Kim Montague, I Have, You Need: The Utility Player of Instructional Routines ROUNDING UP: SEASON 4 | EPISODE 3

In sports, a utility player is someone who can play multiple positions competently, providing flexibility and adaptability. From my perspective, the routine I have, you need may just be the utility player of classroom routines.

Today we're talking with Kim Montague about I have, you need and the ways it can be used to support everything from fact fluency to an understanding of algebraic properties. 

BIOGRAPHY

Kim Montague is a podcast cohost and content lead at Math is Figure-out-able™. She has also been a teacher for grades 3–5, an instructional coach, a workshop presenter, and a curriculum developer. Kim loves visiting classrooms and believes that when you know your content and know your kids, real learning occurs.

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TRANSCRIPT

Mike Wallus: Welcome to the podcast, Kim. I am really excited to talk with you today. 

So let me do a little bit of grounding. For listeners without prior knowledge, I'm wondering if you could briefly describe the I have, you need routine. How does it work, and how would you describe the roles that the teacher and the student play?

Kim Montague: Thanks for having me, Mike. I'm excited to be here. I think it's an important routine. 

So for those people who have never heard of I have, you need, it is a super simple routine that came from a desire that I had for students to become more fluent with partners of ten, hundred, thousand. And so it simply works as a call-and-response. Often I start with a context, and I might say, “Hey, we're going to pretend that we have 10 of something, and if I have 7 of them, how many would you need so that together we have those 10?” And so it's often prosed as a missing addend. With older students, obviously, I'm going to have some higher numbers, but it's very call-and-response. It's playful. It’s game-like. I'll lob out a question, wait for students to respond. I'm choosing the numbers, so it's a teacher-driven purposeful number sequence, and then students figure out the missing number. I often will introduce a private signal so that kids have enough wait time to think about their answer and then I'll signal everyone to give their response.

Mike: OK, so there's a lot to unpack there. I cannot wait to do it. 

One of the questions I've been asking folks about routines this season is just, at the broadest level, regardless of the numbers that the educator selects, how would you describe what you think I have, you need is good for? What's the routine good for? How can an educator think about its purpose or its value? You mentioned fluency. Maybe say a little bit more about that and if there's anything else that you think it's particularly good for.

Kim: So I think one of the things that is really fantastic about I have, you need is that it's really simple. It's a simple-to-introduce, simple-to-facilitate routine, and it's great for so many different grade levels and so many different areas of content. And I think that's true for lots of routines. Teachers don't have time to reintroduce something brand new every single day. So when you find a routine that you can exchange pieces of content, that's really helpful. It's short, and it can be done anywhere. And like I said, it builds fluency, which is a hot topic and something that's important. So I can build fluency with partners of ten, partners of a hundred, partners of thousand, partners of one. I can build complementary numbers for angle measure and fractions. Lots of different areas depending on the grade that you're teaching and what you're trying to focus on.

Mike: So one of the things that jumped out for me is the extent to which this can reveal structure. When we're talking about fluency, in some ways that's code for the idea that a lot of our combinations we're having kids think about—the structure of ten or a hundred or a thousand or, in the case of fractions, one whole and its equivalence. Does that make sense?

Kim: Yeah, absolutely. So we have a really cool place value system. And I think that we give a lot of opportunities, maybe to place label, but we don't give a lot of opportunities to experience the structure of number. And so there are some very nice structures within partners of ten that then repeat themselves, in a way, within partners of a hundred and partners of a thousand and partners of one, like I mentioned. And if kids really deeply understand the way numbers form and the way they are fitting together, we can make use of those ideas and those experiences within other things like addition, subtraction. So this routine is not simply about, “Can you name a partner number?,” but it's laying foundation in a fun experience that kids then are gaining fluency that is going to be applied to other work that they're doing.

Mike: I love that, and I think it's a great segue. My next question was going to be, “Could we talk a little bit about different sequences that you might use at different grade levels?”

