Hey, fellow mathematicians! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam.
And I'm Kim.
And this episode is a MathStratChat episode. What is MathStratChat? Well, ya'll, 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 cool to see everyone's thinking. You're up, Kim.
Thanks. Oh, goodness.
Okay, this Wednesday our math problem was 4 and 1/5 divided by 3. Coming in now? Nope.
How would you solve this problem? Pause the podcast, come back and listen to how we solve the problem. It's 4 and 1/5 divided by 3. (unclear).
It's a good day. It's a good day today.
Alright, you want to go first or do you want me to?
I'm going to go first today.
Okay.
Okay, so I'm going to think about. I'm messing around with a thing, a way of thinking about division of fractions, and so I'm messing with that. And I recognize it might not be. I don't know, maybe people are like, "Why are you doing that?" Well, because I'm messing around with it, and mathematicians do that. We play with relationships. Today, I'm playing with this relationship. So, I'm thinking if I had 4 and a 1/5 brownies, and I'm going to
share it among 3 people. So, I'm going to sort of fair share 4 and 1/5, I'm going to cut 4 and 1/5 into 3 chunks. So, I might, if I was doing that, I might say, "Well, hey, each of us..." If there's three of us, "...each of us, if there's 4 to 1/5 brownies, each of us gets a whole brownie." And if I give each of us a whole brownie, that takes care of 3 of the brownies, and now I have 1 and 1/5 brownie
left. Does that make sense? Yep. And so, then, I might say, "I'm going to go ahead and take that 1 brownie, and I'm going to split it up evenly, and so each of us would get 1/3 of a brownie." That takes care of the 1 brownie. And now I still have a one-fifth of a brownie leftover, at which point, honestly, we might just be like, "Whatever. Who..." You know like, just throw away that one-fifth because it's like
tiny. Maybe these are huge brownies, so it's worth doing something with that one-fifth. But now I'm going to pull on the definition of fractions because if I have to cut 1/5 into 3 chunks, then that's just a fifteenth. Because I could think about the whole brownie. If I had all the fifths cut into thirds, then that would be 15 total, and so it would be a fifteenth. So, everybody would get a whole brownie, and a third of a brownie, and a fifth of a brownie. And I didn't actually
even go farther than that. I just left it at a whole brownie, a third of the brownie. Because literally if I was sitting there with the brownies, I'm not going to like squish them together to figure out kind of how much of a brownie I got. I just, I'm going to eat a brownie, and a third of a brownie, and a fifth of a brownie.
Cool. Alright.
Alright, what did you do?
When I saw 4 and a 1/5, I kind of wanted to live outside of fractions. So, I hope that's okay with you. But I know that there is a really close relationship between decimals, fractions, and percents. I kind of wanted to take it to percents. So (unclear).
You're a percent girl.
I do like percents. So, when I saw 4 and a 1/5, I immediately wrote down 420%.
Okay.
So, then, I just wrote down 420% divided by 3. And so, 300% divided by 3 is 100%. And 120% divided by 3 is 40%. So, then, it would be 140%. Which is the same as 1, and 40% is 2/5. So, I got 1 and 2/5.
Nice. I like it. Now, you have me sort of curious about my 1, and 1/3, and a 1/5, and if that's equal to 1 and 2/5.
Hopefully so.
But it's not. Now, I'm troubled.
Am I wrong?
I don't know. Am I wrong? One of us is wrong. Right?
Oh, Pamela, I (unclear) to 1/5, 20%, and it's 40%.
Wait a minute. How's 1/5, 40%?
No, it is 20%. Okay, I was trying to make me wrong and not you wrong. 1/5 is 20%. So, that is 420%. Yeah?
Yeah.
Divided by 3. So, 300% and 120%.
I know. So, what did I do wrong?
I don't know. I feel like I was listening to you carefully. What did you say? Maybe I was writing?"
Okay, so 3 brownies divided among 3 people is 1 brownie, so that's 1.
Yes, yes.
And then, wouldn't I still have 1 and a 1/5 is left over?
1 and 1/5. Mmhmm. So, that'd be a one-third and a fifteenth.
A third and a... So, what is 1, and a 1/3, and.... Oh! Maybe I'm crazy. I know what I did wrong. I wrote down 1 and a 1/3 and a 1/5, and I was trying to add those together to get those to be.
Yep.
Alright. well, so that's just a... That's not a math error. That's a, "I was listening to your strategy and didn't write down the final number and then when I went back to see what I wrote..."
Okay. But can we pause on that for a second? I know, we need these episodes to be really, really short. But there is a huge distinction between an understanding error and like something you need to have a conversation with a kid about like (unclear).
And really work on developing. Mmhmm.
Yes! Or, like you forgot to put up a dinky little mark. That is a grandly different conversation, and I sometimes think when we just mark the answer right or wrong, we're treating them all the same. So.
Or even marked the work right or wrong.
Yeah.
Because even if I go into the steps, and you know like, "Ah. You know, I see that you got up to here, but I'm taking off points." There's a huge difference between a conceptual "I don't know what am I doing" wrong.
Yes.
And a "Oh, I said fifteenth but wrote fifth."
Yeah
That wrong, that's a different thing. Yeah, good point.
Absolutely. Absolutely. Okay, so we can't wait to see your math strategy, and I wonder if it was like one of ours. Really, truly we wonder! So, represent your thinking, take a picture of your work or screenshot your phone, and share on social media. And while you're there, check out what other people did and comment on their thinking.
Yeah, and tag me on Twitter at @PWHarris. Or Instagram, Pam Harris_math. Or on Facebook, check out Math is Figure-Out-Able. And use the hashtag MathStratChat and check out the next MathStratChat problem that we'll post every Wednesday around 7pm 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 and hope that you'll help us spread the word that Math is Figure-Out-Able!