In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 20, 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 all around the world chat about the strategies they use. It is super cool to see everyone's thinking.
Okay, so this Wednesday, our math problem was 1,323 divided by 27. How would you solve this problem? Go ahead and pause the podcast, and solve it any way you want. The problem is 1,323 divided by 27. Solve it, and then come back to hear how we solve it.
Alright. Kim, I think you go first today. I'm curious what you're thinking about. Go.
Okay. I'm going to say... Actually, the first thing I thought of was 1,350. So, I said to myself, "One hundred 27s is 2,700." And then, if I Halve that and get fifty 27s, that gets me to the 1,350. That I first noticed.
Do you just know that half? You just know that half of 2,700 is 1,350.
Yeah, I don't know why.
I guess it comes from knowing half of 27 is 13.5.
So, then I was at 1,350 is fifty 27s. And then, it's just 27 less. So, one less 27 is fourty-nine 27s.
So, your final answer is 49?
Nice. Cool, cool, cool. Alright, since you did that, I'm going to play around a little bit with equivalent ratios.
I'm thinking about 13. I don't know that I would have done this off the bat, but let's play a little bit.
So, thinking about 1,323 divided by 27 as 1323/27. So, I'm kind of looking at a fraction, and I'm saying to myself, "Can I find an equivalent fraction?" And I'm noticing 27 is just this brilliant 3 times 3 times 3. So, there's lots of 3s in 27. And I'm looking at 1,323. And I added the digits together because I happened to know if you add the digits together... And I can understand that, but I'm not going to really go through that today. But if I add the digits together, it's divisible by 3. If that sum is divisible by 3, then the number is divisible by 3. But also 9. And so, if I add those together... What is that? That's 9. And so, if I add the one 3, two 3 together, that's 9, and so that's divisible by 3 and 9. So, 1,323 is divisible by both of them. So, now I just get to like play with do I want to try dividing by 3? Do I want to try dividing by 9? I'm going to go ahead and divide by 9 because I think I might get there a little quicker. So, if I'm thinking about 1,323 divided by 9, I'm going to break that up into numbers that I know. So, 1,323, is equivalent to 900. Because that's super nice to divide by 9. Plus what would be left over? 423. So, I've got 900 divided by 9 plus 423 divided by 9. 900 divided by 9 is 100. And 423 divided by 9 is... Let me think for a second. That would be like 450 divided by 9. Like 423 is close to 450. How close? Ooh, just one 27 close. So, I kind of have 450 divided by 9, subtract 27 divided by 9. So, that's like 50 subtract... Wait. 450 divided by 9 is 50. And 27 divided by 9 is 3. What am I doing wrong? Because I should be getting 49. Oh, it's just one 27. Right? 450... No.
You went by 9s?
So, you're at 450. So, then wouldn't one 9 less be 41? Oh, you... Oh, sorry. I was writing. When you said you're doing equivalent ratios, I started doing one. And I was kind of not listening to your numbers.
You're not even listening to me. That's fantastic.
No, I just think I'm losing my mind here a little bit. Hang on. Let me just think for a second. I'm trying to do 1,323 divided by 27.
But instead, I... I'm doing two things at once is I think is what my head's doing. So, I'm going to actually write down what I'm. So, 1,323 divided by 27, I could think of as 1,323 divided by 9 and 27 divided 9. So, I can end up with something to all divided by 3. You're right. And so, I had that 100 plus 47. 147 divided by 3 is what I ended up with, which is indeed 49. There you go. I don't know if you followed that. I finally followed it on my paper.
That's excellent. You know what, you said that it might be... I don't remember the words you said. But you wanted to remove the 9s or simplify by 9.
Mmhmm. Divide out 9s.
Thank you. Divide out 9s because it was more. But I actually wonder in this case if 3s would have, then, left with numbers that you recognized.
Like, it had a couple of numbers that were a little bit funky.
Yeah. Like, do you want to say more about that?
Well, so I wrote down. When you were talking out, I wrote down 1,323/27 like you did. But then, when I divided out the 3s, that was 441/9. And then, you got to that same 450/9 that you did. You know, you was near there.
And then, you're kind of done.
Yeah, because it was just one 9 away.
I have no idea if people listening to that could have followed any of that. But hey, it was fun for us, so hopefully ya'll enjoyed that a little bit. And we can't wait to hear your math strategy. I wonder if it was like one of ours...if you could follow ours...or something entirely different.
Represent your thinking, and 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, our favorite, comment on other people's thinking
Ya'll, I'm having a blast reading your strategies that you're posting, so tag me when you post them. On Twitter, at @PWHarris. Or Instagram, PamHarris_math. Or Facebook, Pam Harris, author mathematics education. And use the hashtag MathStratChat. And make sure you check out the next MathStratChat problem that we'll post every Wednesday around 7pm Central Time, and then 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. Let's keep spreading the word that Math is Figure-Out-Able!