In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 30, 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 episode is a MathStratChat episode. What is MathStratChat? Well, every Wednesday evening, I throw out a math problem on social media, people from around the world chat about the strategies they use. It is super to see everyone's thinking.
Okay, so this Wednesday, our math problem was 1,683 divided by 33. How would you solve this problem? Pause the podcast. Solve it however you want. The problem is 1,683 divided by 33. Solve it, and then come back to here how we're going to solve it.
Bam! Alright, Kim, I'm going to go first.
So, I'm thinking about 33s. And I'm thinking about one hundred 33s is 3,300. So, I don't know if you care, but I'm in a ratio table. So, I just wrote down 1 to 33, 100 to 3,300. And then, I'm going to Halve that to get 50. And I actually have to think about this for a second because half of 3,000 is 1,500. And I'm going to add that 1,500 to the 150, which is a half a 300. So, that's 1,650. I did that in my head. Did I do that, right? Yes, yes. Okay. Whoa! Alright, so now I'm close. 1,650 is close to 1,683. And I'm asking myself how close, and it happens to be nicely, 1 unit. Nice problem today. One 33 away. And I'm just 33 under, so I'm going to add 33 to 1,650 to get 1,683. And I'm going to add 1 to 50 to get 51. So, I think the answer is 51.
Okay. Well, you stole the way that I was going to do it.
No, it's fine. So, I'm just, you know, I'm going to do a problem kind of on the fly. I haven't thought about it at all. But I'm thinking the other way to think about division. And so, I wrote 1,683 "line" 33. (unclear).
Like a fraction kind of, mmhmm.
Yeah. And I was thinking, "Okay, 33s. What factors of 33 will work?" So, I was thinking like, "I'll pull out 3." And so, I'm going to scale down both numbers by 3. So, 33 parts. Easy. So, that's 11. And so, if I'm going to divide 1,683 by 3, I'm going to say, "Okay, I know 1500 by 3 is 500. And 180 divided by 360. And 3 divided by 3 is 1. So, I've now got 561 divided by 11. I don't really love it. So, I'm going to get with...
Hang on a second. Sorry, I got lost.
You did 1,500 divided by 3 is 500. And then, you were left over with 183 divided by 3.
183. Mmhmm. Sorry, Yeah.
And that was 61. Oh, okay. So, now you have 561 divided by 11.
Yeah, which is kind of gross.
Is that right?
Well, okay, so then there's this 11 thing happening, which I'm only just starting to play with.
Okay, well, do you want me to tell you what I was going to do? Okay, so then I was thinking like, what elevens do I know.
So, I thought, "Well, I know 550 divided by 11 would be 50." So, like, as I'm staring at the 561, I'm thinking of it as 550 and 11.
You are so good.
And so, I got 50 and the same 1. 51.
And the 1 left over because you have an extra 11 leftover. 11 divided by (unclear).
Yeah. That wasn't as bad as I thought it was going to be.
Whoa! Nicely done. Cool.
Alright. Okay, so we can't wait to see your math strategy. I wonder if your strategy was like one of ours or something entirely different. Try to represent your thinking, and take a picture of your work or screenshot on your phone, and tell the world on social media. And while you're there, the best thing to do is check out what other people did and comment on their thinking because they have so much good stuff to share.
Yeah, and tag me on Twitter at @PWHarris. Or Instagram, PamHarris_math. And Facebook, Pam Harris, author mathematics education. And use the hashtag MathStratChat. And make sure you check out the MathStratChat problem that we'll post every Wednesday evening, 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 movement.