Pam Harris  00:00

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

Kim Montague  00:06

and I'm Kim Montague. We're here to suggest that mathematizing is about thinking and reasoning. It's about creating and using mental relationships. We answer the question, if not algorithms, then what? In last week's podcast, we shared one cool thing that mathy people do. Today we'd like to talk about a few more. 

Pam Harris  00:27

Yeah, we'd like to share three things that we found that mathy people do. So number one, they notice and wonder. Number two, they double numbers and alternatively, they half numbers. And number three, when they come upon a problem, they see what they can do, the relationships they can mess with before they ever think about picking up a calculator.

Kim Montague  00:47

Now to be clear, when we say mathy people, we mean that everyone can, but some of us have that friend who enjoys messing around with numbers who plays around and talks about math. Like it's fun, like it's a puzzle.

Pam Harris  00:59

So the point is when you typically think of a mathy person, what they do, how they think, we want to sort of share some of those things today, because then we can all become mathy people. We don't think that there's a math gene and only certain people can do it. All people can be, but we need to know what those things are so that we can develop it and then we all can sort of be that mathy person. So what are those things? Alright, so come on started not wanting to start us off today. Do you remember telling me Actually, you were asking me about when I go jogging or when I'm in the grocery store? 

Kim Montague  01:33

Yeah, I remember asking you. Do you not mess with numbers at all? Like when you're jogging, you don't look at the house numbers and kind of consider like, if it's prime or composite or like what the double of it would be or, you know, like how much of a percentage of the time that you've been running, or like when you're at the grocery store, you don't consider the price per item or how many pounds you can get for $5. Like none of that comes to mind.

Pam Harris  02:00

I mean, I would look at the thing on the grocery store deal to, you know, we're telling price per ounce or whatever or earner wants to off. If it wasn't there. If the tag wasn't there, I could I could figure price per ounce. But I always figured the unit rate I never did anything else to compare that that unit rate. So Kim No, because I didn't own anything. I didn't have relationships in my head. It was so funny to me that day, because she looked at me like, like, don't you do that? Like, everyone does that. And I kind of had this. I was chagrined a little bit I had kind of had to admit, but but I had to think about why I didn't I didn't think about it for a while. And I came to the conclusion that you had so many more. And just a while ago before I had what at that point where I had little numeracy, you had so much so many more connections in your head, so many more mental relationships, that it was fun for you to play with. I didn't I didn't have anything. You have to have stuff in order to play with it. Yeah. So another one of my favorite stories that you've talked about as well. with you and your boys, and you guys were driving during that one.

Kim Montague  03:03

So I wonder a lot, right? Like when I'm running or whatever. And because I wonder a lot, I feel like I also do it aloud in front of my kids. And ever since they were little, we've played what apparently they call the Wonder game. Only I didn't know that that's what they called it. One night, we were driving to my husband station. And my youngest said, hey, let's play the Wonder game. And I said, What are you talking about? And he said, You know, we're we just kind of wonder aloud about three things and then we pick one and solve it. And I didn't realize that it was a game to them, but apparently it was 

Pam Harris  03:38

When you told me about I thought it was brilliant. I was like, obviously, you've had this sort of tradition that you wonder aloud and your kids pick up on that and hear what you're wondering about and then you kind of choose one that That sounds fun and you guys sort of solve it together. So they they like that was a thing to them. So that's that's noteworthy that mathy people notice and wonder about A lot. So if we can show people that that's a thing, we can help create that and other people. Yeah. So noticing wondering is one thing. What's another. So I learned another thing that mathy people do is they mess with doubles, they mess with doubles of numbers. So when I dove into the research about how we can teach elementary math better, I was messing with sort of single digit doubles. And I was learning that those are really helpful. I learned that kids can think about a most Miss fact like seven plus eight, by thinking about seven plus seven, which a lot of kids know it's funny, they don't know simplisafe, but they know seven plus seven. So if they know simple seven, then they can use that delta and think about seven plus eight, or they could use eight plus eight to help them get one less to get seven plus eight. And so I was sort of learning that that was a thing. And one day, I was given a pre Cal workshop. So I'm a Tiki instructor. I talked about the power of technology, and we were messing around with these gnarly functions and precalculus. We're using graphing technology to mess with them and I just said something I said, Hey, just know, like the doubles are important that I guess it's like a thing for kids to know doubles. His teacher in the back goes, Oh, yeah, like double 35.

05:11

And I was like

Pam Harris  05:12

35. Like it kind of blew my mind a little bit because I was totally just thinking about single digit numbers and their doubles. And she said, Oh, yeah, double 35 shows up everywhere. And I kind of looked her and she goes, you know, like, double 3.5 is seven double 3570, double 350 750 700. And I was like, I mean, yeah, I get well, so interesting. I began to own that double oh my gosh, double 35 shows up everywhere. Like there are tons of times, where if I recognize that double of 35, I can use it in a problem. So double with your kids, a thing that you can do to help create mathematicians and your personal kids or your students is to just randomly throw out a number and then mess with the doubles. You can ask your kids How did you find that double so So Kim will play around play along with me a little bit here. If I were to say the number seven what's the Double of 714. Well, what about double 1428?

06:05

All right, how about double 28? Oh, gosh, 56.