Kim: Sure. So younger students, especially in first grade, we're making a lot of use out of partners of 10 and working on owning those relationships. But then once students understand partners of 10, or when they're messing with partners of 10, the teacher can help make connections moving from partners of 10 to partners of 100 or partners of 20. So if you know that 9 plus 1 is 10, then there's some work to be done to help students understand that 9 tens and 1 ten makes 10 tens or 100. You can also use—capitalize on the idea of “9 and 1 makes 10” to understand that within 20, there are 2 tens. And so if you say “9” and I say “1,” and then you say “19,” and I say “1,” that work can help sharpen the idea that there's a ten within 20 and there's some tens within 30.

So when we do partners of ten, it's a foundation, but we've got to be looking for opportunities to connect it to other relationships. I think that one of the things that's so great I have, you need is that we keep it game-like, but there's so many extensions, so many different directions that you can go, and we want teachers to purposefully record and draw out these relationships with their students. There's a bit to it where it's a call-and-response oral, but I think as we'll talk about further, there's a lot of nuance to number choice and there's a lot of nuance and when to record to help capitalize on those relationships.

Mike: So I think the next best thing we could do is listen to a clip. I've got a clip of you working with a student, and I'm wondering if you could set the stage for what we're about to hear.

Kim: Yeah, one of my very favorite things to do is to sit down with students and interview and kind of poke around in their head a little bit to find out where they currently are with the things that they're working on and where they can sharpen some content and where to take them next. So this is me sitting down with a student, Lanaya, who I didn't know very well, but I thought, let me start off by playing I have, you need with you, because that gives me a lot of insight into your number development. So this is me sitting down with her and saying, let's just play this game that I'd like to introduce to you.

Kim (teacher): Oh, can I do one more thing with you? Can I play a game that I love? 

Lanaya (student): Sure.

Kim (teacher): OK, one more game. It's called I have, you need. And so it's a pretty simple game, actually. It just helps me think about or hear what kids are thinking. So it just is simply, if I say a number, you tell me how much more to get to 100. So if I have 50, you would say you need…

Lanaya (student): 50.

Kim (teacher): …so that together we would have 100. What if I said 92?

Lanaya (student): 8.

Kim (teacher): What if I said 75? 

Lanaya (student): Um…25. 

Kim (teacher): How do you know that one? 

Lanaya (student): Because it's 30 to 70, so I just like minus 5 more.

Kim (teacher): Oh, cool. What if I said 64? 

Lanaya (student): Um…36.

Kim (teacher): What if I said 27?

Lanaya (student): Um…27…8—no, 72? No, 73.

Kim (teacher): I don't remember what I said. [laughs] Did I say…?

Lanaya (student): 27, I think.

Kim (teacher): 27. So then you said 73, is that what you said? And you were about to say 80-something. Why were you going to say 80-something?

Lanaya (student): Because 20 is like 80, like it’s the other half, but I just had to take away more.

Kim (teacher): Perfect. I see. Three more. What if I said 32?

Lanaya (student): Um…68. 

Kim (teacher): What if I said 68? 

Lanaya (student): 32. 

Kim (teacher): [laughs] What if I said 79?

Lanaya (student): Um…21.

Kim (teacher): How do you know that one?

Lanaya (student): Because…wait, wait, what was that one? 

Kim (teacher): What if I said 79? 

Lanaya (student): 79. Because 70 plus 30 is 100, but then I have to take away 9 more because the other half is 1, so yeah.

Kim (teacher): Oh, you want to do it a little harder? Are you willing? Maybe I'll ask you that. Are you willing?

Lanaya (student): Sure.

Kim (teacher): OK. What if I said now our total is 1,000? What if I said 850?

Lanaya (student): Um…250? 

Kim (teacher): How do you know? 

Lanaya (student): Or, actually, that'd be 150. 

Kim (teacher): How do you know?

Lanaya (student): Because, um…uh…800 plus 200 is 1,000. And so I would just have to take—what was the number again? 

Kim (teacher): 850.

