Pam  0:00  
Hey, fellow Mathers, welcome to the podcast where Math is Figure-Out-Able. I'm Pam Harris.

Kim  0:07  
And I'm Kim Montague.

Pam  0:08  
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  0:20  
Okay, so this Wednesday, our math problem was, if six-sevenths is two-thirds of a number, what is one-third of that same number? How would you solve this problem? Pause, solve however you'd like. The problem is, if six-sevenths is two-thirds of a number, what is one-third of that same number?

Pam  0:40  
Bam. Okay, I kind of want to do the easy one, but I'll let you. This one sounds complicated. 

Pam  0:47  
Yeah.

Pam and Kim  0:48  
(unclear) 

Pam  0:49  
Sevenths are tricky, and (unclear).

Kim  0:52  
Yeah.

Pam  0:53  
Decimal stuff. 

Kim  0:54  
Well,

Kim  0:54  
and yeah, but I really love that it's asking about two-thirds of a number, and then asking about one-third of a number. And if you know unit fractions, like if you think of non unit fractions as multiplicative of the unit fraction, man, this is not horrible.

Pam  1:10  
Meaning, that two-thirds is two 1/3s.

Kim  1:13  
Yeah,

Kim  1:13  
it's twice as much. So, we know what it is when it's two-thirds of a number, then one-third is going to be half as much as (unclear). 

Pam  1:21  
Okay,

Pam  1:22  
here's the hard... Yeah, here's the hard part. What's half of six-sevenths.

Kim  1:25  
Three-sevenths.

Pam  1:27  
Nice. 

Kim  1:27  
Yeah. I love problems look like a little meaty, and tricky, and hard. And when you actually like get involved with the problem, you're like making sense of it, you're like, "Hey, that's not that bad."

Pam  1:39  
Okay, cool. So, I'm going to take a more complicated but a different way (unclear).

Kim  1:43  
Clever. Clever. Playful way. 

Pam  1:45  
Clever. I'm going to try to be playful. 

Kim  1:47  
Okay.

Pam  1:47  
If six-sevenths, I'm just going to think about it as 6 somethings. 6 things.

Kim  1:51  
Okay.

Pam  1:52  
Is two-thirds of a number. If 6 is two-thirds of the number, can I chunk 6 into 2 bits? Because I'm saying it's two-thirds of a number. So, I'm going to chunk the 6 into 2 bits. That's got to be two 3s. So, each third is 3s. So, now I know that I'm at three-sevenths. Did I just do that right? Okay, all of a sudden it sounded wrong. 

Kim  2:18  
So, 6 things is two-thirds. 

Pam  2:18  
6 things is two-thirds, then 1... Then 3 things is one-third.

Kim  2:24  
Right.

Pam  2:24  
And what's the thing? It's sevenths. So, three-sevenths is one-third of that

Pam  2:27  
number. 

Kim  2:28  
And to some people, that might not sound like it's all that different than what I did, but there is something different about it because there are times where the denominator is really something that you want to like set aside and picture the amount in the numerator and what's happening, what's being operated on, the amount in the numerator.

Pam  2:45  
Well, can I go one more place with what we just did? 

Kim  2:50  
Yeah, sure. 

Pam  2:51  
So, if 6 things is in 2 chunks, to get the whole number, to get the number, I need 3 of those chunks. So, if three-sevenths is 1 of those chunks, and I need 3 of those chunks to make three-thirds of the number, then that would be nine-sevenths. So, nine-sevenths is the number, then but I only need one-third of it, then I'm going to do one-third of 9 things, and that's three-sevenths. So.

Kim  3:17  
Yeah.

Pam  3:17  
Some more extension kind of.

Kim  3:19  
Nice.

Pam  3:19  
Cool. 

Kim  3:19  
Okay, well, every week, we cannot wait to see what you do on MathStratChat. Join us and let us know how you think about the problems. And, of course, comment on each other's strategies.

Pam  3:28  
We'll post the problems on Wednesdays around 7:00 p.m. Central. And by the way, thanks for the few of you who were telling us that there was a problem on X the other day, Twitter, for whatever reason, wasn't posting. So, thanks for the shout out. We appreciate that you're actually following what we're doing. And, ya'll, when you answer, tag me and use the hashtag MathStratChat, then join us to hear how we're thinking about the problem. We love having you as part of the Math is Figure-Out-Able movement. Math is Figure-Out-Able!