Pam Harris  06:11

Totally. So that's a noteworthy sequence that I might ask kids, because now they have a strategy for figuring seven times eight. If I can think about eight sevens, we just did double sevens and I have two sevens is 14, the double that 14 I have four sevens is 28, and then double that 28 256. If your kids are used to doing that double, and they don't know seven times eight, they could quickly do some doubling and then they have one of the most Miss multiplication facts. So Kim double, I don't know 2142. I mean, that's a pretty easy one, right? Almost everybody a double 21. But brilliantly, that's a strategy for another most missed multiplication fact, if I don't know six times seven, six sevens, but I know three sevens is 21. Double that 21 to get 40 And bam, you've got six, seven. So there's some really nice applications to knowing doubles. Let's get a little bit more random though, like I could I can have some random numbers like double 17. What's double 1734? How do you think about that? Do you use no double 17? Or do you actually think I'm actually no, I thought about double 15

07:20

plus four more. So because you've seen plus double two,

Pam Harris  07:25

because 17 is 15, and two, so if you double those pieces, then you can add them together nice. Or by asking another random number like God or no 4998.

07:34

How do you do that? And that was double 50. subtract two. Oh, a little bit of an

Pam Harris  07:42

overstretch Are you thinking about 49 is 50. Double 50 is 100. But 49 is one less than that. You have to double it right? So okay, cool. So double 49 is 98. Let's see one more. One more random one. How about double 36

08:00

72 Okay, How'd you do that? One? I doubled 30 and doubled six,

Pam Harris  08:05

which is a real typical strategy that kids will often use, right? Could could you've also doubled 35. So 35 to 70. So 36, doubles gonna be 72. So part of what you want to do is not just ask kids to double, but then ask them how they're thinking about it and then share how they're thinking about it's kind of a mini number talk. We're kind of like, talking about how we think about doubling problems.

08:29

Yeah, super

Kim Montague  08:30

doubling, super important. But you know, what else is really great. You could have numbers as well, to theme to find out how to half have a number double with your kids and then throw out a number and work on having as well. You can ask half of 16 or 27 or 150. How about if I give you some numbers to have?

08:50

Well, okay, go.

08:51

Okay, ready? What is half of 6432? What about half of 7236

Pam Harris  09:03

that one I just know.

09:04

Yeah. How do you know that way?

Pam Harris  09:06

You know, I've just dealt with doubling 36 so often that now I just sort of own double 36 half a 72. But when you ask me 64, I actually thought about having 60 and having four. That's how I that's how I have that one. All right, give me one more.

09:23

Half of

Kim Montague  09:27

Oh, here we go half of 336.

Pam Harris  09:32

Let's see, that would be 50 and 18 is 168.

Kim Montague  09:36

And I just heard you talk about how you did it

Pam Harris  09:39

sorted out. So I did half of 300 is out and 50 and then half of 36, because you had three and 30 636 is 18. So 158 to 168. And you might be interested to know friends out there that I actually wrote down the number 336. And then I just wrote down hundred 60 But you heard how he's thinking about 168. It is totally legal that when kids are finding doubles and finding halves that for them to keep track of their mental thinking, it's okay for them to just sketch a number down. Even if it's just the number itself can be really helpful and helping kids focus on the number they're doubling or their number that they're having. So it doesn't all have to be without writing something down. We'll talk more about that in a future episode because both Kim and I feel really strongly about the use of paper and pencil judiciously when kids are working. That that it doesn't have to be that you do it all without writing stuff down. So just a little note there. Alright, so to recap, we want you to notice and wonder and help your students realize that it's a thing to notice and wonder, and also to double numbers and have numbers and the last thing we're going to talk about today is your disposition towards math problems. So, Kim, when you enter a math problem, or really any problem is your first instinct to grab a calculator. Like what going on in your head?

Kim Montague  11:01

Oh, no. So my honest answer would be Do I have an opportunity to do some thinking if somebody asks me a problem, my natural inclination is to think about the numbers and to mess around a little bit. I want to see what I can come up with on my own before I ever grab for a calculator.

Pam Harris  11:18

And the all their other people like that. That's why I created the hashtag math strat chat. It's a place where we can play with numbers and find enjoyment in playing around with numbers. So I'm going to shout out to Steve Hammond. He is the husband of a gal on my team. He's got a math teacher at all, but he enjoys messing with numbers. So he joins us on Facebook when I throw out a master I chat question. And we chat about it with the world to see how everybody's brains thinking about it. And And sure enough, Steve will show up. I'll have some great strategy. Now sometimes it's not the main strategies that we sort of advocate we teach kids because he's just kind of messing around in his own head. And you know, there are people out there that do that and and the world We'd like to share with you in this podcast is, we can all start to do that we can all start to do this bit, where when we run into numbers a math problem, we can say to ourselves, how would I how would I tinker with that? Is there something I could play with those relationships? To be able to find the answer? Steve obviously has a calculator in front of him. He doesn't teach math, there's no real reason for him to play with numbers, except for the pure enjoyment of it, and it can be fun when we own enough relationships to play with.

Kim Montague  12:30

So if you're interested in becoming a little bit more Mafi, you can notice and wonder, you can double numbers and have numbers. And when you come across a problem instead of grabbing for a calculator, you can see what you can do before then. Yeah, excellent.

Pam Harris  12:47

So do you know somebody who plays with Ember, who are the mathy people in your life? We want to hear about it. Yeah, we're inviting you to tell us about a friend who does mathy things and we'll give him a shout out on a future episode. So if you like the podcast, give us a review. We'd appreciate it. I can help people find the podcast. We'd love to have you join us on mass drop chat where you can hang out with other mathy people as they solve problems for fun. Check us out on on our website at math is Figure-Out-Able dot com. If you're interested to learn more math and you want to help students become mathematicians. The math is figured out on the podcast is for you. Because math is here.