Lanaya (student): I would have to add 50—er, have to minus 50 to that number.

Kim (teacher): Um, 640.

Lanaya (student): Uh, thir—360. 

Kim (teacher): What about 545?

Lanaya (student): 400…uh, you said 549?

Kim (teacher): 545, I think is what I said.

Lanaya (student): Um…that'd be 465.

Kim (teacher): How do you know?

Lanaya (student): Because the—I just took away the number of each one. So this is 5 to make 10, and then this is 6 to make 10, and then it's 5 again, I think, or no, it would be 465, right?

Kim (teacher): 465.

Lanaya (student): I don't…

Kim (teacher): Not sure about that one. There's a lot of 5s in there. What if I give you another one? What if I said seven hundred and thirty…721?

Lanaya (student): Uh, that'd be…

Kim (teacher): If it helps to write it down, so you can see it, go ahead.

Lanaya (student): 389, I think?

Kim (teacher): Ah, OK. Because you wanna—you’re making a 10 in the…

Lanaya (student): Yeah.

Kim (teacher): …hundreds and a 10 in the middle and a 10 at the end. 

Lanaya (student): Yeah. 

Kim (teacher): Interesting.

Mike: Wow. So there is a lot to unpack in that clip.

Kim: There is, yeah.

Mike: I want to ask you to pull the curtain back on this a little bit. Let's start with this question: As you were thinking about the sequence of numbers, what was going through your mind as the person who's facilitating?

Kim: Yeah, so as I said, I don't really know Lanaya much at this point, so I'm kind of guessing in the beginning, and I just want her comfortable with the routine, and I'm going to give her maybe what I think might be a simple entry. So I asked [her about] 50 and then I asked [about] 92. Just gives a chance to see kind of where she is. Is she comfortable with those size of numbers? You'll notice that I did 50 and 92 and then I did 75. 75, often, if—I might hear a student talk about quarters with 75, and she didn't, but I did ask her her strategy, and throughout she uses the same strategy, which is interesting. 

But I changed the number choices up and you'll see—if you were to write down the numbers that I did— [I] kind of backed away from the higher numbers. I went to 64 and then 27 and then 32. So getting further and further away from the target number. If I have students who are counting a lot, then it becomes cumbersome for them to count and they might be nudged away from accounting strategy into something a little bit more sophisticated. At one point I asked her [about] 32, and then I asked her [about] the turnaround of that, 68. Just checking to see what she knows about the commutative property. 

Eventually I moved into 1,000. And I mentioned earlier that [with] young students, you start with 10 and maybe combinations of 100, multiples of 10. But I didn't mention that with older grades, we might do hundreds by 1 or thousands by multiples of 100 and then by 5s. So I did that with Lanaya. She seemed to feel very comfortable with the two-digit numbers, and I thought, “Well, let's take it to the thousands.” But if you notice, I did 850, 640, some multiples of 10 still. She seemed comfortable with those, but [she] is still using the strategy of, “Let me go a little bit over. Let me add all the hundreds I need and then make adjustments.” 

Mike: Mm-hmm.

Kim: And so then I decided to do 545 and see what happened in that moment because at that point she's having to readjust more than one digit.

Mike: Yep.

Kim: And when I said the number 545, I thought, “Oh man, this is a poor choice because there's a lot of 5s and 4s.” And so when she kind of maybe fumbled a little bit, I thought, “Is this because I did a poor number choice and there are lots of 4s and 5s, or is it because she's using a particular strategy that is a little more cumbersome?” So I gave her a final problem of 721, and again, that was a little bit more to adjust. So in that moment, I thought, “OK, I know where we need to work. And I need to work with her on some different strategies that aren't always about making tens.” Because as she gets larger numbers or she's getting numbers that are by 1s, that becomes less sophisticated. It becomes more cumbersome. It becomes more adjustment than you maybe are even able to hold. 

