.  

    Download unit guide

    An illustration of a whale with jellyfish and turtles from Amplify Science
    Populations and Resources

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in Glacier Sea has increased. 

    Download unit guide

    Low-poly landscape with trees and mushrooms. A fox sniffs the ground, a rabbit sits nearby, and mountains and sun are in the background.
    Matter and Energy in Ecosystems

    Domains: Life Science, Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Ecologists

    Phenomenon: The biodome ecosystem has collapsed.  

    Download unit guide

    Two people climbing rocky terrain; illustrations show a hiking boot and a belt with gear.
    Harnessing Human Energy

    Domains: Physical Science, Earth and Space Science, Engineering Design

    Unit type: Launch

    Student role: Energy scientists

    Phenomenon: Rescue workers can use their own human kinetic energy to power the electrical devices they use during rescue missions.  

    Illustration of a futuristic space station with large solar panels, orbiting in deep space, emitting a blue glow from its propulsion system.
    Force and Motion

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: The asteroid sample-collecting pod failed to dock at the space station as planned.

    Download unit guide

    Green geometric graphic featuring icons: a baby, thermometer, layers, medical alert, and a flame.
    Phase Change Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different combinations of phase change materials can keep babies at a healthy temperature.  

    Illustration of a roller coaster filled with people, hands raised, going down a steep track against a bright blue sky with clouds.
    Magnetic Fields

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: During a test launch, a spacecraft traveled much faster than expected.  

    An illustration from the Light Waves unit
    Light Waves

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Spectroscopists

    Phenomenon: The rate of skin cancer is higher in Australia than in other parts of the world.

    Download unit guide

    A city skyline at night with a prominent full moon, stars in the sky, and a bridge silhouette on the left.
    Earth, Moon, and Sun

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Astronomers

    Phenomenon: An astrophotographer can only take pictures of specific features on the Moon at certain times.  

    Download unit guide

    Four low-poly dinosaurs with missing body sections are standing in a row; one is yellow, and the others are green. They have purple spikes and red patches on their bodies.
    Natural Selection

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The newt population in Oregon State Park has become more poisonous over time.  

    Download unit guide

    Red geometric background with icons including a mosquito, DNA strand, bar chart, and world map inside a hexagon.
    Natural Selection Engineering Internship

    Domains: Engineering Design, Life Science

    Unit type: Engineering internship

    Student role: Clinical engineers

    Phenomenon: Designing malaria treatment plans that use different combinations of drugs can reduce drug resistance development while helping malaria patients.  

    Two giant tortoises with long necks stand near water; one tortoise feeds on leaves from a tree while the other is near dense vegetation.
    Evolutionary History

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Paleontologists

    Phenomenon: A mystery fossil at the Natural History Museum has similarities with both wolves and whales.    

    Download unit guide

    Welcome, Middle School Science Reviewers!

    Thank you for taking the time to review Amplify Science for grades 6–8. On this site, you’ll find all the resources you need to learn more about this engaging and robust NGSS program. Plus, we make it easy to experience our program firsthand with a live demo account that features our interactive learning platform.

    A person in protective glasses examines a glass of water, surrounded by illustrations of a rocket, telescope, polar bear, clouds, rain, and moon phases on a colorful abstract background.

    Overview

    With Amplify Science, students don’t just passively learn about science concepts.

    No matter where your students are learning—whether at school or at home—they take on the role of scientists and engineers to actively investigate and make sense of real-world phenomena. They do this through a blend of cohesive and compelling storylines, hands-on investigations, collaborative discussions, literacy-rich activities, and interactive digital tools.

    Listen to these educators share how the program empowers students to think, read, write, and argue like real scientists and engineers every day.

    EdReports All-Green

    Amplify Science for grades K–8 has been rated all-green by EdReports.

    Read the review on EdReports.

    A boy stirs a clear liquid in a plastic cup while a girl smiles beside him in a classroom with students and a teacher in the background. EdReports badge is overlaid in the corner.

    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, students build and deepen their understanding, increasing their ability to develop and refine complex explanations of the unit’s phenomenon. It’s this proven program structure and lesson design that enables Amplify Science to address 100% of the NGSS in fewer days than other programs.

    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.

    Unit Sequence

    Our lessons follow a structure that is grounded in regular routines while still being flexible enough to allow for a variety of learning experiences.
     
    In fact, our multi-modal instruction offers more opportunities for students to construct meaning, and practice and apply concepts than any other program. What’s more, our modular design means our units can be flexibly arranged to support your instructional goals.

    Collage of four images: a watercolor desert scene, three kids examining a gadget, a hand placing beads into a container, and a woman in a sunhat in a stylized field.
    Abstract art with vibrant colors featuring a yellow silhouette of a person holding a book against a background of geometric shapes, swirling patterns, and bold textures.

    Unit 1

    Microbiome

    Domain: Life Science

    Unit type: Launch

    Student role: Microbiological researchers

    Phenomenon: The presence of 100 trillion microorganisms living on and in the human body may keep the body healthy.  

    Abstract artwork of a person's side profile with geometric shapes and colorful patterns flowing from the head, holding a small sledgehammer. A vision chart is visible in the corner.

    Unit 2

    Metabolism

    Domain: Life Science

    Unit type: Core

    Student role: Medical researchers

    Phenomenon: Elisa, a young patient, feels tired all the time.  

    Orange abstract background with hexagonal shapes featuring icons of a bar chart, plant, safety vest, test tube, peach, and stethoscope.

    Unit 3

    Metabolism Engineering Internship

    Domains: Life Science, Engineering Design

    Unit type: Engineering internship

    Student role: Food engineers

    Phenomenon: Designing health bars with different molecular compositions can effectively meet the metabolic needs of patients or rescue workers.  

    An image showing a graphic of spiders of different colors with distinct leg and body patterns, including brown, yellow, and blue variations. The background is a dark, textured surface.

    Unit 4

    Traits and Reproduction

    Domain: Life Science

    Unit type: Core

    Student role: Biomedical students

    Phenomenon: Darwin’s bark spider offspring have different silk flexibility traits, even though they have the same parents.  

    Illustration of a person in a red hat and fur-lined coat with eyes closed, surrounded by large orange circles on a dark background.

    Unit 5

    Thermal Energy

    Domain: Physical Science

    Unit type: Core

    Student role: Thermal scientists

    Phenomenon: One of two proposed heating systems for Riverdale School will best heat the school. 

    Abstract artwork depicting a bright sun with blue and orange swirling patterns next to green hills under a sky with shades of blue, orange, and red.

    Unit 6

    Ocean, Atmosphere, and Climate

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.  

    Illustration of a village with houses, fields and mountains under a cloudy sky with waves of wind or rain.

    Unit 7

    Weather Patterns

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Forensic meteorologists

    Phenomenon: In recent years, rainstorms in Galetown have been unusually severe.  

    A polar bear stands on a small ice floe in the ocean with an orange sun in the sky and distant icy mountains in the background.

    Unit 8

    Earth’s Changing Climate

    Domains: Earth and Space Science, Life Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.  

    Abstract geometric design in shades of blue and purple featuring a hexagon with icons of a building, wrench, molecules, sun, paint can, and screwdriver.

    Unit 9

    Earth’s Changing Climate Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.  

    A barren, rocky desert landscape with rover tracks leading to a distant vehicle on a hill under a hazy sky.

    Unit 1

    Geology on Mars

    Domain: Earth and Space Science

    Unit type: Launch

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable. 

    Two prehistoric reptiles with long snouts and tails are near the shore, one on land and one in water, with plants, rocks, and an island in the background.

    Unit 2

    Plate Motion

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean, even though the Mesosaurus species once lived all together.  

    Geometric design featuring a telescope, mountain, sound waves, and cosmic elements on a purple hexagonal background.

    Unit 3

    Plate Motion Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.  

    Illustration of a cross-section of Earth showing a volcano near the ocean. Trees, mountains, and clouds are visible above, with subterranean layers below.

    Unit 4

    Rock Transformations

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.  

    Illustration showing the stages of melting an orange popsicle: whole, partially melted, more melted, and almost completely melted, with wooden sticks, on a purple background.

    Unit 5

    Phase Change

    Domains: Physical Science, Earth and Space Science

    Unit type: Core

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart

    Green geometric background with a hexagonal emblem containing a parachute icon, ruler, bandage, and stacked layers on a gradient pattern.

    Unit 6

    Force and Motion Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Designing emergency supply delivery pods with different structures can maintain the integrity of the supply pods and their contents.  

    Abstract digital artwork featuring numerous red and gray circles overlapping a split background of blue and light purple, creating a dynamic and energetic composition.

    Unit 7

    Chemical Reactions

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Forensic chemists

    Phenomenon: A mysterious brown substance has been detected in the tap water of Westfield.  

    An illustration of a whale with jellyfish and turtles from Amplify Science

    Unit 8

    Populations and Resources

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in Glacier Sea has increased. 

    Low-poly landscape with trees and mushrooms. A fox sniffs the ground, a rabbit sits nearby, and mountains and sun are in the background.

    Unit 9

    Matter and Energy in Ecosystems

    Domains: Life Science, Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Ecologists

    Phenomenon: The biodome ecosystem has collapsed.  

    Two people climbing rocky terrain; illustrations show a hiking boot and a belt with gear.

    Unit 1

    Harnessing Human Energy

    Domains: Physical Science, Earth and Space Science, Engineering Design

    Unit type: Launch

    Student role: Energy scientists

    Phenomenon: Rescue workers can use their own human kinetic energy to power the electrical devices they use during rescue missions.  

    A spacecraft approaches and docks with a space station featuring large blue solar panels, set against a backdrop of outer space.

    Unit 2

    Force and Motion

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: The asteroid sample-collecting pod failed to dock at the space station as planned.

    Green geometric graphic featuring icons: a baby, thermometer, layers, medical alert, and a flame.

    Unit 3

    Phase Change Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different combinations of phase change materials can keep babies at a healthy temperature.  

    Illustration of a roller coaster filled with people, hands raised, going down a steep track against a bright blue sky with clouds.

    Unit 4

    Magnetic Fields

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: During a test launch, a spacecraft traveled much faster than expected.  

    Illustration of Earth with arrows and wavy lines representing solar radiation entering the atmosphere, showing a focus on the Asia-Pacific region.

    Unit 5

    Light Waves

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Spectroscopists

    Phenomenon: The rate of skin cancer is higher in Australia than in other parts of the world.

    A city skyline at night with a prominent full moon, stars in the sky, and a bridge silhouette on the left.

    Unit 6

    Earth, Moon, and Sun

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Astronomers

    Phenomenon: An astrophotographer can only take pictures of specific features on the Moon at certain times.  

    Four low-poly dinosaurs with missing body sections are standing in a row; one is yellow, and the others are green. They have purple spikes and red patches on their bodies.

    Unit 7

    Natural Selection

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The newt population in Oregon State Park has become more poisonous over time.  

    Red geometric background with icons including a mosquito, DNA strand, bar chart, and world map inside a hexagon.

    Unit 8

    Natural Selection Engineering Internship

    Domains: Engineering Design, Life Science

    Unit type: Engineering internship

    Student role: Clinical engineers

    Phenomenon: Designing malaria treatment plans that use different combinations of drugs can reduce drug resistance development while helping malaria patients.  

    Two giant tortoises with long necks stand near water; one tortoise feeds on leaves from a tree while the other is near dense vegetation.

    Unit 9

    Evolutionary History

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Paleontologists

    Phenomenon: A mystery fossil at the Natural History Museum has similarities with both wolves and whales.    

    Access program

    Watch the video to the right plus the ones below showing you how to navigate our digital platform. When you’re ready, follow the instructions below to log into our live demo account.

    • Click the orange button below to access the platform.
    • Choose the resources you’d like to review.
    • Pick your grade level from the drop-down menu.
    • Scroll down to find additional grade-level resources.

    Navigating an Engineering Internship (Part 1)

    This Part 1 video demonstrates how Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. In the process, they apply and deepen their learning from Core units.

    Navigating an Engineering Internship (Part 2)

    This Part 2 video demonstrates how to use the Futura Workspace to manage the immersive experience of the Engineering Internship units. This includes guidance on how to create student groups, how to review student work, and how to send students targeted feedback on their designs.

    Navigating our reporting tools

    Teachers of Amplify Science grades 6–8 have access to a feature called Reporting. When unit assessments are administered digitally, the Reporting tool enables teachers to analyze student performance on the unit assessments.

    Differentiation post-assessment

    Every core unit of Amplify Science 6–8 features a formal formative assessment opportunity at the mid-way point, or “Critical Juncture,” of the unit, which provides an important opportunity for differentiation.

    Get in touch

    Smiling man with short hair and a trimmed beard wearing a light blue collared shirt against a plain white background.

    Have questions? Bob McCarty is standing by and ready to help.

    Robert “Bob” McCarty
    Senior Account Executive
    (435) 655-1731
    rmccarty@amplify.com

    A closer look at grades 6–8 (domain)

    Amplify Science is based on the latest research on teaching and learning and helps teachers deliver rigorous and riveting lessons through hands-on investigations, literacy-rich activities, and interactive digital tools that empower students to think, read, write, and argue like real scientists.

    In the 6–8 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.

    Is your school implementing the domain model? Click here.

    Collage of four images showing children engaged in educational activities such as conducting experiments and crafting in a classroom setting.
    A four-step process: Spark intrigue, Explore evidence, Explain and elaborate, and Evaluate claims, leading to ongoing engagement and building complexity.

    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, students build and deepen their understanding, increasing their ability to develop and refine 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 6–8 program to address 100% of the NGSS in fewer lessons than other programs.

    Scope and sequence

    Every year our grades 6–8 sequence consists of 9 units, with each unit containing 10–19 lessons. Lessons are written to last a minimum of 45-minutes, though teachers can expand or contract the timing to meet their needs.

    A grid of educational icons, each representing a different science topic, such as earth and space science, life science, and physical science, with titles and lesson counts.

    Unit types

    Each unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, while also serving a unique purpose.

    In grades 6–8, there are three types of units:

    • One unit is a launch unit.
    • Three units are core units.
    • Two units are engineering internships.
    Launch units

    Launch units are the first units taught in each year of Amplify Science. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to actively read in all subsequent units.

    Core units

    Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

    Engineering Internship units

    Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

    Units at a glance

    A rover sits on a rocky, reddish hill under a hazy sky, leaving visible tire tracks across the barren landscape.
    Geology on Mars

    Domain: Earth and Space Science

    Unit type: Launch

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable.    

    Two prehistoric marine reptiles with long snouts are near a rocky shoreline, one on land and one in the water, with an island and clouds in the background.
    Plate Motion

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean, even though the Mesosaurus species once lived all together.    

    A geometric badge with a mountain, telescope, and audio wave icons on a purple background with polygonal shapes.
    Plate Motion Engineering Internship

    Domain: Earth and Space Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.    

    Illustration of a volcano by the sea with smoke, trees, mountains, and a cross-section showing a fault line beneath the ground.
    Rock Transformations

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.    

    Illustration of a city skyline at night with buildings, a bridge, and a large full moon in a starry sky.
    Earth, Sun, and Moon

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Astronomers

    Phenomenon: An astrophotographer can only take pictures of specific features on the Moon at certain times.    

    Abstract digital painting of a landscape with green hills, a red-orange horizon, and a large yellow sun surrounded by blue and orange swirling shapes on the right.
    Ocean, Atmosphere, and Climate

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.    

    Illustration of a town with houses and fields under a sky with large clouds and swirling wind patterns, set against a backdrop of hills and mountains.
    Weather Patterns

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Forensic meteorologists

    Phenomenon: In recent years, rainstorms in Galetown have been unusually severe.    

    A polar bear stands on a small ice floe surrounded by water and floating ice under a red sun in an Arctic landscape.
    Earth’s Changing Climate

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.    

    Hexagonal badge with icons including a wrench, building, sun, screwdriver, paint can, and molecules on a purple geometric background.
    Earth’s Changing Climate Engineering Internship

    Domain: Earth and Space Science

    Unit type: Engineering internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.    

    Colorful abstract digital artwork featuring a yellow figure holding a device, with blue and red shapes and textured patterns in the background.
    Microbiome

    Domain: Life Science

    Unit type: Launch

    Student role: Microbiological researchers

    Phenomenon: The presence of 100 trillion microorganisms living on and in the human body may keep the body healthy.    

    An abstract illustration of a person having their mouth and throat examined with a tongue depressor, surrounded by colorful shapes, with an eye chart in the background.
    Metabolism

    Domain: Life Science

    Unit type: Core

    Student role: Medical researchers

    Phenomenon: Elisa, a young patient, feels tired all the time.    

    Geometric orange background with a hexagon icon displaying symbols for statistics, farming, healthcare, safety vest, chemistry, and agriculture.
    Metabolism Engineering Internship

    Domain: Life Science

    Unit type: Engineering internship

    Student role: Food engineers

    Phenomenon: Designing health bars with different molecular compositions can effectively meet the metabolic needs of patients or rescue workers.    

    Six spiders with different colors and stripe patterns are arranged in a grid pattern on a dark background, showing variations in leg and body color.
    Traits and Reproduction

    Domain: Life Science

    Unit type: Core

    Student role: Biomedical students

    Phenomenon: Darwin’s bark spider offspring have different silk flexibility traits, even though they have the same parents.    

    An underwater scene shows a whale surrounded by jellyfish, sea turtles, and fish, with sunlight filtering through the water.
    Populations and Resources

    Domain: Life Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in Glacier Sea has increased.    

    A low-poly landscape with trees, mushrooms, a rabbit sitting, and a fox bending down near another rabbit under a sunny sky with mountains in the background.
    Matter and Energy in Ecosystems

    Domain: Life Science

    Unit type: Core

    Student role: Ecologists

    Phenomenon: What caused the mysterious crash of a biodome ecosystem?    

    Three green dinosaurs and one yellow dinosaur stand in a row on grass, each with purple spikes and a red spot on their backs. The sky is blue with light clouds.
    Natural Selection

    Domain: Life Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The newt population in Oregon State Park has become more poisonous over time.    

    Red-toned graphic with hexagonal badge featuring a world map, a mosquito, a DNA strand, charts, cubes, and circular icons. Geometric background pattern.
    Natural Selection Engineering Internship

    Domain: Life Science

    Unit type: Engineering internship

    Student role: Clinical engineers

    Phenomenon: Designing malaria treatment plans that use different combinations of drugs can reduce drug resistance development while helping malaria patients.  

    Two giant tortoises are near a river; one is by the water and the other is standing on land and stretching its neck toward a leafy tree.

    Evolutionary History

    Domain: Life Science

    Unit type: Core

    Student role: Paleontologists

    Phenomenon: A mystery fossil at the Natural History Museum has similarities with both wolves and whales.    

    Two people climb over rocky terrain strewn with electronic waste, with illustrated insets showing a hiking boot, a solar-powered device, and a person adjusting a belt-like gadget.
    Harnessing Human Energy

    Domain: Physical Science

    Unit type: Launch

    Student role: Energy scientists

    Phenomenon: Rescue workers can use their own human kinetic energy to power the electrical devices they use during rescue missions.    

    A spacecraft approaches a modular space station with large solar panels, set against a backdrop of outer space.
    Force and Motion

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: The asteroid sample-collecting pod failed to dock at the space station as planned.    

    Green geometric background with a hexagonal badge showing a parachute, a box, a ruler, a bandage, and stacked layers.
    Force and Motion Engineering Internship

    Domain: Physical Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Designing emergency supply delivery pods with different structures can maintain the integrity of the supply pods and their contents. 

