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Amplify Desmos Math for Crane Elementary School District

Amplify Desmos Math taps into students’ natural curiosity from the start of every lesson, helping teachers cultivate a classroom of eager, collaborative learners.

Amplify Desmos Math is based on Illustrative Mathematics® IM K–12™ and expands on Desmos Math 6–8 (which received all-green ratings from EdReports) with beautiful print resources, and robust practice, differentiation supports, assessment and reporting. Read the review on EdReports.

About the program

Amplify Desmos Math makes it easy for both teachers and students to make the shift to a problem-based approach by providing captivating activities, powerful teacher-facilitation tools, and lots of support for differentiation and practice.

We’ve combined interactive problem-based lessons with explicit instruction, reinforcement, and practice to enable students to develop math proficiency that lasts. Lessons set a strong foundation in procedural and fact fluency, deepen understanding of concepts, and enable students to apply learning to real-world tasks.

Amplify Desmos Math will be available for 2025–26 school year implementation. Interested districts can pilot the Beta release starting fall 2024.

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Comprehensive

  • Curriculum based on Illustrative Mathematics® IM K–12™
  • Differentiation and personalized practice
  • Robust assessments and reports
  • Student materials in Spanish
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Collaborative

  • Powerful teacher-facilitation supports and tools
  • Students talking and building from each other’s ideas 
  • Every lesson has fully compatible print and digital materials for an inclusive classroom
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Delightful

  • Curiosity-driven lessons that drop students into a real-world problem they want to solve
  • Desmos Classroom technology provides instant, interactive feedback to push students’ thinking
  • Colorful, visual guidance for teachers and students
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Scope and sequence

Click the links below to view the program scope and sequence for grades K–5 and for grade 6–Algebra 1.

Preview lessons

Check out the links below to explore our interactive digital lessons, as well as preview pages from the Teacher Editions and Student Editions. Watch our quick walkthrough video for tips on navigating our lesson resources.

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Grade 1, Unit 3, Lesson 15: 10-frames and Towers

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Grade 2, Unit 1, Lesson 3: Ways to Make 10

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Grade 5, Unit 1, Lesson 3: Cube Figures

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Grade 5, Unit 7, Lesson 7: Bullseye!

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Grade 6, Unit 6, Lesson 16: Subway Fares

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Grade 7, Unit 6, Lesson 14: Unbalanced Hangers

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Grade 8, Unit 4, Lesson 4: More Balanced Moves

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Algebra 1, Unit 2, Lesson 6: Shelley the Snail

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.
 
Listen now and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!
 
Enjoy this episode and explore more from Math Teacher Lounge by visiting our main page. 

Download Transcript

Dr. Erin Maloney (00:00):

It’s the anxiety itself in many ways that can cause people to underperform.

Bethany Lockhart Johnson (00:06):

Welcome back to Math Teacher Lounge. I’m Bethany Lockhart Johnson.

Dan Meyer (00:10):

And I’m Dan Meyer.

Bethany Lockhart Johnson (00:11):

This is episode two of our new season, all about math anxiety. Who has it? What is it? What do we do about it?

Dan Meyer (00:20):

I’m learning so much, learning a ton.

Bethany Lockhart Johnson (00:22):

I loved our first conversation with Dr. Gerardo Ramirez, episode one, our first episode of the season. Really, our goal with that conversation was just to—we need to talk about the basics of it, for reals. Like, what is math anxiety?

Dan Meyer (00:36):

What is it? How do you measure it? How’s it defined? Super-helpful stuff.

Bethany Lockhart Johnson (00:40):

There’s not only one way that it’s measured. But it’s like, in active research right now, how are folks making sense of it? And I think Dr. Ramirez did such a fantastic job of sharing that with our listeners. And I learned a lot. You learned a lot, Dan?

Dan Meyer (00:56):

I did. And I’m also super-excited to take that knowledge that we have developed together and go and build on top of it and keep on climbing up up the mountain here, and learn more about math anxiety. Which is why we’re super-excited to have a guest on, Dr. Maloney, who is going to help us learn more—especially about what happens to the brain when it’s experiencing math anxiety. There’s some really complex stuff that happens there, including the role of parents and educators in creating and resolving math anxiety. And I think we’ll also learn that the whole situation is a bit of a hot mess. And we’ll try to make it a little bit less messy together.

Bethany Lockhart Johnson (01:34):

Little bit less messy. Dan, if we do nothing else, can we make it a little less messy?

Dan Meyer (01:41):

I sometimes prefer more mess, but in this case I prefer less. So.

Bethany Lockhart Johnson (01:45):

I have a two-year-old, so everything is a mess.

Dan Meyer (01:47):

Your life is mess. Yes. <laugh> Right. Well, I’m excited for you folks to hear this. It was a delightful conversation, so yeah, tune in. We are joined by Dr. Erin Maloney.

Bethany Lockhart Johnson (01:56):

Let’s go. We are joined by Dr. Erin Maloney, associate professor in the School of Psychology at the University of Ottawa, where she directs the Cognition and Emotion Laboratory, as well as serving as the Canada Research Chair in Academic Achievement and Well-being. Welcome to the show, Dr. Maloney. We’re so excited to have you in the Lounge.

Dr. Erin Maloney (02:20):

Yeah, thank you so much for having me. This is fantastic.

Bethany Lockhart Johnson (02:24):

So our last season was all about math and joy. And even when I read your title, I felt more joyful. Like, somebody is thinking about academic achievement, but with well-being in mind. I love it.

Dr. Erin Maloney (02:39):

Aw, thank you.

Dan Meyer (02:40):

Cognition and emotion!

Bethany Lockhart Johnson (02:42):

E-mo-tion!

Dr. Erin Maloney (02:43):

I don’t think they can be separate. I think that you have to think about them together, ’cause they’re so intricately connected.

Dan Meyer (02:49):

Love that. People try, but we love that. Yeah. That’s our vibe here, too.

Bethany Lockhart Johnson (02:52):

People try. That was a big problem with my math anxiety. They just wanted…there was no room for my emotion. They’re like, stop weeping at your desk—

Dan Meyer (03:00):

It’s rearranging neurons….

Bethany Lockhart Johnson (03:01):

—you’re distracting the other children. So would you mind telling us the story of how you even got interested in this topic? You know, when you tell people that you study math anxiety—or, actually, I don’t know how you describe it to them; I’m hopeful you bring in that well-being part—but how did you get here? What do you, what do you, what do you…yeah, tell us! We love it!

Dr. Erin Maloney (03:23):

<laugh> I feel like what you’re actually asking is, “How did you make life choices that got you to here?” <Laugh>

Bethany Lockhart Johnson (03:29):

Justify your life choices! Ready? Go!

Dr. Erin Maloney (03:32):

<laugh> Whoo. OK. So, all right. So we often, in psychology, we joke that instead of doing research, we do “me-search.” And that’s, that’s admittedly true in my case. I was a student who absolutely loved math up until about eighth grade, and then something changed, and all of a sudden I was terrified of math and I had absolutely no sense of self-efficacy in it. Despite trying really hard, I was extremely anxious about it. And so I initially, I set out…my parents were completely convinced that I was absolutely capable of doing mathematics and that I was getting in my own way. And when I went to university, I decided to prove them wrong. So I set out to prove that some people just can’t do math, and that’s the end of it. And, you know, 20 plus years later, my parents were right. And it turns out that many people—well, I would argue virtually everyone—can do math. And that if you are really anxious about it, it can get in the way. And interestingly, you know, in, in the years that we’ve been doing this research, there’s really good strategies that can be used—that hopefully we get a chance to chat about—that can really help reduce the amount of anxiety that students are experiencing. But I really did set out, like the bold teenager that I was, to prove my parents wrong. And that backfired <laugh>. So I know it’s kind of a strange answer, but it’s the truth. So I was really interested in understanding why it was some people just could not do math.

