More Math for More People
CPM Educational Program is a non-profit publisher of math textbooks for grades 6-12. As part of its mission, CPM provides a multitude of professional learning opportunities for math educators. The More Math for More People podcast is part of that outreach and mission. Published biweekly, the hosts, Joel Miller and Misty Nikula, discuss the CPM curriculum, trends in math education and share strategies to shift instructional practices to create a more inclusive and student-centered classroom. They also highlight upcoming CPM professional learning opportunities and have conversations with math educators about how they do what they do. We hope that you find the podcast informative, engaging and fun. Intro music credit: JuliusH from pixabay.com.
More Math for More People
Episode 5.14: Popping Corn and HQIMs!
A bag of popcorn, a few movie-theater secrets, and then the big pivot: what actually makes math materials high quality. We invited Bridget Gunn and Dan Henderson to help us pull HQIM out of acronym-land and into real classrooms, where teachers need time, students need voice, and everyone needs coherence. The result is a candid, practical tour of how curriculum design can elevate thinking without burying teachers in prep.
We break down five components that anchor equitable, engaging teaching—planning around big ideas, open and engaging tasks, student questions and conjectures, reasoning and justification, and teaching toward social justice—and show what they look like day to day. Bridget and Dan explain why “good” materials aren’t enough, how high quality design anticipates student strategies, and where author notes, sample questions, and team routines give you the support to listen, probe, and connect ideas. We dig into full-stack lesson arcs that start with experience and grow toward generalization, so students build concepts instead of memorizing steps.
You’ll hear how routines like rough draft talk shift authority to students, and why simple moves—like a quick door question—can spark belonging that pays off in mathematical risk-taking. We also share adoption advice: look past checklists and ask whether a program centers student thinking, connects concepts across units and grades, and gives practical facilitation cues that free your attention for what matters.
Come for the corn puns, stay for the concrete ways HQIM can transform your classroom culture. If this conversation resonates, follow the show, share it with a colleague, and leave a review telling us which “big idea” you want to see woven through your course next.
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SPEAKER_02:December.
SPEAKER_03:I can't believe it's almost the end of 2025. It's crazy.
SPEAKER_06:It is crazy.
SPEAKER_03:So it's 2nd of December.
SPEAKER_06:Yes.
SPEAKER_02:2nd of December? It is 2nd of December. And what's our national day today?
SPEAKER_00:Today is the business of popping corn day.
SPEAKER_03:That really sounds made up.
SPEAKER_00:No, they are. They're all all things are just made up.
SPEAKER_02:So you know that that wasn't much of a you know qualification.
SPEAKER_00:No.
SPEAKER_02:The business of popping corn day.
SPEAKER_00:Everything about these days is made up. It's totally true. And and the business of popping corn day. And I don't have the facts in front of me right now, but I can tell you I like to pop corn.
SPEAKER_02:You like to pop corn? You are you're gonna have facts about popping corn? I like so I remember when popping corn moved from you had to put it in a pan with oil, and you had to like shake and move the pan, you know, and pop it to Jiffy Pop, first of all, which I don't sure I've actually had Jiffy Pop. When I was a kid, we always wanted Jiffy Pop because it looks so cool. I mean, it looks so cool how it like stands and blows the thing up into a big bubble.
SPEAKER_00:It's all right there for you. You don't even have to do anything.
SPEAKER_02:We were never we never got Jiffy Pop because you know it was more expensive. And they had the Jiffy Pop that came in different colors, I think, even. It was like rainbow jiffy pop. And then it moved to the air popper. Like that was a big deal when it moved to the air popper because then you could put it in, it would all spin around, it would pop out into the bowl, and then into microwave popcorn.
SPEAKER_00:Yep.
SPEAKER_02:Which pretty much feels like the only way I would make popcorn now.
SPEAKER_00:Really? I I still make it it it it's a pan, but it has like a crank. Oh so I I put the oil and then I have I have like three or four bags of specialty corn that I choose from.
SPEAKER_02:So is the is the pan like a popping corn pan?
SPEAKER_00:It's a popping corn pan. I I think it's actually called like the popping corn number two or something like that.
unknown:Oh.
SPEAKER_02:I don't know what the popping corn number is. That makes sense. And from then a third popping corn pan or any other third popping corn pans.
