In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 5, 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 podcast where Math is Figure-Out-Able! I'm Pam.
Kim:
And I'm Kim.
Pam:
And this episode is a MathStratChat episode. What is MathStratChat? Well, every Wednesday evening, I throw out a math problem on all the social media and people from around the world chat about the strategies they use. We love seeing everyone's thinking.
Kim:
Okay, y'all, this Wednesday, our math problem was 5 and 1/4 divided by 3. How would you solve this problem? Go ahead and pause the podcast and solve the problem any way you want. The problem is 5 and 1/4 divided by 3. Solve it, and then come on back to hear how Pam and I solved it.
Pam:
Alright. So, Kim, I'm going to ask you to go first today. How were you thinking about 5 and 1/4 divided by 3?
Kim:
Okay, so 5 and 1/4, I think about... Well, it's fourths, and so I know 5 wholes is going to be twenty 1/4's.
Pam:
Mmhmm.
Kim:
Plus another 1/4. So, that's twenty-one 1/4's. So, I wrote down twenty-one 1/4's. And I know that 21 divided by 3 is 7. So, twenty-one 1/4's is going to be 7/4.
Pam:
Got it. Because you're thinking about 21 things, divided by 3 is 7 of those things.
Kim:
Yeah.
Pam:
And in this case, it was fourths, so seven-fourths. Nice.
Kim:
Yep.
Pam:
Nice, I like it. Super straightforward, makes sense, and I can see your reasoning. Cool. So, I decided to take a little bit of partitive approach where I was thinking about literally sharing. So, 5 and 1/4 divided by 3. I thought about like maybe 5 and 1/4 brownies. Say, I don't know, we're hanging around after a party, and there's 5 brownies and 1/4 of a brownie, and there's 3 of us, and we're hungry. And we're like, "Hey, let's split those evenly." So, if we were going to do that, I think we would probably start by giving everybody a brownie, right? Because there's 3 of us, there's 5 and 1/4 brownies. So, if I gave everybody a brownie, then everybody has 1 brownie so far, and we have 2 and 1/4 brownies left. Does that make sense?
Kim:
Mmhmm.
Pam:
So, with those 2 and 1/4 brownies left, I was thinking. Well, then we might say, "Let's cut up those 2 brownies into halves and give everybody a half." So, so far, everybody has a brownie and a half of a brownie. And we've sort of used up 3... The first ones are 3, and then another 1 and a 1/2, so it's like 4 and a 1/2 brownies are gone. And we just had 5 and 1/4. So, we still have a half a brownie and a quarter of a brownie left. Can you picture that? Half and a quarter? That's like 3/4. We have a half a brownie and a quarter brownie left is 3/4. So, if I split up those three quarters, but to those three people, they each get a quarter. So, so far, each of us has gotten a whole brownie, a half a brownie, and a quarter of a brownie, and that's 1 to 3/4's brownies. (unclear).
Kim:
Can I tell you something?
Pam:
Yeah.
Kim:
That when you said you were going to think of it as sharing.
Pam:
Yeah?
Kim:
And you were talking about the three people, I looked at the numbers that I had written, and I was like, "Oh, Kim. You're an Over person. You love to Over."
Pam:
Oh.
Kim:
So, what if it had been 6 brownies divided by 3 people? Then, everybody would have gotten 2. But we don't have 6. We have 3/4 less than 6.
Pam:
Wait, I'm not following you. Say that again? What are you starting from?
Kim:
Yeah, if it had been 6 divided by 3 (unclear).
Pam:
Oh, because the problem... Okay, so hang on. The problem's 5 and 1/4 divided by 3.
Kim:
Yeah.
Pam:
But you're like, "What if we had 6 divided by 3?" Alright, I finally follow you. Okay, go ahead.
Kim:
Okay, then, everybody would be getting 2 brownies.
Pam:
Okay.
Kim:
But we don't have 6. We only have 5 and 1/4 brownies. So, we have 3/4 less than the 6 brownies.
Pam:
Mmhmm.
Kim:
So, since there are 3 people, each of those people like basically has to give back a quarter, if they had gotten 2 brownies.
Pam:
Mmhmm.
Kim:
So, then, I would get the same 1 and 3/4 that you got when you were (unclear).
Pam:
Nice Over. I really like that. That was fun. Ha, cool.
Kim:
Yeah. Alright, cool. So, we can't wait to hear your strategies, listeners. I wonder if your strategy was like one of the ones that we talked about here or something entirely different. Represent your thinking, and then take a picture of it and share it with us, and tell the world on social media. While you're there, check out and comment on what other people did.
Pam:
And tag me on Twitter at@PWHarris. Or Instagram, PamHarris_math. Or look for Math is Figure-Out-Able on Facebook. And make sure you check out the next MathStratChat problem. We post every Wednesday around 7pm, 8pm Central time. Sometime when I get around to it. And pop back here to hear what we're thinking about the problem. Ya'll, we love having you as part of the Math is Figure-Out-Able movement. Help us spread the word that Math is Figure-Out-Able!