In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 23, 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 Harris.
And I'm Kim Montague.
And this is a MathStratChat episode where we talk about the math problem that I threw out on the Wednesday evening on social media and people from around the world chat about the strategies they use. We love seeing everyone's thinking.
So, this Wednesday our math problem was, "If you're walking a 16 minute mile, how fast are you going?" How would you solve this problem? Pause the podcast, solve it however you want. The problem is, "If you're walking a 16 minute mile, how fast are you going? Solve it, and then come on back to here how we're chatting about it.
Nice. Alright. So, Kim, I think (unclear).
(unclear). Alright. So, if we are going 1 mile in 16 minutes, that is equivalent to going a quarter of a mile in 4 minutes. And then... So, I put that on a ratio table, just so you know.
16 to 1, 4 to 0.25. And then, I know I can get from 4 to 60. Kind of like I did last week. Times 15. Kind of boring. And then, that would be a quarter of a mile, 15 times. And that is 3 and 3 quarters.
How did you know?
Well, I'm glad you asked. Because I know 16 quarters. There's my over again. 16 quarters will be 4 miles. So, 15 quarters is 3.75.
I like it. I like it a lot. So, I was scaling on a ratio table as well, but slightly differently. I was also thinking about getting from 16, the 16 mile, up to the 60, so I could see in an hour. And I knew that I could get close by doing 16 times 3. So, 16 times 3 is 48. So, I would go... If I went 16... No, I'm not saying that right. 16 minute mile, I would also do 48...
Minutes for 3 miles. Yeah.
...minutes per 3 miles I can say it. Thanks for helping me.
Do I need time or help, Kim?
Sorry, sorry, sorry, sorry.
Okay. It's almost like I need to label my ratio table better. Okay.
So, then, I'm trying to get from that 48 to 60. And I'm aware that 48 to 60 is 12. So, how can I get from that original 16 to that 12? Well, I know 12 is three-fourths of 16, so I'm just going to put the three-fourths there. And so I had 3 and 3/4 is 3.75 miles per that 60 minutes. So, that's 3.75 miles per hour.
Nice. I like it.
Hey, but, Kim, I have another way to think of it.
Which maybe I just should have done, since I kind of got stuck there with the labels.
Well, hang on a second. Because I didn't put any labels on my ratio table either, and I was getting a little bit stuck on is it miles, is it minutes. And so, when you said that, it was like a nice reminder to me too that sometimes we need to like record the context, so that we're not living in these like just random numbers being thrown around. So, I appreciate you said that.
Just naked? Just running around naked? We don't run around naked when we can be in context. Every time I say that, my mom shakes her head. "Did you really just say that?" And my boys.
We're doing it.
Yeah, there you go. I don't know if all my boys would, but definitely at least one of my boys would shake their head. My daughter would just like give me that look like, "Go, Mom! Go, Mom!" Anyway, okay. So, I'm aware that last week's problem was, "If you're running an 8 minute mile..." Which should be closer to what you do, right? You run, and then... We decided when it was running an 8 minute mile, we were going 7.5 miles per hour.
And this one, "If we're walking a 16 minute mile..." Which would be closer to what I do. I could usually go a little faster than that, but yeah. It's been a hot minute since I had knee surgery. But if I'm walking a 16 minute mile. So, an 8 minute mile was 7.5 miles per hour. If I'm walking twice as slow, half as fast. How do you say that?
Half as fast? So, it was 8 minute mile, now it's a 16 minute mile. Then, what's half as fast as 7.5 miles per hour? Half that would be 3.75 miles per hour.
So, that would be another way if we knew the results from last week. We could do it for this week. Yeah. Cool.
Both Pam and Kim 04:45
ya'll, we can't wait to see your math 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 then tell the world on social media. And while you're there, check out what other people did and make sure that you comment on their thinking, so we can spread this idea that it's about the thinking, the way you're reasoning, not just answer getting.
And it's fun for people to see you comment, right?
Alright, tag Pam on Twitter at @PWHarris.... Did I just say that? (unclear) And on Instagram, PamHarris_math.
I'm taking over. Or Facebook, Pam Harris, author mathematics education. And use the hashtag MathStratChat. And then, check out the next MathStratChat problem that we'll post sometime around 7pm on Wednesdays, and then come 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!