Dan Meyer (05:10):

That makes two for two so far, on guests for this season who did a version of me-search. And I feel like this is pretty common for a lot of researchers. Like, I wanna figure out…my experience as a teacher, the part where you, I think, diverge from a lot of people I knew in grad school, myself included, is that you actually let counter evidence change your perspective on things. Whereas I feel like a lot of us go in: “I know this is true and I’m gonna gather data!” and lo and behold, I’m true! But only now, with the research TM, you know, trademarked research, attached to it. So that’s, really exciting. Thanks for sharing that.

Dr. Erin Maloney (05:43):

No, you’re welcome.

Bethany Lockhart Johnson (05:44):

But don’t people say that the more personal you get, the more universal it is? Right? So if you go and get your doctorate about something that you think is just your experience or in your brain, then people are gonna be gonna be like, “Wait a second; you think that too?” “Wait, that math anxiety isn’t just you?” I don’t know, it sounds like a pretty great path to me. When you tell folks that you study math anxiety or when you’re speaking to folks about your research, do you find that there is a lot of folks who relate to what you’re studying? Or how does that conversation typically go?

Dr. Erin Maloney (06:20):

Yeah, so it is I think an extremely relatable topic. Not in the sense that everyone experiences anxiety about math, but everyone seems to know somebody who’s really anxious about math. Or everyone’s at least aware of the stereotype that like some people are math people and some people aren’t, and that’s just the way it is. So it feels like everyone has feelings about math and everyone seems very happy to share those feelings. So one thing I’ve always found really interesting, and actually, so I, I know you mentioned that you had Gerardo on recently. Gerardo and I have had really interesting conversations about how people are really quick to tell you that they hate math and they can’t do math, and they’re anxious about math. And I’ve yet to have anyone ever tell me they hate reading, they can’t read, they’re really anxious about reading as an adult. So for some reason math seems really different. And in that sense people always seem to be pretty excited to talk about their feelings towards math.

Dan Meyer (07:23):

Yeah, definitely. Been on an airplane or two myself and had those conversations. You know, people asking to be reseated because they found out that I do math for a living or whatever. Or just unburdening themselves, for sure. I’m super-curious: I think that the fact that you are doing the me-search is reason enough to want to dedicate your life to this study. But I am curious: If you were gonna justify to someone else, why is math anxiety important to study? What are its consequences, even outside of math education? What would you say to that?

Dr. Erin Maloney (07:57):

So I think it’s probably not hard to convince people that success in math is important, right? So we know that children who start elementary school behind in mathematics tend to stay behind in mathematics, unless they have any kind of very targeted intervention. We know that children who do worse in mathematics throughout K to 12 education in general get lower-paying jobs when they’re older. We also know that when they do worse than mathematics relative to their peers, there’s fewer jobs that are open to them, relative to if they excelled in math. Right? And so I think in many ways there are really clear consequences for students who are not comfortable with math and who avoid it. But I think one of the really, really interesting things about math anxiety, and maybe part of why I’ve fallen in love with it as a research topic is that it’s the anxiety itself in many ways that can cause people to underperform. So it’s not just the case that people who are bad at math are anxious about it. It’s actually that the anxiety itself can cause you to do worse in math. And that for me is really exciting, ’cause it means that if we can change your mindset, then we can really set you on a path with several more options available to you career-wise. And I think that is really empowering.

Dan Meyer (09:18):

Hmm. Yeah, definitely. And I’d love for you to explore — your laboratory is the cognition and emotion laboratory, which I love, how you’re creating those linkages between how you feel about a thing and what your opportunities or your aptitude for learning it. I’m really curious, can you say more about the, the relationship there? How does feeling anxiety impair your ability to do mathematics?

Dr. Erin Maloney (09:41):

Yeah, so feeling anxiety, typically what you tend to experience is these negative thoughts and ruminations. So you can imagine, you’re somebody who doesn’t really love math, you’re pretty anxious about it; you know, Bethany, maybe you’ve had this kind of experience before. I’m gonna call you out on it. I’ve had it many times, where you sit down to do a math test and all of a sudden you’re not focusing on the actual math test in front of you. You’re focusing on things like the consequences of not doing well on this. Right? Or “my parents are gonna be really disappointed if I don’t pass this test,” or “my teacher is gonna think negatively negative of me,” or sometimes we see things like, “I’m a girl, girls don’t do math.” These types of stereotypes. And what happens is that those thoughts actually tie up really important cognitive resources, like, really important memory resources, that you need to do the math test. And so if you are trying to essentially do two things at once, right? You’re trying to deal with all these negative thoughts that are distracting you and you’re trying to do the math test, then you’re not going to do as well as someone who’s sitting down and doesn’t have all of these distracting thoughts to deal with. And we actually know that from research that we have in our lab right now, where we just ask people like, “Hey, when you did this math test, what kind of stuff are you thinking about?” what we find is that the people who are really anxious about math report a whole bunch of thoughts that are unrelated really to the math test, per se. It’s more about the consequences of doing poorly. And as a result of those thoughts, they actually end up doing worse.

Dan Meyer (11:14):

This has been really helpful to figure out, how the emotional state of doing math affects the ability to do math. And it’s really interesting how you’re saying that the direction of the causality can go from the emotions to the cognition. And I’m just curious then, what is the source of the bad emotions about math? Where does that come from? Is it nature? Is it nurture? Some combination? How do you see it?

Dr. Erin Maloney (11:39):

Yeah, so one, that’s a fantastic question. And there’s been a whole bunch of people all around the world that have been spending a lot of time really trying to pinpoint that down. And I think the answer is that it’s, you know, it’s complex. So most of what it’s looking like right now is that it is a combination of both. So essentially what we find is that kids who start elementary school who are a little bit behind in math—and for the question of why they’re behind, that’s also complex; it could be genetics, it could be just environmental input, before the child ever entered formal schooling kind of thing—but in essence, what we find is that kids that start school behind in mathematics, those are the children who are most likely to develop anxiety about math by the time they’re finished first grade. OK? But we also know that once they’ve developed the anxiety about math, then that’s when they get these thoughts and ruminations that kind of tie up those memory resources, that then is gonna make it harder for them to succeed in math tests. So you get into this sort of vicious cycle, right? Where maybe you start behind a little bit and then you develop the anxiety, the anxiety causes you to underperform relative to what you should be able to, so now you’re even further behind, you get more anxious because you’re not doing as well as you’d like to…but again, kind of coming back to the “Why are the children starting behind in the first place?” Some of that seems to be the role that parents are playing in the household. So some kids come from a household where parents are playing a lot more math games with them, talking about mathematical concepts on a regular basis. Maybe they have older siblings who are, you know, practicing arithmetic and, and mathematical processing in front of them. And so those kids are exposed to more math before they ever even start formal schooling. Those kids seem to do better. And then we also know that the parents’ attitudes matter a lot too. So what we find is that when parents are high in math anxiety themselves, especially when they help their children a lot with their math homework in really early ages, we find that those kids end up being more anxious about math by the end of the school year, and they also end up doing worse in mathematics. So it really does seem to be, you know, kind of a complex set of factors that have something to do with both maybe genetic predisposition to success in math and genetic predisposition to anxiety, but then also the social attitudes and stereotypes about math to which you’re exposed at home that really seem to be coming together to create this anxiety in young children.