It's not about holding it in your head. We could have been writing some things down and we did towards the end. But it's just a lot of adjustment to make, and the strategies that she's using really aren't going to be ones that help later in addition or in subtraction. So it's just kind of playing with number, and she's pretty strong with what she's working on, but there is some work to do there that I would want to do with her.

Mike: It was fascinating because as I was attending to the choices you were making and what she was doing and the back and forth, I found myself thinking a bit about this notion of fluency, that part of it is the ability to be efficient, but also to be flexible at the same time. And I really connect that with what you said because she had a strategy that was working for her, but you also made a move to kind of say, “Let's see what happens if we give a set of numbers where that becomes more cumbersome.” And it kind of exposed— there's this space where, again, as you said, “Now I know where we need to work.” So it's a bit like a formative assessment too.

Kim: Yeah, yeah. Interviewing students, like I said, is my very favorite thing to do. And it's tough because we want kids to be successful, which is a great goal, but I think it's often unfortunate that we leave students with a strategy that we think, “Oh, that's great. They have a strategy and it works for them,” but we aren't really thinking about the long game. We're not thinking about, “Will this thing that they're doing support their needs as the size of the numbers increase, as the type of the numbers change?” And we want them to have choice. And again, I have, you need is fantastic because within this game, this simple routine, you can share strategies. There's a handful of strategies that kids generally use, and in the routine in the game, we get to talk about those strategies. So we have a student who's using the kind of same strategy over and over and it stops working because it's less sophisticated, it's less efficient, it's more cumbersome. Then in the routine, we get to expose other strategies that they can try on and see what works for them based on the numbers that they're being given.

Mike: You made me think about something that, I'm not sure how you could even put my finger on why, but sometimes people are wonky about this notion that students should have a choice of their strategies. In some ways, it makes me think that what you're really suggesting is part of this work around flexibility is building options, right? You're not trapped in a strategy if suddenly the numbers don't make it something that's efficient. You have options, and I think that really jumps out when you think about what happened with Lanaya, but just generally what you're trying to build when you're using this routine.

Kim: Yeah, I mean we are big fans of building relationships, so that strategies are natural outcomes. And I think if you are new to numeracy or you didn't grow up playing with number, it can feel like, “I'm just going to offer multiple and kids have to own them all, and now there's too many things and they don't know how to pick.” But when we really focus on relationship in number, then we strengthen those relationships like in a routine with I have you, need. I grew up messing with number, and the strategies don't feel like a bunch of new things I have to memorize. I've strengthened partners of ten and hundred and thousand, and I understand doubles, and I understand the fact that you can add a little too much and back up. And so those relationships just get used in the way that I solve problems, and that's what we want for kids.

Mike: I love that. 

We've spent a fair amount of time talking about this connection between building fluency and helping kids see and make use of structure. I'm also really taken by some of the properties that jump out of this routine. They're not formal, meaning they come up organically, and I found myself thinking a lot about algebraic reasoning or setting kids up for algebra. Could you just talk a little bit about some of that part of the work?

Kim: I think that when we want kids to own and use properties, one way to go about it is to say, “Today we're going to talk about the commutative property.” And you define it and you verbalize it and you write it down. You might make a poster. But more organically is the opportunity to use it and then name it as it's occurring. So in the routine, if I say “68” and she says “32” and then I say “32” and she says “68,” then we are absolutely using the idea of “68 plus something is 100” and then “32 plus something is 100.” There is something natural about you just [knowing] it's the other addend. In some of the other strategies that we develop through I have, you need, it's about breaking apart numbers in such a way that they are reassociating. And so when that happens for students, then we can name it afterward and say, “Oh, that's just this thing.” And whether we name the property to students or not, it's more important that they're using them. And so we put it in a game, we put it in a form that we just say, “Oh, that's just where you're breaking apart numbers and finding friendly addends to go together.” And I think it's really more important that teachers really understand the strategies that work so that they invite students to participate in experiences where they're using them.

