Pam Harris  00:01

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

Kim Montague  00:08

And I'm Kim. 

Pam Harris  00:10

And we're here to suggest that mathematizing is not about mimicking or rote memorizing, but it's about thinking and reasoning, about creating and using mental relationships, empowering teachers and students. We answer the question, if not algorithms, then what in the world are you gonna do? 

Kim Montague  00:30

Welcome to this week's podcast, y'all. Thanks for joining us. A few weeks ago, we asked you to share someone that you know who you think is one of those mathy people. 

Pam Harris  00:41

And y'all we got a fantastic email from our friend Aaron Houston. And we had a blast talking about the stuff that pinged for us. So Kim, tell us how he started his email. 

Kim Montague  00:51

Okay, I'm just gonna read a little bit to you. Aaron said, "On your latest podcast episode you invited us to tell you about mathy people that we know. I am a very mathy person. And I believe one of the reasons I was able to get there was because of my dad. He's a former math teacher turned lawyer. And he's definitely mathy. He used to do mathy stuff with my brother and me all the time, especially if we were eating together at a restaurant." And oh my gosh, it totally reminds me of my own kids, right? Sometimes you're sitting around at a restaurant, and there's nothing to do. And so they just look at the menus. And also, um, right now, my kids are getting older. They're at that stage where they transition between a kid meal and an adult meal. And so Cooper, you know, is the younger, and he's trying to convince me at this stage of his life that he needs two kid meals. I'm like that's, "Not happening. You can get off the kid menu and order an adult meal." But they don't have this special drink or the special cookie or whatever comes with it. And so I've said to him, "Check out the menu and compare the prices." So he does a lot of that comparing what's going to be the better deal about you know, can I get two kid meals for the price of the adult meal mom would make against 

Pam Harris  02:06

Nice. Yeah. So Excellent. So he gets an opportunity to do some math right then and there, try to convince you of his choice and so he has a reason, right? It's a reason for him to actually do some computation. That's awesome. Hey, let me tell you what else Aaron said. So he said, quote, "When we were really little," he, meaning his dad, "Would give us cash to pay the bill. But we had to figure out what the change would be first."

Kim Montague  02:30

Oh, nice. 

Pam Harris  02:31

And he says, "I know my compliments of 100 because of this" unquote. So Kim, it's I Have, You Need, right there in the restaurant that's so awesome. The partners of 100 are so important. What a great way to get your kids involved, that they get the change as long as they can figure out what the change is. Amazing. So y'all, if that's new to you, if you've never heard of us talk about I Have, You Need the routine that Kim made up that we love. It helps kids develop partners of 100 like if I have 47 what do you need to make 100? So if I have 47 you need 53 to make 100. If you want to hear more about that, you can check out Episode 7 called One Thing Mathy People Do, where again, we talk about helping students develop partners of 10, hundred and 1000. And how those relationships show up everywhere so that knowing them can really help you do more math. 

Kim Montague  03:24

Can I just mention too, that you talked about I Have, You Need in your Multiplicative Reasoning online workshop, and I'm having a blast reading comments from people who were thinking about other partners that they want to build, like 60 for time 180 for triangles, 360 for circles, and it's just got me thinking about what other compliments do we want to encourage people to make sense of? 

Pam Harris  03:47

Oh, nice, nice, good. Okay. Cool. Alright. What else did he say?

Kim Montague  03:51

Aaron also wrote that, "When we were a little older, he would also let us guess the price of the meal, which is brilliant. I might guess $25 and 83 cents, and he would tell us how many numbers we had correct? Like how many digits were correct. So that my brother would guess $25 and 25 cents? And he would say that no numbers were correct." So each time they guessed the dad would tell them how many numbers were correct. "Maybe then I would guess $36 and 71 cents and two numbers are correct. And this would go on until we had all four numbers and then we were just working through different permutations for what those four numbers were." 

Pam Harris  04:27

Oh, my goodness, that's the game Mastermind. I loved that game growing up. In fact, I have that - we have that game in our game closet right now. That's an amazing game to get kids messing around with permutations because you tell them which numbers are right and then what places right. 

Kim Montague  04:47

I totally forgot about Mastermind. I remember playing that game so simple and so cool. And I played it as a kid traveling with my parents. I remember my mom pulling the game out when we were going on camping trips, and the colors, right? With the pegs? 

