See Amplify CKLA Skills in action.

Step inside a kindergarten classroom and watch students light up during a fun, interactive lesson. From phonics and decoding to fluency, see how structured practice with Amplify CKLA Skills builds the confidence and abilities students need to become strong readers.

Follow along as a real teacher brings Unit 7, Lesson 10: Review Single-Syllable, Short-Vowel Words to life. You’ll see students building foundational reading skills—and you might even pick up a few instructional tips along the way!

A teacher sits at a table with two young students, guiding them as they look at a book together in a classroom setting.

Inside the classroom

Oral segmenting

The lesson kicks off with a phonemic warm-up: segmenting words like frost and raising a finger for each sound. After practicing together, individual students take turns modeling for the class, blending movement and sound to show what they know. 

Sound/spelling review

The teacher presents cards with letters and digraphs, prompting the whole class to say the sounds and match them to hand motions. She traces key letters, reinforces spelling patterns, and invites individual students to identify sounds, letters, and digraphs aloud.

Spelling and handwriting practice

Students follow along as the teacher models how to identify, read, and write words with digraphs, first working together and then on their own, while the teacher moves around the room to offer guidance. This routine supports phonics, spelling, and handwriting all at once.

Introduce the story

Students review digraphs they’ve just practiced by identifying and circling them in sample words they’ll encounter in an upcoming story. Then, they set a purpose for reading: getting ready to listen for key details.

Read the story

The teacher models fluent reading using a big book. Then, the class reads aloud together, tracking each word with their fingers. To wrap up, students point out digraphs, punctuation, and details in the story to show what they’ve learned.

Discuss the story

Students respond to questions about the story, first as a class and then with a partner, using the book to support their answers. They listen closely to their partners, build on each other’s thinking, and share their partners’ ideas with the whole class. 

Partner reading

Students reread the story in pairs, applying their decoding skills together. Because the text is 100% decodable, they can rely on what they’ve learned and on each other when they get stuck. The teacher stays close by to offer support as needed.

Winter Wrap-Up 03: Ideas to build math fluency

Promotional graphic for "Math Teacher Lounge" episode featuring Valerie Henry, Ed.D., on ideas to build math fluency, with a photo of Valerie Henry in the bottom right corner.

Join us for the third episode in our Winter Wrap-Up! In this episode from season 3 of Math Teacher Lounge: The Podcast, we sit down with Dr. Valerie Henry to talk about math fluency and what that means for students. Listen as we dig into the research, hear Val’s three-part definition of fluency, and explore her five principles for developing it.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:03)

Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.

Dan Meyer (00:11):

Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.

Bethany Lockhart Johnson (00:26):

I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.

Dan Meyer (00:30):

I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?

Bethany Lockhart Johnson (01:05):

Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?

Dan Meyer (02:08):

I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.

Bethany Lockhart Johnson (02:38):

Wait, did you pass the first time? Your test?

Dan Meyer (02:40):

Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.

Bethany Lockhart Johnson (03:32):

So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.

Valerie Henry (04:36):

Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.

Dan Meyer (04:41):

Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.

Valerie Henry (05:12):

The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,

Bethany Lockhart Johnson (07:12):

You mean without having to kind of muscle through it? Or say more about you mean.

Valerie Henry (07:16):

Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”

Bethany Lockhart Johnson (08:53):

That’s such an important distinction. My brain literally just did that actually!

Valerie Henry (08:58):

<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.

Bethany Lockhart Johnson (09:05):

Right.

Valerie Henry (09:07):

So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.

Dan Meyer (09:55):

I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.

Valerie Henry (10:21):

And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.

Bethany Lockhart Johnson (10:30):

Mm, yeah.

Valerie Henry (10:30):

So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.

Bethany Lockhart Johnson (11:18):

I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?

Valerie Henry (11:30):

I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.

Bethany Lockhart Johnson (12:06):

And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.

Valerie Henry (12:15):

Yes.

Bethany Lockhart Johnson (12:16):

Some of us might remember quite vividly.

Valerie Henry (12:18):

<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.

Bethany Lockhart Johnson (13:10):

If I put it in front of you enough times, you’ll become fluent.

Valerie Henry (13:14):

Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.

Dan Meyer (14:01):

It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.

Valerie Henry (14:35):

My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”

Dan Meyer (15:38):

There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?

Valerie Henry (15:57):

I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.

Bethany Lockhart Johnson (17:09):

So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.

Valerie Henry (17:22):

Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—

Bethany Lockhart Johnson (17:33):

Not waiting until you’ve gotten all the way through addition. But making “Ooh!”

Valerie Henry (17:38):

Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.

Bethany Lockhart Johnson (18:11):

What are the other principles?

Valerie Henry (18:13):

The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.

Bethany Lockhart Johnson (18:27):

Don’t put away those manipulatives. Don’t put away those tools.

Valerie Henry (18:31):

Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.

Bethany Lockhart Johnson (19:07):

I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—

Dan Meyer (19:35):

Thank you, Dr. Henry.

Valerie Henry (19:37):

You’re welcome!

Dan Meyer (19:41):

With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.

Bethany Lockhart Johnson (20:49):

Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”

Dan Meyer (20:55):

Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?

Tracy Zager (21:00):

I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!

Bethany Lockhart Johnson (21:10):

Ooh!

Dan Meyer (21:13):

A language fluency, perhaps. All right, Graham. How about you?

Graham Fletcher (21:16):

For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.

Dan Meyer (21:33):

Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?

Tracy Zager (21:40):

I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.

Graham Fletcher (23:53):

And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.

Bethany Lockhart Johnson (24:10):

So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?

Graham Fletcher (24:41):

What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.

Tracy Zager (25:22):

When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—

Bethany Lockhart Johnson (26:18):

Crayons, markers.

Tracy Zager (26:18):

Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.

Bethany Lockhart Johnson (27:03):

I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.

Tracy Zager (27:14):

Yay!

Bethany Lockhart Johnson (27:14):

And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.

Tracy Zager (27:41):

That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”

Bethany Lockhart Johnson (28:37):

That’s kinda true. Knowing you both, it’s kinda true.

Tracy Zager (28:42):

Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—

Bethany Lockhart Johnson (28:58):

But they’re making sense of numbers!

Tracy Zager (28:59):

Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.

Bethany Lockhart Johnson (29:45):

That’s huge.

Dan Meyer (29:46):

That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.

Graham Fletcher (30:47):

Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”

Tracy Zager (32:44):

I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.

Bethany Lockhart Johnson (34:41):

They’re invested!

Tracy Zager (34:45):

They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.

Graham Fletcher (35:47):

It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.

Tracy Zager (35:55):

I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.

Dan Meyer (37:20):

I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?

Graham Fletcher (37:57):

You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.

Bethany Lockhart Johnson (38:19):

If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?

Graham Fletcher (38:35):

Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.

Dan Meyer (39:25):

Bethany and I will be working the same challenge with people in our life.

Bethany Lockhart Johnson (39:29):

Yes.

Dan Meyer (39:29):

Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.

Bethany Lockhart Johnson (39:42):

I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.

Stay connected!

Join our community and get new episodes every other Tuesday!

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

What Valerie Henry says about math

“A lot of very fluent adults don’t always have every fact memorized. ”

– Val Henry

Meet the guest

Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops  fluency,  number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.

An older person with short gray hair and glasses, wearing a blue sweater, is outdoors with greenery and a fence in the background.
Podcast cover for "Math Teacher Lounge" with Bethany Lockhart Johnson and Dan Meyer; bold text on orange and teal semicircle background.

About Math Teacher Lounge: The podcast

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

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

Grade K

Unit 1: Count Sequence and Numbers to 5

Module 1: Represent Numbers to 5 with Objects

Lesson 1: Represent 1 and 2Connecting Cubes
Lesson 2: Represent 3 and 4Skye’s Style
Matching Groups
Designing Shoes With Skye

Unit 2: Count Sequence and Numbers to 10

Module 7: Represent Numbers 6 to 10 with Objects

Module 10: Compare Numbers to 10

Lesson 4: Compare Groups Within 10 by CountingMore, Fewer, or the Same
Fingers and Counters
Lesson 5: Compare Groups Within 10 by MatchingComparing Words
Forest Friends

Module 11: Add To and Take From Within 10

Module 12: Put Together and Take Apart Within 10

Lesson 3: Solve Put Together Problems Within 10How Many Objects in Pictures?
How Will You Count?
What Does It Mean to Add?
Lesson 4: Solve Take Apart Problems Within 10What Does It Mean to Subtract?
Lesson 5: Solve Word Problems Within 10The Bus Depot

Module 13: Ways to Make Numbers to 10

Lesson 4: Ways to Make 10Harry’s Hamster Wheel
Harry Explores Space
Lesson 5: Make 10 From a Given NumberShowing What We Know About 10
Lesson 1: Ways to Make 6 and 7Harry Explores the Ocean

Unit 3: Geometry

Module 14: Analyze and Compare Three-Dimensional Shapes

Module OpenerWhat’s That Shape?
Lesson 5: Build ShapesBuilding Solid Shapes

Module 15: Describe Position of Objects

Module 16: Analyze and Compare Two-Dimensional Shapes

Lesson 7: Compare Two-Dimensional and Three-Dimensional ShapesSo Much Sorting
What’s That Shape Called?
Another Shape

Unit 4: Number and Operations in Base Ten

Module 17: Place Value Foundations-Represent Numbers to 20

Lesson 3: Compose Ten Ones and Some More Ones to 19Investigate: Packing Snacks
Lesson 4: Represent Numbers to 20Getting Ready for the Game
How Many on the Field?
Pass, Shoot, Score

Module 18: Place Value Foundations-Represent Number to 20 with a Written Numeral

Lesson 1: Count and Write 11 to 14Jersey Jam!
Lesson 3: Count and Write 16-19People at the Park

Grade 1

Unit 1: Ways to Add and Subtract

Module 2: Subtraction Strategies

Lesson 2.1: Represent SubtractionPacking a Picnic
Lesson 2.2: Count BackWhat’s the Difference?
Lesson 2.3: Count on to SubtractLeaping Lily Pads!

Module 3: Properties of Operations

Lesson 3.6: Determin Equatl and Not EqualReplanting Huli

Module 4: Apply Addition and Subtraction Relationships

Lesson 4.2: Represent Related FactsSame Number, Different Ways
Lesson 4.3: Identify Related FactsKitten Coaster
Lesson 4.6: Solve for Unknow AddendTutu’s Garden in Maui

Module 5: Understand Add to and Take From Problems

Lesson 5.4: Solve Add To and Take From ProblemsA Community Working Together
Helping Others
Making 10

Module 6: Understand Put Together and Take Apart Problems

Lesson 6.3: Represent Addend and Unknown Problems with Objects and DrawingInvestigate: Let’s Grow!

Module 8: Data

Lesson: 8.2 Represent Data with Picture GraphsShapes Ying Saw

Unit 3: Numbers to 120

Module 10: Count and Represent Numbers

Lesson 10.4: Decompose Numbers in Different WaysInvestigate: Game Points
Lesson 10.5: Represent, Read, and Write Numbers from 100 to 110From Head to Claw
From Wing Tip to Wing Tip
Measuring More Wingspans
Lesson 10.5: Represent, Read, and Write Numbers from 110 to 120From Head to Claw
From Wing Tip to Wing Tip
Measuring More Wingspans

Unit 4: Addition and Subtractoin in Base Ten

Module 12: Understand Addition and Subtraction with Tens and Ones

Lesson 12.1: Representing Adding TensMeeting Yara
It’s a Match
From Park to Table
Lesson 12.3: Add and Subtract TensHow Many Cubes?
Boris’s Thimbles
How Many Tens?

Module 13: Two-Digita Addition and Subtraction

Lesson 13.1: Use Hundred Charts to Show Two-Digit Addtion and Subtraction.Investigate: Squashes at the Playground
Lesson 13.2: Understand and Explain Place Value AdditionTown Helpers
Making Squash Butter

Unit 6: Measurment

Module 16: Fraction Foundations

Lesson 16.1: TAke Apart Two-Dimensional ShapesFair and Square
Lesson 16.2: Identify Equal or Unequal PartsOne of the Parts, All of the Parts
Lesson 16.4: Partition Shapes into FourthsA Bigger Part

Grade 2

Unit 1: Numbers and Data

Module 1: Fluency for Addition and Subtraction Within 20

Lesson 1.5: Use the Make a Ten Strategy to AddExploring Within 10
Ways to Make 10

Module 1: Fluency for Addition and Subtraction Within 21

Lesson 1.6: Use a Tens Fact to SubtractExploring Within 10
Ways to Make 10

Module 2: Equal Groups

Lesson 2.1: Identify Even and Odd NumbersCan You Share?
Is It Even or Odd?
Lesson 2.2: Write Equations to Represent Even NumbersEverybody, Find A Partner!

Module 3: Data

Lesson 3.5: Draw bar graphs to Represent DataAwesome Aquariums

Unit 2: Place Value

Module 4: Understand Place Value

Lesson 4.1: Group Tens as HundredsWhat Makes a Hundred?
Lesson 4.2: Understand Three-Digit NumbersWhat’s the Value?
Lesson 4.4: Represent Numbers with Hundreds, Tens, and OnesMail Call!
What’s Your Name?

Module 5: Read, Write, and Show Numbers to 1000

Lesson 5.3: Different Ways to Write NumbersA New Representation
Lesson 5.4: Different Ways to Show NumbersAll the Ways!

Module 6: Use Place Value

Lesson 6.1: Count Within 1000Investigate
Turtle Hurdle
Lesson 6.5: Use Symbols to Compare NumbersTime to Line Up!

Unit 3: Money and Time

Module 7: Coins

Lesson 7.1: Relate Place Value to CoinsInvestigate
Lesson 7.2 Identify and Find Value of CoinsDiscovering Coins (Part 1)
Lesson 7.3: Compute the Value of Coin CombinationsHow Much Money?
Lesson 7.4: Show Amounts in Different WaysDiscovering Coins (Part 2)
The Toy Stand

Module 8: Dollar Amounts

Lesson 8.3: Solve Problems Involving MoneyThe Craft Stand at the Block Party

Unit 5: Three-Digita Addition and Subtraction

Module 16: Three-Digit Addition

Lesson 16.1: Use Drawing to Represent Three-Digit AdditionThere’s Something About Berries
Lesson 16.2: Decomposte Three-Digit AddendsBaking With Skunk

Unit 6: Measurement

Module 18: Lengths in Inches, Feet, and Yards

Lesson 18.4: Make Line Ploits to Show Measurement DataMessy Measurements
Bracelets and Wristbands

Module 20: Relate Addition and Subtraction to Length

Lesson 20.1: Relate Inches to a Number LineInvestigate
Time to Line Up!
What’s That Number?
Lesson 20.2: Add and Subtract Lengths in InchesLengths of Jungle Animals
Lesson 20.3: Relate Centimeters to a Number LineInvestigate
Time to Line Up!
In Full Bloom

Unit 7: Geometry and Fractions

Module 21: Two- and Three- Dimensional Shapes

Lesson 21.2 Identify and Draw Three-Dimensional ShapesMore to Measure
Lesson 21.2: Identify and Draw Two-Dimensional ShapesFrame It!
Measure It, Draw It

Grade 3

Unit 1: Understand Multiplication and Area

Module 1: Understand Multiplication

Lesson 1.1: Count Equal GroupsEqual Groups
Lesson 1.3: Represent Multiplication with ArraysArrays of Flavor
Lesson 1.4: Understand the Commutative Property of MultiplicationArrays of Flavor

Module 2: Relate Multiplication and Area

Lesson 2.1 Understand Area by Counting Unit SquareInvestigate: Comparing Rugs
Which Covers More Space?
Lesson 2.2: Measuring Area by Counting Unit SquaresTiling Figures
Area Hunt
Lesson 2.3: Relate Area to Addition and MultiplicationRectangles and Arrays

Unit 2: Multiplication and Division

Module 7: Relate Multiplication and Division

Lesson 7.7: Build Fluency with Multiplication and DivisionRelating Quotients to Familiar Products

Module 8: Apply Multiplication and Division

Lesson 8.3: Use Multiplication and Division to Solve Problem SituationsIt’s Chili in Here!
Lesson 8.4: Solve Two-Step ProblemsDivision and Multiplication Equations

Unit 3: Addition and Subtraction Strategies

Module 9: Addition and Subtraction Strategies

Lesson 9.3: Use Properties to AddHow Would You Solve It?
Lesson 9.4: Use Mental Math to Assess ReasonablenessAdding Strategically

Module 10: Addition and Subtraction Within 1000

Lesson 10.1: Use Expanded Form to AddWhat Is an Algorithm?
Lesson 10.2: Use Place Value to AddAdding Your Way
Using Fewer Digits
Lesson 10.5: Choose a Strategy to Add or SubtractDetermining Sums of 2 or More Addends

Unit 4: Fractions

Module 13: Understand Fractions as Numbers

Lesson 13.4: Represent and Name Fractions on a Number LineFractions on the Number Line
Lesson 13.5: Express Whole Numbers as FractionsCat Crossing
Lesson 13.6: Represent and Name Fractions Greater Than 1Location, Location, Location

Unit 5: Measurement and Data

Module 18: Represent and Interpret Data

Lesson 18.4: Make a Bar GraphPuppy Pile
2, 5, or 10?
Egg-cellent Pick
Lesson 18.5: Use Line Plots to Display Measurement DataHow Long Is It?
More Precise Measurements
Same Lengths, Different Names
Lesson 18.6: Make Line Plots to Display Measurement DataThe Plot Chickens
Let’s Make a Line Plot

Unit 6: Geometry

Module 19: Define Two-Dimensional Shapes

Lesson 19.1: Describe ShapesPiho’s Shapes
Lesson 19.4: Define QuadrilateralsRectangles, Squares, and Rhombuses

Module 20: Categorize Two-Dimensional Shapes

Lesson 20.1: Draw QuadrilateralsMore Quadrilaterals

Grade 4

Unit 1: Place Value and Whole Number Operations

Module 3: Interpret and Solve Problem Situations

Lesson 3.1: Explore Multiplicative ComparisonsSticker Mania
Lesson 3.4: Use Comparison to Solve Problem SituationsRepresenting “Times as Many”
Going Swimming

Unit 2: Multiplication and Division Problems

Module 4: Mental Math and Estimation Strategies

Lesson 4.3: Estimate Products by 1-Digit NumbersA Reasonable Answer

Module 5: Multiply by 1-Digit Numbers

Lesson 5.1: Represent MultiplicationInvestigate: Packing Lei
Lesson 5.2: Use Area Models and the Distributive Property to MultiplyCounting Flowers for Lei
Lesson 5.4: Multiplying Using Partial ProductsThree of a Kind
Lesson 5.6: Multiplying 3-Digit and 4-Digit NumbersA Lei Making Workshop

Unit 3: Extend and Apply Multiplication

Module 8: Extend and Apply Multiplication

Lesson 8.1: Multiply with TensGrowing Flowers for the Lei
Lesson 8.3: Relate Area Model and Partial ProductsDouble Decomposition
Lesson 8.4: Multiplying Using Partial ProductsRevisiting Strategies
Lesson 8.7: Solve Multi-step Problems and Assess ReasonablenessHow Many Supplies?

Unit 4: Fractions and Decimals

Module 10: Algebraic Thinking and Number Theory

Lesson 10.1: Investigate FactorsHamster Homes
Lesson 10.2: Identify FactorsFactor or Multiple?
Lesson 10.4: Identify Prime and Composite NumbersA Number Game
Lesson 10.5 Generate and Analyze Number PatternsHow Does It Grow?

Module 11: Fraction Equivalence and Comparison

Lesson 11.1: Compare Fractions Using Viaula ModelsInvestigate: Building Your Own Number Line
Lesson 11.2: Compare Fractions Using BenchmarksFraction Strips
Lesson 11.6: Compare Fractions Using Common DenominatorsChop It
Lesson 11.7: Use Comparison to Order FractionsAll Kinds of Fractions

Module 12: Relate Fractions and Decimals

Lesson 12.1: Represent Tenths as Fractions and DecimalsA New Way to Write Tenths
Lesson 12.2 Represent Hundredths as Fractions and DecimalsA New Way to Write Hundredths
Lesson 12.3: Identify Equivalent Fractions and DecimalsAre They Equivalent?
Lesson 12.4: Compare DecimalsHow Can You Compare?
Robot Factory
What’s the Order

Module 13: Use Fractions to Understand Angles

Lesson 13.2: Explore AnglesAngle Adventures
Lesson 13.3: Relate Angles to Fraction Part of a CircleThe Spin on Angles
Lesson 13.6: Join and Separate AnglesAngles in Motion

Module 14: Understand Addition and Subtraction of Fractions with Like Denominators

Lesson 14.2: Joining Parts of the Same WholePizza Problems

Module 15: Add and Subtract Fractions and Mixed Numbers with Like Denominators

Lesson 15.1: Add and Subtract Fractions to Solve ProblemsMath Pizzeria

Unit 6: Two-Dimensional Figures and Symmetry

Module 18: Symmetry and Patterns

Lesson 18.3: Generate and Identify Shape PattersHow Does It Grow?

Grade 5

Unit 1: Whole Numbers, Expressions, and Volume

Module 1: Whole Number Place Value and Multiplication

Lesson 1.3: Use a Pattern to Multiply by Multiplies of 10, 100, and 1000Partial Products Everywhere
Monarch Butterflies
All About That Base
Lesson 1.5: Multiply Multi-Digit NumbersHow Do They Compare?

Module 2: Understand Division of Whole Numbers

Lesson 2.4: Use Partial QuotientsEmptying the Water Tank

Module 5: Volume

Lesson 5.2: Understand VolumeWhich is Largest
Lesson 5.3: Estimate VolumePacking the Barge
Lesson 5.6: Find Volume of Composed FiguresPutting it Together
Figures Made of Prisms

Unit 3: Multiplying Fractions and Mixed Numbers

Module 8: Understand Multiplication of Fractions

Lesson 8.1: Explore Groups of Equal Shares to Show MultiplicationInvestigate: Sharing Sandwiches
Investigate: Folding Paper
Lesson 8.2: Represent Multiplication of Whole Numbers by FractionsSharing More Sandwiches
Lesson 8.3: Represent Multiplication with Unit FractionOne Part of One Part
Lesson 8.4: Represent Multiplication of FractionsDance Breaks
Parts of Parts
Making Food
Lesson 8.5: Use Representations of Area to Develop ProceduresOne Part of One Part
Installing Turf
Rows and Columns
Lesson 8.6: Interpret Fraction Multiplication as ScalingChores at Animal Haven
The Re-size-inator
Lesson 8.7: Multiplying FractionsMessy Multiplication

Module 9: Understand and Apply Multiplication of Mixed Numbers

Lesson 9.3: Practice Multiplication with Fractions and Mixed NumbersMessy Multiplication
Applying Fraction Multiplication

Unit 4: Divide Fractions and Convert Customary Units

Module 10: Understand Division with Whole Numbers and Unit Fractions

Lesson 10.1: Interpret a Fraction as DivisionDivision Story Problems
Making Generalizations

Unit 5: Add and Subtract Decimals

Module 13: Decimal Place Value

Lesson 13.1: Understand ThousandthsWhat Is One Thousandth?
Lesson 13.2: Read and Write Decimals to ThousandthsSay What?
Lesson 13.3: Round DecimalsWhich Way Down the Mountain?
Rounding Races
Lesson 13.4: Compare and Order DecimalsInvestigate: Numbers Between Numbers
The Claw
Selling Collectibles

Unit 6: Multiply Decimals

Module 15: Multiply Decimals and Whole Numbers

Lesson 15.1: Understand Decimal Multiplication PatternsPlace Value Patterns
Powers of 10 Parade

Unit 7: Divide Decimals and Convert Customary Units

Module 17: Understand Decimal Division Patterns

Lesson 17.1: Understand Decimal Division PatternsPowers of 10 Parade

Unit 8: Graphs, Patterns, and Geometry

Module 19: Graphs and Patterns

Lesson 19.1: Describe a Coordinate SystemCreating a Coordinate System
Lesson 19.2: Understand Ordered PairsBullseye!
Lesson19.4: Generate and Identify Numerical PattermsCoordinating Satellite Repairs

Grade 6

Unit 1: Number Systems and Operations

Module 1: Integer Concepts

Lesson 1: Identify and Interpret IntegersCan You Dig It?
Lesson 2: Compare and Order Integers on a Number LineOrder in the Class

Module 3: Fraction Division

Lesson 1: Understand Fraction DivisionFlour Planner
Fill the Gap

Module 4: Fluency with Multi-Digit Decimal Operations

Lesson 1: Add and Subtract Multi-Digit DecimalsDishing Out Decimals
Decimal Diagrams and Algorithms
Lesson 4: Divide Multi-Digit DecimalsMovie Time

Unit 2: Ratio and Rate Reasoning

Module 5: Ratio and Rates

Lesson 1: Understand the Concept and Language of RatiosPizza Maker
Lesson 2: Represent Ratios and Rates with Tables and GraphsFruit Lab
Disaster Preparation
Lesson 3: Compare Ratios and RatesModel Trains
Lesson 4: Find and Apply Unit RatesWorld Records
Lesson 5: Solve Ratio and Rate Problems Using Proportional ReasoningWelcome to the Robot Factory
More Soft Serve

Module 6: Apply Ratios and Rates to Measurement

Lesson 2: Use Rate Reasoning to Convert withing Measurement SystemsSoft Serve
Many Measurements

Module 7: Understand, Express, and Compare Percent Ratios

Lesson 1: Understand, Express, and Compare Percent RatiosLucky Duckies

Unit 3: Expressions, Equations, and Inequalities

Module 8: Numerical and Algebraic Expressions

Lesson 3: Write Algebraic Expressions to Model SituationsProducts and Sums

Module 9: Solve Problems Using Equations and Inequalities

Lesson 1: Write Equations to Represent SituationsWeight for It
Five Equations
Lesson 2: USe Additions and Subtraction Equations to Solve ProblemsHanging Around
Hanging It Up
Lesson 3: Use Multiplication and Division Equations to Solve ProblemsHanging Around
Hanging It Up
Lesson 4: Use One-Step Equations to Solve a Variety of ProblemsSwap and Solve
Lesson 5: Write and Graph InequalitiesTunnel Travels

Module 10: Real-World Relationships Between Variables

Lesson 1: Represent Equations in Tables and GraphsSubway Fares
Lesson 2: Write Equations from Verbal DescriptionsSubway Fares

Unit 4: Relationships in Geometry

Module 11: Polygons on the Coordinate Plane

Lesson 4: Find the Perimeter and Area on the Coordinate PlaneShapes on a Plane

Module 12: Area of Triangles and Special Quadrilaterals

Lesson 1: Develop and Use the Formula for Area of ParallelogramsExploring Parallelograms, Part 1
Exploring Parallelograms, Part 2
Off the Grid, Part 1
Lesson 2: Develop and Use the Formula for Area of TrianglesExploring Triangles
Triangles and Parallelograms
Off the Grid, Part 2
Lesson 3: Develop and Use the Formula for Area of TrapezoidsPile of Polygons
Lesson 4: Find Area of Composite FiguresPuzzling Areas
Letters

Module 13: Surface Area and Volume

Lesson 1: Explore Nets and Surface AreaRenata’s Stickers

Unit 5: Data Collection and Analysis

Module 14: Data Collection and Displays

Lesson 2: Display Data in Dot PlotsMinimum Wage
Lesson 3: Make Histograms and Frequency TablesThe Plot Thickens

Module 15: Measure of Center

Lesson 2: Find Measures of CenterToy Cars
Lesson 3: Choose a Measure of CenterHoops

Grade 7

Unit 1: Proportional Relationships

Module 1: Identify and Represent Proportional Relationships

Lesson 1: Explore RelationshipsPaint
Lesson 2: Recognize Proportional Relationships in TablesTwo and Two
Lesson 3: Compute Unit Rates Involving FractionsDinoPops
Lesson 4: Recognize Proportional Relationships in GraphsScale Factor Challenges
Lesson 5: Use Proportional Relationships to Solve Rate ProblemsScaling Robots
Lesson 6: Practice Proportional Reasoning with Scale DrawingsScaling Machines
Make it Scale
Tiles
Will It Fit

Module 2: Proportional Reasoning with Percents

Lesson 1: Percent ChangeMosaics
Percent Machines
Lesson 2: Markups and DiscountsMore and Less
All the Equations
Lesson 3: Taxes and Gratuities100%
Lesson 5: Simple InterestBack in My Day

Unit 2: Rational Number Operations

Module 3: Understand Addition and Subtraction of Rational Numbers

Lesson 1: Add or Subtract a Positive Integer on a Number lineFloats and Anchors
Lesson 3: Use a Number Line to Add and Subtract Rational NumbersDraw Your Own

Module 4: Add and Subtract Rational Numbers

Lesson 1: Compute Sums of IntegersMore Floats and Anchors
Lesson 2: Compute Differences of IntegersMore Floats and Anchors
Lesson 4: Apply Properties to Multi-step Addition and Subtraction ProblemsInteger Puzzles

Unit 3: Model with Expressions, Equations, and Inequalities

Module 7: Solve Problems Using Expressions and Equations

Lesson 1: Write Linear Expressions in Different Forms for Different SituationsCollect the Squares
Lesson 3: Write Two-Step Equations for SituationsKeeping it True
Lesson 5: Apply Two-Step Equations fo Find Angle MeasuresFriendly Angles
Missing Measures

Module 8: Solve Problems Using Inequalities

Lesson 1: Understand and Apply Properties to Solve One-Step InequalitiesI Saw the Signs
Lesson 2: Write Two-Step Inequalities for SituationsUnbalanced Hangers
Shira the Sheep
Lesson 3: Apply Two-Step Inequalities to Solve ProblemsBudgeting
Write Them and Solve Them

Unit 4: Geometry

Module 9: Draw and Analyze Two-Dimensional Figures

Lesson 2: Draw Circles and Other FiguresCan You Build It

Module 10: Analyze Figures to Find Circumference and Area

Lesson 1: Derive and Apply Formulas for CircumferenceMeasuring Around
Lesson 2: Derive and Apply a Formula for the Area of a CircleWhy Pi?
Lesson 4: Areas of Composite FiguresArea Challenges

Unit 5: Sampling and Data Analysis

Module 13: Use Statistics and Graphs to Compare Data

Lesson 3: Compare Means Using MAD and Repeated SamplingCrab Island

Module 14: Understand and Apply Experimental Probability

Lesson 1: Understand Probability of an EventHow Likely
Lesson 2: Find Experimental Probability of Simple EventsProb-bear-bilities

Module 15: Find Theoretical Probability of Simple Events

Lesson 1: Find Theoretical Probability of Simple EventsIs It Fair?

Grade 8

Unit 1: Transformational Geometry

Module 1: Transformations and Congruence

Module 2: Transformations and Similarity

Lesson 1: Investigate Reductions and EnlargementsSketchy Dilations
Lesson 2: Explore DilationsDilation Mini Golf
Lesson 3: Understand and Recognize Similar FiguresSocial Scavenger Hunt

Unit 2: Linear Equations and Applications

Module 3: Solve Linear Equations

Lesson 1: Solve Multi-Step Linear EquationsEquation Roundtable
Lesson 3: Apply Linear Equations

Module 4: Angle Relationships

Lesson 1: Develop Angle Relationships for TrianglesPuzzling It Out
Lesson 3: Explore Prarallel Lines Cut by a TransversalPuzzling It Out

Unit 3: Relationships and Functions

Module 5: Proportional Relationships

Lesson 2: Derive y = mxTurtle Time Trials
Lesson 3: Interpret and Graph Proportional RelationshipsTurtle Time Trials
Lesson 4: Compare Proportional RelationshipsTurtle Time Trials

Module 6: Understand and Analyze Functions

Lesson 1: Understand and Graph FunctionsGuess My Rule
Lesson 2: Derive and Interpret y = mx + bFlags
Translations
Lesson 3: Interpret Rat of Change and Initial ValueStacking Cups (Optional)
Lesson 4: Construct FunctionsWater Cooler
Lesson 5: Compare FunctionsUps and Downs
Lesson 6: Describe and Sketch Nonlinear FunctionsTurtle Crossing
The Tortoise and the Hare

Module 7: Systems of Linear Equations

Lesson 1: Represent Systems by GraphingMake Them Balance
Lesson 2: Solve Systems by GraphingLine Zapper

Unit 4: Statistics and Probability

Module 8: Scatter Plots

Lesson 1: Construct Scatter Plots and Examine AssociationRobots
Dapper Cats
Lesson 2: Draw and Analyze Trend LinesInterpreting Scatter Plots
Find the Fit (called Fit Fights in Desmos Math)
Lesson 3: Interpret Linear Data in ContextInterpreting Slopes
Scatter Plot City
Animal Brains

Module 9: Two-Way Tables

Lesson 1: Construct and Interpret Two-Way Frequency TablesFinding Associations
Lesson 3: Interpret Two-Way Relative Freqency TablesFinding Associations

Unit 5: Real Numbers and the Pythagorean Theorem

Module 10: Real Numbers

Lesson 2: Investigate RootsRoot Down

Module 11: The Pythagorean Theorem

Lesson 1: Prove the Pythagorean TheoremTriangle Tracing Turtle
Lesson 3: Apply the Pythagorean TheoremTaco Truck

Unit 6: Exponents, Scientific Notation, and Volume

Module 12: Exponents and Scientific Notation

Lesson 1: Know and Apply Properties of ExponentsCircles
Power Pairs
Lesson 2: Understand Scientific NotationSpecific and Scientific (formerly Solar System)
Lesson 3: Compute with Scientific NotationBalance the Scale

Module 13: Volume

Lesson 1: Find Volume of CylindersCylinders
Lesson 2: Find Volumes of ConesCones

Algebra 1

Intro/Launch

Unit 1: Real Numbers and Connections to Algebra

Module 2: Linear Equations and Inequalities in One Variable

Lesson 2.2: Write and Solve EquationsWorking Backwards
Solving Strategies
Same Position
Lesson 2.3: Rewrite Formulas and Solve Literal EquationsVarious Variables
Lesson 2.4: Write and Solve InequalitiesPizza Delivery

Unit 2: Linear Functions and Equations

Module 3: Linear Equations in Two Variables

Lesson 3.1: Linear Equations in Standard FormShelley the Snail
Five Representations
Lesson 3.2: Slopes of Lines and Rates of ChangePlane, Train, and Automobile

Module 4: Linear Functions and Models

Lesson 4.3: Characteristics of Linear FunctionsCraft-a-Graph

Module 5: Relationships Among Linear Functions

Lesson 5.3: Compare Linear FunctionsSubway Seats
Lesson 5.4: Inverses of Linear FunctionsChip the Robot

Unit 3: Build Linear Functions and Models

Module 6: Fit Linear Functions to Data

Lesson 6.1: Scatter Plots, Correlation, and Fitted LinesCorrelation Coefficient
How Hot Is It?
City Slopes
Behind the Headlines
City Data
Lesson 6.2: Residualts and Best-Fit LinesResidual Fruit
Penguin Populations

Module 7: Discrete Linear Functions

Lesson 7.1: Arithmetic Sequences Defined RecursivelySequence Carnival
Lesson 7.2: Arithmetic Sequences Defined ExplicitlyMore Visual Patterns

Module 8: Piecewise-Defined Functions

Lesson 8.1: Graph Piecewise-Defined FunctionsPumpkin Prices

Unit 4: Linear Systems

Module 9: Systems of Linear Equations

Lesson 9.1: Solve Linear Systems by GraphingLizard Lines
Lesson 9.2: Solve Linear Systems by SubstitutionShape It Up

Module 10: Linear Inequalities

Lesson 10.2: Graph Systems of Linear InequalitiesQuilts
Seeking Solutions

Unit 5: Exponential Functions and Equations

Module 11: Exponential Functions and Models

Lesson 11.1: Exponential Growth FunctionsCarlos’s Fish

Unit 6: Build Exponential Functions and Models

Module 13: Fit Exponential Functions to Data

Lesson 13.1: Scatter Plots and Fitted Exponential CurvesDetroit’s Population, Part 1
Detroit’s Population, Part 2

Module 14: Discrete Exponential Functions

Lesson 14.1: Geometric Sequences Defined RecursivelySequence Carnival
Lesson 14.2: Geometric Sequences Defined ExplicitlyMore Visual Patterns

Unit 8: Quadratic Functions and Equations

Module 17: Use Graphing and Factoring to Solve Quadratic Equations

Lesson 17.1: Solve Quadratic Equations by Graphing Quadratic FunctionsRevisiting Visual Patterns, Part 1
Quadratic Visual Patterns
On the Fence
Plenty of Parabolas
Lesson 17.3: Solve Quadratic Equations by Factoring ax^2+bx+cStomp Rockets
Two for One
Robot Launch
Lesson 17.4: Use Special Factoring Patterns to Solve Quadratic EquationsParabola Zapper
Shooting Stars

Module 18: Use Square Roots to Solve Quadratic Equations

Lesson 18.2: Solve Quadratic Equations by Completing the SquareSquare Tactic
Lesson 18.3: Use the Quadratic Formula to Solve EquationsStomp Rockets in Space

Unit 9: Function Analysis

Module 20: Function Analysis

Lesson 20.1: Choose Among Linear, Exponential, and Quadratic ModelsSorting Relationships

Unit 10: Data Analysis

Module 22: Numerical Data

Lesson 22.1: Data Distributions and Appropriate StatisticsFinding Desmo

Disclaimer

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

Grade 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.

S3-03: Instructional strategies for integrating science and literacy

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

We’re continuing our investigations around science and literacy with Doug Fisher, Ph.D., professor and chair of educational leadership at San Diego State University. We talk about the importance of integrating science and literacy, as well as practical guidance for teachers who want to unite the two disciplines in their own classrooms.

Listen as we discuss how science and literacy can be powerful allies and specific strategy areas to focus on when integrating the two disciplines. And don’t forget to grab your Science Connections study guide to track your learning and find additional resources!

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

DOWNLOAD TRANSCRIPT

Douglas Fisher (00:00):

It’s not that you have to become a reading specialist to integrate literacy into science. It’s how our brains work.