    Illustration of a roller coaster car full of people with raised arms, speeding down a loop against a blue sky with clouds.
    Magnetic Fields

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: During a test launch, a spacecraft traveled much faster than expected.    

    Illustration of a person in a red coat and hat with arms crossed, eyes closed, surrounded by large orange and brown circles, possibly representing snow or lights.
    Thermal Energy

    Domain: Physical Science

    Unit type: Core

    Student role: Thermal scientists

    Phenomenon: One of two proposed heating systems for Riverdale School will best heat the school.    

    An orange popsicle gradually melts, shown in four stages from solid to completely melted, with wooden sticks visible, against a purple background.
    Phase Change

    Domain: Physical Science

    Unit type: Core

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart.    

    A green background with a picture of a person and a sandwich.
    Phase Change Engineering Internship

    Domain: Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different combinations of phase change materials can keep babies at a healthy temperature.    

    Digital illustration showing red and blue molecules on a blue background transitioning to a lighter background, representing molecular diffusion across a boundary.
    Chemical Reactions

    Domain: Physical Science

    Unit type: Core

    Student role: Forensic chemists

    Phenomenon: A mysterious brown substance has been detected in the tap water of Westfield.    

    Illustration of Earth with yellow arrows and colored waves approaching from the left, representing incoming solar or cosmic radiation.
    Light Waves

    Domain: Physical Science

    Unit type: Core

    Student role: Spectroscopists

    Phenomenon: The rate of skin cancer is higher in Australia than in other parts of the world.    

    A closer look at grades 6–8

    Amplify Science is based on the latest research on teaching and learning and helps teachers deliver rigorous and riveting lessons through hands-on investigations, literacy-rich activities, and interactive digital tools that empower students to think, read, write, and argue like real scientists.

    In the 6–8 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.

    Is your school implementing the domain model? Click here.

    Collage of four images showing children engaged in educational activities such as conducting experiments and crafting in a classroom setting.
    A four-step process diagram: Spark intrigue, Explore evidence, Explain and elaborate, and Evaluate claims, connected by arrows, with an engagement statement below.

    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, students build and deepen their understanding, increasing their ability to develop and refine 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 6–8 program to address 100% of the NGSS in fewer lessons than other programs.

    Scope and sequence

    Every year our grades 6–8 sequence consists of 9 units, with each unit containing 10–19 lessons. Lessons are written to last a minimum of 45-minutes, though teachers can expand or contract the timing to meet their needs.

    A grid of educational icons, each representing a different science topic, such as earth and space science, life science, and physical science, with titles and lesson counts.

    Unit types

    Each unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, while also serving a unique purpose.

    In grades 6–8, there are three types of units:

    • One unit is a launch unit.
    • Three units are core units.
    • Two units are engineering internships.
    Launch units

    Launch units are the first units taught in each year of Amplify Science. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

    Core units

    Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

    Engineering Internship units

    Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

    Units at a glance

    Abstract digital artwork featuring a yellow human figure, red shapes, and a blue-toned screen, with vibrant, multicolored patterns and textures in the background.
    Microbiome

    Domain: Life Science

    Unit type: Launch

    Student role: Microbiological researchers

    Phenomenon: The presence of 100 trillion microorganisms living on and in the human body may keep the body healthy.  

    An abstract illustration of a person receiving an oral examination, with colorful geometric shapes and an eye chart in the background.
    Metabolism

    Domain: Life Science

    Unit type: Core

    Student role: Medical researchers

    Phenomenon: Elisa, a young patient, feels tired all the time.  

    Abstract orange background with geometric shapes, featuring icons of a vest, bar chart, leaf, beaker, fruit, medical stethoscope, and an envelope within a hexagonal frame.
    Metabolism Engineering Internship

    Domains: Life Science, Engineering Design

    Unit type: Engineering internship

    Student role: Food engineers

    Phenomenon: Designing health bars with different molecular compositions can effectively meet the metabolic needs of patients or rescue workers.  

    Six spiders with varying body colors (brown, yellow, blue, and red) and patterns are arranged on a dark, textured background, seemingly in a diagram or chart formation.
    Traits and Reproduction

    Domain: Life Science

    Unit type: Core

    Student role: Biomedical students

    Phenomenon: Darwin’s bark spider offspring have different silk flexibility traits, even though they have the same parents.  

    Illustration of a person with closed eyes in a red winter coat and hat, surrounded by falling snow and orange circles on a dark background.
    Thermal Energy

    Domain: Physical Science

    Unit type: Core

    Student role: Thermal scientists

    Phenomenon: One of two proposed heating systems for Riverdale School will best heat the school. 

    Abstract illustration of a sun with blue and orange rays over a colorful landscape featuring green hills and a vibrant sky.
    Ocean, Atmosphere, and Climate

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.  

    Illustration of clouds above a small town and farmland, with wind currents depicted swirling through the landscape under a blue sky.
    Weather Patterns

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Forensic meteorologists

    Phenomenon: In recent years, rainstorms in Galetown have been unusually severe.  

    A polar bear stands on a small floating ice sheet in the ocean, surrounded by melting ice, with a red sun in the sky.
    Earth’s Changing Climate

    Domains: Earth and Space Science, Life Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.  

    A purple hexagonal graphic with icons including a building, wrench, screwdriver, sun, molecules, paint bucket, and tiles on a geometric patterned background.
    Earth’s Changing Climate Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.  

    A robotic rover sits on a hill in a rocky, reddish landscape, with visible tracks in the dust leading to its current position under a hazy sky.
    Geology on Mars

    Domain: Earth and Space Science

    Unit type: Launch

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable. 

    Two green prehistoric reptiles with long snouts are near the shore; one is on land while the other swims in blue water, with plants, rocks, and an island in the background.
    Plate Motion

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean, even though the Mesosaurus species once lived all together.  

    A purple geometric background featuring a hexagonal badge with a telescope, mountain, audio wave, and star symbols inside.
    Plate Motion Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.  

    Illustration showing an ocean, forest, and mountains with a smoking volcano, plus a cross-section of underground tectonic plates.
    Rock Transformations

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.  

    Four stages of an orange popsicle melting on a stick, from fully frozen on the left to completely melted on the right, against a plain background.
    Phase Change

    Domains: Physical Science, Earth and Space Science

    Unit type: Core

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart

    Green geometric background with an outlined hexagon containing icons: a parachute, ruler, letter "A," bandage, stacked blocks, and a folded corner paper.
    Force and Motion Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different combinations of phase change materials can keep babies at a healthy temperature. Domains: Engineering Design, Physical Science

    Abstract illustration showing red and blue circles on a split blue and light background, representing molecular movement across a membrane or barrier.
    Chemical Reactions

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Forensic chemists

    Phenomenon: A mysterious brown substance has been detected in the tap water of Westfield.  

    An underwater scene with a large whale surrounded by turtles, jellyfish, and various fish swimming in different directions.
    Populations and Resources

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in Glacier Sea has increased. 

    Low-poly digital illustration of a fox hunting a rabbit in a forest with pine trees, mushrooms, mountains, and the sun in the background. Another rabbit sits near the trees.
    Matter and Energy in Ecosystems

    Domains: Life Science, Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Ecologists

    Phenomenon: The biodome ecosystem has collapsed.  

    Two people climb over rocks filled with electronic devices; inset illustrations show a boot, a belt of batteries, and a radio.
    Harnessing Human Energy

    Domains: Physical Science, Earth and Space Science, Engineering Design

    Unit type: Launch

    Student role: Energy scientists

    Phenomenon: Rescue workers can use their own human kinetic energy to power the electrical devices they use during rescue missions.  

    A spacecraft approaches and docks with a modular space station featuring large blue solar panels, set against a black space background.
    Force and Motion

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: The asteroid sample-collecting pod failed to dock at the space station as planned.

    Green graphic with hexagonal emblem showing an infant, a thermometer, layered materials, a medical symbol, and a flame icon.
    Force and Motion Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing emergency supply delivery pods with different structures can maintain the integrity of the supply pods and their contents.

    Illustration of a roller coaster car with passengers raising their arms as they descend a steep track against a blue sky with clouds.
    Magnetic Fields

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: During a test launch, a spacecraft traveled much faster than expected.  

    Illustration of the Earth with arrows representing radiation or energy entering the atmosphere from space, focused on the Asia-Pacific region.
    Light Waves

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Spectroscopists

    Phenomenon: The rate of skin cancer is higher in Australia than in other parts of the world.

    A city skyline at night with illuminated windows, a large full moon, stars in the sky, and a bridge visible on the left side.
    Earth, Moon, and Sun

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Astronomers

    Phenomenon: An astrophotographer can only take pictures of specific features on the Moon at certain times.  

    Four polygonal dinosaurs walking in a row, three green and one yellow, each with a rock and purple spikes on their backs, set against a grassy background with a blue sky.
    Natural Selection

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The newt population in Oregon State Park has become more poisonous over time.  

    Red geometric background featuring a hexagonal emblem with icons of a world map, mosquito, DNA strand, bar chart, and interconnected blocks.
    Natural Selection Engineering Internship

    Domains: Engineering Design, Life Science

    Unit type: Engineering internship

    Student role: Clinical engineers

    Phenomenon: Designing malaria treatment plans that use different combinations of drugs can reduce drug resistance development while helping malaria patients.  

    Two tortoises with long necks are by a river; one is browsing leaves from a bush while the other is walking near the water's edge.
    Evolutionary History

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Paleontologists

    Phenomenon: A mystery fossil at the Natural History Museum has similarities with both wolves and whales.    

    Welcome, Jordan K-8 reviewers!

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    A closer look at grades 6–8 (domain)

    Amplify Science California is based on the latest research on teaching and learning and helps teachers deliver rigorous and riveting lessons through hands-on investigations, literacy-rich activities, and interactive digital tools that empower students to think, read, write, and argue like real scientists.

    In the 6–8 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.

    Is your school implementing the integrated model? Click here.

    Collage of four images showing children engaged in educational activities such as conducting experiments and crafting in a classroom setting.
    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, students build and deepen their understanding, increasing their ability to develop and refine 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 6–8 program to address 100% of the California NGSS in fewer lessons than other programs.

    Scope and sequence

    Every year of our grades 6–8 sequence consists of 9 units, with each unit containing 10–19 lessons. Lessons are written to last a minimum of 45 minutes, though teachers can expand or contract the timing to meet their needs.

    A grid of educational icons, each representing a different science topic, such as earth and space science, life science, and physical science, with titles and lesson counts.

    Unit types

    Each unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, while also serving a unique purpose.

    In grades 6–8, there are three types of units:

    • One unit is a launch unit.
    • Three units are core units.
    • Two units are engineering internships.
    Launch units

    Launch units are the first units taught in each year of Amplify Science California. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to actively read in all subsequent units.

    Core units

    Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

    Engineering Internship units

    Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

    Units at a glance

    A barren, rocky desert landscape with rover tracks leading to a distant vehicle on a hill under a hazy sky.
    Geology on Mars

    Domain: Earth and Space Science

    Unit type: Launch

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable.    

    Two prehistoric reptiles with long snouts and tails are near the shore, one on land and one in water, with plants, rocks, and an island in the background.
    Plate Motion

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean, even though the Mesosaurus species once lived all together.    

    Download unit guide

    Geometric design featuring a telescope, mountain, sound waves, and cosmic elements on a purple hexagonal background.
    Plate Motion Engineering Internship

    Domain: Earth and Space Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.    

    Illustration of a cross-section of Earth showing a volcano near the ocean. Trees, mountains, and clouds are visible above, with subterranean layers below.
    Rock Transformations

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.    

    Download unit guide

    A city skyline at night with a prominent full moon, stars in the sky, and a bridge silhouette on the left.
    Earth, Sun, and Moon

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Astronomers

    Phenomenon: An astrophotographer can only take pictures of specific features on the Moon at certain times.    

    Download unit guide

    Abstract artwork depicting a bright sun with blue and orange swirling patterns next to green hills under a sky with shades of blue, orange, and red.
    Ocean, Atmosphere, and Climate

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.    

    Ilustración de un pueblo con casas, campos y montañas bajo un cielo nublado con olas de viento o lluvia.
    Weather Patterns

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Forensic meteorologists

    Phenomenon: In recent years, rainstorms in Galetown have been unusually severe.    

    Download unit guide

    Un oso polar se encuentra sobre un pequeño témpano de hielo en el océano con un sol naranja en el cielo y lejanas montañas heladas al fondo.
    Earth’s Changing Climate

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.    

    Download unit guide

    Abstract geometric design in shades of blue and purple featuring a hexagon with icons of a building, wrench, molecules, sun, paint can, and screwdriver.
    Earth’s Changing Climate Engineering Internship

    Domain: Earth and Space Science

    Unit type: Engineering internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.    

    Abstract art with vibrant colors featuring a yellow silhouette of a person holding a book against a background of geometric shapes, swirling patterns, and bold textures.
    Microbiome

    Domain: Life Science

    Unit type: Launch

    Student role: Microbiological researchers

    Phenomenon: The presence of 100 trillion microorganisms living on and in the human body may keep the body healthy.    

    Abstract artwork of a person's side profile with geometric shapes and colorful patterns flowing from the head, holding a small sledgehammer. A vision chart is visible in the corner.
    Metabolism

    Domain: Life Science

    Unit type: Core

    Student role: Medical researchers

    Phenomenon: Elisa, a young patient, feels tired all the time.    

    Download unit guide

    Orange abstract background with hexagonal shapes featuring icons of a bar chart, plant, safety vest, test tube, peach, and stethoscope.
    Metabolism Engineering Internship

    Domain: Life Science

    Unit type: Engineering internship

    Student role: Food engineers

    Phenomenon: Designing health bars with different molecular compositions can effectively meet the metabolic needs of patients or rescue workers.    

    Imagen que muestra un gráfico de arañas de diferentes colores con patrones distintos de patas y cuerpo, incluidas variaciones de color marrón, amarillo y azul. El fondo es una superficie oscura y texturizada.
    Traits and Reproduction

    Domain: Life Science

    Unit type: Core

    Student role: Biomedical students

    Phenomenon: Darwin’s bark spider offspring have different silk flexibility traits, even though they have the same parents.    

    Download unit guide

    An illustration of a whale with jellyfish and turtles from Amplify Science
    Populations and Resources

    Domain: Life Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in Glacier Sea has increased.    

    Download unit guide

    Low-poly landscape with trees and mushrooms. A fox sniffs the ground, a rabbit sits nearby, and mountains and sun are in the background.
    Matter and Energy in Ecosystems

    Domain: Life Science

    Unit type: Core

    Student role: Ecologists

    Phenomenon: What caused the mysterious crash of a biodome ecosystem?    

    Download unit guide

    Four low-poly dinosaurs with missing body sections are standing in a row; one is yellow, and the others are green. They have purple spikes and red patches on their bodies.
    Natural Selection

    Domain: Life Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The newt population in Oregon State Park has become more poisonous over time.    

    Download unit guide

    Red geometric background with icons including a mosquito, DNA strand, bar chart, and world map inside a hexagon.
    Natural Selection Engineering Internship

    Domain: Life Science

    Unit type: Engineering internship

    Student role: Clinical engineers

    Phenomenon: Designing malaria treatment plans that use different combinations of drugs can reduce drug resistance development while helping malaria patients.  

    Two giant tortoises with long necks stand near water; one tortoise feeds on leaves from a tree while the other is near dense vegetation.
    Evolutionary History

    Domain: Life Science

    Unit type: Core

    Student role: Paleontologists

    Phenomenon: A mystery fossil at the Natural History Museum has similarities with both wolves and whales.    

    Download unit guide

    Two people climbing rocky terrain; illustrations show a hiking boot and a belt with gear.
    Harnessing Human Energy

    Domain: Physical Science

    Unit type: Launch

    Student role: Energy scientists

    Phenomenon: Rescue workers can use their own human kinetic energy to power the electrical devices they use during rescue missions.    

    Illustration of a futuristic space station with large solar panels, orbiting in deep space, emitting a blue glow from its propulsion system.
    Force and Motion

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: The asteroid sample-collecting pod failed to dock at the space station as planned.    

    Download unit guide

    Green geometric background with a hexagonal emblem containing a parachute icon, ruler, bandage, and stacked layers on a gradient pattern.
    Force and Motion Engineering Internship

    Domain: Physical Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Designing emergency supply delivery pods with different structures can maintain the integrity of the supply pods and their contents. 

    Illustration of a roller coaster filled with people, hands raised, going down a steep track against a bright blue sky with clouds.
    Magnetic Fields

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: During a test launch, a spacecraft traveled much faster than expected.    

    Illustration of a person in a red hat and fur-lined coat with eyes closed, surrounded by large orange circles on a dark background.
    Thermal Energy

    Domain: Physical Science

    Unit type: Core

    Student role: Thermal scientists

    Phenomenon: One of two proposed heating systems for Riverdale School will best heat the school.    

    Download unit guide

    Ilustración que muestra las etapas de fusión de una paleta de naranja: entera, parcialmente derretida, más derretida y casi derretida por completo, con palitos de madera, sobre un fondo morado.
    Phase Change

    Domain: Physical Science

    Unit type: Core

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart.    

    Download unit guide

    Green geometric graphic featuring icons: a baby, thermometer, layers, medical alert, and a flame.
    Phase Change Engineering Internship

    Domain: Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different combinations of phase change materials can keep babies at a healthy temperature.    

    Obra de arte digital abstracta que presenta numerosos círculos rojos y grises superpuestos sobre un fondo dividido de azul y violeta claro, creando una composición dinámica y enérgica.
    Chemical Reactions

    Domain: Physical Science

    Unit type: Core

    Student role: Forensic chemists

    Phenomenon: A mysterious brown substance has been detected in the tap water of Westfield.    

    Download unit guide

    An illustration from the Light Waves unit
    Light Waves

    Domain: Physical Science

    Unit type: Core

    Student role: Spectroscopists

    Phenomenon: The rate of skin cancer is higher in Australia than in other parts of the world.    

    Download unit guide

    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.

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    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.

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    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!

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    The middle school science articles serve as sources for evidence collection and were authored by science and literacy experts at the Lawrence Hall of Science.

    Student Investigation Notebooks

    Available for every unit, the Student Investigation Notebooks provide space for students to:

    • record data
    • reflect on ideas from texts and investigations
    • construct explanations and arguments

    Available with full-color article compilations for middle school units

    Digital student experience

    Students access the digital simulations and modeling tools, as well as lesson activities and assessments, through the digital student experience. Students can interact with the digital student experience as they:

    • conduct hands-on investigations
    • engage in active reading and writing activities
    • participate in discussions
    • record observations
    • craft end-of-unit scientific arguments

    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
    • unit and chapter overview documentation
    • differentiation strategies
    • standards alignments
    • in-context professional development

    Hands-on materials kits

    Hands-on learning is at the heart of Amplify Science Florida. Each unit kit contains:

    • consumable and non-consumable hands-on materials
    • print classroom display materials
    • premium print materials for student use (sorting cards, maps, etc.)

    Explore more programs.

    Our programs are designed to support and complement one another. Learn more about our related programs.

    Desmos Math 6–A1 correlations with Carnegie Math Texas

    To view this protected page, enter the password below:



    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.

