# Math is Figure-Out-Able!

Math teacher educator Pam Harris and her cohost Kim Montague answer the question: If not algorithms, then what? Join them for ~15-30 minutes every Tuesday as they cast their vision for mathematics education and give actionable items to help teachers teach math that is Figure-Out-Able. See www.MathisFigureOutAble.com for more great resources!

## Math is Figure-Out-Able!

# #MathStratChat - December 6, 2023

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 6, 2023.

Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.

Check out #MathStratChat on your favorite social media site and join in the conversation.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

**Pam **00:00

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

**Kim **00:07

And I'm Kim.

**Pam **00:08

And it's short because this is a MathStratChat episode where we chat about our math strategies. Every Wednesday evening, I throw out a math problem on social media and people from around the world chat about strategies they use and comment on each other's thinking.

**Kim **00:22

Okay, so this week our math problem was seven-fourteenths times eight-thirds. And we're curious how would you solve this problem? Pause the podcast. Go ahead and solve it. Take as much time as you want. The problem is seven-fourteenths times eight-thirds. Come on back to here how we solve it.

**Pam **00:38

Bam! Alright. Go ahead, Kim. You do the obvious.

**Kim **00:43

Well, I was thinking of... Yeah, I don't know.

**Pam **00:44

Oh. Or do you want to do something fun, and I'll do the obvious?

**Kim **00:46

Well...

**Pam **00:47

I shouldn't say "obvious" because that's not maybe nice if it's not obvious for someone else.

**Kim **00:55

Um, I'm going to...

**Pam **00:57

You're thinking.

**Kim **00:58

Well, I mean, last week I did something. Maybe I'll do both.

**Pam **01:03

You'll do both? You don't get two.

**Kim **01:05

Well...

**Pam **01:05

Kim, you only get one.

**Kim **01:06

I'm going to do what I did last week in a different way. Is that cool?

**Pam **01:09

Oh. Yeah, that's (unclear).

**Kim **01:10

Alright.

**Pam **01:10

Okay.

**Kim **01:10

So, the seven-fourteenths is screaming half. So, this is half of eight-thirds. So, but instead of saying I need half of eight-thirds by looking at the 8, I'm going to say that I know half of eight-thirds is eight-sixths. I mean is... Yeah. Eight-sixths.

**Pam **01:37

Yeah. You had to rethink that. What did you re-think?

**Kim **01:41

Because I didn't write that down as I was saying it. I was writing eight-thirds as I said eight-sixths. So, yeah. (unclear).

**Pam **01:48

How do you know? How do you know that half of eight-thirds is eight-sixths?

**Kim **01:51

Yeah, because of eight of the 1/3s. And instead of taking half as many, I'm going to make the size half as much.

**Pam **01:59

Oh, nice.

**Kim **02:00

So, I have eight-sixth, which is the same as four-thirds.

**Pam **02:07

Because half of a third is a sixth.

**Kim **02:09

Mmhm.

**Pam **02:09

So, half of eight-thirds is eight-sixths.

**Kim **02:13

Yeah.

**Pam **02:14

Yeah. And then, you simplified that to be four-thirds.

**Kim **02:16

Yeah.

**Pam **02:16

But you could have thought about half of 8 anythings

**Kim **02:19

Yes.

**Pam **02:19

Is 4 of those things.

**Kim **02:21

Yeah.

**Pam **02:21

So, it was eight-thirds. And it's four-thirds.

**Kim **02:24

Yeah, but I did that last week. So, I wanted to (unclear).

**Pam **02:26

No, I like how you thought about half of thirds as sixths.

**Kim **02:32

Yeah.

**Pam **02:33

That makes me wish I would have thought about that. So, just for fun, I'm going to try to do what I did last week. But I will admit, I haven't thought about it yet, so this may... Okay, so I'm thinking about eight-thirds of one-half.

**Kim **02:46

Okay.

**Pam **02:47

Which, eight-thirds is like 2 and 2/3.

**Kim **02:49

Mmhm.

**Pam **02:51

So, I'm not sure why that's easier for me to think of, but it is at the moment. So, 2 and 2/3 of 1/2. Two 1/2s is 1. Now, I need two-thirds of one-half. So, a third of one-half is a sixth, so two-thirds of one-half would be two-sixths. So, 1 and 2/6. Or 1 and a 1/3. Which is also like your four-thirds.

**Kim **03:18

Nice.

**Both Pam and Kim **03:20

(unclear).

**Pam **03:20

I had to work on that one.

**Kim **03:21

I mean, and I was just about to comment. The richness that you, like the ownership that you have over those relationships, just when you're talking about it, is so evident. Right? Like, you kind of went in and out of lots of things there. And I mean, I think many of us can say, "I know half of 8 is 4, so four-thirds. You know? Like, just... Yeah.

**Both Pam and Kim **03:46

(unclear).

**Kim **03:46

It's a great strategy, right? And we want kids to see that.

**Both Pam and Kim **03:51

(unclear)

**Pam **03:52

Yeah. And it's probably what we design when we design. You know, we design these problems forever ago, and then we actually record them today, so we don't really remember. But we were thinking about one-half of something. And, you know, what we're really hoping is that when people see seven-fourteenths times eight-thirds that their gut reaction is, "Ooh, icky." But then, if that's their gut reaction. I shouldn't say we're hoping that's the reaction. But if that's their gut reaction that they take a breath and go, "Wait, can I think about these? Are there relationships that I own that I don't just have to knee jerk do some rule that my sixth grade teacher taught me? But can I think about seven-fourteenths?" Oh, yeah, that is just one-half. And then, can I think about one-half of 8 things. So, we're really trying to nudge there. And I was just having fun with other relationships.

**Both Pam and Kim **04:38

Yeah.

**Kim **04:39

That's super cool.

**Pam **04:39

Nice.

**Kim **04:40

Alright, everyone. We can't wait to see your strategy. Maybe it's like one of ours. Will you please represent your thinking, take a picture of your work, and share it with the world on social media. And don't forget to comment on other people's work.

**Pam **04:53

And if you'll tag me, then I can comment on it too, and use the hashtag MathStratChat and make sure you check out the problem that we post next Wednesday around 7pm, that MathStratChat problem, and come back here to hear how we're thinking about the problem. Thanks for being part of the Math is Figure-Out-Able movement and spreading the word that Math is Figure-Out-Able!