Math is Figure-Out-Able with Pam Harris

One Thing Mathy People Do

August 04, 2020 Pam Harris Episode 7
Math is Figure-Out-Able with Pam Harris
One Thing Mathy People Do
Chapters
Math is Figure-Out-Able with Pam Harris
One Thing Mathy People Do
Aug 04, 2020 Episode 7
Pam Harris

In this episode Pam and Kim share one of their favorite instructional routines: I Have, You Need. They discuss some of the most common patterns that mathmaticians play with, partners of 10, 100, and 1000. These "partners of ___ " patterns pop up everywhere! You'll never guess where they pop up daily for Pam (hint: its when she's the most worked up).

Try out I Have, You Need with your friends, colleagues, and students! A quick way to build anyone's reasoning abilities and to help us all become better mathematicians.

Download the guide to playing I Have, You Need HERE
Find the transcript for this episode HERE

Talking Points:  

  • We can all be "mathy people"
  • What Kim thinks when she hears the number 36
  • The routine that made the biggest impact on Pam's college students
  • Taking ownership of your students' progression
  • I Have, You Need resolves the subtracting across zero horror
  • How I Have, You Need applies to middle and high school students


Show Notes Transcript

In this episode Pam and Kim share one of their favorite instructional routines: I Have, You Need. They discuss some of the most common patterns that mathmaticians play with, partners of 10, 100, and 1000. These "partners of ___ " patterns pop up everywhere! You'll never guess where they pop up daily for Pam (hint: its when she's the most worked up).

Try out I Have, You Need with your friends, colleagues, and students! A quick way to build anyone's reasoning abilities and to help us all become better mathematicians.

Download the guide to playing I Have, You Need HERE
Find the transcript for this episode HERE

Talking Points:  

  • We can all be "mathy people"
  • What Kim thinks when she hears the number 36
  • The routine that made the biggest impact on Pam's college students
  • Taking ownership of your students' progression
  • I Have, You Need resolves the subtracting across zero horror
  • How I Have, You Need applies to middle and high school students


Pam Harris :

Hey fellow mathematicians! Welcome to the podcast where math is Figure-Out-Able. I'm Pam Harris.

Kim Montague :

And I'm Kim Montague. And we answer the question, if not algorithms, then what? In our last episode, Pam talked about real math, fake math and mathematizing your world. So today, we're going to talk a little bit about what that looks like. So Pam, we were going to call this episode 'what mathy people do',

Pam Harris :

Right. And then we had this long conversation about that we don't want to give the wrong impression, because we believe that all people can be mathy people. It's just that maybe we're not yet because we don't even know that, that it's a thing like we don't know exactly what it means to be a mathy person. But it can be helpful to know what those mathy things are that people do in their heads. I think sometimes we've looked at people and gone like, I don't even know what you're doing in your head. So, so if we can point out those things - like I began to be able to develop a as a mathematician, when I could understand more what mathy people were doing in their heads, and then I became more of a math person, because to be that sort of mathy person, remember, we think everybody could be a math person, but to be that mathy person, what we think that means is that you have a dense brain structure, that means you have lots of connections in your head, when you solve problems, you want to have at least a few directions that you can go, a few relationships that you can use. Because mathy, people don't just follow a rule and do the same steps all the time, mathy people let the numbers or the structure influence which relationship they might use today to solve that problem. And they might even use a different one the next day to solve the problem.

Kim Montague :

Sure. So when we hear or think of a particular number, lots of things come to mind.

Pam Harris :

Yeah, so for example, Kim, if I asked you if I just said the number 36 What comes to your mind?

Kim Montague :

36. So I think six squared. I think of three dozen, I think one more than 35. If I'm thinking about money, I'm thinking quarter a dime a penny, I think 64.

Pam Harris :

64? Kim?

Kim Montague :

Yeah

Pam Harris :

The rest of you guys might be wondering, 64? I said the number 36. Why? Why would 64 come to mind when I say the number 36?

Kim Montague :

Oh, sure. It's the partner of 36 to 100.

