In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 21, 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.
And I'm Kim.
And this is a MathStratChat episode where every Wednesday evening, we throw out a math problem on social media, and people from around the world chat about the strategies...MathStratChat...they chat about the strategies they use. We love seeing everyone's thinking.
So, this Wednesday, our math problem was 16 is 32% of what? How would you solve this problem? Pause the podcast, solve it however you'd like, and then come on back to hear how we solved it. Remember, the problem was 16 is 32% of what?
Alright, Kim, let's hear it. What do you got?
Alright. Okay. So, the first thing that jumped out at me was there's a 16 and a 32, and it just has to be half. So, if the ratio of 16 to 32 is 1/2.
Okay, I'm going first. Stop right now. I'm going first. You just hold that thought because you're going to do something crazy. It's going to blow my mind, and I got to get my thinking out before.
Okay. Alright, I'm listening.
I've not solved this problem. What I'm realizing, Kim, is that you're doing something I can't anticipate, and so I want to own the relationships before I hear what you're doing.
And, listeners, this is a real thing. Like, we highly recommend that you own the relationships before you ever hear someone else's strategy. It's why we sit tell you to pause the podcast. Okay, so if you don't mind, I want to own these first. So.
I've got 16 lined up to 32 on a percent bar, and I'm thinking to myself, "What can I scale 32 to, in order to scale it to 100?" Because I want to find the 100%. And I'm thinking I could divide it by 8. I was going to say 4, but I could do either one. I'm going to divide by 8 though. I'm going to divide it by 8 to get 4%. And so, I divide the 16 by 8 to get 2. So, 2 now is lined up to 4%. I'm going to scale the 4% times 25 to get up to the 100%. So, 2 times 25 is 50. So, 16 is 32% of 50. It does make me wonder if I would have divided by 4 though. Divided by 4...
So, if I take the 32% and divide by 4, that would land me on 8%. 16 divided by 4 lands me on 4. So, now we've got 4. Oh, no I don't want to get to 8% because I can't get from 8% to 100 nicely. That's why not. Okay, never mind. Thanks for letting me run it, but there you go. Alright, what were you thinking? Say that again.
So, the numbers in the problem just, when I saw with 16 and 32, I just.. 16 is half of 32, so there's got to be something there.
So, I pictured putting it on a ratio table, which maybe I should sketch more of a percent bar. But anyway, the 16 of the 32 would go together. So, if I was thinking about 100 being the next percent that I wanted to get to... Instead of trying to get from 32 to 100, I'm thinking about the relationship of the 16 to the 32 and what would maintain that relationship if it were 100? So, then, it would be 50 to 100.
Oh, I see what you're saying. So, if you have 16 on the top and 32% on the bottom.
And 100% on the bottom, it's like you're saying to yourself, how can I get from the 32 to the 16. You divide by 2. So, how can you get from the 100 to the unknown? You divide by 2.
You know what this reminds me of? It reminds me of when you're scaling... I'm going to say this so wrong, and you can fix me.
Within and between.
Within or between,
Yes, that's exactly what you're doing.
Huh. Okay, I want my brain to do that next time. I have access to that.
You do! Absolutely.
Alright, we can't wait to see what you did to solve this problem. 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 please comment on their thinking as well.
And tag me on Twitter at @PWHarris. And Instagram, Pam Harris_math. And on Facebook, Math is Figure-Out-Able. And use the hashtag MathStratChat. And make sure you check out the MathStratChat problem that we'll post Wednesdays around 7pm Central Time, and then 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 moment...
Movement. I'm thinking "moment". That too. Let's keep spreading the word that Math is Figure-Out-Able.