Math is Figure-Out-Able with Pam Harris

More Cool Things Mathy People Do

August 11, 2020 Pam Harris Episode 8
Math is Figure-Out-Able with Pam Harris
More Cool Things Mathy People Do
Chapters
Math is Figure-Out-Able with Pam Harris
More Cool Things Mathy People Do
Aug 11, 2020 Episode 8
Pam Harris

After last weeks discussion on partners of 10, 100, and 100, Pam and Kim thought of three more habits "mathy people" have in common. Listen in as they discuss:
1. What it means for mathematicians to "Notice and Wonder"
2. Double and halving
3. Creating habits of thinking (as opposed to grabbing for a calculator)
Tune in to next week's episode to hear all about Pam's method of categorizing levels of mathematical thinking, what she calls "The Development of Mathematical Reasoning".
Find this episode's transcript HERE
Talking Points

  • The prime numbers in your neighborhood
  • The Wonder Game
  • Math-Strat-Chat
  • Our first shout-out
Show Notes Transcript

After last weeks discussion on partners of 10, 100, and 100, Pam and Kim thought of three more habits "mathy people" have in common. Listen in as they discuss:
1. What it means for mathematicians to "Notice and Wonder"
2. Double and halving
3. Creating habits of thinking (as opposed to grabbing for a calculator)
Tune in to next week's episode to hear all about Pam's method of categorizing levels of mathematical thinking, what she calls "The Development of Mathematical Reasoning".
Find this episode's transcript HERE
Talking Points

  • The prime numbers in your neighborhood
  • The Wonder Game
  • Math-Strat-Chat
  • Our first shout-out
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're here to suggest that mathematizing is about thinking and reasoning. It's about creating and using mental relationships.

Pam Harris :

We answer the question, if not algorithms, then what?

Kim Montague :

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 :

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 halve 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 :

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 number who plays around and talks about math. Like it's fun, like it's a puzzle.

Pam Harris :

And 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 it's that there's a math gene only some certain people can do it, all people can be, but we need to know what those things are so that we can develop them and then we all can sort of be that mathy person. So what are those things? Alright, so Kim I want you 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 :

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 :

I mean, I would look at the thing on the grocery store deal to, you know, where it tells you the price per ounce or whatever, or every once in a while, if it wasn't there, if the tag wasn't there, I could figure price per ounce. But I always figured the unit rate and never did anything else to compare 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 kind of had to admit, but I had to think about why I didn't. I had to think about it for a while. And I came to the conclusion that you had so many more - and this is a while ago, at that point where I had little numeracy. You had 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.

Kim Montague :

Yeah.

Pam Harris :

So another one of my favorite stories that you've talked about was with you and your boys, and you guys were driving, you remember that one?

Kim Montague :

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's 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, where 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 :

And when you told me about it 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 sounds fun and you guys sort of solve it together. So they like that was a thing to them. So that's noteworthy that mathy people notice and wonder about a lot. And so if we can show people that that's a thing, we can help create that in other people.

Kim Montague :

Yeah. So noticing wondering is one thing. What's another?

Pam Harris :

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 could teach elementary math better, I was messing with sort of single digit doubles. And I was learning that those were really helpful. I learned that kids can think about a most missed fact like seven plus eight, by thinking about seven plus seven, which a lot of kids know it's funny, they don't know seven plus eight, but they know seven plus seven. So if they know seven plus seven, then they can use that to help them 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. One day, I was giving a pre Cal workshop. So I'm a T-cubed instructor. I talked about the power of technology, and we were messing around with these gnarly functions and precalculus. We were using graphing technology to mess with them and I just said something. I said, Hey, do you guys know? Like the doubles are important? Like, I guess it's like a thing for kids, to know, doubles. This teacher in the back goes, Oh yeah, like double 35. And I was like 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 7, double 35 is 70 double 350 is 700. And I was like, I mean, yeah, I guess. Well, so interesting. I began to own that double and 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 in 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 Kim play along with me a little bit here. If I were to say the number seven what's double of 7?

Kim Montague :

14.

Pam Harris :

Well, what about double 14?

Kim Montague :

28

Pam Harris :

All right, how about double 28?

Kim Montague :

Oh, gosh, 56.

Pam Harris :

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, I just had double sevens so now you have two sevens is 14, then double that 14 I have four sevens is 28, and then double that 28 to 56. 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 missed multiplication facts. So Kim double, I don't know 21

Kim Montague :

42.

Pam Harris :

I mean, that's a pretty easy one, right? Almost everybody, can 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 42. And bam, you've got six sevens. 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 17?

Kim Montague :

34.

Pam Harris :

How do you think about that? Do you know double 17? Or do you actually think about it.

Kim Montague :

Actually no, I thought about double 15 plus four more. So double 16 plus double 2,

Pam Harris :

Because 17 is 15, and 2, so if you double those pieces, then you can add them together nice. What if I ask you another random number like I don't know, 49?

Kim Montague :

98.

Pam Harris :

How do you do that?

Kim Montague :

And that was double 50. subtract two.

Pam Harris :

Oh, a little bit of an over strategy. You were thinking about 49 as 50. Double 50 is 100. But 49 is one less than that. We 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?

Kim Montague :

72

Pam Harris :

Okay, How'd you do that one?

Kim Montague :

I doubled 30 and doubled six.

Pam Harris :

Which is a real typical strategy that kids will often use, right? Could could you've also doubled 35? Oh there's that 35 I was talking about! So 35 doubled to 70. So 36, doubled is 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.

Kim Montague :

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

Pam Harris :

Whoa, Okay, go.

Kim Montague :

Okay, ready? What is half of 64?

Pam Harris :

32.

Kim Montague :

What about half of 72

Pam Harris :

36 that one I just know.

Kim Montague :

Yeah. How do you know that way?

Pam Harris :

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

Kim Montague :

Half of - Oh, here we go half of 336.

Pam Harris :

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

Kim Montague :

And I just heard you talk about how you did it!

Pam Harris :

Sure enough. So I did half of 300 is 150 and then half of 36, because you had 336 half of 36 is 18. So 150 and 18 is 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 168, but you heard how he's thinking about 168. It is totally legal that when kids are finding doubles and finding halfs 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 it can be really helpful at helping kids focus on the number they're doubling or their number that they're halving. 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. All right. 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 halve 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's going on in your head?

Kim Montague :

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. And y'all there other people like that, that's why I created the #MathStratChat. It's a place where we can play with the 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 not a math teacher at all, but he enjoys messing with numbers. So he joins us on Facebook when I throw out a MathStratChat question. And we chat about it with the world to see how everybody's brains thinking about it. And sure enough, Steve will show up and he'll have some great strategy. Now, sometimes it's not the main strategies that we sort of advocate, what we teach kids, because he's just kind of messing around in his own head. And ya'll there are people out there that do that and what 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 or a math problem, we can say to ourselves, how would I how would I tinker with that? Is there something I could play with in 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. So if you're interested in becoming a little bit more mathy, you can notice and wonder, you can double numbers and halve numbers. And when you come across a problem, instead of grabbing for a calculator, you can see what you can do before then.

Pam Harris :

Yeah, excellent. So do you know somebody who plays with numbers, who are the mathy people in your life? We want to hear about it.

Kim Montague :

Yeah!

Pam Harris :

We are inviting you to tell us about a friend who does mathy things and we'll give him a shout out on a future episode. Also, if you like the podcast, give us a review. We'd appreciate it, that can help people find the podcast. We'd love to have you join us on MathStratChat where you can hang out with other mathy people as they solve problems for fun. Check us out on on our website at mathisFigureOutAble.com. 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.