SPEAKER_00:Definitely a hand crank situation, so you don't have to shake the pan.
SPEAKER_02:You just burn.
SPEAKER_00:Yeah. And I I remember the air popper. And my folks still have an air popper.
SPEAKER_02:Air popper was cool because you couldn't ever burn the air popper pretty much.
SPEAKER_00:That was pretty cool. It was fun to watch catching your mouth, like if you held it over your head or whatever. I don't I didn't really do that.
SPEAKER_02:I mean it was yeah.
SPEAKER_00:I don't like that. I'm I made that up.
SPEAKER_02:That was I didn't like it that it you it was hard to get the butter on it because you had to like the butter was on a little pan, the thing that was supposed to drip on, and that didn't really work. You just had to pour it on afterwards.
SPEAKER_00:We had we had one. You know how I was talking about the hand crank? The crank would go by itself, like it was motorized. And at the top of the dome where the it was gonna pop, you put butter on it, and it was like a filter that dripped the butter on as it heated up. That was pretty good. Did it work?
SPEAKER_02:Yeah.
SPEAKER_00:Yeah.
SPEAKER_02:Yeah. I feel like the auto butter things didn't work as successfully. Maybe they didn't make as much butter as I wanted. When I I pretty much wanted like butter, you know, popcorn dipped in butter when I was a child.
SPEAKER_00:You know. I think my second or third job was working in the movie theater.
SPEAKER_02:At home.
SPEAKER_00:And just to put some context to it, Bill and Ted's Excellent Adventure.
SPEAKER_02:Nice.
SPEAKER_00:Pet Cemetery, those kind of movies were coming out at the time. But I was an usher. And it was actually one of the first public speakings I'd have to do because I was collecting money for like the Will Rogers Institute and stuff like that. And with a popcorn, two things. One, when they needed butter, I would have to go get this five-gallon thing of butter-like substance.
unknown:Right.
SPEAKER_00:And the butter-like substance, instantly my face would break out in acne just by opening the can, right? Like whatever I don't even know what it was, but it was gross. Second thing is, it's tricky if you go to the movie theater during the morning because you're getting last night's popcorn. You are not getting fresh popcorn because we had to save it because it's so you know, popcorn's expensive and valid. Oh, yeah. Yeah, exactly. You don't want to repop that stuff.
SPEAKER_02:Waste all those things. Oh man.
SPEAKER_00:I remember those days.
SPEAKER_02:Yeah. Yeah. Popcorn, I start with popcorn that has like sometimes it has too much salt. Like it has to have just the right amount of salt.
SPEAKER_00:Too much salt is a bad thing. Too much salt is right.
SPEAKER_02:I remember I like I like that now, you know, I can go to places and I can get like, you know, basically like cattle corn or you know, fancier popcorn. They just make corn.
SPEAKER_00:I had a friend who asked me one time, do you want some yeast on this popcorn? And the the theater had like popcorn yeast or whatever. Yeah. Sure. But they mistaken the yeast for a for granulated sugar. They were like in the same container. We ate it, but we still ate it. I'm sure it was really it wasn't it wasn't that good.
SPEAKER_02:It wasn't what you expected, but yeah, yeah, interesting.
SPEAKER_00:Yeah.
SPEAKER_02:So just the other just the other night I went to a Broadway show here in Portland, Shucked.
SPEAKER_06:Okay.
SPEAKER_02:Which it's not really about corn, but corn is kind of the You Shuck a corn. Yeah. Well, uh yeah. But it's not like it's not like a musical about corn. It's a musical about this really, really small town that you know grows corn, and corn is kind of the center of the theme. But I would say more more than that, it's really about corny jokes. Like it is like just full of puns, non-stop, not like continuous and like groaners, like so, and and and you know, some very like you know, definitely not always in the like mainstream, you know, like clean jokes, but like it's you know, it's along the lines of you know, Book of Mormon, or some things that are pretty like this. But uh very, very it's so so funny. So, so funny. I was sounds amazing. It was far more hysterical than I anticipated. So yeah, very good. Very cool. I'll have to check it out. Yeah, definitely. If it's if it's in your area, I highly recommend it. I would definitely either, and like I say, it was very funny.
SPEAKER_00:Okay, very entertaining. Excellent.