Eric Cross (00:10):

Welcome to Science Connections. I’m your host, Eric Cross. This season, we’re making the case for our favorite underdog, which of course is science. Each episode we’re showing how science can be better utilized in the classroom, and making the case for why it’s so important to do so. In our last episode, we examined the evidence showing that science and English instruction can support each other. And now on this episode, we want to give you some more strategies for really making that a reality in your own home or classroom or community. So to help me, I’m joined on this episode by Dr. Douglas Fisher, Professor and Chair of Educational Leadership at San Diego State University. Dr. Fisher is actually someone who has conducted literacy training at my own school, so I’m excited to be able to share some of his wisdom with all of you. Oh, and just a heads up, Dr. Fisher dropped some gems about the ways teachers can integrate literacy and science in their classrooms. So you may want to have a notepad. Ready. And now here’s my conversation with Dr. Douglas Fisher.

Eric Cross (01:12):

Well, Doug, thank you for your time and for being willing to come and talk about literacy and science. I know you’re busy, all over the place, and so I was super-excited that we were able to lock you in and talk about this. And, on this episode, we’re gonna talk about the ways that science and literacy can support each other. And one of the reasons why I’m really excited for you is because you said some really key things for me as a science teacher, when you talked about literacy and supporting students. That just resonated so deeply in me. And I was like, “I need more Doug!” Because we’re on that same frequency. And I know it’s a subject that you’ve spent a lot of time writing about. So can you tell us a little bit about how this became an area of interest or a passion for you? Just literacy, and all of the work that you’ve put into it?

Douglas Fisher (01:54):

Yeah. So I’ve wanted to be a teacher for a really long time. And I went to San Diego State as an undergraduate, and I was taking English class and we were assigned topics. You know, like, you’ll do an assignment, you’ll write a paper for this English class. And I got the topic “illiteracy,” and I was a freshman at San Diego State reading all of these things about adults who don’t read very well or not at all. And I ended up writing my very first college essay on illiteracy — at the time, you know, called illiteracy, at the time. And so I got super interested in this. And so as I moved through college and into my teaching career, literacy became a really important thing for me to think about, because it’s the gatekeeper. You know, you can be taken advantage of, if you’re not very literate. People can use vocabulary against you, if you’re not very literate. We know that people who have higher levels of literacy have better health outcomes. They have better lifespans, longer lifespans. I mean, there’s just — literacy impacts so much more than “Are you reading your fourth-grade textbook?” It really has lifelong implications.

Eric Cross (03:01):

That part that you said about being taken advantage of … I just got a flyer in the mail yesterday. It was one of these mailers that looked like it was an authentic debt-reduction type of thing, but it was really just like a marketing email. If you read the fine print at the very bottom, it had all of this jargon about “This is a paid, you know, for-profit company.” But when you look at it, it had official stamps all over it. And I could imagine if someone’s receiving that, that probably fools a lot of people. Is that kinda like what you’re talking about, like being taken advantage of?

Douglas Fisher (03:28):

Yes. I had a student turn 18, got a letter from a “credit card company” that was offering her daily compounding interest. And if you don’t know what that means — at 23 percent! — if you dunno what that means, you are gonna be a victim. Literacy really influences a lot of our life. It’s also how our brain works. We have a language-based system in our brain. We read, write, speak, listen, and view. And the things we learn, we learn through speaking, reading, writing, listening, and viewing. From what we know, we are the only species that has an external storage mechanism. Like, we have the ability to store complex information outside of our body, in the form of notes. We can type them. We can write them. And we can then go back and retrieve that information, that complex orthographic information later. And it means the same thing. We can say we have a storage system and we’ve been doing this for a really long time. Way back to, you know, hieroglyphics and messages on cave walls. And throughout the ages of humans learning, how to store information that they can re-access again later. That’s become a super-complicated system. It’s how computers operate. And we send messages to each other and we text each other and we write things down, and we’re really good at putting ideas, information out there. Now, if it’s just speaking and listening, then we can forget it. We can say, “No, you said this,” or “I said that.” But when it’s written, and it’s print literacy, you know, it’s the orthographics there, you can go back to the same message and over and over again. Now, you might change the interpretation of it, but the message is still there.

Eric Cross (05:16):

Right. And that is such a key element, at least of modern education, is this written element of it. It’s what many schools live and die by. They’re quantitatively and qualitatively analyzed by it. It’s public. They can see it. And so there’s this heavy emphasis. And why do you think science and literacy can be powerful allies together?

Douglas Fisher (05:38):

Awesome. Well, it’s hard to learn science if you’re not literate.

Eric Cross (05:42):

This is true.

Douglas Fisher (05:42):

But that’s a one-way direction. And yes, science teachers and scientists do a lot of reading, writing, speaking, and listening and viewing. They use the five literacy processes all the time. When we interview scientists, they spend a lot of their time reading the work of other scientists and writing their findings, writing grant proposals, presenting at conferences, you know. So a huge part of the work of a scientist is not just at a bench conducting experiments. But even if you’re conducting experiments, you’re using your literacy processes to think about what you’re seeing in your experiment. So that’s a one-way direction. And I do think literacy has an influence on science. But since science goes the other way, it influences literacy. As you learn more and you understand more about the world, your background knowledge grows, your vocabulary grows, you become more literate in those different areas. And how you think. So if I’m learning about life science; I’m learning how the world works in a more, biologic physical world. And that knowledge helps me think about when I’m reading a novel, and there’s an appeal to some science knowledge or a concept that gets played with, you know, perhaps time-space continuums … well, if I don’t have the science knowledge of how I think the world works, it’s hard for me to understand what this author is doing. So it does go both ways. They feed each other. And the more literate we become, the more complex science information we can understand. ‘Cause our background knowledge and our vocabulary influence how much we understand about what we read. And as we access more complex science information, it starts to change the way we think about other things in our world.

Eric Cross (07:23):

There was a couple of things that you said in that, but one of the first things that kind of perked my ears is when you said grant proposals. Because I have friends that are scientists — and this is one of the things that when I was in school, they don’t talk about — but how much of their research is reliant upon getting funding —

Douglas Fisher (07:37):

Mm-hmm. <affirmative>,

Eric Cross (07:38):

— which you don’t think about if you’re becoming a chemist or a physicist or a biologist or working in the field, is that that funding, coming from the NSF or anywhere else. And sometimes students ask in class like, “Why am I writing so much? Like, I want to go into science!” Or “I wanna do this!” And this is a real-life example of how the writing could actually apply, in addition to all of the things of collecting data and conclusions and results. But that grant proposal thing just really perked my ears, yeah.

Douglas Fisher (08:01):

And if you can’t write a grant proposal, your ideas and experiments are not gonna get funded. And if you can’t write a strong proposal, that compellingly convinces your readers to fund you, you’re not gonna get funded. But then once you get the grant, you have to write publications. You have to share your work with other people. Make PowerPoint presentations and write journal articles or books or whatever. So it’s a cycle that literacy influences the things we do, including the things we do in science.

Eric Cross (08:31):

Now to get in maybe some data, if you were trying to convince someone that like this happy marriage can exist, what would be like your number one piece of evidence to support this, this back and forth of supporting each other?

Douglas Fisher (08:44):

Awesome. So the quote I’ll often say — and this is from studies from more than two decades ago now — but in general, in high school science, students are introduced to 3000 unfamiliar words, 3000. Each year! Because there are words that are used in a scientific way that are used commonly in other places. And there are discipline-specific words. So 3000 words a year in high school science. The Spanish 1 textbook only has 1500 words in it. So science teachers have double the academic-language vocabulary demand that a typical introductory world-language class has. So just the vocabulary alone should say to us, literacy is gonna be important if you’re gonna learn science. And if you don’t understand these technical words, and you don’t understand the way science uses this particular word in this particular way… . When you say the word “process,” it means something very specific In science. “Division” — cellular division is not the way we think about it in mathematics; there’s a similar concept, but cellular division is different than dividing numbers. And those are words that get used in multiple areas. Then you have all these technical terms that you have to be able to use, to understand the concepts. To share the concepts. To talk to other people. Whether you’re in, you know, fifth grade and talking science, or you’re a university professor, there’s a shared language, appropriate for our grade level, that we have shared meanings of.

Eric Cross (10:22):

And we’re essentially … what I’m hearing you say is … most of the people that are listening to this are science teachers. We’re we’re also language teachers. In a sense.

Douglas Fisher (10:29):

So my frustration is when people say, “Every teacher’s a teacher of reading.” And I don’t like that. I’ve written against that phrase. I don’t think all teachers are teachers of reading, any more than all teachers are teachers of chemistry. Or all teachers are teachers of algebra. But what I will say is the human brain learns through language. And all of us — every teacher that I’ve ever met understands that language is important in my class. If my students don’t have strong listening skills and speaking skills; reading, writing, and viewing skills; I’m gonna have a hard time getting them to learn things. If I can help them grow their speaking, listening, reading, writing, and viewing in my content area, I’m gonna do a service for my learning of my subject and also their more broad literacy development.

Eric Cross (11:16):

  1. So, at a high level, what does it look like to integrate science and literacy? We’ve done education for the last, what, hundred years?

Douglas Fisher (11:24):

Mm-hmm. <affirmative>

Eric Cross (11:25):

—kind of pretty similarly, right? Kind of siloed way. What does this look like at the 30,000-foot level? You’re a professor, department chair. Run schools. Speak everywhere. Like, when you think about this from that high level, what does it look like?

Douglas Fisher (11:39):

A high level? Every time I meet with students in a science class, you know, biology or fifth grade or whatever? They should be reading, they should be writing, they should be speaking and listening. Every class. So what print do you want them to access? And it can be a primary source document, it can be an article, it can be from a textbook. Are they reading something? Are they writing to you? Because writing is thinking. If they are writing, they are thinking. As soon as their brain goes somewhere else, they stop writing. The pen won’t move or the fingers don’t type. And then speaking and listening, of course, is the dynamic of our classes. So every day we should see some amount of reading, writing, speaking, and listening, viewing in our classes. That’s at a high level. There are some generic things that seem to work across the literacy. So, learning how to take notes. Focusing on vocabulary. Using graphic organizers. These are generic things that as educators we can use in our classes. Then there’s more specialized things. So, scientists and science teachers think differently than historians and literary critics and art critics. So scientists, if you look at the disciplinary literacy work, there’s a whole body of research where they interview and study high-end experts in their field: chemistry, physics, biology, et cetera. And there are some characteristics that were more disciplined, specific. Scientists like cause and effect relationships. They look for them when they’re reading. They like sourcing information. “Where this come from?” “What’s the history of this idea?” Scientists have a long view in terms of time. Historians have a shorter view of time. English teachers have even shorter view of time. Scientists tend to think in long periods of time. And so all of that influences how a scientist reads and how we should apprentice young people after they get past the generic “I know how to take notes. I know how to study my vocabulary. I know how to do summary writing for my teacher in my notebooks and things,” there’s some generic tools. Once we get past those, we need to be looking at specifically how do people in science use literacy.

Eric Cross (13:52):

I’ve never had my thought process of reading deconstructed just now, but we just described how scientists read. I was like, “Yeah, that’s pretty much how I read, right there.” I also like how you said how we should apprentice young people. And I feel like you as the literacy guy, you chose that word very specifically, as far as apprenticing young people. That is a view, I think, that’s really important to hold. ‘Cause that’s what we’re doing essentially … is, if we’re doing what we should be doing, we are apprenticing these young people.

Douglas Fisher (14:18):

Yes.

Eric Cross (14:18):

And helping them develop. Now, let’s imagine there’s a listener out there and they’re interested in getting better at integrating science and literacy instruction. They want to start somewhere. Before we dive in, do you have any initial words of encouragement for the person who’s like, “Everything is like a priority right now,” in their classroom or in their world?

Douglas Fisher (14:37):

Yeah. So I’ll talk about elementary for just a moment. When we’re reading informational texts in our literacy block, we should be reading information that is aligned to what kids need to learn in science and history in, in that grade level. Why are we reading things that are gonna be in conflict with what they’re gonna learn in science later that day in fourth grade, for example? So when we look at our standards, our expectations, what is it that third graders need to know in history, science, mathematics, language arts? And when we’re reading text and we’re learning to apply our reading strategies during our literacy block, why aren’t we reading topics that build our background knowledge for our science time? So we’re seeing some synergy there. We should be looking at life cycles in grades that are appropriate for life cycles and knowing there’s more to life cycles than the frog and the plant or the seed. There are all kinds of life cycles. And we call ’em life cycles for a reason. That’s a general concept. Now in science, we’re looking at this particular lifecycle right now. And so that’s a high level. If we could get more connection to the content standards during our literacy blocks, it would be very good. When we talk about the time at which we call “science” in the day, in more of the K–8 continuum, the science needs to include some primary source documents. Some real things that students are reading. Read about a scientist; read about a scientist’s discovery; read about what they discovered. So that we’re building our background knowledge. So when we go to do things, activities, labs, simulations, we have background knowledge and we understand what we’re experiencing. It can’t be like—I watched this awesome lesson on lenses and the teacher had all these different lenses in the room and the students came in and they were brand new. They don’t know anything. They were picking ’em up. They’re exploring them. They’re trying to figure out, and they’re trying to come up with theories about what this is and how it works. And then the teacher gave them a reading, a short reading, on refraction of light. And they read this thing. And the clarity that they had about what these lenses must do, well! All of a sudden they’re putting them up to the lights! They’re asking if they can go get the lights out of the storage unit! ‘Cause there’s — and they’re shining different lights through the lenses to see what happens to the light. Because that little bit of reading turned some focus on for the students. And it allowed them to take what I’m thinking about, what I’m trying to figure out, how this thing works in another direction. That’s the power of using literacy in our classes.

Eric Cross (17:20):

And what I’m hearing essentially is transfer across disciplines, across content areas, ultimately. And in an elementary school classroom, would it be fair to say, probably the teacher has more autonomy to be able to do that, since they’re teaching all the subjects? But secondary, logistically, planning and those types of things … from what you’ve seen, is it fair to say this kind of needs to be like a top-down, full vertical alignment, to teach like this?

Douglas Fisher (17:45):

I think that would be awesome to do that. But if I’m a sixth grade English Language Arts teacher and I’m working with my sixth grade science teacher, the conversation should be, “What units are you teaching?” Because I’m choosing informational text. My job is to teach them how to find central ideas. My job is to teach them how to find the details in the text. My job is to have them make a claim and support that claim with evidence. The stuff I use is generic. Yes, we do read some literature and some narratives, but we also read about 50% of the text in English around informational text. So if I can help you and accomplish my standards as well, fantastic. So let’s have this conversation and say, “Oh, this is what you’re teaching in science in the next three weeks? I’m gonna choose some texts and we’re gonna analyze ’em for central idea. We’re gonna analyze ’em for details. We’re gonna, for mood or tone or whatever that we’re teaching. And by the way, I’m building background knowledge. So when they come to you, they know some stuff about what you’re going to be teaching next.” So I don’t think it’s impossible to say teams of teachers could come together and say, “What do we believe that our students need to know and learn and be able to do? And then how do we choose things that are gonna help them accomplish exactly that?”

Eric Cross (19:01):

And that’s empowering. Because that’s one thing that we can control maybe is this East-West, peer-to-peer, different content areas. A system may not be able to change as quickly, but I can definitely go talk to my English team or math team and check in and kind of see, “Hey, where do we have overlap in that?” And I know the times that I’ve accidentally had overlap with the teams, it’s super-exciting. And the students have been more bought in! Because it’s like, we’ve done something on the human microbiome and we’ve talked about genetics and all these different things, and then when they read The Giver, or they read some book about genetics, they have all this knowledge. And they’re excited. And they talk about colorblindness or they come to my class and they’re like, “Hey, we read about this!” It’s almost like they saw a magic trick, the fact that these things linked up. And the engagement has been so much higher when it’s the same content in different classes, but through different lenses. At least, that’s what I’ve seen in my years of teaching.

Douglas Fisher (19:54):

I saw a lesson on space junk that was so cool. Middle-school students learning space junk. And the history teacher had a part of it, science teacher had a part of it, English Language Arts teacher had a part of it. And these students, I mean, you watch them look up all the time, ’cause there’s space junk up there. Where’d it come from? Why is it there? What are the politics of this? How do we clean it up? I mean, it was just so interesting to watch them when the teachers came together. And the teachers met their standards in this couple-week-long space-junk exploration. Investigation was met. Politics was met. All these different things. Economy. You know, how much does it cost to clean up this problem? So there’s really cool opportunities when teachers come together and realize we can work together and improve the literacy and learning of our students.

Eric Cross (20:50):

Absolutely. So before this recording, we picked your brain a bit. And I know that there were three specific strategy areas that you wanted to touch on. And one of those — which is kind of coming back to the 3000-words language teachers — was vocabulary. So what are the opportunities that you see, as far as the way of educators to approach vocabulary? Because, you know, there’s a lot. We got a lot of it. The 3000 words.

Douglas Fisher (21:14):

Yeah. There’s a lot of it. So the worry is, we make a vocabulary list and have students look up the words in definitional kinds of things. That’s not really gonna help. Students need to be using the words. They need to be using the words in their conversations, in their writing, in how they think about your content in science. So vocabulary is a huge predictor of whether or not you understand things. Vocabulary is also a pretty good predictor if you can read on grade level. So when we think about vocabulary, there’s something called word solving. You show students a piece of text and you’re reading it, you’re sharing your thinking, and you say, “Oh, here’s a context clue!” Or “I know this prefix or suffix or root!” And in science, a lot of the words are prefixed, suffixed, or root words. We tend to add things together with a lot of prefixes and suffixes and have roots and bases in science. So we can help students think about, “Oh, what does geo- mean? We already know what geo- means here. It means the same thing in this word. Let’s apply that knowledge.” So word solving is part of it, showing students how we think about words that we might not know. The second is more direct instruction of vocabulary. As students encounter the words, we work on what it means, how we say it. We practice it a few times. The process is called orthographic mapping. It’s kind of a scientific idea here. But you have the sound and the recognition of by-the-word, by sight, and what it means. And your brain starts to automatically recognize that word in the future. So I don’t have to slow down, disrupt my fluency, and try to figure out what the word is saying. ‘Cause I’ve seen it enough. I’ve heard it pronounced enough, I’ve pronounced it enough, and I know what it means. So teachers should be saying, “What words in sixth grade science, what words in third grade science, do my students really need to know?” And I’m gonna have them encounter those words over and over. I’m gonna have them use the words. I’m gonna have them see the words. I’m gonna have them say the words. I’m gonna say the word and we’re gonna be over and over with these terms, so that students incorporate them into their normal view of, “These are the things I know about the world.” By the way, when they go to read that next thing, and they understand “geology,” you know, for sixth graders, for example, they know how to say it. They don’t stumble on it. And it activates a whole bunch of memories in their brains. “This is what geology is.” There are branches of geology, there’s physical geology, there’s all this thinking that activates as they read.

Eric Cross (23:35):

There was a practice that I participated in and am trying to incorporate — I don’t know what the name of it is. But essentially what happened was we were dissecting a flower. And the instructor had us name parts of the flower. But we got to come up with our own names for it.

Douglas Fisher (23:49):

Ah.

Eric Cross (23:50):

So, for instance, the stamen we call “the fuzzy Cheeto.” And we all used our own words and then everything was legitimized. And so we went through and learned the whole activity using our own vocab words. But then, in the end, after we presented and talked about it, then the words, the actual academic language was attached to our word. And we were able to say, “OK, the fuzzy Cheeto is the stamen,” and this, this, this, and this. But it was such an interesting practice, because it kind of legitimized all of our definitions. But we weren’t stumbling on these long Latin terms and things like that. Is there a name for that? Or. … ?

Douglas Fisher (24:29):

Yes. I don’t know the name for that. I think it’s really smart. So here’s what I would say about that, is: we don’t learn words, we learn concepts. Words are labels for our concepts. So what that teacher did for you was allow you to develop concept, a concept knowledge. “There’s a part of this plant, it goes like this, we’re gonna call it fuzzy Cheeto. Now I have this concept. And look, it occurred in all these plants. And those people called it that and that other group called it that. We called it a fuzzy Cheeto. Here’s the part of it.” And then the concept is in your brains. And the teacher said, “It’s really called stamen.” And it’s an instant transfer, because you already had the concept. What we often see is students are trying to learn a really hard academic word and the concept for the word at the same time. And so it slows down the whole process. And there’s higher levels of forgetting. Because human beings, we don’t learn words; we learn concepts. If you don’t have the concept, if I gave you a word out of the blue that you’ve never seen, never heard, and a week from now I asked you to remember it, you probably would not, because it didn’t register. It wasn’t part of your schema. You didn’t have a way to organize the information. You don’t have a concept. So that teacher? It’s a great idea. Got you to develop concept knowledge. And then said, “Here’s a real label for it: What some other people called it when they had the chance to come up with their own names.”

Eric Cross (25:50):

Shout out to my teacher, who was—

Douglas Fisher (25:51):

Right.

Eric Cross (25:52):

It was learned then. It was a great practice. And the fact that you’re right, like, I just mean from my own personal experience, I agree that learning concepts versus complicated words. And it’s interesting that you said higher levels of forgetfulness, you know. And you often hear that complaint about it: “Students forget! Students forget!” But this complex topic and this complex word that’s new to me, and I have to remember both of those things.

Douglas Fisher (26:12):

That’s right.

Eric Cross (26:13):

And the other neat thing that it did, is it actually honored the background and like the founts of knowledge of all the different groups in the classroom. You just said something about “this group called it this and this group called it this,” and so by letting different groups share all of those names, now we’re starting to build these kind of interesting connections. That’s at least what I remember experiencing. And so this, even this practice of this approach is very layered, beyond just kind of generating new knowledge of things. So I appreciate that aspect of it. Now another area that you mentioned was complex text.

Douglas Fisher (26:41):

Yeah.

Eric Cross (26:42):

And how we can get students into complex text. So what can we do there?

Douglas Fisher (26:46):

I think science is an ideal place to get students reading things that are hard for them. And I do believe that some parts of school should be a struggle. Not all day, every day. But there should be doses of struggle, which are good for our brains. And these complex pieces of texts that don’t give up their meanings easily allow students to go back and reread the text and maybe mark the text and talk to peers about the text and answer questions with their groups. And the whole point of complex text is to say, “We persevere through it. We may not understand it fully on our first read. But we go back and we might underline, we might highlight. We might write some margin notes. Our teacher might say, ‘What did this author mean here?’ And we go back and look at that part and we take it apart. What do we think about that? And we talk to each other. It’s showing that when we read things, we work to understand. We work through our thinking, often in the presence of other people. And our understanding grows as we go into the text over and over and over again.” So I said geology earlier. There’s about a two-page article on “what is geology” that sixth graders often read. And some kids find it super boring. It’s a once-read, “OK, geology, I don’t really understand it. There’s a bunch of words in here that I don’t understand.” But if you go back to it a few times and you start taking apart, “What are the branches of geology? Oh, I’m gonna go reread that.” How are these two branches related to each other?” “What are the subtypes of each branch of geology?” “How do geologists do their work?” You start asking questions where students are going back into the text. You spend a little bit of time. Now, the introduction to geology, the students know so much more. So whatever you do next— video experiments, whatever—they have a frame of reference, because of that deep, complex read. It’s probably better than simply telling them, “Here’s the information.”

Eric Cross (28:45):

Right. And I even feel like as an educator, when I reflect on my own learning in the classroom, and then looking at it through the perspective of an educator <laugh>, you find this difference between how you were taught and then what the data says good teaching is.

Douglas Fisher (28:59):

Mm-hmm. <affirmative> mm-hmm. <affirmative>.

Eric Cross (29:00):

It’s so easy to slide back into how you were taught!

Douglas Fisher (29:02):

Yeah.

Eric Cross (29:02):

Even though, you know, you mentally assent to, “This is the best way. This is the data shows.” And you find yourself kind of sliding back at times.

Douglas Fisher (29:10):

Yep. And there’s good evidence to support what you just said, that most people teach the way they experienced school. And it is very hard to change that. And people have studied this. And it’s very hard to change that. Because it worked for us. And we have an n of 1, and it worked for us. Now, remember, there were a whole bunch of other kids in the class that it may not have worked for. And we chose to be in school the rest of our lives, and some of your peers did not choose to be in school the rest of their lives. In fact, some of them hated school and found no redeeming qualities of their experience. So just because it worked for us in a case of one, n of 1, doesn’t mean it worked for all of the kids, or even the majority of them.

Eric Cross (29:57):

Very well said. It’s that, what is that, the survivor bias? Survivorship bias? Where you were the one that made it. But you don’t think about all the other folks. ‘Cause we’re thinking about ourselves.

Douglas Fisher (30:05):

That’s right.

Eric Cross (30:06):

Great case for empathy too, is thinking about the people left and right. Because my friends are like, “I hated science.” And I say, “Who hurt you? Like, what did they do? It’s so amazing, so much fun!”

Douglas Fisher (30:16):

“What happened to you? Science is the coolest. Right? It’s so amazing!”

Eric Cross (30:21):

But I also had a unique experience in seventh grade with my teacher who did some of these things, and made it accessible for so many of us, in opening opportunities that I wouldn’t have had otherwise. But you’re absolutely right. That was my story. That wasn’t the story of everybody that was around me. And I think that’s really important. Now, I know this is also a big one for you, but I wanna talk about writing. What are the opportunities that you see in terms of writing specifically?

Douglas Fisher (30:51):

So would love it if science teachers had short and longer writing tasks in the science time. Of course, you can integrate some of the science writing, the longer ones, in the English language arts time, especially if you’re the elementary teacher and you can have control of the whole day. But I said this earlier; I’ll say it again. Writing is thinking. While you are writing, there’s nothing else you can do but think about what you are writing. Your brain cannot do something else. So if a science teacher wants to know, do their students really understand the concepts? Have them write. Now some of the shorter ones, I like something called “given word” or “generative sentences”: “I’m gonna give you a word: CELL. C-e-l-l. We’re in science. I want you to write the word ‘cell,’ c-e-l-l, in the third position of a sentence. So it’s gonna go word, word, cell, and then more words.” You could also say, “I want the sentence longer than seven words,” or whatever. But the key is, I’m telling you where I want the word. You will know instantly if your students have a sense of what the word “cell” means in the context of science. If they write “my cell phone,” they don’t get it. If they write about spreadsheet cells or jail cells or whatever, they didn’t get it. But if they talk to you about plant cells and animal cells and the components of those cells, and then once they have that sentence down, you can say to them, “Now write three or four more sentences that connect to that sentence.” It’s super simple. So whatever concepts you’re teaching, put ’em in a specific position. Now you don’t have to only put it in the third position. You can say the first position, the fifth position, the fourth position. But it forces them to think about what they know about the word and then how to construct a sentence for you. That’s a very simple way to get some writing from your students that helps you think about what they understand. Other kinds of writing, you can have quick writes, you can have exit-slip writes. There’s something in the research space called the muddiest part, where halfway through the lesson you have them write so far what has been the least understood or the most confusing part of this lesson. And they do a quick write, right there, at the muddiest part. And as a teacher, you flip through these and you start to say, “Oh, these are the points that are confusing to my students.” So if 80% of them all have the same thing, I gotta reteach that. If these five got, “This is the muddiest part,” If these five thought, “This is the muddiest part,” these seven, “I thought this was the muddiest part,” what do I need to do? Because it’s gonna be hard to move forward if this is their area of confusion. There are also all kinds of writing prompts that have a little bit longer. My favorite one is RAFT. What’s your Role? Who’s your Audience? What’s the Format? And what’s the Topic we’re writing about? Super flexible writing prompt. When you teach something, we don’t want students to only think they write to their teacher. So your role is an atom. You are writing to the other atoms. What do you wanna write about? What’s the topic? What’s the format of it? Is it a love letter? Is it a text message? Is it … so we, we mix it up with students in saying, how do they show some knowledge through a prompt that we give them? And then of course, longer pieces as they get older. More opinion pieces through fifth grade. More claims and arguments starting in sixth grade. So that they’re starting to see, “I have to use the evidence from things I’ve learned, read, listened to, watched, and construct something: an opinion, an argument where I back it up with reasons or evidence.” And those longer pieces, you know, less frequently. The shorter pieces, pretty regularly. So the teacher sees the thinking of the students.

Eric Cross (34:29):

When you were speaking about these really creative writing prompts, there were specific students coming into mind, that were coming into mind … they’re, they’re great science students, but they also have this really strong artsy side drawing, creative writing, and things like that. And when you said something about atoms talking to each other, it elicited, in my brain, certain students that would really love this aspect of creativity in the sciences. And it’s not how we’re typically trained as science teachers, to kind of incorporate this, like you said. A book of props. But I’m imagining, like, as a science teacher, if I took this, this would be a great way to reach more students to be able to show what they know, in a way that might resonate with their own intrinsic “Oh, I get to write creatively!” So I was kind of writing furiously as you were sharing all that information there.

Douglas Fisher (35:12):

So here, I’ll give you another example for elementary people. Again, with RAFT. There’s a book called Water Dance. It’s a pretty popular book for elementary teachers. It’s really about the life cycle of water. For example, you are a single drop of water. You are writing to the land. The format is a letter. And you’re explaining your journey. Now, if they can do this, they’re essentially explaining to you the cycle of water. But you got it in a way that people are now, “Oh, I’m a drop of water. So it’s me. My perspective. Where do I go from? Where do I start?” Because you can start anywhere in the cycle, right? My drop could have started in the clouds. My drop could have started in the ground. My drop could have started in the lake. But it has to show you the journey. So there are many ways of showing you the right answers.

Eric Cross (36:02):

And that’s using the RAFT protocol.

Douglas Fisher (36:04):

That’s RAFT: Role, Audience, Format, Topic. It’s been around 20 or 30 years.

Eric Cross (36:09):

You just gave the name to something a teacher shared in our podcast community, Science Connections: The Community, on Facebook. Teacher shared a Google slide deck and on it were just three slides. And the role that the student had to have is they had to show, then tell, the story of a journey of a piece of salmon being eaten, a piece of starch from pasta being eaten, and then an air molecule in a child’s bedroom. And they had to give the path of travel and the experience from the mouth and then breaking down into protein and all those kinds of things. And this teacher shared it and I wish I knew the teacher’s name because I wanna give ’em credit, but they shared it. And so I used it with my students and then had ’em read aloud their stories and dramatize it. And they were so into it!

Douglas Fisher (36:49):

So cool.

Eric Cross (36:50):

But through it, I was able to see that they understood different parts of the body. They understood cell respiration. The whole thing. And it was fun! To watch them get so into this creative writing. And now I know the name of it. That’s been 30 years they were using RAFT. So you just talked a bit about complex texts and writing. And before we go, I wanted to circle back to something that you said, because I think it’s important, and if you could elaborate on it a little bit, about the value of struggle. Can you talk more about that?

Douglas Fisher (37:21):

Sure. I do believe in a lot of the U.S. we’re in an anti-struggle era of education. And it predates Covid. I think it made it worse during Covid. We front load too much. We pre-teach too much. We reduce struggle. We quote, “over-differentiate” for students. And there’s value in struggle. The phrase, “productive struggle” — if you haven’t heard it, Google productive struggle — it’s an interesting concept, that we actually learn more when we engage in this productive struggle. Now, productive struggle originally came from the math world, and it was this idea that it’s worth struggling through things to learn from it, that you’re likely to get it wrong, and then there was productive success. And there are times when we want students to experience success and we make sure we put things in place for productive success. But there are times where we want them to struggle through a concept. ‘Cause it feels pretty amazing when you get on the other side, when you know you struggled and you get to the other side. If you think about the things, listeners, think about the things in your life where you struggled through it and you are most proud of what you accomplished. I want students to have that. I don’t wanna eliminate scaffolding, eliminate differentiation. But I do want some regular doses of struggle. So if you look at the scaffolding, we have a couple choices. We have front-end scaffolds, distributed scaffolds, and back-end scaffolds. Right now we mostly use front-end scaffolds: We pre-teach, we tell students words in advance, that kind of stuff. But what if we refrained from only using front-end scaffolds, and we use more distributed scaffolds, when they encounter. So there’s a difference between “just in case” and “just in time” support for students. So we tend to plan on the “in advance, here are all the things we’re gonna do to remove the struggle before students encounter the struggle.” What if instead we said, “Let them encounter some struggle. Here’s the supports we’re gonna provide. We’re gonna watch; we’re gonna remove those scaffolds, and allow them to have an experience of success, where they realize, ‘I did it. I got it.’” Every science teacher I’ve ever worked with, when they do an experiment or a lab or simulation, they are looking for productive struggle. They don’t tell the answers in advance. They don’t tell if the answers are right. That’s your data. What does your data tell you? I mean, this is what you do. But then the other part of your day when you move into, like, reading, you don’t do that. You fall into the trap of removing struggle. And so allow them to grapple with ideas. Allow them to wonder what words mean. Allow them to say, “I’m not getting this, teacher! It’s really frustrating!” And you say, “Yeah, this is really hard. This is why we’re doing it at school. ‘Cause it’s really hard. If it was easy, I’d have you do it at home. But we’re doing it here, ’cause it’s really hard and it’s OK not to get it at first.” And create a place where errors are seen as opportunities to learn, and struggling through ideas and clarifying your own thinking and arguing with other people to reach an agreement or reach a place where we agree to disagree is part of the power of learning.

Eric Cross (40:38):

There’s a teacher, who I took this from. My master teacher when I was student teaching. And she said that there’s no such thing as failure in science, just data. And I took that same mantra. And I resonate with what you said about how science teachers, all of us, hold onto that productive struggle, because it’s part of being a scientist. It’s part of the experiments. That genuine “aha” moment. Or it didn’t work out? That’s great! That’s totally fine! Let’s write about it and let’s take photos and let’s publish it and let’s be scientists. That’s totally true. As we wrap up, Dr. Fisher, is there any final message that you have to listeners about bringing science and literacy together? I know you speak everywhere, but for everyone that’s listening, if you can put out your encouragement or message or suggestion … you’ve given so many great tips and practical applications. But, any final thoughts on the subject?

Douglas Fisher (41:32):

I think many science teachers are intimidated because they think they have to be reading teachers. And there’s a knowledge base to reading. And some teachers are reading teachers and science teachers, and I don’t wanna dismiss that. But it’s not that you have to become a reading specialist to integrate literacy into science. It’s how our brains work. And so as you think about the way in which you are learning and the ways in which you want your students to learn, what role does language play? What role does speaking, listening, reading, writing, viewing, play in your class? And then provide opportunities for students to do those five things each time you meet with them.

Eric Cross (42:12):

Dr. Fisher, thank you so much for being here and for your encouragement, and sharing your wisdom and experience. And then personally serving my city, here in San Diego, and my students, when they make it to your high school and ultimately the alma mater of San Diego State University.

Douglas Fisher (42:30):

That’s right.

Eric Cross (42:31):

Yeah. We really, really appreciate you in serving all kids and lifting the bar and making things more equitable for all students. And encouraging teachers. So thank you.

Douglas Fisher (42:39):

Thank you very much.

Eric Cross (42:42):

Thanks so much for listening to my conversation with Dr. Douglas Fisher, Professor and Chair of Educational Leadership at San Diego State University. Check out the show notes for links to some of Doug’s work, including the book he co-authored titled Reading and Writing in Science: Tools to Develop Disciplinary Literacy. Please remember to subscribe to Science Connections so that you can catch every episode in this exciting third season. And while you’re there, we’d really appreciate it if you can leave us a review. It’ll help more listeners to find the show. Also, if you haven’t already, please be sure to join our Facebook group, Science Connections: The Community. Next time on the show, we’re going to continue exploring the happy marriage between science and literacy instruction.

Speaker  (43:26):

I had this moment of realization I felt a few months ago: I’m like, if I don’t teach them how to use the AI as a tool, as a collaborator, then they’re gonna graduate into a world where they lose out to people who do know how to do that.

Eric Cross (43:39):

That’s next time on Science Connections. Thanks so much for listening.

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What Dr. Douglas Fisher says about science

“There are really cool opportunities when teachers come together and realize we can work together to improve the literacy and learning of all our students.”

– Dr. Doug Fisher

Professor and Chair of Educational Leadership, San Diego State University

Meet the guest

Douglas Fisher, Ph.D., is professor and chair of Educational Leadership at San Diego State University and a leader at Health Sciences High & Middle College having been an early intervention teacher and elementary school educator. He is the recipient of an International Reading Association William S. Grey citation of merit, an Exemplary Leader award from the Conference on English Leadership of NCTE, as well as a Christa McAuliffe award for excellence in teacher education. He has published numerous articles on reading and literacy, differentiated instruction, and curriculum design as well as books, such as The Restorative Practices PlaybookPLC+: Better Decisions and Greater Impact by DesignBuilding Equity, and Better Learning Through Structured Teaching.

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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. 

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

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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.

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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 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.

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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!

Families and caregivers, welcome to Amplify Desmos Math Texas K–5!

Welcome to the Amplify Desmos Math Texas K–5 Caregiver Hub. We’re here to support your student as they explore math, work with friends to solve problems, and learn new and interesting concepts—and to support you as you go on this math journey with them! Below are some suggestions and resources for how you can support their learning at home.

Learn more about Amplify Desmos Math Texas.

Para la versión en español, haga clic aquí.

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Unit Caregiver Resources

For every unit of the program, we’ve created a Caregiver Resource that provides a summary of key concepts. You’ll find a Caregiver Resource for each unit, in both English and Spanish.

Unit 1: Beginning Number Concepts

Unit 2: Numbers 1–10

Unit 3: Shapes, Coins, and Financial Literacy

Unit 4: Understanding Addition and Subtraction

Unit 5: Make and Break Apart Numbers Within 10

Unit 6: Numbers 0–20

Unit 7: Solid Shapes All Around Us

Unit 1: Adding, Subtracting, and Working With Data

Unit 2: Story Problems Within 10

Unit 3: Adding and Subtracting Within 20

Unit 4: Numbers to 99 and Financial Literacy

Unit 5: Adding Within 120

Unit 6: Length Measurement Within 120 Units

Unit 7: Geometry and Time

Unit 1: Working With Data and Developing Financial Literacy

Unit 2: Adding and Subtracting Within 100

Unit 3: Measuring and Solving Problems Using Length

Unit 4: Numbers to 1,200

Unit 5: Geometry and Time

Unit 6: Adding and Subracting Within 1,000

Unit 7: Equal Groups and Area

Unit 1: Introducing Multiplication

Unit 2: Adding, Subtracting, and Rounding Larger Numbers

Unit 3: Relating Multiplication to Division

Unit 4: Fractions as Numbers

Unit 5: Measurement and Financial Literacy

Unit 6: Sorting and Classifying Shapes

Unit 1: Fraction Equivalence and Comparison

Unit 2: Extending Operations to Fractions

Unit 3: From Hundredths to One Billion

Unit 4: Mathematical Relationships and Financial Literacy

Unit 5: Multiplying and Dividing Multi-Digit Numbers

Unit 6: Angles and Properties of Shapes

Unit 1: Volume, Factors, and Expresssions

Unit 2: Multiplying and Dividing Fractions

Unit 3: Multi-Digit Multiplication and Division and Financial Literacy

Unit 4: Place Value Patterns and Decimal Operations

Unit 5: Measurement, Fraction Operations, and Data

Unit 6: Geometry and Algebraic Reasoning

Sub-Unit Summaries

Access Amplify Desmos Math at home.

