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!