SPEAKER_02:So, what are you gonna do for the business of popping corn?
SPEAKER_00:I am see you stress the business part. I was just gonna pop some corn. Well, I know.
SPEAKER_02:But if I'm celebrating, the business part of it is apparently an important part of the day. They wouldn't have labeled it, you know, the business of popping corn.
SPEAKER_00:Maybe I'll actually read the label on the thing to see what kind of business produces.
SPEAKER_02:Your business could be, you know, the the companies that are making it, but it also could be the busyness of popping corn.
SPEAKER_00:I'm gonna I'm gonna get busy and pop some corn. How about you?
SPEAKER_02:I'm I think I'm definitely gonna eat some popcorn today. I might not pop it myself, but it will be popped corn.
SPEAKER_00:I love it.
SPEAKER_02:So there you go. Enjoy your popped corn. Indeed, so so we're here today with Bridget Gunn and Dan Henderson. Hi. Bridget works on yeah, that's Dan. Bridget works on the PL team with us, and Dan is on the curriculum assessment team. And we brought them here today because we know they are people who can answer our questions about HQIM.
SPEAKER_00:Yeah, what's that actually?
SPEAKER_02:Beginning with yeah, did you know what HQIM is, Joel?
SPEAKER_00:I had to look it up.
SPEAKER_02:Okay, what'd you find out?
SPEAKER_00:I think it's high quality instructional materials.
SPEAKER_02:I think I think that is targeted.
SPEAKER_00:But I I did have to look it up for sure. Yeah. And I saw that there was a very nice article about well, actually, I it seems like the whole publication was about HQIM, but there was an article in there. And I and I'm not a big acronym fan, so I might start saying high quality instructional materials. But Bridget and Dan were authors of this article.
SPEAKER_02:They were. They were amongst the authors of this article. So we brought them here to help answer our questions about HQIM. We already answered the question, what is it? Well, what does it stand for? Yes. But my first question, beyond what it stands for, then, is what is what what makes something a high quality instructional material like? I feel like this is not just something you dub upon yourself. Someone has to put some like criteria on it. So that's our first question, Bridget or Dan.
SPEAKER_03:What is an HQ? What makes something an HQIM?
SPEAKER_01:Bridget, you want to try?
SPEAKER_03:Sure. I'll try. You're gonna have to nose goes or something.
SPEAKER_04:So we kind of took took the idea that like there are a lot of good curriculum materials or instructional materials, I guess, that like follow the standards and have math problems in them. But that high-quality instructional materials kind of go one or a few steps further than that. And then we looked at um the California math framework. They have a section on equitable and engaging teaching. So we kind of looked at high-quality instructional materials through that lens. And they have five components of equitable and engaging teaching. And we think that high-quality instructional materials do those five things and really help teachers on their journey to equitable and engaging teaching.
SPEAKER_00:And what are the five things?
SPEAKER_04:The five things are perpleid teaching around big ideas, to use open and engaging tasks, to invite student questions and conjectures, to prioritize reasoning and justification. And this is also kind of our interpretation of these five things, but that though doing those four things can help you teach towards social justice, which is the fifth component of equitable and engaging teaching.
SPEAKER_02:And so are you suggesting or saying that if something is a high quality instructional material, it does those things automatically? Or that would be included in like if it meets the criteria of being an HQIM, it's gonna do those things? Or are you suggesting that some do that better than others? Or like how connect those two for me?
SPEAKER_01:So California just adopted a bunch of curricula, and states across the country are looking to adopt new curricula, and schools everywhere are looking at curricula and trying to decide what to pick. We were thinking what do they really need to know in addition to like checking your ed reports or whatever, what do you really want to look at? Uh we identified some things that good curriculum do that we think high-quality curriculum could do a little bit more. One way to think about it is like like uh good material, sorry, like a cookbook. They give you good recipes and clear steps, you can follow all those things. But a high quality material is more like a like a master chef apprenticeship, where you get the recipes, but you also learn how to think about how things go together and how to rise given what you've got. That sort of thing.
SPEAKER_03:So I like that analogy.
SPEAKER_06:Yeah.
SPEAKER_03:So so what other things did you tell us? Did you talk about then? So how do those things go together?