In addition to a print Student Edition workbook, your student will have digital access to all learning, practice, and assessment materials through the Amplify platform. The digital curriculum can be accessed in school and at home by following these instructions:

  • Select the Amplify Desmos Math button.
  • Select Log in with Amplify.
  • Enter your student’s username and password provided by your student’s teacher.
  • Select the desired grade level.

Once logged in, caregivers can view student work by opening previous assignments.

Learn how to navigate the student home page.

Materials overview

Amplify Desmos Math Texas supports blended learning with supporting print materials and a unique digital experience. All K–5 lessons are available in a write-in Student Edition book. Many of the lessons include hands-on activities with manipulatives, tools that help students understand abstract concepts by making them tangible. Your student will also work with digital devices for an age-appropriate number of lessons.

When students use devices, teachers can monitor their work in real time, making sure they get the exact support that they need at every part of the lesson, in and outside of class.

Una interfaz digital que muestra los nombres anónimos de los estudiantes y su estado de participación en diversas actividades. La interfaz incluye opciones para realizar resúmenes, capturas de pantalla y vistas individuales de los estudiantes.

Components of a lesson

Students in an Amplify Desmos Math Texas classroom can be seen (and heard!) asking questions, debating answers, justifying their thinking, grappling with problems, and working together and independently.

A typical Amplify Desmos Math Texas lesson includes:

  • Warm-up: A short, attention-getting problem to pique students’ interest in the lesson.
  • Activities: One to two mini-activities that challenge students’ problem-solving skills.
  • Synthesis: Discussion to review and bring together the important concepts from the lesson.
  • Show What You Know and Reflection: Questions for students to show what they know from the lesson. (Note: The Show What You Know lesson assessment is optional for kindergarten and grade 1.)
  • Centers: Student-led activity stations that reinforce the math learned during lesson activities through interactive and often game-like formats. In kindergarten and grade 1, time for Centers is built into the last 15 minutes of every lesson.

To support, strengthen, and stretch students’ learning after the lesson, Amplify Desmos Math Texas offers options for:

  • Differentiation: Mini-Lessons, Centers, Extensions, Boost Personalized Learning, and Fluency Practice.
  • Practice: Additional problems your student’s teacher may assign for classwork or homework.

Support math learning at home.

You can support your student’s math learning outside of school in many ways:

Your student’s teacher may assign practice problems at the end of each lesson for classwork or homework. If your student has already completed the practice problems for the lesson, ask them to walk you through how they solved each problem, or talk about any parts that were challenging for them. Ask your student follow-up questions to encourage the use of math language as they explain their thinking, such as, “How do you know?,” “How can you show your thinking?,” or “How would you describe that?” If students are stuck, ask support questions, such as, “What information do you know here?” or “How could you represent this problem?”

Your student’s teacher may introduce a Center game with students in the lesson or beyond the lesson. These games are aligned to the math of the unit and can be played with students outside of class. Your student’s teacher may introduce a Center game to students during or after completing a lesson, or you may need to teach the game before you play by using easy-to-follow instructions. Try out the following Center games with your student!

Each unit in Amplify Desmos Math begins with a Read-Aloud to engage students and provide context for the math of the unit. Elements and characters from the Unit Story then appear in lessons throughout the unit.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Relate math to daily activities at home, whether grocery shopping, preparing a meal, or planning for a trip to the store. Your student can help you figure out how many more apples there are than oranges in the grocery cart, show how to split a sandwich into fourths, or figure out how much change you’ll receive in exchange for a $10 bill. Encourage your student to point out ways that you use math in your daily tasks.

Remind your student that getting stuck is part of the process—a necessary and beneficial part of learning. Many students (and adults) fear making mistakes, but research shows that mistakes help our brains grow! When your student gets stuck on a problem, encourage them to keep trying different strategies even if they’re not sure they’re right.

A curiosity-driven K–12 program that builds lifelong math proficiency

Amplify Desmos Math thoughtfully combines conceptual understanding, procedural fluency, and application. Each math 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.

What is Amplify Desmos Math?

Amplify Desmos Math supports teachers in building students’ lifelong math proficiency. The program:

  • Supports social classrooms, invites mathematical creativity, and evokes wonder, creating a welcoming learning space where students are empowered to see themselves and their classmates as having brilliant mathematical ideas.
  • Provides teachers with clear, step-by-step moves to build systematically from students’ prior knowledge to grade-level learning.
  • Connects students to each other’s thinking and to an understanding that they can use math to make sense of the world.
  • Enables access to grade-level understanding for every student, every day.

A powerful suite of math resources

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

Data informs instruction. Comprehensive student profiles provide full data on students’ assets and skills, empowering teachers to provide just-in-time scaffolds throughout core instruction and targeted intervention when needed.

Educational software interface featuring a New York math problem about measuring platform heights using a 9-inch tube, illustrated with a playful, colorful design.

Experience Amplify Desmos Math

Click the links below to explore our interactive digital lessons, where you’ll also find print Teacher Edition and Student Edition pages for each lesson.

For helpful navigation tips and more program information, download our Grades K–5, Grades 6–Algebra 1, and Grades 9–12 program guides.

You can also watch a product expert walk through a lesson and the available program components with a lesson walkthrough video.

Diagnostic screening and progress monitoring assessments

Integrated mCLASS® Assessments go beyond accuracy to reveal students’ math thinking through an asset-based approach. This data provides better insights about what students know, what math assets to leverage, and where students need support.

A laptop displays a math problem with illustrated students and a virtual keyboard. Behind it, a chart shows percentages for a Math 2 Beginning-of-Year Screener assessment.

Personalized learning and support

Amplify Desmos Math includes digital, adaptive practice that provides the personalized support a student needs to access grade-level math every day. Boost Personalized Learning activities target a skill or concept aligned to the day’s core lesson, with each student receiving personalized scaffolds based on what they already know. This technology complements daily learning and provides another layer of support to the in-lesson differentiation and instructional guidance provided to teachers. Click here to try a Boost Personalized Learning activity. More activities coming soon!

The Fluency Practice of Amplify Desmos Math uses an evidence-based approach to memory retention—spaced repetition—for the basic operations. Students around the world have answered more than 120 million multiplication questions within our application. Try it now! 

Contact us

Support is always available. Our team is committed to helping you every step of the way. Contact your dedicated Indiana representative here for program access, samples, and additional information.

A woman with long brown hair and a white top smiles at the camera in front of an orange background, showcasing her passion for the Science of Reading and dedication to Indiana middle school education.

Elizabeth Sillies Callahan

Southern IN
(513) 407-5801

A woman with long brown hair and blue eyes smiles gently at the camera. The background is a light purple circle, reflecting her passion for the Science of Reading and dedication to Indiana middle school education.

Jody Kammer

Central IN
(310) 402-7837

Woman with long brown hair, large black glasses, and a nose ring, wearing a striped shirt and dark blazer, posing in front of a neutral background—professional style suited for the Indiana Department of Education.

Amanda Knipper

Northern IN
(260) 894-5123

A woman with wavy red hair and blue eyes, dressed in a purple turtleneck, smiles at the camera against a dark background—reflecting the approachable spirit of Indiana middle school teachers.

Paige Lawrence

District enrollment below 1200
(980) 421-2608

Welcome, Program 3 reviewers!

We’re honored to introduce you to Amplify California Language Arts. We’re confident you’ll find this comprehensive program to be a powerful tool for bringing the vision of the California ELA/ELD Framework to life in classrooms across the state.

Please start with the video on the right to learn how to navigate the program and access key features referenced within our submission. Below you’ll find additional resources to support your review.

Your review samples

We’re excited for you to begin your review of Amplify California Language Arts, a comprehensive biliteracy program for kindergarten through grade 6.

Reviewer Binders (K–6)

Your physical samples should have arrived in grade-specific boxes with three Reviewer Binders.

  • The first binder will contain logistical program review information and the printed Evaluation Criteria Map.
  • The second binder will contain the printed Standards Maps for grades K–2.
  • The third binder will contain the printed Standards Maps for grades 3–6.

Physical samples (trade books)

Your review of the program will be entirely digital with the exception of the trade books that you will be receiving as physical samples. You can expect to receive 13 boxes of physical materials for your review. Twelve boxes of trade books, one for each grade K–5, in English and Spanish, and one box containing your Reviewer Binders.

As you begin the process of organizing your materials, please refer to the inventory checklist found inside each box as well as within your Reviewer Binder.

Digital review materials

In order to access your digital review materials, you’ll need to log in to our platform using your unique login credentials found on a Digital Review Credential flyer inside of your Reviewer Binder. Once you have located the flyer:

  • Click the orange button below to access the platform.
  • Click “Log in with Amplify.”
  • Enter the username and password provided on your Digital Review Credential flyer.

Navigation tips

Before you get started, please review these important functionality notes:

Criteria Map and Standards Maps must be opened on Microsoft Word on your desktop to function as intended. If you open the documents without Microsoft Word on your desktop, citations will be cut off at the bottom of most tables within the document.

Many of our citations are deep-links to PDFs, meaning they will take you to the right page or the first page in the sequence for the citation in question. To ensure this functionality works, please disable any PDF-viewing extensions or plug-ins such as Adobe Acrobat Pro Browser Extension.

[Reviewer program navigation video] Grades K–5

[Reviewer program navigation video] Grade 6

Click here for additional information on navigating the program for grade 6.

Category 1: English Language Arts (ELA) and English Language Development (ELD) content/alignment to standards

Evaluation Criteria Map

Linked below is the Evaluation Criteria Map. Please note that you will need to be logged into the digital platform to access the links in the Evaluation Criteria Map.

ELA Standards Maps

The links below provide the Standards Maps for Amplify California Language Arts for each grade level.

ELD Standards Maps

Category 2: Program organization

Amplify California Language Arts’ biliteracy program is a comprehensive curriculum provides a full year of evidence-based instruction for each grade level, with both integrated and designated English Language Development instruction designed to give multilingual/English learners the tools to thrive. Amplify’s biliteracy program for grades K–6 includes:

  • Core English language arts instruction: Amplify Core Knowledge Language Arts (CKLA) California (grades K–5) and Amplify ELA California (grade 6) covering knowledge building and foundational skills.
    • Provides upper grade foundational skills instruction for grades 3–6.
  • Core Spanish language arts instruction: Amplify Caminos California, a fully parallel SLA program that works in tandem with English core instruction across all grades.
    • Provides upper grade foundational skills instruction for grades 3–6.
  • Designated English Language Development: Language Studio California is the designated English Language Development companion that directly aligns with and supports core English instruction. 
  • Newcomer Support: Amplify California Language Arts Newcomer Support to facilitate instruction for students who are new to both English and the United States.

Program structure

Amplify’s California Language Arts programs are built on what the research shows: Strong readers need both word recognition and language comprehension. Our comprehensive curriculum suite follows the Simple View of Reading bringing together foundational skills and knowledge building to deliver instruction grounded in the Science of Reading.

This model is integral to the structure of the Amplify biliteracy program, which directly aligns with the CA CCSS ELA and ELD standards by combining rigorous decoding and skills instruction with research-based knowledge and language development instruction. In its early grades, the Amplify biliteracy program uses a two-strand structure—Skills/Lectoescritura and Knowledge/Conocimiento—to effectively address this learning challenge while meeting standards expectations for both language development and academic content mastery.

Diagram with three orange squares labeled: "Language comprehension," "Word recognition," and "Skilled reading," connected by multiplication and equals signs, with Spanish headings above each square.

[Reviewer highlight video] Program organization for Category 2

[Reviewer highlight video] Program structure for grades K–2

[Reviewer highlight video] Program structure for grades 3–5

[Reviewer highlight video] Program structure for grade 6

Amplify Caminos California lessons are designed to allow all students time to work toward learning objectives, including peer collaboration and discussion. Since each lesson activity is aligned to subsequent activities, students’ understanding and analysis develops progressively throughout the lesson.

Each lesson follows a predictable structure with clearly marked components, beginning with warm-up routines, progressing through explicit instruction with guided practice, and concluding with independent application activities. The program provides detailed teacher language, including question stems and discussion prompts, ensuring clear and consistent delivery of instruction.

Amplify CKLA California and Amplify Caminos California empower teachers to deliver effective instruction and keep students engaged with the following resources:

  • Teacher Guides
  • Assessment Guides
  • Authentic texts and trade books
  • Knowledge Image Cards
  • Knowledge Flip Books
  • Remediation and intervention resources
  • Decodable readers
  • Student Readers and novels
  • Student Activity Books
  • Dedicated ELD support with Language Studio California
  • Poet’s Journals
  • eReaders
  • Sound Library featuring articulation videos and songs
  • Instructional routine modeling videos
  • Assignable Practice Games
  • On-demand professional development

Amplify ELA California students stay engaged with the following resources:

  • Teacher Guides that include:
    • Detailed lesson plans
    • Standards alignment and exit tickets
    • Real-time differentiation strategies
    • Robust reporting
  • Student Editions that include:
    • High-quality narrative and informational texts
    • Videos, audio supports, and digital experiences that capture their attention
    • Personal Writing Journal to keep all student writing in one place
  • Dedicated ELD support with Language Studio California
  • Trade books

Core literacy philosophy

Support every learner. Meet all learning needs with a Multi-Tiered System of Supports (MTSS) that brings together universal screening, scaffolded core instruction, support for multilingual/English learners, and data-driven intervention to ensure every student gets what they need to succeed.

Deliver consistent foundational skills instruction. Daily explicit, systematic skills instruction in grades K–2, with targeted yet flexible support for students still building decoding confidence in grades 3–6, ensures mastery of essential reading foundations.

Build lasting knowledge across all grades. Through coherently sequenced, content-rich instruction that revisits key vocabulary and concepts with increasing complexity, students build meaningful connections that deepen their vocabulary and reading comprehension.

Strengthen reading through writing at every level. Regular writing instruction grounded in the Science of Writing supports reading comprehension, improves sentence-level writing, and provides the foundation for high-quality composition. As students progress through the upper grades, they engage in increasingly complex analytical tasks—synthesizing ideas, drawing generalizations, and interpreting multiple textual layers through both focused quick-writes and comprehensive essays. 

Foster oral language development. Structured opportunities for academic conversation and evidence-based dialogue build students’ ability to express complex ideas with precision and allow them to participate confidently in classroom discussions.

Measure growth with comprehensive assessments. Assessments range from in-the-moment checks for understanding to summative assessments that measure progress toward skills mastery and standards proficiency, providing the data needed to drive targeted instruction.

Scope and sequence

Below you can view the scope and sequence documents for each grade level. 

Routines

Amplify CKLA California, Amplify Caminos California, and Amplify ELA California include several structured instructional routines that provide predictable patterns for both teachers and students:

Discussion and collaboration routines:

  • Turn and Talk: Partners discuss text-specific content using sentence starters and frames
  • Think-Pair-Share: Students engage in individual thinking, partner discussion, and whole-class sharing
  • Partner reading: Students sit shoulder-to-shoulder, taking turns reading and listening

Foundational Skills routines:

  • Sound-spelling review: Warm-up activities that reinforce phonics patterns
  • Oral blending warm-ups: Teacher-guided practice progressing to independent application
  • Finger-tapping: Techniques for blending sounds
  • Chaining activities: Students manipulate letters to transform one word into another
  • Word Work: Daily short activities focused on domain-specific and academic vocabulary

Knowledge-building routines:

  • Teacher modeling: Demonstration of proper intonation, expression, and pacing
  • Choral reading: Whole-class reading practice
  • Partner reading: Paired fluency practice

Close reading routines

The program includes carefully structured close reading activities that guide students through multiple encounters with complex texts. These routines help students develop deeper comprehension through systematic analysis and discussion.

Each routine includes comprehensive instructional guides with clear-cut directions for implementation, straightforward explanations of concepts, and suggestions for discussion.

Cross-Linguistic Transfer routines

The Cross-Linguistic Transfer (CLT) routines are easy-to-implement, 10–15 minute mini-lessons designed to help bridge English and Spanish literacy and language development. These structured routines are organized by grade bands for K–2, grades 3–5 and grade 6, covering five skill areas:

  • Oral language
  • Reading
  • Vocabulary
  • Language
  • Writing

[Reviewer highlight video] Amplify’s program alignment to Cross-Linguistic Transfer criteria

Designated English Language Development materials

Language Studio California is a K–8 content-based companion for English language learners. Built on Amplify CKLA California and Amplify ELA California’s carefully sequenced Knowledge Domains, it combines engaging content knowledge with targeted supports and research-based strategies to help students move swiftly toward language proficiency. This program includes:

  • Real-world content to provide authentic opportunities to practice reading, writing, speaking, and listening.
  • Scaffolding strategies and differentiated instruction to offer targeted support along five English proficiency levels.
  • Progress monitoring tools to help teachers provide consistent and effective support.
  • Teacher Guides that:
    • Provide impactful progress monitoring tools including formative and summative assessments, and Language Proficiency Assessment rubrics.
    • Offer varied differentiation strategies including Support, Challenge, and Access supports in each lesson segment.
    • Are organized into thoughtful lesson segments—Talk Time, Building Background, On Stage and more—that make learning objectives concrete.
  • Activities that:
    • Expand on domain knowledge from core content and read-alouds and prompt collaborative conversation to practice oral fluency.
    • Support hands-on language activities to promote authentic interaction in the classroom.
    • Help students bridge experiences and knowledge with images, vocabulary activities, graphic organizers, anticipation guides, writing space, and more.

Category 3: Assessments

Systematic MTSS alignment

In alignment with the additional 2025 Guidance 3.1.a, the assessment systems align with MTSS tiers, including universal screening, diagnostic assessments for students demonstrating a need for additional support, and progress monitoring tools that complement California’s required reading difficulties screening schedule per SB 114.

Tier 1:
Universal/ differentiated support
Tier 2: 
Supplemental/ targeted
support
Tier 3: 
Intensified/ intensive
support
Core instruction assessments





Frequency of administration
Amplify CKLA California, Amplify Caminos California, Amplify ELA California assessments

Daily, Weekly, Monthly
Amplify CKLA California, Amplify Caminos California, Amplify ELA California assessments

Daily, Weekly, Monthly
Amplify CKLA California, Amplify Caminos California, Amplify ELA California assessments

Daily, Weekly, Monthly
Universal screening assessments

Frequency of administration
mCLASS DIBELS and Lectura


3 times per year – BOY, MOY, EOY
mCLASS DIBELS and Lectura


3 times per year – BOY, MOY, EOY
mCLASS DIBELS and Lectura


3 times per year – BOY, MOY, EOY
Formal progress monitoring assessments


Frequency of administration
mCLASS DIBELS and Lectura



3 times per year – BOY, MOY, EOY
mCLASS DIBELS and Lectura



Monthly
mCLASS DIBELS and Lectura



Bi-weekly
Informal progress monitoring assessments




Frequency of administration
Amplify CKLA California, Amplify Caminos California, Amplify ELA California core assessments

Daily
Intervention Toolkit progress monitoring assessments



When linked to a lesson in the toolkit
Intervention Toolkit progress monitoring assessments



When linked to a lesson in the toolkit
Diagnostic assessment







Frequency of administration
Amplify skill diagnostic assessment


Amplify Spanish skill diagnostic assessment

Optional after universal screening assessment is administered
Amplify skill diagnostic assessment


Amplify Spanish skill diagnostic assessment

After universal screening assessment is administered

Universal assessment system

Amplify’s mCLASS® DIBELS® 8th Edition (K–8) and mCLASS Lectura (K–6) are universal and dyslexia screening assessments that should be administered three times per year (BOY, MOY, and EOY) to all students. The assessments evaluate student literacy risk, determine progress toward grade-level goals, and indicate the level of instructional  support a student may need. Beginning-of-year screenings require adequate instructional time before administration, particularly in grades K–1, while mid-year and end-of-year assessments evaluate instructional effectiveness and guide tier placement adjustments. These screenings also identify students at risk for dyslexia. Universal screening provides essential data for targeting instruction and measuring instructional system effectiveness.

Core instruction assessments

Amplify CKLA California, Amplify Caminos California, and Amplify ELA California provide a comprehensive suite of assessments for grades K–6 that range from low-stakes, informal formative assessments to more formal summative assessments. These assessments incorporate a variety of methods and question types, including multiple-choice questions, open-ended questions, and oral and written responses.

Formative assessments:

  • Checks for Understanding: Incorporated into each lesson segment throughout daily instruction. Quick pulse-checks that provide immediate feedback during lesson delivery (grades K–5). 
  • Daily formative assessments: Highlighted moments within each lesson for teachers to plan to track mastery of Primary Focus objectives and standards of each lesson to get a clear snapshot of individual and whole-class progress (grades K–5). 
  • Activity pages: Completed as part of lessons and can be used to assess lesson content understanding through various formats (grades K–5).
  • Exit Tickets: Located at the end of lessons, these provide a quick gauge of students’ ability to meet the lesson’s focus standards (grade 6).  
  • Writing Prompts: Prompts integrated throughout lessons during writing activities that provide skill snapshots within lessons and tracks patterns of skill development over time (grade 6).
  • Independent reading activities (Solos): At the end of every lesson, students complete an independent reading activity (“Solo”) with reading questions that are scored to measure comprehension (grade 6).

Summative assessments:

  • Skills end-of-unit assessments (grades K–2) 
  • Knowledge end-of-domain assessments (grades K–2) 
  • End-of-unit assessments (grades 3–5) 
  • Unit essays: A culminating end-of-unit set of lessons that guide students through crafting an essay with a rubric to score mastery of writing skills (grade 6)
  • Unit reading assessments: Auto-scored responses and two constructed response items evaluate comprehension, content understanding, and reading skills using the passages students read during the unit (grade 6)

Performance assessments

Student Performance Assessments are multi-day assessments administered in Grades K–5 at the beginning, middle, and end of year to help teachers gauge student mastery of grade-level Core content. These assessments provide critical data to help teachers set targeted instructional goals and monitor individual and class-wide progress towards core objectives.

Progress monitoring

Amplify’s mCLASS® DIBELS® 8th Edition and mCLASS Lectura provide formal progress monitoring in the discrete skills that are indicative of reading growth and predictive of overall success to provide the most instructionally meaningful information to teachers.

Informal progress monitoring tools can be found within the Intervention Toolkit, including materials for teachers to record, track, and evaluate student progress.

Diagnostic assessment

Interventions within Amplify’s literacy programs are informed by a skill diagnostic assessment that provides detailed data on foundational literacy skill deficits. The Amplify Skill Diagnostic Assessment and Amplify Spanish Skill Diagnostic assessment serve as critical tools in this process, administered specifically to students identified as at risk for reading difficulty through universal screening assessments—particularly those demonstrating mCLASS DIBELS 8th Edition or mCLASS Lectura composite scores in the Well Below or Below Benchmark ranges. These diagnostic assessments provide teachers with the precise skills to begin intervention and remediation.

Category 4: Universal Access

Amplify CKLA California, Amplify Caminos California, and Amplify ELA California are developed using the Universal Design for Learning framework to proactively ensure that all learners can access and participate in meaningful, challenging learning opportunities.

Universal Design for Learning

Amplify CKLA California, Amplify Caminos California, and Amplify ELA California incorporate opportunities for engagement, representation, action, and expression based on the guidelines of Universal Design for Learning.

  • Multiple Means of Engagement: The programs incorporate interesting and motivating ways for students to interact with information and content. The Universal Access section in the introduction of each lesson provides specific lesson-level options based on the needs of individual classrooms and students. Scaffolding for students with various levels of need is incorporated into the design of each lesson.
  • Multiple Means of Representation: The programs provide multiple means of presenting content to maximize student understanding. This includes digital component files that allow for a range of presentations of images and text to support learning. Amplify provides access to universal supports such as point-of-use audio for all core texts, embedded definitions for critical vocabulary, and glossaries in multiple languages. The programs include clarification on language found throughout the program, with sidebars that include support on transition words and syntax, and illustrations to help students understand the concepts they are learning.
  • Multiple Means of Action and Expression: The programs include a range of methods for all students, including Multilingual/English Learners, to navigate and demonstrate learning. This includes physical actions, a range of methods for response, appropriate tools for composition, and varied scaffolding. Lessons provide multiple ways for students to interact with text, allowing their brains to process the language through distinct pathways. Activities harness multiple learning modes, using media tools, digital apps, and a variety of visual and physical experiences to strategically support and enhance student learning.
  • Accessibility: Universal access features include visual aids, enlarged materials, physical objects, and multiple learning modalities through activities like Push & Say and Wiggle Cards. The Universal Access section in the introduction of each lesson provides specific lesson-level options based on the needs of individual classrooms and students.

Embedded differentiation

Amplify CKLA California, Amplify Caminos California, and Amplify ELA California provide built-in differentiation strategies in every lesson for all students.

  • Pre-teaching supports include mini-lessons on:
    • Core vocabulary building
    • Core connections
    • Essential background information building
    • What Have We Already Learned?/What Do We Already Know?
  • Differentiated Support for Core Instruction tables, located in the overview of each K–2 Skills Teacher Guide, provide a list of specific opportunities for reteaching and additional support in each lesson based on skill.
  • Support and Challenge Sidebars in lesson margins offer educators immediate guidance in implementing point-of-use differentiation techniques.
  • Flexible Grouping within lessons provides opportunities for teachers to facilitate small groups, partners, or individualized support based on students’ needs. In the Skills Strand, teachers receive specific guidance for differentiated small group instruction, with targeted support and activities outlined for both Group 1 (students needing additional support) and Group 2 (on-level students) based on data. 
  • Amplify ELA California and Amplify Caminos California provide point-of-use supports embedded within key core lesson activities with six levels of differentiation. The goal of these supports is to fully enable access to grade-level content for all students, including students with disabilities, English learners, and students ready for an additional level of challenge.
  • The Universal Access section of Advance Preparation in each lesson includes varied strategies to ensure all students can access and engage in each lesson.
  • Frequent use of graphic organizers and visual supports in lessons provide opportunities for differentiation based on need. The program also includes a variety of technological supports, such as eReaders with audio.
  • Extension opportunities are suggested throughout lessons, often embedded in writing tasks, which include prompts to use more complex and descriptive vocabulary, figurative language,  multi-clause and complex sentences, and  informational text characteristics.

Assessment-driven MTSS resources

  • The K–6 Intervention Toolkit is available online and provides easy-to-use resources that assist teachers in filling gaps in students’ reading skills, with activities to support print concepts, phonological awareness, phonics, fluency, and other key skills.
  • Fluency packets (Grades 2–6)
  • Foundational Skills Intervention Program for Grades 3–6 support students who would benefit from direct and explicit intervention instruction in the full continuum of foundational skills in the upper grades
  • Flexible Instructional Time including:
    • Pausing Points built into the curriculum that provide teachers with dedicated time to address specific student needs through targeted reteaching, remediation, practice, and extension activities 
    • Pausing Point activities designed to support multilingual/English learners’ competence and confidence through differentiated whole-group, small-group, or individual instruction
  • Boost Reading and Boost Lectura are student-led digital intervention programs that follow the scope and sequences of Amplify CKLA California and Amplify Caminos California respectively, to reinforce the same foundational skills taught in core instruction. It integrates easily into daily routines, while the robust data provided by mCLASS® DIBELS® 8th Edition offers a detailed view of how students progress across all instructional tiers.

Category 5: Instructional Planning and Teacher Support

Amplify CKLA California, Amplify Caminos California, and Amplify ELA California teachers are empowered to deliver effective instruction with various print and digital resources. The program provides comprehensive planning and support materials designed to help teachers prepare for and execute lessons effectively and fulfill the requirements of Category 5.

Implementation supports across K–6

Planning and preparation resources

  • Unit Overviews that provide important background and context for the texts students will read, including highlighted elements within the text and guidance for how students will work with those elements
  • Sub-unit Overviews (Grade 6) that provide an overview of Lesson Objectives and reading and writing assignments, as well as a list of any projections, multimedia, or digital apps that can be projected from the teacher’s included digital license
  • Lesson-by-lesson preparation checklists (Grade 6) accompanying each Sub-unit Overview
  • Lesson Briefs for each individual lesson providing important background and context
  • Content knowledge materials regarding topics that students will examine

Point-of-use instructional guidance

  • Teacher Editions that feature insets of the same text and activity instructions as the corresponding Student Edition, wrapping teacher instruction around these materials
  • Activity guidance at point of use
  • Lesson standards clearly called out
  • Discussion suggestions embedded in lessons
  • Differentiation tips at point of use
  • Detailed Instructional Guides in each activity that include sequencing and grouping suggestions, tips for facilitating discussion, possible student responses and exemplars
  • On-the-Fly supports (Grade 6)—quick call-outs to the identifying features of “on track” and “needs support” students accompanied by short models of student guidance to foster strong performance

Multimedia and digital support

  • Teacher tip videos provide modeling and guidance for implementing key foundational skills routines within the program
  • Digital platform access where teachers can access printable PDFs of differentiated support materials for multilingual/English learners and students struggling to read, including translated Unit Background and Context documents and Text Previews
  • Teacher Dashboard and reporting tools provide real-time visibility into student progress and work for immediate instructional response

Caregiver supports

Communication and overview resources

  • Caregiver Hub available in English and Spanish that provides an overview of the curriculum
  • Caregiver Letters for each K–2 Knowledge Domain and unit in Grades 3–5 that provide an overview of the content, the skills students learn, as well as practical methods that continue the learning and knowledge building at home
  • Unit-specific Caregiver Letters (Grade 6) that provide detailed information regarding what students will read and learn in each unit, including conversation starters that allow caregivers to ask questions and discuss specific aspects of a unit with their student
  • Welcome letters that explain the assessment and placement process while inviting parent involvement and offering support
  • Editable Home-School Communication letters available in English and Spanish
  • Editable Progress Reports for teachers to update parents and guardians on what their child is learning

Content and learning support materials

  • Unit Background and Context documents that provide an introduction and overview to the unit’s topic and themes, available in English and Spanish
  • Text Previews that provide a brief introduction to formative, independent reading assignments (called Solos in Grade 6), available in English and Spanish
  • Unit Overview and Support documents (Grade 6) designed for caregivers that provide information about important questions, assignments, and key aspects of the unit texts, available in English and Spanish
  • Conversation starters included in Knowledge Strand Caregiver Letters to discuss domain topics at home

Home practice and extension activities

  • Take-Home pages in the Skills Strand that include copies of decodable passages, enabling students to share their reading progress with families and continue practicing their skills outside of school
  • Take-Home Letters in the Skills Strand that provide specific guidance for parents to support skills practice at home, such as sound-sorting activities, with detailed instructions and materials for home practice activities
  • Take-Home pages in the Knowledge Strand that provide suggested activities families can do together to reinforce and extend learning beyond the classroom
  • Games and activities on Take-Home Pages that extend classroom instruction, including all the materials and instruction necessary to help families assist students in a fun and engaging way
  • Digital access to decodable texts through the Amplify Caregiver Hub, allowing students to practice their reading skills both in class and at home
  • Weekly spelling lists and directions to decoding activities that can be practiced at home

Welcome, K–8 Program 2 reviewers!

We’re honored to introduce you to Amplify California Language Arts. We’re confident you’ll find this comprehensive program to be a powerful tool for bringing the vision of the California ELA/ELD Framework to life in classrooms across the state.

Please start with the video on the right to learn how to navigate the program and access key features referenced within our submission. Below you’ll find additional resources to support your review.

Your review samples

We’re excited for you to begin your review of Amplify Core Knowledge Language Arts (CKLA) California and Amplify ELA California, Language Studio California for grades K–8. Physical and digital review materials will vary by grade level.

Reviewer Binders (K–8)

Your physical samples should have arrived in grade-specific boxes with three Reviewer Binders.

  • The first binder will contain logistical program review information and the printed Evaluation Criteria Map.
  • The second binder will contain the printed Standards Maps for grades K–4.
  • The third binder will contain the printed Standards Maps for grades 5–8.

Physical samples (K–5)

You can expect to receive 15 boxes of physical materials for your review. As you begin the process of organizing your materials, please refer to the inventory checklist found inside each box as well as within your Reviewer Binder. Please note you will not receive any physical samples for grades 6–8 ELA or Language Studio for grades K-8. Your review of the program for grades 6–8 ELA and Language Studio for grades K-8 will be entirely digital.

Digital samples

In order to access your digital samples, you’ll need to log in to our platform using your unique login credentials found on a Digital Review Credential flyer inside of your Reviewer Binder. Once you have located the flyer:

  • Click the orange button below to access the platform.
  • Click “Log in with Amplify.”
  • Enter the username and password provided on your Digital Review Credential flyer.

Navigation tips

Before you get started, please review these important functionality notes:

Criteria Map and Standards Maps must be opened on Microsoft Word on your desktop to function as intended. If you open the documents without Microsoft Word on your desktop, citations will be cut off at the bottom of most tables within the document.

Many of our citations are deep-links to PDFs, meaning they will take you to the right page or the first page in the sequence for the citation in question. To ensure this functionality works, please disable any PDF-viewing extensions or plug-ins such as Adobe Acrobat Pro Browser Extension.

[Reviewer program navigation video] Grades K–5

[Reviewer program navigation video] Grades 6–8

Click here for additional information on navigating the digital materials for grades 6–8.

Category 1: English Language Arts (ELA) and English Language Development (ELD) Content/Alignment to Standards

Evaluation Criteria Map

Linked below is the Evaluation Criteria Map for grades K–8. Please note that you will need to be logged into the digital platform to access the links in the Evaluation Criteria Map.

ELA Standards Maps

The links below provide the Standards Maps for Amplify California Language Arts for each grade level. Please note that you will need to be logged into the digital platform to access the links in the Standards Maps.

ELD Standards Maps

Category 2: Program Organization

The Amplify California Language Arts Program 2 submission includes Amplify CKLA California for Grades K–5, Amplify ELA California for Grades 6–8, and Amplify Language Studio California for Grades K–8. This comprehensive curriculum provides a full year of evidence-based instruction for each grade level, with both integrated and designated English Language Development instruction designed to give English learners the tools to thrive.

Program structure

Amplify’s California Language Arts programs are built on what the research shows: Strong readers need both word recognition and language comprehension. Our comprehensive curriculum suite follows the Simple View of Reading and The Reading Rope–bringing together foundational skills and knowledge building to deliver instruction grounded in the Science of Reading.

Flowchart illustrating skilled reading as the product of language comprehension and word recognition, grounded in the science of reading.
Diagram illustrating the interplay between language comprehension and word recognition in reading, as seen in early literacy stages. It highlights pathways through knowledge, vocabulary, and sentence understanding, reflecting principles from the CKLA reading program.

Each lesson follows a predictable structure with clearly marked components, beginning with warm-up routines, progressing through explicit instruction with guided practice, and concluding with independent application activities. The program provides detailed teacher language, including question stems and discussion prompts, ensuring clear and consistent delivery of instruction.

[Reviewer highlight video] Program organization for Category 2

[Reviewer highlight video] Program structure for grades K–2

[Reviewer highlight video] Program structure for grades 3–5

[Reviewer highlight video] Program structure for grades 6–8

Amplify CKLA California empowers teachers to deliver effective instruction and keeps students engaged with with the following resources:

  • Teacher Guides
  • Assessment Guides
  • Authentic texts and trade books
  • Knowledge Image Cards
  • Knowledge Flip Books
  • Remediation and intervention resources
  • Decodable readers
  • Student Readers and novels
  • Student Activity Books
  • Dedicated ELD support with Language Studio California
  • Poet’s Journals
  • eReaders
  • Sound Library featuring articulation videos and songs
  • Instructional routine modeling videos
  • Assignable Practice Games
  • On-demand professional development

Amplify ELA California students stay engaged with the following resources:

  • Teacher Guides that include:
    • Detailed lesson plans
    • Standards alignment and exit tickets
    • Real-time differentiation strategies
    • Robust reporting
  • Student Editions that include:
    • High-quality narrative and informational texts
    • Videos, audio supports, and digital experiences that capture their attention
    • Personal Writing Journal to keep all student writing in one place
  • Dedicated ELD support with Language Studio California
  • Trade Books

Core literacy philosophy

Support every learner. Meet all learning needs with a Multi-Tiered System of Supports (MTSS) that brings together universal screening, scaffolded core instruction, support for English learners, and data-driven intervention to ensure every student gets what they need to succeed.

Provide intentional ELD support. Honor students’ linguistic assets while building academic English through both integrated and designated instruction.

Deliver consistent foundational skills instruction. Daily explicit, systematic skills instruction in grades K–2, with targeted yet flexible support for students still building decoding confidence in grades 3–8, ensures mastery of essential reading foundations.

Build lasting knowledge across all grades. Through coherently sequenced, content-rich instruction that revisits key vocabulary and concepts with increasing complexity, students build meaningful connections that deepen their vocabulary and reading comprehension.

Strengthen reading through writing at every level. Regular writing instruction grounded in the Science of Writing supports reading comprehension, improves sentence-level writing, and provides the foundation for high-quality composition. As students progress through the upper grades, they engage in increasingly complex analytical tasks—synthesizing ideas, drawing generalizations, and interpreting multiple textual layers through both focused quick-writes and comprehensive essays. 

Foster oral language development. Structured opportunities for academic conversation and evidence-based dialogue build students’ ability to express complex ideas with precision and allow them to participate confidently in classroom discussions.

Measure growth with comprehensive assessments. Assessments range from in-the-moment checks for understanding to summative assessments that measure progress toward skills mastery and standards proficiency, providing the data needed to drive targeted instruction.

Scope and sequence

Below you can view the scope and sequence for each grade level. 

