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.

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.

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Pam:

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!