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!
