In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 1, 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 Harris.
Kim:
And I'm Kim Montague.
Pam:
And this episode is a MathStratChat episode. What is MathStratChat? Well, every Wednesday evening, I throw out a math problem on Twitter, Facebook, Instagram, all the social media. People from around the world chat about the strategies they use. It is super to see everyone's thinking.
Kim:
So, this Wednesday, our problem was one-fourth plus two-thirds. How would you solve this problem? Go ahead and pause the podcast and solve the problem any way you want. The problem is one-fourth plus two-thirds. Solve it, and then come on back to here how we solved it.
Pam:
Alright, Kim, I want to hear from you first today. So, how are you thinking about one-fourth plus two-thirds?
Kim:
Okay, you know when I was thinking about 1/4, I kind of wanted to think about $0.25. But then, I looked at the other number, and it was two-thirds. So, I actually thought about a clock, and I thought about a fourth of a clock is 15 minutes.
Pam:
Okay. Fourth of an hour?
Kim:
Yeah, of the hour. And two-thirds of the hour will be 40 minutes. So, 15 minutes and 40 minutes would be 55 minutes.
Pam:
Can I ask you? I think a quarter hour, a lot of people know, is 15 minutes. But how do you know two-thirds of an hour? Did you just know that?
Kim:
You know, I just feel like 20, 20, and 20 just made sense to me. I don't know that there's like a way that I know that. I just think of 3 chunks of 20 is 60.
Pam:
Okay. Mmhmm. So, like a third of an hour, 1/3 of an hour is 20 minutes.
Kim:
Yeah.
Pam:
So, two of those 1/3s would be 40 minutes. That makes sense?
Kim:
Mmhmm.
Pam:
So, once you got 55 minutes, did you turn it back into a fraction?
Kim:
I did. And so, that would be 11/12 because each 1/12 of an hour is 5 minutes, so if I have 11 of them, that would be 55 minutes.
Pam:
So, your final answer was?
Kim:
Eleven-twelfths.
Pam:
Eleven-twelfths. Okay, that makes sense. Cool. But in the meanwhile, you had 55/60?
Kim:
Oh, you know, I don't actually know that I ever thought about that.
Pam:
Oh, that's interesting.
Kim:
I think I... I just was thinking 55 minutes.
Pam:
Ah, okay. Alright. Cool. I think that's legal. So, I was also thinking time. So, a quarter of an hour is, like you said, 15 minutes. I'm kind of picturing the hand on an analog clock being on the 3.
Kim:
Mmhmm.
Pam:
And so, that's kind of like 3. Each of those hours are kind of like 5 minute chunks. So, if I see the hand on...
Kim:
Each? Where the hand goes, you mean?
Pam: Yeah, so like, 1:
00 is 5 minutes after the hour. Two...
Or 1:
00. Where the 1 is, that would be like 5 minutes after the hour, and where the two is, if the minute hand was there, that would be 10 minutes after the hour. So, since we're on the 3, that's like 15. It's like three, 5 minute chunks, if I'm on the 3. So 15 minutes I could think of as 3 out of the 12, 5 minute chunks. So, three-twelfths. 3... I wasn't really thinking about three-twelfths. I was just think about the 3.
Kim:
Mmhmm.
Pam:
And then, two-thirds. The reason I asked about how you think about two-thirds is because I think about the circle and kind of the peace sign.
Kim:
Yes.
Pam:
If you sort of split a circle into 3 equal parts, it's kind of the peace sign. And so, I was thinking to myself, "If I need 2 of those thirds, where is that?" Like, where? What would I say how much? It's kind of on the 8?
Kim:
Yeah.
Pam:
Yeah, if I picture the peace (unclear). So, that would be like 8/12 or 8 out of those 12, 5 minute chunks. So, I've got three-twelfths and eight-twelfths is eleven-twelfths. So, that's kind of how I was thinking about that one. You like that?
Kim:
Nice!
Pam:
Alright, super. Cool.
Kim:
(unclear) Alright. Alright, well we can't wait to see your strategy. I wonder if your strategy was like one of ours or something entirely different. Represent your thinking, 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:
Yeah, and tag me on Twitter at @PWHarris. Or Instagram, PamHarris_math. And Facebook, Pam Harris, author mathematics education. And use the hashtag MathStratChat. So, make sure you check out the MathStratChat problem we post next Wednesday
at around 7:
00 p.m. Central Standard 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. Let's keep spreading the word that Math is Figure-Out-Able!