# 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 - January 17, 2024

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 17, 2024.

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 **00:01

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

**Kim **00:07

And I'm Kim.

**Pam **00:08

And 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 the strategies they use and comment on each other's thinking.

**Kim **00:21

Okay, so this week, our math problem was three-twelfths times eight-fifths. Solve the problem. And...

**Pam **00:32

Yes?

**Kim **00:32

Like, my brain empties like half the time we're doing this. Pause the podcast. Solve the problem.

**Pam **00:38

Are you trying to do for memory? Is that what's going on here?

**Kim **00:40

(unclear) just looking out my window.

**Pam **00:42

Alright, and then, post your strategy. But hey, before you listen to us, solve it, and then come back. Alright, Kim, here we go. Three-twelfths times eight-fifths. Alright (unclear).

**Kim **00:51

Alright, I'm going to... Do you want to go first?

**Pam **00:53

No, go ahead.

**Kim **00:54

No, it's okay.

**Pam **00:55

You sure?

**Kim **00:56

Yeah.

**Pam **00:57

Three-twelfths is equivalent to one-fourth.

**Kim **01:00

Yep.

**Pam **01:00

So, I'm thinking about one-fourth of eight-fifths. And since one-fourth is a half of a half. And I'll explain later why I'm doing that, but.

**Kim **01:10

Okay.

**Pam **01:10

I can think about one-fourth as a half of a half. So, a half of a half of eight-fifths is like... I can think about a half of 8 anything's.

**Kim **01:18

Yep.

**Pam **01:19

So, I'm think about eight-fifths, but I just think about 8 anything's. And a half of 8 anything's is 4 of those things.

**Kim **01:25

Mmhm.

**Pam **01:26

And so, that's a half of eight-fifths is four-fifths. But now, I need a half of that because I was trying to find a fourth. So, a half of four-fifths is a half of 4 of those things, which is 2 of those things. Two-fifths.

**Kim **01:39

And when you say "8 of those things," it's like you're almost setting aside the fact that your unit is one-fifth, and you're like stripping out the 8 and saying, "I need a fourth of this," and then you're putting it back into the unit of one-fifth.

**Pam **01:53

Yeah, absolutely.

**Kim **01:53

Yeah.

**Both Pam and Kim **01:54

Yeah.

**Kim **01:54

Cool. Alright.

**Pam **01:56

And I'll just mention, that's a really multiplicative way of thinking about fractions.

**Kim **02:00

Yeah.

**Pam **02:00

Not as... So, like eight-fifths. So, not as 8 out of the possible 5.

**Kim **02:04

Right.

**Pam **02:04

But as thinking about eight 1/5s. 8 of those one-fifths. Like 8 times one-fifth.

**Kim **02:10

Mmhm.

**Pam **02:10

8 of those things. That's a multiplicative way of thinking about it. Which is our goal. Our goal is to think about fractions multiplicatively. Not as just a part whole representation.

**Kim **02:19

Right.

**Pam **02:20

Yeah.

**Both Pam and Kim **02:20

Alright.

**Pam **02:21

Got anything?

**Kim **02:22

Yeah, I've got three-twelfths is a fourth. I'm going to stick with that. For eight-fifths, I want to call that 1 and 3/5.

**Pam **02:34

Okay.

**Kim **02:34

Because I know 1 and 3/5 is 1.6 or 1 and 6/10. So, I'm going to say my problem. I've transformed a little bit into 1/4 of 1.6. Which is just my 0.4. $0.40.

**Pam **02:48

So, I'm curious. When I wrote down the 1.6, and then I wrote down the 1/4, then I smiled because I know a fourth of 16...

**Kim **02:57

Yeah.

**Pam **02:57

...is 4. And then, did you think that or did you actually think about a fourth?

**Kim **03:01

I though like 1.6 like $1.60. So, 1/4 of $1.60 is $0.40.

**Pam **03:06

$0.40.

**Kim **03:07

Yeah.

**Pam **03:08

And then, your 0.4 is equivalent to my two-fifths.

**Kim **03:10

Yeah.

**Pam **03:11

Nice. Hey, I didn't want to forget to talk about why I did one-fourth as a half and a half.

**Kim **03:16

Oh, yeah.

**Pam **03:16

So, I could have thought about one-fourth of 8. And a fourth of 8 is 2.

**Kim **03:21

Yeah.

**Pam **03:21

And just kind of straight to the two-fifths. But often, people will think about finding a fourth of something as a half, and then a half again. And I do support that strategy. And then, eventually, for being able to think of not having to do half and half again, but I can just divide by 4.

**Kim **03:35

Yeah.

**Pam **03:36

Anyway, (unclear).

**Kim **03:37

Yeah. I love it. Alright, everyone.

**Pam **03:39

We love fractions!

**Kim **03:41

We do love fractions. We can't wait to see what you do with these fractions. Share your strategy with us and the world by taking a picture of your thinking. And then, when you're posting it, comment what other people did.

**Pam **03:53

Absolutely. That helps us spread the word and spread the math is figure-out-able movement. And so, use the hashtag MathStratChat and tag m, and then check out the next problem that will post Wednesday evenings around 7pm Central Time, and then come back here to hear how we're thinking about the problem. Ya'll, thank you for joining us as part of the Math is Figure-Out-Able movement. Let's keep spreading the word that Math is Figure-Out-Able!