Bethany Lockhart Johnson (14:24):

I feel like everything you’re saying is <laugh>…it makes so much sense and yet it’s so often not talked about, right? Because it’s just more like, it gets boiled down to, “Oh, they’re just not a math person,” instead of all these other factors that are at play. And I completely remember the anxiety I felt, whether it was a test or not, walking into my math classroom when I was in ninth grade. And there’s no way I was set up and ready to learn. Right? <Laugh>. And something with—we mentioned Dr. Ramirez, he was talking about validating that anxiety. If teachers validate that like, “Oh, you know what, sometimes you might feel stumped, or this might feel overwhelming.” Even the power in creating space for that in the classroom, right? And acknowledging that it doesn’t—math doesn’t have to “come easy” to you in order for you to have access or make sense, is such a powerful concept. And I love the way that you are looking at all these different factors and saying, “Hey, it’s both simple and also a lot more complicated than we’re we’re making it.” Right?

Dr. Erin Maloney (15:36):

No, and I agree with that sentiment so much. Like, I think, though—one thing I will sort of caution is that I think when teachers are validating the anxiety, or when parents are validating the anxiety, I think there’s a very fine line that needs to be walked where we need to be able to say, you know, “It’s OK to struggle with something. That’s, that is completely OK.” And as we’re, you know, as we’re working towards something that’s really valuable, right? We can, we can work hard at something and by working hard at it, we’re going to get better. And I think that type of validating is really, really important and valuable. I think what we wanna be careful of is not to say things like, “Oh, it’s OK. I also never loved math.” And, you know, “Oh, I was never a math person either.” And so even though we might be bringing comfort to the the child, I think that that’s sending the wrong message. And so sometimes it’s really well intentioned and really not great—

Bethany Lockhart Johnson (16:37):

A hundred percent.

Dr. Erin Maloney (16:38):

—in terms of the messaging. So that’s the only…so just for people listening, the only sort of caution that I would give there is that I think there’s nuances to the validating of the feelings that are important.

Bethany Lockhart Johnson (16:50):

I am so glad you said that because as a kindergarten teacher, I vividly remember—and this is as early as, you know, the kids are five years old, right?—and I remember in a parent-teacher conference, a parent saying, “Oh, I wasn’t a math person either,” or, “Oh, no, ugh.” And they were so quick, like you said, they wouldn’t say that about reading, but they were so quick to talk about their lack of natural math aptitude, right? And, and it was really interesting because you know that even if they’re not saying that specific thing at home, those attitudes are absolutely carrying over at home. And they’re absolutely carrying over to, to how they interact with their kiddo around math and around what’s happening in the conversations about math. And I felt like a lot of times my work as a teacher was also to help support parents through their own math anxiety, and help give them some new language for how they can talk about math. And that math is more than just getting to an answer quickly. Like, let’s talk about, let’s go on math walks, let’s go on number walks, what numbers are around the home? Or oh, is that bigger than this? Do you have more of this? And even those little things, I, my hope was that it was starting to shift the conversation around what math was possible in the home, particularly when you saw that it was the parents who had palpable math anxiety. Right? And how much you know that that’s gonna impact what’s happening when you sit down to do homework together.

Dr. Erin Maloney (18:22):

Yeah. And I love that you have worked to encourage parents to do that. So we do similarly. Like even from a research perspective, where I will often give talks to parents and teachers and we talk about the idea of trying to mathematize everything, right? So just the idea that math is absolutely everywhere, and you know, whether it’s a matter of playing games in the car with your kids where you’re thinking of a number and it’s “My number is higher than 42, but lower than 80, and what number do you think I might be thinking of?” And, and gradually trying to get the child to that number. Or, you know, asking questions like, “What’s your favorite even number and why?” And just little things like that that, that I think can make math fun for kids, that help—I don’t even know how to explain it, but just that idea of bringing joy into it, so it’s not always this heavy subject that kids have to come to. So we definitely try to talk to parents about the idea of, like I said, mathematizing everything. And usually it’s well-received, ’cause often parents find it empowering, right? They’re like, “Oh, well, I could do that! But like, that’s not math!” And you’re like, “No, but it is.”

Dan Meyer (19:33):

Yep.

Dr. Erin Maloney (19:34):

Like, it is! And sometimes parents will say like, “Well, I don’t know how to do fractions.” And you’re like, “OK, but how do you bake?” “Well, I don’t know! I just, like, I know how to do those fractions!” And you’re like, “OK, but that’s the starting point. Let’s work with that.” Like, let’s, you know. And I think a lot of times, it’s reminding the parents that they’re actually far more capable than what they think they are, despite the fact that maybe they struggled with math when they were younger.

Dan Meyer (19:58):

Yeah. This is so interesting. And I feel like part of the challenge around conversations about anxiety and math and how to, how to resolve it and where it comes from, is that it, like, it presupposes a single definition of math. And so, you know, we’re talking about like how to be more mindful about math. But you know, like if kids were walking every day through a treacherous street, you know, the solution might not be become more mindful about that street. It’s just like, we gotta fix the treacherous nature of the street, really. You know, I love that we’re talking also about redefining what math is, making it more playful. That feels like a super-important component here. I’d love to know more about what you know about the role of gender in all of this. Are there differences in the way boys and girls experience math anxiety and how it relates to achievement in math?

Dr. Erin Maloney (20:48):

Yeah, so, there’s really, really interesting research on gender in math anxiety. So in general, we find that girls tend to experience more anxiety about math than boys do. So one hypothesis is that it has to do with just social stereotypes that, you know, girls are, are good at reading; boys are good at math, kind of thing. So there’s some evidence to suggest that that might be playing a role. There’s other evidence to suggest as well that maybe boys actually do experience as much anxiety, they just don’t really own up to it.

Dan Meyer (21:20):

Ooh, yikes.

Dr. Erin Maloney (21:21):

So thoughts are, you know, there’s a bit of an apprehension for males to admit experiencing the anxiety. But I think one of the things that is extremely interesting about it—at least to me—is that we don’t tend to see gender differences in young children. So in early elementary school, even though we’ll see that kids as young as six years old will experience anxiety about math, and that that anxiety is related to how well they do in math and how much they enjoy math, it doesn’t seem to vary as a function of gender at that young age. It doesn’t seem to be related to gender until kids are at about sixth, seventh grade that we really start to see this gender difference coming online. And so that, to me, suggests that it’s probably something more social than biological at play. It probably has something more to do with these stereotypes and stuff. But another really interesting—or at least, I’m biased, but to me—another really interesting line of research that comes into play—and some of this is stuff out of my own lab—so we know that boys in general tend to do better at spatial processing than girls. And we know that spatial processing is really important for math, right? So math and space are pretty connected. And by spatial processing, I mean things like being able to picture something rotating in your mind or, you know, envisioning how these puzzle pieces might fit together. And so we know that boys tend to do better at that type of processing. And the gender difference there seems to be related to gender differences in math anxiety. So there’s some speculation, too, that it might be that as the math starts to become more reliant on spatial processing, that that’s when we see this separation between boys and girls with respect to how much anxiety they feel about math. So a lot of this is to say, I think the answer to the gender question right now is what I think what we would officially call a bit of a hot mess, <laugh> where I think there’s probably more questions than answers. But I think that there’s definitely something going on. And it really seems to be coming on later in elementary school.

Dan Meyer (23:32):

That’s a refreshingly honest admission from a social scientist, that it’s a hot mess and not perfectly clear, <laugh> so I appreciate that. It’s interesting what you said about the spatial reasoning. In our work creating curriculum at Amplify, I find we lean a lot on trying to tie abstract math towards spatial topics. Like, can you estimate a quantity before you calculate it? Can you identify a pattern and where it breaks before you prove it abstractly? And, I dunno, it’s just interesting to me. I’m just thinking out loud about how I feel like math becomes more abstract rather than more spatial. The farther you venture into secondary math…I’m wondering if I misunderstand what you’re meaning by spatial, and the progression of math from K–12.