    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 K

    Topic Opener Numbers 0 to 5

    Topic Opener Numbers 0 to 5Connecting Cubes

    Topic 1: Numbers 0 to 5

    Lesson 1-2 Recognize 1, 2, and 3 in Different ArrangementsSkye’s Style
    Lesson 1-5 Recognize 4 and 5 in Different ArrangementsMatching Groups
    Designing Shoes with Skye
    3-ACT MATH: Set the TableInvestigate: Cafeteria Math

    Topic 3: Numbers 6 to 10

    Lesson 3-2: Read, Make, and Write 6 and 7Moving and Grooving
    Lesson 3-4: Read, Make, and Write 8 and 9Moving and Grooving
    Lesson 3-6: Read, Make, and Write 10Moving and Grooving
    Lesson 3-7: Count Numbers to 10Fingers as Math Tools

    Topic 4: Compare Numbers 0 to 10

    Lesson 4-1: Compare Groups to 10 by MatchingMore, Fewer, or the Same
    Forest Friends
    Lesson 4-2: Compare Numbers Using Numerals to 10Fingers and Counters
    Lesson 4-3: Compare Groups to 10 by CountingComparing Words

    Topic 6: Understand Addition

    Interactive Math StoryInvestigate: Casey’s Town
    Lesson 6-1: Explore AdditionHow Many Objects in Pictures?
    The Bus Depot
    Lesson 6-2: Represent Addition as Adding ToHow Will You Count?
    Lesson 6-3: Represent Addition as Putting TogetherHow Many Objects?
    Lesson 6-4: Represent and Explain Addition with EquationsWhat Does It Mean to Add?

    Topic 7: Understand Subtraction

    Lesson 7-1: Explore SubtractionWhat Does It Mean to Subtract?
    The Bus Depot

    Topic 8: More Addition and Subtraction

    Lesson 8-5: Decompose 6 and 7 to Solve ProblemsHarry Explores the Ocean
    Lesson 8-6: Decompose 8 and 9 to Solve ProblemsHarry Explores the Ocean
    Lesson 8-8: Decompose 10 to Solve ProblemsHarry Explores the Ocean

    Topic 12: Identify and Describe Shapes

    Lesson 12-2: Circles and TrianglesWhat’s That Shape Called?
    Lesson 12-3: Squares and Other RectanglesAnother Shape

    Topic 13: Analyze, Compare, and Create Shapes

    Lesson 13-1: Analyze and Compare Two-Dimensional (2-D) ShapesAnother Shape
    So Much Sorting

    Grade 1

    Topic 1: Understand Addition and Subtraction

    Lesson 1-4: Take FromPacking for a Picnic
    What’s the Difference?
    Lesson 1-7: Change UnknownReplanting Huli
    Lesson 1-8: Practice Adding and SubtractingLeaping Lily Pads!

    Topic 2: Fluently Add and Subtract Within 10

    enVision STEM ProjectA Community Working Together
    Topic 2 Interactive Math StoryInvestigate: Let’s Grow!
    Lesson 2-8: Solve Word Problems with Facts to 10Tutu’s Garden in Maui
    The Kalo Plants
    Helping Others

    Topic 3: Addition Facts to 20: Use Strategies

    Lesson 3-5: Make 10 to AddMaking 10
    Lesson 3-6: Continue to Make 10 to AddKitten Coaster

    Topic 6: Represent and Interpret Data

    Lesson 6-1: Organize Data into Three CategoriesShapes Ying Saw

    Topic 7: Extend the Counting Sequence

    Lesson 7-1: Count by 10s to 120Meeting Yara
    Grade 1 Lesson 7-5: Count on an Open Number LineTime to Line Up!
    Grade 1 Lesson 7-5: Count on an Open Number LineWhat’s That Number?

    Topic 8: Understand Place value

    Lesson 8-1: Make Numbers 11 to 19Same Number, Different Ways
    Lesson 8-2: Numbers Made with TensInvestigate: Game Points
    It’s a Match

    Topic 9: Compare Two-Digit Numbers

    Lesson 9-3: Compare NumbersInvestigate: Where Am I?
    Grade 1 Lesson 9-5: Compare Numbers on a Number LineGreater Than, Less Than, or Equal to
    Grade 1 Lesson 9-5: Compare Numbers on a Number LineIn Full Bloom

    Topic 10: Use Models and Strategies to Add Tens and Ones

    Lesson 10-1: Add Tens Using ModelsHow Many Cubes?
    Boris’s Thimbles
    How Many Tens?

    Topic 11: Use Models and Strategies to Subtract Tens

    Lesson 11-1: Subtract Tens Using ModelsBoris’s Thimbles
    Lesson 11-2: Subtract Tens Using a Hundred ChartHow Many Tens?

    Topic 14: Reason with Shapes and Their Attributes

    Lesson 14-1: Use Attributes to Define Two-Dimensional (2-D) ShapesShapes Ying Saw

    Grade 2

    Topic 1: Fluently Add and Subtract Within 20

    Lesson 1-1: Addition Fact StrategiesExploring Within 10
    Lesson 1-3: Make a 10 to AddWays to Make 10

    Topic 8: Work with Time and Money

    Lesson 8-1: Solve Problems with CoinsInvestigate: Activities at the Block Party
    Discovering Coins (Part 1)
    Discovering Coins (Part 2)
    Lesson 8-2: Continue to Solve Problems with CoinsHow Much Money?
    Discovering Coins (Part 2)
    Lesson 8-5: Problem Solving: ReasoningThe Toy Stand
    The Craft Stand at the Block Party

    Topic 12: Measuring Length

    Lesson 12-8: Compare LengthsLengths of Jungle Animals

    Topic 15: Graphs and Data

    Lesson 15-1: Line PlotsMessy Measurements
    Lesson 15-2: More Line PlotsBracelets and Wristbands
    Lesson 15-3: Bar GraphsAwesome Aquariums

    Grade 3

    Topic 1: Understand Multiplication and Division of Whole Numbers

    Lesson 1-1: Relate Multiplication and AdditionEqual Groups
    Lesson 1-3: Arrays and PropertiesArrays of Flavor

    Topic 4: Use Multiplication to Divide: Division Facts

    Lesson 4-1: Relate Multiplication and DivisionIt’s Chili in Here
    Relating Quotients to Familiar Products
    Lesson 4-8: Solve Multiplication and Division EquationsDivision and Multiplication Equations

    Topic 6: Connect Area to Multiplication and Addition

    Lesson 6-1: Cover RegionsInvestigate: Comparing Rugs
    Which Covers More Space?
    Lesson 6-2: Area: Nonstandard UnitsTiling Figures
    Lesson 6-3: Area: Standard UnitsArea Hunt
    Lesson 6-4: Area of Squares and RectanglesRectangles and Arrays

    Topic 7: Represent and Interpret Data

    Lesson 7-3: Make Bar GraphsPuppy Pile
    2, 5, or 10?

    Topic 8: Use Strategies and Properties to Add and Subtract

    Topic 8 VocabularyInvestigate: Create a Photo Gallery
    Lesson 8-2: Algebra: Addition PatternsPanda Patterns
    Lesson 8-3: Mental Math: AdditionHow Would You Solve It?

    Topic 9: Fluently Add and Subtract within 1,000

    Lesson 9-1: Use Partial Sums to AddAdding Your Way
    What is an Algorithm?
    Lesson 9-2: Use Regrouping to AddUsing Fewer Digits
    Lesson 9-3: Add 3 or More NumbersDetermining Sums of 2 or More Addends
    Lesson 9-6: Use Strategies to Add and SubtractAdding Strategically

    Grade 4

    Topic 7: Factors and Multiples

    3-ACT MATH: Can-Do AttitudeHamster Homes
    Lesson 7-2: FactorsFactor or Multiple?
    Lesson 7-4: Prime and Composite NumbersA Number Game
    Lesson 7-5: MultiplesFactor or Multiple?
    How Does It Grow?

    Topic 8: Extend Understanding of Fraction Equivalence and Ordering

    Lesson 8-2: Equivalent Fractions: Number LinesInvestigate: Building Your Own Number Line
    All Kinds of Fractions
    Lesson 8-5: Use Benchmarks to Compare FractionsFraction Strips
    Lesson 8-5: Use Benchmarks to Compare FractionsChop It

    Topic 9: Understand Addition and Subtraction of Fractions

    Lesson 9-1: Model Addition of FractionsPizza Problems
    Lesson 9-4: Model Subtraction of FractionsPizza Problems
    Lesson 9-2: Decompose FractionsMath Pizzeria

    Topic 10: Extend Multiplication Concepts to Fractions

    Lesson 10-1: Fractions as Multiples of Unit FractionsEqual Groups of Fractions

    Topic 12: Understand and Compare Decimals

    Topic 12 Review What You KnowInvestigate: Different Units
    Lesson 12-1: Fractions and DecimalsA New Way to Write Tenths
    A New Way to Write Hundredths
    Lesson 12-2: Fractions and Decimals on the Number LineAre They Equivalent?
    What’s the Order?
    Lesson 12-3: Compare DecimalsHow Can You Compare?
    Robot Factory

    Grade 5

    Topic 3: Fluently Multiply Multi-Digit Whole Numbers

    Lesson 3-5: Multiply 3-Digit by 2-Digit NumbersPartial Products Everywhere
    Lesson 3-7: Practice Multiplying Multi-Digit NumbersHow Do They Compare?

    Topic 5: Use Models and Strategies to Divide Whole Numbers

    Lesson 5-4: Use Partial Quotients to DivideEmptying the Water Tank

    Topic 8: Apply Understanding of Multiplication to Multiply Fractions

    Lesson 8-3: Multiply Fractions and Whole NumbersMaking Food
    Lesson 8-4: Use Models to Multiply Two FractionsInvestigate: Folding Paper
    Parts of Parts
    One Part of One Part
    Lesson 8-5: Multiply Two FractionsMaking Food
    Messy Multiplication
    Lesson 8-6: Area of a RectangleInstalling Turf
    Rows and Columns
    Lesson 8-7: Multiply Mixed NumbersApplying Fraction Multiplication
    Messy Multiplication
    Lesson 8-8: Multiplication as ScalingChores at Animal Haven
    The Re-size-inator

    Topic 9: Apply Understanding of Division to Divide Fractions

    Topic 11: Understand Volume Concepts

    Lesson 11-1: Model VolumeWhich is Largest
    3-ACT Math: Fill ‘er UpPacking the Barge
    Lesson 11-3: Combine Volumes of PrismsPutting It Together
    Figures Made of Prisms

    Algebra 1

    No lessons focused on only shape patterns.

    Topic 1: Solving Equations and Inequalities

    Lesson 1-2: Solving Linear EquationsWorking Backwards
    Solving Strategies
    Lesson 1-3: Solving Linear Equations With a Variable on Both SidesSame Position
    Lesson 1-4: Literal Equations & FormulasSubway Seats
    Various Variables
    Lesson 1-5: Solving Inequalities in One VariablePizza Delivery

    Topic 2: Linear Equations

    Lesson 2-3: Standard FormShelley the Snail
    Five Representations

    Topic 3: Linear Functions

    Lesson 3-4: Arithmetic SequenceMore Visual Patterns
    Sequence Carnival
    Lesson 3-5: Scatter Plots and Lines of FitCorrelation Coefficient
    How Hot Is It?
    City Slopes
    Lesson 3-6: Analyzing Lines of FitResidual Fruit
    Penguin Populations
    Behind the Headlines
    City Data

    Topic 4: Systems of Linear Equations and Inequalities

    Lesson 4-1: Solving Systems of Linear 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 FunctionsCraft-a-Graph
    Pumpkin Prices

    Topic 6: Exponents and Exponential Functions

    Lesson 6-3: Exponential FunctionsCarlos’s Fish
    Lesson 6-5: Geometric SequencesRevisiting Visual Patterns, Part 1
    Sequence Carnival
    More Visual Patterns

    Topic 8: Quadratic Functions

    Lesson 8-1: Key Features of a Quadratic FunctionRevisiting Visual Patterns, Part 1
    Quadratic Visual Patterns
    On the Fence
    Lesson 8-3: Quadratic Functions in Standard FormPlenty of Parabolas
    Two for One
    Lesson 8-4: Modeling with Quadratic FunctionsStomp Rockets
    Robot Launch
    Lesson 8-5: Linear, Exponential and Quadratic ModelsSorting Relationships

    Topic 9: Solving Quadratic Equations

    Lesson 9-1: Solving Quadratics Using Graphs and TablesStomp Rockets
    Lesson 9-2: Solving Quadratic Equations by FactoringParabola Zapper
    Shooting Stars
    Lesson 9-4: Completing the SquareSquare Tactic
    Lesson 9-5: The Quadratic Formula and the DiscriminantStomp Rockets in Space

    Topic 10: Working with Functions

    Lesson 10-1: The Square Root Function ( & average rate of change)Plane, Train, and Automobile
    Lesson 10-3: Analyzing Functions Graphically (Abs, Quad, Sq.Root, Exp, Cubic)Craft-a-Graph
    Detroit’s Population, Part 1
    Detroit’s Population, Part 2
    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.

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    2023

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    2020

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    Dyscalculia: What educators should know

    Two children seated at a table engage with colorful number cubes and a pencil beside a worksheet—a delightful way to explore math. This playful setup subtly acts as an informal dyscalculia screener, helping spot characteristics of dyscalculia in young learners.

    Some kids love math. Some kids like math. Some kids struggle with math, or struggle with math anxiety. And some kids have dyscalculia, a specific learning disorder that affects one’s ability to understand numbers and learn math facts.

    As awareness has continued to grow, educators today are curious to know: What are the characteristics of dyscalculia? How can I help a child with dyscalculia? What should I know about dyscalculia screeners? We’re here to provide some answers.

    Dyscalculia: What it is and is not

    According to the Child Mind Institute, dyscalculia (sometimes called “developmental dyscalculia”) is a term used to describe specific learning disabilities that affect a child’s ability to understand, learn, and perform math and number-based operations.

    Honora Wall, Ed.D., founder of the Dyscalculia Training and Research Institute, calls it “a type of neurodivergence: A difference in brain development or function.”

    That’s an important distinction: Dyscalculia is a neurological condition that affects numerical cognition and processing. It has nothing to do with being “bad at math” or not “trying hard enough.”
    Between 5 and 7% of elementary school-aged children may have dyscalculia, which is believed to affect girls and boys equally.

    It is important to note that not all difficulties in math are caused by dyscalculia. Dyslexia, ADHD, and other conditions can also pose challenges for math students.

    Nor is dyscalculia simply “math dyslexia.” Dyscalculia and dyslexia are entirely separate learning disorders that affect different areas of cognition and involve distinct difficulties.

    How dyscalculia might present itself

    Dyscalculia manifests in various ways in the math classroom. Here are some examples of how it can appear:

    • When engaging in activities like games involving dice, students may need to count the individual dots to recognize a number rolled, rather than intuitively recognizing it.
    • Students might have difficulty connecting the numerical symbol “5” (for example) to the word “five.” Making this connection is essential for associating numbers with their meanings.
    • Students may be delayed in learning to count, or lose track or rely on visual aids (like their fingers) when they count.

    Such students may also have a hard time:

    • Solving math problems.
    • Recognizing or creating patterns.
    • Learning basic math functions.
    • Estimating how long a task will take.
    • Processing visual-spatial ideas such as charts and graphs, or even telling left from right.
    • Remembering phone numbers or zip codes.
    • Playing games that involve counting or keeping score.
    • Telling time.

    The connection between mathematics anxiety and dyscalculia

    Math anxiety is an emotional response to math that presents as apprehension or fear. Some call it mathematics phobia. It may include physical symptoms such as sweating, rapid heartbeat, shortness of breath, and other physical symptoms of anxiety. It’s similar to other types of anxiety, but it’s exclusive to math.

    But, most important in this context, it’s not itself a neurological or cognitive condition.

    So dyscalculia and math anxiety are not the same, but they may go hand in hand—perhaps with one exacerbating the other. Students with dyscalculia might develop math anxiety due to repeated challenges and frustrations in learning math.

    Understanding this connection—and working to alleviate math anxiety—is crucial for educators aiming to create a supportive learning environment.

    Tips for assisting students with dyscalculia

    Here are some practical strategies educators can use to support students with dyscalculia:

    • Teach positive self-talk and persistence: Encourage students to develop a “growth mindset,” reinforcing that effort and persistence (as well as making mistakes) are essential to overcoming challenges.
    • Provide organizational aids: Use graph paper to help students line up numbers correctly, which aids in precision during calculations.
    • Use manipulatives: Tools like counters and blocks can make math feel more tangible, helping students grasp abstract concepts.
    • Focus on singular tasks: Present one math problem at a time to prevent students from feeling overwhelmed and allow for focused attention.
    • Allow more time: Give students the opportunity to work at their own pace, acknowledging that they may need more time to process numerical information.
    • Grant calculator access: Allowing calculators can reduce stress and help students solve problems more efficiently.
    • Make math fun and engaging: Incorporate interactive platforms such as Desmos Classroom to create an enjoyable and interactive learning experience.

    More to explore

    Welcome, Idaho K-8 Science Reviewers!

    Thank you for taking the time to review Amplify Science. On this site, you’ll find all the resources you need to learn more about this engaging and robust NGSS program. Below, you will also have the opportunity experience our program firsthand with a demo account to access the digital platform.

    Amplify Science for grades K–8 has been rated all-green by EdReports. Read the review on EdReports.

    Collage of educational settings: top left, two young girls using laptop in library; bottom right, middle school science project display on tablet; bottom left, two boys with tablet discussing.

    Overview

    With Amplify Science, students don’t just passively learn about science concepts. Instead, they take on the roles of scientists and engineers to actively investigate and make sense of real-world phenomena. They do this through a blend of cohesive and compelling storylines, hands-on investigations, collaborative discussions, literacy-rich activities, and interactive digital tools.

    Listen to these educators share how the program empowers students to think, read, write, and argue like real scientists and engineers every day.

    Grades K–5

    Grades 6–8

    Amplify Science Grades K-5 Tour for Idaho Educators

    Amplify Science Grades 6-8 Tour for Idaho Evaluators

    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, students build and deepen their understanding, increasing their ability to develop and refine 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 program to address 100 percent of the NGSS and Idaho Standards in fewer days than other programs:

    • In just 120 lessons at grades 6–8
    • In just 66 lessons at grades K–2
    • In just 88 lessons at grades 3–5
    A four-step process diagram with icons: spark a real-world problem, explore sources, explain and elaborate, and evaluate claims, all linking to engage with cohesive storylines.

    Unit types

    Each unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, while also emphasizing a particular science and engineering practice.

    A laptop and two screens display educational content about ecosystems, featuring illustrated plants, animals, and experiments with colorful liquids.
    Two young students sit at a classroom table, one holding up a clear cup of water while the other observes closely. Papers and pencils are spread out on the table.

    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.

    Two children play an educational board game at a table with worksheets, plastic cubes, and small containers of colored items.

    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.

    Two children sitting at a table with laptops are talking to each other in a classroom setting, with books and baskets in the background.

    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.

    Several open textbooks and notebooks are spread out on a table as a person writes in one of the notebooks with a pencil.

    Argumentation units

    Argumentation units are introduced at grade 3 and provide students with regular opportunities to explore and discuss available evidence, time and support to consider how evidence may be leveraged in support of claims, and independence that increases as they mount written arguments in support of their claims.

    A person points to a photo in a textbook about coral reefs, with a laptop and notebook open on the desk.

    Launch units

    Launch units are the first units taught in each year of Amplify Science. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

    Three students at a classroom table examine a sealed plastic bag with food inside, while one looks surprised; another student stands in the background.

    Core units

    Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

    Four students sit at a table using laptops, focused on their screens in a classroom setting with one student in the background.

    Engineering Internship units

    Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

    Idaho Science Standards Alignment

    Amplify Science was built from the ground up to fully embrace the instructional shifts outlined in A Framework for K-12 Science Education (2012), the same framework on which Idaho Science Content Standards were founded. Most grade levels’ respective set of Amplify Science units therefore fully address the necessary Idaho Science Content Standards (see correlation). Grade 1 teachers should plan to also use the companion mini-lesson provided below to achieve full standards coverage for their grade.

