In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 14, 2022.
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.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Hey, fellow mathematicians. Welcome to the podcast where Math is Figure-Out-Able! I'm Pam. And this episode is a MathStratChat episode. What'sKim:
And I'm Kim. MathStratChat? Well, every Wednesday evening, I throw out a math problem on Twitter, Facebook, and Instagram. People from all around the world chat about the strategies they use. It is super cool to see everyone's thinking. Okay, so this Wednesday, our problem was 1,236 divided by 24. How would you solve this problem? Pause the podcast. Solve the problem any way you want. The problem is 1,236 divided by 24. Go ahead and solve it, and then come back to hear how we solve it.Pam:
Alright, Kim, who's going first today?Kim:
I'll go first.Pam:
Alright, you're on.Kim:
Is that okay? Alright. 1,236 divided by 24. There are a lot of 12s popping out. And so, what I'm going to do is I'm going to divide both by 12. I'm going to scale down.Pam:
Ooo. Equivalent ratio. Nice.Kim:
And I'm writing 103 divided by 2. So, I'm just going to cut that in half. Halve 100, halve 3. And I'm getting 51.5? Yep, 51.5.Pam:
Man, I want my brain to do that next time. Bam! That is really nice. That is not what I did.Kim:
Well, what did you do?Pam:
Alright, I want my brain to do that next time. But I'll tell you what my brain did this time.Kim:
Okay, so I'm thinking about 24s. And I was playing around with the relationship that popped in my head last week that I could get to 1,200 from 24 by thinking about 24 to 12. So, I wrote down a ratio table 1 to 24. And then, I said one-half. The equivalent ratio would be one-half to 12. Therefore, 50. Equivalent ratio of 50 to 1,200. So, now I've got fifty 24s is 1,200. I need 1 more. So, fifty-one 24s would be 1,224. So, then I said, "How far apart am I? I've got..." Fifty-one 24s is 1,224. But I need 1,236. So, how far apart are those? They're 12 apart. How do I get from 24 to 12? That's a half. So, I need a half of 24. So, now I need fifty-one and a half 24s to get to 1,236.Kim:
And you... Am I right? You already had that piece on your ratio table, that half to 12?Pam:
Did I recognize that I had it? No, actually. In the moment. That's funny.Kim:
Oh. Well, you could have said no.Pam:
I could have said, "Yeah, absolutely. I had that right there. Mmhmm. I just wrote it twice, 'cuz."Kim:
Listen, so you said you wanted your brain to do what I did, and I want my brain to do more of what you do. Because I see often that you will scale down before you scale up. And I don't think about that quite as much. I live in the land of like whole numbers more often, and then scale back down at the end. And I see you do that quite a bit. I'm like, "Oh, I've got to force myself to be thinking about that." So, there you go.Pam:
To think about how to get from 24 to 12. To get, then, to 1,200.Kim:
To get bigger. Yeah.Pam:
Yeah. To get bigger. Nice.Kim:
Very cool. Alright.Pam:
Super cool. Something we encourage middle school teachers to think about. Yeah?Kim:
Sure. Alright, we can't wait to see your strategies. I wonder if your strategy was like one of ours or something entirely different. Represent your thinking by taking a picture of your work or screenshot your phone, and then tell the world on social media. While you're there, check out what other people did and go ahead and comment on their thinking as well.Pam:
Yeah, and tag me on Twitter @PWHarris, or Instagram: PamHarris_math, or Facebook:
Pam Harris, author, mathematics education, and use the #MathStratChat. And make sure you check out the next MathStratChat problem that willpost on Wednesdays at 7:
00 pm, Central Time, and then hop back here to see what we're thinking about the problem. See? Hear? Hear what 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.