Pam Harris :

So that's interesting. Now, y'all before I became numerically powerful, I didn't know it was a thing to know the partners of a number to 100. So 36 plus 64 is 100. And that's a thing. It's a thing to know the partners of 10, 100, and 1000. Who knew? Well, mathy, people do and so if we all want to become mathy people, which we believe we can, then it's a thing to sort of be able to recognize numbers' partners to 10 or partners to 100 or partners to 1000. These are relationships that mathy people own, and then they can use them. Because these are important relationships, Kim came up with this routine called I have You Need. It's an instructional routine that she played with her students. So I would do the same instructional routine with people in workshops. I did it with people in my university class, but one day, we were in a workshop, and Kim said to me, I'm not sure you really appreciate how important the partners of 100 are. And I was like, No, no, I get it. You know, they're important. She goes, Yeah, but you don't own them. I was like ummm, I don't? And the reason I think at that moment, if I remember correctly, Kim it's because we were solving some problem and that relationship did not come to my mind.

Kim Montague :

Yeah.

Pam Harris :

And it did two years and so you just kind of politely poked me a little bit to say that is important. So y'all I take whatever Kim says seriously, and I took it seriously. And so from that moment, on in my University classes we would play I have, You Need this routine we're going to tell you about every day. In my university class, we play the very first day of the semester. And then we would play it every class period a little bit, I assign it for homework. Interestingly, at the end of that semester, I always ask my students, what's the best thing we did in class this semester? And what would you have me improve? What's the thing that you would ask me to do better next semester, so I can improve? And that semester, and ever since I always get students that will say, the most important thing we did all semester was learn their partners of 100 partners have 1000 playing I have you need. And that was so interesting to me. I was like, wow, this really is important. And then I would ask him, like, why is that the most important thing and they said, because those relationships show up everywhere. So today in the podcast, we thought we'd share that with you. We thought you shared this important thing that mathy people do, so that we can all become more mathy. So let me tell you a little bit more about this routine. The routine is, let's say that it's total 100. So we're going to play I have You Need total 100 and it simply goes like this if I say I have 70 then Kim, What do you need to make 100

Kim Montague :

30

Pam Harris :

And if I say I have 90: What do you need?

Kim Montague :

10

Pam Harris :

And if I say I have 40 you need

Kim Montague :

60

Pam Harris :

And if I have 20 you need

Kim Montague :

80

Pam Harris :

if I have 85 you need

Kim Montague :

15.

Pam Harris :

Now Kim's pausing a little bit because we talked about this I want to make sure that there was a little bit of time for the listeners to think a little bit before she just gives the answer so I'm gonna do a couple more. Kim just pause about the same amount of time but everybody out there in listening-land think about if you know these partners of to 100. If I give you the number, what do you need to add to it to get to 100 so if I say I have 65 you need

Kim Montague :

35

Pam Harris :

If I have 55 you need

Kim Montague :

45

Pam Harris :

How about if I have 35? What do you need?

Kim Montague :

65. Now you might have noticed that so far, I did sort of decades, I did multiples of 10. So I did numbers like 80, 90, 40, 20 and then I did some multiples of 5: 85, 65, 55, 35. Then eventually you want to get to the point where you can do any random number like if I were to say I have 67 32

Pam Harris :

So 67 plus 33 is 100 What if I said I have 82? You need

Kim Montague :

18.

Pam Harris :

So I should be able to say any random number like I have 27 what do you need Kim?

Kim Montague :

73.

Pam Harris :

Bam, I mean, that's just like uncanny. And I'll tell you how we don't have those written down. I was just saying numbers and Kim was spitting them back. And so that's a goal then we're gonna talk a little bit later in the podcast why that's such a goal. But that's a thing to know that we can play this I have you need routine to get ourselves and our students better at those partners of 10, 100, and 1000.

Kim Montague :

Yeah, so teachers and parents, we would highly recommend first work on partners of 10. If you have older kids, you can do the decades 20, 40, 60. And you can see if they own the partners of 10 that way.