Routines

Amplify CKLA California and Amplify ELA California include several structured instructional routines that provide predictable patterns for both teachers and students:

Discussion and collaboration routines:

  • Turn and Talk: Partners discuss text-specific content using sentence starters and frames
  • Think-Pair-Share: Students engage in individual thinking, partner discussion, and whole-class sharing
  • Partner reading: Students sit shoulder-to-shoulder, taking turns reading and listening

Foundational Skills routines:

  • Sound-spelling review: Warm-up activities that reinforce phonics patterns
  • Oral blending warm-ups: Teacher-guided practice progressing to independent application
  • Finger-tapping: Techniques for blending sounds
  • Chaining activities: Students manipulate letters to transform one word into another
  • Word Work: Daily short activities focused on domain-specific and academic vocabulary

Knowledge-Building Routines:

  • Teacher modeling: Demonstration of proper intonation, expression, and pacing
  • Choral reading: Whole-class reading practice
  • Partner reading: Paired fluency practice

Close reading routines

The program includes carefully structured close reading activities that guide students through multiple encounters with complex texts. These routines help students develop deeper comprehension through systematic analysis and discussion.

Each routine includes comprehensive instructional guides with clear-cut directions for implementation, straightforward explanations of concepts, and suggestions for discussion.

Designated English Language Development materials

Language Studio California is a K–8 content-based companion for English language learners. Built on Amplify CKLA California’s and Amplify ELA California’s carefully sequenced Knowledge Domains and units, it combines engaging content knowledge with targeted supports and research-based strategies to help students move swiftly toward language proficiency. This program includes:

  • Real-world content to provide authentic opportunities to practice reading, writing, speaking, and listening.
  • Scaffolding strategies and differentiated instruction to offer targeted support along with five English proficiency levels.
  • Progress-monitoring tools to help teachers provide consistent and effective support.
  • Teacher Guides that:
    • Provide impactful progress monitoring tools including formative and summative assessments and Language Proficiency Assessment rubrics.
    • Offer varied differentiation strategies including Support, Challenge, and Access Supports in each lesson segment.
    • Are organized into thoughtful lesson segments—Talk Time, Building Background, On Stage and more—that make learning objectives concrete.
  • Activities that:
    • Expand on domain knowledge from core content and read-alouds and prompt collaborative conversation to practice oral fluency.
    • Support hands-on language activities to promote authentic interaction in the classroom.
    • Help students bridge experiences and knowledge with images, vocabulary activities, graphic organizers, anticipation guides, writing space, and more.

Category 3: Assessments

Systematic MTSS alignment

In alignment with the additional 2025 Guidance 3.1.a, the assessment systems align with MTSS tiers, including universal screening, diagnostic assessments for students demonstrating a need for additional support, and progress monitoring tools that complement the California’s required universal screening schedule per SB 114.

Tier 1:
Universal/ differentiated support
Tier 2: 
Supplemental/ targeted support
Tier 3: 
Intensified/ intensive support
Core instruction assessments





Frequency of administration
Amplify CKLA California, Amplify Caminos California, Amplify ELA California assessments

Daily, Weekly, Monthly
Amplify CKLA California, Amplify Caminos California, Amplify ELA California assessments

Daily, Weekly, Monthly
Amplify CKLA California, Amplify Caminos California, Amplify ELA California assessments

Daily, Weekly, Monthly
Universal screening assessments

Frequency of administration
mCLASS DIBELS and Lectura


3 times per year – BOY, MOY, EOY
mCLASS DIBELS and Lectura


3 times per year – BOY, MOY, EOY
mCLASS DIBELS and Lectura


3 times per year – BOY, MOY, EOY
Formal progress monitoring assessments

Frequency of administration
mCLASS DIBELS and Lectura



3 times per year – BOY, MOY, EOY
mCLASS DIBELS and Lectura



Monthly
mCLASS DIBELS and Lectura



Bi-weekly
Informal progress monitoring assessments




Frequency of administration
Amplify CKLA California, Amplify Caminos California, Amplify ELA California core assessments

Daily
Intervention Toolkit progress monitoring assessments




When linked to a lesson in the toolkit
Intervention Toolkit progress monitoring assessments




When linked to a lesson in the toolkit
Diagnostic assessment






Frequency of administration
Amplify skill diagnostic assessment

Amplify Spanish skill diagnostic assessment

Optional after universal screening assessment is administered
Amplify skill diagnostic assessment

Amplify Spanish skill diagnostic assessment

After universal screening assessment is administered

Universal assessment system

Amplify’s mCLASS® DIBELS® 8th Edition and mCLASS Lectura are universal and dyslexia screening assessments that should be administered three times per year (BOY, MOY and EOY) to all students. The assessments evaluate student literacy risk, determine progress toward grade-level goals, and indicate the level of instructional  support a student may need. Beginning-of-year screenings require adequate instructional time before administration, particularly in grades K–1, while mid-year and end-of-year assessments evaluate instructional effectiveness and guide tier placement adjustments. These screenings also identify students at risk for dyslexia. Universal screening provides essential data for targeting instruction and measuring instructional system effectiveness.

Core instruction assessments

Amplify CKLA California and Amplify ELA California provide a comprehensive suite of assessments for Grades K–8 that range from low-stakes, informal formative assessments to more formal summative assessments. These assessments incorporate a variety of methods and question types, including multiple-choice questions, open-ended questions, and oral and written responses.

Formative assessments:

  • Checks for Understanding: Incorporated into each lesson segment throughout daily instruction. Quick pulse-checks that provide immediate feedback during lesson delivery (grades K–5). 
  • Daily formative assessments: Highlighted moments within each lesson for teachers to plan to track mastery of Primary Focus objectives and standards of each lesson to get a clear snapshot of individual and whole-class progress (grades K–5). 
  • Activity pages: Completed as part of lessons and can be used to assess lesson content understanding through various formats (grades K–5).
  • Exit Tickets: Located at the end of lessons, these provide a quick gauge of students’ ability to meet the lesson’s focus standards (grades 6–8).  
  • Writing Prompts: Prompts integrated throughout lessons during writing activities that provide skill snapshots within lessons and tracks patterns of skill development over time (grades 6–8).
  • Independent reading activities (Solos): At the end of every lesson, students complete an independent reading activity (“solo”) with reading questions that are scored to measure comprehension (grades 6–8).

Summative assessments:

  • Skills end-of-unit assessments (grades K–2) 
  • Knowledge end-of-domain assessments (grades K–2) 
  • End-of-unit assessments (grades 3–5) 
  • Unit essays: A culminating end-of-unit set of lessons that guide students through crafting an essay with a rubric to score mastery of writing skills (grades 6–8)
  • Unit Reading Assessments: Auto-scored responses and two constructed response items evaluate comprehension, content understanding, and reading skills using the passages students read during the unit (grades 6–8)

Performance Assessments

Student Performance Assessments are multi-day assessments administered in Grades K-5 at the beginning, middle, and end of year to help teachers gauge student mastery of grade-level Core content. These assessments provide critical data to help teachers set targeted instructional goals and monitor individual and class-wide progress towards core objectives.

Progress monitoring

Amplify’s mCLASS® DIBELS® 8th Edition and mCLASS Lectura provide formal progress monitoring in the discrete skills that are indicative of reading growth and predictive of overall success to provide the most instructionally meaningful information to teachers.

Informal progress monitoring tools can be found within the Intervention Toolkit, including materials for teachers to record, track, and evaluate student progress.

Diagnostic assessment

Interventions within Amplify’s literacy programs are informed by a skill diagnostic assessment that provides detailed data on foundational literacy skill deficits. The Amplify Skill Diagnostic Assessment and Amplify Spanish Skill Diagnostic assessment serve as critical tools in this process, administered specifically to students identified as at risk for reading difficulty through universal screening assessments—particularly those demonstrating mCLASS DIBELS 8th Edition or mCLASS Lectura composite scores in the Well Below or Below Benchmark ranges. These diagnostic assessments provide teachers with the precise skills to begin intervention and remediation.

Category 4: Universal Access

Amplify CKLA California and Amplify ELA California were built on the principles of Universal Design for Learning (UDL) and reviewed by CAST, a nonprofit education research and development organization. The program is developed using the Universal Design for Learning framework to proactively ensure that all learners can access and participate in meaningful, challenging learning opportunities.

Universal Design for Learning

The programs incorporate opportunities for engagement, representation, action, and expression based on the guidelines of Universal Design for Learning.

  • Multiple Means of Engagement: The programs incorporate interesting and motivating ways for students to interact with information and content. In Amplify CKLA California, the Universal Access section in the introduction of each lesson provides specific lesson-level options based on the needs of individual classrooms and students. Scaffolding for students with various levels of need is incorporated into the design of each lesson.
  • Multiple Means of Representation: The programs provide multiple means of presenting content to maximize student understanding. This includes digital component files that allow for a range of presentations of images and text to support learning. Amplify provides access to universal supports such as point-of-use audio for all core texts, embedded definitions for critical vocabulary, and glossaries in multiple languages. Amplify CKLA California includes clarification on language found throughout the program, with sidebars that include support on transition words and syntax, and illustrations to help students understand the concepts they are learning.
  • Multiple Means of Action and Expression: The programs include a range of methods for all students, including English Learners, to navigate and demonstrate learning. This includes physical actions, a range of methods for response, appropriate tools for composition, and varied scaffolding. In Amplify ELA California, lessons provide multiple ways for students to interact with text, allowing their brains to process the language through distinct pathways. Activities harness multiple learning modes, using media tools, digital apps, and a variety of visual and physical experiences to strategically support and enhance student learning.
  • Accessibility: Universal access features include visual aids, enlarged materials, physical objects, and multiple learning modalities through activities like Push & Say and Wiggle Cards. The Universal Access section in the introduction of each lesson provides specific lesson-level options based on the needs of individual classrooms and students.

Embedded differentiation

Amplify CKLA California and Amplify ELA California provide built-in differentiation strategies in every lesson for all students.

Throughout the Teacher Guides, point-of-use Differentiation icons provide targeted instructional strategies and supports. These icons indicate specific guidance for advanced learners, students who need additional support, and English learners, allowing teachers to easily identify and implement appropriate scaffolds and extensions during instruction. In addition, teachers are provided with recommendations for resources to use with each group of students.

  • Pre-teaching supports include mini-lessons on:
    • Core vocabulary words
    • Core Connections
    • Essential Background Information or Terms
    • What Have We Already Learned/What Do We Already Know?
  • Differentiated Support for Core Instruction tables, located in the overview of each K–2 Skills Teacher Guide, provide a list of specific opportunities for reteaching and additional support in each lesson based on skill.
  • Support and Challenge Sidebars in lesson margins offer educators immediate guidance in implementing point-of-use differentiation techniques.
  • Flexible Grouping within lessons provides opportunities for teachers to facilitate small groups, partners, or individualized support based on students’ needs. In the Skills Strand, teachers receive specific guidance for differentiated small-group instruction, with targeted support and activities outlined for both Group 1 (students needing additional support) and Group 2 (on-level students) based on data. 
  • Amplify ELA California provides point-of-use supports embedded within key core lesson activities with six levels of differentiation. The goal of these supports is to fully enable access to grade-level content for all students, including students with disabilities, English learners, and students ready for an additional level of challenge.
  • The Universal Access section of Advance Preparation in each lesson includes varied strategies to ensure all students can access and engage in each lesson.
  • Frequent use of graphic organizers and visual supports in lessons provide opportunities for differentiation based on need. The program also includes a variety of technological supports, such as eReaders with audio.
  • Extension opportunities are suggested throughout lessons, often embedded in writing tasks, which include prompts to use more complex and descriptive vocabulary, figurative language,  multi-clause and complex sentences, and  informational text characteristics.

Assessment-Driven MTSS resources

  • The K–8 Intervention Toolkit is available online and provides easy-to-use resources that assist teachers in filling gaps in students’ reading skills, with activities to support print concepts, phonological awareness, phonics, fluency, and other key skills
  • Fluency Packets (Grades 2–5)
  • Foundational Skills Intervention Program for Grades 3–8 support students who would benefit from direct and explicit intervention instruction in the full continuum of foundational skills in the upper grades
  • Flexible Instructional Time including:
    • Pausing Points built into the curriculum that provide teachers with dedicated time to address specific student needs through targeted reteaching, remediation, practice, and extension activities 
    • Pausing Point activities designed to support English learners’ competence and confidence through differentiated whole-group, small-group, or individual instruction
  • Boost Reading is a K–5 student-led digital intervention program. Boost Reading follows Amplify CKLA California’s scope and sequence to reinforce the same foundational skills taught in core instruction. It integrates easily into daily routines, while the robust data provided by mCLASS® DIBELS® 8th Edition offers a detailed view of how students progress across all instructional tiers.

Category 5: Instructional Planning and Teacher Support

Amplify CKLA California and Amplify ELA California teachers are empowered to deliver effective instruction with various print and digital resources. The program provides comprehensive planning and support materials designed to help teachers prepare for and execute lessons effectively and fulfill the requirements of Category 5.

Implementation supports across K–8

Planning and preparation resources

  • Unit Overviews that provide important background and context for the texts students will read, including highlighted elements within the text and guidance for how students will work with those elements
  • Sub-unit Overviews (Grades 6–8) that provide an overview of Lesson Objectives and reading and writing assignments, as well as a list of any projections, multimedia, or digital apps that can be projected from the teacher’s included digital license
  • Lesson-by-lesson preparation checklists (Grades 6–8) accompanying each Sub-unit Overview
  • Lesson Briefs for each individual lesson providing important background and context
  • Content knowledge materials regarding topics that students will examine

Point-of-use instructional guidance

  • Teacher Editions that feature insets of the same text and activity instructions as the corresponding Student Edition, wrapping teacher instruction around these materials
  • Activity guidance at point of use
  • Lesson standards clearly called out
  • Discussion suggestions embedded in lessons
  • Differentiation tips at point of use
  • Detailed Instructional Guides in each activity that include sequencing and grouping suggestions, tips for facilitating discussion, possible student responses and exemplars
  • Student Supports in all core lessons that provide teachers with targeted supports in daily core instruction, addressing which might serve the student best in the moment—support, strengthen, stretch—with additional call-outs for newcomers

Multimedia and digital support

  • Teacher tip videos provide modeling and guidance for implementing key foundational skills routines within the program
  • Digital platform access where teachers can access printable PDFs of differentiated support materials for English learners and students struggling with reading, including translated Unit Background and Context documents and Text Previews
  • Teacher dashboard and reporting tools (Grade 6–8) provide real-time visibility into student progress and work for immediate instructional response

Caregiver supports

Communication and overview resources

  • Caregiver Hub available in English and Spanish that provides an overview of the curriculum
  • Caregiver Letters for each K–2 Knowledge Domain and unit in Grades 3–5 that provide an overview of the content, the skills students learn, as well as practical methods that continue the learning and knowledge building at home
  • Unit-specific Caregiver Letters (Grades 6–8) that provide detailed information regarding what students will read and learn in each unit, including conversation starters that allow caregivers to ask questions and discuss specific aspects of a unit with their student
  • Welcome letters that explain the assessment and placement process while inviting parent involvement and offering support
  • Editable Home-School Communication letters available in English and Spanish
  • Editable Progress Reports for teachers to update parents and guardians on what their child is learning

Content and learning support materials

  • Unit Background and Context documents that provide an introduction and overview to the unit’s topic and themes, available in English and Spanish
  • Text Previews that provide a brief introduction to formative, independent reading assignments (called Solos in Grades 6–8), available in English and Spanish
  • Unit Overview and Support documents (Grades 6–8) designed for caregivers that provide information about important questions, assignments, and key aspects of the unit texts, available in English and Spanish
  • Conversation starters included in Knowledge Strand Caregiver Letters to discuss domain topics at home

Home practice and extension activities

  • Take-Home pages in the Skills Strand that include copies of decodable passages, enabling students to share their reading progress with families and continue practicing their skills outside of school
  • Take-Home Letters in the Skills Strand that provide specific guidance for parents to support skills practice at home, such as sound-sorting activities, with detailed instructions and materials for home practice activities
  • Take-Home pages in the Knowledge Strand that provide suggested activities families can do together to reinforce and extend learning beyond the classroom
  • Games and activities on take-home pages that extend classroom instruction, including all the materials and instruction necessary to help families assist students in a fun and engaging way
  • Digital access to decodable texts through the Amplify Caregiver Hub, allowing students to practice their reading skills both in class and at home
  • Weekly spelling lists and directions to decoding activities that can be practiced at home

Welcome, K–8 Program 1 reviewers!

We’re honored to introduce you to Amplify California Language Arts. We’re confident you’ll find this comprehensive program to be a powerful tool for bringing the vision of the California ELA Framework to life in classrooms across the state.

Please start with the video on the right to learn how to navigate the program and access key features referenced within our submission. Below you’ll find additional resources to support your review.

Your review samples

We’re excited for you to begin your review of Amplify Core Knowledge Language Arts (CKLA) California and Amplify ELA California. Physical and digital review materials will vary by grade level.

Reviewer Binders (K–8)

Your physical samples should have arrived in grade-specific boxes with three Reviewer Binders.

  • The first binder will contain logistical program review information and the printed Evaluation Criteria Map.
  • The second binder will contain the printed Standards Maps for grades K–4.
  • The third binder will contain the printed Standards Maps for grades 5–8.

Physical samples (K–5)

You can expect to receive 15 boxes of physical materials for your review. As you begin the process of organizing your materials, please refer to the inventory checklist found inside each box as well as within your Reviewer Binder. Please note you will not receive any physical samples for grades 6–8. Your review of the program for grades 6–8 will be entirely digital.

Digital samples (K–8)

In order to access your digital samples, you’ll need to log in to our platform using your unique login credentials found on a Digital Review Credential flyer inside of your Reviewer Binder. Once you have located the flyer:

  • Click the orange button below to access the platform.
  • Click “Log in with Amplify.”
  • Enter the username and password provided on your Digital Review Credential flyer.

Navigation tips

Before you get started, please review these important functionality notes:

Criteria Map and Standards Maps must be opened on Microsoft Word on your desktop to function as intended. If you open the documents without Microsoft Word on your desktop, citations will be cut off at the bottom of most tables within the document.

Many of our citations are deep-links to PDFs, meaning they will take you to the right page or the first page in the sequence for the citation in question. To ensure this functionality works, please disable any PDF-viewing extensions or plug-ins such as Adobe Acrobat Pro Browser Extension.

[Reviewer program navigation video] Grades K–5

[Reviewer program navigation video] Grades 6–8

Click here for additional information on navigating the digital materials for grades 6–8.

Category 1: English Language Arts (ELA) and English Language Development (ELD) Content/Alignment to Standards

Evaluation Criteria Map

Linked below is the Evaluation Criteria Map for grades K–8. Please note that you will need to be logged into the digital platform to access the links in the Evaluation Criteria Map.

ELA Standards Maps

The links below provide the Standards Maps for Amplify California Core Language Arts for each grade level. Please note that you will need to be logged into the digital platform to access the links in the Standards Maps.

Category 2: Program Organization

The Amplify California Language Arts Program 1 submission includes Amplify CKLA California for Grades K–5 and Amplify ELA California for Grades 6–8. This comprehensive curriculum provides a full year of evidence-based instruction for each grade level, transitioning from foundational literacy to advanced text analysis.

Program structure

Amplify’s California Language Arts programs are built on what the research shows: Strong readers need both word recognition and language comprehension. Our comprehensive curriculum suite follows the Simple View of Reading and The Reading Rope–bringing together foundational skills and knowledge building to deliver instruction grounded in evidence-based literacy practices.

Flowchart illustrating skilled reading as the product of language comprehension and word recognition, grounded in the science of reading.
Diagram illustrating the interplay between language comprehension and word recognition in reading, as seen in early literacy stages. It highlights pathways through knowledge, vocabulary, and sentence understanding, reflecting principles from the CKLA reading program.

Each lesson follows a predictable structure with clearly marked components, beginning with warm-up routines, progressing through explicit instruction with guided practice, and concluding with independent application activities. The program provides detailed teacher language, including question stems and discussion prompts, ensuring clear and consistent delivery of instruction.

[Reviewer highlight video] Program organization for Category 2

[Reviewer highlight video] Program structure for grades K–2

[Reviewer highlight video] Program structure for grades 3–5

[Reviewer highlight video] Program structure for grades 6–8

Amplify CKLA California empowers teachers to deliver effective instruction and keeps students engaged with the following resources:

  • Teacher Guides
  • Assessment Guides
  • Authentic texts and trade books
  • Knowledge Image Cards
  • Knowledge Flip Books
  • Remediation and intervention resources
  • Decodable readers
  • Student Readers and novels
  • Student Activity Books
  • Poet’s Journals
  • eReaders
  • Sound Library featuring articulation videos and songs
  • Instructional routine modeling videos
  • Assignable Practice Games
  • On-demand professional development

Amplify ELA California students stay engaged with the following resources:

  • Teacher Guides that include:
    • Detailed lesson plans
    • Standards alignment and exit tickets
    • Real-time differentiation strategies
    • Robust reporting
  • Student Editions that include:
    • High-quality narrative and informational texts
    • Videos, audio supports, and digital experiences that capture their attention
    • Personal Writing Journal to keep all student writing in one place
  • Trade Books

Core literacy philosophy

Support every learner. Meet all learning needs with a Multi-Tiered System of Supports (MTSS) that brings together universal screening, scaffolded core instruction, support for English learners, and data-driven intervention to ensure every student gets what they need to succeed.

Deliver consistent foundational skills instruction. Daily explicit, systematic skills instruction in grades K–2, with targeted yet flexible support for students still building decoding confidence in grades 3–8, ensures mastery of essential reading foundations.

Build lasting knowledge across all grades. Through coherently sequenced, content-rich instruction that revisits key vocabulary and concepts with increasing complexity, students build meaningful connections that deepen their vocabulary and reading comprehension.

Strengthen reading through writing at every level. Regular writing instruction grounded in the Science of Writing supports reading comprehension, improves sentence-level writing, and provides the foundation for high-quality composition. As students progress through the upper grades, they engage in increasingly complex analytical tasks—synthesizing ideas, drawing generalizations, and interpreting multiple textual layers through both focused quick-writes and comprehensive essays. 

Foster oral language development. Structured opportunities for academic conversation and evidence-based dialogue build students’ ability to express complex ideas with precision and allow them to participate confidently in classroom discussions.

Measure growth with comprehensive assessments. Assessments range from in-the-moment checks for understanding to summative assessments that measure progress toward skills mastery and standards proficiency, providing the data needed to drive targeted instruction.

Scope and sequence

Below you can view the scope and sequence for each grade level. 

Routines

Amplify CKLA California and Amplify ELA California include several structured instructional routines that provide predictable patterns for both teachers and students:

Discussion and collaboration routines:

  • Turn and Talk: Partners discuss text-specific content using sentence starters and frames
  • Think-Pair-Share: Students engage in individual thinking, partner discussion, and whole-class sharing
  • Partner reading: Students sit shoulder-to-shoulder, taking turns reading and listening

Foundational Skills routines:

  • Sound-spelling review: Warm-up activities that reinforce phonics patterns
  • Oral blending warm-ups: Teacher-guided practice progressing to independent application
  • Finger tapping: Techniques for blending sounds
  • Chaining activities: Students manipulate letters to transform one word into another
  • Word Work: Daily short activities focused on domain-specific and academic vocabulary

Knowledge-building routines:

  • Vocabulary preview: Introduction of new words before reading
  • Read-aloud procedures: Established routines for introducing and discussing complex texts
  • Text discussions: Structured comprehension conversations with scaffolded questioning

Fluency routines:

  • Teacher modeling: Demonstration of proper intonation, expression, and pacing
  • Choral reading: Whole-class reading practice
  • Partner reading: Paired fluency practice

Close reading routines

The program includes carefully structured close reading activities that guide students through multiple encounters with complex texts. These routines help students develop deeper comprehension through systematic analysis and discussion.

Each routine includes comprehensive instructional guides with clear-cut directions for implementation, straightforward explanations of concepts, and suggestions for discussion.

Category 3: Assessments

Systematic MTSS alignment

In alignment with the additional 2025 Guidance 3.1.a, the assessment systems align with MTSS tiers, including universal screening, diagnostic assessments for students demonstrating a need for additional support, and progress monitoring tools that complement California’s required universal screening schedule per SB 114.

Tier 1:
Universal/ differentiated support
Tier 2: 
Supplemental/ targeted support
Tier 3: 
Intensified/ intensive support
Core instruction assessments




Frequency of administration
Amplify CKLA California, Amplify ELA California assessments


Daily, Weekly, Monthly
Amplify CKLA California, Amplify ELA California assessments


Daily, Weekly, Monthly
Amplify CKLA California, Amplify ELA California assessments


Daily, Weekly, Monthly
Universal screening assessments

Frequency of administration
mCLASS DIBELS and mCLASS Lectura

3 times per year – BOY, MOY, EOY
mCLASS DIBELS and mCLASS Lectura

3 times per year – BOY, MOY, EOY
mCLASS DIBELS and mCLASS Lectura

3 times per year – BOY, MOY, EOY
Formal progress monitoring assessments


Frequency of administration
mCLASS DIBELS and mCLASS Lectura


3 times per year – BOY, MOY, EOY
mCLASS DIBELS and mCLASS Lectura


Monthly
mCLASS DIBELS and mCLASS Lectura


Bi-weekly
Informal progress monitoring assessments



Frequency of administration
Amplify CKLA California, Amplify ELA California core assessments


Daily
Intervention Toolkit progress monitoring assessments


When linked to a lesson in the toolkit
Intervention Toolkit progress monitoring assessments


When linked to a lesson in the toolkit
Diagnostic assessment



Frequency of administration
Amplify skill diagnostic assessment


Optional after universal screening assessment is administered
Amplify skill diagnostic assessment


After universal screening assessment is administered

Universal assessment system

Amplify’s mCLASS® DIBELS® 8th Edition (K–8) and mCLASS Lectura (K–6) are universal and dyslexia screening assessments that should be administered three times per year (BOY, MOY and EOY) to all students. The assessments evaluate student literacy risk, determine progress toward grade-level goals, and indicate the level of instructional  support a student may need. Beginning-of-year screenings require adequate instructional time before administration, particularly in grades K–1, while mid-year and end-of-year assessments evaluate instructional effectiveness and guide tier placement adjustments. These screenings also identify students at risk for dyslexia. Universal screening provides essential data for targeting instruction and measuring instructional system effectiveness.

Core instruction assessments

Amplify CKLA California and Amplify ELA California provide a comprehensive suite of assessments for Grades K–8 that range from low-stakes, informal formative assessments to more formal summative assessments. These assessments incorporate a variety of methods and question types, including multiple-choice questions, open-ended questions, and oral and written responses.

Formative assessments:

  • Checks for Understanding: Incorporated into each lesson segment throughout daily instruction. Quick pulse-checks that provide immediate feedback during lesson delivery (grades K–5). 
  • Daily formative assessments: Highlighted moments within each lesson for teachers to plan to track mastery of Primary Focus objectives and standards of each lesson to get a clear snapshot of individual and whole-class progress (grades K–5). 
  • Activity pages: Completed as part of lessons and can be used to assess lesson content understanding through various formats (grades K–5).
  • Exit Tickets: Located at the end of lessons, these provide a quick gauge of students’ ability to meet the lesson’s focus standards (grades 6–8).  
  • Writing Prompts: Prompts integrated throughout lessons during writing activities that provide skill snapshots within lessons and tracks patterns of skill development over time (grades 6–8).
  • Independent reading activities (Solos): At the end of every lesson, students complete an independent reading activity (“Solo”) with reading questions that are scored to measure comprehension (grades 6–8).

Summative assessments:

  • Skills end-of-unit assessments (grades K–2) 
  • Knowledge end-of-domain assessments (grades K–2) 
  • End-of-unit assessments (grades 3–5) 
  • Unit essays: A culminating end-of-unit set of lessons that guide students through crafting an essay with a rubric to score mastery of writing skills (grades 6–8)
  • Unit Reading Assessments: Auto-scored responses and two constructed response items evaluate comprehension, content understanding, and reading skills using the passages students read during the unit (grades 6–8)

Performance Assessments

Student Performance Assessments are multi-day assessments administered in Grades K–5 at the beginning, middle, and end of year to help teachers gauge student mastery of grade-level Core content. These assessments provide critical data to help teachers set targeted instructional goals and monitor individual and class-wide progress towards core objectives.

Progress monitoring

Amplify’s mCLASS® DIBELS® 8th Edition and mCLASS Lectura provide formal progress monitoring in the discrete skills that are indicative of reading growth and predictive of overall success to provide the most instructionally meaningful information to teachers.


Informal progress monitoring tools can be found within the Intervention Toolkit, including materials for teachers to record, track, and evaluate student progress.

Diagnostic assessment

Interventions within Amplify’s literacy programs are informed by a skill diagnostic assessment that provides detailed data on foundational literacy skill deficits. The Amplify Skill Diagnostic Assessment and Amplify Spanish Skill Diagnostic assessment serve as critical tools in this process, administered specifically to students identified as at risk for reading difficulty through universal screening assessments—particularly those demonstrating mCLASS DIBELS 8th Edition or mCLASS Lectura composite scores in the Well Below or Below Benchmark ranges. These diagnostic assessments provide teachers with the precise skills to begin intervention and remediation.

Category 4: Universal Access

Amplify CKLA California and Amplify ELA California were built on the principles of Universal Design for Learning (UDL) and reviewed by CAST, a nonprofit education research and development organization. The program is developed using the Universal Design for Learning framework to proactively ensure that all learners can access and participate in meaningful, challenging learning opportunities.

Universal Design for Learning

The programs incorporate opportunities for engagement, representation, action, and expression based on the guidelines of Universal Design for Learning.

  • Multiple Means of Engagement: The programs incorporate interesting and motivating ways for students to interact with information and content. In Amplify CKLA California, the Universal Access section in the introduction of each lesson provides specific lesson-level options based on the needs of individual classrooms and students. Scaffolding for students with various levels of need is incorporated into the design of each lesson.
  • Multiple Means of Representation: The programs provide multiple means of presenting content to maximize student understanding. This includes digital component files that allow for a range of presentations of images and text to support learning. Amplify provides access to universal supports such as point-of-use audio for all core texts, embedded definitions for critical vocabulary, and glossaries in multiple languages. Amplify CKLA California includes clarification on language found throughout the program, with sidebars that include support on transition words and syntax, and illustrations to help students understand the concepts they are learning.
  • Multiple Means of Action and Expression: The programs include a range of methods for all students, including English learners, to navigate and demonstrate learning. This includes physical actions, a range of methods for response, appropriate tools for composition, and varied scaffolding. In Amplify ELA California, lessons provide multiple ways for students to interact with text, allowing their brains to process the language through distinct pathways. Activities harness multiple learning modes, using media tools, digital apps, and a variety of visual and physical experiences to strategically support and enhance student learning.
  • Accessibility: Universal access features include visual aids, enlarged materials, physical objects, and multiple learning modalities through activities like Push & Say and Wiggle Cards. The Universal Access section in the introduction of each lesson provides specific lesson-level options based on the needs of individual classrooms and students.

Embedded differentiation

Amplify CKLA California and Amplify ELA California provide built-in differentiation strategies in every lesson for all students.

  • Pre-teaching supports include mini-lessons on:
    • Core vocabulary building
    • Core connections
    • Essential background information building
    • What Have We Already Learned?/What Do We Already Know?
  • Differentiated Support for Core Instruction tables, located in the overview of each K–2 Skills Teacher Guide, provide a list of specific opportunities for reteaching and additional support in each lesson based on skill.
  • Support and Challenge Sidebars in lesson margins offer educators immediate guidance in implementing point-of-use differentiation techniques.
  • Flexible Grouping within lessons provides opportunities for teachers to facilitate small groups, partners, or individualized support based on students’ needs. In the Skills Strand, teachers receive specific guidance for differentiated small-group instruction, with targeted support and activities outlined for both Group 1 (students needing additional support) and Group 2 (on-level students) based on data. 
  • Amplify ELA California provides point-of-use supports embedded within key core lesson activities with six levels of differentiation. The goal of these supports is to fully enable access to grade-level content for all students, including students with disabilities, English learners, and students ready for an additional level of challenge.
  • The Universal Access section of Advance Preparation in each lesson includes varied strategies to ensure all students can access and engage in each lesson.
  • Frequent use of graphic organizers and visual supports in lessons provide opportunities for differentiation based on need. The program also includes a variety of technological supports, such as eReaders with audio.
  • Extension opportunities are suggested throughout lessons, often embedded in writing tasks, which include prompts to use more complex and descriptive vocabulary, figurative language,  multi-clause and complex sentences, and  informational text characteristics.

Assessment-driven MTSS resources

  • The K–8 Intervention Toolkit is available online and provides easy-to-use resources that assist teachers in filling gaps in students’ reading skills, with activities to support print concepts, phonological awareness, phonics, fluency, and other key skills
  • Fluency Packets (Grades 2–5)
  • Foundational Skills Intervention Program for Grades 3–8 support students who would benefit from direct and explicit intervention instruction in the full continuum of foundational skills in the upper grades
  • Flexible Instructional Time including:
    • Pausing Points built into the curriculum that provide teachers with dedicated time to address specific student needs through targeted reteaching, remediation, practice, and extension activities 
    • Pausing Point activities designed to support English learners’ competence and confidence through differentiated whole-group, small-group, or individual instruction
  • Boost Reading is a K–5 student-led digital intervention program. Boost Reading follows Amplify CKLA California’s scope and sequence to reinforce the same foundational skills taught in core instruction. It integrates easily into daily routines, while the robust data provided by mCLASS® DIBELS® 8th Edition offers a detailed view of how students progress across all instructional tiers.

Category 5: Instructional Planning and Teacher Support

Amplify CKLA California and Amplify ELA California teachers are empowered to deliver effective instruction with various print and digital resources. The program provides comprehensive planning and support materials designed to help teachers prepare for and execute lessons effectively and fulfill the requirements of Category 5.

Implementation supports across K–8

Planning and preparation resources

  • Unit Overviews that provide important background and context for the texts students will read, including highlighted elements within the text and guidance for how students will work with those elements
  • Sub-unit Overviews (Grades 6–8) that provide an overview of Lesson Objectives and reading and writing assignments, as well as a list of any projections, multimedia, or digital apps that can be projected from the teacher’s included digital license
  • Lesson-by-lesson preparation checklists (Grades 6–8) accompanying each Sub-unit Overview
  • Lesson Briefs for each individual lesson providing important background and context
  • Content knowledge materials regarding topics that students will examine

Point-of-use instructional guidance

  • Teacher Editions that feature insets of the same text and activity instructions as the corresponding Student Edition, wrapping teacher instruction around these materials
  • Activity guidance at point of use
  • Lesson standards clearly called out
  • Discussion suggestions embedded in lessons
  • Differentiation tips at point of use
  • Detailed Instructional Guides in each activity that include sequencing and grouping suggestions, tips for facilitating discussion, possible student responses and exemplars
  • Student Supports in all core lessons provide teachers with targeted supports in daily core instruction, addressing which might serve the student best in the moment—support, strengthen, stretch—with additional call-outs for newcomers

Multimedia and digital support

  • Teacher tip videos provide modeling and guidance for implementing key foundational skills routines within the program
  • Digital platform access where teachers can access printable PDFs of differentiated support materials for English learners and readers struggling with text, including translated Unit Background and Context Documents and Text Previews
  • Teacher Dashboard and reporting tools (Grade 6–8) that provide real-time visibility into student progress and work for immediate instructional response

Caregiver supports

Communication and overview resources

  • Caregiver Hub available in English and Spanish that provides an overview of the curriculum
  • Caregiver Letters for each K–2 Knowledge Domain and unit in Grades 3–5 that provide an overview of the content, the skills students learn, as well as practical methods that continue the learning and knowledge building at home
  • Unit-specific Caregiver Letters (Grades 6–8) that provide detailed information regarding what students will read and learn in each unit, including conversation starters that allow caregivers to ask questions and discuss specific aspects of a unit with their student
  • Welcome letters that explain the assessment and placement process while inviting parent involvement and offering support
  • Editable Home-School Communication letters available in English and Spanish
  • Editable Progress Reports for teachers to update parents and guardians on what their child is learning

Content and learning support materials

  • Unit Background and Context documents that provide an introduction and overview to the unit’s topic and themes, available in English and Spanish
  • Text Previews that provide a brief introduction to formative, independent reading assignments (called Solos in Grades 6–8), available in English and Spanish
  • Unit Overview and Support documents (Grades 6–8) designed for caregivers that provide information about important questions, assignments, and key aspects of the unit texts, available in English and Spanish
  • Conversation starters included in Knowledge Strand Caregiver Letters to discuss domain topics at home

Home practice and extension activities

  • Take-Home pages in the Skills Strand that include copies of decodable passages, enabling students to share their reading progress with families and continue practicing their skills outside of school
  • Take-Home Letters in the Skills Strand that provide specific guidance for parents to support skills practice at home, such as sound-sorting activities, with detailed instructions and materials for home practice activities
  • Take-Home pages in the Knowledge Strand that provide suggested activities families can do together to reinforce and extend learning beyond the classroom
  • Games and activities on Take-Home Pages that extend classroom instruction, including all the materials and instruction necessary to help families assist students in a fun and engaging way
  • Digital access to decodable texts through the Amplify Caregiver Hub, allowing students to practice their reading skills both in class and at home
  • Weekly spelling lists and directions to decoding activities that can be practiced at home

S5-01. Investigating math anxiety in the classroom

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

Season 5 is here! This season, we’ll be talking all about math anxiety: what it is, what causes it, and what we can do to prevent or ease this anxiety in the math classroom. To launch this very important theme, we sat down with Dr. Gerardo Ramirez, associate professor of educational psychology at Ball State University.
 
As someone who’s been studying math anxiety for more than a decade, he had some interesting research and advice to share on why math anxiety affects so many students (and adults), and tips for how to start reducing it.
 
Listen now and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!
 
Enjoy this episode and explore more from Math Teacher Lounge by visiting our main page.

Download Transcript

Dan Meyer (00:01):
Hey, folks. Welcome back to Math Teacher Lounge. I’m one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:05):
And I am your other host. I’m Bethany Lockhart Johnson. Season five! Hello!

Dan Meyer (00:11):
Bethany, how are you doing? How have you been spending the long break between our recording sessions?

Bethany Lockhart Johnson (00:16):
As much as I loved sharing content from previous seasons, I am so thrilled that we’re back for season five. I have been, you know, chasing a toddler. I think he’s already tired of me saying, “Ooh, can we count that?” He’s like [sighs] “One two, one two.” Like, he’s done already.