    Grade 1 Companion

    Standard: 1-LS-1.3 Use classification supported by evidence to differentiate between living and non-living things.

    Recommended placement: Following Lesson 1.1 of the Animal and Plant Defenses unit.

    Resources: Classroom Slides

    Science (K-2) Evaluation Form

    Science (3-5) Evaluation Form

    Science (Middle School Physical Science) Evaluation Form

    Science (Middle School Life Science) Evaluation Form

    Science Evaluation Form Middle School Earth and Space Science

    A boy sits on the floor reading a book to a girl beside him in a classroom setting.
    A butterfly flies above potted plants next to a watering can and a caterpillar on a milkweed plant under sunlight in a grassy field.

    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.  

    A hand pulls a white string attached to a pegboard with rubber bands and a white ball hanging from the center.

    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.  

    Silhouette of a playground structure and toy train against a blue sky with clouds and two large 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.  

    Illustration of sea turtles swimming among underwater plants, with a shark and another turtle visible 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.  

    A hand holds a flashlight and shines it through a transparent sheet with an image, projecting the image onto a wall in a dark room.

    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.  

    A split illustration shows a cityscape at night with a crescent moon and stars on the left, and a cityscape during the day with the sun, clouds, and an airplane on the right.

    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.  

    A grey elephant uses its trunk to pick apples from a tree, with a few apples still hanging on the branches and a small sprout growing nearby.

    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.  

    A hand picks up a red bean from a table scattered with more red beans, spilled white liquid, a cup, and a wooden stick.

    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.  

    A building labeled "Recreation Center" stands near a cliff edge with a blue flag, surrounded by trees and overlooking a beach and water.

    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.  

    Illustration of a high-speed train traveling on an elevated track with a green landscape and blue sky in the background.

    Balancing Forces

    Domain: Physical Science

    Unit type: Modeling

    Student role: Engineers

    Phenomenon: The town of Faraday is getting a new train that floats above its tracks.  

    A group of wolves stands in the foreground, with a bear, elk, and several birds visible in a grassy, hilly landscape with scattered trees.

    Inheritance and Traits

    strong>Domain: Life Science

    Unit type: Investigation

    Student role: Wildlife biologists

    Phenomenon: An adopted wolf in Graystone National Park (“Wolf 44”) has some traits that appear similar to one wolf pack in the park and other traits that appear to be similar to a different wolf pack. 

    A small bird stands on soil, looking closely at a yellow snail, with green blades of grass on the left and a blue sky background.

    Environments and Survival

    Domains: Life Science, Engineering Design

    Unit type: Engineering design

    Student role: Biomimicry engineers

    Phenomenon: Over the last 10 years, a population of grove snails has changed: The number of grove snails with yellow shells has decreased, while the number of snails with banded shells has increased.  

    An orangutan hangs from a vine in a dense green forest with the sun visible in the background.

    Weather and Climate

    Domains: Earth and Space Science, Engineering Design

    Unit type: Argumentation

    Student role: Meteorologists

    Phenomenon: Three different islands, each a contender for becoming an Orangutan reserve, experience different weather patterns.  

    Illustration of city buildings at night with illuminated windows, a full moon, visible stars, and a silhouetted figure in one window.

    Energy Conversions

    Domains: Physical Science, Earth and Space Science, Engineering Design

    Unit type: Engineering design

    Student role: System engineers

    Phenomenon: The fictional town of Ergstown experiences frequent blackouts.  

    A streetlamp illuminates a cricket, which is watched by a gecko. Yellow arrows indicate the flow of light from the lamp to the cricket and then to the gecko’s eye.

    Vision and Light

    Domain: Physical Science, Life Science, Engineering Design

    Unit type: Investigation

    Student role: Conservation biologists

    Phenomenon: The population of Tokay geckos in a rain forest in the Philippines has decreased since the installation of new highway lights.  

    Two dolphins swimming underwater, facing each other against a blue background.

    Waves, Energy, and Information

    Domains: Physical Science, Life Science, Earth and Space Science, Engineering Design

    Unit type: Modeling

    Student role: Marine scientists

    Phenomenon: Mother dolphins in the fictional Blue Bay National Park seem to be communicating with their calves when they are separated at a distance underwater.

    Earth orbits the Sun in space, with dotted blue lines showing the orbital path and a white arrow indicating Earth's rotation direction.

    Patterns of Earth and Sky

    Domains: Physical Science, Earth and Space Science

    Unit type: Investigation

    Student role: Astronomers

    Phenomenon: An ancient artifact depicts what we see in the sky at different times — the sun during the daytime and different stars during the nighttime — but it is missing a piece.  

    Illustration of layered red and brown rocky cliffs beside a flowing blue river under a partly cloudy sky.

    Earth’s Features

    Domain: Earth and Space Science

    Unit type: Argumentation

    Student role: Geologists

    Phenomenon: A mysterious fossil is discovered in a canyon within the fictional Desert Rocks National Park.  

    Red blood cells scattered across a dynamic, abstract red and white background.

    Modeling Matter

    Domain: Physical Science

    Unit type: Modeling

    Student role: Food scientists

    Phenomenon: Chromatography is a process for separating mixtures. Some solids dissolve in a salad dressing while others do not. Oil and vinegar appear to separate when mixed in a salad dressing.  

    Illustration of wind carrying airborne particles over a coastal hill, with arrows indicating the movement up and over the hill toward the sea.

    The Earth System

    Domains: Earth and Space Science, Physical Science, Engineering Design

    Unit type: Engineering Design

    Student role: Water resource engineers

    Phenomenon: East Ferris, a city on one side of the fictional Ferris Island, is experiencing a water shortage, while West Ferris is not. 

    Illustration of a cheetah standing near plants, looking at a sloth hanging from a tree branch, with various foliage and mushrooms in the scene.

    Ecosystem Restoration

    Domains:Physical Science, Life Science, Earth and Space Science, Engineering Design

    Unit type: Argumentation

    Student role: Ecologists

    Phenomenon: The jaguars, sloths, and cecropia trees in a reforested section of a Costa Rican rain forest are not growing and thriving.  

    A rover stands on a rocky, reddish terrain with visible tire tracks leading to it; distant hills are seen under a hazy sky.

    Geology on Mars

    Domain: Earth and Space Science

    Unit type: Launch

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable.  

    Illustration of a city skyline at night with a large full moon, a few stars in the sky, and a bridge on the left side.

    Earth, Moon, and Sun

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Astronomers

    Phenomenon: An astrophotographer can only take pictures of specific features on the Moon at certain times.  

    Illustration of a person wearing a red hat and winter coat with fur hood, eyes closed and arms crossed, surrounded by large orange circles.

    Thermal Energy

    Domain: Physical Science

    Unit type: Core

    Student role: Thermal scientists

    Phenomenon: One of two proposed heating systems for Riverdale School will best heat the school.  

    Abstract digital artwork featuring a large yellow sun with blue and orange rays over a colorful landscape with green hills and red horizon.

    Ocean, Atmosphere, and Climate

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.  

    Illustration of clouds above a small town with fields and mountains, showing wind patterns and atmospheric movement in the sky.

    Weather Patterns

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Forensic meteorologists

    Phenomenon: In recent years, rainstorms in Galetown have been unusually severe.  

    An underwater scene with a large whale, several turtles, jellyfish, and fish swimming surrounded by shafts of light.

    Populations and Resources

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in Glacier Sea has increased.  

    Low-poly illustration of a forest with trees, mushrooms, a rabbit, and a fox catching another animal under a blue sky with mountains and the sun in the background.

    Matter and Energy in Ecosystems

    Domains: Life Science, Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Ecologists

    Phenomenon: The biodome ecosystem has collapsed.

    Illustration of six spiders with different colored bodies and legs arranged in a chart-like formation on a dark background.

    Traits and Reproduction

    Domain: Life Science

    Unit type: Core

    Student role: Biomedical students

    Phenomenon: Darwin’s bark spider offspring have different silk flexibility traits, even though they have the same parents.  

    Abstract digital artwork featuring vibrant colors, geometric shapes, a yellow human silhouette, and various patterns layered together.

    Microbiome

    Domain: Life Science

    Unit type: Launch

    Student role: Microbiological researchers

    Phenomenon: The presence of 100 trillion microorganisms living on and in the human body may keep the body healthy.  

    Illustration of a person receiving an oral examination with a tongue depressor and light, featuring abstract colorful shapes and an eye chart in the background.

    Metabolism

    Domain: Life Science

    Unit type: Core

    Student role: Medical researchers

    Phenomenon: Elisa, a young patient, feels tired all the time. 

    A spacecraft approaches a large modular space station with blue solar panels, orbiting in outer space against a black background.

    Force and Motion

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: The asteroid sample-collecting pod failed to dock at the space station as planned.

    Green geometric background with a hexagonal badge displaying a parachute, ruler, letter A, stacked layers, bandage, and a folded paper icon.

    Force and Motion Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Designing emergency supply delivery pods with different structures can maintain the integrity of the supply pods and their contents.  

    Two prehistoric aquatic reptiles with long snouts swim near the shore of a tropical landscape with rocks, plants, and an island in the distance.

    Plate Motion

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean, even though the Mesosaurus species once lived all together.  

    Illustration of a volcanic landscape with mountains, trees, an ocean, and a cross-section showing tectonic plates beneath the surface.

    Rock Transformations

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.  

    Four low-poly dinosaurs, three green and one yellow, are walking in a row on grass with rocks and red spots on their bodies under a blue sky.

    Natural Selection

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The newt population in Oregon State Park has become more poisonous over time.  

    Two large tortoises are near a river; one is on the riverbank reaching for leaves on a tree, while the other is on the opposite bank among grass and trees.

    Evolutionary History

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Paleontologists

    Phenomenon: A mystery fossil at the Natural History Museum has similarities with both wolves and whales.    

    Two people stand atop rocky terrain littered with electronic devices; inset illustrations show a boot, a person with electronics in a vest, and a radio.

    Harnessing Human Energy

    Domains: Physical Science, Earth and Space Science, Engineering Design

    Unit type: Launch

    Student role: Energy scientists

    Phenomenon: Rescue workers can use their own human kinetic energy to power the electrical devices they use during rescue missions.  

    An orange popsicle melting in four stages from solid to almost fully liquid, set against a plain background.

    Phase Change

    Domains: Physical Science, Earth and Space Science

    Unit type: Core

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart.  

    Green graphic with icons showing a swaddled baby, a thermometer, layers of blankets, a medical symbol, and a heat source within a hexagonal frame.

    Phase Change Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different combinations of phase change materials can keep babies at a healthy temperature.  

    Digital illustration showing red and blue molecule-like circles on a blue background, with a boundary dividing two differently shaded sides.

    Chemical Reactions

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Forensic chemists

    Phenomenon: A mysterious brown substance has been detected in the tap water of Westfield.  

    Illustration of people riding a roller coaster on a blue day, with arms raised as the car descends a tall loop against a sky with clouds.

    Magnetic Fields

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: During a test launch, a spacecraft traveled much faster than expected.  

    Illustration of the Earth with arrows representing radiation or energy entering the atmosphere from space over the Asia-Pacific region.

    Light Waves

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Spectroscopists

    Phenomenon: The rate of skin cancer is higher in Australia than in other parts of the world.  

    An illustrated polar bear stands on a small piece of floating ice in the ocean, with icebergs and an orange sun in the background.

    Earth’s Changing Climate

    Domains: Earth and Space Science, Life Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.

    Hexagonal badge with icons including a wrench, building, sun, molecules, construction materials, screwdriver, paint bucket, and a letter T, all on a geometric blue background.

    Earth’s Changing Climate Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.  

    Access program

    In addition to the grade-level sample boxes that we provided, we’ve also created custom demo accounts just for Idaho reviewers.

    To access the digital portion of the program, click the link below, select “Log In with Amplify,” and then refer to the Start here digital access flyer for your personalized login credentials.

    A spiral-bound teacher’s guide and a laptop displaying a digital curriculum, both titled “Balancing Forces: Investigating Floating Trains” from Amplify Science.

    Resources

    Welcome, Ohio educators!

    Designed from the ground up to teach students to think, read, write, and argue like real scientists and engineers, Amplify Science combines literacy-rich activities with hands-on learning and digital tools to engage students in exploring compelling phenomena in every unit.

    Students in a classroom interact with educational technology, featuring a diagram and charts on a screen, while working collaboratively on a laptop.

    Overview

    Developed by UC Berkeley’s Lawrence Hall of Science, our program features:

    • phenomena-based approach where students construct a more complex understanding of each unit’s anchor phenomenon.
    • A blend of cohesive storylines, hands-on investigations, rich discussions, literacy-rich activities, and digital tools.
    • Newly crafted units, chapters, lessons, and activities designed to deliver true 3-dimensional learning.
    • An instructional design that supports all learners in accessing all standards.

    Approach to literacy

    Two young children sit at a classroom table reading a book together, with educational materials spread out in front of them.

    [Video] Literacy in action (K–5)

    Watch students use scientific text to obtain information and practice reading skills, while using writing prompts to create arguments using evidence.

    A student sits at a desk writing with a pencil while focused on his work, with classroom materials visible in the background.

    [Video] Literacy in action (6–8)

    Watch students use scientific text to obtain information and practice reading skills, while using writing prompts to create arguments using evidence.

    A teacher in a green shirt helps a young student with writing at a classroom table, with other students and large numbers visible on the wall in the background.

    Literacy-rich science instruction (K–5)

    Immersing young students in reading, writing, and arguing like real scientists and engineers.

    Two students sit at a table in a classroom, working on an assignment together. Other students are also seated and appear to be engaged in their work. Papers and books are spread out on the tables.

    Active Reading in grades 6–8

    Engaging middle school students in complex science texts.

    Elementary school

    Get started by watching this class share what they’re figuring out with Amplify Science. >

    In Grades K–3 we recommend the national grade level units of Amplify Science to provide students with the appropriate grade level literacy and background knowledge. Individual units are available to purchase.

    When you’re ready:

    1. Find a summary of each unit below including each unit’s student role and anchor phenomenon.
    2. Download some helpful resources to support your review.
    3. Explore the digital Teacher’s Guide by clicking the orange “Review now” button.
    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.

    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.

    Silueta de una estructura de parque infantil contra un cielo azul con nubes y tres soles amarillos.

    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.

    Illustration of sea turtles swimming among seaweed in the ocean, with a large shark in the background.

    Unit 1

    Animal and Plant Defenses

    Student role: Marine scientists

    Phenomenon: Spruce the Sea Turtle will soon be released back into the ocean, where she will survive despite predators.

    An illustration from the Light and Sound unit

    Unit 2

    Light and Sound

    Student role: Light and sound engineers

    Phenomenon: A puppet show company uses light and sound to depict realistic scenes in puppet shows.

    An illustration from the Spinning Earth unit

    Unit 3

    Spinning Earth

    Student role: Sky scientists

    Phenomenon: The sky looks different to Sai and his grandma when they talk on the phone at night.

    An elephant standing next to a tree uses its trunk to pick a fruit from a branch while more fruit hangs above.

    Unit 1

    Plant and Animal Relationships

    Student role: Plant scientists

    Phenomenon: No new chalta trees are growing in the fictional Bengal Tiger Reserve in India.

    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.

    Unit 2

    Properties of Materials

    Student role: Glue engineers

    Phenomenon: Different glue recipes result in glues that have different properties.

    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.

    Unit 3

    Changing Landforms

    Student role: Geologists

    Phenomenon: The cliff on which Oceanside Recreation Center is situated appears to be receding.

    Una ilustración de un tren de alta velocidad moderno y aerodinámico que viaja por una vía elevada con un paisaje verde de fondo.

    Unit 1

    Balancing Forces

    Student role: Engineers

    Phenomenon: The fictional town of Faraday is getting a new train. Unlike typical trains, this one floats, which is causing some concern among the town’s citizens.

    An illustration from the Inheritance and Traits unit

    Unit 2

    Inheritance and Traits

    Student role: Wildlife biologists

    Phenomenon: An adopted wolf in Graystone National Park has some traits in common with one wolf pack in the park and other traits in common with a different pack.

    An illustration from the Environments and Survival unit

    Unit 3

    Environments and Survival

    Student role: Biomimicry engineers

    Phenomenon: Over 10 years, a population of grove snails has changed. Populations with yellow shells have decreased, while those with banded shells have increased.

    An illustration from the Weather and Climate unit

    Unit 4

    Weather and Climate

    Student role: Meteorologists

    Phenomenon: Three different islands, each a contender for becoming an orangutan reserve, experience different weather patterns.

    An illustration from the Energy Conversions unit

    Unit 1

    Energy Conversions

    Student role: System engineers

    Phenomenon: The fictional town of Ergstown experiences frequent blackouts. Their electrical system seems to be failing.

    An illustration from the Earth's Features unit

    Unit 2

    Earth’s Features

    Student role: Geologists

    Phenomenon: A mysterious fossil is discovered in a canyon within the fictional Desert Rocks National Park.

    An illustration from the Modeling Matter unit

    Unit 3

    Modeling Matter

    Student role: Food scientists

    Phenomenon: Some ingredients dissolve in a salad dressing while others, like oil and vinegar, appear to separate.

    An illustration from the Earth System unit

    Unit 4

    The Earth System

    Student role: Water resource engineers

    Phenomenon: East Ferris, a city on one side of the fictional Ferris Island, is experiencing a water shortage, while West Ferris is not.

    An illustration from the Patterns of Earth and Sky unit

    Unit 1

    Patterns of Earth and Sky

    Student role: Astronomers

    Phenomenon: An ancient artifact depicts what we see in the sky at different times of the day, but it appears to be missing a piece.

    An illustration from the Vision and Light unit

    Unit 2

    Vision and Light

    Student role: Conservation biologists

    Phenomenon: The population of Tokay geckos in a rain forest in the Philippines has decreased since the installation of new highway lights.

    An illustration from the Waves, Energy, and Information unit

    Unit 3

    Waves, Energy, and Information

    Student role: Marine scientists

    Phenomenon: Mother dolphins in the fictional Blue Bay National Park communicate with their calves despite the distance between them.

    An illustration from the Ecosystem Restoration unit

    Unit 4

    Ecosystem Restoration

    Student role: Ecologists

    Phenomenon: The jaguars, sloths, and cecropia trees in a reforested section of a Costa Rican rain forest are not growing or thriving.

    Middle school

    When you’re ready:

    1. Find a summary of each unit below including each unit’s student role and anchor phenomenon.
    2. Download some helpful resources to support your review.
    3. Explore the digital Teacher’s Guide by clicking the orange “Review now” button.
    Illustration of a cross-section of Earth showing a volcano near the ocean. Trees, mountains, and clouds are visible above, with subterranean layers below.

    CORE

    Rock Transformations

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.

    Ilustración que muestra las etapas de fusión de una paleta de naranja: entera, parcialmente derretida, más derretida y casi derretida por completo, con palitos de madera, sobre un fondo morado.

    CORE

    Phase Change

    Domains: Physical Science, Earth and Space Science

    Unit type: Core

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart.

    Green geometric graphic featuring icons: a baby, thermometer, layers, medical alert, and a flame.

    ENGINEERING INTERNSHIP

    Phase Change Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different combinations of phase change materials can keep babies at a healthy temperature.

    Illustration of a person in a red hat and fur-lined coat with eyes closed, surrounded by large orange circles on a dark background.

    CORE

    Thermal Energy

    Domain: Physical Science

    Unit type: Core

    Student role: Thermal scientists

    Phenomenon: One of two proposed heating systems for Riverdale School will best heat the school.