Pam Harris :

So like with young learners, you might do something like total of 10. I have eight you need...

Kim Montague :

two.

Pam Harris :

And if I have three you need

Kim Montague :

Seven.

Pam Harris :

But if you want to do that with older kids, like Kim was just saying, you could say I have 80 you need...

Kim Montague :

20.

Pam Harris :

And if I have 30, you need

Kim Montague :

70.

Pam Harris :

And in a huge way that's sort of checking those older kids' partners of 10. So Kim, tell us about that experience, you told me about your third grade teacher friend.

Kim Montague :

Yeah, I had a friend once who taught third grade and she was kind of lamenting one day about how her kids didn't own their partners of 10. They were kind of struggling and she said, Man, these kids came to me they don't even know their partners have 10. And I said, Wow, it's October. You know, it's one thing if they come to you and they don't already have their partners of 10. But by October that's kind of on you, you know, it's a thing to figure out kind of where your kids are, and then work on it. If they don't come to you with those partners. You know, you got to kind of work on it with them.

Pam Harris :

Yeah, at some point the rubber hits the road, you can't just say bummer. They came to me without what I need or you know, then let's recognize and work on it. So first, we would recommend that you work on partners of 10. Make sure they know those. Work on partners of 100. That's the next thing. As you do this routine teachers and parents, first work on those multiples of 10 those decades 20 30, 40. Work on those first. Once kids know those pretty well then go to the multiples of fives, 55, 75, 95. And then once they've got multiples of fives, then work on any random number, the ones like 67, 83, 52. As you do that, in each of those categories, the decades first and the fives in the ones, in each of those categories, use the bigger numbers first. So Like if I begin playing with any kid random kid, and I just say, hey, if I have 87, you need, I'll use a number 87 closer to 100 first. Before I'll say, I have 13. What do you need? Because it's actually kind of funny when you play this game with kids and you say something like, Hey, I have 85. What do you need? They'll be like, okay, I can do that I count up from 85 to 100. They figure it out they say, 15, then if you turn right around and go, I have 15. What do you need? They'll go, oh, crud. Because 15 is so much further from 100 if they're still counting up, then they might not recognize that they could just count back 15 from 100. So one way that you can sort of mess with that a little bit and help kids recognize that. You can give kids a number like hey, I have 77 Kim, what do you need to make 100

Kim Montague :

23

Pam Harris :

And then you can write back go, I have 23 what do you need

Kim Montague :

77

Pam Harris :

77. And so then, especially if I write those down, I can write those two partners down 77 plus 23 equals 100. 23 plus 77 equals 100. And I can just notice it and just go, huh, look at that. And then kids can start to go, Oh, I could sort of count back from 100. I can use what I know about the other partner. And that could kind of help. So again, just to recap: do the decades first, then the fives then the ones and do the bigger numbers close to the total first and then do the smaller numbers. And then you can play total 1000! All right, Kim, you ready?

Kim Montague :

I think so

Pam Harris :

If I have 654, what do you need?

Kim Montague :

346.

Pam Harris :

Bam. And that's unbelievable. So you kind of want to be able to play total 1000. So Kim, we've talked about what and how to play, why are partners of 10 and 100 and 1000. Why are those so important?

Kim Montague :

Oh my gosh, subtraction. One of the things that I noticed as a third grade teacher is that subtraction across zeros was a nightmare. I think every third grade teacher listening will say the same thing.

Pam Harris :

Fourth grade, fifth grade

Kim Montague :

Yeah, you're right. So you know, all the crossey-outies and like, where does the 10 go? Where do the nines go? It's kind of like that nightmare series of days that you're practicing that. And what I found out was that if I worked on partners of 100, then my students weren't considering all those crossey-outies and using traditional algorithms. They were really thinking about how far away to the next hundred am I?

Pam Harris :

So for example, if I did something like 100 minus 57, your students didn't line em up?

Kim Montague :

Yeah,

Pam Harris :

or cross the zeros out and turn one of them into nine and one of them into the ten? They just thought, Well, what do I need from 57 to get to 100? Bam.