SPEAKER_04:So one of the things we talked about is well, we kind of think that all five of these things really work together. So planning teaching around big ideas is this idea that math concepts are interconnected. And so instead of learning just like your six times table, you might talk about multiplicative thinking and reasoning, which is like additive reasoning, subtractive, then moves into proportional reasoning. So like teaching around big ideas helps students connect what they are currently learning to things that they already know and sets them up for success in future learning.
SPEAKER_01:Should we clarify that like so we think like good materials uh do that? They help you plan instruction around big ideas. We should not adopt materials, they don't do that. On top of that, we think high-quality materials also offer support for student interaction. Like uh CPM uses those study team teaching strategies.
SPEAKER_06:That would be one of those supports efforts. I mean quiet now.
SPEAKER_02:There's no there's no need to be quiet.
SPEAKER_00:I know.
SPEAKER_02:Well that's a podcast, someone has to be talking.
SPEAKER_00:What when I was looking over the article, it it seemed it seemed like, okay, there's five things. Those five things seem pretty big to me. Like, like it it's not a simple one, two, three, four, five checklist or something like that. Like it's it's a bigger idea than that. And what stood out to me, and I'm interested to hear what you have to say about this, is that it it's not just about the students, it kind of frees up the teacher to be in a beneficial teaching mode almost.
SPEAKER_04:Yeah, I feel like the the kind of difference between good materials and high quality instructional materials is that high quality instructional materials do free up the time. So you're not sitting there as a teacher figuring out, okay, where do I put this lesson so that it connects to all these things? Because we're about to do this. Like that's a lot of brain space for one person to do on their own. So high quality instructional materials kind of free you of that brain space. They give you the open and engaging task that's already connected through a storyline that naturally invites questions and conjectures so that you can step in and figure out how to facilitate those conversations.
SPEAKER_05:Right.
SPEAKER_04:And it might even help you facilitate those conversations by providing, you know, an author's vision that says, hey, when we wrote this, this is what we were thinking. These are questions we might ask in our classroom. Um, consider doing this activity, consider doing this exhibit visit and asking these questions as your closure for the day.
SPEAKER_00:And again, what made me think about that too is your conclusion. I kept thinking I kept going back to that teacher lens of that your thinking matters, your voice matters, you matter, and reflect and revise. And with a high quality instructional material, it's just seemed like that was able to happen in a more what's the right word, like a conducive space, a free space, or like a I'm saying, I'm probably saying this all wrong, but like a visionary space of like as a teacher, I appreciate that that what I bring to the table matters as much as what I'm trying to let students bring to the table.
SPEAKER_04:I completely agree with that. I feel like I feel like that's why so in that framework, they talk about teaching towards social justice as like not necessarily bringing just bringing in like social justice topics or topics that you might think of when you think of that phrase, but that there's an idea that we are trying to develop students into students with positive math identity and agency. You're right, Joel, like high-quality instructional materials kind of create the environment where teachers can then have some breathing room to step back and really observe what's happening in their classrooms, really like try to understand how their students are understanding these concepts and then facilitate discussions around them. So you're kind of gaining back that agency of like, as a teacher, what's going on in your own classroom. Because you're kind of like putting the pieces together to create this, this environment.
SPEAKER_02:I can see how I can see how this would also be. So I'm like what I'm seeing and hearing is like that the high-quality instructional materials and those five things, right, are really kind of creating the conducive environment for the student centered classroom and bringing kids into the conversation and those pieces and changing the teacher role, right? Is what I hear you saying. Like the teacher role shifts and changes. And it and at the same time, the teacher role needs to shift and change, right? You couldn't just bring a high-quality instructional material into your classroom and then just teach the way you were always teaching. Does that feel accurate?
SPEAKER_01:Yes. If I was just I'm sitting over here kind of being quiet and thinking about the difference between my master's degrees in curriculum and instruction, and that's the sort of reality that's playing in my head right now. Instructional part obviously being instruction and the curriculum part being the materials part. Well I'm trying to think through parsing out what your question is about like how does the instructional material shift your instruction and vice versa. That's why I'm being quiet. You can edit that whole thing out if you want to, but no worries.
SPEAKER_02:It feels like I was gonna say, what is your brain putting together with it?
