In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 8, 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.
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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 Twitter, Facebook, Instagram, all the social media, and people from around the world chat about the strategies they use. About one percent of the time someone uses an algorithm. That's not very interesting, so we just focus on what everybody else is thinking, and it's super fun to hear how people are reasoning about the relationships.Kim:
Absolutely. So, this Wednesday our math problem was five-sixths minus one-fourth. How would you solve this problem? Pause the podcast, solve it any way you want. Remember, that the problem was five-sixths minus one-fourth. Solve it, and then come on back to hear how we solve it.Pam:
Alright, Kim. So, I've been thinking about what you did last time. I thought in our last problem because, listeners, you might notice that we're kind of doing problems in a sequence. So, last week's problem could be somewhat related to this week's problem. So, this week's problem of five-sixths minus one-fourth, I decided to go with minutes. And so, I thought about five-sixths of an hour. I had to think about what one-sixth of an hour is, and so a sixth of an hour, that's like 60 divided by 6, is sort of 10 minutes. And so, a 10 minute chunk would be 1/6 of an hour. I'm going to be real Kim-like, and I'm going to back up that one-sixth from the total. I could do 5 times 10 minutes, but instead I'm going to take 10 minutes away from 60 minutes, so I ended up with 50 minutes. So, 5/6 of an hour is 50 minutes. 1/4 of an hour is 15 minutes, so 50 minutes minus 15. Is that 35 minutes? So, then, I'm thinking about 35/60. And honestly how I go from 35/60. If I wanted to create an equivalent fraction that had no common factors, then I would think about where 35 is on a clock, and that's on the seven. And I know that then it's 7 out of the 12, 5 minute chunks, or 7/12.Kim:
Nice. It's really funny that you did what I did because I did what you did last week.Pam:
Yeah, I did.Pam:
Can I just tell you how fun it is for me when I see 35/60 that I don't even... I've gotten so I've had enough practice, enough experience. That's the word I want. Enough experience thinking about time now and using a clock as a model that I see that 35, and it just instantly, bam, 7.Kim:
It's just like seven-twelfths. Yeah. Okay, so you tried what I did last week. Talk to us about that.Kim:
I did, I did. So, I was thinking about five 1/6s of a clock. And so, for each of those, If I thought about there are... Oh, let's see if I can explain this. Talking about your thinking is hard sometimes.Pam:
So, if there are twelve 5 minute chunks on a clock, but I was really wanting to think about it in terms of six chunks on the clock, then every two clicks of the 5 minute hand would be a 1/6. So, if my minute hand went from the 12, and it clicked all the way to the 2, then that would be a sixth of the clock. Does that make sense?Pam:
Yeah. Because one-sixth is twice as big as one-twelfth.Kim:
That's what you're saying. So, if you could think about twelfths being every time you go sort of to a number, if the minute hand goes to a number that's a twelfth, then you'd have to go 2 of those to get a sixth,Kim:
Right. So, then that would mean that 5 of those 6 would be on the 10 of the clock. So, 10 out of the 12, 5 minute chunks would be 5/6.Pam:
So, I just wrote down ten-twelfths. And then, I thought about the fourth of the clock would be like you described last week. It would be when the 5 minute hand, or the minute hand, had gone all the way to the 3. So, 3 out of 12. So, then I wrote down... I had written down ten-twelfths minus three-twelfths, and then that gave me seven-twelfths. And it's funny that you say that because I was like, "Oh, am I right?" But when I saw the 7, I was like, "Oh, that's 35 minutes." Like, you kind of describe. And I thought 7/12 is also 35/60, so I knew that I was correct.Pam:
Bam! Nice. So, I'm just going to ask you that took you a hot minute to explain to us your thinking.Kim:
Yes, it did.Pam:
Did it actually take you that long to... You know when you said, so I wrote (unclear).Kim:
To think about?Pam:
No, it didn't. You know, I kind of closed my eyes, and I pictured the clock, and so when I pictured 5/6 I knew right away, "Oh, that's on the 10." But I don't know that saying"That's on the 10." (unclear).Pam:
Would explan your thinking. Yeah.Kim:
Yeah. And when I saw 1/4, I was like, "Oh, that's on the 3, so the 10 amount, minus the 3 amount, that's the 7 amount." And so, it went pretty quickly. It's just talking about it takes a little bit of time to make sure that I'm making sense.Pam:
Sure. Absolutely. Cool.Kim:
Alright, so we can't wait to hear your math strategy. I wonder if it was like Pam's, or maybe like mine, or something entirely different. Represent your thinking if you can, and take a picture of your work or screenshot your phone, and tell the world on social media. While you're there, we would love it if you checked out what other people did and comment on their thinking as well.Pam:
Yeah, and please tag me on Twitter at @PWHarris. Or Instagram, PamHarris_math. And Facebook, Pam Harris, author mathematics education. And use the hashtag MathStratChat. And make sure you check out the next MathStratChat problem everyWednesday evening around 7:
00 p.m. 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. Let's keep spreading the word that Math is Figure-Out-Able!