    Abstract art with vibrant colors featuring a yellow silhouette of a person holding a book against a background of geometric shapes, swirling patterns, and bold textures.

    LAUNCH

    Microbiome

    Domain: Life Science

    Unit type: Launch

    Student role: Microbiological researchers

    Phenomenon: The presence of 100 trillion microorganisms living on and in the human body may keep the body healthy.

    Abstract artwork of a person's side profile with geometric shapes and colorful patterns flowing from the head, holding a small sledgehammer. A vision chart is visible in the corner.

    CORE

    Metabolism

    Domain: Life Science

    Unit type: Core

    Student role: Medical researchers

    Phenomenon: Elisa, a young patient, feels tired all the time.

    Orange abstract background with hexagonal shapes featuring icons of a bar chart, plant, safety vest, test tube, peach, and stethoscope.

    ENGINEERING INTERNSHIP

    Metabolism Engineering Internship

    Domains: Life Science, Engineering Design

    Unit type: Engineering internship

    Student role: Food engineers

    Phenomenon: Designing health bars with different molecular compositions can effectively meet the metabolic needs of patients or rescue workers.

    Two people climbing rocky terrain; illustrations show a hiking boot and a belt with gear.

    LAUNCH

    Harnessing Human Energy

    Domains: Physical Science, Earth and Space Science, Engineering Design

    Unit type: Launch

    Student role: Energy scientists

    Phenomenon: Rescue workers can use their own human kinetic energy to power the electrical devices they use during rescue missions.

    A girl runs with a colorful kite displaying literacy skills; text reads "Amplify. Science of Reading: A Primer | Part One" on a grassy landscape background.

    CODING SCIENCE INTERNSHIP

    Coding Science Internship: Coral Restoration (Optional)

    Domains: Life Science, Coding Science

    Unit type: Coding Science Internship

    Student role: Coding science interns

    Phenomenon: Implementing a restoration project to improve the health of coral reef populations in Hawaii.

    Abstract artwork depicting a bright sun with blue and orange swirling patterns next to green hills under a sky with shades of blue, orange, and red.

    CORE

    Ocean, Atmosphere, and Climate

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.

    An illustration from the Weather Patterns unit

    CORE

    Weather Patterns

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Forensic meteorologists

    Phenomenon: In recent years, rainstorms in Galetown have been unusually severe.

    An illustration from the Earth's Changing Climate unit

    CORE

    Earth’s Changing Climate

    Domains: Earth and Space Science, Life Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.

    Abstract geometric design in shades of blue and purple featuring a hexagon with icons of a building, wrench, molecules, sun, paint can, and screwdriver.

    ENGINEERING INTERNSHIP

    Earth’s Changing Climate Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.

    A city skyline at night with a prominent full moon, stars in the sky, and a bridge silhouette on the left.

    CORE

    Earth, Moon, and Sun

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Astronomers

    Phenomenon: An astrophotographer can only take pictures of specific features on the Moon at certain times.

    An illustration from the Chemical Reactions unit

    CORE

    Chemical Reactions

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Forensic chemists

    Phenomenon: A mysterious brown substance has been detected in the tap water of Westfield.

    An illustration from the Light Waves unit

    CORE

    Light Waves

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Spectroscopists

    Phenomenon: The rate of skin cancer is higher in Australia than in other parts of the world.

    An illustration of a whale with jellyfish and turtles from Amplify Science

    CORE

    Populations and Resources

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in Glacier Sea has increased.

    Low-poly landscape with trees and mushrooms. A fox sniffs the ground, a rabbit sits nearby, and mountains and sun are in the background.

    CORE

    Matter and Energy in Ecosystems

    Domains: Life Science, Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Ecologists

    Phenomenon: The biodome ecosystem has collapsed.

    A girl runs with a colorful kite displaying literacy skills; text reads "Amplify. Science of Reading: A Primer | Part One" on a grassy landscape background.

    CODING SCIENCE INTERNSHIP

    Coding Science Internship: Coral Restoration (Optional)

    Domains: Life Science, Coding Science

    Unit type: Coding Science Internship

    Student role: Coding science interns

    Phenomenon: Implementing a restoration project to improve the health of coral reef populations in Hawaii.

    A barren, rocky desert landscape with rover tracks leading to a distant vehicle on a hill under a hazy sky.

    LAUNCH

    Geology on Mars

    Domain: Earth and Space Science

    Unit type: Launch

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable.

    Two prehistoric reptiles with long snouts and tails are near the shore, one on land and one in water, with plants, rocks, and an island in the background.

    CORE

    Plate Motion

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean, even though the Mesosaurus species once lived all together.

    Geometric design featuring a telescope, mountain, sound waves, and cosmic elements on a purple hexagonal background.

    ENGINEERING INTERNSHIP

    Plate Motion Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.

    Una nave espacial se acerca a una estación espacial modular con paneles solares extendidos en una ilustración ambientada en el espacio.

    CORE

    Force and Motion

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: The asteroid sample-collecting pod failed to dock at the space station as planned.

    Green geometric background with a hexagonal emblem containing a parachute icon, ruler, bandage, and stacked layers on a gradient pattern.

    ENGINEERING INTERNSHIP

    Force and Motion Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Designing emergency supply delivery pods with different structures can maintain the integrity of the supply pods and their contents.

    Illustration of a roller coaster filled with people, hands raised, going down a steep track against a bright blue sky with clouds.

    CORE

    Magnetic Fields

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: During a test launch, a spacecraft traveled much faster than expected.

    Imagen que muestra un gráfico de arañas de diferentes colores con patrones distintos de patas y cuerpo, incluidas variaciones de color marrón, amarillo y azul. El fondo es una superficie oscura y texturizada.

    CORE

    Traits and Reproduction

    Domain: Life Science

    Unit type: Core

    Student role: Biomedical students

    Phenomenon: Darwin’s bark spider offspring have different silk flexibility traits, even though they have the same parents.

    Four low-poly dinosaurs with missing body sections are standing in a row; one is yellow, and the others are green. They have purple spikes and red patches on their bodies.

    CORE

    Natural Selection

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The newt population in Oregon State Park has become more poisonous over time.

    Red geometric background with icons including a mosquito, DNA strand, bar chart, and world map inside a hexagon.

    ENGINEERING INTERNSHIP

    Natural Selection Engineering Internship

    Domains: Life Science, Earth and Space Science

    Student role: Clinical engineers

    Phenomenon: Designing malaria treatment plans that use different combinations of drugs can reduce drug resistance development while helping malaria patients.

    Illustration of a cross-section of Earth showing a volcano near the ocean. Trees, mountains, and clouds are visible above, with subterranean layers below.

    CORE

    Rock Transformations (optional)

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.

    Two giant tortoises with long necks stand near water; one tortoise feeds on leaves from a tree while the other is near dense vegetation.

    CORE

    Evolutionary History

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Paleontologists

    Phenomenon: A mystery fossil at the Natural History Museum has similarities with both wolves and whales.

    A girl runs with a colorful kite displaying literacy skills; text reads "Amplify. Science of Reading: A Primer | Part One" on a grassy landscape background.

    CODING SCIENCE INTERNSHIP

    Coding Science Internship: Coral Restoration (Optional)

    Domains: Life Science, Coding Science

    Unit type: Coding Science Internship

    Student role: Coding science interns

    Phenomenon: Implementing a restoration project to improve the health of coral reef populations in Hawaii.

    Resources to support your review

    Select a topic below to explore helpful resources with more information about Amplify Science, the program’s development, and pedagogy.

    Two young girls, one with braided hair and the other with blonde hair, smiling and looking at a laptop screen in a classroom.
    Four-step educational infographic depicting problem-solving process: engaging with real-world problems, exploring multiple sources, constructing explanations, and applying knowledge to new problems.
    Integrated 5e model

    Learn how the 5E elements are integrated throughout every unit.

    Two children engaged in an animated conversation while sitting at a school desk with laptops and books.
    Phenomena and storylines (K–5)

    Read more about the real-world phenomena featured in each unit.

    Children doing schoolwork at home
    Phenomena and storylines (6–8)

    Read more about the real-world phenomena featured in each unit.

    A screenshot from a video titled "amplify science in action: a week in the..." featuring a smiling woman sitting in a classroom setting.
    [Video] Planning in action (K–5)

    Watch how easy it is for Amplify Science teachers to prep their 3-D instruction.

    A woman smiling and gesturing while speaking, seated in a classroom with computers and educational materials around her, with a paused video screen featuring text about "amplify science.
    [Video] Planning in action (6–8)

    Watch how easy it is for Amplify Science teachers to prep their 3-D instruction.

    Two young children sit at a classroom table, one smiling broadly, during an Amplify Science educational activity.
    [Video] Hands-on in action (K–5)

    Watch Amplify Science students conduct hands-on investigations.

    A student in a classroom uses a dropper to add liquid to clear plastic cups during a science experiment. Other students and lab materials are visible in the background.
    [Video] Hands-on in action (6–8)

    Watch Amplify Science students conduct hands-on investigations.

    Two young girls sit side by side at a desk, looking at a laptop screen and working together in a classroom setting.
    [Video] Simulations and modeling tools (K–5)

    Watch how students investigate phenomena with the help of digital tools.

    Two students sit at a table in a classroom, working on laptops and talking, with other students visible in the background.
    [Video] Simulations and modeling tools (6–8)

    Watch how students investigate phenomena with the help of digital tools.

    A young girl wearing safety goggles stretches a gooey substance from a cup in a kitchen or classroom setting.
    Summary of Investigations (K–5) coming soon

    Explore the types of investigations that students conduct.

    A young person wearing gloves looks through a microscope at a table with laboratory supplies, including bottles, slides, and a tray, against a plain blue background.
    Summary of Investigations (6–8) coming soon

    Explore the types of investigations that students conduct.

    A young boy and girl sitting in a classroom, reading a book together with focused expressions.
    Program structure and components (K–5)

    Take a closer look at how the program is organized.

    Teacher assisting two students working on laptops in a classroom; other students are in the background.
    Program structure and components (6–8)

    Take a closer look at how the program is organized.

    Digital collage of various devices displaying educational content about earth’s energy system, including graphs and text explanations.
    [Video] New! Classroom Slides

    Learn more about our customizable PowerPoints for every lesson.

    A laptop screen displays a writing lesson with prompts and a student's response in Amplify Classwork. The student's answer discusses dangers related to a specific scenario involving a sick child.
    Classwork (6–8)

    A new, intuitive approach to reviewing student work online.

    An adult sits on a couch using a laptop while a child next to them does homework in a notebook.
    Remote and hybrid learning guide

    Amplify is here to help! Amplify Science will soon feature product enhancements and new resources that will help manage the new landscape of back-to-school 2020.

    Educational presentation slides from grade 8 amplify science materials spanish kit, displaying various science topics like geology and biology.
    Spanish-language supports

    Learn more about the Spanish-language supports in Amplify Science.

    students collaborating and using laptops
    English Learners

    Learn how we make learning accessible for English learners.

    Amplify Science California supports you every step of the way on your journey to the California NGSS.
    Students needing support

    Learn how we make learning accessible for students who need more support.

    Teacher using a tablet while conducting an mCLASS reading intervention with three young students seated around a table in a classroom.
    Students ready for more

    Learn how we make learning more rigorous for students ready for a challenge.

    Two boys work together on a laptop while a woman—likely one of their middle school teachers—sits beside them, observing and smiling in a classroom setting.
    Accessibility

    Read more about text design and accessibility, including embedded Read-Aloud audio.

    A teacher discusses educational content in front of a whiteboard while students in the classroom raise their hands eagerly.
    Approach to assessment (K–5)

    Learn about our embedded formative and summative assessments.

    Two students sit at desks writing in notebooks and using laptops in a classroom setting.
    Approach to assessment (6–8)

    Learn about our embedded formative and summative assessments.

    A teacher and a young student looking at a laptop together in a colorful classroom decorated with children's artwork.
    NGSS Benchmark assessments

    Learn more about the Next Generation Science Standards Benchmark assessments created by Amplify.

    A young girl in a classroom gives a thumbs up with both hands, smiling broadly, while other students look on in the background.
    NGSS Benchmark assessments

    NGSS alignment by performance expectation.

    Two students in a classroom, one looking at the camera and the other listening intently, with a whiteboard displaying educational content in the background.
    NGSS alignment (6–8)

    NGSS alignment by performance expectation.

    Ready to explore with digital access and physical samples?

    Start your digital review and request physical samples with these three easy steps.

    1. Note these Ohio specific login credentials for your digital access.
      Username: t.ohscience@tryamplify.net
      Password: AmplifyNumber1
    2. Click Review now.
    3. Complete the form and select Log in with Amplify to input the Ohio specific login.
    A woman sits at a desk in a classroom, working on a laptop with an open binder and papers in front of her.

    Contact an Amplify representative

    For any questions, fill out the form to the right and a member of our sales team will reach out to you soon.

    Katie Cannon
    Senior Account Executive

    Casie Rayes
    Account executive

    Matt Paupore
    Senior Account Executive

    Welcome, Nebraska educators!

    Designed from the ground up for the NGSS to teach students to think, read, write, and argue like real scientists and engineers, Amplify Science combines literacy-rich activities with hands-on learning and digital tools to engage students in exploring compelling phenomena in every unit.

    Students in a classroom interact with educational technology, featuring a diagram and charts on a screen, while working collaboratively on a laptop.

    Overview

    Developed by UC Berkeley’s Lawrence Hall of Science, our program features:

    • phenomena-based approach where students construct a more complex understanding of each unit’s anchor phenomenon.
    • A blend of cohesive storylines, hands-on investigations, rich discussions, literacy-rich activities, and digital tools.
    • Newly crafted units, chapters, lessons, and activities designed to deliver true 3-dimensional learning.
    • An instructional design that supports all learners in accessing all standards.

    Explore your grade level

    Then select your grade level below to learn more about how we make this type of rich learning accessible to all students at every grade.

    Elementary school

    When you’re ready:

    1. Find a summary of each unit below including each unit’s student role and anchor phenomenon.
    2. Download some helpful resources to support your review.
    3. Explore the digital Teacher’s Guide by clicking the orange “Review now” button.
    A boy reads a book with an illustrated background featuring a dinosaur skull, the Earth, trees, clouds, and water.
    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.

    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.

    Silueta de una estructura de parque infantil contra un cielo azul con nubes y tres soles amarillos.

    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.

    Illustration of sea turtles swimming among seaweed in the ocean, with a large shark in the background.

    Unit 1

    Animal and Plant Defenses

    Student role: Marine scientists

    Phenomenon: Spruce the Sea Turtle will soon be released back into the ocean, where she will survive despite predators.

    An illustration from the Light and Sound unit

    Unit 2

    Light and Sound

    Student role: Light and sound engineers

    Phenomenon: A puppet show company uses light and sound to depict realistic scenes in puppet shows.

    An illustration from the Spinning Earth unit

    Unit 3

    Spinning Earth

    Student role: Sky scientists

    Phenomenon: The sky looks different to Sai and his grandma when they talk on the phone at night.

    An elephant standing next to a tree uses its trunk to pick a fruit from a branch while more fruit hangs above.

    Unit 1

    Plant and Animal Relationships

    Student role: Plant scientists

    Phenomenon: No new chalta trees are growing in the fictional Bengal Tiger Reserve in India.

    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.

    Unit 2

    Properties of Materials

    Student role: Glue engineers

    Phenomenon: Different glue recipes result in glues that have different properties.

    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.

    Unit 3

    Changing Landforms

    Student role: Geologists

    Phenomenon: The cliff on which Oceanside Recreation Center is situated appears to be receding.

    Una ilustración de un tren de alta velocidad moderno y aerodinámico que viaja por una vía elevada con un paisaje verde de fondo.

    Unit 1

    Balancing Forces

    Student role: Engineers

    Phenomenon: The fictional town of Faraday is getting a new train. Unlike typical trains, this one floats, which is causing some concern among the town’s citizens.

    An illustration from the Inheritance and Traits unit

    Unit 2

    Inheritance and Traits

    Student role: Wildlife biologists

    Phenomenon: An adopted wolf in Graystone National Park has some traits in common with one wolf pack in the park and other traits in common with a different pack.

    An illustration from the Environments and Survival unit

    Unit 3

    Environments and Survival

    Student role: Biomimicry engineers

    Phenomenon: Over 10 years, a population of grove snails has changed. Populations with yellow shells have decreased, while those with banded shells have increased.

    An illustration from the Weather and Climate unit

    Unit 4

    Weather and Climate

    Student role: Meteorologists

    Phenomenon: Three different islands, each a contender for becoming an orangutan reserve, experience different weather patterns.

    An illustration from the Energy Conversions unit

    Unit 1

    Energy Conversions

    Student role: System engineers

    Phenomenon: The fictional town of Ergstown experiences frequent blackouts. Their electrical system seems to be failing.

    An illustration from the Vision and Light unit

    Unit 2

    Vision and Light

    Student role: Conservation biologists

    Phenomenon: The population of Tokay geckos in a rain forest in the Philippines has decreased since the installation of new highway lights.

    An illustration from the Earth's Features unit

    Unit 3

    Earth’s Features

    Student role: Geologists


    Phenomenon: A mysterious fossil is discovered in a canyon within the fictional Desert Rocks National Park.

    An illustration from the Waves, Energy, and Information unit

    Unit 4

    Waves, Energy, and Information

    Student role: Marine scientists

    Phenomenon: Mother dolphins in the fictional Blue Bay National Park communicate with their calves despite the distance between them.

    An illustration from the Patterns of Earth and Sky unit

    Unit 1

    Patterns of Earth and Sky

    Student role: Astronomers

    Phenomenon: An ancient artifact depicts what we see in the sky at different times of the day, but it appears to be missing a piece.

    An illustration from the Modeling Matter unit

    Unit 2

    Modeling Matter

    Student role: Food scientists

    Phenomenon: Some ingredients dissolve in a salad dressing while others, like oil and vinegar, appear to separate

    Illustration of a pixelated green mountain cliff deconstructing into a digital grid, with red dots floating over a tranquil sea and flying white birds.

    Unit 3

    The Earth System

    Student role: Water resource engineers

    Phenomenon: East Ferris, a city on one side of the fictional Ferris Island, is experiencing a water shortage, while West Ferris is not.

    An illustration from the Ecosystem Restoration unit

    Unit 4

    Ecosystem Restoration

    Student role: Ecologists

    Phenomenon: The jaguars, sloths, and cecropia trees in a reforested section of a Costa Rican rain forest are not growing or thriving.

    Middle school

    When you’re ready:

    1. Find a summary of each unit below including each unit’s student role and anchor phenomenon.
    2. Download some helpful resources to support your review.
    3. Explore the digital Teacher’s Guide by clicking the orange “Review now” button.
    A person in a black hoodie smiles while working on a laptop, surrounded by illustrations of rockets, satellites, popsicles, and the Earth.
    Abstract art with vibrant colors featuring a yellow silhouette of a person holding a book against a background of geometric shapes, swirling patterns, and bold textures.

    LAUNCH

    Microbiome

    Domain: Life Science

    Unit type: Launch

    Student role: Microbiological researchers

    Phenomenon: The presence of 100 trillion microorganisms living on and in the human body may keep the body healthy.  

    Abstract artwork of a person's side profile with geometric shapes and colorful patterns flowing from the head, holding a small sledgehammer. A vision chart is visible in the corner.

    CORE

    Metabolism

    Domain: Life Science

    Unit type: Core

    Student role: Medical researchers

    Phenomenon: Elisa, a young patient, feels tired all the time.  

