In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 12, 2022.
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.
Pam:
Hey, fellow mathematicians. Welcome to the podcast where Math is Figure-Out-Able. I'm Pam Harris.
Kim:
And I'm Kim Montague.
Pam:
And this episode is a MathStratChat episode. What is MathStratChat? Every Wednesday evening, I throw out a math problem on Twitter, Facebook, and Instagram. People from all around the world chat about the strategies they use. It's super cool to see everyone's thinking.
Kim:
Okay, so this Wednesday, our math problem was three-fourths of 10. How would you solve this problem? Pause the podcast, solve the problem any way you want. Remember, the problem was three-fourths of 10. Solve it, and then come back to hear how we solved it. Go. Okay, Pam, do you want to solve it first? Or do you want me to?
Pam:
I want you to first. So, Kim, three-fourths of 10? What are you thinking about?
Kim:
Three-fourths of 10. I kind of like this problem because when I see three-fourths, I like to think about 75%.
Pam:
Mmhmm.
Kim:
And so, 75% of 10 is just 7.5. And I'm thinking about,"How do I know that?"
Pam:
How do you know that?
Kim:
How do I know that? 75% of 10.
Pam:
I can think of a way.
Kim:
Yeah, go for it.
Pam:
I wonder if you're thinking about 75% of 100.
Kim:
Mmhmm. (unclear).
Pam:
(unclear). 100 is 75, but you're clear that you're a place value...
Kim:
Yeah.
Pam:
Scaled down by 10.
Kim:
Yeah, I think that's probably it.
Pam:
Okay.
Kim:
Is that what you did? What did you do?
Pam:
No. So, I could stay in percents, but I really was thinking about fractions. But either way.
Kim:
Okay, alright.
Pam:
So, I can think of one-half of 10.
Kim:
Okay.
Pam:
So, a half of 10, or 50% of 10, is 5.
Kim:
Okay.
Pam:
And then. But I want to find a quarter, so I'm going to half that again. So, a quarter then of 10 would be half of the 5, which is 2 1/2.
Kim:
Mmhmm.
Pam:
So, if I have half of 10 and a quarter of 10. Five and 2 1/2 that's going to be, add those together to be 7 1/2.
Kim:
Nice.
Pam:
That's what I was thinking of.
Kim:
Nice.
Pam:
But I just thought of one more.
Kim:
Okay.
Pam:
Because three-quarters of 10 is almost four-quarters of 10.
Kim:
Mmm.
Pam:
This feels very Kim-like to me.
Kim:
I know what you're doing.
Pam:
Do you want to finish it?
Kim:
Nah, that's okay. I'm taking a drink of water.
Pam:
So, four quarters of 10 is 10. We just found one quarter of 10 to be 2 1/2.
Kim:
Mmhmm.
Pam:
So, to get three-quarters, I can subtract that quarter. So, four-quarters minus three-quarters, or 10 minus 2 1/2, is also 7 1/2.
Kim:
Yeah, It's really nice because of the 10.
Pam:
Yeah. And I think it's also nice because of the three-quarters. There's different ways that we can think of three-quarters. So, what did we do? We just thought of three-quarters as, I thought of it as three, one-quarters.
Kim:
Mmhmm.
Pam:
You thought of it as 75%.
Kim:
Mmhmm.
Pam:
And then, I also thought of it as four-quarters minus a quarter.
Kim:
Nice. Okay.
Pam:
And I kind of also thought of it as a half and a quarter.
Kim:
Yeah.
Pam:
Maybe I didn't ever think of it as three, one-quarters. I really thought of it as a half and a quarter. But you could have thought of it as, once you found that one-quarter, you could (unclear). Yeah.
Kim:
Yeah.
Pam:
Okay.
Kim:
Cool. Okay, so you heard what we did. We can't wait to see your math strategy. Represent your thinking. You can take a picture of your work or screenshot your phone, and tell the world on social media. And while you're there, check out what other people did and comment on their thinking.
Pam:
And while you're at it, tag me on Twitter: @PWHarris. Or
Instagram:
Pam Harris_math. Or Facebook: Pam Harris, Author Mathematics Education. And make sure you use the hashtag, MathStratChat. So, make sure you check out the MathStratChat problem we post next Wednesday right around 7pm Central Time, and then pop back here to hear what 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!