Dan Meyer (00:36):
Too much counting. Yeah, I worry about that so much, that my love of mathematics might be perceived by my kids as smothering. Yeah, I worry about the same. We shared with you folks some bangers of reruns, in my humble opinion. Some great guests. But, we’ve been excited—me and Bethany—to hop back on the mics, on the ones and twos, and explore some new ideas together.

Bethany Lockhart Johnson (01:01):
Well, I loved our season talking about joy in mathematics. And personally I could…like, we could turn this whole podcast into joy in mathematics. However, we’re kind of going a different route. Because if you ask folks why they don’t feel joy in mathematics, a lot of times at the root of that is some really intense math anxiety. So this whole season, we’re going to be delving into math anxiety. Exploring what it is, who has it, why do we think it happens, what do we think we can do about it, and how can we navigate through it, so that we can experience that joy in math? These are questions that we’re gonna explore over the course of the season. Dan Meyer, how do you feel about that?

Dan Meyer (01:49):
It feels big and it feels personal. I mean, as we shared in our math stories back from season…whatever it was, math anxiety was a huge part.

Bethany Lockhart Johnson (01:59):
It was last season, Dan.

Dan Meyer (02:00):
Last…? I mean, who can remember? Big part of your journey. I’ve had some very punctuated but intense moments of anxiety in math class. And socially, we have built math up to be this incredibly powerful thing. You know, restricting movement on economic ladders, preventing people from getting into careers they want. Whether or not they have much to do with math class, math anxiety is a really large part of educational but also social life. And yeah, I’m really excited to explore it with you. We’re bringing on some really excellent guests. Some researchers, yes. But not just researchers! Also people who practice in the field and know firsthand what it looks like to resolve issues of anxiety with students.

Bethany Lockhart Johnson (02:45):
Yeah, you’re right, Dan. My math story contained quite a bit of math anxiety, so I am particularly invested in this season. I mean, I still navigate math anxiety. And, you know, many of us do, and let’s talk about it. And let’s—I love that you reminded me. We’re gonna have a lot of great researchers all throughout the season, and a lot of times folks feel like the research happening, there’s sometimes a gap between researchers and what’s actually happening in the classroom. Not in all cases, but a lot of times. Right? And I remember a lot of conversation about the latest research when I was in grad school, but unless you’re actively studying something, sometimes we don’t know what’s happening. Right? We’re really focused on what’s happening right in front of us in our classroom. So let’s take some of that research; let’s break it down; let’s talk to some of the folks who are thinking about this for the bulk of their day, right?

Dan Meyer (03:41):
Yep. So we got our first guest coming up in a moment here.

Bethany Lockhart Johnson (03:45):
So to kick off this season, we’re starting episode one by talking to Dr. Gerardo Ramirez, Associate Professor of Educational Psychology at Ball State University. And he’s been researching math anxiety for more than a decade. He’s worked with so many amazing folks in the field. He’s worked with students, he’s worked with teachers, with educators…I’m just so excited to talk to him. If you look up math anxiety, you see his name as one of the folks who is really thinking about this at so many different angles, and we get to talk to him. So enjoy our conversation with Dr. Gerardo Ramirez.

Dan Meyer (04:29):
We are so excited to have Dr. Gerardo Ramirez on the show with us. Dr. Ramirez is an Associate Professor of Educational Psychology at Ball State University. Thanks so much for joining us.

Dr. Gerardo Ramirez (04:40):
Yeah, thank you for inviting me to talk about math anxiety.

Bethany Lockhart Johnson (04:43):
So with your interview, Dr. Ramirez, we are actually launching the season. We’re gonna be talking about all different aspects of math anxiety, and it feels pretty perfect that you are first guest of the season, because of the sheer breadth of research and conversations you’ve had about math anxiety. Could you start us off kind of telling us a story of how did you get interested in studying math anxiety? Or why, you know, why did you dive into this topic that, you know, I think a lot of folks might…like, if you’re on a plane, and you say, “Oh, I study math anxiety,” what kind of reaction are you gonna get?

Dr. Gerardo Ramirez (05:24):
Oh, sure. Yeah. I think most people are actually very interested because they all have their own story about feeling anxious about math, or just being anxious about evaluation situations that involve math. And, yeah, they wanna share those stories. People feel quite comfortable talking about their anxiety about math, for some reason. But for me, I started off, when I was in undergrad, I was studying to take the GRE quiz. I was hoping to go into a psych program. But I wasn’t exactly sure what direction yet. As I took some of the practice tests, there’s some situations in which I was very nervous about taking the practice test. And I just noticed that I did really poorly on some of these exams. And so I became very interested in issues like choking under pressure, which means when you underperform relative to what you expected to perform. And so, as I was researching these issues, I started to come across this whole field of math anxiety. And I saw that while there are some people who choke under pressure during tests, there are other people who just have a strong general fear of mathematics.

Dan Meyer (06:29):
That’s really helpful. I can imagine you’re doing a lot of free psychology sessions, free therapy for people on airplanes when they bring to you their own stories of math. So let’s thank you for your service in that sense. I’m super-curious. So Bethany and I have both taught math. We both have seen firsthand what it looks like when a student is anxious in math class, though maybe we don’t have kind of the clinical language to describe it. And I’m curious, from a clinical sense, how do we define math anxiety?

Dr. Gerardo Ramirez (06:57):
Sure. So first off, math anxiety is not something that you would find in the DSM, for instance. But we generally define that as a fear or apprehension to situations that involve math. So it doesn’t have to necessarily be educational situations. It could be someone asks you a math-related question during a party, or you have to calculate the tip at a restaurant, for instance. It doesn’t have to be about schooling situations, although that’s obviously where it seems to matter a lot for many people. So it is basically a fear or apprehension to situations that involve math. And I think distinguishing the term “fear” from “anxiety” is really important here. A lot of times people use those terms interchangeably, and the term “fear” is obviously within our definition of math anxiety. But oftentimes what differentiates anxiety from fear is that, anxiety is—think of it like a recipe. Anxiety is fear plus a little bit of unknown. OK? So if, for instance, if you hated snakes, and they threw a snake at you, you’d be in intense fear. Whereas if you hated snakes and they said, “There is a snake in the room, but I’m not gonna tell you where,” that’s gonna cause anxiety. And so the reason why we call it math anxiety is because a lot of times people experience this fear for a possible unknown future that involves math or possible unknown evaluations that people might have about your competence, because of math. And so for a lot of kids, they feel anxious about how they’re gonna do on a test or whether they’re gonna be able to pass a class or whether they’ll be able to understand what you’re saying in your lessons, for instance. And so the anxiety component really gets at fear of something that’s unknown, but related to mathematics situations.

Dan Meyer (08:47):
Math is somewhere in the ceiling right now. Perhaps I might be surprised with a math situation!

Dr. Gerardo Ramirez (08:52):
Yeah. yep.

Dan Meyer (08:52):
So I have this tendency to assume that every other subject that we teach has it better and easier than math does. It’s not true. I know this is not true. But I’m kind of curious here. Is math anxiety, like, part of a general just set of anxiety around schooling itself? Like, is there a reading anxiety, a writing anxiety, and does that all just flow from the same kind of fount of anxiety around schooling or situations about learning? And what makes math special in this regard? If it is its own special anxiety, for instance?

Dr. Gerardo Ramirez (09:27):
There are different…so some people obviously suffer from generalized anxiety. Right? And so they would, you know, feel anxious both for evaluative and non-evaluative situations. But in the research that we’ve done and that other people have done, there are differences between things like reading anxiety, math anxiety; I’ve also studied spatial and creativity anxiety. A lot of times what we’re trying to do in these studies is we measure all of the above, and we try to show that, look, math anxiety predicts math situations above and beyond these other things. So yeah, we definitely distinguish those things. And so what’s special about math is that, well, I think the symbolic nature is a big part of it. The abstract symbolic nature is just not as tangible to students. They can’t touch it. And so it doesn’t allow ’em to use their full cognitive faculties to play with it, as you might see, for instance, in science. Or it doesn’t allow people to relate math to their own interests the way you might see, for instance, in English. So maybe I hate reading novels, but I’m interested in zombies and you give me a book on zombies, well, ok, great, you’ve connected my personal assets to the topic. Whereas with math, either that’s harder to do or instructors don’t do such a good job of setting that connection up.

Bethany Lockhart Johnson (10:46):
Also, I think, you know, I’ve heard of students being really anxious, let’s say, during a reading session, when teachers used to do—hopefully they’re still not doing it—the popcorn reading, where you just randomly call on a student to read out a sentence. Right? But you don’t really hear students or adults talking about, “Oh, no, no, no, I don’t read; I don’t mess with reading.” You know? Whereas with math, you do hear, “Oh, I’m not a math person. Oh no, no, no, don’t ask me any math questions.” And that is such a distinction.

Dr. Gerardo Ramirez (11:18):
Yeah. And I think a lot of that’s because it’s just so common. As an adult, to be nervous about reading is kind of an uncommon thing. So people feel a stigma around admitting that. But math is something that everyone feels like they’re inadequate in. And so there’s a lot of comfort in telling you how they’re just one of the many people who don’t like math. And that, you know, can have a lot of different consequences and outcomes. I think on the one hand, I think for a lot of kids it becomes a normalized message that if you fear math, that’s OK, join the club. Right? But we have to be careful about that, ’cause a lot of math anxiety researchers will oftentimes say, part of what leads to math anxiety is adults normalizing that it’s OK to be scared of math. So I think a lot of times adults, teachers, for instance, math teachers, they’ll tell kids, “You know, if you’re scared, that’s OK.” And so a lot of the math anxiety community says, “No, no, no, you’re not supposed to do that.” But my recent view is different. I view that as a form of validation. Because math is hard. And so telling kids, “Hey, look, it’s actually easy if you just try,” I don’t think that’s true. It’s actually just hard. And I think even if it was easy, to the kid, it feels hard! And I think something that’s not really well-studied right now in our field is the value of validating people’s math negative math experiences. We don’t want to validate that, ’cause we think that we’re gonna reinforce that. But actually, I think the opposite. I think when you validate people’s negative math experiences, it helps ’em to feel that they can handle it. They can start to take control over their own emotions.

Bethany Lockhart Johnson (12:52):
I love that. And I, I actually, I think that’s so powerful, what you’re talking about, that validation. I taught kindergarten, and I vividly remember being in a parent-teacher conference and that parent saying, “Oh, I wasn’t a math person either,” right? Or, you know, their language and their experience with their own math schooling, their anxiety about math was actually impacting their students’ experience of math. Or the conversation that, when I would go to talk about a math assessment, let’s say, you could see the parent actually tensing up. And there was this moment of validation, that I felt like we needed to make space for that in the conversation with the parents, right?

Dr. Gerardo Ramirez (13:38):
Yeah.

Bethany Lockhart Johnson (13:38):
Like, this is a real thing. And we are working on teaching students that math is something that gets to—your experience with math gets to look all sorts of different ways. And it’s OK if we, you know, make a mistake, or if we kind of only get this part, but we’ve really got that part. Or let’s talk about it; let’s write about it. So I really feel like that that validation is something that’s so missing. And instead of the validation, like you said, you see folks being like, “Oh yeah, me neither. I’m not a math person either.” Right?

Dr. Gerardo Ramirez (14:10):
Yeah. I think…part of the reason why people are comfortable sharing this because they’re looking for validation also. When they say, “Oh, I’m not a math person,” you know, I think they’re hoping that, you’ll say like, “Yeah, me neither,” or “Of course not, ’cause math is terrible.” Right? They’re looking for validation, not to reinforce their perspective, but to feel that it’s OK not to be a math person. And I think that’s one of the techniques that I’m trying to work on in my research right now, is to provide evidence that actually people will work harder when you validate their math experience. You don’t have to tell them a positive story per se. If your current story is “Math is hard and I’m very, very anxious; I’m scared,” then we can just validate that and help you work through that. And it actually will strengthen our relationships. Because if you’re a student and you’re struggling with math and I tell you, “Yeah, it’s hard; it’s OK to struggle with math,” that makes you feel seen. And that’s gonna lead you to want to ask me more for help, because I’m someone who understands you. And that’s a great, you know, remediation opportunity.

Dan Meyer (15:14):
A common thread that I think I’m seeing here in several answers is that math sometimes asks students to disassociate part of themselves. Where success in math oftentimes means working from an a level of abstraction with symbols, like you said, that can feel alien. Like, who am I here? And in the same way, I love that you’re proposing we validate and reassociate people with a very deeply felt part of themselves that is anxious about mathematics.

Dr. Gerardo Ramirez (15:44):
Yeah. I mean, I think that’s what validation’s supposed to do, right? So a lot of us, when we feel these strong emotions, we wonder, “Is this even a real thing? Are other people feeling this? Is there something wrong with me?” So we feel the emotions, but we can’t actually deal with them, because we wonder if they’re legitimate. And so when someone says, like, “Yeah, this is hard,” it crystallizes that emotion. And once something is made real, you can actually choose how you want to deal with it. Some kids are gonna deal with it by staying anxious. But some people are gonna choose to deal with it by saying, “Well, there’s nothing I can do about it now; I have to take this math test, so I’m just gonna think positive.” And that’s great. If the kid can end up saying that to themselves, that’s much more effective than me telling the kid, “Hey, you just gotta think positive. You’re gonna start the test anyway.” And so we want the kid to make meaning of their experience, and the way we do that is by crystallizing their emotions through validation.

Dan Meyer (16:36):
Yeah. I love that. And so what you’re proposing there, I think, sounds like, a solution, like a post-talk solution after students are feeling anxiety.

Dr. Gerardo Ramirez (16:43):
Yes.

Dan Meyer (16:43):
To validate and empathize.

Dr. Gerardo Ramirez (16:45):
Yes.

Dan Meyer (16:45):
And over the course of our season, we hope to explore a lot about solutions to math anxiety that are preventative, that reduce the odds of anxiety arising, through instruction and curriculum, before it arises. And I’m just wondering if you’ve seen anything that would hint at either specific or general words of wisdom you wanna share with the educators, about not just addressing it after the fact, but preventing math anxiety before it arises?

Dr. Gerardo Ramirez (17:14):
To be honest, at this point, I haven’t seen enough evidence for me to recommend anything concretely as an intervention for math anxiety, or an intervention to prevent its development. All I can really do here is rely a lot on the more broad cognitive-behavioral research on anxiety, which says that one of the ways we prevent people from developing anxiety is by helping them to make more positive appraisals of challenge situations. So a lot of times, when kids are challenged, they don’t know how to interpret that. “What does it mean that I’m struggling with this thing?” And so that’s where I think a lot of teachers can help students’ interpretations of that. ‘Cause if you leave kids to their own devices, they’re gonna think, “I’m struggling because I’m stupid. I’m struggling because I’m not good enough. I’m struggling because my dad is right; I’m gonna be a failure.” You know? They’re going to impose an interpretation to a challenge situation regardless. And so, as teachers, one thing we can do is we can help shape that interpretation and say, “What does it mean to struggle with math? People will say it means you’re stupid. That’s one interpretation. What’s another one? It means that your brain is working really hard to think through something. That’s another interpretation. What’s better? What do you think is more helpful?” And then, helping students to see how interpretations matter to how you ultimately feel about something. And that’s a very metacognitive way of thinking about things. So yeah, I would say that one way to prevent it is to help students to take more positive interpretations of their experience. But another way, and I think a more successful way, I think, is to give students early experiences where they feel efficacious dealing with math. One of the ways you do that, for instance, is by obviously making sure that the students understand the material—but that’s obvious; people are trying to do that. One of my favorite recommendations is to keep reassigning assignments, the same exact assignment, for, say, three weeks, back-to-back. So if in week one you do the homework assignment, you do OK, you don’t do so great, when week two you do it, you give the exact same assignment, and now the student can see like, “Wow, OK, this was much easier.” And then, week three, you give the exact same assignment; now the kid’s feeling really confident. And the reason why that’s great is because it helps kids to see that they’re growing in confidence. A lot of times kids don’t get to see that because we’re constantly throwing new assessments at them. And so they’re never seeing that growth. All they’re seeing is a new challenge, a new challenge, a new challenge. So I think we need to set up situations where they can feel that they’re growing, when we keep the assessment static. That can be a formative assessment, for instance—doesn’t have to be a summative assessment.

Bethany Lockhart Johnson (19:55):
That feels so powerful and it feels like it really connects to that validation piece, right? We are actually helping to create a culture in our math classroom where we might struggle with something, but we keep revisiting it. And it’s not so much to reach mastery, but as Dr. Megan Franke — we talked to her about this partial understanding and about pulling on those threads of things that you do understand, so that you can build your confidence…build, not just confidence, but build your…I guess, kind of get your footing, right? You’re saying, “Well, I do understand this. I see how this works.” And if I’m revisiting an assignment, I feel like that would give me permission to like, “Hey, I don’t have to have this figured out on the first pass. You know?

Dr. Gerardo Ramirez (20:44):
Yes, yes. Yeah. I mean, I’m gonna give you a silly analogy, but I think it works. You know, a lot of times people will have nightmares, right? And they’ll keep having the same nightmare over and over again, right? And so one reason that we suspect this happens is because they haven’t worked through whatever that nightmare’s supposed to be about. So if, say, I’m scared of driving, I may be having the same dream about driving and crashing over and over. And we keep having these nightmares. And I think math anxiety is kind of like a waking nightmare, where you keep rehashing something because you haven’t had the chance to finally address that dragon. You know? And so if someone was having a lot of fear over driving, then one behavioral approach would be, you know, to work with a therapist to actually get behind the wheel and maybe drive around the same track over and over until you feel comfortable at that, and then the nightmares stop. Well, the same thing is true, I think, about math, math and math anxiety, is that you wanna give people these opportunities to feel confident by going back to that original experience that caused them to feel anxious, and saying, “This one assignment that we did in week three that really freaked you out, let’s try it again now in week five. How was that?” “Yeah, it wasn’t so bad. It was still kind of annoying.” “OK, we’ll we’ll come back to it.” “Now it’s week seven. Now let’s go back to that assignment. How is it now?” “That’s actually…it wasn’t that terrible.” And that gives people the opportunity to reflect on how they’ve grown past that nightmare.

Bethany Lockhart Johnson (22:05):
I have to say, Dan talked about you being like a therapist. I’m like, wait, “How did you know, Dr. Ramirez? I did have this recurring dream! I did! And I had to face it. No, but I had such intense math anxiety in high school and it was debilitating. And the biggest thing for me, I thought I was the only one. I thought there was something wrong with me. I thought, “Why can’t I figure this out?” There wasn’t a conversation about “Here are some tools,” or “Here are some, some, some…”. Like, “This is OK, for you to feel scared about this or overwhelmed!”

Dr. Gerardo Ramirez (22:41):
Mm-hmm. Mm-hmm.

Bethany Lockhart Johnson (22:42):
You know, I think often when we talk about how widespread math anxiety is, I think a lot of folks automatically jump to high schoolers or college students avoiding math courses. But we see this in really young kids.

Dr. Gerardo Ramirez (22:56):
Yeah. So people are…people are just constantly making meaning of themselves, regardless of the age range. And that’s true even with young kids; they are trying to figure out who they are. Right? And so one of the things you see oftentimes with young kids is you ask ’em, “What are you good at?” And they say, “Everything!” And that’s their attempt to, you know, make meaning of themselves. But sometimes they’re not good at everything. Sometimes they actually struggle in math. And I think even early on, they have to make meaning of that. They say, “Well, I’m good at everything except math.” And how do you make sense of that? Well, why not math? “Oh, because math is terrible. It’s not for everybody. You know, it’s not something that I like.” And so, yeah, in a lot of the studies that we did early on, we basically went into these first-grade classrooms with the purpose of trying to assess whether we can actually show variability in kids’ math anxiety, even early on. In other other words, do kids even report feeling anxious about math situations? Or do they tell us that they’re great at everything? And what we found was that in fact, a good chunk of kids are, again, perfectly willing to tell you that “No, certain situations involving math make me very anxious.” Counting or addition, or doing a problem on the board. And the way we do that is by—I think there are probably more sophisticated ways that can be done, but this is the best we have at this point—is we go in there and we ask them, we show them a bunch of smiley faces and anxious faces. And we say, “I want you to tell me how you feel about these different situations that involve math.” And so we say, “If you feel kind of nervous, I want you to point to this face. If you feel very nervous, point to this face.” And we basically will read to them situations. We’ll say, “How would you feel if your teacher asked you to open up your new math textbook and you saw all the numbers inside of it?” And they’ll point to the really nervous face. So right now, those are some of the more reliable assessments for math anxiety among young kids. And that work showed us that even young kids are self-reporting math anxiety.

Dan Meyer (24:51):

Obviously this is worth our study, because we would hope people would not feel anxious in general, and especially if we have a mandated…kids are mandated to be in math classes for their entire childhood. So I see the need for this study, these studies. I’m curious: What are the consequences, though? Like what, what correlates with math anxiety? What are other reasons why we should care about math anxiety and work to remediate it?

Dr. Gerardo Ramirez (25:16):
Oh, sure. So it correlates with their actual math performance. It can correlate when they choose to do homework. Right? So a lot of times, the parents report having to fight with their kids over math homework a lot. And you also oftentimes see a lot of frustration over mathematics specifically. And so it can, you know, not only affect their academic ongoing outcomes, like math tests and math assignments, but it can also affect their relationship with their parents. So if every time you come home, your dad’s screaming at you because you haven’t done your math homework, and when he asks you to solve the problem in front of them, you don’t remember, ’cause you were checked out, ’cause you’re so stressed out, that’s gonna cause a really negative experience. You know, a lot of times people grow up and they still remember their dad screaming at them over the math homework. You know, it’ll affect your relationship with your teacher. So if you’re making me feel incompetent, if you’re stressing me out, you’re not the kind of person I wanna come to for help. So it can predict relational outcomes as well as academic outcomes. And down the line, of course, when it affects students’ opportunities to get into things like AP classes, it affects students standardized test performance and their choice of colleges, as well as scholarship opportunities.

Dan Meyer (26:29):
Once you show that it correlates to performance, then that opens up a whole range of other correlations that are pretty important, it sounds like. Whether that’s career options or, you know, post-secondary education and the like.

Dr. Gerardo Ramirez (26:40):
Yeah. And a lot of times, when people are choosing a career at college, a lot of times students will make a decision specifically based on what career has less math requirements or less math courses. So I think this finding needs to be verified further. But, there’s some studies showing that, for instance, elementary ed teachers, one factor that feeds into the decision to go into elementary ed is the math requirements are very low in elementary ed. So that can…obviously it’s not what we wanna hear, because these are our first formal math teachers, right? For our kids.

Bethany Lockhart Johnson (27:16):
It feels so powerful, the impact that math anxiety can have, not only while you’re in, let’s say, elementary school, high middle school, high school, but then the impacts beyond that in terms of your career. And I shared this last season, when we talked about our personal math story, but I know when I was navigating the deepest part of my math anxiety, I really felt like, maybe this is a reason I can’t be an elementary school teacher. Because I was so worried that I wouldn’t be able…not that I wouldn’t understand the math for fourth grade, fifth grade, but that there was something about my ability to teach it or understand it or develop a love and passion for it that I wouldn’t be able to do. And I really had to reclaim it in my own way. But, you know, something that I think is so powerful about your research is just the applicability — not only to the field of mathematics, but folks’ everyday lives. And the way that you have talked in the past about math being a gatekeeper…I have a family member who, brilliant American Sign Language interpreter. I mean, amazing. Like a dance with her fingers. I could just watch it all day. And she actually didn’t complete the program because she couldn’t complete the math requirements. And I remember talking to her about like, “Well, have you gone to the free tutoring? Have you gone to, you know, this or that?” But it was a paralyzing fear, you know? So Dr. Ramirez, what do you wish educators understood about math anxiety? Or the research about math anxiety? Or maybe even the general public at large, what do you wish folks understood about math anxiety?

Dr. Gerardo Ramirez (28:58):
Oh, I think that a lot of students, they struggle with math. And I think we wanna normalize that struggle as much as possible. We want to create a culture where it’s OK to do math slow; it’s ok to take your time. And I know that’s not possible with a lot of these requirements that a lot of math teachers have to do. But I think if we want to prevent math anxiety, we have to create opportunities to tell better stories. So that’s ultimately what I tell people is, why do people develop math anxiety? Because they had experiences that challenged their competency and they told a negative story. And so making space to reflect in math classrooms about what does it mean to go slow in math, or what does it mean to make mistakes, and then helping kids to tell better stories, I think it’s really the best thing we can do as math educators. ‘Cause you know, your job is not to be a therapist ultimately. You know, there’s only so much math teachers can do. But I think one of the most powerful things we can create is setting up students’ experiences where they feel confident, and they can tell better stories, so they can have better dreams about math.

Dan Meyer (30:06):
Really appreciate this introduction to math anxiety. It’s been a fantastic kickoff to our season. Dr. Ramirez, thank you so much for joining us.

Dr. Gerardo Ramirez (30:14):
Sure. Thank you.

Dan Meyer (30:16):
Thank you folks so much for listening to that conversation with Dr. Gerardo Ramirez, Associate Professor of Educational Psychology at Ball State University.

Bethany Lockhart Johnson (30:25):
Dan, OK, if not for your frantic signaling, I would’ve probably asked another 20 questions. I need to know what you thought .

Dan Meyer (30:34):
I found it interesting at all points. And especially I think I started to understand a little bit better where the anxiety comes from for some students. I got a little bit here, which is that I think math, more than other disciplines, involves alienation. Check that word. You like that? Alienation? I’m into it. I’m feeling it. It’s like…to get good at math, to be successful in math, you gotta, as a kid, lose your attachment to the world you understand. And I mean, “got to” as in like, “you are asked to” — many times, unfortunately, by curriculum and instruction. Which is to say, you’re turning things you can hold onto into numerals. Right? You’re turning the world and its patterns that you can see and touch into Xs and Ys. And I just don’t know that other disciplines deal with that as much. Maybe I’m wrong and just guilty of, you know, “grass is always greener” syndrome here. But I think that’s an experience that kids have in math. And I thought that Dr. Ramirez got at that when he’s talking about the need to validate a student’s experience of anxiety. Like, in treating anxiety, sometimes we alienate people further by just like saying, “Oh, no, no, no, it’s just like, you need to, you know, drill yourself more, practice more,” and kind of invalidate that. So this feeling of alienation, I think permeates a lot of math instruction. I’m looking forward to learning more about that with our future episodes

Bethany Lockhart Johnson (32:00):
Alienation. That’s interesting. I definitely felt, I definitely felt isolated and alone many times in my math journey, when I was having my…you know, in high school, when I was feeling like, “Clearly everyone can look at tan, sign, cosign, and that means something to them.” Right? I think it’s really interesting, because I’m thinking about the other disciplines; I’m running through them, and I’m like, even in science, which can seem abstract, so oftentimes there’s these experiments that accompany these concepts, where you’re like, “Look at this concept made real in front of you.” Right? . And so yeah, that’s really interesting.

Dan Meyer (32:39):
You’re always one step away from blowing something up! Or, you know, dissecting something that’s tangible to you.

Bethany Lockhart Johnson (32:46):
Yeah. That’s really interesting. I did really love how he brought up the abstract. And how, I think, even validating it…he talked so much about validation. Which to me was like, YES. If somebody just said, “Hey, it’s not only possible to have math anxiety, but it also doesn’t mean that you don’t belong here.” If somebody had said that, it would’ve literally changed the trajectory, you know? And I wonder what those conversations could look like in our classrooms, where teachers celebrate that. Like, WHOA, this is a new way to think of this. This is a new way. Asking how many, or what do you notice for this image, through a mathematical lens, or looking…we talked to Alison Hintz and Antony Smith, like mathematizing books, like looking through these lenses — it’s an invitation to step into this other world, right? But there’s not only one way to do it. And I think oftentimes it’s like that anxiety of “Am I gonna say the right thing?” or “Am I gonna notice the right thing?” Right? How do we create that space more, where there’s so many possibilities and we want kiddos to notice what they notice, right?

Dan Meyer (33:54):
You gotta become a certain kind of person to be successful in math class. I feel like is part of the implied deal. Where you’ve gotta—like how you said—say a certain thing or think about a certain thing a certain kind of way. You’re trying to become someone who is not necessarily you. Which I think is fundamentally an experience of alienation, separating you from important parts of yourself.

Bethany Lockhart Johnson (34:19):
I will never, ever dive into mathematics on the scale and level that you have with your PhD. You understand math in a way that my brain just…I won’t get there, right? And yet I’m allowed to call myself a mathematician, with all of my deep dives in elementary math and my love of early numeracy and thinking about how we start thinking about counting and numbers. Right? It’s like, if we make more space for what mathematicians can look like, and what is your personal relationship with math…I mean, that to me feels really exciting. ‘Cause I think we both have something to offer each other.

Dan Meyer (35:03):
I think I have never found early math more interesting than when I talk to early math educators. And learn just like all the different ways that students come to understand a concept that I had thought was simple. Like addition of whole numbers. Whoa! There’s a lot of ways kids do that work, and their brains think those thoughts. And, yeah. That’s a good word there you’re offering us and our listeners.

Bethany Lockhart Johnson (35:27):
Yeah. Yeah. I’m really excited about this season. I think there’s — again, there’s no way we’re gonna cover all facets of math anxiety. But I think having the chance to explore it over the course of a season is going to be really fascinating. And really, I hope, destigmatize it and open up the conversation for our listeners. And, you know, if you listeners…we wanna know what you thought of this episode. Do you have any particular questions? Do you have questions related to math anxiety? Questions related to this episode? We are in development for this season, so we’re gonna do our best to get those questions answered. You can keep in touch with us in our Facebook discussion group, Math Teacher Lounge Community, and on Twitter at MTLshow.

Dan Meyer (36:14):
Next time, we’re gonna go deeper into the causes and consequences of math anxiety.

Dr. Erin Maloney (36:20):
It’s not just the case that people who are bad at math are anxious about it. It’s actually that the anxiety itself can cause you to do worse in math. And that for me is really exciting, ’cause it means that if we can change your mindset, then we can really set you on a path with several more options available to you.

Dan Meyer (36:41):
Til next time folks,

Bethany Lockhart Johnson (36:41):
Bye.

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What Dr. Gerardo Ramirez says about math

“A lot of students struggle with math, and we want to normalize that struggle as much as possible. We have to find opportunities to tell better stories and reflect on our experiences.”

– Dr. Gerardo Ramirez

Associate Professor of Educational Psychology, Ball State University

Meet the guest

Dr. Gerardo Ramirez obtained his Ph.D. from the University of Chicago, where he studied the  role of teachers and parents in shaping the math attitudes of their students, as well as reappraisal techniques to help students cope with anxiety during testing situations.

Dr. Ramirez is currently an associate professor at Ball State, where he examines the role of frustration, empathy, and cultural capital in shaping students’ success and persistence.

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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!

S4 – 02. Bethany and Dan share their math biographies

Promotional graphic for "math teacher lounge," season 4 episode 2, featuring photos and names of math teaching guests Bethany Lockhart and Dan Meyer.

In this episode, co-hosts Bethany Lockhart Johnson and Dan Meyer get personal and share their “math bios”—their early experiences with math and how those experiences turned them into the educators they are today.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:00):

We’re recording. What’s up, everybody. This is Dan Meyer with Math Teacher Lounge.

Bethany Lockhart Johnson (00:08):

And I’m Bethany Lockhart Johnson. We are so excited to be back. Season Four, Episode Two. Hi, Dan.

Dan Meyer (00:16):

Hey, Bethany, how are you doing today?

Bethany Lockhart Johnson (00:18):

I’m so excited to be talking with you! You know, as we record this, our reunion at NCTM is getting closer and closer.

Dan Meyer (00:28):

The NCTM live show is gonna be bonkers. I don’t think people are ready for it. You think you know what we’re about on MTL from listening to us, but the live show is gonna be outta control. You cannot imagine how many clowns and elephants Bethany wants to have at the live show. We’re still—we’re trying to talk her down from like three to one, but we’ll see.

Bethany Lockhart Johnson (00:44):

All I want is the t-shirt cannon. Because I used to go to these baseball games and they would have a t-shirt cannon. And I thought, I wanna operate a t-shirt cannon! So like, if I could be standing on stage aiming t-shirts at people who are jumping up and down requesting a t-shirt? I don’t know. Doesn’t that sound fun?

Dan Meyer (01:01):

Sounds awesome. High point of my college education was catching a t-shirt. No, it was—it was a burrito. It was a burrito cannon. But I think it was just a t-shirt cannon, but it was a burrito cannon. And I caught a burrito at a game and it was probably the most memorable moment of all of college education for me.

Bethany Lockhart Johnson (01:16):

Was the burrito still warm?

Dan Meyer (01:18):

Oh yeah. I think it got—like, I think it might’ve been warm at one point and then it got warmed back up through the muzzle velocity of the cannon. So it was a pretty great system they had going on there. <Laugh> Yeah. <Laugh> Anyway, I’m off topic, but, we’re thrilled to—I’m thrilled to chat with you and we’re thrilled to be listened to by you folks out there in MTL land. In the lounge itself. We got a fun show today.

Bethany Lockhart Johnson (01:40):

So if you listen to Episode One—which if you haven’t, hope you go back and listen to it—if you listen to Season Four, Episode One, you’re gonna hear—we asked Huon, KT, who is this delight of a joyful teacher. We asked her to talk to us about what’s her math bio. And we want to ask all of our guests—like, I wanna go back and ask every single guest we’ve ever had to tell us their math bio.

Dan Meyer (02:06):

Yep.

Bethany Lockhart Johnson (02:06):

Because, while seemingly simple in nature, our students enter our math classroom already having had this relationship with math and these notions about their role in math or what they think about math. And it impacts our school year with them if we’re a teacher. And it impacts our relationship with math as we move through our education and beyond. Right? And I I’m so excited about this question, ’cause I think it also ties into this theme for Season Four, which is joyful math, and diving into “When has math felt joyful? When has it not? Does it feel like—how do we think about how our math bio, our relationship with math, has evolved into a joyful or less joyful place?”

Dan Meyer (02:54):

I get it. And what’s really key here, I think, is that teaching more than other professions is a generational profession. You know what I’m saying? Like, no one is like, “Well, you know, I sold insurance to you and now you’re selling insurance to, you know, my grandkids; that’s amazing!” But people are always posting photos when, like, you teach someone who then becomes a teacher later. Teaching is a generational sort of thing. So the kinds of joyful experiences that we offer or don’t offer students now affect the experiences that students who haven’t even been born yet will have, you know, some 20, 30 years later. That, to me, is a trip. And well-worth exploring, you know, how we got here, mathematically speaking.

Bethany Lockhart Johnson (03:39):

I remember a friend had sent me this image of an assignment that her son got that was asking for their Mathography. They wanted to know about their history of mathematics. And this was their first assignment. And this teacher, I would like to imagine, read them all and used it to inform conversations about students’ relationship with math. And, you know, some of the questions they asked were thinking about whether you consider yourself, quote, unquote, “good at math.” Like “what kind of experiences have you had? What do you like or dislike about math? What is, you know—what do you expect to learn in math this year?” Just asking students to actually pause and examine and reflect on their relationship and then also looking forward to, like, what kind of a classroom community do we wanna create? And I loved that assignment. And yeah, so today’s episode Dan, guess what?

Dan Meyer (04:32):

What’s going on? What’s happening?

Bethany Lockhart Johnson (04:33):

I figured we should ask each other about our math bio.

Dan Meyer (04:39):

I think the people out there would love to know this about us. ‘Cause you know, we’re both awesome. But also what’s really cool here is that like, I don’t know this about you. Like not, not a lot. You know, the folks at Amplify, they kind of assembled me and Bethany together in the same way that record labels assembled pop boy bands, girl bands, that kind of thing, back in the day. You know, grabbing some stars from screen or film and just like throwing ’em together and saying, “All right, now you’re here to perform together.” And so it’s just a really good moment for us to, like, settle back and just know who we’ve been working with for the last three seasons and change here. I love it.

Bethany Lockhart Johnson (05:15):

Well, I don’t know. I don’t actually agree with that, Dan. Because don’t you remember? We knew each other beforehand. And while I would like to think of us as…oh, I’ll say One Direction—well, no, One Direction is now defunct. Who’s another band that got formed by one of those shows and is still together and still—

Dan Meyer (05:33):

BTS! K-Pop, you know! Let’s go!

Bethany Lockhart Johnson (05:35):

K-pop. BTS.

Dan Meyer (05:38):

Let’s go, Bethany <laugh>.

Bethany Lockhart Johnson (05:39):

So can we incorporate some K-pop into the NCTM Math Teacher Lounge live episode? Don’t answer now. Don’t answer now. OK. So not only are we gonna share our math bios, but we want to encourage you listeners to share your math bio with somebody in your life. It could be a child in your life, maybe talking to your kiddo about what was it like. What was math like for you? It could be a student that you have. It could be a partner, a friend, a parent. I mean, the sky’s the limit. Share your math bio. And most of all, share with us. We wanna hear about your math bio and you can share it with us at Twitter, at MTLShow, or in our Facebook group, Math Teacher Lounge.

Dan Meyer (06:26):

Stop on by, please. All right. I’m gonna just share like, just a couple of quick, signposts. Not the full bio. Gotta leave them wondering about something here. But here’s a few quick highlights and lowlights of my math bio and how, maybe, it made me the teacher that I was and the educator I am. Is that cool?

Bethany Lockhart Johnson (06:44):

Wait, I didn’t even, I didn’t ask you yet.

Dan Meyer (06:46):

Ask me what?

Bethany Lockhart Johnson (06:47):

Hey, Dan!

Dan Meyer (06:49):

Is there like a magical word? Like, what’s your math bio? <Laugh> Oh, go for it. No, no, that’s right. They won’t know what I’m talking about. Why is he talking about his math bio? Bethany—

Bethany Lockhart Johnson (06:57):

That whole lead-in that we just gave? They might not know.

Dan Meyer (07:00):

Yeah. We just talked about math bios for the last 20 minutes. But yeah, they might not know what we’re—

Bethany Lockhart Johnson (07:04):

<laugh> So Dan, why don’t you go first? ‘Cause I know you were gonna ask me to go first, but why don’t you go first? Dan? What’s your math bio?

