In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 19, 2023.
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.
Hey, fellow mathematicians! Welcome to the MathStratChat episode of the podcast Math is Figure-Out-Able. I'm Pam Harris.
Kim:
And I'm Kim Montague.
Pam:
And what is MathStratChat? Well, every Wednesday evening, I throw out a math problem on social media, and people from around the world share the strategies they use. We love to see your thinking!
Kim:
So, this Wednesday, our math problem that we shared was 3 and 1/3 divided by 4. How would you solve this problem? Pause the podcast, solve it any way you want, and then come back and listen to how we solve it. The problem was 3 and 1/3 divided by 4.
Pam:
Alright. So, Kim, I've been playing with a strategy the last few MathStratChat episodes. People might be like, "Pam, stop with your stupid divide out strategy, like share the brownie with people." Check out how it works on this problem. So, if I have 3 and 1/3 divided by 4. By the way, I'm going first today, Kim.
Kim:
It's totally fine(unclear).
Pam:
Here we go. Taking over. I'm excited! Alright, so if I have 3 and 1/3 brownie shared with 4 people. You might be like, "Pam, that's a terrible strategy." Or is it? Because let's say that I've got those 4 people, and they're looking hungrily at those 3 and 1/3 brownies. I'm going to go ahead and give everybody a 1/2 of a brownie. So, if I give 4 people 1/2 of a brownie, I've gotten rid of 2 brownies, right? So, I now have only 1 and 1/3 brownie left. Well, 1 and 1/3 brownies, that's like 4/3 because I have 3/3 and 1/3. So, that's 4/3. And I have four 1/3's to split among 4 people. That means they each get a third.
Kim:
Nice.
Pam:
Everybody got a half of a brownie and a third of a brownie. Bam! That's a pretty slick strategy for that problem.
Kim:
Nice. Yeah, it is nice.
Pam:
Thank you. I appreciate that. Alright.
Kim:
I did not think about fair sharing or dealing out. What I actually thought about was... Oh, gosh, here I am with the division words. I... Is it partitive? Is it quotitive? I think it's quotitive. So, I actually thought about an equivalent division problem.
Pam:
Ah, partitive.
Kim:
So... Thank you. I can never get those right. But, so 3 and a 1/3, I didn't want to mess with, and so I thought, "Let me think about how to get out of the thirds." So, I thought about scaling up, times 3. And so, instead of 3 and a 1/3, I made the problem 10 divided by 12.
Pam:
Okay, how'd you get the 10.
Kim:
So, 3 and a 1/3 times 3 is 10.
Pam:
You might want to spell that out a little bit.
Kim:
3 times 3 is 9, and 1/3 times 3 is 1. So, then 9 and 1 is 10.
Pam:
Brilliant.
Kim:
So, then, that would be the first part of the division problem. And so, then, I also need to scale the divided by 4.
Pam:
Mmhmm.
Kim:
And so, that would be divided by 12. So, 3. So, then, that that gave me 10 divided by 12. So, scaled both them up times 3. And then, I just have 10 divided by 12, which is 10/12.
Pam:
Nice.
Kim:
Which is equivalent to five-sixths.
Pam:
Yeah, and let me just share maybe with people who are listening. So, I... And this might be what you have on your paper. Maybe I should have asked. I wrote 3 and 1/3, and then the fraction bar 4. So, visually it looks like 3 and 1/3 over 4. So, it's kind of like a compound fraction, we sometimes call it. So, then, you said to yourself, you're going to find an equivalent fraction. So, then, I wrote equals. And you said 3 and a 1/3 times 3. And so, I have this like scaling mark. 3 and 1/3 times 3 is 10. And then, 4 times 3, scaling mark, is 12. And you end up with a fraction ten-twelfths.
Kim:
Yep.
Pam:
Yeah, which is five-sixths. And now, you have me wondering is a half plus a third, five-sixths. And now, I'm thinking about a clock, and I just thought about the minute hand on the sixth, and then plus another 20 minutes. Sure enough, sticks me up on the 10. And that's ten-twelfths, so five-sixth. Cool. Nice, problem. Alright.
Kim:
Yeah, it was a good problem. Well chosen, Pamela. Alright. We can't wait to see your strategies, and I wonder if it was like one of ours. Represent your thinking, take a picture of your work, and tell the world on social media. While you're there, check out what other people did and please comment on their thinking as well.
Pam:
And when you do, tag me on Twitter at @PWHarris or Instagram, PamHarris_math. And on Facebook, look for Math is Figure-Out-Able and use the hashtag MathStratChat. And make sure you check out our next MathStratChat problem that we're going to post every Wednesday ad infinitum, as the world continues to spin around. You'll see MathStratChat problems every Wednesday. And then, pop back here to hear how we are 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.