Pam  00:00

Hey fellow mathematicians. Welcome to the podcast where math is always figure-out-able. I'm Pam. 

Kim  00:08

And I'm Kim. 

Pam  00:09

And this MathStrat... Geez. And this episode... 

Kim  00:12

[Laughs] We can't do this anymore.

Pam  00:15

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.

Kim  00:40

Canada.

Pam  00:41

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.

Kim  00:54

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.

Pam  01:20

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." 

Kim  01:28

Yeah!

Pam  01:28

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? 

Kim  01:35

Yep. 

Pam  01:35

So, if I'm running an 8 minute mile, in 8 minutes, I went 1 mile. 

Kim  01:40

Yep.

Pam  01:41

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...

Kim  02:10

Yeah. 

Pam  02:11

...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. 

Kim  02:27

To go 7 miles. 

Pam  02:28

Thank you. 

Kim  02:29

Yeah, I'm with you. Mmhmm.

Pam  02:29

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.

Kim  02:48

Mmhmm.

Pam  02:49

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?

Kim  03:02

I followed you. I'm not sure. Let me tell you what I was thinking. 

Pam  03:07

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. 

Kim  03:16

Yeah. 

Pam  03:16

Okay, what were you thinking? 

Kim  03:18

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...

Pam  03:52

Nice.

Kim  03:54

...by multiplying by 15. So, then, I would carry along that half a mile 15 times would be 7.5.

Pam  04:03

Because you know a half times 15 is 7.5. Or half of 15 is 7.5.

Kim  04:08

Yeah. 

Pam  04:08

So, again, in an hour, in 60 minutes, you went 7.5 miles, 7.5mph. 

Kim  04:13

Yeah.

Pam  04:13

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.

Kim  04:23

Maybe, yeah.

Pam  04:23

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. 

Kim  04:49

Close. You'll have (unclear).

Pam  04:50

No, except for you didn't have the 56. Yeah.

Kim  04:52

But we both use that 4 and the half.

Pam  04:55

Yes, we both had a 4 and a half. Yeah. In the final.

Kim  04:59

Cool. 

Pam  04:59

But you had the 15, and I had the... Yeah. Cool. That is cool.

Kim  05:03

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.

Pam  05:25

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!