Pam  00:01

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

Kim  00:09

And I'm Kim Montague. 

Pam  00:11

And this episode is a MathStratChat episode that is going to prove to be fun because we are both cracking up just a little bit. Hey, what's MathStratChat? Well, every Wednesday evening, I throw out a math problem on social media, and people from around the world chat about the strategies they use. It is super to see everyone's thinking. Kim, why are you laughing?

Kim  00:31

You're going to steal my thinking. Okay, so this Wednesday our math problem was 1,176 divided by 48. So, we're interested how would you solve this problem? Pause the podcast. As always, solve the problem any way you want. It is 1,176 divided by 48. Solve it, and come back to hear how we're going to solve it on the fly. 

Pam  00:51

We're solving on the fly. So, ya'll sometimes Kim and I look at the problems a little bit ahead of time. Not very often. We look at them a little bit ahead of time. And I'll say, "Hey, I'll do this strategy." And she'll say, "I'll do that strategy." We don't do that all the time, but we do do it sometimes. This time, we are on the fly. So, neither of us have thought about this at all. So, I'm looking at 1,176 divided by 48, and I'm saying to myself what is 1,176 close to? It feels to me that it's close to 1,200. Ooh. Which is nice because once I can think about 1,200 and 48. 12 is a factor of 48. So, I'm tempted. And I'm just scratching down a ratio table. And I'm thinking about 48s. And I'm thinking I know one hundred 48s would be 4,800. Therefore, fifty 48s would be half that, 2,400. Therefore, twenty-five 48s would be half of 2,400, which would be 1,200. Now, I'm in the ballpark. So, now I've got twenty-five 48s are 1,200. But I need 1,176. Which is... I'm playing a little I Have, You Need in my head. Which is 24 away from 1,200. So, somehow, I need to get to 24 from 48. So, that's half. So, I've literally written 0.5 in the ratio table to get that 24. And so, now I don't need twenty-five 48s. I need to half 48 less than that, so that would be 24.5. So, I think the answer is 24.5. 

Kim  02:25

Okay (unclear). 

Pam  02:26

You were doing your own work. You weren't even listening to me, huh?

Kim  02:28

I kind of was not because as soon as you...

Both Pam and Kim  02:30

(laughs)

Kim  02:32

Well, listen. And I haven't really solved it. But I was looking at the numbers because as soon as you said 1,200, I was like, "Oh, that's what I was going to do. Straight 100, and then 25, and then...

Pam  02:44

Back up. Mmhm.

Kim  02:45

Alright, so 1,176 divided by 48. I'm going to do equivalent ratios. So, I don't really love 1,176. So, I'm going to just divide out 2 to start, and see what it leaves me with. Half of 1,100 is 550. Half of 76 is 38. So, that's 588 divided by 24. And then, let's see what I got there. That's kind of like 600 divided by 24, which would be 50. But then, that's 12/24 too much. So, that's a half too much. So, did you get 49.5? I don't even know what you got.

Pam  03:38

I got 24.5. How did you get? I followed you to the (unclear). 

Kim  03:42

Oh, no, no, no, no. 25 because 600 divided by 24 is 25.

Pam  03:47

Well, I was going to ask you how you got 50 there. How do you know it was 25? 

Kim  03:50

Because in my head, I said 60 divided by 12 is 5. But it was 24 (unclear)

Pam  03:57

Oh! So, if 60 divided by 12 is 5, then...

Kim  04:00

Divided by 24. 

Pam  04:01

...600 divided by... Wait, wait. You do that faster than me. Go ahead.

Kim  04:08

What I said to myself was not 600 divided by 24. I said to myself 600 divided by 12. But that was incorrect. 600 divided by 12 is 50 because 60 divided by 12 is 5. So, 600 divided by 12 is 50. But the problem was actually 600 divided by 24, so that is 25.

Pam  04:35

Nice. And I love it when you do that because my brain is still working on, if you can think about 600 divided by 12 being 50, then 600 divided by something twice as big, the answer has to be half as big, right? 

Kim  04:48

Yeah, yeah. But 600 divided by 24 was too much because I was really looking for 588 divided by 24. Yep. And so it was half too much.

Pam  04:59

Nice.

Kim  05:00

So, 24.5.

Pam  05:00

I like that. Hey, so when you started talking, I actually heard something different, and then I followed what you did. So, if you don't mind, I want to finish what I heard. 

Kim  05:10

Yeah.

Pam  05:10

I wrote a fraction as well. 1176/48 as a fraction. And then, I wrote equals. And that 1,200 was like screaming at me. So, I wrote 1,200/48, minus the extra. Right? If it's 1,176, it's almost 1,200. So, now I have two fractions with a subtraction sign in between. 1200/48 minus 24/48. So, that 24 divided by 48 is the half. Then, I would have to reason about 1,200 divided by 48. And I was wondering if I could do something similar to what you did before. Like, if I could think about 4,800 divided by... No, that's a little different than what you did. But I could think 4,800 divided by 48 is 100, so half of that would be 50. And half again to get 1,200 would be 25. So, there's 25 minus 0.5. Anyway, it was a little fun to play with. I would call that like a smart-partial-quotient, even though I wrote it as fractions. It's not really equivalent ratios because little Over strategy there. Anyway, it was cool. 

Kim  06:10

Yeah.

Pam  06:10

Fun numbers.

Kim  06:11

Yes. Okay, so we can't wait to see your math strategy. I wonder if it was like one of ours, or maybe even something different. Represent your thinking, and take a picture of your work or screenshot your phone, and tell the world on social media. Let's get everybody playing. While you're there, check out what other people did, and definitely comment on their thinking,

Pam  06:31

Hey, and twag... (laughs) twag. Twag me on Twitter. Is it still called Twitter anymore? I don't even know. Tag me on X at @PWHarris. And Instagram, Pam Harris_math. And Facebook, Pam Harris, author, mathematics education. Make sure you use the hashtag MathStratChat. And then, check out our next MathStratChat problem that we'll post every Wednesday around 7 pm Central Time, and pop back here to hear how we're thinking about the problem. We love having you as part of the Math is Figure-Out-Able movement. Let's keep spreading the word that Math is Figure-Out-Able!