Pam Harris  05:01

Yep, yep totally. Yeah and you totally put like the white color for if you have the place right and the red color if you have the color right but not in the right place. Yeah all the things. So what a cool way to play Mastermind when you're out with your kids by guessing the amount on the bill. That's excellent. Way to go Aaron's Dad. So let me keep going. Aaron also said, quote, "Other times he," there dad, "he might just think of a number between one and 100 or a number between one and 1000. And we would guess and he would tell us higher or lower as we guessed, and narrow it down to the answer." Kim, you play that game all the time! 

Kim Montague  05:40

I do. I do play Guess My Number. And we added things like if the numbers is odd, or what is the sum of the digits? I wouldn't ever just let them go like higher, lower, higher, lower.  Um, do you guys play?

Pam Harris  05:53

Like so what would, I do, but let me tell you, when I began to play this game, I totally would just have kids guessing numbers. And then I would say, "My number's higher than that number," and then they would say, okay, they would choose a number higher. And then I would say, "No, my number is lower than that number." And then they would choose the number lower. And I totally thought I had the corner on this game. And then one day, I heard you playing with your kids. And I was like, "Ah, it could be so much better," because you added so much like tons more mathy things because as your kids got good at it, then they could sort of bring in more math things. And I thought it was a really natural way for you to bring in some vocabulary that your kids can kind of get used to. Alright, so yes, I want to play. 

Kim Montague  06:31

Well. Yeah. And let me add to that as my kids have gotten older, we still continue to play, but not only have the size of the numbers that I give them increased, um, there's more questions that we can ask each other, right? They know more content now. So we can bring that in. So let me just tell you, we can either play where I give you clues. But it's also fun for me to just think of a number and you have to ask things about the number I'm thinking of. 

Pam Harris  06:58

Okay, so let's try that way. 

Kim Montague  06:59

Okay. So alright. 

Pam Harris  07:00

Alright, you think of a number. And y'all we have not done this ahead of time. It's live on the air mathematizing. Here we go. Okay, Kim, 

Kim Montague  07:09

I've got a number.

Pam Harris  07:10

Is your number between zero and 100? 

Kim Montague  07:14

No.

Pam Harris  07:16

Is your number greater than 100? 

Kim Montague  07:18

Yes. 

Pam Harris  07:19

Okay. Is your number even?

Kim Montague  07:24

No.

Pam Harris  07:27

Is your number a whole number? 

Kim Montague  07:29

Yes. 

Pam Harris  07:30

Okay. So it's a whole odd number greater than 100. Is your number less than 1000? 

Kim Montague  07:36

Yes.

Pam Harris  07:40

What is the sum of the digits of your number?

Kim Montague  07:45

Eight. You're going really fast here. Can you slow down and let people think? 

Pam Harris  07:50

Oh, sorry.

Kim Montague  07:52

That's a great question. 

Pam Harris  07:53

I'm excited! Okay, so it's a whole number. It's odd and the digits sum to eight. So is your number 701?

Kim Montague  08:06

No.

Pam Harris  08:07

Is your number 107?

Kim Montague  08:10

Ooo. I love that you did that. It was a huge moment when my youngest figured out that that was a thing, right? So no, it's not 107.

Pam Harris  08:19

Is your number a permutation of seven zero and one, like 117? 

Kim Montague  08:26

No. 

Pam Harris  08:26

Okay, so I have the wrong, odd numbers. Is your number bigger than 500? 

Kim Montague  08:32

No.

Pam Harris  08:34

Is your number bigger than 250? 

Kim Montague  08:36

No. 

Pam Harris  08:38

Okay, so it's between zero and 250? No, it's between 100 and 250. That's odd. It's odd. Um, what else could I ask? Here, I'm gonna ask this question, Kim. What would be another good question for me to ask?

Kim Montague  08:54

Oh, you could ask if it was divisible by something or if it was prime or composite.

Pam Harris  09:00

Is your number prime? 

Kim Montague  09:02

It is.

Pam Harris  09:04

Okay, a prime number between 100 and 250. I bet you anything people are listening to this podcast and like screaming numbers at their phone right now. They're like try 117. Oh except 117 wouldn't add eight, but 100, let's see. 100 and...has to add to 8... 124? Nope, that's even. 133.

Kim Montague  09:34

No, that does not sum to eight.

Pam Harris  09:39

Oh duh... 143 

Kim Montague  09:42

Correct.

Pam Harris  09:44

Are you serious!?