Dr. Erin Maloney (24:20):

Yeah, so I think you can still have—you can have math be abstract, but still really relying on spatial processing. Right? And I think part of that is maybe a bit of us having different definitions of when we say “spatial.” So in cognitive science, when we talk about spatial representations or spatial reasoning, it’s really like anything you’re picturing in your mind, any time you’re really picturing these things in your mind and manipulating those images at all. So if you imagine, even like at a simple level, but it’s gonna hold when you’re going more complex as well. So doing like equivalence problems, for example, where you have to balance the equations.

Dan Meyer (24:58):

Yeah.

Dr. Erin Maloney (24:59):

Even just being able to envision things kind of moving around that equal sign and bringing one piece of the equation from this side to the other is actually an extremely spatial kind of reasoning. Right? Or when you’re expanding, that’s actually extremely extremely spatial, despite the fact that it might not feel like it initially. Obviously anything in geometry is going to be very spatial. So I think, in that sense, we would argue that the spatial processing is still playing a pretty important role. But it’s maybe a different type of spatial processing than what we’re seeing at a very early level in elementary school. That said, you can completely disagree with me too. ‘Cause I could also just be wrong, and that’s fair. My kids tell me I’m wrong all the time. So I’m used to <laugh> being told that I’m wrong.

Dan Meyer (25:47):

Well, we’re a bit more deferential on this here show, with our guests. So I would not do that. But it makes sense, what you’re saying about how these are things that you manipulate in your mind, whether they are Xs and Ys or numbers and fractions. These are all things that we manipulate. That ties into differences in this spacial reasoning category, it sounds like, which then contributes to math anxiety. And it does start to feel like there’s a lot going on here, is what it feels like.

Bethany Lockhart Johnson (26:14):

You mean hot mess?

Dan Meyer (26:16):

I meant hot mess.

Dr. Erin Maloney (26:17):

Yeah. <laugh>, I think that’s the technical term, right? I’m pretty sure that’s the technical term for it.

Dan Meyer (26:21):

I didn’t know the citation for it. So I didn’t say it. But I knew who in literature named that. But yeah.

Dr. Erin Maloney (26:28):

I’ll write something at some point.

Dan Meyer (26:30):

We’ll cite Maloney, 2022. Yeah. Yes.

Bethany Lockhart Johnson (26:34):

So I will say that one of my dreams in thinking about this season and last season, but particularly this season, since we’re really getting to talk to some researchers who get to think about this, and have really interesting conversations about it all the time…one of my dreams is that we’re bringing—’cause we do have some folks who are researchers that are listening, right? But then we also have teachers and folks who are in the classroom every day, and parents and caregivers listening. And so I think one of the beautiful things about the way that I hear you talking about it is you’re thinking about the research, but it’s so applicable. Right? And I wonder if there’s anything else you can say around it. I wanna reduce that divide, that gap, between the research that’s happening and then what’s happening with the kiddos and in the classroom and at home. And I don’t know if it’s like a magic wand thing where like <laugh> if there were changes you’d wanna see at a societal level, to try to combat math anxiety, but you see where I’m going. You know, it’s like <laugh>….

Dr. Erin Maloney (27:39):

  1. So I’m gonna answer maybe in two ways. So I think the first thing that I’m hearing from you is that idea of diminishing this divide, right? And so one thing I try to keep in mind, as someone who’s a researcher and working in the lab, I will often be called in to talk to teachers and give professional development sessions. And they often want the sage-on-the-stage academic, that stands up there and tells you the answers to things. And one of the first things that I’m gonna admit when I get up there is, “I am not on the front lines.” So what I do in the lab, for me to tell you that that’s gonna work in a classroom of 30 kids who may or may not have eaten dinner that day, and may or may not have snow pants, and may or not…like it’s–

Bethany Lockhart Johnson (28:23):

Mmm, yes.

Dr. Erin Maloney (28:24):

You know, I think we also need to be a little bit reasonable. So I try really hard in my own program of research to make sure that I’m always talking to teachers and to principals and to curriculum designers to make sure that the ideas that I have make sense. In fact, one of the most recent book chapters that I wrote, I wrote in collaboration with a really good friend of mine who’s a principal, an elementary school principal, and a former math consultant. And we wrote it together, to really say like, “Hey, here’s how we can help each other inform how research can inform practice and how practice can also inform research.” ‘Cause he can come to me and say, “I’m doing this. I can’t find anything in the literature to support this, but I’m sure it works!” And we can design something in the lab to test whether or not it seems like it’s gonna work.

Bethany Lockhart Johnson (29:11):

That’s huge. Yeah.

Dr. Erin Maloney (29:12):

Empirically. And so I think that open communication is massive. One thing that we’re doing in my own lab to try to keep that open communication available. So to anyone listening who’s ever tried to get access to a journal article, they’re held behind paywalls, right? So one, the way it works, my understanding of this anyway, is that the journal owns the formatted version of the paper. So what we do is we put up audio recordings of all of the research papers that we ever publish. So I’m pretty sure I own the words as the author, and the journal owns the prettified version that you can buy. So we audio-record all of our papers, so that if teachers or parents ever want to hear the actual science that’s going into some of these decisions, they have access to at least the stuff that we do in our lab. And we also put up an infographic for every paper, just highlighting kind of the main questions and main findings. And we do that because I think that the only way for the information to actually be useful is if it gets into the hands of the stakeholders that actually need that information.

Bethany Lockhart Johnson (30:21):

And is accessible. That’s huge. That’s huge!

Dr. Erin Maloney (30:24):

Yeah. Yeah. So that’s one way that we try to do it. And like I said, the other thing, we try to always be working with principals and with teachers. I joke that the way that I remedied this in my own life…so my husband’s a teacher; it’s like, I just married one! It’s fine! <laugh> I can grill him on a regular basis, and be like, “I wanna try this experiment. Do you think it’s gonna work?” And he can say, like, “It’s not going to. Here’s why.”

Dan Meyer (30:47):

That’s awesome. Marrying a participant—you know, a research participant—is unethical, of course. Would not clear IRB. But turning your partner into a participant? Like, what are you gonna do? That’s great.

Dr. Erin Maloney (30:57):

Yeah, no, that’s fair game.

Dan Meyer (30:58):

Yep.

Dr. Erin Maloney (30:59):

Yeah. So that’s—I think we we compensate each other <laugh>. So, no…so I do joke a little bit about that. He was a teacher simply ’cause he wanted to be one. Not ’cause I needed him to be one. But, I think that communication part is, is really key. That’s one thing. Then the other part of the question or the other sort of piece of the question that I was hearing is that idea of, how do we fix math anxiety. Right? Like, what’s the great, “I’m glad that there’s a whole bunch of time and effort and energy going into trying to understand this, but what, where are we at?” And I think with that, it’s really, really promising. So there’s been a lot of research coming out looking at how best to help children or even adults manage their own anxiety about math. And there’s a few really interesting strategies that seem to be quite effective. So one, and I don’t know if—um, it feels weird calling him Dr. Ramirez, just ’cause I know him well!—but I don’t know if Dr. Ramirez would’ve talked about this when he chatted with you, but he has some really interesting work on expressive writing. Did he chat about that at all?

Bethany Lockhart Johnson (32:07):

He didn’t, but I’ve read some of his work about it and I think it’s so fascinating.