Mike: Yeah, I mean, what hits me about that is there's something about making use of a relationship, fleshing it out through this process of I have, you need, and then at the end coming back and saying, “Oh, we have a formal name for that.” That's different than saying, “Here's the thing, here's the definition. Remember the definition, remember the name.” It just works so much more smoothly and sensibly because I've been able to apply that relationship and it feels like it's inside of me now. I have an understanding and now I've just attached a name to that thing. That just feels really, really different.

Kim: Yeah, I mean, if we give students the right experiences, then they have those experiences to draw on. And I'm a big fan of saying that some kids just have more experiences than others. And all kids can, but it's our job to provide the right experiences for students that they can use and that they can think back on and that they can connect to other experiences that they have. Using the relationships of number is so powerful, and I think we just need to do more and more so that kids are just stronger in the properties and stronger in connections and relationships so that then when they go solve problems, they're using what they know.

Mike: Nice. So something that I want to call out for listeners who, again, this might be new for them, is there's really two parts to this routine. There's the call-and-response, whether it's with an individual student or whether it's with a whole class of students. And then there's what happens after that call-and-response. So how do you think about the choices a teacher has after they've called a number and kids have responded? What are some of the choices available to a teacher in that moment?

Kim: Well, I think if you're playing, then you are kind of on a mission to learn more about students. For me, I'm always trying to figure out where students are and what they know and what they're tinkering with right now so that then I can make informed choices about what to do next. So I might make choices that are about my entire class. I might make choices based on, I'm watching particular students as we play to see where are they kind of dropping off. Where—you know, if I'm watching a video of myself playing this routine with a class, I'm scanning to, say, those students wait a little bit longer and I want to strengthen some work when we do multiples of 5 because they're chiming in just a little bit late. So I'm looking for who's fluent, who's not, who's counting on by 1s, who needs another nudge. I'm ready to bump them a little bit further along. It's not about speed. This isn't a speed routine. I absolutely think we give kids some time to wait, but just enough. So like I said, we introduce a private signal, then they let me know when the majority of class is ready. Then I call for everyone to reply. But there is some bit of this where if you're counting by 1s to get up from 68 to 100, then there's some intervention [needed]. There's some work that we can do to strengthen you. 

So it's important to give some think time, it's important to use the private signal, and it's about the teacher being responsive to what they notice. “Am I pulling a small group to give some students more experience, making connections?” “Am I moving some students to another set of numbers?” “Am I purposefully pairing students to give them what they need while I'm working with somebody else?” So it's an information-finding routine if I'm noticing and I'm aware of what's going on.

Mike: I noticed with Lanaya, there were points where you called, she responded, and you went right in and you called after and she responded—and there were other points where you decided to say something equivalent to, “Tell me how you know.” How do you think about the points where you just keep on rolling or you pause and you ask that probing question?

Kim: That's a great question. So when I make a shift is often a time that I will ask, “How do you know?” First of all, it's super important to ask, “How do you know?” when students have both right and wrong answers. We have a lot of kids who are only asked, “How do you know?” when it's wrong. And then they backpedal, right? And then they just pick a new answer. And I think giving kids confidence to commit to their answer and say, “Yeah, I know it's that, and here's how I know.” We continue to build that in students, that we are not the ones who hold all the answers when we question. And so, in a shift is often when I think about making a change. So if I'm asking about combinations of 10 and then I shift to a 5, multiples of 5, maybe the first or second time I ask them how they know.

I think about, “Have kids had a chance to verbalize their thinking?” There are moments where you completely understand what Lanaya is saying. And then there's a few where maybe if you're not a careful listener of students, you might think, “I'm not sure she knows what she's saying.” But over time, when you're a practiced listener of students, even though their words may not be fantastic, they're kind of sharing their thinking. And so it will bog it down to ask, “How do you know?” every single time. But in those shifts where I want to know, “Are you changing your strategy up?,” “Are you continuing to do the same thing every time?,” I think it's important to ask.