Kim Montague  09:44

I'm serious! Yah! 

Pam Harris  09:49

Sweet.

Kim Montague  09:49

I answered the question really quickly: Is it prime or composite? Is that, that's prime right? (unclear) some time.

Pam Harris  09:58

Well, that's a good question. So Kim, what are you thinking right now to determine if 143 is prime? 

Kim Montague  10:04

Well, I'll be perfectly honest with you. The first thing I thought was it's not divisible by seven because 20 times seven is 140. So I left sevens alone. 

Pam Harris  10:13

Nice. First thing I did was think if the sum of the digits are eight, then it's not divisible by two, no by three, six or nine, because the sum of the digits is eight, right? So that's, I know those. I also knew it was odd. So it's not divisible by two.

Kim Montague  10:33

Right. 

Pam Harris  10:34

Or four or 8. Uh.. 11. Is it divisible by 11? Because it has that pattern, that 

Kim Montague  10:43

Oh! 

Pam Harris  10:45

Of 11 sometimes, have right? So is it divisible by 11? 

Kim Montague  10:48

Is divisible by 11. 13 times 11. Golly I was totally wrong. So yeah, math teachers were wrong. 

Pam Harris  10:57

Hey, hey, but -

Kim Montague  10:59

We learned something! I need to do 11s more. 

Pam Harris  11:03

So we're not failures, right? Because in a huge way, what we just did was have fun figuring out if 143 was prime. 

Kim Montague  11:11

Yeah. 

Pam Harris  11:11

And a relatively new pattern for me is this pattern of 143, where it's sort of add the one and the three together to get the middle four has something to do with multiples of 11. And that's a relatively new pattern I've just been able to sort of recognize, which made me then wonder if it was a multiple of 11. But even as we're just discussing the kinds of things that we think about to determine if that number was prime, I think kids can learn from that and so it's not a fail at that point. Then we can sort of poke fun at each other and go, "Oh, it isn't prime." But we had a blast playing the game and we learned something about 143. What were you gonna say? 

Kim Montague  11:50

I was gonna say if Luke were here, he would have told me that I was wrong.

Pam Harris  11:55

Go Luke. Hey, y'all. So, interesting story that you might find about this game is so I, in our church, we don't choose what we do. We can just sort of say yes or no when they ask us to do it. And so a few years ago, the head of our church asked us if I would be willing to do the singing with the young kids in our church, okay? At this point, my kids are like, "Mom don't sing in front of people." I've been known to be off tune just a little bit. But I said, "Yes." And so for five years, I did the singing with kids, three to 12. And I had a blast. But it was interesting, because I noticed that what most of the adults would do with kids is that when it was time to sort of review some of the songs or whatever, then they would always play these like language based games. Everything had to do with letters and words and stuff. And I was like, why can't we play some number based games? And so I totally played Guess My Number with the kids. And it was always funny because the adults would kind of perk up. The adults in the room started playing the game too. And they had a blast with it. And sometimes I'd have to say, "hey, like, shh, like, let the kids play. Don't call out the answer before you let the kids sort of answer." So I think there are times where maybe we've been kind of used to playing. I don't know, on road trips, we might play the license plate game with letters, but maybe we could play some of these mathy games and we can help our kids be more mathy more mathematicians. Hey, Aaron. Oh, go ahead, Kim.

Kim Montague  13:13

I was gonna say, um, the fact that you and I laugh about it and joke about it and find enjoyment in it can be something that we pass on to our kids. We all can. 

Pam Harris  13:23

Absolutely that playing mathy things is fun. And it can be interesting to look for being clever about math relationships. Absolutely. Alright. So Aaron, you are the man. Thanks for your letter as the inspiration for this whole episode of our podcast. We love it. So everybody, listeners, if you have a mathy person in your life, we would love to hear about them and the mathy things that you have heard them do. So you can totally send those to Pam@mathisFigureOutAble.com, or Kim@mathisfigureoutable.com and we'd love to share about your mathy person on one of our future podcasts. Alright, don't forget #MathStratChat on your favorite social media on Wednesday evenings love to have you join us there. Thanks tons for the podcast reviews that you've given us on your favorite podcast app. We'd love to have you give us a rating and tell us what you think about the podcast. So, fellow mathematicians, if you are interested to learn more math, and you want to help students develop as mathematicians then the Math is Figure-Out-Able Podcast is for you. Because math is Figure-Out-Able!