Dr. Erin Maloney (32:11):

Yeah! So, OK, well, I’ll tell you about his work on it.

Bethany Lockhart Johnson (32:13):

Yes, please. Please.

Dr. Erin Maloney (32:14):

Because it’s super-useful. So when we talked about that idea of how anxiety causes these thoughts and ruminations, and they tie up the memory resources that you need, what Gerardo has found is that when you get students to write about their anxiety for about 10 minutes before they do a test, what ends up happening is they end up doing better on the test, relative to if they would not have written about their anxiety at all. And this is particularly true for students who are really high in anxiety. OK? And the idea is that all of those thoughts that they were going to have about the test or the consequences of the test, et cetera, you just kind of get ’em…it’s like a mind dump where you get ’em all onto the page at first before you even go to do the test. And now when you go to do the test, you’re not having to do two things at once. You’re no longer dealing with these thoughts ’cause you got ’em all out on the paper beforehand. And so Gerardo has some really interesting work showing that that works for math anxiety. And then it also works for just testing anxiety in general. And so that’s a strategy that I love. I also—part of what I really love about it is it’s so low-cost, right? You need a paper and a pencil and it’s great. So those are always my favorite strategies, the ones that don’t really cost us anything. So that’s one way of dealing with like the cognitive part of the anxiety. The other thing you can do is try to deal with the anxiety part of the anxiety. So for that, what we find is that the typical strategies that you’re gonna see for anxiety tend to work for math anxiety. So things like focused breathing. Right? Making sure you’re doing deep inhales and exhales. That really diaphragmatic breathing seems to be quite helpful. We know that what we call progressive desensitization is really key. That’s the idea of doing things, you know, starting with the questions that you know how to handle. And then gradually working up to the more difficult questions. So you’re sort of gradually exposing yourself to the more complex stuff. And how that can play out on an actual test at school is, you sit down, and instead of just starting with question number one, you actually read the whole test, see which questions you feel like you know the best, start with those questions, and that helps build your confidence so that you’re better able to tackle the questions that are maybe a little bit outside of where you’re currently at. So that seems to be really helpful. The other part that I will say, too, that’s extremely helpful: So we know that anxiety really ties up those memory resources. And so the more you can make the math automatic, the more immune it’s going to be to anxiety in the moment. And so I know that this part can be a little bit controversial, because we don’t wanna necessarily demotivate children, and kill the enthusiasm for math that we’re trying to cultivate…but really, you know, really committing your arithmetic facts to memory can be extremely helpful. So really learning those times tables, really learning your addition and subtraction facts. ‘Cause what happens is, then when you’re in a situation where you need that information, even if you’re anxious and you’re working with fewer cognitive resources than what you would normally have, you actually don’t need that many cognitive resources to be able to pull something from memory that you’ve memorized. So it really helps to kind of protect you against some of the negative impacts of the anxiety while you’re doing that test.

Bethany Lockhart Johnson (35:37):

And you’re not using all your cognitive resources to figure out seven times eight, because you can really focus on what you’re trying to do with that. Oh, that’s fascinating. Yeah. Yeah.

Dr. Erin Maloney (35:47):

Yes. No, a hundred percent right. And so I know that’s one that, like I said, I know it can be somewhat controversial because it’s…you know, we’ve talked about—or we haven’t talked about in this conversation, but we often talk about—the idea of drilling and killing. Right? So you drill the facts, you kill the, the enthusiasm. But I think that there are ways that we can drill arithmetic facts, or help make them automatic, but still fun, right? It doesn’t have to always be in a high-pressure kind of way.

Bethany Lockhart Johnson (36:16):

Totally. And we’ve talked about fluency, and I’m sure we’ll talk about it more in the Lounge. And that is interesting, that link between anxiety when the fluency isn’t there, that—or, of course we hear about anxiety with timed tests, but the idea of that IS something you can do to reduce it, because you have those facts just at your ready. Right?

Dr. Erin Maloney (36:37):

Yeah. So I actually, again, I’m gonna be a little bit controversial. So I don’t hate timed tests in the way that a lot of people do. But I love time to practice. So I think once we’ve got to a point where children have a fairly decent understanding of skills, of a skill, once they’ve got a fairly decent grasp on it, then I love the idea of the timed practice. So it can be still in a low-pressure situation, where in many ways it doesn’t matter if you get the answer to the question correct. But we’re practicing doing it in a situation in which you might be feeling a little bit of pressure, but it’s not real pressure, if that makes sense. And I think that can be really, really useful for students. And again, it can be done in a fun way, right? It doesn’t have to be these super-intense ways. It can be fun. But I think that in life there are situations in which the time that it takes you to complete a problem matter. And I think that we have to make sure that we don’t get too far away from that.

Dan Meyer (37:40):

Yeah. It feels like we should do an entire other episode thinking about ways to develop that fluency and automaticity that don’t contribute to anxiety, or create further disparities between people who are high math anxiety and low math anxiety. Not a small question, I’m sure. And I appreciate you alluding to all of that. You know, this whole thing, as you said, is quite the hot mess. And I feel like you, Dr. Maloney, have helped us make this a little less messy, in our heads, and hopefully the listeners’ heads. I really appreciate that. I just love…you’ve mentioned lots of resources that you have. You’ve alluded to them: audiobook-style readings of your research, which I need ’cause I just finished, you know, Harry Potter, the seventh book, so I need a new thing to listen to like that. Also infographics. Can you tell our listeners where they can find this work of yours, and if there are any other kinds of resources that you wanna plug for our listeners here?

Dr. Erin Maloney (38:32):

Yeah, for sure. So all of our resources can be found on my lab website. So the address for that is www.ErinMaloney.ca. So there we have, like you said, the infographics and the audio articles and all that stuff. And then we also have a link to a new kids’ book out, actually, that a colleague of mine and I have published recently, that really walks through some of these strategies on combating math anxiety. The book is written as a children’s book, so it’s Peyton & Charlie Challenge Math. But it secretly is a book that would also work for adults. So if you are a parent that’s a little bit anxious about math, or a teacher that maybe is a little bit anxious, and you wanna see how some of these strategies can play out, in that book—we linked to it on the website, but it is available for purchase on Amazon. And the one thing I will say about the book, ’cause this is something that we were pretty proud of, so Sheri-Lynn Skwarchuk, who is a school psychologist, and I wrote the book. And it’s available for purchase at our cost price, so we don’t actually make any money on the book. It was literally just a way of getting some of the science out to people who might be able to benefit from it.

Bethany Lockhart Johnson (39:45):

Reducing that divide!

Dr. Erin Maloney (39:46):

Yeah, well that’s what we’re trying to do! Right? So I think in the U.S., I think it’s like $6 on Amazon. And then in terms of other resources, we’re in the process right now of creating some informational videos and and stuff like that that hopefully will be useful for parents and for teachers, just in terms of understanding a little bit more about the anxiety and understanding how to deal with the anxiety in the classroom more, at home or wherever it might be coming up.

Dan Meyer (40:15):

Well, thanks so much. I really appreciate—we appreciate!—you coming on, and hearing about how you’re trying to bridge so many different barriers from research to practice, and school to home. It’s just really inspiring. And we’d love to have you back on sometime. So thank you so much for joining us.

Bethany Lockhart Johnson (40:29):

I feel like we’ve just hung out! Don’t you, Dan?

Dan Meyer (40:31):

Are we rolling here? Oh my gosh, we’re rolling. I just thought we’re just hanging. Yeah,

Bethany Lockhart Johnson (40:34):

I thought we were just hanging!

Dr. Erin Maloney (40:36):

I know, I do, I really appreciate that it has a very kind of chill vibe to it.