Mike: So I have one last practitioner question before we move on from this. I'm wondering about annotation and the extent to which it's important and whether there are different points in time where it is, where it's not. How do you think about that?

Kim: Yeah, I think that's a really important question. You can very easily hear something like this interview with Lanaya and think, “Oh, I'm just [doing] call-and-response.” Which—there can be moments of that, but an important piece is annotation to draw out strategies that kids are using. So I might introduce this routine to a class and I might [do] call-and-response a day or two or a couple of times, depending on how many times that week or how often we get to play. 

But at some moment there's a chance to say, “Hang on a second. How did you think about that?” If I say “65” and some kids call it back, I'll say, “How did you come up with that?” And then I ask students to share their strategies, and this is the sharing part. This is the part where students get to learn from each other. And so a kid might say, “I added 5 to get to 70 and then I added 30 more to get to 100.” And some kid will listen and I'm going to record that on a number line, making the jumps that they say out loud. And another student might say, “Wait a second, that's not what I did.” And so there's this opportunity to share strategy, and then we can say, “Well, try that on.” But if I'm not representing what students are saying on a number line, it could be really hard for others to hold onto it. It's not about [holding] everything in your head. So I often record on a number line as we're starting to share strategies or if I want to uncover a mistake that somebody makes, or if I see the kids all using one strategy, I want to draw attention back.

Another really important thing is that I might want to lighten the mental load by recording the number that I said. If I'm saying, “721” and I'm not writing anything down, you might be trying to hold “7-2-1” or “720 and 1” at the same time that you're trying to do some figuring, and it's not about who can hold more. So depending on the age, the size of the numbers, I might just [quickly] sketch the number that I said because they can stare at the number while they're also doing some figuring. Or they might write the number down on their notebooks so that they can do some figuring.

Mike: One of the things that jumped out is the fact that you talked about when you stop to annotate, one of the ways that you do it is to annotate on a number line as opposed to—I think what I had in my mind initially is a set of equations. Which is not to say that you couldn't do that, but I thought it was interesting that you said, “Actually, I will go to a number line for my annotations.”

Kim: So I think making thinking visible is hugely helpful. And if a student says—let's say I give the number 89. If somebody says, “Well, I thought about adding 1 to get to 90 and then I added 10 more to get to 100,” then their strategy of adding 1 more to get to that next friendly number is one of the major strategies that we would want to develop in students when they're adding. But another student might say, “Oh, that's interesting. I started at 89 and I added 10 first to get to 99, and then I added the 1.” And that's a different major strategy that we want to develop. And when you put them both up on a number line, you can see that that missing addend, that missing part is 11, but they're handling it in two different ways. And so it's a beautiful representation of thinking of things in different ways, but that they're equivalent and that you can talk about it when you see it on the board. Equations are fantastic ways to represent, but I have an affinity for number lines to represent student thinking.

Mike: Love it. 

As a fellow podcaster, you know that the challenge of hosting one of these is we have a short amount of time to talk about something that I suspect we could talk about for hours. Talk to folks who want to keep learning about I have, you need and any other resources you would recommend for people thinking about their practice. Where could someone go if they wanted to continue this journey?

Kim: They could listen to the Math is Figure-Out-Able podcast, first of all. We have had several episodes where we talk about this routine and revisit it over and over again because it's super powerful. We also have a free download that I think you're going to share. It's mathisfigureoutable.com/youneed, so you can see something that would be helpful. And we have, at Math is Figure-Out-Able, an online coaching support called Journey, where we just get to work with teachers on a regular basis to unpack the practices and the routines that you're using and spend a lot of time working with teachers and students in the classroom to develop these kinds of things that are more bang for your buck, to make the most that you can in the time that you have with your students.

Mike: That's awesome. And yes, for listeners, we will include links to everything that Kim just mentioned. 

I wish that we could keep going. I think this is probably a good place to stop, Kim. Thank you so much for joining us. It's been a pleasure.

Kim: Oh, Mike, thank you. Appreciate you having me.

Mike: Absolutely. 

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