    Orange abstract background with hexagonal shapes featuring icons of a bar chart, plant, safety vest, test tube, peach, and stethoscope.

    ENGINEERING INTERNSHIP

    Metabolism Engineering Internship

    Domains: Life Science, Engineering Design

    Unit type: Engineering internship

    Student role: Food engineers

    Phenomenon: Designing health bars with different molecular compositions can effectively meet the metabolic needs of patients or rescue workers.  

    Imagen que muestra un gráfico de arañas de diferentes colores con patrones distintos de patas y cuerpo, incluidas variaciones de color marrón, amarillo y azul. El fondo es una superficie oscura y texturizada.

    CORE

    Traits and Reproduction

    Domain: Life Science

    Unit type: Core

    Student role: Biomedical students

    Phenomenon: Darwin’s bark spider offspring have different silk flexibility traits, even though they have the same parents.  

    Illustration of a person in a red hat and fur-lined coat with eyes closed, surrounded by large orange circles on a dark background.

    CORE

    Thermal Energy

    Domain: Physical Science

    Unit type: Core

    Student role: Thermal scientists

    Phenomenon: One of two proposed heating systems for Riverdale School will best heat the school.  

    Abstract artwork depicting a bright sun with blue and orange swirling patterns next to green hills under a sky with shades of blue, orange, and red.

    CORE

    Ocean, Atmosphere, and Climate

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.  

    An illustration from the Weather Patterns unit

    CORE

    Weather Patterns

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Forensic meteorologists

    Phenomenon: In recent years, rainstorms in Galetown have been unusually severe.  

    An illustration from the Earth's Changing Climate unit

    CORE

    Earth’s Changing Climate

    Domains: Earth and Space Science, Life Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.  

    Abstract geometric design in shades of blue and purple featuring a hexagon with icons of a building, wrench, molecules, sun, paint can, and screwdriver.

    Engineering Internship

    Earth’s Changing Climate Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.  

    A barren, rocky desert landscape with rover tracks leading to a distant vehicle on a hill under a hazy sky.

    LAUNCH

    Geology on Mars

    Domain: Earth and Space Science

    Unit type: Launch

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable.  

    Two prehistoric reptiles with long snouts and tails are near the shore, one on land and one in water, with plants, rocks, and an island in the background.

    CORE

    Plate Motion

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean, even though the Mesosaurus species once lived all together.   

    Geometric design featuring a telescope, mountain, sound waves, and cosmic elements on a purple hexagonal background.

    ENGINEERING INTERNSHIP

    Plate Motion Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.  

    Illustration of a cross-section of Earth showing a volcano near the ocean. Trees, mountains, and clouds are visible above, with subterranean layers below.

    CORE

    Rock Transformations

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.  

    Ilustración que muestra las etapas de fusión de una paleta de naranja: entera, parcialmente derretida, más derretida y casi derretida por completo, con palitos de madera, sobre un fondo morado.

    CORE

    Phase Change

    Domains: Physical Science, Earth and Space Science

    Unit type: Core

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart.  

    Green geometric graphic featuring icons: a baby, thermometer, layers, medical alert, and a flame.

    ENGINEERING INTERNSHIP

    Phase Change Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different combinations of phase change materials can keep babies at a healthy temperature.  

    An illustration from the Chemical Reactions unit

    CORE

    Chemical Reactions

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Forensic chemists

    Phenomenon: A mysterious brown substance has been detected in the tap water of Westfield.   

    An illustration of a whale with jellyfish and turtles from Amplify Science

    CORE

    Populations and Resources

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in Glacier Sea has increased.  

    Low-poly landscape with trees and mushrooms. A fox sniffs the ground, a rabbit sits nearby, and mountains and sun are in the background.

    CORE

    Matter and Energy in Ecosystems

    Domains: Life Science, Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Ecologists

    Phenomenon: The biodome ecosystem has collapsed.  

    Two people climbing rocky terrain; illustrations show a hiking boot and a belt with gear.

    LAUNCH

    Harnessing Human Energy

    Domains: Physical Science, Earth and Space Science, Engineering Design

    Unit type: Launch

    Student role: Energy scientists

    Phenomenon: Rescue workers can use their own human kinetic energy to power the electrical devices they use during rescue missions.  

    Illustration of a futuristic space station with large solar panels, orbiting in deep space, emitting a blue glow from its propulsion system.

    CORE

    Force and Motion

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: The asteroid sample-collecting pod failed to dock at the space station as planned.   

    Green geometric background with a hexagonal emblem containing a parachute icon, ruler, bandage, and stacked layers on a gradient pattern.

    ENGINEERING INTERNSHIP

    Force and Motion Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Designing emergency supply delivery pods with different structures can maintain the integrity of the supply pods and their contents.  

    Illustration of a roller coaster filled with people, hands raised, going down a steep track against a bright blue sky with clouds.

    CORE

    Magnetic Fields

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: During a test launch, a spacecraft traveled much faster than expected.  

    An illustration from the Light Waves unit

    CORE

    Light Waves

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Spectroscopists

    Phenomenon: The rate of skin cancer is higher in Australia than in other parts of the world.   

    A city skyline at night with a prominent full moon, stars in the sky, and a bridge silhouette on the left.

    CORE

    Earth, Moon, and Sun

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Astronomers

    Phenomenon: An astrophotographer can only take pictures of specific features on the Moon at certain times.  

    Four low-poly dinosaurs with missing body sections are standing in a row; one is yellow, and the others are green. They have purple spikes and red patches on their bodies.

    CORE

    Natural Selection

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The newt population in Oregon State Park has become more poisonous over time.  

    Red geometric background with icons including a mosquito, DNA strand, bar chart, and world map inside a hexagon.

    ENGINEERING INTERNSHIP

    Natural Selection Engineering Internship

    Domains: Engineering Design, Life Science

    Unit type: Engineering internship

    Student role: Clinical engineers

    Phenomenon: Designing malaria treatment plans that use different combinations of drugs can reduce drug resistance development while helping malaria patients.   

    Two giant tortoises with long necks stand near water; one tortoise feeds on leaves from a tree while the other is near dense vegetation.

    CORE

    Evolutionary History

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Paleontologists

    Phenomenon: A mystery fossil at the Natural History Museum has similarities with both wolves and whales.    

    Resources to support your review

    Select a topic below to explore helpful resources with more information about Amplify Science, the program’s development, and pedagogy.

    Dos niñas están sentadas en una mesa, mirando juntas la pantalla de una computadora portátil en un salón de clases. Al fondo se ven estanterías con libros y materiales de clase.
    Two children engaged in an animated conversation while sitting at a school desk with laptops and books.
    Phenomena and storylines (K–5)

    Read more about the real-world phenomena featured in each unit.

    Children doing schoolwork at home
    Phenomena and storylines (6–8)

    Read more about the real-world phenomena featured in each unit.

    Four-step educational infographic depicting problem-solving process: engaging with real-world problems, exploring multiple sources, constructing explanations, and applying knowledge to new problems.
    Integrated 5e model

    Learn how the 5E elements are integrated throughout every unit.

    A woman smiling and gesturing while speaking, seated in a classroom with computers and educational materials around her, with a paused video screen featuring text about "amplify science.
    [Video] Planning in action (K–5)

    Watch how easy it is for Amplify Science teachers to prep their 3-D instruction.

    A screenshot from a video titled "amplify science in action: a week in the..." featuring a smiling woman sitting in a classroom setting.
    [Video] Planning in action (6–8)

    Watch how easy it is for Amplify Science teachers to prep their 3-D instruction.

    Two children sitting at a table, one in a yellow shirt and the other in pink, smiling and looking forward.
    [Video] Hands-on in action (K–5)

    Watch Amplify Science students conduct hands-on investigations.

    A boy in a science classroom observes a reaction in a clear cup. Other students and lab materials are in the background.
    [Video] Hands-on in action (6–8)

    Watch Amplify Science students conduct hands-on investigations.

    Two children in school uniforms work together on laptops in a classroom setting, with focus on learning and collaboration.
    [Video] Simulations and modeling tools (K–5)

    Watch how students investigate phenomena with the help of digital tools.

    Students sitting at a table using laptops, engaging in a classroom activity.
    [Video] Simulations and modeling tools (6–8)

    Watch how students investigate phenomena with the help of digital tools.

    A young girl wearing safety goggles stretches a gooey substance from a cup in a kitchen or classroom setting.
    Summary of Investigations (K–5)

    Explore the types of investigations that students conduct.

    A young person wearing gloves looks through a microscope at a table with laboratory supplies, including bottles, slides, and a tray, against a plain blue background.
    Summary of Investigations (6–8)

    Explore the types of investigations that students conduct.

    A young boy and girl sitting in a classroom, reading a book together with focused expressions.
    Program structure and components (K–5)

    Take a closer look at how the program is organized.

    Teacher assisting two students working on laptops in a classroom; other students are in the background.
    Program structure and components (6–8)

    Take a closer look at how the program is organized.

    Digital collage of various devices displaying educational content about earth’s energy system, including graphs and text explanations.
    [Video] New! Classroom Slides

    Learn more about our customizable PowerPoints for every lesson.

    A laptop screen displays a writing lesson with prompts and a student's response in Amplify Classwork. The student's answer discusses dangers related to a specific scenario involving a sick child.
    Classwork (6–8)

    A new, intuitive approach to reviewing student work online.

    students collaborating and using laptops
    English Learners

    Learn how we make learning accessible for English learners.

    Amplify Science California supports you every step of the way on your journey to the California NGSS.
    Students needing support

    Learn how we make learning accessible for students who need more support.

    Teacher using a tablet while conducting an mCLASS reading intervention with three young students seated around a table in a classroom.
    Students ready for more

    Learn how we make learning more rigorous for students ready for a challenge.

    Two young children sit at a table looking at an open book, with other books placed in front of them. A play button is visible over the image.
    [Video] Literacy in action (K–5)

    Watch students use scientific text to obtain information and practice reading skills, while using writing prompts to create arguments using evidence

    A student writes in a notebook, holding a pencil, focused on the task.
    [Video] Literacy in action (6–8)

    Watch students use scientific text to obtain information and practice reading skills, while using writing prompts to create arguments using evidence.

    A teacher in a green shirt helps a young student with writing at a classroom table, with other students and large numbers visible on the wall in the background.
    Literacy-rich science instruction (K–5)

    Immersing young students in reading, writing, and arguing like real scientists and engineers.

    Two students sit at a table in a classroom, working on an assignment together. Other students are also seated and appear to be engaged in their work. Papers and books are spread out on the tables.
    Active Reading in grades 6–8

    Engaging middle school students in complex science texts.

    Two boys work together on a laptop while a woman—likely one of their middle school teachers—sits beside them, observing and smiling in a classroom setting.
    Accessibility

    Read more about text design and accessibility, including embedded Read-Aloud audio.

    A teacher discusses educational content in front of a whiteboard while students in the classroom raise their hands eagerly.
    Approach to assessment (K–5)

    Learn about our embedded formative and summative assessments.

    Two students sit at desks writing in notebooks and using laptops in a classroom setting.
    Approach to assessment (6–8)

    Learn about our embedded formative and summative assessments.

    A teacher and a young student looking at a laptop together in a colorful classroom decorated with children's artwork.
    NGSS Benchmark assessments

    Learn more about the Next Generation Science Standards Benchmark assessments created by Amplify.

    A young girl in a classroom gives a thumbs up with both hands, smiling broadly, while other students look on in the background.
    NGSS alignment (K–5)

    NGSS alignment by performance expectation.

    Two students in a classroom, one looking at the camera and the other listening intently, with a whiteboard displaying educational content in the background.
    NGSS alignment (6–8)

    NGSS alignment by performance expectation.

    Two children sit at a table with Chromebooks, facing each other and talking, in a classroom with books and storage bins in the background.
    Remote and hybrid learning guide

    Amplify is here to help! Amplify Science will soon feature product enhancements and new resources that will help manage the new landscape of back-to-school 2020.

    Educational presentation slides from grade 8 amplify science materials spanish kit, displaying various science topics like geology and biology.
    Spanish-language supports

    Learn more about the Spanish-language supports in Amplify Science.

    Ready to start exploring with digital access?

    A woman sits at a desk in a classroom, working on a laptop with an open binder and papers in front of her.

    Contact an Amplify representative

    Laina Armbruster
    larmbruster@amplify.com
    (602) 791-4135

    Bob McCarty
    rmccarty@amplify.com
    (435) 655-1731

    Kristin McDonald
    kmcdonald@amplify.com
    (515) 240-0244

    Welcome to Grade 7

    BACK TO MAIN 6–8 PAGE

    Amplify Science California is so effective you can cover 100% of the NGSS in fewer lessons than other programs.
     
    Plus, you can breathe a sigh of relief knowing we give you enough materials to support 200 students. In fact, our material kits:

    • Support small groups of 4-5 students.
    • Make organization and finding materials easy.
    • Last longer with only one of the nine kits requiring refills.
    A collage showing a rocky landscape, a forest with foxes, two kids doing a science experiment, and hands tending to seedlings in a plastic container.

    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.
    A barren, rocky desert landscape with rover tracks leading to a distant vehicle on a hill under a hazy sky.

    Unit 1

    Geology on Mars

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable.

    Two prehistoric reptiles with long snouts and tails are near the shore, one on land and one in water, with plants, rocks, and an island in the background.

    Unit 2

    Plate Motion

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean.

    See how this unit works

    Geometric design featuring a telescope, mountain, sound waves, and cosmic elements on a purple hexagonal background.

    Unit 3

    Plate Motion Engineering Internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.

    Illustration of a cross-section of Earth showing a volcano near the ocean. Trees, mountains, and clouds are visible above, with subterranean layers below.

    Unit 4

    Rock Transformations

    Student role: Geologists


    Phenomenon: Rock samples from different U.S. regions look different, but have similar mineral compositions.

    See how this unit works

    Illustration showing the stages of melting an orange popsicle: whole, partially melted, more melted, and almost completely melted, with wooden sticks, on a purple background.

    Unit 5

    Phase Change

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart.

    See how this unit works

    Green geometric graphic featuring icons: a baby, thermometer, layers, medical alert, and a flame.

    Unit 6

    Phase Change Engineering Internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different phase change materials helps keep babies’ temperatures healthy.

    Abstract digital artwork featuring numerous red and gray circles overlapping a split background of blue and light purple, creating a dynamic and energetic composition.

    Unit 7

    Chemical Reactions

    Student role: Forensic chemists

    Phenomenon: A mysterious reddish-brown substance has been detected in the tap water of Westfield.

    See how this unit works

    An illustration of a whale with jellyfish and turtles from Amplify Science

    Unit 8

    Populations and Resources

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in the fictional Glacier Sea has experienced a puzzling increase.

    See how this unit works

    Low-poly landscape with trees and mushrooms. A fox sniffs the ground, a rabbit sits nearby, and mountains and sun are in the background.

    Unit 9

    Matter and Energy in Ecosystems

    Student role: Ecologists

    Phenomenon: A sealed biodome built by a group of Econauts mysteriously crashed despite following the advice of experts.

    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.
    A laptop displays a PowerPoint presentation in presenter view, with slides about observing objects in plastic containers and related sensory instructions.

    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

    A printed teacher’s guide labeled “Plate Motion: Mystery of the Mesosaurus Fossils” is displayed next to a laptop showing the same curriculum’s digital interface.

    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

    Assorted craft supplies including a bottle of rubbing alcohol, plastic containers, colorful beads, small dropper bottles, plastic cups, and clear plastic spoons on a white background.

    Materials Kits

    Our kits include enough non-consumable materials to support 200 student uses. In other words, you have enough materials to support all five periods and small groups of 4-5 students each. 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

    A laptop screen displaying a map with three ecosystem options, each illustrated by different animal icons and accompanied by relevant data lists.

    Simulations and Practice Tools

    Our digital Simulations and Practice Tools are powerful resources for exploration, data collection, and student collaboration. They allow students the ability to explore scientific concepts that might otherwise be invisible or impossible to see with the naked eye.

    Video overview of digital tools

    List of digital tools by unit

    Device calendars by unit

    Two science textbooks, one in Spanish and one in English, titled "Movimento de placas" and "Plate Motion," both featuring an illustrated Mesosaurus fossil on the cover.

    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)

    Cover of a science textbook showing a girl doing an experiment, surrounded by animals, jellyfish, a rocket, and scientific symbols, with the title "Amplify Science.

    Student Edition Hardcover

    This durable Student Edition is grade-level specific and contains all of the articles that students refer to throughout the year. Districts may choose to pair these traditional student texts with our digital student experience or new 2-volume consumable notebook set.

    A person with headphones works on a laptop; a line from their head transforms into a rocket, symbolizing imagination, innovation, and the foundational skills essential for multilingual learners.

    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

    Navigating the program

    • Click the orange button below to access the platform.
    • Choose the resources you’d like to review.
    • Pick your grade level from the drop-down menu.
    • Scroll down to find additional grade-level resources.

    Navigating a Launch Unit

    Launch units are the first units taught in each year of the program. The goal of a Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year.

    Navigating an Engineering Internship

    Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. In the process, they apply and deepen their learning from Core units.

    Navigating a Core Unit

    Core units introduce a real-world problem and support students as they figure out the anchoring phenomenon and gain an understanding of the unit’s DCIs, SEPs, and CCCs.

    Navigating Classwork and Reporting

    Classwork is our new online grading tool that gives you quick and easy access to unreviewed work, student portfolios of work, and automatically generated differentiation groups.

    Welcome to Earth and Space Science

    BACK TO MAIN 6–8 PAGE

    Amplify Science California is so effective you can cover 100% of the NGSS in fewer lessons than other programs.
     
    Plus, you can breathe a sigh of relief knowing we give you enough materials to support 200 students. In fact, our material kits:

    • Support small groups of 4-5 students.
    • Make organization and finding materials easy.
    • Last longer with only one of the nine kits requiring refills.
    A collage of images: top left, digital art of a desert scene; top right, three kids doing a science experiment; bottom left, a hand holding a jar and two others beside; bottom right, digital art of a person and child in a field.

    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.
    A barren, rocky desert landscape with rover tracks leading to a distant vehicle on a hill under a hazy sky.

    Unit 1

    Geology on Mars

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable.

    Two prehistoric reptiles with long snouts and tails are near the shore, one on land and one in water, with plants, rocks, and an island in the background.

    Unit 2

    Plate Motion

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean.

    See how this unit works

    Geometric design featuring a telescope, mountain, sound waves, and cosmic elements on a purple hexagonal background.

    Unit 3

    Plate Motion Engineering Internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.

    Illustration of a cross-section of Earth showing a volcano near the ocean. Trees, mountains, and clouds are visible above, with subterranean layers below.

    Unit 4

    Rock Transformations

    Student role: Geologists


    Phenomenon: Rock samples from different U.S. regions look different, but have similar mineral compositions.

    See how this unit works

    A city skyline at night with a prominent full moon, stars in the sky, and a bridge silhouette on the left.

    Unit 5

    Earth, Moon, and Sun

    Student role: Astronomers

    Phenomenon: Pictures of specific features on the Moon can only be taken by an astrophotographer at certain times.

    See how this unit works

    Abstract artwork depicting a bright sun with blue and orange swirling patterns next to green hills under a sky with shades of blue, orange, and red.

    Unit 6

    Ocean, Atmosphere, and Climate

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.

    Ilustración de un pueblo con casas, campos y montañas bajo un cielo nublado con olas de viento o lluvia.

    Unit 7

    Weather Patterns

    Student role: Forensic meteorologists

    Phenomenon: The strong storms in Galetown didn’t just begin. They have become more and more severe over the years.