Dan Meyer (40:41):

Chill vibe. Like a lounge.

Bethany Lockhart Johnson (40:42):

It’s the lounge!

Dan Meyer (40:43):

Thank you. You get us; you get us. <laugh>

Bethany Lockhart Johnson (40:45):

Dan Meyer. I was shopping for children’s books, and there was this book, and it was talking about being at home with Mom. And it’s going through all the things that the child did that day with Mom. It’s like, “We played outside, we ran through the sprinklers, we even did some homework.” And it shows them sitting at the table with the homework, that’s clearly math homework, in front of them. And the mom is like, “Harrumph!” Like a very perplexed, anxious face. And there’s all these question marks above her. And it’s just like,

Dan Meyer (41:24):

“There should not be numbers on that paper!”

Bethany Lockhart Johnson (41:25):

Exactly. And the child is like, “Ohhhh,” you know. And I mean, I have to give credit to the illustrator, because they really did capture the clear message of this interaction, which was sitting down to do math homework or think about math together is a source of angst. Right? According to this author and according to too many people. And so I think what’s really important is that we recognize those images when we see them out there and speak back to them, and say, “Hey, wait a second.” Yeah, it can feel like that, and it doesn’t have to. And what’s going on that that’s just the assumed way that it’s gonna feel, to sit down and math together. You know?

Dan Meyer (42:11):

Yeah. It feels like we all have a lot of work to do on the whole math-anxiety front. Dr. Maloney helped us see how parents play a part, educators play a part, society and how they create people plays its own part in how we all define math as a thing where we evaluate student thought or where students play it with their thoughts, has its own huge part as well. So yeah, it was a really fantastic conversation with Dr. Maloney. I hope you folks will check out the show notes, where you will find links to Dr. Maloney’s website. A lot of her work, which as you heard, is very geared towards practitioners and parents and even directly at kids, especially the new children’s book she co-authored, Peyton & Charlie Challenge Math.

Bethany Lockhart Johnson (42:55):

Next time we’re gonna dive even more into the nitty gritty of combating math anxiety. To do that, we’re actually gonna be joined—I am so excited about this—by Dr. Rosemarie Truglio from Sesame Workshop.

Rosemarie Truglio (43:09):

Our core audience are two- to four-year-olds, and they love math. And what’s not to love? Children don’t come with this math anxiety. Math anxiety is learned.

Dan Meyer (43:23):

So excited.

Dr. Erin Maloney (43:24):

Sesame Street was a huge part of my childhood and my toddler doesn’t know it yet, but Sesame Street is coming. It’s coming. Like, we’re we’re gonna introduce Sesame Street to him. We just haven’t yet.

Dan Meyer (43:37):

Sesame Street straight raised me.

Bethany Lockhart Johnson (43:38):

Right?

Dan Meyer (43:39):

Yeah. Don’t tell my parents. But that’s, yeah, that’s true. I’m excited, too. It’s gonna be a blast.

Bethany Lockhart Johnson (43:45):

I’m really excited. I think that the more we dive into this topic—which, again, we’re gonna look at math anxiety from a lot of different angles—and I’m excited to talk to Dr. Truglio about how we can take this research and these conversations that are happening about math and how it can actually impact what’s happening in homes. ‘Cause we wanna help create positive relationships with mathematics, with kids in math. I’m so excited. And I hope you folks keep listening. We love having you here in the Lounge. And if you haven’t already, please subscribe to Math Teacher Lounge, wherever you get podcasts. And if you like what you’re hearing, please leave us a rating and a review. It helps more listeners to find the show, and let other folks know about this show. Recommendations are great. Thanks so much for listening.

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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.

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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!

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Amplify CKLA 2nd Edition Pilot Packs

Pilot educator,

This is the beginning of the Amplify Core Knowledge Language Arts (CKLA) 2nd Edition journey in your classroom! Making this important, evidence-based shift shows your commitment and dedication to your students. We truly appreciate the work you’re doing and are here to help you along the way.

We know it can be overwhelming to start a new curriculum, but we’re here to help! Within this site, you’ll find resources to help you get started before your implementation training, including a materials checklist, unit and domain summaries, support videos, and more! These tools will support your 6–12 weeks of core literacy instruction with Amplify CKLA. We hope this site is helpful in getting you started with your pilot.

Thank you for all you do,

—The Amplify CKLA team

Get started

To get started with your new pilot of Amplify CKLA, you’ll first want to review the following:

You may also find these documents helpful as you begin your pilot:

CKLA_PilotPackMicrosite_MaterialsModule_Hero_112822-01

Pilot Pack components checklist

Below you’ll find the Amplify CKLA Pilot Pack components you should have received in your shipment, outlined by grade level and teacher/student materials. Please click your grade-level teacher materials and student materials to review the list and ensure that you received all of the materials.

An orange workbook cover featuring a ladybug illustration, part of "Amplify Core Knowledge Language Arts." The text "Skills 5" is shown at the bottom.

Teacher materials

Skills Unit 5 Teacher Guide

Orange book cover for "Skills 6" from Amplify Core Knowledge Language Arts, featuring outlined hands and items like hats and pants. Subtext: Teacher Guide, TK Masterscripts.

Teacher materials

Skills Unit 6 Teacher Guide

Orange language arts workbook cover with a white shower sketch, water drops, and the word "Skills 7" at the bottom. Drawings include fish, bird, and words like "bath," "th," "finch," and "splash.

Teacher materials

Skills Unit 7 Teacher Guide

Book cover titled "Ox and Man" shows people running with an ox on a green hillside.

Teacher materials

Skills Unit 5 Big Book: Ox and Man

Teacher materials

Skills Unit 6 Big Book: Kit

Teacher materials

Skills Unit 7 Big Book: Seth

Kindergarten_small-letter-cards

Teacher materials

Skills Small Letter Card Set

Teacher materials

Skills Large Letter Cards

Teacher materials

Knowledge Domain 2 Teacher Guide: The 5 Senses

Teacher materials

Knowledge Domain 3 Teacher Guide: Stories

Colorful illustration of a lush hillside with a variety of plants and a house in the background, titled "knowledge 4 plants" for a kindergarten workbook.

Teacher materials

Knowledge Domain 4 Teacher Guide: Plants

Teacher materials

Knowledge Domain 2 Image Cards: The 5 Senses

Cover of "knowledge 3" kindergarten image cards featuring a colorful illustration of children and animals engaging with storybook characters in a fantasy setting.

Teacher materials

Knowledge Domain 3 Image Cards: Stories

Illustration on a book cover showing various plants, a garden, and a red house, under a bright sun, titled "knowledge 4 - plants" for kindergarten level.

Teacher materials

Knowledge Domain 4 Image Cards: Plants

Illustration of children exploring giant sensory organs in a vibrant landscape, representing the five senses in a playful educational setting.

Teacher materials

Knowledge Domain 2 Flip Book: The 5 Senses

Teacher materials

Knowledge Domain 3 Flip Book: Stories

Illustration on a book cover showing various plants, a garden, and a red house, under a bright sun, titled "knowledge 4 - plants" for kindergarten level.

Teacher materials

Knowledge Domain 4 Flip Book: Plants

Back cover of an amplify core knowledge language arts pilot sample card deck, with qr code and isbn, featuring education-themed illustrations.

Teacher materials

Sound Cards Sampler

Educational poster titled "sound posters" for kindergarten, featuring various illustrations like a boat, globe, and animals on a red background with a qr code on the bottom right.