Dan Meyer (07:12):

Oh, wow. Well, thank you for the formal invitation to share my math bio, Bethany Lockhart Johnson. So, I’ll just share—I just wanna share a couple items here, not the full history. Gotta leave ’em—leave a little mystery in there, you know what I’m saying? But here’s a few highlights and lowlights, and I think what it means for me as an educator. So, I was homeschooled for eight years. That was big—did a lot of math learning on my own. Couple of lowlights from that, a lot of highlights, in terms of just like being able to, like, learn at my own rate and just jump on ahead and pursue different wacky things. But I tried to switch into public school in fourth grade and I lasted, um, four hours. I didn’t even go to class. I enrolled and then it was like, boom, I was out of there. Because we went to the school; we met the teacher, saw the room, very nice person and place. But I got the homework assignment and the homework assignment was gibberish. I had no idea what to do and such was this feeling of just, like, despair and hopelessness, I was like, I cannot be a part of this. I remember the assignment. It was about identifying scalene, isosceles, and equilateral triangles. I’ll tell you this: I am quite good at that now. But at the time, like, I didn’t know what those words meant. And you know, at that moment we had Encyclopedia Britannica, could not Google this or even Ask Jeeves or AltaVista this so well back then. It just—it was an entry moment of failure and realizing that so much of math is like a, kind of a social kind of construct. And if you’re not part of that social circle, what can you do? So that was a bummer. Another bummer was eighth-grade math, learned it all by way of videotape. You know, put in the tape and watch—not gonna say the person’s name and not this person’s fault—but it was just like watching someone work on a whiteboard. Kind of a precursor to Khan Academy, kind of a drag. Went to high school—

Bethany Lockhart Johnson (09:02):

Wait, wait, wait, wait. We were—I’m not ready to jump to high school. Wait. Can you pause for just a second?

Dan Meyer (09:06):

Yeah. Rock on.

Bethany Lockhart Johnson (09:07):

I just need you to go back to the triangle thing. So in that moment, what did that mean for you that you had had all these experiences with math and then you encounter math in a completely different sphere, a public school, and it did not have a connection or meaning to you because prior to that, it sounds like it was pretty positive. Right? Explore these things you’re curious about; there’s not, like, a level you need to stick with…

Dan Meyer (09:33):

Yep, yep. Yeah. I think that’s right. Maybe it was a little bit of a classic, like, “Oh, I didn’t have a growth mindset; my mindset was like, ‘Oh, I’m good at math because I am, you know, born that way,’” and all of a sudden, that identity was, you know, thrown into question. And, you know, my foundation was all of a sudden quite shaky. And yeah, that’s—you know, I think I taught a lesson recently where I was like, “Hey, this whole thing with a less-than or equal-to sign and a greater-than or equal-to sign, like what those signs are: it’s just, it’s language. And if it’s confusing to you, it’s not because you’re bad at math; it’s ’cause language is oftentimes confusing ’cause people have to agree on it.” So I dunno, that sort of thing is kind of filtered in, filtered back in periodically, some sympathy for like how a lot of math is like just socially agreed upon ways of working with, you know, numbers, shapes, patterns, that kind of thing.

Bethany Lockhart Johnson (10:20):

OK.

Dan Meyer (10:21):

Anyway.

Bethany Lockhart Johnson (10:21):

  1. And in this home school—I have a lot of questions about that, but I’ll stick to one—were you in a community of people that you talked about these math ideas with? Were you homeschooled solo? You have a sibling, so I think you were together, right?

Dan Meyer (10:39):

Yeah. Yeah. I’ve got a twin sister. So we were, you know, like, right on with each other the whole way through there. And yeah, so we had—but it wasn’t, it wasn’t like a—it was a lot of individual work, with my flavor of homeschooling.

Bethany Lockhart Johnson (10:54):

  1. Got it. And the tapes—wait, before you go to high school, the tapes, the VHS tapes, which I’m just loving this image—

Dan Meyer (11:02):

Yeah.

Bethany Lockhart Johnson (11:02):

Was that a positive experience? Was that because that was an area of math that whoever was homeschooling you wasn’t that comfortable with? Why was it that route for the tapes, and what was that? Was that joyful for you?

Dan Meyer (11:15):

Yeah, definitely not joyful. Yeah, it was like, if you had questions, you couldn’t really ask them of the VHS tape. It didn’t work out so well in that way. And it was a lot of operational-type math. It was, you know—there was no give and take; it was all kind of take. From the video teacher. And yeah, I was doing that because my homeschool teacher, my mom, who is very smart in lots of areas, did not have the math knowledge or confidence, especially to help with math at eighth grade. And that was a big reason why, flash-forward to the next year, went to high school.

Bethany Lockhart Johnson (11:48):

Nice segue. OK.

Dan Meyer (11:50):

<laugh> You caught up to high school…I encountered just like four years of just crazy-good, just bonkers-good math teachers who just really changed a lot for me. Especially, Mr. Bishop and Mr. Cavender, very cool folks who did a lot. And especially, I think Mr. Bishop and Cavender both modeled for me what curiosity from a knowledgeable adult looks like. Like someone who, you know, now I can say to myself, “Oh, they were kind of like putting on an act of being very curious about answers they were hearing for the 2000th time from a student,” let’s say, but what a powerful experience that was for me to feel like, “Oh, wow, my thoughts are interesting to someone besides myself.” I got like, maybe it’s two real highlights that I’ll just point to, from my math bio that made me the math teacher and person that I am. Let’s see here. Maybe three, if you you’ll indulge me. One is just like the idea that you could do math wherever you have your brain, a pencil and a paper. And so I remember like in high school, I was in church with my family and kind of a little bit bored of whatever’s going on. And I just had the Bolton and I like drew a pentagon, a regular one, then a hexagon, a regular one, and kept on drawing, like adding sides to the shape. And it was like, it was becoming a circle. And, you know, I was able to take the area of each of those shapes and say, you know, “What happens as you send the number of sides to infinity?” And watch as the formula for area of a circle, Pi R squared, popped out. And it was kind of a literal religious experience, in that moment, just like, “Wow, like my brain’s so cool and math is so cool and paper and pencil’s so cool.” And so there’s that. Just that kind of experience was pretty awesome. And then I would just say like, I’ve had some really fantastic experiences with math in the world itself. Stuff like—let’s see, this is gonna invite more questions from Bethany, probably, maybe I should avoid—I got, I have a Guinness—I have a Guinness world record that’s almost 20 years old. This Guinness world record is—it’s old enough to drive basically at this point. And almost old enough to drink. But like it was—it was a record for chaining the longest paper clip chain together in 24 hours. And the only way I was able to break that record was through mathematics. Where, like, I would be finishing a box of clips. And I would say to my buddy who was there, “I just finished a box of clips.” And that person would type in the number of clips that I had just done. And then a mathematical formula that I had created would tell me how many—how long the chain was at that point. It was being rolled around a spool. And like, it’s just like, wow. So math just made this possible. You know, math revealed that the record I was trying to beat was beatable, because I did the math on it. It was, like, thousands of feet long in 24 hours. And other folks might be like, “Oh, like, that’s that’s huge!” But me, I was like, “All right, let’s divide this out. You know, divide by 24 hours in a day, divide by 60 minutes an hour, 60 seconds in a minute. Oh, that’s like one clip every four seconds. That’s really slow.” You know, think about that <counts aloud>, “Clip, two, three, four. Clip two, three…” It was just slow. So math helped me, you know, wreck that record. Which to my knowledge still still stands. Don’t get any ideas, Math Teacher Lounge Folks! Is this news to you, Bethany? You haven’t blinked in the last, like, five minutes. I’m curious if this is new.

Bethany Lockhart Johnson (15:20):

It is news to me. And I have so many questions. Because OK, if four seconds was slow, so then what was your like—so then I’m assuming a hundred clips per box? Like, what was the rate, you know, per box? How long did it take you to complete a box? What did this friend like? Did this friend stick with you for the whole 24 hours? Did you really do it for 24 hours? Or once you beat the record, did you rest? How did you account for biological function? Like, needs? Like a restroom?

Dan Meyer (15:51):

<Interrupting> Like what?

Bethany Lockhart Johnson (15:51):

Eating.

Dan Meyer (15:51):

Like what, Bethany? OK.

Bethany Lockhart Johnson (15:52):

Um, Sleep.

Dan Meyer (15:55):

So yeah, maybe we dive into some of the specifics in a different time.

Bethany Lockhart Johnson (15:59):

Just tell me one of ’em. Tell me one.

Dan Meyer (15:59):

I’ll just say. So as to discourage other Math Teacher Lounge listeners from taking this on—back off of the record, folks!—this was back in college, so I was a little more limber back then. But I did one—I think it was 1.8 seconds per clip. For an entire 24 hours. Just like, so just like think about it, would you? If you’re gonna step to me on this one, just think about that, OK? And then, and then, you know, make an informed decision.

Bethany Lockhart Johnson (16:28):

Wait. Wait, wait, I just wanna tell you one thing. I’m picturing somebody with a straw, and like, giving you water as you keep clipping. I’m picturing, like, music, I…

Dan Meyer (16:37):

That’s not far. That’s not far. That’s not far from—yeah.

Bethany Lockhart Johnson (16:40):

So many questions! OK. Go on. Sorry, sorry, sorry. Go on. This is your bio.

Dan Meyer (16:44):

We gotta, I gotta wrap this up. I wanna hear your bio. But, like, I would just say like this move to this sense that math is actually a thing that’s useful for more than just a grade; it’s useful for more than just, you know, the societal, you know, adulation that comes from being a math nerd. That kind of thing. And so that, I think that affected a lot of math teaching for me. And, if I gotta, like, summarize math teaching itself in a journey, it went from like, “Hey kids, aren’t I awesome?” to, “Hey kids, isn’t math awesome?” to “Hey kids, aren’t you awesome?” And like that journey was facilitated by lots and lots of people, you know, a lot of personal growth, but at this point, at one point I was like, “Hey, math can help you get records and whatnot. It’s really useful.” And now I’m like, “Wow, your brain’s just doing just really interesting things. I can help you understand how interesting those things are, and maybe make them more interesting, or interesting in a different way, with some help here.” Let’s put a pin in that. That’s the math bio.

Bethany Lockhart Johnson (17:50):

  1. So I have no doubt that if you ask someone in your life, listeners, for their math bio, that you will discover things about them that you never knew. Literally the questions that I have…I have so many question. And Dan is very good at, you know, bringing me back. Bring me back, like, come on, come on. But I just wanna say, overall, your journey seems pretty joyful. It seems pretty joyful. It seems pretty full of confidence. I don’t wanna say “ego” in a negative way, but I wanna say you were buoyed by these experiences that allowed you to feel like math was a place for you to thrive.

Dan Meyer (18:36):

Right.

Bethany Lockhart Johnson (18:36):

Where you could try out things. You could try it out and just, “I could do that!” Right? Like…your relationship just felt very, like…you felt like you had autonomy, agency, perhaps much like you, you operate in this world. Dan, is that, is that right <laugh>?

Dan Meyer (18:54):

Yeah, I think it’s fair to say. And without telling too much of her story, my twin sister with whom I share most things, including genetics, you know—she had a very different experience in math early on. She’s brilliant. She’s a doctor. And not, you know, the book kind of doctor that I am, but like a real, you know, medical doctor. She’s brilliant. But we were—we encountered different messages about who math was made for, early on in, you know, in our entire math learning. And she—we both digested the messages that we were sent, and took, you know, different, different paths because of them, for sure.

Bethany Lockhart Johnson (19:31):

Funny how that works. I thank you, Dan. I do. For in all sincerity, I appreciate you sharing that. And I think that it’s exciting to hear how it influenced your teaching. It feels like you want to cultivate those experiences for your students. And I’ve been in the room when you’ve presented; I was in a room where you taught a class live. It felt like you were making space for the students to have these aha moments. And it feels like in your work at Desmos, and now Amplify, you’re trying to create these products that allow folks to recreate these amazing math moments. Right? And that it’s for everyone and that it’s accessible and it can be very positive. I feel like I have this new perspective on kind of the energy you bring to your teaching. So thank you for sharing that.

Dan Meyer (20:24):

Yeah. Been a pleasure. Thanks for your questions here, Bethany. And it’s been—it’s been fun to reflect on it. And I do—I do feel very lucky in lots of ways. Privileged. Lucky. I know, like—I think the world has been set up for my success in lots of ways, as who I am. But I do just…yeah, I feel—I want more people to experience what it’s like when you walk into a math classroom and it’s like, “Hey, this place is for you. You have interesting thoughts about this. Let’s get ’em out.” So that’s awesome. I would love to hear about you and how you…I mean, we have taught different kinds of kids. You know, I taught kids who I think were somewhat set in, they’re a little bit more solid at secondary in who they are as a math learner. Like “I know who math is and who I am with math.” And I’m really excited to hear what your math bio allowed you to do with students who were perhaps open to the idea that they are very mathematical or at least not yet closed off to those possibilities. So, yeah. What are some of the high, the, you know, the high and low water marks of the making of Bethany Lockhart Johnson, math teacher? <Laugh>

Bethany Lockhart Johnson (21:24):

Thanks for asking, Dan. <Laugh> I’ve shared aspects of my math bio because I think it really informs the way that I talk to people about math and think about math. And I like to share it because I want folks to consider their own journey with math, as we like engage with problem-solving and sense-making and thinking about the students in our classroom. My dad is a math and computer science major. So he had a computer very early on. I wish he had invested in Apple early on when he had like one of the first Apple computers ever. And, sorry, dad, but it’s true. I do wish you had done that.

Dan Meyer (22:10):

I’m sure he does too.

Bethany Lockhart Johnson (22:11):

Oh, he does. So math and computers and conversations about counting, you know, it felt like it was kind of just normal. Like it was around me. And I went to Montessori, which is a private school that—oh, they have some public Montessori—but it’s very self-directed. And so we would have these kind of charts, these goals for the day that you explored. And so we would explore math in very, I don’t know, very organic ways, with these natural materials. And I feel like I excelled at math, but it wasn’t something that I was conscious of. It was just like, “Oh, well, yeah. Math, it’s, you know, something we do.” And then when I went to—when I left Montessori in fourth grade, I remember that year being a lot of like repetition. I was like, well, we did this. We covered this. And except for the mission project that we hadn’t done, that was all new. And that’s it. For another time I’ll share about that. But <laugh> then, they actually, I was moved with a group of students to the fifth grade math class, ’cause we had already done the work that we were doing. And so, it wasn’t that it felt like it came easily, but it did make sense. What we were doing made sense. And then it all kind of changed. There was a lot of change in my family. There was, like, missed school time. And we moved and I went to a new middle school and I was in this environment with students who—it was like an accelerated program. And so I was in this environment with students who were pretty competitive with each other. And I remember going—and I was not from of a competitive environment; like Montessori is not competitive. It’s not about that.

Dan Meyer (24:02):

Right. Right.

Bethany Lockhart Johnson (24:02):

It’s—it was very strange to me that I would be competing against anyone, even competing against myself. And I, you know, knew how to set goals. But it was a different level of energy. And I felt like, because I wasn’t competitive in that nature, I felt like that kind—I felt on the outside of a lot of the energy. Besides the regular, like, middle-school feeling outside of things. And I remember the first friend that I made. Hi, Susan! She had said to me, this was like maybe our second week of school, she’s like, “Oh, at lunchtime, come with me to math club.” And I was like, “OK.” And I remember walking into that room and I had no idea what was going on. And so that was one of the first times where I was just like, “Whoa, I have absolutely no concept of what they’re talking about or what.” These are my peers. I felt very—it was very—it was strange. It was strange. I was like, “This doesn’t feel like a space for me at all.” When I think ordinarily I was kind of excited about the idea of going to math club at lunch, you know? And over middle school, I kind of just got progressively more and more behind. It started with missing some work and then missing more and then checking out. And, you know, the problem was that I really made it about myself. That, like, it wasn’t something that I was then good at or could do. When really it was that well, pre-algebra, I was having a really hard time in like the rest of my life. And so I wasn’t real present in that class. And so when I got to algebra, it didn’t make a whole lot of sense. And then if I missed Monday, Tuesday, and Wednesday, well, Thursday is gonna be hard, you know? And, it just got progressively harder and harder. So I had this great idea that between eighth grade and ninth grade, I was going to take this accelerated geometry class. ‘Cause that was the ninth grade class, it was geometry. And I would take it. It was like geometry in three weeks or something. So then when I entered high school, I would’ve gotten this like jumpstart. But I wish I had said, “Oh, I’ll take this, and then in ninth grade I’ll take geometry.” So like I’ve already kind of gotten a preview of the material. But instead I went to the 10th grade math, which was like intermediate algebra, trigonometry. I had absolutely no clue what was going on. And I had a very, very difficult time and I wasn’t ready for that class. But it was exacerbated by the fact that this teacher felt very free to let the freshmen in that class know that they shouldn’t be in that class. That this class was for 10th graders.

Dan Meyer (26:49):

Oh wow. Oh, wow.

Bethany Lockhart Johnson (26:51):

And we had a rather contentious relationship. And I will never forget that we were in the hallway, and he says to me, “You don’t belong here.” And I’ve talked to—I’ve talked to a girlfriend of mine about her experiences with this teacher and she has the fondest memories.

Dan Meyer (27:13):

Wow.

Bethany Lockhart Johnson (27:14):

She—in fact, almost everyone I’ve spoken with, you know, if we are talking about past teachers or, “Oh, what was that class like?” I mean, they just have these wonderful memories! And for me, my sense of like belonging was already so on a tight rope anyway, that to have this adult, this teacher, tell me, “You do not belong here,” just crushed me. And in hindsight, I think he was saying like, “This class is too hard for you.” I mean, maybe. <Laugh> But all I heard was “You don’t belong here.” And I extrapolated it to connect to math and to anything having to do with math in general. And it just got worse and worse through high school in the world of math. My next math class was even—I had to repeat that class, and still didn’t understand what was going on, and felt more out of place, and, you know, it’s one of those things that I just kind of had started to accept that, I guess, math isn’t for me. I guess I’m just not a math person. Or whatever these stories are that I started to create and build and find evidence for around me that was informing that this wasn’t for me. And I had always done well in school. I was in, you know, accelerated classes. I felt like I was capable of problem solving. And yet in math, I just felt like I had all of this evidence saying that I didn’t belong there. And so when I went to college, I took whatever two math classes were—you know, I was in performing arts and then I did ethnic studies as well. And I remember you had to take two math classes that were GEs. There were these classes that if you don’t wanna deal with math, you go take those classes. And I was like, “Oh yeah, I’ll take that. I’ll take that.” The gulf widened, you know? <Laugh> And I didn’t feel like anxiety when I had to do things like balance my checkbook or navigate math in everyday spaces. It was just, it would never occur to me that I would like seek out opportunities to engage with math or think about it or talk about it.

Dan Meyer (29:35):

That is—yeah, that’s just so wild, how, I don’t know, like it’s often, from the student’s perspective, it is them in a vacuum with math, and the two of them interact and decide if, you know, if they’re right for each other. But from the grown-up perspective, it’s just, you know, it’s a little bit clearer that your story with math was not just you in math, but you with, you know, various external things happening. With family, various teachers playing their different roles—sometimes, you know, really tragic and horrible roles—and then like the compounding mathematical debt that it feels like you were kind of building up, as challenges in one year didn’t get resolved and moved into the next year and so on. And all that makes me wonder—it makes me, like really, really scared, first of all, because I would bet that your teacher might not even remember that moment, that for you is part of just a pivotal moment in your math story, and how many kids have I played—have I been a part of their story in that way and wouldn’t even recall? You know what I’m saying? So that’s a scary part. And then also I’m just wondering, like, how can we, how can we help kids who are in those moments recognize that, “Oh, this kid is like absent a bunch,” and give them more resources to be successful rather than say, “Well, you just gotta try harder now.” Those are things I’m wondering, hearing your story. Thank you for sharing that. I’d love to know more about how you then became a teacher and what all that did for you as you helped students.

Bethany Lockhart Johnson (31:06):

Well, but to answer what you were saying, it wasn’t that I wasn’t—I was always absent physically, but at least like mentally at that point, because it had become so difficult. It didn’t make sense to me. So I was just really checked out in math class, you know? So in hindsight, you know, as a teacher, for sure I can look back, and especially hearing these stories and these experiences my friend had with this teacher and just like chalks up as one of like her most favorite teachers ever! And you know, he clearly did a great job for so many students. But for me, and I think for some people, they would’ve taken those challenges and, you know, it would have fortified them in a different way or something. But for me, I took it upon myself to mean certain things about myself and about my ability and what I was capable of. And so I think, I think in some ways, you know, yeah, it’s all, it’s all interconnected. You know, when your students walk in the door, they’re not this—the things that are impacting them in their life are coming into the room with them. And I don’t think we can take that for granted and think, “Well, if they just focus hard enough…”

Dan Meyer (32:21):

Yeah.

Bethany Lockhart Johnson (32:23):

So let’s go back to my love of Oprah. You know, Oprah talks about living your best life. And something I really appreciate about Oprah is that she encourages you to examine, like, sticking points, right? Like she doesn’t just say, “Well, this…just pretend nothing ever happened, and everything’s fine!” You know, she really talks about making time for reflection. And I kind of got mad that anytime I thought about math, or math schooling came up. Or, you know, whatever, any time that came up that I just felt UGH about it. And I felt like a failure. And I’m like, “You know what, what if I took a math class? And I’m an adult at this point. I’ve graduated. I have—I’ve left college. I have my degrees. But I said, “What if I took a math class?” So I went down to, the city college and I found out that you have to take this exam, like a placement exam. And I went and took the placement exam. And I remember it’s one of the responsive tests where if you get it right, the next question’s a little harder. And so I’m taking it, panicking, because it’s getting more like…I just, you know. And I remember it placed me in like, whatever, Algebra Something, this class that was far more advanced than I thought I should be in. And I was like, there’s been a mistake! You know, and I went to the counselor and said, you know, “I got these results, but I couldn’t answer a lot of the questions on the test.” She’s like, “No, no, no, that’s how it works.” So I go take this class and the class was hard. And I decided that I was just gonna keep showing up. And every day before class, I kid you not, they had a little math…it was like a math center where you could go in and they had a bunch of tables and you’d sit at the table and you could sit and do your work or whatever. If you had a question, you walked up and put your name on a clipboard and then somebody would come and help you. So I did that, every single—like before every single class I would go in. I’d sit there. I’d do the work. I’d go. And I’d get help. Like somebody would walk over and you know, some kid for whom they’re like this…you know, they’re math—it might be you, Dan! It could be you! It could have been you! You know, would walk over and be like—

Dan Meyer (34:38):

Yeah, I was in Help like that. Naw, it’s awesome. Love, love those people. Yeah.

Bethany Lockhart Johnson (34:42):

And you know, I did it. And I did so well in the class. I did exceedingly well in the class. And I said—

Dan Meyer (34:50):

Take that! Take that, everything! Every other math experience!

Bethany Lockhart Johnson (34:53):

I said, what?

Dan Meyer (34:55):

Yeah!

Bethany Lockhart Johnson (34:55):

Wait a second.

Dan Meyer (34:56):

Yeah.

Bethany Lockhart Johnson (34:57):

And it was that I was present. I was not afraid to look at what didn’t make sense. And if something didn’t make sense, it didn’t mean there was something wrong with me. Whaaaaat?

Dan Meyer (35:10):

Yeah. Yeah.

Bethany Lockhart Johnson (35:10):

So I was just in such a different space. And then I took another math class and that class was even harder. And I did the same thing where I went to the little lab and, you know, and it just buoyed me. And it made me realize that, like, this story, that my experience with it was very powerful and that was a real lived experience, but that it didn’t have to define my relationship with math. But then! I decided I wanted to go back to school to become a classroom teacher. And I totally—this was a couple years after that math class experience. So now, you know, I’m healing my relationship with math through basic positive experiences, da, da, da, you know, doing other work. But fast-forward, for a whole number of reasons, decided to become a classroom teacher. And I freaked out. All of my—like, I’m studying for the GRE and the CSET and all the things you have to the hoops you have to jump through to apply to the masters program and the credential program. And I freaked out. I was so close to quitting, Dan. Because I was convinced that the reason I couldn’t be a classroom teacher is because I wasn’t capable in math. Like I was—it was all that resurfaced. And even though I now had evidence to say something different, to the contrary, it was still so visceral. And I was so scared. But I passed that Math CSET.

Dan Meyer (36:47):

Get it.

Bethany Lockhart Johnson (36:47):

I did well enough on the GRE—

Bethany Lockhart Johnson (36:50):

Yes!

Bethany Lockhart Johnson (36:50):

You know, I finished my credential. I worked really, really hard. I had to work so hard in my student placement, when I was student teaching for a fifth-grade class, ’cause I felt like, “Oh my God!” I mean, now I could do the mathematics, but I couldn’t TEACH it to someone, you know? But I had amazing professors at UCI, and my math professors really like just—and my mentor teacher! shout out to Jennifer! shout out to Phil!—these amazing mentor teachers who just loved teaching and who loved—like you said, you have these teachers in your life who you got to see the way that they listened to students. They taught me about that love of listening to students. And then I fell in love with, you know, CGI, cognitively guided instruction, and started learning all about all of these educators who just wanna learn from students’ thinking. And it was just so powerful. And I realize as a kindergarten teacher that I have this really special role in helping to create space for a positive school experience. Like we get to talk about—I talk about my students as mathematicians; they’re writers; they’re thinkers; they’re problem-solvers. And I also want to make space for parents. Some of them, this is their first kid in kindergarten, and they brought all of their experiences, a lot of it negative, that they had had with mathematics. So I felt like it was such an exciting opportunity to help show parents how they could have conversations about math with their students. That also, I hope helped heal their own anxiety with mathematics.

Dan Meyer (38:41):

Right, right.

Bethany Lockhart Johnson (38:42):

Like, I’ve not even scratched the surface of math learning. But I just have such a changed perspective and relationship with math. And I just fell in love with the sense-making. And I fell in love with the journey of it. I still experience math anxiety about a wide variety of things, but I do love it. And I feel like there’s a space for me in relationship with math. And that really excites me.

Dan Meyer (39:09):

Yeah. Wow. Listen to that folks. We, we don’t deserve her! Bethany Lockhart Johnson! She got some math game and could have gone off there and, you know, become an accountant or something. And she chose to hang with kids and their parents. That’s so wild that you’re like rehabbing parents and their self-conception about mathematics at the same time. I think that is so cool.

Bethany Lockhart Johnson (39:32):

Well, thanks Dan Meyer. I gotta tell you, I don’t know when or if I’ve ever shared that much of my math story. So there is a certain amount of vulnerability there. But thanks for listening. And I’m glad that, you know—I think there’s space for us to talk about these things that we care deeply about, but that can be really complicated.

Dan Meyer (39:56):

Yes. Yes. And I love how you you’ve really sharpened the point on what I feel like I know in my brain, but not my body all the time: That individual teachers are huge. Like, individual teachers, and individual moments of teaching, are just not something to play with. You know, like that kid that’s in fifth grade having a tough time, like there could be a month or a day-long period where all of a sudden, like, you’re just like, “Oh yeah, I’m back in the mix; like, me and math are still buddies.” And there’s also like moments that you had, where like one casual word from a teacher can just really put a huge wedge between you and a discipline that needs and wants you and your intellect in it.That’s a really powerful testimonial. Not just for math, but for teaching, your teaching bio.

Bethany Lockhart Johnson (40:43):

I agree with you. And I also, I also…you know, I think we can’t put this—we are human. Teachers are human. And so I’m sure there’s things I’ve said to students. Twenty-second story: a student stapled his finger in my class. <Laugh> And I remember holding his hand and saying, “Why did you do that?” And I wasn’t yelling at him, but it was like, I am sure the panic in my face…like, that’s what he’s gonna remember about kindergarten. Right? <Laugh>.

Dan Meyer (41:19):

Yeah.

Bethany Lockhart Johnson (41:20):

That. He will remember that. He won’t remember the really cool city project we did. He’s gonna remember his teacher holding his hand, in his face: “Why did you do that?”

Dan Meyer (41:30):

Yeah. Yeah.

Bethany Lockhart Johnson (41:30):

You know, so we’re human. And yes, it was awful that that teacher said that to me. There were a thousand other ways that he could have said whatever it was he was thinking. And that did deeply wound me. But despite his influence—because teachers do have a lot of power and I think they need to examine that power, ongoing—it still doesn’t have to define us. So I don’t wanna put this pressure, like—

Bethany Lockhart Johnson (41:55):

Sure.

Bethany Lockhart Johnson (41:56):

“So never ever say anything negative!” You know, we’re human.

Dan Meyer (42:00):

I feel like that kid is currently on some office-supply podcast talking about “your office-supply bio” and saying, “Let me tell you how I first got really freaked out by staples. Here’s the deal: I only use paper clips. And here’s why.”

Bethany Lockhart Johnson (42:15):

“Here’s why.” But then—callback!—he’s going to stumble upon THIS podcast and think, “And because I’m so adept with paper clips, I can beat that record!”

Dan Meyer (42:30):

Though—aaay! whoa! Settle down!

Bethany Lockhart Johnson (42:31):

BOOM.

Dan Meyer (42:31):

Don’t get any ideas, kid. No way. Uh-uh. I don’t like that at all. That’s not what—that’s not what I want to have happen here. No, thank you.

Bethany Lockhart Johnson (42:41):

Well, I’m spent, Dan. I need a nap.

Dan Meyer (42:45):

Yeah. I need a box of Kleenex. I need a nap. I need a—yeah, for sure, a baba. Uh-huh. Definitely. Hey, so look, I’m not expecting you folks out there in the lounge to kind of give us the same depth or breadth. You know, we are here, of course, for your entertainment. Feast on our stories and dramas. But I would love to know at some point, like, what are a few, a few moments that really came to define you mathematically? Came to influence you as a teacher? I think we would do really well for each other to understand that about all of our processes. So yeah, I would just toss in a plug in for Twitter, @MTLShow, or Facebook, Math Teacher Lounge; it would be fantastic to hear from you.

Bethany Lockhart Johnson (43:24):

Thanks so much for listening.

Dan Meyer (43:25):

Thanks, folks. Bye now.

Stay connected!

Join our community and get new episodes every other Tuesday!

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

What Dan Meyer says about math teaching

“Teaching, more than other professions, is a generational profession. The kinds of joyful experiences we offer, or don’t offer, now affect the experiences students that haven’t even been born yet will have years later.”

– Dan Meyer

Meet the guests

Dan Meyer

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Bethany Lockhart Johnson

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

A woman with curly hair and glasses smiles outdoors; a man with short dark hair smiles indoors in front of a blurred math teacher lounge, highlighting valuable math teacher resources.
A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

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

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

The power of phenomena in the science classroom

In conversation, something “phenomenal” is something exceptional, extraordinary.
But in science, an event does not have to be “phenomenal” for it to be a phenomenon.
In fact, a phenomenon in science can be as ordinary and predictable as gravity.
To qualify as a scientific phenomenon, an event simply has to be observable.
That is, a scientific phenomenon is an observable event that occurs in the universe. It’s something we can use our science knowledge to explain or predict. Examples of science phenomena include the erosion of dunes or soil, or the formation of bubbles or ice.
And you know what else is observable? The positive impact of phenomena-based learning on the science classroom. That’s why phenomena-based learning is baked into the Next Generation Science Standards (NGSS).

Let’s take a look at why the power of science phenomena to deliver engagement and learning is, dare we say, extraordinary!

The power of phenomena-based learning in science

Many of us learned science a different way, by starting with a general or abstract principle then applying it in the real world.

But when you start with phenomena in science, you start with the observable real-world event. You ask questions: Why is brown water coming out of the pipes built for drinking water? Where did all the monarch butterflies go? You help students see why science is relevant, right from the outset of the inquiry.

Even everyday phenomena—like sunburns, or vision loss—can generate real learning opportunities. Explaining phenomena and designing solutions helps students learn in context, leading to deeper and more transferable knowledge.

The challenge of predicting or explaining the phenomenon becomes the motivation for learning. And it has the added benefit of being how real scientists proceed with their work!

The power of phenomena science lies in its capacity to bring real life into the classroom. A phenomena-based science curriculum engages students by starting with the real and relatable rather than the abstract. It also trains students to be inquisitive, expansive, critical thinkers.

When you shift to a phenomena-based approach, you help students shift from learning about to figuring out.

How the NGSS support phenomena-based learning

The NGSS help students make sense of phenomena in the natural world and in human-designed machines and products.

Learning to explain phenomena and solve problems is the main way that students engage in the three dimensions of the NGSS—they use Science and Engineering Practices (SEPs) to develop and apply Disciplinary Core Ideas (DCIs) and Crosscutting Concepts (CCCs).

Phenomena-centered classrooms also help teachers monitor student progress. As students work toward explaining phenomena, three-dimensional formative assessment is easily embedded throughout instruction.

How to bring phenomena into the science classroom

The power of phenomena-based learning lies in real-world relevance. Also, phenomena don’t generate learning all by themselves—student questions about phenomena guide teaching and learning.

That’s why it’s helpful to make sure students can connect to the phenomenon at hand. The following are a few steps you can take to integrate this approach into your classroom:

  • Ask students what they’re curious about. Why do leaves change color? What is lightning? Why do ice cubes stick to my finger?
  • Connect iterations of a given phenomenon to students’ lives. When discussing how sunlight warms the earth, a teacher might use examples of the sun heating sand, or asphalt depending on where students live.
  • Use one broad anchor phenomenon for the focus of a unit, and investigate related phenomena that relate to students’ interests and experiences. For example, exploring what we see in the sky will lead to different investigations depending on whether students live in an urban area or far from city lights.

Note that an engaging phenomenon does not have to be flashy or unexpected. Even if students think they already know why it rains, they may discover that they actually can’t explain it. Pushing students to inquire more will help them go beyond repeating things they’ve read, and go from learning facts to asking questions that reveal more about the world around them.

How Amplify Science can help

Amplify Science employs phenomena-based learning throughout the curriculum, which is itself phenomena-based and designed around the NGSS.

In one example, 6th graders take on the role of medical students in a hospital, working to diagnose a patient and analyze the metabolism of world-class athletes. In another, 8th graders work to explain Australia’s high skin cancer rates by investigating how light works and interacts with the world it shines on.

And what’s more, Amplify Science for grades 6–8 received an all-green rating from EdReports!

Learn more.

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

Amplify Desmos Math for the Archdiocese of Miami

Welcome Catholic school educators, 

Amplify Desmos Math thoughtfully combines conceptual understanding, procedural fluency, and application. Each math 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.

What is Amplify Desmos Math?

Amplify Desmos Math supports teachers in building students’ lifelong math proficiency. The program:

  • Supports social classrooms, invites mathematical creativity, and evokes wonder, creating a welcoming learning space where students are empowered to see themselves and their classmates as having brilliant mathematical ideas.
  • Provides teachers with clear, step-by-step moves to build systematically from students’ prior knowledge to grade-level learning.
  • Connects students to each other’s thinking and to an understanding that they can use math to make sense of the world.
  • Enables access to grade-level understanding for every student, every day.

A powerful suite of math resources

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

Data informs instruction. Comprehensive student profiles provide full data on students’ assets and skills, empowering teachers to provide just-in-time scaffolds throughout core instruction and targeted intervention when needed.

Ready to Explore?

Ready to explore as a teacher? Follow these instructions:

Ready to explore as a student? Follow these instructions:

Educational software interface featuring a New York math problem about measuring platform heights using a 9-inch tube, illustrated with a playful, colorful design.

Experience Amplify Desmos Math

Click the links below to explore our interactive digital lessons, where you’ll also find print Teacher Edition and Student Edition pages for each lesson.

For helpful navigation tips and more program information, download our Grades K–5 and Grades 6–Algebra 1 program guides.

You can also watch a product expert walk through a lesson and the available program components with a lesson walkthrough video.

Personalized learning and support

Amplify Desmos Math includes digital, adaptive practice that provides the personalized support a student needs to access grade-level math every day. Personalized Learning activities target a skill or concept aligned to the day’s core lesson, with each student receiving personalized scaffolds based on what they already know. This technology complements daily learning and provides another layer of support to the in-lesson differentiation and instructional guidance provided to teachers. Click here to try a Boost Personalized Learning activity. More activities coming soon!

The Fluency Practice of Amplify Desmos Math uses an evidence-based approach to memory retention—spaced repetition—for the basic operations. Students around the world have answered more than 120 million multiplication questions within our application. Try it now! 

Educational software on a laptop screen showing a student activity to complete a bar graph by categorizing dragonflies, designed for the New York math curriculum.

Contact us

Support is always available. Our team is dedicated to helping you every step of the way. Contact your dedicated Florida representative here for program access, samples, and additional information.

A smiling man with short hair wears a green polo shirt against a plain background, exuding the kind of confidence that comes from teaching an inspiring math lesson.

Jeff Rutter

Field Manager
Miami-Dade and Monroe Counties
jrutter@amplify.com
(727) 407-5801

A smiling person with long blonde hair wears a textured blue top against a plain background, embodying the essence of personalized learning.

Amanda Shelley

Account Executive
Broward County Schools
ashelley@amplify.com
(321)-693-3518

A man with short, dark hair and a full beard smiles confidently. He is wearing a pink patterned shirt and a green jacket, reminiscent of an engaging math lesson. The light gray background subtly complements his dynamic style.

Tom Gantt

District Manager
Miami Resident
tgantt@amplify.com
(305)-546-2979

Welcome to Amplify Desmos Math!

To view this protected page, enter the password below:



mCLASS® with DIBELS® 8th Edition is Washington approved!

mCLASS DIBELS 8th Edition and mCLASS Rapid Automatic Naming (RAN) helps teachers identify COVID-related learning loss and literacy needs firsthand through a quick five-minute assessment that can be done virtually or in person. What’s more, it helps teachers take immediate instructional action that’s right for each and every student.

Now that mCLASS has been approved by the Washington Department of Education and the Dyslexia Advisory Council, every district can confidently address student needs and meet the state’s dyslexia legislation.

A teacher helps a young student with a tablet; below, a girl listens attentively. Icons of a book and a puzzle piece appear on colored backgrounds.

What is mCLASS?

mCLASS® DIBELS® 8th Edition and mCLASS RAN is an integrated, gold standard literacy system for grades K–6.

The mCLASS comprehensive system includes efficient one-minute measures, a built-in Enhanced Early Learning Measures screener, teacher-led and student-driven instruction, intervention, and robust reports for teachers and administrators.

With mCLASS, you can say goodbye to cobbling together tools and second guessing the results of other screeners.

A girl sits at a desk reading and writing, with educational words in the background; text highlights mCLASS as a gold standard in early literacy.