SPEAKER_01:Well, it sort of feels like the thinking about the instructional shifts, right? Like the center of student voice and putting equity in the center of the the conversation is two big things that kind of have to happen. If you're not gonna listen to what students say and take seriously their ideas, then there's nothing the materials can do for you. But if you are willing to take that leap and listen to students, then instructional materials can guide you with the kinds of questions that will be open and engaging for them that'll help change their perspective of the world and of math and of themselves. So that's the kind of instructional piece. I feel like we have like specific pieces embedded in the CPM curriculum that do that, right? Like we build in rough draft talk and all the siding team strategies like SWAT meets and things like that. And those routines shift the authority of the classroom.
SPEAKER_06:Which make it more equitable just from the job. That's uh instructional piece. The materials piece, I'm thinking like the focus on the big ideas.
SPEAKER_01:Super traditional instruction is organized around like the very small day-to-day, can I do this skill? Can I remember to carry the one when I'm adding multi-digit numbers or whatever? Big idea just keeps happening over and over and over and over again. And this like within the the seventh grade curriculum, right? We just have this idea of proportional reasoning just keeps happening, right? It starts on that first date with the pencil topic, and it just keeps going. And you just encounter it over and over and over again in these different ways. And that helps students connect it to the world and wrap their heads around a really big shift. Right. When you think about it, like in elementary school, the only way to think about difference between numbers is like six is one more than five. Right. Like that's the extent of your ability to think about difference. That's super advanced if you're in second grade. It's not so advanced when you're in seventh grade. Because then you learn to think proportionally, you think okay, six is twenty percent more than five. Right. It's like that kind of relationship. What else is like what's what's 20% bigger than than an old 20? It's not just one more again. It's a different thinking. So it's a big idea, and it takes some time to wrap your head around and it just keeps happening over and over and over again. It happens in a ton of different contexts and all that stuff, but it's just a bigger thing that you have to think about a time.
SPEAKER_06:I'm angling, I'm sorry. No, you're fine. No.
SPEAKER_02:Well, and what I'm hearing you say is that like like the material, the the curriculum materials themselves can have to lend themselves to this different, these different shifts in these ways of thinking, right? And shifting what's happening. And the teacher also shifts what they're doing. And these two things will happen together, right? Like you can't really it's hard to do one without the other either way, right? It's it's hard to move and do the do these, make these five changes, right? Without a highly quality instructional material. And it would be challenged actually to like stand and deliver with a high quality instructional material. They don't, they don't, they're not, they're like co-compatible in that way.
SPEAKER_01:Yeah. Is that co-compatible is an interesting phrase. But I know I think they're they're almost codependent, right? Like you can't really have one without the other. Yeah. Think about like the we we made a point, I think, in the article about full stack lessons. Because she's the one that most recently actually read the article again. We did we did say that, right? Uh Excel. Yeah, so like the that full stack idea is is the idea that like you start with some experience and then you describe it linguistically, and then you start to ask questions about it, or then estimate and error, and then you finally calculate something, and then you can reveal what the answer is, and then you can flip it around and change the given and the little yeah or the question uh or helps you get like a full range of like exploration on a question. Um and you can't if uh if the materials aren't aren't there to support it, then you're not gonna successfully do that in your lesson. But if you're not trying to do that in your lesson, high quality materials are gonna feel really weird. There's gonna be a whole bunch of stuff that's kind of left on the table.
SPEAKER_00:So they're back to that codependent phrase.
SPEAKER_06:Mm-hmm.
SPEAKER_00:Yeah.
SPEAKER_06:Mm-hmm.
SPEAKER_00:I and I I I I like what you're saying there too about so the the material the high quality material of what I'm hearing you say is it's gonna back you up. So it's a shift. Like when we're talking about a shift, sometimes I think, oh, uh, as a teacher, I must be doing something wrong because I need to shift this way. But maybe what you're doing is okay and it's promoting, but what a high-quality material would do is back you up in opening multiple avenues, opening discussions, opening different thought processes.