    See how this unit works

    Un oso polar se encuentra sobre un pequeño témpano de hielo en el océano con un sol naranja en el cielo y lejanas montañas heladas al fondo.

    Unit 8

    Earth’s Changing Climate

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.

    See how this unit works

    Abstract geometric design in shades of blue and purple featuring a hexagon with icons of a building, wrench, molecules, sun, paint can, and screwdriver.

    Unit 9

    Earth’s Changing Climate Engineering Internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.

    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.
    A laptop displays a PowerPoint presentation in presenter view, with slides about observing objects in plastic containers and related sensory instructions.
    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

    A printed teacher’s guide labeled “Plate Motion: Mystery of the Mesosaurus Fossils” is displayed next to a laptop showing the same curriculum’s digital interface.
    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

    Assorted rocks, plastic jars, stacks of clear plastic cups, wrapped candies, and scattered dice laid out on a white background.
    Materials Kits

    Our kits include enough non-consumable materials to support 200 student uses. In other words, you have enough materials to support all five periods and small groups of 4-5 students each. Plus, our unit-specific kits mean you just grab the tub you need and then put it all back with ease.

    A laptop screen displaying a map with three ecosystem options, each illustrated by different animal icons and accompanied by relevant data lists.
    Simulations and Practice Tools

    Our digital Simulations and Practice Tools are powerful resources for exploration, data collection, and student collaboration. They allow students the ability to explore scientific concepts that might otherwise be invisible or impossible to see with the naked eye.

    Video overview of digital tools

    Two booklets titled "El clima cambiante de la Tierra: la desaparición del hielo" and "Earth’s Changing Climate: Vanishing Ice" with landscape illustrations on the 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.

    Cover of the "Amplify Science" Grade 8 textbook featuring illustrations of space, insects, technology, crowds, and scientific diagrams.
    Student Edition Hardcover

    This durable Student Edition is grade-level specific and contains all of the articles that students refer to throughout the year. Districts may choose to pair these traditional student texts with our digital student experience or new 2-volume consumable notebook set.

    A person with headphones works on a laptop; a line from their head transforms into a rocket, symbolizing imagination, innovation, and the foundational skills essential for multilingual learners.
    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

    Navigating the program

    • Click the orange button below to access the platform.
    • Choose the resources you’d like to review.
    • Pick your grade level from the drop-down menu.
    • Scroll down to find additional grade-level resources.

    Navigating a Launch Unit

    Launch units are the first units taught in each year of the program. The goal of a Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year.

    Navigating an Engineering Internship

    Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. In the process, they apply and deepen their learning from Core units.

    Navigating a Core Unit

    Core units introduce a real-world problem and support students as they figure out the anchoring phenomenon and gain an understanding of the unit’s DCIs, SEPs, and CCCs.

    Navigating Classwork and Reporting

    Classwork is our new online grading tool that gives you quick and easy access to unreviewed work, student portfolios of work, and automatically generated differentiation groups.

    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!

    A closer look at grades 6–8

    Amplify Science California is based on the latest research on teaching and learning and helps teachers deliver rigorous and riveting lessons through hands-on investigations, literacy-rich activities, and interactive digital tools that empower students to think, read, write, and argue like real scientists.

    In the 6–8 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.

    Is your school implementing the domain model? Click here.

    Collage of four images showing children engaged in educational activities such as conducting experiments and crafting in a classroom setting.
    A four-step process diagram with icons: spark a real-world problem, explore sources, explain and elaborate, and evaluate claims, all linking to engage with 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, students build and deepen their understanding, increasing their ability to develop and refine 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 6–8 program to address 100% of the California NGSS in fewer lessons than other programs.

    Scope and sequence

    Every year our grades 6–8 sequence consists of 9 units, with each unit containing 10–19 lessons. Lessons are written to last a minimum of 45-minutes, though teachers can expand or contract the timing to meet their needs.

    Chart displaying educational science topics for grades 6 to 8, categorized by grade level, duration in days, and number of classes. Includes subjects like microbiome, geology, and natural selection.

    Unit types

    Each unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, while also serving a unique purpose.

    In grades 6–8, there are three types of units:

    • One unit is a launch unit.
    • Three units are core units.
    • Two units are engineering internships.
    Launch units

    Launch units are the first units taught in each year of Amplify Science California. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

    Core units

    Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

    Engineering Internship units

    Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

    Units at a glance

    Abstract art with vibrant colors featuring a yellow silhouette of a person holding a book against a background of geometric shapes, swirling patterns, and bold textures.
    Microbiome

    Domain: Life Science

    Unit type: Launch

    Student role: Microbiological researchers

    Phenomenon: The presence of 100 trillion microorganisms living on and in the human body may keep the body healthy.  

    Abstract artwork of a person's side profile with geometric shapes and colorful patterns flowing from the head, holding a small sledgehammer. A vision chart is visible in the corner.
    Metabolism

    Domain: Life Science

    Unit type: Core

    Student role: Medical researchers

    Phenomenon: Elisa, a young patient, feels tired all the time.  

    Download unit guide

    Orange abstract background with hexagonal shapes featuring icons of a bar chart, plant, safety vest, test tube, peach, and stethoscope.
    Metabolism Engineering Internship

    Domains: Life Science, Engineering Design

    Unit type: Engineering internship

    Student role: Food engineers

    Phenomenon: Designing health bars with different molecular compositions can effectively meet the metabolic needs of patients or rescue workers.  

    Imagen que muestra un gráfico de arañas de diferentes colores con patrones distintos de patas y cuerpo, incluidas variaciones de color marrón, amarillo y azul. El fondo es una superficie oscura y texturizada.
    Traits and Reproduction

    Domain: Life Science

    Unit type: Core

    Student role: Biomedical students

    Phenomenon: Darwin’s bark spider offspring have different silk flexibility traits, even though they have the same parents.  

    Download unit guide

    Illustration of a person in a red hat and fur-lined coat with eyes closed, surrounded by large orange circles on a dark background.
    Thermal Energy

    Domain: Physical Science

    Unit type: Core

    Student role: Thermal scientists

    Phenomenon: One of two proposed heating systems for Riverdale School will best heat the school. 

    Download unit guide

    Abstract artwork depicting a bright sun with blue and orange swirling patterns next to green hills under a sky with shades of blue, orange, and red.
    Ocean, Atmosphere, and Climate

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.  

    An illustration from the Weather Patterns unit
    Weather Patterns

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Forensic meteorologists

    Phenomenon: In recent years, rainstorms in Galetown have been unusually severe.  

    Download unit guide

    An illustration from the Earth's Changing Climate unit
    Earth’s Changing Climate

    Domains: Earth and Space Science, Life Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.  

    Download unit guide

    Abstract geometric design in shades of blue and purple featuring a hexagon with icons of a building, wrench, molecules, sun, paint can, and screwdriver.
    Earth’s Changing Climate Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.  

    A barren, rocky desert landscape with rover tracks leading to a distant vehicle on a hill under a hazy sky.
    Geology on Mars

    Domain: Earth and Space Science

    Unit type: Launch

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable. 

    Two prehistoric reptiles with long snouts and tails are near the shore, one on land and one in water, with plants, rocks, and an island in the background.
    Plate Motion

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean, even though the Mesosaurus species once lived all together.  

    Download unit guide

    Geometric design featuring a telescope, mountain, sound waves, and cosmic elements on a purple hexagonal background.
    Plate Motion Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.  

    Illustration of a cross-section of Earth showing a volcano near the ocean. Trees, mountains, and clouds are visible above, with subterranean layers below.
    Rock Transformations

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.  

    Download unit guide

    Ilustración que muestra las etapas de fusión de una paleta de naranja: entera, parcialmente derretida, más derretida y casi derretida por completo, con palitos de madera, sobre un fondo morado.
    Phase Change

    Domains: Physical Science, Earth and Space Science

    Unit type: Core

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart

    Download unit guide

    Green geometric background with a hexagonal emblem containing a parachute icon, ruler, bandage, and stacked layers on a gradient pattern.
    Force and Motion Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Designing emergency supply delivery pods with different structures can maintain the integrity of the supply pods and their contents.  

    An illustration from the Chemical Reactions unit
    Chemical Reactions

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Forensic chemists

    Phenomenon: A mysterious brown substance has been detected in the tap water of Westfield.  

    Download unit guide

    An illustration of a whale with jellyfish and turtles from Amplify Science
    Populations and Resources

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in Glacier Sea has increased. 

    Download unit guide

    Low-poly landscape with trees and mushrooms. A fox sniffs the ground, a rabbit sits nearby, and mountains and sun are in the background.
    Matter and Energy in Ecosystems

    Domains: Life Science, Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Ecologists

    Phenomenon: The biodome ecosystem has collapsed.  

    Download unit guide

    Two people climbing rocky terrain; illustrations show a hiking boot and a belt with gear.
    Harnessing Human Energy

    Domains: Physical Science, Earth and Space Science, Engineering Design

    Unit type: Launch

    Student role: Energy scientists

    Phenomenon: Rescue workers can use their own human kinetic energy to power the electrical devices they use during rescue missions.  

    Illustration of a futuristic space station with large solar panels, orbiting in deep space, emitting a blue glow from its propulsion system.
    Force and Motion

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: The asteroid sample-collecting pod failed to dock at the space station as planned.

    Download unit guide

    Green geometric graphic featuring icons: a baby, thermometer, layers, medical alert, and a flame.
    Phase Change Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different combinations of phase change materials can keep babies at a healthy temperature.  

    Illustration of a roller coaster filled with people, hands raised, going down a steep track against a bright blue sky with clouds.
    Magnetic Fields

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: During a test launch, a spacecraft traveled much faster than expected.  

    An illustration from the Light Waves unit
    Light Waves

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Spectroscopists

    Phenomenon: The rate of skin cancer is higher in Australia than in other parts of the world.

    Download unit guide

    A city skyline at night with a prominent full moon, stars in the sky, and a bridge silhouette on the left.
    Earth, Moon, and Sun

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Astronomers

    Phenomenon: An astrophotographer can only take pictures of specific features on the Moon at certain times.  

    Download unit guide

    Four low-poly dinosaurs with missing body sections are standing in a row; one is yellow, and the others are green. They have purple spikes and red patches on their bodies.
    Natural Selection

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The newt population in Oregon State Park has become more poisonous over time.  

    Download unit guide

    Red geometric background with icons including a mosquito, DNA strand, bar chart, and world map inside a hexagon.
    Natural Selection Engineering Internship

    Domains: Engineering Design, Life Science

    Unit type: Engineering internship

    Student role: Clinical engineers

    Phenomenon: Designing malaria treatment plans that use different combinations of drugs can reduce drug resistance development while helping malaria patients.  

    Two giant tortoises with long necks stand near water; one tortoise feeds on leaves from a tree while the other is near dense vegetation.
    Evolutionary History

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Paleontologists

    Phenomenon: A mystery fossil at the Natural History Museum has similarities with both wolves and whales.    

    Download unit guide

    A closer look at grades 6–8 (domain)

    Amplify Science California is based on the latest research on teaching and learning and helps teachers deliver rigorous and riveting lessons through hands-on investigations, literacy-rich activities, and interactive digital tools that empower students to think, read, write, and argue like real scientists.

    In the 6–8 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.

    Is your school implementing the integrated model? Click here.

    Collage of four images showing children engaged in educational activities such as conducting experiments and crafting in a classroom setting.
    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, students build and deepen their understanding, increasing their ability to develop and refine 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 6–8 program to address 100% of the California NGSS in fewer lessons than other programs.

    Scope and sequence

    Every year of our grades 6–8 sequence consists of 9 units, with each unit containing 10–19 lessons. Lessons are written to last a minimum of 45 minutes, though teachers can expand or contract the timing to meet their needs.

    A grid of educational icons, each representing a different science topic, such as earth and space science, life science, and physical science, with titles and lesson counts.

    Unit types

    Each unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, while also serving a unique purpose.

    In grades 6–8, there are three types of units:

    • One unit is a launch unit.
    • Three units are core units.
    • Two units are engineering internships.
    Launch units

    Launch units are the first units taught in each year of Amplify Science California. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to actively read in all subsequent units.

    Core units

    Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

    Engineering Internship units

    Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

    Units at a glance

    A barren, rocky desert landscape with rover tracks leading to a distant vehicle on a hill under a hazy sky.
    Geology on Mars

    Domain: Earth and Space Science

    Unit type: Launch

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable.    

    Two prehistoric reptiles with long snouts and tails are near the shore, one on land and one in water, with plants, rocks, and an island in the background.
    Plate Motion

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean, even though the Mesosaurus species once lived all together.    

    Download unit guide

    Geometric design featuring a telescope, mountain, sound waves, and cosmic elements on a purple hexagonal background.
    Plate Motion Engineering Internship

    Domain: Earth and Space Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.    

    Illustration of a cross-section of Earth showing a volcano near the ocean. Trees, mountains, and clouds are visible above, with subterranean layers below.
    Rock Transformations

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.    

    Download unit guide

    A city skyline at night with a prominent full moon, stars in the sky, and a bridge silhouette on the left.
    Earth, Sun, and Moon

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Astronomers

    Phenomenon: An astrophotographer can only take pictures of specific features on the Moon at certain times.    

    Download unit guide

    Abstract artwork depicting a bright sun with blue and orange swirling patterns next to green hills under a sky with shades of blue, orange, and red.
    Ocean, Atmosphere, and Climate

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.    

    Ilustración de un pueblo con casas, campos y montañas bajo un cielo nublado con olas de viento o lluvia.
    Weather Patterns

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Forensic meteorologists

    Phenomenon: In recent years, rainstorms in Galetown have been unusually severe.    

    Download unit guide

    Un oso polar se encuentra sobre un pequeño témpano de hielo en el océano con un sol naranja en el cielo y lejanas montañas heladas al fondo.
    Earth’s Changing Climate

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.    

    Download unit guide

    Abstract geometric design in shades of blue and purple featuring a hexagon with icons of a building, wrench, molecules, sun, paint can, and screwdriver.
    Earth’s Changing Climate Engineering Internship

    Domain: Earth and Space Science

    Unit type: Engineering internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.    

    Abstract art with vibrant colors featuring a yellow silhouette of a person holding a book against a background of geometric shapes, swirling patterns, and bold textures.
    Microbiome

    Domain: Life Science

    Unit type: Launch

    Student role: Microbiological researchers

    Phenomenon: The presence of 100 trillion microorganisms living on and in the human body may keep the body healthy.    

    Abstract artwork of a person's side profile with geometric shapes and colorful patterns flowing from the head, holding a small sledgehammer. A vision chart is visible in the corner.
    Metabolism

    Domain: Life Science

    Unit type: Core

    Student role: Medical researchers

    Phenomenon: Elisa, a young patient, feels tired all the time.    

    Download unit guide

    Orange abstract background with hexagonal shapes featuring icons of a bar chart, plant, safety vest, test tube, peach, and stethoscope.
    Metabolism Engineering Internship

    Domain: Life Science

    Unit type: Engineering internship

    Student role: Food engineers

    Phenomenon: Designing health bars with different molecular compositions can effectively meet the metabolic needs of patients or rescue workers.    

    Imagen que muestra un gráfico de arañas de diferentes colores con patrones distintos de patas y cuerpo, incluidas variaciones de color marrón, amarillo y azul. El fondo es una superficie oscura y texturizada.
    Traits and Reproduction

    Domain: Life Science

    Unit type: Core

    Student role: Biomedical students

    Phenomenon: Darwin’s bark spider offspring have different silk flexibility traits, even though they have the same parents.    

    Download unit guide

    An illustration of a whale with jellyfish and turtles from Amplify Science
    Populations and Resources

    Domain: Life Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in Glacier Sea has increased.    

    Download unit guide

    Low-poly landscape with trees and mushrooms. A fox sniffs the ground, a rabbit sits nearby, and mountains and sun are in the background.
    Matter and Energy in Ecosystems

    Domain: Life Science

    Unit type: Core

    Student role: Ecologists

    Phenomenon: What caused the mysterious crash of a biodome ecosystem?    

    Download unit guide

    Four low-poly dinosaurs with missing body sections are standing in a row; one is yellow, and the others are green. They have purple spikes and red patches on their bodies.
    Natural Selection

    Domain: Life Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The newt population in Oregon State Park has become more poisonous over time.    

    Download unit guide

    Red geometric background with icons including a mosquito, DNA strand, bar chart, and world map inside a hexagon.
    Natural Selection Engineering Internship

    Domain: Life Science

    Unit type: Engineering internship

    Student role: Clinical engineers

    Phenomenon: Designing malaria treatment plans that use different combinations of drugs can reduce drug resistance development while helping malaria patients.  

    Two giant tortoises with long necks stand near water; one tortoise feeds on leaves from a tree while the other is near dense vegetation.
    Evolutionary History

    Domain: Life Science

    Unit type: Core

    Student role: Paleontologists

    Phenomenon: A mystery fossil at the Natural History Museum has similarities with both wolves and whales.    

    Download unit guide

    Two people climbing rocky terrain; illustrations show a hiking boot and a belt with gear.
    Harnessing Human Energy

    Domain: Physical Science

    Unit type: Launch

    Student role: Energy scientists

    Phenomenon: Rescue workers can use their own human kinetic energy to power the electrical devices they use during rescue missions.    

    Illustration of a futuristic space station with large solar panels, orbiting in deep space, emitting a blue glow from its propulsion system.
    Force and Motion

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: The asteroid sample-collecting pod failed to dock at the space station as planned.    

    Download unit guide

    Green geometric background with a hexagonal emblem containing a parachute icon, ruler, bandage, and stacked layers on a gradient pattern.
    Force and Motion Engineering Internship

    Domain: Physical Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Designing emergency supply delivery pods with different structures can maintain the integrity of the supply pods and their contents. 

    Illustration of a roller coaster filled with people, hands raised, going down a steep track against a bright blue sky with clouds.
    Magnetic Fields

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: During a test launch, a spacecraft traveled much faster than expected.    

    Illustration of a person in a red hat and fur-lined coat with eyes closed, surrounded by large orange circles on a dark background.
    Thermal Energy

    Domain: Physical Science

    Unit type: Core

    Student role: Thermal scientists

    Phenomenon: One of two proposed heating systems for Riverdale School will best heat the school.    

    Download unit guide

    Ilustración que muestra las etapas de fusión de una paleta de naranja: entera, parcialmente derretida, más derretida y casi derretida por completo, con palitos de madera, sobre un fondo morado.
    Phase Change

    Domain: Physical Science

    Unit type: Core

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart.    

    Download unit guide

    Green geometric graphic featuring icons: a baby, thermometer, layers, medical alert, and a flame.
    Phase Change Engineering Internship

    Domain: Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different combinations of phase change materials can keep babies at a healthy temperature.    

    Obra de arte digital abstracta que presenta numerosos círculos rojos y grises superpuestos sobre un fondo dividido de azul y violeta claro, creando una composición dinámica y enérgica.
    Chemical Reactions

    Domain: Physical Science

    Unit type: Core

    Student role: Forensic chemists

    Phenomenon: A mysterious brown substance has been detected in the tap water of Westfield.    

    Download unit guide

    An illustration from the Light Waves unit
    Light Waves

    Domain: Physical Science

    Unit type: Core

    Student role: Spectroscopists

    Phenomenon: The rate of skin cancer is higher in Australia than in other parts of the world.    

    Download unit guide

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    A closer look at grades 6–8

    Amplify Science is based on the latest research on teaching and learning and helps teachers deliver rigorous and riveting lessons through hands-on investigations, literacy-rich activities, and interactive digital tools that empower students to think, read, write, and argue like real scientists.