University of Oregon

Together with the University of Oregon (U of O), we have made the DIBELS® (Dynamic Indicators of Basic Early Literacy Skills) assessment that you know and love more powerful and user-friendly than ever before.

As the only licensed provider of the digital DIBELS 8th Edition assessment, we make it faster and easier to understand where every student is in their early literacy journey. As an all-in-one universal and dyslexia screener, DIBELS 8th edition gives teachers actionable data with targeted instructional recommendations to ensure all students’ reading needs are met. To learn more about DIBELS 8th edition as a screener for reading difficulties, download the University of Oregon’s “Dyslexia Screening and DIBELS 8th Edition” whitepaper.

Why mCLASS?

It’s a single solution that meets all of the state’s requirements for Early Screening of Dyslexia.

  • It’s a universal early literacy and dyslexia screener with Enhanced Early Learning Measures and a diagnostic tool in one.
  • It allows for real-time assessment and instant scoring as well as offline assessment capabilities.
  • It includes explicit literacy instruction and intervention strategies based on student performance.
  • It’s flexible and can be implemented in a variety of scenarios, including in-person, remote, and hybrid learning environments.
  • It includes a variety of parent notification resources and at-home reading strategies.
  • It’s continually enhanced with new features and regular updates that are made available to our entire user community.
Tablet displaying a student performance table. Columns for assessment times; rows for performance levels. Percentages and student counts are provided in each assessment area and level.

Instant data and action

Quick and actionable reports provide detailed insight into students’ reading development across foundational literacy skills for classroom teachers and literacy specialists, principals and district leaders, and parents and guardians at home.

What’s more, mCLASS® DIBELS® 8th Edition and mCLASS RAN gives you instant results and clear next instructional steps for each and every student.

Enhanced Early Learning Measures

Early intervention is critical. That’s why we help you meet state dyslexia legislation with one single powerful tool—no additional assessment system required.

Our additional measures in vocabulary, spelling, and rapid automatic naming (RAN) address the full range of skills associated with dyslexia risk and help identify students at varying levels of risk for reading difficulties, including dyslexia.

A young man with a beard, wearing a yellow hoodie, is working on a laptop at a desk beside a bookshelf with a fishbowl and soccer ball.

Assess anywhere

mCLASS has created a collection of resources to help you plan for a variety of assessment scenarios.

Whether your school is engaged in in-person, hybrid, or remote instruction, we know how important it is for teachers and administrators to have a full (and firsthand!) picture of every student’s literacy development.

Personalized practice

Boost Reading (formerly Amplify Reading) is the practice and remediation companion to mCLASS. At its heart, there are three main areas that make Boost Reading a unique and essential supplemental learning program.

  • The program meets all students where they are with powerful individualized instruction and practice.
  • Age-appropriate narratives create a learning experience that leaps off the screen.
  • Research shows Boost Reading improves student performance–particularly among English Learners–reducing the overall percentage of students at risk of reading difficulty.
Young girl with curly hair sits indoors, looking at a tablet device with a focused expression.

Funding

Schools may utilize LAP Funds, Early Literacy Grants, or federal CARES Act funds to purchase assessments to meet Washington’s screening legislation.

Get in touch

Ready to discuss how mCLASS can support your specific needs? Please contact your Amplify Account Executive:

Alicia O’Neil

Senior Account Executive

(425) 890-6103

aoneil@amplify.com

Erin Elfving-Strayhan

Senior Account Executive

(971) 291-9854

estrayan@amplify.com

Kristen Rockstroh

Account Executive

(480) 639-8367

krockstroh@amplify.com

mCLASS® with DIBELS® 8th Edition is Oregon approved!

mCLASS with DIBELS 8th Edition and mCLASS Rapid Automatic Naming (RAN) helps teachers identify COVID-related learning loss and literacy needs firsthand through a quick, five-minute assessment that can be done virtually or in person. What’s more, it helps teachers take immediate instructional action that’s right for each and every student.

A teacher helps a young student with a tablet; below, a girl listens attentively. Icons of a book and a puzzle piece appear on colored backgrounds.

What is mCLASS?

mCLASS® with DIBELS® 8th Edition and mCLASS RAN is an integrated, gold standard literacy system for grades K–6.

The mCLASS comprehensive system includes efficient one-minute measures, a built-in Enhanced Early Learning Measures screener, teacher-led and student-driven instruction, intervention, and robust reports for teachers and administrators.

With mCLASS, you can say goodbye to cobbling together tools and second guessing the results of other screeners.

A girl sits at a desk reading and writing, with educational words in the background; text highlights mCLASS as a gold standard in early literacy.

University of Oregon

Together with the University of Oregon, we have made the DIBELS® (Dynamic Indicators of Basic Early Literacy Skills) assessment that you know and love more powerful and user-friendly than ever before.

As the only licensed provider of the digital DIBELS 8th Edition assessment, we make it faster and easier to understand where every student is in their early literacy journey.

Why mCLASS?

It’s a single solution that meets all of the state’s requirements for Early Screening of Dyslexia.

  • It’s a universal early literacy screener, dyslexia screener, and a diagnostic tool in one.
  • It allows for real-time assessment and instant scoring as well as offline assessment capabilities.
  • It includes explicit literacy instruction and intervention strategies based on student performance.
  • It’s flexible and can be implemented in a variety of scenarios, including in-person, remote, and hybrid learning environments.
  • It includes a variety of parent notification resources and at-home reading strategies.
  • It’s continually enhanced with new features and regular updates that are made available to our entire user community.

Amplify Reading is the proven, adaptive skills practice and remediation companion for mCLASS. Try it for free for the remainder of the school year with a no-cost trial.

Request a free trial today!
Tablet displaying a student performance table. Columns for assessment times; rows for performance levels. Percentages and student counts are provided in each assessment area and level.

Instant data and action

Quick and actionable reports provide detailed insight into students’ reading development across foundational literacy skills for classroom teachers and literacy specialists, principals and district leaders, and parents and guardians at home.

What’s more, mCLASS® with DIBELS® 8th Edition and mCLASS RAN gives you instant results and clear next instructional steps for each and every student.

Dyslexia screener

Early intervention is critical. That’s why we help you meet state dyslexia legislation with one single powerful tool—no additional assessment system required.

Our additional measures in vocabulary, spelling, and rapid automatic naming (RAN) address the full range of skills associated with dyslexia risk and help identify students at varying levels of risk for reading difficulties, including dyslexia.

A child sits at a desk using a laptop. Next to the desk is a bookshelf with books, a fishbowl, and a soccer ball.

Assess anywhere

mCLASS has created a collection of resources to help you plan for a variety of assessment scenarios.

Whether your school is engaged in in-person, hybrid, or remote instruction, we know how important it is for teachers and administrators to have a full (and firsthand!) picture of every student’s literacy development.

Personalized practice

Amplify Reading is the practice and remediation companion to mCLASS. At its heart, there are three main areas that make Amplify Reading a unique and essential supplemental learning program.

  • The program meets all students where they are with powerful individualized instruction and practice.
  • Age-appropriate narratives create a learning experience that leaps off the screen.
  • Research shows Amplify Reading improves student performance–particularly among English Learners–reducing the overall percentage of students at risk of reading difficulty.

A young girl with curly hair sits indoors, looking at a tablet device with a focused expression.

Funding

Schools may utilize Early Literacy Grants or federal CARES Act funds to purchase assessments to meet Oregon’s screening legislation.

Get in touch

Ready to discuss how mCLASS can support your specific needs? A brief 30-minute call is all we need to determine if mCLASS with DIBELS 8th Edition is the right fit for you.

Simply fill out the form below and we’ll be in touch.

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Patric Momsen

District Manager

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Jonathan Cohen

Account Executive

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Immanuel Moon

Field Manager

Welcome, Arizona educators!

The Arizona Department of Education just released its first-ever list of approved universal literacy screeners. According to the state, these screeners “shall be used by schools in the 2020-2021 school year to meet the requirements of both the Move On When Reading (MOWR) legislation and the dyslexia screening legislation.”
 
We’re excited to announce that mCLASS® with DIBELS® 8th Edition and mCLASS RAN is on that list.

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Why mCLASS?

mCLASS® with DIBELS® 8th Edition and mCLASS RAN is a single solution that meets all of the requirements of the law.

  • It’s a universal early literacy screenerdyslexia screener, and diagnostic tool in one.
  • It includes immediate and actionable literacy instruction and intervention strategies based on student performance.
  • It’s flexible and can be implemented in a variety of scenarios, including in-person, remote, and hybrid learning environments.
  • It allows for non-paper assessment and scoring as well as offline assessment capabilities.
  • It includes a variety of parent notification resources and at-home reading strategies.
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Funding

Schools may utilize Move On When Reading (MOWR)Early Literacy Grants, or federal CARES Act funds to purchase assessments to meet both MOWR legislation and the dyslexia screening legislation (A.R.S §15-701 and A.R.S. §15-4704).
 
Visit our CARES Act resource hub or download this CARES Act flyer to learn more.

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More than a test

mCLASS is an integrated, gold standard literacy system that closes the knowing-doing gap. By combining assessment, reporting, and instruction in one, it eliminates the need for cobbled together tools.

  • Data gathered through efficient one-minute measures is made available to teachers instantly.
  • Easy-to-read reports make teachers aware of potential reading difficulties as well as observed patterns.
  • Ready-to-teach literacy instruction and intervention strategies help teachers target specific skill deficits immediately.

Remote learning

mCLASS has created a collection of resources to help you plan for a variety of scenarios for the 2020–2021 school year.
 
Whether your school is engaged in in-person, hybrid, or remote instruction, we know how important it is for teachers and administrators to have a full picture of every student’s literacy development.
 
Download our Remote and Hybrid Learning Guide to learn more.

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Personalized practice

Amplify Reading is the practice and remediation companion to mCLASS.
 
At its heart, there are three main areas that make Amplify Reading a unique and essential supplemental learning program for the 2020-2021 school year.

  • The program meets all students where they are with powerful individualized instruction and practice.
  • Age-appropriate narratives create a learning experience that leaps off the screen.
  • Research shows Amplify Reading improves student performance–particularly among English Learners–reducing the overall percentage of students at risk of reading difficulty.

Get in touch

Ready to discuss how mCLASS can support your specific needs? A brief 30-minute call is all we need to determine if mCLASS with DIBELS 8th Edition is the right fit for you.
 
Simply fill out the form below and we’ll be in touch.

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Tommy Gearhart

Senior Account Executive

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Laina Armbruster

Account Executive

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Laina Armbruster

Field Manager

Request a meeting

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

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

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

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

DOWNLOAD TRANSCRIPT

Jennifer Roberts (00:00:00):

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

Eric Cross (00:00:07):

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

Eric Cross (00:00:12):

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

Eric Cross (00:01:17):

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

Jennifer Roberts (00:01:30):

Donnie goes first.

Eric Cross (00:01:31):

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

Donnie Piercey (00:01:38):

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

Eric Cross (00:02:47):

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

Jennifer Roberts (00:02:51):

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

Eric Cross (00:03:00):

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

Jennifer Roberts (00:03:04):

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

Donnie Piercey (00:03:31):

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

Jennifer Roberts (00:03:35):

Have to guess which one. Yes. <laugh>

Eric Cross (00:03:37):

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

Jennifer Roberts (00:03:45):

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

Eric Cross (00:03:53):

The gaming backpack.

Jennifer Roberts (00:03:54):

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

Eric Cross (00:03:58):

What?

Donnie Piercey (00:03:58):

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

Jennifer Roberts (00:04:01):

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

Donnie Piercey (00:04:13):

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

Jennifer Roberts (00:04:23):

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

Donnie Piercey (00:04:25):

Yeah, evens out. Evens out.

Eric Cross (00:04:27):

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

Donnie Piercey (00:05:31):

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

Jennifer Roberts (00:06:47):

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

Donnie Piercey (00:06:51):

For sure. Yeah.

Jennifer Roberts (00:06:52):

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

Donnie Piercey (00:07:21):

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

Eric Cross (00:07:39):

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

Jennifer Roberts (00:07:47):

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

Jennifer Roberts (00:08:38):

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

Donnie Piercey (00:10:07):

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

Donnie Piercey (00:10:54):

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

Donnie Piercey (00:11:56):

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

Jennifer Roberts (00:12:26):

We did that last week <laugh>.

Donnie Piercey (00:12:28):

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

Jennifer Roberts (00:12:50):

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

Eric Cross (00:12:53):

Please.

Jennifer Roberts (00:12:54):

OK.

Eric Cross (00:12:54):

Please.

Jennifer Roberts (00:12:55):

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

Eric Cross (00:16:17):

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

Donnie Piercey (00:16:43):

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

Eric Cross (00:16:49):

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

Donnie Piercey (00:16:51):

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

Jennifer Roberts (00:20:03):

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

Donnie Piercey (00:20:49):

Oh, a hundred percent, right?

Jennifer Roberts (00:20:51):

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

Donnie Piercey (00:21:09):

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

Jennifer Roberts (00:21:20):

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

Eric Cross (00:22:18):

That’s collaborating! It’s collaborating!

Donnie Piercey (00:22:20):

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

Jennifer Roberts (00:22:22):

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

Donnie Piercey (00:22:26):

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

Jennifer Roberts (00:22:33):

I think Eric calls it Jarvis.

Eric Cross (00:22:35):

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

Jennifer Roberts (00:23:24):

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

Eric Cross (00:23:27):

Sure.

Jennifer Roberts (00:23:27):

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

Eric Cross (00:23:40):

Right.

Jennifer Roberts (00:23:40):

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

Eric Cross (00:24:01):

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

Donnie Piercey (00:26:01):

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

Jennifer Roberts (00:27:00):

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

Donnie Piercey (00:28:03):

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

Eric Cross (00:29:41):

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

Donnie Piercey (00:30:54):

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

Eric Cross (00:30:58):

That was amazing!

Donnie Piercey (00:31:00):

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

Eric Cross (00:31:59):

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

Donnie Piercey (00:32:03):

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

Eric Cross (00:32:27):

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

Jennifer Roberts (00:32:43):

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

Eric Cross (00:32:47):

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

Jennifer Roberts (00:33:09):

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

Donnie Piercey (00:34:59):

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

Jennifer Roberts (00:35:02):

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

Eric Cross (00:35:12):

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

Jennifer Roberts (00:35:16):

Oh yeah.

Eric Cross (00:35:17):

Can you tell me more about that?

Jennifer Roberts (00:35:19):

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

Eric Cross (00:37:08):

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

Jennifer Roberts (00:37:23):

What’s up now, Donnie?

Eric Cross (00:37:24):

Yeah, what are you doing?

Donnie Piercey (00:37:25):

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

Eric Cross (00:39:21):

This is awesome.

Jennifer Roberts (00:39:21):

I wanna do this project.

Donnie Piercey (00:39:23):

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

Eric Cross (00:40:04):

OK, that’s a good matchup.

Donnie Piercey (00:40:06):

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

Eric Cross (00:41:59):

Explosions.

Donnie Piercey (00:42:00):

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

Eric Cross (00:42:20):

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

Donnie Piercey (00:42:24):

Go for it.

Eric Cross (00:42:25):

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

Donnie Piercey (00:42:29):

Oh yeah. <laugh>

Eric Cross (00:42:30):

“Neon” on it. Just all ’80s out.

Donnie Piercey (00:42:33):

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

Jennifer Roberts (00:42:53):

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

Donnie Piercey (00:43:02):

For real?

Jennifer Roberts (00:43:02):

For real.

Donnie Piercey (00:43:03):

So did he talk with that cadence and tone?

Jennifer Roberts (00:43:06):

Yes.

Donnie Piercey (00:43:06):

Like in real life? Wow.

Jennifer Roberts (00:43:07):

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

Donnie Piercey (00:43:14):

That’s incredible!

Jennifer Roberts (00:43:15):

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

Donnie Piercey (00:43:20):

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

Jennifer Roberts (00:43:23):

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

Donnie Piercey (00:43:31):

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

Eric Cross (00:43:35):

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

Donnie Piercey (00:43:44):

Six am!

Eric Cross (00:43:44):

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

Donnie Piercey (00:43:56):

Yelling at kids!

Eric Cross (00:43:56):

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

Donnie Piercey (00:44:02):

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

Eric Cross (00:44:14):

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

Jennifer Roberts (00:44:36):

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

Donnie Piercey (00:44:56):

Hmm.

Jennifer Roberts (00:44:57):

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

Donnie Piercey (00:45:18):

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

Jennifer Roberts (00:45:44):

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

Donnie Piercey (00:46:21):

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

Eric Cross (00:46:35):

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

Donnie Piercey (00:47:04):

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

Jennifer Roberts (00:47:09):

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

Donnie Piercey (00:47:11):

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

Eric Cross (00:47:16):

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

Jennifer Roberts (00:47:28):

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

Eric Cross (00:47:32):

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

Jennifer Roberts (00:47:53):

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

Donnie Piercey (00:51:13):

They know what it is.

Jennifer Roberts (00:51:13):

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

Eric Cross (00:51:53):

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

Donnie Piercey (00:51:57):

Me too.

Eric Cross (00:51:59):

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

Donnie Piercey (00:52:04):

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

Eric Cross (00:52:10):

Of course.

Donnie Piercey (00:52:10):

Of course.

Eric Cross (00:52:13):

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

Donnie Piercey (00:52:20):

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

Jennifer Roberts (00:52:48):

Oh yeah. We did that.

Donnie Piercey (00:52:48):

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

Jennifer Roberts (00:54:15):

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

Donnie Piercey (00:54:21):

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

Eric Cross (00:54:44):

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

Donnie Piercey (00:55:10):

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

Eric Cross (00:56:35):

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

Jennifer Roberts (00:57:28):

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

Donnie Piercey (00:57:56):

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

Eric Cross (00:58:00):

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

Donnie Piercey (00:58:03):

SergeantPepperD.

Jennifer Roberts (00:58:04):

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

Eric Cross (00:58:13):

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

Donnie Piercey (00:58:22):

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

Eric Cross (00:59:35):

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

Donnie Piercey (00:59:39):

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

Eric Cross (00:59:44):

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

Jennifer Roberts (01:00:04):

Thank you for having us, Eric.

Donnie Piercey (01:00:05):

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

Eric Cross (01:00:10):

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

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What Jennifer Roberts says about science

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

– Jennifer Roberts

High School English Teacher

Meet the guests

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

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

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

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A laptop screen displays the “Science Connections: The Community” private group page, with science-themed icons decorating the background and edges.

About Science Connections

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

S2-05: Moving students forward with project-based learning

A promotional image for the podcast "Science Connections" featuring guest Janis Lodge and the topic "Moving students forward with project-based learning." Season 2, Episode 5.

In this episode, Eric Cross sits with K–5 educator Janis Lodge to chat about building on her own science curriculum to create meaningful project-based learning experiences. Janis shares her work teaching Gifted and Talented Education (GATE), and how to use those practices to help accelerate the learning of all students. Eric and Janis also talk about making time for science within K–5 classrooms. Explore more from Science Connections by visiting our main page.

DOWNLOAD TRANSCRIPT

Janis Lodge (00:00):
To me, the reward of having those kids feel like they accomplished something and the way that they can take ownership of it and go in so many different directions, I cannot take that away from them. That’s such an opportunity that if I have the means to do it, I have to just take it and run with it.

Eric Cross (00:18):
Welcome to Science Connections. I’m your host, Eric Cross. My guest today is Janis Lodge. Janis is a third-grade teacher in Orange County, California, with a specialization in gifted and talented education. Recently, Janis was awarded the Orange County Council for the Gifted and Talented Education Classroom grant. This grant funds a project that provides an extension to her third-grade science unit about environments and survival. Through this project, students will think like a biomimicry engineer as they design a robot that is inspired by an innovation found in nature. In this episode, we discuss how she uses interdisciplinary teaching practices to make time for science learning; why gifted and talented education strategies can benefit all students; and her process for creating a problem-based lesson that ultimately earned her a grant for her classroom. And now, please enjoy my conversation with Janis Lodge. One, welcome! Thanks for being here.

Janis Lodge (01:14):
Of course, I am happy to do it. I’m excited for the opportunity.

Eric Cross (01:17):
Of course! Yeah. Elementary school teachers in science, I feel like there’s so many things to have conversations about. And some of the things that you’ve really focused on, I think, are, really, really important. But I wanna start off with your journey of you becoming a teacher in the classroom. And so, would you kind of give your background, your origin story? How did you end up as a third-grade teacher?

Janis Lodge (01:37):
Well, my story is definitely not a traditional story. Before I was a teacher, I was actually living in Maui, Hawaii. I moved there right after college. I went to Chico State in Northern California. And I got a degree in graphic design. And after I graduated, well, I should give a little bit of a backstory. My last summer before graduating, I spent the whole summer in Maui and I just fell in love with it. So when I graduated, I decided instead of applying for jobs in Northern California, I’m just gonna put some resumes out in Maui and see if I can get a job. And I did. I ended up getting a job doing graphic design and marketing for a kite surf company out there. And I ended up just staying for seven years on the island. And after about seven years, I kind of got a little bit of island fever and decided I wanted to come back to California. I wasn’t sure exactly what I wanted to do, but I just had this calling that I need to do something a little more fulfilling with my life. And I started thinking about different ideas and dreams I had. And I actually started thinking about when I was younger, right? I had this dream. If you were to ask me when I was 10 years old what I wanted to be when I grow up, it would be elementary school teacher.

Eric Cross (02:48):
Really?

Janis Lodge (02:48):
Believe it or not. When I was younger, I transformed my bedroom into a classroom. My stuffed animals were my students. I just thought I’m gonna be the next best teacher ever. And you know, as I went through life and kind of went in different directions, I kind of lost sight of that dream a little bit. But for some reason, when I decided to change careers, I just remembered that. And so I just decided to go get my teaching credential and see if it worked out. And it was probably the best decision I made. I feel like everything just fell perfectly into place. I ended up getting a job at an amazing school, and now, five years later, I’m a third grade teacher.

Eric Cross (03:28):
So one of the questions I have to ask, and talking to elementary school teachers, this comes up a lot: How do you make time for science as an elementary school teacher who’s teaching everything? And let me kind of premise this with, at least for those of us in California, and I’m sure the rest of the states too, but we know this; There’s kind of this pressure with pacing and then even, depending on what school you’re at, math and English tend to get the bulk of things. And maybe there’s this perception also of like, well, I gotta teach math and English, and sometimes science gets put to the back burner for different reasons.

Janis Lodge (03:57):
Well, you’re exactly right. The beginning of the year, we were provided with a pacing from the district. And you know, they try to keep us on track, saying, “You should be starting Unit 2 at this time.” But other than that, there’s really no specific guidelines of how many days we’re supposed to be teaching or for how long. But one kind of secret that I’ve discovered is that I can weave science into the other subjects, specifically with language arts. So quite often what I do is I take a look at the language arts standard, and if it’s identifying the key details and the main idea, well I can do that with the science books used from the curriculum. So I’ll just pull those readers and we’ll do the exact same skill, start with the same standard, but we’ll use the content from science. By doing that, we call that kind of like interdisciplinary study. And the students really enjoy that more, too, because they’re using the same skills but they’re diving deeper into the content.

Eric Cross (04:54):
Right.

Janis Lodge (04:55):
And so also that helps build the background knowledge. So then when it comes to time where, if I want to do a science lab or a science investigation, now they already have that background knowledge ’cause we already dove deep into the reading and they can apply that pretty quickly right away into their lab or whatever activity they’re doing.

Eric Cross (05:12):
Can you give an example maybe of how you might pull out something that might be a skill that you’re trying to develop, maybe in an English content, but you would pull that out in a science lesson, maybe? What would you do?

Janis Lodge (05:25):
We’re actually doing that right now. So we’re in our second unit of science and they’re studying inheritance and traits and they’re looking at different organisms to see how they have adaptations to help them survive in their environment. So coincidentally part of the literacy skills is to look at multiple sources, do research, and summarize and make analysis of what they’re reading. And so we have different varied resources. I have websites; I have books, ebooks, videos, and pictures. And they’re choosing which four sources they want to use. And then, then they’re coming up with a summary at the end and then putting together a Google Slides presentation based on whatever organism that they chose.

Eric Cross (06:05):
Did you have a science background before becoming an elementary school teacher?

Janis Lodge (06:11):
Um, none. Besides what I, you know, took in high school and college.

Eric Cross (06:16):
Did you find it easy to kind of lean into the science, or was it something you just kind of jumped into and said, “All right, I’m gonna get after it”?

Janis Lodge (06:23):
What’s interesting is if, you know, throughout my education, my favorite subjects were English and reading and writing and art. And quite honestly, science wasn’t my favorite subject. But I think because of that, that inspires me to come up with creative ways of presenting the information to them and making it exciting and engaging for them, because I don’t want them to feel that way. I want them to be excited about all subjects. And I think that’s the beauty of combining the different subjects like I mentioned before. Like I say, you know, “What would a scholar do? Think like a wildlife biologist. And like with my project, think like a biomimicry engineer.” And so it kind of shifts their thinking. Like, it’s not just, “Oh, we have to study science.” It’s like, “No, you are the scientist; you are a meteorologist; or you are an author. How would an author write about this? How would an illustrator capture this in a photo or a comic strip?” And so, when you really combine those disciplines, you can take it to another level. So even if science isn’t their favorite subject, like maybe it wasn’t for me growing up, they can still take something they’re passionate about and apply the science content to it and they really resonate with them.

Eric Cross (07:37):
You leaned into your strengths. Which are more like, coming into it, you had all these kind of creative strengths. You have that background as a graphics designer. You were into the arts. But then with those strengths, did that kinda give you more confidence to dive into the science work, because you approached it from your assets that you were already coming to the table with?

Janis Lodge (07:55):
Yeah.You said it perfectly. If you look at it from a different lens, there’s all these different ways you can approach science.

Eric Cross (07:59):
I find it in my own science class, too. We’re all teaching the same standards. But how I approach it is through Eric Cross’s kind of personality and understanding and my angle, and another teacher might do it a different way. But we’re all leading to the same destination.

Janis Lodge (08:14):
Exactly.

Eric Cross (08:15):
That kind of leads me to my next question, and this is having to do with the project that you just alluded to. The biomimicry project. So you did a biomimicry project. Would you consider that like a project based-learning assignment?

Janis Lodge (08:26):
Well, this will be the third year that I’ve taught this unit. And when I wrapped it up last year, it’s through the Amplify Science program, and they do a wonderful job of having a lot of investigations and really thinking like a biomimicry engineer. But the final part of the unit was to design a robot inspired by a giraffe, to eliminate invasive plants in a particular environment. And the project part of it at the end was to create a model using Popsicle sticks and pipe cleaners. And then the other part of it was a digital simulation where they would put in different shape structures of teeth, and kind of reconfigure the shape of the mouth. And then they’d put in what they think is effective, and then the computer would say, oh, you’re 98% successful or 70% successful. And I remember at the end of it the students were like, “OK, well when do we make the robots?” And I thought, “Well, we’re just doing the simulation, or we’re just doing this model out of Popsicle sticks; we’re not actually gonna make a robot.” And they just seemed so disappointed. And that’s kind of how the wheels started turning my head like, “Well, what if they actually could make a robot? The only thing stopping me is I don’t have the materials to do it.” So, shortly after that unit wrapped up, coincidentally I saw the email about this grant opportunity that was being offered through the Orange County Council for Gifted Education. And they said, If you have a project that you wanna get funded that would promote GATE strategies within the classroom, then you can submit this proposal. So that’s how the ball got rolling for that proposal. And I researched different robotics kits and different companies and I found one that was really user-friendly for third graders, and not so difficult for me to learn as well.

Eric Cross (10:10):
You’re a risk taker. Like, I’m already seeing this as I’m talking to you. Is that just who you are or do you have a network? Like what keeps you taking these risks?

Janis Lodge (10:18):
I don’t really consider it a risk, because it’s exciting for me. Like I said, I don’t know that much about robotics, but the idea of learning more and then teaching that to my students is exciting. And you know, there was a little bit of risk ’cause I’m deviating a little bit from the curriculum, from the standard lesson, but to me, the reward of having those kids feel like they accomplished something, and the way that they can take ownership of it and go in so many different directions, and on top of that, develop coding skills and computer science skills and robotic skills, to me it was just like I cannot take that away from them. That’s such an opportunity that if I have the means to do it, I have to just take it and run with it. So I think just being inspired by the potential outcomes of what could happen is what made me take that risk.

Eric Cross (11:05):
Did you just kind of create this from scratch? Did you work with a team of people? How did you come to the point where you were ready to present this for the grant?

Janis Lodge (11:12):
Pretty much from scratch. Like I said, the Amplify unit, it does teach them about robotics that were inspired by nature. So some of the materials that they read, and there’s some videos that show really great examples. There’s like a robotic arm that was inspired by an elephant trunk. There’s a book that shows what this field is, biomimicry engineer, they actually show like what they do in that field. And I thought this is a perfect way to apply it because the curriculum’s already pretty much set it up for me; now I just have to add this one final component to it. And essentially it becomes project-based learning at that point, because they’re taking their knowledge and their skills that they’ve learned up to that point. Even the unit that we’re doing doing right now is building up to it. So it’s kind of that final—instead of giving them a test at the end and saying, “OK, tell me what you learned about inheritance and traits and environments,” they can actually take that knowledge and apply it to an innovation or creation that comes out of their own mind, which is so much more powerful.

Eric Cross (12:11):
Do they connect to any other learning goals as they’re doing these projects?

Janis Lodge (12:15):
Well, I think first and foremost, the 21st century skills that from day one I tell them, the four Cs: collaboration, creativity, communication, and critical thinking. All of those are woven in through this lesson. From the beginning, we talked about the whole engineering design process. So from the beginning, they start with a question and oftentimes that actually can be the hardest for them to think about, “What’s a scientific question or a problem that I wanna solve?” If they’re passionate about, maybe, a sport or the environment or something within their school, I go, “There it is. OK, that’s the problem. How can you design something inspired by nature to solve that problem?” And then, from there they go into the planning and the designing and the testing and then the improving. So going through that engineering design process, I think, is what really makes them feel like they are the engineer going through this. And they can make mistakes. They can take risks. A lot of my students I’ve found are afraid to take risks. They wanna make sure they succeed. And they need that challenge to know that if they do fail, that’s OK. We can just revisit this. We can test it. We can look at it in a different way.

Eric Cross (13:27):
You maybe wonder about, how do you assess something like this?

Janis Lodge (13:30):
I think that’s where all those stages along the way are important. Because I wanna make sure that they have a plan and that it’s based on the knowledge that they’ve gained in the unit. I think one of the other things about project-based learning is the final product of how they demonstrate their mastery. And in my classroom I oftentimes give them a choice of how they’re gonna present that to me. So maybe they’re going to write it out like an essay. Maybe they’re gonna create a Google slide. Maybe they’re gonna make a video. Maybe they’re going to—obviously in this part they will have the model, but they’ll have to have some way to explain it to me. And I think giving them that choice gives them the opportunity to show it in the way that’s meaningful to them.

Eric Cross (14:14):
And are you using like a rubric when you’re grading these assignments? Or, how do you actually grade it?

Janis Lodge (14:20):
Yes. So we have a rubric that’s provided to us for the written component that all the students will do at the end. But I can take that same rubric and see if they’ve applied that to the project. So even the verbiage wouldn’t really need to change. I think it’s still important that the students are able to demonstrate this in written form and so all of them will still complete that written component, but to also give them the opportunity to show that in the modality of their choice. I think is really important too.

Eric Cross (14:48):
Right. And you have some students that feel much more comfortable being able to present orally versus—

Janis Lodge (14:53):
Exactly.

Eric Cross (14:53):
—versus writing versus maybe doing a video. I mean, we see that in middle school and in high school too. Students show their knowledge or their understanding of a topic depending on the medium in different ways, and some better than others. Some may find that they can communicate it a lot better orally, but when pen goes to paper or fingers go to keyboard, you might grade it completely different, ’cause they’re not able to transfer what’s in their mind into writing. And the way you’re doing it, and giving that student choice, they probably have so much more buy-in, I’d imagine, because they get to pick what they get to do.

Janis Lodge (15:21):
Right.

Eric Cross (15:22):
You said something earlier and I wanna come back to it. So you mentioned GATE, and GATE is not something that I hear a lot in my world, but it was something I heard a lot when I was in school. There were kind of all of these perceptions and ideas about GATE. You’re a GATE teacher, correct?

Janis Lodge (15:38):
Right.

Eric Cross (15:39):
What is GATE, and what is it like being a GATE teacher? What are the misconceptions, if any, that you might have heard or come across?

Janis Lodge (15:46):
Well, so GATE stands for Gifted and Talented Education. And first and foremost, I think a misconception is that we’re just kind of doing whatever we want; we come up with our own lessons and teach a totally different curriculum. Which is definitely a myth. Because we start with the exact same standards as any other third grade class that you’d walk into. That’s definitely where we start. But I think in addition to the standards, we also implement what are called GATE standards: So they’re Depth, Complexity, Acceleration, and Novelty. And there’s a lot of tools that we use in the classroom, different strategies. You’ll see things like the prompts of Depth and Complexity. We’ll use things like “think like a disciplinarian”; I’m doing “think like a biomimicry engineer.” But really, all they are are just thinking tools and strategies to elevate students thinking and kind of go below that surface level of the content to dive deeper. It also provides opportunities for acceleration. So for example, our last science unit, it was on magnetic force, and there was a handful of students that just grasped the concepts right away, and they’re ready for something else. They’re ready for more rigor. They need some challenge. And so at that point I can kind of pull that group aside and provide some differentiation for them. And I said, “OK, well, you understand the concept of magnetic force, balanced forces. So now what I want you to do is think about something that you’re really passionate about, and how could you use magnetic force somewhere in that field—again to solve a problem, problem-based learning—and present it to me?” So they create this form, it’s like a “think like a disciplinarian” frame, and one of them was “think like a hockey player.” And he’s trying to think of a way that he can incorporate magnetic force. Anyway, I could go on and on. But basically it’s finding what these students’ passions are. And I do that with all my students. And I should probably preface this by saying that even though these are standards that I implement in my classroom because it’s a GATE classroom, these are practices and tools that can be applied to any learner, at any age. And they really just enrich the education for all students.

Eric Cross (18:02):
So your classroom is, is a mixed classroom. There’s GATE students and then general—

Janis Lodge (18:05):
Right.

Eric Cross (18:07):
—students, non-GATE students, in the same class. It’s interesting because I imagine GATE is kind of scaffolding up to a higher level, but then, you also said something that I’ve noticed when I’m creating scaffolds for my students to support them, who may not be at a grade level, maybe in reading or literacy or math, those same scaffolds can help all students.

Janis Lodge (18:27):
So yeah, I don’t just go, “OK, you’re my GATE students; I’m gonna use these practices on you.” I use it for the whole class. But I’m also surprised by having that mix of these different learning styles. A lot of times students are inspired by other students, or, you know, we have this big thing about one of the prompts is Multiple Perspectives. I try to do that as much as I can, because students are inspired by the ideas of their peers. And quite often, if they hear it from a peer, it could be exactly what I just said, but they heard their student say it in a different way and it just clicks and they’re like, “Wow, I get that.”

Eric Cross (19:00):
I think a lot of teachers struggle or, or maybe feel ill-equipped, to support higher-level students. Did you get trained to be a GATE teacher? First lemme ask that question: Did you get special training for this?

Janis Lodge (19:13):
Yes. I went through a course, I think it was like a six-week certification course, through my district.

Eric Cross (19:19):
OK, so you got a special training, which—I’ve been in the classroom for nine years; I teach at a university as an adjunct professor; but I’ve never been trained on teaching gifted or accelerated students. And I’m kind of wondering now, like, do you feel like it made you a better teacher?

Janis Lodge (19:33):
Absolutely.

Eric Cross (19:34):
And if so, how do I get to do this?

Janis Lodge (19:36):
Well, it’s through the county. I mean, anybody can get trained and certified how to teach this way. But, just like you said, I think coming out of that, my eyes were just open, and my biggest takeaway is that these practices, even though they are designed for gifted and talented, it really kind of reshaped my thinking about how I, number one, present material to the students, that I’m doing it in an engaging way, and I’m not just lecturing at them; there’s opportunities for them to collaborate and communicate and use multiple resources. So, you know, how I’m teaching has changed. And then also, how I’m providing opportunities for them to demonstrate their learning. And a lot of that is project-based learning, because once they have the knowledge and skills they need to do something with it. I mean, that’s really the true definition of innovation, is taking the skills or taking something that you’ve learned, and now go with it. Run with it.

Eric Cross (20:32):
How can we take what you’ve learned and then kind of spread it, so teachers have this in their toolkit, too? Like for me, I have multiple ways to be able to support reading and literacy and math and tools and sentence frames. And my students who have special learning plans, I have a have a lot of tool sets for that. I wanna build my tool sets for this other area for my students who want to continue, who wanna run, or go beyond, or even stretch themselves. I think we need to take some of the things that you’re doing and not make them kind of like this exclusive group, but also let’s share it with everyone, ’cause if everybody can access it—

Janis Lodge (21:03):
I agree.

Eric Cross (21:03):
—we might see a lot more potential or a lot more opportunities for students who might not otherwise have them.

Janis Lodge (21:08):
And one thing: My school, I’m really proud to say that my principal has seen that. You know, he’s like, “Well why are we just keeping this in the GATE classroom?” So he’s working on getting all of our teachers certified.

Eric Cross (21:19):
No, I love what you’re doing and your principal sounds, sounds awesome for doing that and recognizing that this can benefit more students than just the ones who, you know, pass the Raisin Test, I think it’s what it was called when I was taking it, or whatever it is back then.

Janis Lodge (21:31):
Exactly.

Eric Cross (21:32):
We’ve talked about project-based learning, the GATE classroom…I kind of wanna come back to you as we wrap up. Thinking about, like, the jobs that you and I do, and the people that listen to this podcast, we have one of the few jobs that people remember us for a lifetime. And I wanna ask you, who was someone that was maybe inspirational in your educational career, that inspired you, or is maybe one of the most memorable? You might have several…but who is someone that was memorable to you in your career, and why? Why were they memorable to you?