Teacher materials

Sound Posters Sampler

Student materials

Skills Unit 6 Reader: Kit

Student materials

Skills Unit 7 Reader: Seth

Student materials

Skills Unit 5 Activity Book

Student materials

Skills Unit 6 Activity Book

Student materials

Skills Unit 7 Activity Book

Student materials

Chaining Folder

Book cover titled "look at the", marked as a "pilot sample" with educational doodles on a red background, labeled "picture reader" for "kindergarten" skills.

Student materials

Picture Reader Sampler

Educational book cover titled "amplify core knowledge language arts" featuring colorful illustrations of animals, fruits, and plants across four seasonal themes.

Student materials

Knowledge Domains 2, 3, and 4 Sampler

Teacher materials

Skills Unit 2 Teacher Guide

Teacher materials

Skills Unit 3 Teacher Guide

Teacher materials

Skills Unit 4 Teacher Guide

Teacher materials

Skills Unit 2 Big Book: Gran

Teacher materials

Skills Unit 3 Big Book: Fables

Teacher materials

Skills Vowel Code Flip Book

Teacher materials

Skills Large Letter Cards

A grade 1 spelling cards booklet titled "core knowledge language arts" from the center for early reading-amplify, featuring educational symbols like a pencil and sun on a orange cover.

Teacher materials

Skills Spelling Cards

Teacher materials

Knowledge Domain 2 Teacher Guide: The Human Body

Teacher materials

Knowledge Domain 3 Teacher Guide: Different Lands, Similar Stories

Teacher materials

Knowledge Domain 5 Teacher Guide: Early American Civilizations

Teacher materials

Knowledge Domain 2 Image Cards: The Human Body

Teacher materials

Knowledge Domain 3 Image Cards: Different Lands, Similar Stories

Teacher materials

Knowledge Domain 5 Image Cards: Early American Civilizations

Teacher materials

Knowledge Domain 2 Flip Book: The Human Body

Teacher materials

Knowledge Domain 3 Flip Book: Different Lands, Similar Stories

Teacher materials

Knowledge Domain 5 Flip Book: Early American Civilizations

Illustration of a grandmother embracing two children, with a house labeled "gran" in the background, surrounded by foliage.

Student materials

Skills Unit 2 Reader: Gran

Student materials

Skills Unit 3 Reader: Fables

Illustration of various animals, including a puffin, deer, fox, otter, and others, on a green background with the title "the green fern zoo.

Student materials

Skills Unit 4 Reader: The Green Fern Zoo

Student materials

Skills Unit 2 Activity Book

Student materials

Skills Unit 3 Activity Book

Student materials

Skills Unit 4 Activity Book

Student materials

Skills Individual Code Chart

Illustration of a colorful educational book cover titled "amplify core knowledge language arts" for grade 1, featuring diverse thematic circles like farming, space, and cultures.

Student materials

Knowledge Domains 2, 3, and 5 Sampler

Green book cover titled "Skills 2," showing a white outline drawing of a mole above the word "mole." Background features doodles and words like "bite" and "bat.

Teacher materials

Skills Unit 2 Teacher Guide

Bright green cover of a textbook titled "Skills 3," featuring a graduation cap illustration. The text mentions "Core Knowledge Language Arts" and "Grade 2 Teacher Guide.

Teacher materials

Skills Unit 3 Teacher Guide

Green educational worksheet displaying a large letter "V" surrounded by various illustrations representing words starting with "V," such as a volcano and violin.

Teacher materials

Skills Vowel Code Flip Book

A green educational workbook cover titled "Amplify Core Knowledge Language Arts," featuring a large white letter 'C' and doodles of animals and objects in the background.

Teacher materials

Skills Consonant Code Flip Book

Cover of "Core Knowledge Language Arts: Spelling Cards, Grade 2" featuring symbols like an eye, lightbulb, key, paw, and letters on a green background.

Teacher materials

Skills Spelling Cards

Cover illustration of a book titled "Knowledge 1: Fairy Tales and Tall Tales." Shows a giant lumberjack, castle, fish, and a person facing the scene, surrounded by trees and a river.

Teacher materials

Knowledge Domain 1 Teacher Guide: Fairy Tales and Tall Tales

Cover of a book titled "Knowledge 4, Greek Myths," showing illustrations of mythical figures, creatures, and landscapes under a sunny sky.

Teacher materials

Knowledge Domain 4 Teacher Guide: Greek Myths

Illustrated book cover showing a garden scene with butterflies, insects, flowers, and greenery under a blue sky. Title reads "Knowledge 8: Insects" from the Core Knowledge Language Arts series.

Teacher materials

Knowledge Domain 8 Teacher Guide: Insects

Illustrated book cover featuring Greek mythological characters, including a lion-headed figure and an archer, with a landscape of mythical creatures and structures in the background.

Teacher materials

Knowledge Domain 4 Image Cards: Greek Myths

Colorful illustration of a natural scene with insects, flowers, and a pond on a book cover titled "Knowledge 8 Insects" for Grade 2 language arts.

Teacher materials

Knowledge Domain 8 Image Cards: Insects

Illustration of a giant lumberjack with an axe, a cow, and people on a castle wall, in a colorful storybook design. Titled "Knowledge 1: Fairy Tales and Tall Tales.

Teacher materials

Knowledge Domain 1 Flip Book: Fairy Tales and Tall Tales

Illustration of Greek mythology featuring Artemis aiming a bow, a Minotaur in a labyrinth, and mythical symbols. Labeled "Knowledge 4 Greek Myths" for a language arts program.

Teacher materials

Knowledge Domain 4 Flip Book: Greek Myths

Colorful illustration of a garden with flowers, a beehive, butterflies, bees, and a beekeeper by a pond. The book is titled "Knowledge 8: Insects" for Grade 2 Language Arts.

Teacher materials

Knowledge Domain 4 Image Cards: Greek Myths

Illustrated book cover titled "Bedtime Tales" showing a man sitting on a bed with two children, one boy and one girl, leaning against him. Colorful patterns are in the background.

Student materials

Skills Unit 2 Reader: Bedtime Tales

Children play jump rope on a basketball court near a park. The words "Kids Excel" are on the image.

Student materials

Skills Unit 3 Reader: Kids Excel

A workbook cover featuring a stylized illustration of a mole, labeled "mole" and "oe." It includes sketches of a bed, clock, and letters. Title: "Skills 2 Activity Book, Grade 2.

Student materials

Skills Unit 2 Activity Book

Image of a green activity book cover titled "Skills 3" with a graduation cap illustration and various educational doodles in the background.

Teacher materials

Skills Unit 3 Activity Book

A chart featuring various hand-drawn doodles, including a sailboat, dog, hat, bell, and cooking pot, used for language arts.

Student materials

Skills Individual Code Chart

Cover of a Grade 2 activity book titled "Knowledge" by Amplify, featuring colorful illustrations of myths and folktales, including "Kite" and "Why the Sky Is Far Away.

Student materials

Knowledge Domains 1, 4, and 8 Sampler

Illustrated book cover titled "Unit 2 Animal Classification," featuring a leopard, frog, turtle, crane, rocks, and foliage under a partly cloudy sky.

Teacher materials

Unit 2 Teacher Guide: Animal Classification

Cover of a textbook titled "Unit 5: Light and Sound" featuring an illustration of a bouncing cow and various objects like a tree and lemon slices on a table.

Teacher materials

Unit 5 Teacher Guide: Light and Sound

Book cover titled "Unit 3: Native American Regions and Cultures" with an illustration of a desert landscape and sky designs.

Teacher materials

Unit 8 Teacher Guide: Native Americans: Regions and Culture

Illustrated cover depicting a dog chasing a bee under a tree with a sun and lens flare in the background. Text reads "Unit 5, Light and Sound, Image Cards, Grade 3" with Amplify logo.