    In the 6–8 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.

    Is your school implementing the domain model? Click here.

    Collage of four images showing children engaged in educational activities such as conducting experiments and crafting in a classroom setting.
    A four-step process diagram: Spark intrigue, Explore evidence, Explain and elaborate, and Evaluate claims, connected by arrows, with an engagement statement below.

    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, students build and deepen their understanding, increasing their ability to develop and refine 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 6–8 program to address 100% of the NGSS in fewer lessons than other programs.

    Scope and sequence

    Every year our grades 6–8 sequence consists of 9 units, with each unit containing 10–19 lessons. Lessons are written to last a minimum of 45-minutes, though teachers can expand or contract the timing to meet their needs.

    A grid of educational icons, each representing a different science topic, such as earth and space science, life science, and physical science, with titles and lesson counts.

    Unit types

    Each unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, while also serving a unique purpose.

    In grades 6–8, there are three types of units:

    • One unit is a launch unit.
    • Three units are core units.
    • Two units are engineering internships.
    Launch units

    Launch units are the first units taught in each year of Amplify Science. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

    Core units

    Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

    Engineering Internship units

    Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

    Units at a glance

    Abstract digital artwork featuring a yellow human figure, red shapes, and a blue-toned screen, with vibrant, multicolored patterns and textures in the background.
    Microbiome

    Domain: Life Science

    Unit type: Launch

    Student role: Microbiological researchers

    Phenomenon: The presence of 100 trillion microorganisms living on and in the human body may keep the body healthy.  

    An abstract illustration of a person receiving an oral examination, with colorful geometric shapes and an eye chart in the background.
    Metabolism

    Domain: Life Science

    Unit type: Core

    Student role: Medical researchers

    Phenomenon: Elisa, a young patient, feels tired all the time.  

    Abstract orange background with geometric shapes, featuring icons of a vest, bar chart, leaf, beaker, fruit, medical stethoscope, and an envelope within a hexagonal frame.
    Metabolism Engineering Internship

    Domains: Life Science, Engineering Design

    Unit type: Engineering internship

    Student role: Food engineers

    Phenomenon: Designing health bars with different molecular compositions can effectively meet the metabolic needs of patients or rescue workers.  

    Six spiders with varying body colors (brown, yellow, blue, and red) and patterns are arranged on a dark, textured background, seemingly in a diagram or chart formation.
    Traits and Reproduction

    Domain: Life Science

    Unit type: Core

    Student role: Biomedical students

    Phenomenon: Darwin’s bark spider offspring have different silk flexibility traits, even though they have the same parents.  

    Illustration of a person with closed eyes in a red winter coat and hat, surrounded by falling snow and orange circles on a dark background.
    Thermal Energy

    Domain: Physical Science

    Unit type: Core

    Student role: Thermal scientists

    Phenomenon: One of two proposed heating systems for Riverdale School will best heat the school. 

    Abstract illustration of a sun with blue and orange rays over a colorful landscape featuring green hills and a vibrant sky.
    Ocean, Atmosphere, and Climate

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.  

    Illustration of clouds above a small town and farmland, with wind currents depicted swirling through the landscape under a blue sky.
    Weather Patterns

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Forensic meteorologists

    Phenomenon: In recent years, rainstorms in Galetown have been unusually severe.  

    A polar bear stands on a small floating ice sheet in the ocean, surrounded by melting ice, with a red sun in the sky.
    Earth’s Changing Climate

    Domains: Earth and Space Science, Life Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.  

    A purple hexagonal graphic with icons including a building, wrench, screwdriver, sun, molecules, paint bucket, and tiles on a geometric patterned background.
    Earth’s Changing Climate Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.  

    A robotic rover sits on a hill in a rocky, reddish landscape, with visible tracks in the dust leading to its current position under a hazy sky.
    Geology on Mars

    Domain: Earth and Space Science

    Unit type: Launch

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable. 

    Two green prehistoric reptiles with long snouts are near the shore; one is on land while the other swims in blue water, with plants, rocks, and an island in the background.
    Plate Motion

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean, even though the Mesosaurus species once lived all together.  

    A purple geometric background featuring a hexagonal badge with a telescope, mountain, audio wave, and star symbols inside.
    Plate Motion Engineering Internship

    Domains: Earth and Space Science, Engineering Design

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.  

    Illustration showing an ocean, forest, and mountains with a smoking volcano, plus a cross-section of underground tectonic plates.
    Rock Transformations

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.  

    Four stages of an orange popsicle melting on a stick, from fully frozen on the left to completely melted on the right, against a plain background.
    Phase Change

    Domains: Physical Science, Earth and Space Science

    Unit type: Core

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart

    Green geometric background with an outlined hexagon containing icons: a parachute, ruler, letter "A," bandage, stacked blocks, and a folded corner paper.
    Force and Motion Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different combinations of phase change materials can keep babies at a healthy temperature. Domains: Engineering Design, Physical Science

    Abstract illustration showing red and blue circles on a split blue and light background, representing molecular movement across a membrane or barrier.
    Chemical Reactions

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Forensic chemists

    Phenomenon: A mysterious brown substance has been detected in the tap water of Westfield.  

    An underwater scene with a large whale surrounded by turtles, jellyfish, and various fish swimming in different directions.
    Populations and Resources

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in Glacier Sea has increased. 

    Low-poly digital illustration of a fox hunting a rabbit in a forest with pine trees, mushrooms, mountains, and the sun in the background. Another rabbit sits near the trees.
    Matter and Energy in Ecosystems

    Domains: Life Science, Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Ecologists

    Phenomenon: The biodome ecosystem has collapsed.  

    Two people climb over rocks filled with electronic devices; inset illustrations show a boot, a belt of batteries, and a radio.
    Harnessing Human Energy

    Domains: Physical Science, Earth and Space Science, Engineering Design

    Unit type: Launch

    Student role: Energy scientists

    Phenomenon: Rescue workers can use their own human kinetic energy to power the electrical devices they use during rescue missions.  

    A spacecraft approaches and docks with a modular space station featuring large blue solar panels, set against a black space background.
    Force and Motion

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: The asteroid sample-collecting pod failed to dock at the space station as planned.

    Green graphic with hexagonal emblem showing an infant, a thermometer, layered materials, a medical symbol, and a flame icon.
    Force and Motion Engineering Internship

    Domains: Engineering Design, Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing emergency supply delivery pods with different structures can maintain the integrity of the supply pods and their contents.

    Illustration of a roller coaster car with passengers raising their arms as they descend a steep track against a blue sky with clouds.
    Magnetic Fields

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: During a test launch, a spacecraft traveled much faster than expected.  

    Illustration of the Earth with arrows representing radiation or energy entering the atmosphere from space, focused on the Asia-Pacific region.
    Light Waves

    Domains: Physical Science, Life Science, Earth and Space Science

    Unit type: Core

    Student role: Spectroscopists

    Phenomenon: The rate of skin cancer is higher in Australia than in other parts of the world.

    A city skyline at night with illuminated windows, a large full moon, stars in the sky, and a bridge visible on the left side.
    Earth, Moon, and Sun

    Domains: Earth and Space Science, Physical Science

    Unit type: Core

    Student role: Astronomers

    Phenomenon: An astrophotographer can only take pictures of specific features on the Moon at certain times.  

    Four polygonal dinosaurs walking in a row, three green and one yellow, each with a rock and purple spikes on their backs, set against a grassy background with a blue sky.
    Natural Selection

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The newt population in Oregon State Park has become more poisonous over time.  

    Red geometric background featuring a hexagonal emblem with icons of a world map, mosquito, DNA strand, bar chart, and interconnected blocks.
    Natural Selection Engineering Internship

    Domains: Engineering Design, Life Science

    Unit type: Engineering internship

    Student role: Clinical engineers

    Phenomenon: Designing malaria treatment plans that use different combinations of drugs can reduce drug resistance development while helping malaria patients.  

    Two tortoises with long necks are by a river; one is browsing leaves from a bush while the other is walking near the water's edge.
    Evolutionary History

    Domains: Life Science, Earth and Space Science

    Unit type: Core

    Student role: Paleontologists

    Phenomenon: A mystery fossil at the Natural History Museum has similarities with both wolves and whales.    

    A closer look at grades 6–8 (domain)

    Amplify Science is based on the latest research on teaching and learning and helps teachers deliver rigorous and riveting lessons through hands-on investigations, literacy-rich activities, and interactive digital tools that empower students to think, read, write, and argue like real scientists.

    In the 6–8 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.

    Is your school implementing the domain model? Click here.

    Collage of four images showing children engaged in educational activities such as conducting experiments and crafting in a classroom setting.
    A four-step process: Spark intrigue, Explore evidence, Explain and elaborate, and Evaluate claims, leading to ongoing engagement and building complexity.

    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, students build and deepen their understanding, increasing their ability to develop and refine 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 6–8 program to address 100% of the NGSS in fewer lessons than other programs.

    Scope and sequence

    Every year our grades 6–8 sequence consists of 9 units, with each unit containing 10–19 lessons. Lessons are written to last a minimum of 45-minutes, though teachers can expand or contract the timing to meet their needs.

    A grid of educational icons, each representing a different science topic, such as earth and space science, life science, and physical science, with titles and lesson counts.

    Unit types

    Each unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, while also serving a unique purpose.

    In grades 6–8, there are three types of units:

    • One unit is a launch unit.
    • Three units are core units.
    • Two units are engineering internships.
    Launch units

    Launch units are the first units taught in each year of Amplify Science. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to actively read in all subsequent units.

    Core units

    Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

    Engineering Internship units

    Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

    Units at a glance

    A rover sits on a rocky, reddish hill under a hazy sky, leaving visible tire tracks across the barren landscape.
    Geology on Mars

    Domain: Earth and Space Science

    Unit type: Launch

    Student role: Planetary geologists

    Phenomenon: Analyzing data about landforms on Mars can provide evidence that Mars may have once been habitable.    

    Two prehistoric marine reptiles with long snouts are near a rocky shoreline, one on land and one in the water, with an island and clouds in the background.
    Plate Motion

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Mesosaurus fossils have been found on continents separated by thousands of kilometers of ocean, even though the Mesosaurus species once lived all together.    

    A geometric badge with a mountain, telescope, and audio wave icons on a purple background with polygonal shapes.
    Plate Motion Engineering Internship

    Domain: Earth and Space Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Patterns in earthquake data can be used to design an effective tsunami warning system.    

    Illustration of a volcano by the sea with smoke, trees, mountains, and a cross-section showing a fault line beneath the ground.
    Rock Transformations

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Geologists

    Phenomenon: Rock samples from the Great Plains and from the Rocky Mountains — regions hundreds of miles apart — look very different, but have surprisingly similar mineral compositions.    

    Illustration of a city skyline at night with buildings, a bridge, and a large full moon in a starry sky.
    Earth, Sun, and Moon

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Astronomers

    Phenomenon: An astrophotographer can only take pictures of specific features on the Moon at certain times.    

    Abstract digital painting of a landscape with green hills, a red-orange horizon, and a large yellow sun surrounded by blue and orange swirling shapes on the right.
    Ocean, Atmosphere, and Climate

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: During El Niño years, the air temperature in Christchurch, New Zealand is cooler than usual.    

    Illustration of a town with houses and fields under a sky with large clouds and swirling wind patterns, set against a backdrop of hills and mountains.
    Weather Patterns

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Forensic meteorologists

    Phenomenon: In recent years, rainstorms in Galetown have been unusually severe.    

    A polar bear stands on a small ice floe surrounded by water and floating ice under a red sun in an Arctic landscape.
    Earth’s Changing Climate

    Domain: Earth and Space Science

    Unit type: Core

    Student role: Climatologists

    Phenomenon: The ice on Earth’s surface is melting.    

    Hexagonal badge with icons including a wrench, building, sun, screwdriver, paint can, and molecules on a purple geometric background.
    Earth’s Changing Climate Engineering Internship

    Domain: Earth and Space Science

    Unit type: Engineering internship

    Student role: Civil engineers

    Phenomenon: Designing rooftops with different modifications can reduce a city’s impact on climate change.    

    Colorful abstract digital artwork featuring a yellow figure holding a device, with blue and red shapes and textured patterns in the background.
    Microbiome

    Domain: Life Science

    Unit type: Launch

    Student role: Microbiological researchers

    Phenomenon: The presence of 100 trillion microorganisms living on and in the human body may keep the body healthy.    

    An abstract illustration of a person having their mouth and throat examined with a tongue depressor, surrounded by colorful shapes, with an eye chart in the background.
    Metabolism

    Domain: Life Science

    Unit type: Core

    Student role: Medical researchers

    Phenomenon: Elisa, a young patient, feels tired all the time.    

    Geometric orange background with a hexagon icon displaying symbols for statistics, farming, healthcare, safety vest, chemistry, and agriculture.
    Metabolism Engineering Internship

    Domain: Life Science

    Unit type: Engineering internship

    Student role: Food engineers

    Phenomenon: Designing health bars with different molecular compositions can effectively meet the metabolic needs of patients or rescue workers.    

    Six spiders with different colors and stripe patterns are arranged in a grid pattern on a dark background, showing variations in leg and body color.
    Traits and Reproduction

    Domain: Life Science

    Unit type: Core

    Student role: Biomedical students

    Phenomenon: Darwin’s bark spider offspring have different silk flexibility traits, even though they have the same parents.    

    An underwater scene shows a whale surrounded by jellyfish, sea turtles, and fish, with sunlight filtering through the water.
    Populations and Resources

    Domain: Life Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The size of the moon jelly population in Glacier Sea has increased.    

    A low-poly landscape with trees, mushrooms, a rabbit sitting, and a fox bending down near another rabbit under a sunny sky with mountains in the background.
    Matter and Energy in Ecosystems

    Domain: Life Science

    Unit type: Core

    Student role: Ecologists

    Phenomenon: What caused the mysterious crash of a biodome ecosystem?    

    Three green dinosaurs and one yellow dinosaur stand in a row on grass, each with purple spikes and a red spot on their backs. The sky is blue with light clouds.
    Natural Selection

    Domain: Life Science

    Unit type: Core

    Student role: Biologists

    Phenomenon: The newt population in Oregon State Park has become more poisonous over time.    

    Red-toned graphic with hexagonal badge featuring a world map, a mosquito, a DNA strand, charts, cubes, and circular icons. Geometric background pattern.
    Natural Selection Engineering Internship

    Domain: Life Science

    Unit type: Engineering internship

    Student role: Clinical engineers

    Phenomenon: Designing malaria treatment plans that use different combinations of drugs can reduce drug resistance development while helping malaria patients.  

    Two giant tortoises are near a river; one is by the water and the other is standing on land and stretching its neck toward a leafy tree.

    Evolutionary History

    Domain: Life Science

    Unit type: Core

    Student role: Paleontologists

    Phenomenon: A mystery fossil at the Natural History Museum has similarities with both wolves and whales.    

    Two people climb over rocky terrain strewn with electronic waste, with illustrated insets showing a hiking boot, a solar-powered device, and a person adjusting a belt-like gadget.
    Harnessing Human Energy

    Domain: Physical Science

    Unit type: Launch

    Student role: Energy scientists

    Phenomenon: Rescue workers can use their own human kinetic energy to power the electrical devices they use during rescue missions.    

    A spacecraft approaches a modular space station with large solar panels, set against a backdrop of outer space.
    Force and Motion

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: The asteroid sample-collecting pod failed to dock at the space station as planned.    

    Green geometric background with a hexagonal badge showing a parachute, a box, a ruler, a bandage, and stacked layers.
    Force and Motion Engineering Internship

    Domain: Physical Science

    Unit type: Engineering internship

    Student role: Mechanical engineering interns

    Phenomenon: Designing emergency supply delivery pods with different structures can maintain the integrity of the supply pods and their contents. 

    Illustration of a roller coaster car full of people with raised arms, speeding down a loop against a blue sky with clouds.
    Magnetic Fields

    Domain: Physical Science

    Unit type: Core

    Student role: Physicists

    Phenomenon: During a test launch, a spacecraft traveled much faster than expected.    

    Illustration of a person in a red coat and hat with arms crossed, eyes closed, surrounded by large orange and brown circles, possibly representing snow or lights.
    Thermal Energy

    Domain: Physical Science

    Unit type: Core

    Student role: Thermal scientists

    Phenomenon: One of two proposed heating systems for Riverdale School will best heat the school.    

    An orange popsicle gradually melts, shown in four stages from solid to completely melted, with wooden sticks visible, against a purple background.
    Phase Change

    Domain: Physical Science

    Unit type: Core

    Student role: Chemists

    Phenomenon: A methane lake on Titan no longer appears in images taken by a space probe two years apart.    

    A green background with a picture of a person and a sandwich.
    Phase Change Engineering Internship

    Domain: Physical Science

    Unit type: Engineering internship

    Student role: Chemical engineering interns

    Phenomenon: Designing portable baby incubators with different combinations of phase change materials can keep babies at a healthy temperature.    

    Digital illustration showing red and blue molecules on a blue background transitioning to a lighter background, representing molecular diffusion across a boundary.
    Chemical Reactions

    Domain: Physical Science

    Unit type: Core

    Student role: Forensic chemists

    Phenomenon: A mysterious brown substance has been detected in the tap water of Westfield.    

    Illustration of Earth with yellow arrows and colored waves approaching from the left, representing incoming solar or cosmic radiation.
    Light Waves

    Domain: Physical Science

    Unit type: Core

    Student role: Spectroscopists

    Phenomenon: The rate of skin cancer is higher in Australia than in other parts of the world.    

    Welcome, Utah K-8 reviewers!

    To view this protected page, enter the password below:



    Math resources that tap into your students’ curiosity

    As a teacher, you create a collaborative math community with students at its center.

    We’re here to help.

    Amplify Desmos Math

    Complete core program (Grades K–12)

    A new, curiosity-driven K–12 program that builds lifelong math proficiency.

    Amplify Desmos Math provides:

    • The ability to transform every classroom into an engaged math community that invites, values, and develops student thinking.
    • Supports and guidance for teachers to systematically build from students’ prior knowledge to grade-level learning.
    • Actionable, asset-based data that informs instruction and personalizes learning, building on what students already know.

    Amplify Classroom

    Free teaching and learning platform (Grades K–12)

    Amplify Classroom is an interactive teaching and learning platform with hundreds of free K–12 lessons, virtual manipulatives, and teaching tools. With a free teacher account, you can access:

    • Interactive lessons and activities that strengthen classroom learning while building math fact-fluency
    • Polypad virtual manipulatives that allow you to model mathematical concepts in a creative way.
    • A Teacher Dashboard with real-time visuals that provide visibility into student thinking.
    • A lesson-building tool where you can customize or create your own lessons.

    mCLASS® Math

    Screening and progress monitoring (Grades K–8)

    Expect more from your assessments with mCLASS® Math, a complete K–8 benchmark and progress monitoring assessment system. mCLASS Math provides educators not only with reliable measures of student achievement, but also with an asset-based approach that analyzes student responses to uncover underlying mathematical thinking.

    Boost Math

    Targeted intervention and practice (Grades K–8)

    Boost Math is a K–8 intervention and practice math program that brings grade-level, core-aligned math within reach for every learner. By turning assessment data into targeted learning pathways connected to core math topics, Boost Math helps streamline MTSS and support teachers in delivering the right instruction at the right time.

    Ready to learn more?

    Fill out this form and we’ll be in touch soon.

    Explore more programs

    Our programs are designed to support and complement one another. Learn more about our related programs.

    Our programs

    At Amplify, we support teachers in delivering inspiring, impactful lessons that celebrate and develop the thinking of all their students. See how we build high-quality programs.