Kim Montague :

Yeah

Pam Harris :

That's a brilliant strategy. That's really, really helpful. Right?

Kim Montague :

So as an elementary teacher, Pam, I'm thrilled with the routine we've just talked about 10s, hundreds, thousands, and we didn't mention earlier but even partners of one. What role does I have you need play in middle school and high school, maybe you can talk about the partners of one for just a second.

Pam Harris :

So I could play I have, you Need total one where I could use decimals. And I could say, so .57 or 57 100ths. So what do I need, and you're kind of just using the same relationships as 100. But kids have to think a little differently it sort of trips their brain and so that could be great. You can also play total one, where you could say, I have four fifths, what do I need to make 100? I just need one more Fifth. I know that sounds a little bit Elementary, but you'd be surprised that it could be kind of helpful for kids. So yeah, we can absolutely play close to one that's a great kind of lower middle school thing to do. So you asked about middle and high school. Well, funny enough, if students of Middle and High School don't know their partners of 10 100 and 1000, then that's a thing to do. Like we would want to start there. But also, as we get kids to kind of realize that there are these delightful relationships with those nice numbers, the nice numbers of 10 hundred, thousand, one, we can also have nice numbers like 180, the sum of the measures of the angles of a triangle. So you could play a little bit of I have you need with 180. Or just that sense of what are these things that add together to be 180 is helpful. But also you could think about radian measure precalculus teachers and trig. If we could think about the fact that we have these nice friendly numbers that we are dealing with, well, could I deal with two pi for radian measure? And then I could think about the pieces that make those angles up. So if I know where two pi is, can I know where half of pie is, or we tend to call that pi halves because we like to be silly. As mathematicians, we, we like to sound like we're really intense. So instead of saying half a pie, we say pi halves, but by knowing there's this sort of sense of these nice numbers and the totals, that can help us with some of these things in higher math. So listeners go play I have you need by yourself when you're driving in the car, when you're tooteling around your house, play with your personal kids, play with your classes, with your significant other, build your relationships with partners of 10, hundred and thousand in order to be more dense when you think of numbers. Yeah, you also let me tell you, now that I own those partners, I start to play with partners of 60

Kim Montague :

60?

Pam Harris :

Right? Because so I'm on the elliptical, right, I got a minute left. I got a minute left. And so I start thinking about things like, Okay 10 seconds have gone by, let's see, that's a sixth of a minute. And so I've got five sixths to go. Now 12 seconds have gone by! So that's a fifth of a minute, and I got four fifths to go. Now 15 seconds have gone by! That's a fourth of a minute. I've got three fourths to go. And I can play with more relationships, because I sort of own more with 60. And so those are some fun relationships that I've started to play with.

Kim Montague :

So one cool thing that mapping people do, partners of numbers.

Pam Harris :

Excellent, especially that 10 hundred and thousand and then we can move on to others once we know those. Hey, y'all if you want to have more information about this cool routine, we have a downloadable guide for you. You can print it, you can put it in your lesson plan folder, hang it on your wall. So both Kim and I have this technique when we were in the classroom where we would have an index card and we would have kind of important things that we would do in those last 38 seconds before the bell rang or before the kids moved on to specials or whatever. And so on that index card that you have hanging by your door you could put I have You Need that could remind you to play I have You Need. Y'all you can download this our nice downloadable that we have for you it's a whole guide on the routine. The instructional routine I have you need. You can go to mathisFigureOutAble.com/youneed. That's mathisFigureOutAble.com/youneed to download it or we'll post it in the show notes for you to download at your pleasure. Y'all if you wouldn't mind like the podcast give us a nice review so more people can see it. That helps people find the podcast, we appreciate it. Check out the website mathisFigureOutAble.com. We'd love to have you join us Wednesday night on MathStratChat. So if you're interested to learn more math and you want to help students become mathematicians then the Math is Figure-Out-Able Podcast is for you because math is FIgure-Out-Able.