SPEAKER_01:Yeah, exactly. It would it would back you up in it uh in a couple of specific ways that we sort of try and highlight or like we'll point out in our in our teacher notes or in our author's vision uh what we think students will probably say based on our experience with students and field testing and all that. And then we highlight what kind of responses you might give to those things. And we also highlight like extension questions, we call them encourage deeper thinking questions. So there for everybody to like, hey, you had this thought, you may as well explore the landscape of math that's around this problem. Um when I was a when I was a geometry teacher, we were playing around with Pythagorean triples just because we had a day before Thanksgiving, so this is well timed. Um playing around with Pythagorean triples, and uh had a group of students just be like screwing around and were like, well, what about A to the third, B to the third equals C to the third? And I was like, that's interesting. See if you can find it, right? Like, does it work? Try some numbers. They couldn't find any. And I asked them, like, why? Why do you think that is? Like, can you give me an argument for why that's not working at all? Um they thought about it for a couple minutes and they decided that instead of that they would try another even number. They'd try A to the fourth power, B to the fourth power, and C to the fourth power. And I was happy with that. They were fine, they were continuing their thinking, right? It's a nice big open exploration. I didn't have the heart to tell them, but or you'll hear the podcast. You get that that openness is there for them to explore, and you want to encourage it as long as they're thinking mission accomplished.
SPEAKER_02:So you're good. You're good. As we so as we get toward it, kind of the end of the time that we have here, like what are the big things, the big takeaways that you would want someone to remember as they're thinking about high quality instructional materials and good teaching?
SPEAKER_01:Well, my short and sweet answer is by CPM curriculum. Well, shouldn't say that on your podcast. Yeah. What's my what's my longer answer to that, Bridget?
SPEAKER_04:Well, my longer answer. I'm really encouraged by again, I live in California, so I guess I'll say the California framework matters out here. And I'm really encouraged by the focus on I think developing an environment where students feel like they matter in a math classroom more than their answers matter. So I feel like a high-quality instructional material is going to give you the space as a teacher to kind of find those moments when your students are having really brilliant ideas and allow you to dive into that conversation with them. We talk about um a lesson that's in our eighth grade curriculum about like finding as many equations that have a solution of four as you can, and the idea that a student could kind of in their middle school way write down x equals four and say that I'm done is like the best start to a conversation. Is that a correct answer is what does it mean to be, you know, have a solution of four. So I think finding instructional materials that help you say you're right, or yeah, explain that to me more so that your students start to really feel as though they're a part of this math classroom community and learning community as as you can.
SPEAKER_00:Yeah. I'm I'm excited. You know, that again, this publication is the CMC communicator. So I to hear districts, states, schools talk about this kind of thing, it'll be interesting for me to follow what unfolds from these discussions.
SPEAKER_01:One of the things we didn't highlight in our article that I think I would look for if I was looking for a curriculum for my own uh school or my own students, is sort of the care with which students' ideas are centered the whole way through. And then we highlighted some ways that it's centered uh within a lesson. But uh we've also included door questions in our in our latest core connection courses and in the inspiring connection courses. And I heard the greatest thing. At the conference this year. Richard, I think you were there for that conversation, actually. So tell me if I got this wrong. It starts with that door question. You ask a question at the door, it's just getting the kid's opinion on random stuff. Right. It's intentionally not related to the lesson. It's intentionally just out of the blue. Like every day. And you get this moment with the kid or with your your students. It's like they feel like their answer matters to you in some way. What they have to say matters to you. And then that translates like eventually like, oh, maybe they care what I think in English. And then that translates you, like, oh, maybe they care about me.
SPEAKER_06:I love that.
SPEAKER_03:That's awesome.
SPEAKER_02:Thank you so much for coming on the podcast today and talking about high-quality instructional materials and the California math framework and how teachers can be better teachers with the materials they're using. So we appreciate that.
SPEAKER_04:Thank you for having us.
SPEAKER_01:Yeah. Yeah. Come back again. I can hang up and Bridget can answer all the questions, and I'll be quiet this time.
SPEAKER_02:So that is all we have time for on this episode of the More Math for More People podcast. If you are interested in connecting with us on social media, find our links in the podcast description. And the music for the podcast was created by Julius H and can be found on pixabay.com. So thank you very much, Julius. Join us in two weeks for the next episode of More Math for More People. What day will that be, Joel?
SPEAKER_00:It'll be December 16th, National Underdog Day. So looking at all the underdogs. Typically, I think of underdogs in a sports context, but there's underdogs everywhere that we can take a look at and talk about, and I know that Misty will have some stories as well.