In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 16, 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 always figure-out-able. I'm Pam.
And I'm Kim.
And this MathStrat... Geez. And this episode...
[Laughs] We can't do this anymore.
And this episode is a MathStratChat episode. I will get these words out. What is MathStratChat? Well, it's someplace where we're having a lot of fun obviously. 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. Hey, just last week, I saw Germany, Japan, Australia. Some countries were I don't recognize the script.
Definitely had Canada. Some countries I don't organize the script. So, I'm not even sure what to call those languages. But I didn't recognize the way your name was written. So, we love having everybody from around the world jump in, and we like to see their thinking.
Yeah. Okay, so this Wednesday, our problem was a little bit different. The problem was, "If you're running an 8 minute mile, how fast are you going?" How would you solve this problem? Pause the podcast, think about it, solve it however you want. The problem is, "If you're running an 8 minute mile, how fast are you going?" Solve it, and then come back to hear how we solve it.
Okay, so this one's a little tricky because you could say, "How fast you going?" "Well, I'm going an 8 minute mile. That's how fast I'm running."
So, is there another way to talk about how fast you're going if you're running an 8 minute mile? So, I'm going to start if you don't mind? Kim, is that okay?
So, if I'm running an 8 minute mile, in 8 minutes, I went 1 mile.
So, I could think about in twice that. 16 minutes, I would have gone 2 miles. Ooh, that starts me thinking about, "I wonder how many miles I would run in an hour?" Because that's a way to talk about speed, is miles per hour. If I could find out, if I'm doing that 8 minute mile, how many miles? So, if it took me 8 minutes to do a mile, I think it would take me 7 minutes... 7 minutes. No. It would take me 56 minutes...
...to go... How am I saying this? 7 times that, right? So an 8 minute mile, if I did that seven times, then I've gone 56... No, I'm not doing that right. It would take me 56 minutes... No.
To go 7 miles.
Yeah, I'm with you. Mmhmm.
56 minutes to go. Yes, 56 minutes to go 7 miles. But I want to find out how far I would go in 60 minutes. So, I've got that kind of extra 4 minutes hanging around, right? So, if I'm running an 8 minute mile, then in that 4 minutes, that extra 4 minutes hanging around, I would have only gone a half a mile.
So, I would have gone 7.5 miles in 60 minutes. In 7.5 miles in 60 minutes is also 7.5 miles per hour. Did that make sense?
I followed you. I'm not sure. Let me tell you what I was thinking.
Okay. Alright. Yeah. Because that's true, right? Like, sometimes you can kind of follow what someone else is doing, but when you're like wanting to get your own thinking out, it's harder to kind of latch on to someone else's.
Okay, what were you thinking?
Well, I was thinking that if you were doing an 8 minute mile, that's 8 minutes for 1 mile. And I actually sketched on a ratio table. I don't know that we often talk about what we put on a piece of paper, but I put 8 minutes for 1 mile. And then, I saw, well 8 is not going to nicely get me to 60 minutes, so I actually scaled down, and I said, "How far would I go in 4 minutes?" And that would be a half a mile. So, if 8 minutes for 1 mile, that's 4 minutes for half a mile. And the reason I did that was because I could get from 4 minutes to 60 minutes...
...by multiplying by 15. So, then, I would carry along that half a mile 15 times would be 7.5.
Because you know a half times 15 is 7.5. Or half of 15 is 7.5.
So, again, in an hour, in 60 minutes, you went 7.5 miles, 7.5mph.
Ooh, I like that. I like that a lot. I wonder if my thinking if I wouldn't have gotten lost when I had that little hiccup, if I wouldn't have gotten us lost. I would have recorded my thinking in a ratio table.
Because I think my ratio table... If you don't mind because now I'm stuck in my thinking. So, similarly, if I had the 8 to 1 in the ratio table, and I scaled up times 7, then I would have clearly seen that times 7 there to get me to 56. Then, I would have scaled up the 7 times the 1 and also gotten me to 7. But I still need that half. So, it's funny. We're going to end up with the same things in our ratio table, just in a different order.
Close. You'll have (unclear).
No, except for you didn't have the 56. Yeah.
But we both use that 4 and the half.
Yes, we both had a 4 and a half. Yeah. In the final.
But you had the 15, and I had the... Yeah. Cool. That is cool.
I'm super curious about what other people did for this particular problem. We want to see your strategy. So, maybe it was like Pam's, maybe it was like mine, or something entirely different. We would love it if you would represent your thinking and take a picture to share with the world. And hey, people love it when you like and comment on their thinking, so do that while you're there.
Yeah, and tag me on Twitter at @PWHarris. Or Instagram, PamHarris_math. And on Facebook, Pam Harris, author mathematics education. And when you do, use the hashtag MathStratChat. And then, check out the next MathStratChat problem we'll post next Wednesday around 7pm Central Time, and hop 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. Thanks for spreading the word that Math is Figure-Out-Able!