Teacher materials

Unit 5 Image Cards: Light and Sound

Book cover with a stylized illustration of a person in a rocky landscape under a cloudy sky. Text reads: "Unit 8 Native Americans: Regions and Cultures, Image Cards, Grade 2.

Teacher materials

Unit 8 Image Cards: Native Americans: Regions and Cultures

Colorful illustration of various animals including a jaguar, heron, frog, turtle, and fish in a natural setting, featured on the cover of an educational material titled "Rattenborough’s Guide to Animals.

Student materials

Unit 2 Reader: Rattenborough’s Guide to Animals

Cover of "Adventures in Light and Sound," Unit 5 Reader by Amplify, showing illustrations of a dog jumping near a tree, with abstract shapes and colors in the background.

Student materials

Unit 5 Reader: Adventures in Light and Sound

Book cover featuring a landscape painting of cliffs under a cloudy sky, labeled "Unit 8: Native American Stories," with "Amplify Core Knowledge Language Arts" at the top.

Student materials

Unit 8 Reader: Native American Stories

Illustrated book cover featuring a leopard, frog, turtle, crane, and jewel-like objects in a natural setting. Title reads "Unit 2 Animal Classification, Grade 3.

Teacher materials

Unit 2 Activity Book: Animal Classification

Illustrated cover of an educational book titled "Unit 5: Light and Sound" for Grade 1, depicting a tree, playing squirrels, a sun, and large glasses on a white table.

Student materials

Unit 5 Activity Book: Light and Sound

Cover of a book titled "Unit 8: Native Americans: Regions and Cultures," featuring an illustration of a person walking through a desert landscape.

Student materials

Unit 8 Activity Book: Native Americans: Regions and Cultures

Cover of a Unit 3 Poetry workbook featuring gold illustrations of mythical creatures and designs on a brown background.

Teacher materials

Unit 3 Teacher Guide: Poetry

A geology textbook cover with an image of wavy, layered rock formations. The text on the cover reads "Unit 5 Geology.

Teacher materials

Unit 5 Teacher Guide: Geology

Cover of "Unit 7: American Revolution" shows people in colonial attire ringing a large bell indoors.

Teacher materials

Unit 7 Teacher Guide: American Revolution

A journal cover titled "Poet's Journal" for Grade 6, Unit 2. The design includes brown illustrations of a sun, dinosaur, leaves, and other decorative elements on a tan background.

Student materials

Unit 3 Poet’s Journal

Textbook cover titled "Unit 5: Geology: The Changing Earth" featuring a photo of wave-like rock formations with layered patterns.

Student materials

Unit 5 Reader: Geology: The Changing Earth

Illustration of colonial people and a large bell, with text: "Unit 7 American Revolution: The Road to Independence.

Student materials

Unit 7 Reader: American Revolution: The Road to Independence

Textbook cover titled "Unit 5: Geology" featuring a photo of layered rock formations with swirling patterns and vivid colors.

Student materials

Unit 5 Activity Book: Geology

Illustration of people ringing a large bell in a historical setting, with men, women, and a child present. Text on the cover reads "Unit 7 American Revolution" for Grade 4.

Student materials

Unit 7 Activity Book: American Revolution

Textbook cover titled "Unit 2: Early American Civilizations" with an illustrated figure in red, white, and green, adorned with feathers and holding a staff.

Teacher materials

Unit 2 Teacher Guide: Early American Civilizations

Book cover featuring illustrations of an umbrella, microscope, compass, bird, and stars. Label indicates Unit 3 on poetry for 5th-grade language arts.

Teacher materials

Unit 3 Teacher Guide: Poetry

Cover of a workbook titled "Adventures of Don Quixote," featuring an illustration of Don Quixote and Sancho Panza on horseback under a crescent moon.

Teacher materials

Unit 4 Teacher Guide: The Adventures of Don Quixote

Textbook cover titled "Unit 2: Early American Civilizations: Maya, Aztec, and Inca," featuring colorful illustration of a figure in traditional attire.

Student materials

Unit 2 Reader: Early American Civilization

Cover of "Poet's Journal," Grade 6, Unit 5. Features illustrations of an umbrella, crow, book, key, and a telescope against a brown background. Amplify Core Knowledge Language Arts at top.

Student materials

Unit 3 Poet’s Journal

Cover of "Adventures of Don Quixote" by Argentina Palacios, Dover Children's Thrift Classics. It features an illustration of Don Quixote and his horse near windmills.

Student materials

Unit 4 Reader: The Adventures of Don Quixote (trade book)

Cover of a Grade 5 activity book titled "Unit 2: Early American Civilizations" features a colorful illustration of an Aztec-style figure.

Student materials

Unit 2 Activity Book: Early American Civilization

Cover illustration of "Adventures of Don Quixote" from Unit 4, featuring Don Quixote on horseback with a spear, under a crescent moon, in a vintage purple-toned style.

Student materials

Unit 4 Activity Book: The Adventures of Don Quixote

Access the Amplify CKLA digital experience

You will receive your teacher demo account login information from your sales representative.

Contact us

Contact your account executive to sign up for implementation training.

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

Bay Area
Lance Burbank
Account Executive
(415) 830-5348
lburbank@amplify.com

Central Valley and Central Coast
Demitri Gonos
Senior Account Executive
(559) 355-3244
dgonos@amplify.com

Ventura and L.A. County
Jeff Sorenson
Associate Account Executive
(310) 902-1407
jsorenson@amplify.com

Orange and L.A. County
Lauren Sherman
Senior Account Executive
(949) 397-5766
lsherman@amplify.com

San Bernardino and L.A. County
Michael Gruber
Senior Account Executive
(951) 520-6542
migruber@amplify.com

Riverside and L.A. County
Brian Roy
Senior Account Executive
(818) 967-1674
broy@amplify.com

San Diego County
Kirk Van Wagoner
Senior Account Executive
(760) 696-0709
kvanwagoner@amplify.com

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

Under 2300 students in Southern CA, Central Coast, and Southern Central Valley Counties
Charissa Snyder
Account Executive
(720) 936-6802
chsnyder@amplify.com

research hub line art for desmos math

Our research

Amplify Desmos Math

Amplify Desmos Math is a curiosity-driven K–12 program that builds students’ lifelong math proficiency. Our structured, problem-based approach builds on students’ curiosity while strategically developing math fluency and lasting grade-level understanding.

Efficacy

Pdf cover with title "The Effect of Desmos Middle School on Mathematics Achievement in Nine States," labeled as an education research study from March 2023 by WestEd.

The Effect of Desmos Math Curriculum on Middle School Mathematics Achievement in Nine States

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Research base

A cover page for an Amplify Desmos Math PDF titled "Foundational research," featuring two women working together at a desk with a laptop and papers.

Amplify Desmos Math: The research behind the K–12 math program

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District success stories

Cover page of a PDF titled "Making the shift to more student-centered math instruction" with an outline of Illinois and a marked location for Decatur Classical Elementary School.

Decatur Classical Elementary School, Illinois: Kindergarten through grade 2 proficiency grows 34% with Amplify Desmos Math in one year.

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Cover page of a PDF document titled "Supporting teachers in successful implementation" by Amplify, focused on a school district's approach to math education.

Crane Elementary School District, Arizona: 5 schools earn all possible math growth points using Amplify Desmos Math.

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Cover page of a PDF titled "Anchoring math instruction in shared values" by Amplify Desmos Math, featuring a simple outline map with a location marker and an orange label reading "District Success Story.

Superior School District, Wisconsin: Achieving 5.2% growth in middle school with Amplify Desmos Math

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Explore more of our research.

Learn more about the research behind our programs.