Janis Lodge (22:02):
Yeah. Well, obviously, when I was younger, I was definitely inspired by all my teachers. The fact that I turned my bedroom into a classroom…I just was just in awe of this profession. But I think one that really resonated with me was my junior year in high school. I was taking a newspaper class and the teacher was Mrs. Kavanaugh, and she really taught us everything from writing the articles to the editing, to putting the pages together. And I remember in that class I was working on this program called QuarkXPress. I don’t even know if it exists anymore. But I was just fascinated with putting all these pieces together that we’d worked on for so long and getting the articles, picking the pictures, the illustrations and the titles. And I remember her looking at me saying, “You really enjoy this, don’t you?” And I said, “Yeah.” And she said, “Well, I have a computer graphics elective class that you should take next year.” And I thought, “OK, I’d love to do this, this opportunity to expand my knowledge and my skills.” So because of that, I took the computer graphics class the next year and I just remember throughout the whole time, she was just constantly encouraging me and acknowledging my skills. And I find myself doing that as a teacher as well. ‘Cause that really resonated with me. And it’s funny, this summer I was going through some boxes of some old stuff from high school, and I found this handout that I had made, because I remember my senior year of high school, she said, “Janis, you know what? You’re doing such a great job; we have these new, incoming students coming into the newspaper class, and I’d love for you to actually teach them how to do this pagination on this QuarkXPress program. I want you to put something together and actually teach it to them.” I thought, “Wow, she believes in me that much that she’s gonna let me teach this to the incoming students.” But I think my takeaway from that was that she gave me the opportunity to take those skills and actually do something with them, to apply them right away.

Eric Cross (23:53):
Mrs. Kavanaugh. Miss Kavanaugh. Shout-out to Miss Kavanaugh. As you told that story, I heard you as a teacher because I’m hearing she’s applying these GATE strategies in that situation. That’s what that’s what I heard.

Janis Lodge (24:08):
Yeah, absolutely.

Eric Cross (24:09):
She personalized this learning. She created a specialized opportunity. You presented to a real audience that was authentic. It had this personalization in it and this rigor and this challenge and it made a huge impact. And it’s just amazing to listen to you and hear this come full-circle, and now you’re doing this with little ones. And I just wanna thank you for your time in doing the interview, sharing your story with how you became a teacher, your students, the projects that you do. And just like so many teachers, going the extra mile for your kids and bringing in these really important 21st century skills; they’re gonna be so much better off for it. And I know it makes my job easier when I get them in the classroom, so thank you.

Janis Lodge (24:49):
Yeah. Well, thank you for the opportunity.

Eric Cross (24:51):
My pleasure. Thanks so much for listening and we wanna hear more about you and the educators who inspire you. You can nominate them as a future guest on Science Connections by emailing STEM@amplify.com. That’s S -T-E-M at amplify dot com. And be sure to click subscribe, wherever you listen to podcasts, and join our Facebook group, Science Connections: The Community. Until next time.

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What Janis Lodge says about science

“The reward of having kids feel like they accomplished something and take ownership is such an opportunity [with project-based learning] that I have to run with it. Being inspired by the potential outcomes of what could happen is what made me take that risk.”

– Janice Lodge

3rd Grade Teacher, De Portola Elementary

Meet the guest

Janis Lodge is a third grade teacher in Orange County, California. Her career in education started six years ago when she decided to follow her passion of making a positive difference in the lives of young scholars. Prior to teaching, Janis lived in Maui, Hawaii for seven years, working in the field of graphic design, marketing, and hospitality. She has found that her interest in innovation, project-based learning, and inquiry-driven exploration has helped shape her into the educator she is today. STEAM is integrated regularly into her classroom, and her students continually develop 21st century skills through a variety of unique projects. ​​Janis is also a PAL (Peer Assistance Leadership) Advisor for her school, where she helps young leaders (4th-6th graders) cultivate their leadership skills and empowers them to make a positive difference in their school and community. Janis was recently awarded the Orange County Council for the Gifted & Talented Education Classroom Grant, which will provide an extension to the third grade Amplify Science Unit: Environments and Survival.

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About Science Connections

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

S1-04: Connecting with students and caregivers in the science classroom: Ryan Rudkin

Promotional graphic for "science connections", season 1, episode 4, featuring a smiling woman named Ryan Rudkin, themed with science illustrations like atoms and a globe, highlighting how to engage students

In this special episode, our host Eric Cross sits down with veteran middle school teacher Ryan Rudkin. Ryan shares her expertise after almost two decades in the classroom, discussing ways to incorporate aspects of problem-based learning into the K–8 science classroom. Eric and Ryan talk about how to increase parent engagement, involve community members, and add excitement to lessons.

Explore more from Science Connections by visiting our main page.

Download Transcript

Ryan Renee Rudkin (00:00):

I know there’s other goals in mind, you know, standards and test scores. But at the end of the day, I wanna come back and I want them to come back.

Eric Cross (00:35):

My name’s Eric Cross, host of our science podcast, and I am with Ryan Rudkin, middle-school teacher out here in California just to the north up near Sacramento? El Dorado Hills?

Ryan Renee Rudkin (00:46):

Yeah. 20 miles east of Sacramento.

Eric Cross (00:49):

Nice. And I am down here in San Diego. And so Ryan, to start off, what I wanna do is ask you about your origin story, like a superhero. So how did you become a middle-school science teacher to become part of this elite profession of science folks that get to do awesome things with kids?

Ryan Renee Rudkin (01:08):

I would agree with you that it is definitely an elite profession. I got my credential and I thought I was gonna teach third or fourth grade elementary school. And the second day I got called for a sub job for middle school. And I just thought, “We’ll take it,” you know? And by second period, I knew: This is where I belong. The kids, middle school, students are just a species of their own. And you have to appreciate them. And if you do appreciate them, then you’re in the right spot. And I quickly looked at my coursework and I was able to get authorizations in science, history, and English, and I love science. So I chose science. And the rest is history. It’s been a wild ride and I wouldn’t have changed or asked for anything different. I love it.

Eric Cross (02:02):

I definitely agree with you. So, your history—you’ve been in various middle-school classrooms. Can you tell us a little bit about that? What classrooms have you been in? What disciplines of science have you taught or are currently teaching?

Ryan Renee Rudkin (02:14):

I was hired for seventh grade life science, and then I did that for a few years and then I got moved into eighth physical science, and I was there for 12 years. Love eighth grade science. I love eighth graders. Chemistry and physics are my favorite. There’s just so much opportunity for just awesome labs, great conversations, student discourse, all of that. And then the past three years I’ve been in sixth grade and now we’re integrated. So,a sixth grade integrated science and I also teach social studies and a technology design class.

Eric Cross (02:52):

Oh, nice. What do you do in your technology design class? That sounds cool.

Ryan Renee Rudkin (02:56):

Right now it’s mostly internet media and we use WeVideo, it’s an editing-video program, and we produce and put on our school weekly news bulletin. And then we weave in other projects. We do some interdisciplinary projects. Right now my students are working on a mythology God, Goddess, and Monster project that relates to our social studies curriculum. And we’re learning about Greece. So yeah, we just try to give them added projects and they’re using the WeVideo platform. By sixth grade, they’re coming to us now with wonderful skills with all the tech. I mean, if I need help, I ask them like, “How do you do something on Google Docs?” Or, “How do you do something on Drive?” The kids are definitely tech-savvy.

Eric Cross (03:49):

They must love being the teacher in the classroom. They get to—it kind of switches power roles, where they get to teach the teacher something.

Ryan Renee Rudkin (03:56):

Yes. And especially WeVideo, sometimes we’ve had some hiccups, and the kids show everybody, and that’s part of the design class. They’re trying to solve—we’re teaching them how to solve their own problems. So if there’s any kind of issue with anything with the technology, honestly, I usually tell them, “Go ask a friend,” or we kind of shout out, “Hey, who knows how to troubleshoot this?” And the kids are eager to help each other, which is nice.

Eric Cross (04:21):

And they have this authentic experience where they’re actually doing real problem-solving, as opposed to something that we manufactured. Like, those are real things that we have to deal with in life. And that’s exactly like how we solve it, right? We just go ask people! We look it up, and the ahas are genuine too. Throughout!

Ryan Renee Rudkin (04:36):

Yes, especially thinking on the fly. Especially yesterday, I was in the middle of teaching and my laptop froze, and it’s like, “OK, everybodytake a couple minutes, you know, work on this, this, or that while I switch out laptops!” And so I’m modeling, too, how to solve my own problems. And I think it teaches the kids how to do that too.

Eric Cross (04:59):

I’ve always thought it was interesting that when teachers get to teach in real time, how do we handle stress and frustration when it’s really happening? And I think the tech—at times, failure is the real one where you feel this chill or this sweat that kind of comes over you and you’re trying to present or cast or the video won’t play and things like that. I think I’ve done enough times in my years of teaching where now my students know what to do, or they want to come up and help, and we’re good with it. But I remember in the beginning when those things would kind of glitch or go wrong or the wifi goes down, and you’re like, OK, what do we need now?

Ryan Renee Rudkin (05:33):

I think it’s honestly, after the fact, when I think in the moment, I’m not thinking of feeling stressed, but just afterwards, then I’m like, “Oh my gosh, this has just been a wild day.” But yeah, you just have to kind of go with it. And that’s just the beast of middle school. I just added to the list of why we love it.

Eric Cross (05:53):

You said something about interdisciplinary work, and I wanna kind of ask about that. Because it sounds like you’ve had your hand in several different areas of science and grade levels. Working, doing design courses, working with tech. Are there certain lessons that are your favorites to teach? The ones that you really enjoy, or that no matter what, you’re like, “We need to do this; this is such a rich experience for students”?

Ryan Renee Rudkin (06:17):

Yeah. I definitely try to do lessons or activities along the way. I like to do projects at the end of my units. When I taught physics, we did a project and it was mainly an assessment tool called the Wheeling and Dealing. The kids, they would all get a different car. And then they to sell their car. And so they had to pretend to be a car salesman, and they did that with their knowledge of the physics unit. So everything we did on forces and speed and motion. So I like doing culminating projects like that. And you’re kind of tricking them into assessing them.

Eric Cross (06:57):

When I think about your car salesman project, I’m thinking of a bunch of students, but they’re like on Shark Tank, but they’re just littler versions. And they’re doing these sales pitches, but they’re speaking in scientific terms as they’re trying to do it. Do you record these or do they just exist in the classroom?

Ryan Renee Rudkin (07:12):

No…And that was a long time ago, when I taught eighth grade. I wish I had; I wish I had recorded. That was definitely—it was fun, ’cause the kids, they would get their little piece of paper and they—some of ’em didn’t know what car it was. And so they’re like “A Boo… A Boo-gatti? What’s a Boo-gatti?” And then someone from across the room would be like, “Ooh, I want it! Here, I’ll trade you my Ford Focus!” And <laugh> so they would kind of wheel-and-deal which car they would…and then once they got their choice, then they would do the project.

Eric Cross (07:44):

So they’re really embodying this persona of a car salesman. The wheeling and doing back-and-forth and trying to trade a Bugatti for a Ford Focus. <Laugh>

Ryan Renee Rudkin (07:53):

I know. <Laugh> I like to make my class, my learning environment, enjoyable. You know, I gotta be there; they gotta be there. So I know there’s other goals in mind—you know, standards and test scores—but at the end of the day, I wanna come back, and I want them to come back. And I just have that as a priority.

Eric Cross (08:18):

Well, based on the projects that you’re doing and the way that you approach education with students, I can see why middle-school students would want to come back, even if they had the option not to. Just because of the cool things that you’re doing. Now we’re on this—hopefully, fingers crossed—tail end of COVID in the classroom and schools, and I know it’s impacted all of us differently. Has student engagement changed since COVID and if so, how, and what have you done in these last two years to maybe adjust your approach, to continue that engagement and that richness that you provide for your kids?

Ryan Renee Rudkin (08:57):

I definitely—I think for me, I recognize that when the students are in my classroom, I want them to, I dunno, for lack of a better word, just escape the noise at home. And I know we’ve always had students that are going through divorce situations or their dog died, other things, but I think with COVID, it’s definitely been compounded. And just creating a safe place for the kids to want to be and…it’s hard. We’ve had a lot of students that have been out, absent, for various reasons and on quarantine. And they’re struggling with doing work from home, ’cause their parents are stressed and their parents are dealing with their work issues. And so I think just having grace for the kids and just keeping…I don’t know, I guess like I said, I’ve always had student engagement as top of my list.

Eric Cross (10:06):

It sounds like—the things I hear you say really have to do with who these students are as people.

Ryan Renee Rudkin (10:12):

Yeah.

Eric Cross (10:13):

And then as a second, who they are as students. How do relationships fit into your engagement? ‘Cause I’m hearing this connection that you seem to be making with kids as you’re talking about things that are beyond academics: their home life, how they’re impacted.

Ryan Renee Rudkin (10:28):

Yes.

Eric Cross (10:28):

Is there anything that you do to build these relationships, or to connect with your students, to make them feel wanted or feel connected to the classroom or to you?

Ryan Renee Rudkin (10:37):

Yeah, I do. I do a few things to build those connections. And again, this timeframe in their life is so out of their control, their peer relationships, relationships with their parents. And when they’re in my classroom, I want them to feel loved and appreciated. Something I do it’s called Phone Fridays. And in one of the social media groups, someone posted about it, and I’ve been doing it for over a year now, actually. So on Fridays I call parents and give good news. And so I’ll pick maybe one or two students. And it could be academic reasons. It could be behavior, I’ve seen a slight improvement of behavior. Maybe a role model in the classroom. And my goal is to get everybody every trimester. So everybody gets a phone call by the end of the trimester. And it’s funny ’cause sometimes the parents are a little like “Uh-oh”! When they pick up, they see the caller ID, and their school’s calling. ‘Cause Some kids don’t get good calls. So it’s a really—I would say every single parent that I’ve called, I usually get a follow-up email, either to me or my admin, just saying it’s such a cool idea I do this; thank you so much. And yeah, I just call and give good news and just put ’em on the spot. And usually the kids are a little embarrassed, but you can tell, even though they’re kind of—I think they’re faking it, that they’re embarrassed! ‘Cause You know that they got the Phone Friday, and everybody’s like, “Who’s gonna get the phone Friday?!” And so it’s a very big deal in my class.

Eric Cross (12:07):

What a great way to—I mean, it seems like that hits on so many levels. You’re making these positive calls home. You’re praising publicly, which a lot of times can happen where students can get criticized or redirected publicly and then praised privately, which is a lot of times the reverse what we should be doing. But here you are praising them publicly. And then you’re not only building a relationship with yourself, but you’re also connecting them with their parent or whoever is caring for them, because now when they go home, there’s this, “Hey, your teacher called; you’re doing awesome!” So it’s this kind of triangle that’s forming there. I think that’s super-cool and a great thing for teachers to do.

Ryan Renee Rudkin (12:45):

It takes, you know, the last five minutes of my class. I do it every class. And then I have a system. Like I said, I keep track of all the kids. That way, by the end of the trimester I’ve gotten everybody. Sometimes I let the students, whoever I call first, then I let them pick a peer and I tell them, “OK, we have to have a solid reason. Why are we calling?” And a couple times they’ll have a student, like one of my energized ones, they’ll raise their hand. “How About me? How about me?” And I and the kids kind of laugh a little and I said, “Well, how about this? Let’s make a goal. How about next week we’re gonna make a goal and we’re gonna have a reason to call home.” So just working on the kids that need a little push in the right direction. That’s other reasoning to it. But yeah, it’s fun. I love it.

Eric Cross (13:33):

And you have the community. You have this goal setting. We were talking a little earlier about this transition—so you’re becoming this…your school’s going through the IB process, is that right?

Ryan Renee Rudkin (13:44):

Yes.

Eric Cross (13:44):

And we were talking about the ATL skills and one of them is goal-setting management. You already kind of organically do this in your classroom, which is really neat. I know being an IB teacher, a lot of times I find the things that I’ve already been doing and find, “Oh, this is actually an approach to learning!” or “This is something that has a title!” I just thought it was just being helpful! Ah…So the kids are connected. You have this process where you’re calling parents; it’s working; students are involved, so it’s building this community. Now you’re engaging students. Do you have any favorite student engagement tools that you use in your classroom or when you’re teaching that you feel like you get a lot of bang for your buck? There’s so many things out there these days. And so many approaches, tools, web apps. Do you have any favorites that you use?

Ryan Renee Rudkin (14:40):

No. Nothing comes up top of my mind right now. Mostly just projects, like I said. And being excited. I think having my students see me excited about something…and I’m honest when we’re doing something that’s not quite my favorite, then I’m honest about that too. But just having my—like, we just started thermal energy this week and I told my students, I said, “OK guys, I’m gonna weave in some chemistry in there. I’m gonna weave in some particle motion,” and they’re like, “Oh! That’s when you taught eighth grade, huh!” Cause I talk a lot about when I taught eighth grade before. I don’t know, just showing my own enthusiasm, I think, is a good payoff to me. That’s a bang for your buck. Other things…I try to give ’em cool videos and Mark Grober, he’s definitely a favorite of mine I like to show my students. I like to bring in guest speakers from our community. When I taught eighth grade for physics, I always brought in a local CHP officer and they would bring in the radar and lidar guns and the kids would mark off the parking lot and they would calculate their speed. And then they would verify it with the radar gun. Two years ago when I taught math, I brought in a local landscaper company, a father-and-son outfit, and they showed the kids how they would do bids on jobs. And so, relate it to our chapter on volume and area. So just making that connection with real life. Plus it’s just a nice opportunity, too, for the community to come in. With our design class, put on our newscast. And then one of our units in our sixth grade curriculum is weather. And so I brought in a local weatheruh, chief meteorologist. And he actually talked to the students about his job as a meteorologist and then also being on the news and putting on a newscast. So we got him on our green screen and did a little like Mark Finan, you know, little cameo on our newscast for the week for school. So that was kind of cool.

Eric Cross (16:45):

They must have been excited.

Ryan Renee Rudkin (16:47):

Yeah. They’re pretty starstruck by him. So that was pretty fun.

Eric Cross (16:51):

This person was on their local news? So they would know him?

Ryan Renee Rudkin (16:56):

Yeah, he’s on Channel 3 out of Sacramento. Yeah. KCRA Channel 3, Mark Finan.

Eric Cross (17:00):

So all these guest speakers that you have…how do you reach out to these people? And you sound like you get a lot of success. Do you ever get nos? Like if I’m sitting here listening and that inspires me, but you’re getting celebrities and you see a few people…like, how do you reach out to them? And does everybody say yes? How does it go?

Ryan Renee Rudkin (17:21):

Well, usually at my back-to-school night, I always ask the parents if they have a career or hobby that could lend itself to the curriculum. And so sometimes I’ll hear about—students will talk about, like, “My mom’s a doctor.” And so I’ll reach out to parents and just say, “Hey, you know, your kiddo said, you’re a doctor. May I ask what type?” And most of the time the nos that I’ve received are just because of schedule conflicts. You just have to get creative! Look in your community and see what you have. People want to come and talk to kids. I’ve had some presentations that the person is so intelligent and amazing, but they just, weren’t very kid-friendly. I mean, that happens. Butsomeone knows someone. And just ask! I mean, it doesn’t hurt to ask to have ’em come out, come hang out for the day, with my students. Andone time I had a nurse practitioner she was in the cardiac unit. And so she brought in hearts and led a heart dissection with my students. And we did a station set-up. I’ve had elaborate ones like that, or just a mom come in to tell my students about her job as a nutritionist and relate it to our unit on metabolism. And so just did like a little 15-minute Q&A with the kids on nutrition. And I would just say, look at your community and/or post on social media. I always do that. Post in your school’s PTA groups. So the parents know someone, that’s for sure. Or someone’s retired. One time I had—I think he was a grandfather of one of the kids—he was into rocks. And he had a bunch of meteorites <laugh> and brought in his meteorites.

Eric Cross (19:15):

Bring in your rocks!

Ryan Renee Rudkin (19:15):

I know! Right? And he <laugh> just brought in his meteorite collection! I was like, sure, come on in!

Eric Cross (19:23):

That’s one of the things I love about being a middle-school teacher is that my students have such varied interests and I’ll get the Rock Kid every once in a while and he’ll come in and he’ll have all these rocks and crystals. And a lot of times there’s a grandfather that’s responsible for this inherited geologic treasure that they have.

Ryan Renee Rudkin (19:45):

Yeah, something like that—I mean rocks are not my favorites, but I don’t really tell the kids that. I was like, “Sure, yeah, come on in! We can have a whole-day lesson on rocks!”

Eric Cross (19:55):

<Weakly> “This is great!”

Ryan Renee Rudkin (19:58):

Just utilizing your resources. That’s all it’s about.

Eric Cross (20:02):

Well, I think the back-to-school night was really helpful. That’s something that’s super doable. You have a bunch of parents and you just simply ask, “Who do you know? What do you do?” And then just collecting that and then just asking people to come in. I’ve I’ve been reluctant to do it more often than I’ve wanted to, because I haven’t figured out—and maybe you can help me with this—I have three class periods a day plus other class periods that are not necessarily science. And I don’t want to dominate a person’s schedule. Do they tend to be willing to stay all day? Or do you do, one class gets it, and you record it? Like, how do you balance out the speakers with your school schedule?

Ryan Renee Rudkin (20:39):

Mostly they’ll they’ll just come for the whole day. When I taught eighth grade, I had five classes, so that was easy. That was an all-day thing. And then usually I’ll offer to call lunch, have lunch delivered, or snacks during the day. I mean—

Eric Cross (20:53):

Feeding them is key.

Ryan Renee Rudkin (20:54):

Yeah. Just something kind of nice. Donuts in the morning. I mean, you’d be very surprised. Most people that are in the field or retired, like I said, they’re more than willing to come. And even if they have to wait an hour, while you teach another class that doesn’t pertain to it, then they’ll either leave or come back or just hang out in the back and pretend to be a student during that history class that you have.

Eric Cross (21:20):

It’s my own limiting belief where I feel guilty. I don’t think about it. I need to think about it through the perspective that you do, that these people WANT to talk. I just assume everybody’s so busy. But I do know, the times I’ve had speakers come out, at the end of the day, they’re so energized or they’re so happy or they’re so grateful. ‘Cause They’re like, “This is what it’s like to teach every day?” I’m like, “Yeah, this is what it’s like.”

Ryan Renee Rudkin (21:42):

I think too, a lot of parents…usually being being in the stops at elementary. A Lot of parents don’t get the opportunity to come help out in the classroom, because the middle school kids, you know, it’s not very cool or it’s just not needed like in the elementary classes. So a lot of times, like I said, you’d be surprised. A lot of the parents they’re more than happy to come and hang out. And again, some students, they don’t want their mom or dad to be there, but then I talk it up. I’m like, “Everyone’s gonna be so like impressed that your dad’s a doctor,” or “your mom’s a doctor” or —so then I kind of like downplay it. Like, “Oh, whatever, you’re you’re faking it. It’ll be fine. Don’t be embarrassed.” Leading up to their parent coming into the classroom.

Eric Cross (22:36):

Right. Kind of redirect that energy toward something positive. With guest speakers, projects, pacing, all these awesome things that you have going on, how do you find balance as a teacher, as a person? And what encouragement would you give to new or aspiring teachers? We work in a profession that will take as much as you give it. And you fall asleep at night worrying about other people’s kids and we love it. And teachers by personality can just give and give and give and give. But in order for us to last—I’m thinking about those new teachers who are going into it, who are gonna go in and be there before the sun gets up and stay after the sun gets down. How do you maintain balance, taking care of yourself? You’ve been in education for—how long have you been teaching for?

Ryan Renee Rudkin (23:29):

Sixteen. This is my 16th year.

Eric Cross (23:31):

Enough to be that veteran. So how do you find balance? And then, what encouragement would you give to new or aspiring teachers?

Ryan Renee Rudkin (23:39):

I would say each year, pick one or two things to add on. You can’t add on 10 things, even though you’re gonna find 10 things that are awesome. But just make a little list, put ’em in a file, and every year, just get good at what you do and then just add on one or two things. And reflect on what’s not going well that you can get rid of to make room to add something else. Try to be patient with yourself. And don’t reinvent the wheel. There’s so many things out there that you can borrow and make it your own. Again, I think that’s a time-saver, just leaning on your colleagues. And take lots of notes, because then when you do it again next year, you can refresh yourself and, “Oh yeah, this lesson, wasn’t the best…” What can you add in to make it a little bit better? And yeah, I would say just take on one or two things each year. And then by the time you get to, you know, being a veteran, you can do all these awesome things and it’ll feel natural ’cause you’ve been practicing and just adding in one thing at a time. I coached Science Olympiad a bunch of years ago, and Science Olympiad is so rewarding. It’s just so amazing.

Eric Cross (24:59):

What is Science Olympiad, for the people who’ve never heard of it?

Ryan Renee Rudkin (25:03):

Oh, Science Olympiad is so awesome. Google it. I think it’s just ScienceOlympiad.org. It’s 23 different events across all disciplines of science, different topics. And then you have a team of 15 students. And so your 15 students have to cover the 23 events. So for example, if the student’s on the anatomy team, usually there’s a team of two kids they’re gonna study and learn. They provide all the rules and the guidelines. So the students learn and study whatever the parameters are for that year. And then they take a test. And then they compete against other schools. And there’s build events, the engineering events, they can build things like trebuchets matchbox cars or mousetrap cars. Oh gosh, there’s all kinds of things. There’s like a Rube Goldberg device. It changes every year. And it’s so rewarding to see the kids; they pick their area of science that they love. And sometimes you have to put them on an event that they don’t know, and then they end up loving it. It’s so rewarding as a teacher to see these kids that are just on fire and you know that one day they’re gonna go off and do amazing things. They just commit. They commit to their event. And then they blow it outta the water and they win medals and just the recognition…it’s super, it’s just an amazing program.

Eric Cross (26:42):

One of the competitions that’s really low-tech that I’ve taken into my classroom is Write It, Do It. Have you done that one before?

Ryan Renee Rudkin (26:50):

Oh, yes. Yeah. That’s one. Yep.

Eric Cross (26:52):

It’s such a low-tech, simple one to do, but it teaches such great skills. And for those people who haven’t heard of the Write It, Do It project, you create kinda some abstract art out of random crafts. That’s very difficult to describe. You have pipe cleaners and foam and balls and you know, all these different things. And you make it. And then one person on the team is the writer, and they look at it and they write the procedures, and then their teammate, who’s in a different room and doesn’t get to see it, gets all the materials to build it and the procedures, and they have to rebuild it as closely as possible to the actual original. Even though they don’t get to see the original. So they have to rely on their partner’s ability to write procedures step-by-step. And it was fun to watch my students become teammates in that. And they learned how to communicate in a really fun competition. So I expanded it to do it with all of my students as an activity, just to teach them how write descriptively, to write procedurally, to be technical writers. And it’s, it’s fun! It’s fun to see what they build based on what the students say. <Laugh> And it’s also fun to watch them interact with each other, which for seventh graders, usually it’s conflict. <Laugh> But, like, playful conflict. <Laugh> It’s pretty funny to see what they build.

Ryan Renee Rudkin (28:11):

They’re like, “Man, what are you talking about? That doesn’t mean this; it means this!”

Eric Cross (28:16):

<Laugh> I know part of me feels guilty, but not enough to stop the project. ‘Cause I know for some of ’em, it’s gonna be a really trial by fire being able to practice their skills with writing procedures.

Ryan Renee Rudkin (28:27):

But they’re learning among themselves how to provide more details and to be more thorough with their writing and and their thoughts, put their thoughts onto paper. So yeah, that’s a funny event. Definitely.

Eric Cross (28:41):

Earlier you had mentioned something about connecting your kids with kids and students outside of your classroom. What is it that you do with that? Because I thought that was a really cool project. Can you speak to that a little bit?

Ryan Renee Rudkin (28:57):

Yes, I’ve done—they haven’t had it in a few years, but there’s something called the Pringles Challenge. And if you Google that, I’m sure it’s on the Internet still. So you sign your class up, or your classes, and you get partnered with another school somewhere in the U.S., someplace else. And you decide individually teams, whatever they build. And they make a package to ship a single Pringle chip through the mail. And then you actually mail a Pringle chip through the mail. And then your partner team or partner school, they send their chips to you and then you open everything and then you can take pictures and video. And then there was a whole scoring process where you would score when you receive the chips. And then you input all the data on the website so you can see like how your—and most schools would trade pictures, so that the kids found out how their chip survived. March Mammal Madness is so much fun. Again, Google that.

Eric Cross (30:01):

Did you say March Mammal Madness?

Ryan Renee Rudkin (30:02):

Yes.

Eric Cross (30:03):

Like March Madness, with mammals?

Ryan Renee Rudkin (30:05):

Yes.

Eric Cross (30:05):

  1. What is this?

Ryan Renee Rudkin (30:06):

It starts up in March. And you can sign your students up. And that one—it’s not too interactive with other schools, but this is opportunity to get the kids interacting within your site or within your district. Or if you have teacher friends at other schools. There’s like 60…I think it’s 64 animals? And they have this massive bracket that they post. And then you can have the students, I did it—it would be very time-consuming to have the kids individually research each animal. So I just gave one animal per student and so as a class we researched all the animals and then, I think it’s every three days or so, they have these bouts. And it’s all posted on YouTube. Google it. It’s kind of fun.

Eric Cross (30:56):

I’ve already got the website up, ready to go! Folks, everybody who needs to Google this: <articulates carefully> March Mammal Madness. And is it Arizona State University? Is that the main site, ASU?

Ryan Renee Rudkin (31:04):

Yes.

Eric Cross (31:04):

So people, listen to this. Check it out. March Mammal Madness. Look, I’m doing this! I’m already,—you’ve already sold me on this.

Ryan Renee Rudkin (31:14):

It is so much fun, oh my gosh. And then, then the kids—each round, they pick their pick, just like basketball. They do their picks and then you wait for the video. And they do it live on—I think it’s live on Instagram, or the next day on YouTube. And then the kids get all excited. And then usually the kids, whatever animal they got as their research animal, they’re rooting for that one to win, the whole thing.

Eric Cross (31:42):

But we still have time; we still have time to—

Ryan Renee Rudkin (31:45):

You can jump in anytime. Even if it’s already started, you can jump into it. It usually lasts—I believe it’s a two-week from beginning to end. When they do the first round, the wild card, and then all the way to the winner, I believe it’s a two-week process. Oh, maybe three, actually.

Eric Cross (31:59):

I’m already seeing this lead-up to the video being watched in class to see…I’m already thinking about like, “How do I prevent my students from finding the video?” Or like, “When does it go live so that I could be the one to show them so they didn’t go find it early?”

Ryan Renee Rudkin (32:13):

It takes time out of the class, but I believe it’s one of those things where you have to just…it takes 10 minutes out of the class, but it’s important. So when they each round and then the next day, they release the YouTube video. Last year, when it got down to the final round, we were on spring break. And so I told my students, “You guys, let’s do some optional Zooms. And so I had a bunch of kids log on and we all watched the videos together. So that was kind of fun. And then this year, the other thing, the first time I’ve ever done this and it’s going really well is—on social media, I was talking with one of the teachers from Ohio who teaches science and she and I decided we’re gonna do penpals for our students this year. Paper-And-Pen penpals. So that’s been a lot of fun. We just partnered up all the students, her students and my students, and once a month we send and receive the letters to each other. So that’s been a really cool experience.

Eric Cross (33:14):

If you keep doing that, and you need more teachers to be involved, can my students be penpals with your students?

Ryan Renee Rudkin (33:20):

Yeah!

Eric Cross (33:20):

If you open it up to more people? I think that, to get a letter, old-school? Letter in the mail? It would be so exciting.

Ryan Renee Rudkin (33:28):

It is. We mail them, the teacher and I, we just put them all together in one package. But yeah, it’s an actual handwritten letter.

Eric Cross (33:37):

The only letters I feel like I get in the mail now are bills.

Ryan Renee Rudkin (33:42):

Right? Exactly.

Eric Cross (33:42):

But I feel like the digital version of that is if someone calls me, it’s probably bad news. I don’t know if I’m the only one that’s like that, but I’m like, “Who’s calling me? Why aren’t you texting me? What’s going on? Text me first, then call! I need to know who’s going on, and if you’re unknown, you’re going to voicemail.

Ryan Renee Rudkin (34:00):

Exactly. The penpals has been a lot of fun.

Eric Cross (34:03):

You’ve been in education for a while. You’re on the other side of what it’s like to be a student in the classroom. Which can be surreal in itself, when we think about our own experiences as being a student. Is there a teacher or a learning experience that’s had an impact on you while you were a student in school that really stands out to you? And you can interpret the question however you want. But is there someone that’s memorable or an experience that’s memorable that you still carry with you today?

Ryan Renee Rudkin (34:32):

Definitely. My favorite teacher, and we actually still keep in contact on social media is Mrs. Sheldon. She was my fifth and sixth grade teacher. I had the pleasure when I was in elementary school, I was in an all-day contained GATE class—Gifted and Talented Education class. I vividly remember doing so many amazing projects. We built this big, giant—she brought in a big ol’, like, TV box. It was big, big, big. And you could stick like three kids inside there, standing up shoulder-to-shoulder. And we built this big dragon. The head, and we had the whole rest of the class in a big sheet behind us, and we would do a little parade around the school. And she had that thing for years after. They had to repair it every year, and they would do the little parade around school. She did a lot of traveling and when we would go on vacation and then come back, that was always the big deal: “Where did Mrs Sheldon go?” And she had sand from Egypt and pictures from the rainforest. And later when I became a teacher and then I looked her up and we reconnected I did ask her, “Did you go to those places? Or did you, like, lie about it? <Laugh> To get us engaged?

Eric Cross (35:52):

You went for the real questions!

Ryan Renee Rudkin (35:54):

I did. And she laughed and thought that was funny. And she did travel for real. But yeah, she’s an amazing woman. We still keep in contact. And I remember, you know, little things…like we would be out there doing our PE time and she’d have her long skirt, you know, dress on, with her tennies, and she’s out there playing kickball with us. Just a very kindhearted, smart, amazing woman. I’m very fortunate and I’m grateful that we are able to keep in contact. Love social media for that reason. So.

Eric Cross (36:33):

Yeah. And that’s Miss Sheldon?

Ryan Renee Rudkin (36:35):

Mrs. Sheldon. Marlene Sheldon. Yeah.

Eric Cross (36:37):

Shout-Out to Marlene Sheldon influencing the next generation of teachers, with engagement with your world travels and all those different things.

Eric Cross (37:04):

Ryan, thank you so much for one, serving our students. And in the classroom, our middle-school students who need us. I think that middle school especially, elementary school, those years are when students are really starting to decide, “What am I good at?” And the experiences that we create for our students really shape what they believe they can do. These really cool, engaging experiences, these projects that you’re giving them, whether they’re doing these car sales, Shark Tanks, or they’re doing penpals, or you have guest speakers, or they’re designing planets. These are things that students don’t forget. And then when they move on to higher grades, they remember more than anything, I think, how they felt about something. And it sounds like you’re crafting these awesome experiences. And so I just wanna thank you for your time. I know as a teacher it’s very short. And I thank you for being on the podcast with us.

Ryan Renee Rudkin (38:04):

Thank you. This has been a great experience. I just—I really enjoy my students. And I feel very, very grateful and very blessed for finding where I belong.

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What Ryan Rudkin says about science

“I like to make my class and my learning environment enjoyable. I know there’s other goals in mind… but at the end of the day, I want to come back and I want [students] to come back. It’s so rewarding as a teacher to see these kids that are just on fire… and you know that one day they’re going to go off and do amazing things. ”

– Ryan Renee Rudkin

Middle school science teacher

Meet the guest

Ryan Rudkin is a middle school science educator near Sacremento, California. Although she originally thought she would teach elementary students, Ryan connected with middle school and never looked back. Now in her 16th year in the classroom, Ryan also supports teachers in her district with professional development. Ryan’s favorite part of teaching science is seeing students grapple with concepts and explore phenomena.

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About Science Connections: The podcast

Welcome to Science Connections: The Podcast! 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.

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Special miniseries, Episode 1

Language is always an asset, with Kajal Patel Below

To kick off our season focused on how the Science of Reading serves multilingual/English learners (ML/ELs), Amplify Vice President of Biliteracy Kajal Patel Below joins Susan Lambert for a retrospective discussion of the history of literacy education through a biliteracy lens. Together, they discuss the significance of a recent joint statement put out by The Reading League and the National Committee for Effective Literacy. Below sheds light on why this statement is so monumental, and what it means for serving ML/ELs going forward.

Meet Our Guest(s):

Guest on Science of Reading podcast in a Special Mini-Series Episode 1: Language is always an asset, with Kajal Patel Below

Kajal Patel Below

Kajal Patel Below is Vice President of Biliteracy at Amplify, where she collaborates with multiple teams to leads initiatives across Amplify’s Spanish offerings and in service of multilingual/English learners. In this role, she works with national experts in the field and keeps her finger on the pulse of what schools and districts need to serve ML/ELs, especially in Spanish.

Meet our host, Susan Lambert

Susan Lambert is the Chief Academic Officer of Elementary Humanities at Amplify, and the host of Science of Reading: The Podcast. Her career has been focused on creating high-quality learning environments using evidence-based practices. Lambert is a mom of four, a grandma of four, a world traveler, and a collector of stories.

As the host of Science of Reading: The Podcast, Lambert explores the increasing body of scientific research around how reading is best taught. As a former classroom teacher, administrator, and curriculum developer, Lambert is dedicated to turning theory into best practices that educators can put right to use in the classroom, and to showcasing national models of reading instruction excellence.

Retrato de una mujer caucásica sonriente con cabello rubio corto, involucrada en un podcast sobre la ciencia de la lectura, con gafas, lápiz labial rojo y un collar de perlas.

Quotes

“It must be acknowledged that there is more scientific research, or there has been more scientific research, conducted with monolingual English-speaking children, and that additional research related to teaching literacy development for English learners and emergent bilinguals is needed to advance our understanding of their literacy development.”

—Kajal Patel Below

“We have an underserved area that's experiencing a massive growth in student population. And so it's really important to then focus on it. Schools are adjusting, they're quick, they're doing the best they can, but we need to be having these conversations around research [and] best practices so that we can set schools up for success and students up for success.”

—Kajal Patel Below

“I just think we have an exciting future in this country. I was in a classroom last week, I saw some of their writing. I saw them speaking, heard them speaking in two languages fluently, easily, excitedly. I just got very excited. These kids are going to be our doctors and our teachers and our engineers and they’re bilingual or multilingual.”

—Kajal Patel Below

“Their language is an asset, whatever language it is and however much it is.”

—Kajal Patel Below