In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 26, 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.
Check out #MathStratChat on your favorite social media site and join in the conversation.
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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 episode is a MathStratChat episode.
Hey, what's MathStratChat? Every Wednesday, Pam throws out a problem on Twitter, Facebook, and Instagram, and people from all around the world chat about the strategies they use. It's super fun to see everyone's thinking,
Alright, this Wednesday, our math problem was 144 subtract 48. 144 minus 48. How would you solve this problem? Pause the podcast, solve the problem any way you want, the problem is 144 subtract 48. Solve it, and then come back to hear how we solved it. Alright.
I'm going to go first.
Okay, you're up, Kim. Go, go, go.
I'm feeling it.
You're stealing the thing I usually say...
...and now you're going first. All the things.
So, 144 minus 48. I'm just going to subtract 44 to get to a friendly number, get to 100. And then, I just have 4 more to take away. So, I'm calling it 96.
Bam! Nice strategy. And it makes a lot of sense for these numbers. Totally cool.
There's also something kind of fun, when I designed this problem, to think about which is 144 is a bunch of 12s. I think a lot of people might recognize that it's a bunch of 12s. And I think it's twelve 12s. So, 144 is twelve 12s. Well, 48 is nicely a bunch of 12s as well. It's four 12s. So, if I have nine 12s, subtract four...
Wait, wait, wait. Twelve 12s.
Excuse me. I looked at your... I don't even know what I looked at. Twelve 12s, subtract four 12s is eight 12s.
And then, darn it all, if that's one that I just have to actually think about eight 12s. I usually have to think and say, it's somewhere in the 90s, so 96. I just have to think about that just a little bit.
Cooper would love your strategy because he's obsessed with 12s.
Oh, nice, nice.
Like, he knows a ton of 12s. So, yeah, he would like that one. Nicely done.
So, while we're at it, though, f I could just kind of play a little bit. When I look at 144, I see 12, so those pop. But now that I know there's 12s and I know there's twelve 12s, I could also see six 24s. Like, if there's twelve 12s, then there's going to be half as many things that are twice as big. So, twelve 12s or six 24s because in 48, there's two 24s. So, now I have six 24s, subtract two 24s. Is that four 24s?
And then, I could also think about four 24s as being 96. So, just kind of another thing to play with. And if (unclear)
Go the other way.
Oh, go the other way.
Yeah, yeah. Like, you went from 12 to 6. What about like 24s?
Well, then I would have twenty-four 6s. Like, I had six 24s. The other direction would be twenty-four 6s. Is that right?
I was actually going to go to 4s.
I don't know why, though. Like, if I go to 4s, then I would have... I have to think for a second. I'm actually going for the 6 times 24. I'm thinking about it as 24 times 6. And if I'm going to go to 4s, 24 divided by 6 is 4. So, 6 times 4 is 24, and I end up with 4... Wait, that's not right. What did I do wrong? 24 divided by... Oh. No? Yeah. 6 times 6 is 36. I did two different factors. So, then, I could end up with 4 times 36. And I could choose to play with that one or not. Yeah, kind of fun.
Super fun to play around though.
I think I did something wrong. 4 times 36. Is that equivalent to 96? No. What did I do wrong? 24 times 6. Is that correct? Yes. So, if I divide 24 by 6, I get 4. And if I multiply 6 by 4... By 6, I get 36. 4 times 36. How come 4 times 36 feels a whole lot bigger than 24 times 6?
I don't know.
Well, am I right?
I just started writing down what you were saying. 24 times 6. I was just listening to you. 24 times 6.
Oh, I know what I'm doing wrong. I'm a dork. I'm forgetting to subtract off the extra.
I've been messing around with the 12 times 12, but I wasn't subtracting the 48. I couldn't figure out why was I getting more than 96? Wow. Okay, Kim, we're done for the day. I'm not doing any more math today. Alright, ya'll, we can't wait to see your math strategy. Was that fun to hear my brain kind of like freak out? Oh, for heaven's sakes.
Hey, it's real.
So, I found a lot of ways to think about 144, and then couldn't figure out why they weren't equivalent to 96. And I was forgetting to subtract the 48 from the original problem. For heaven's sakes, I wonder if your strategy was like Kim's. Not mine! It was probably something completely different. What were you going to say? No?
Oh, I was going to say represent your thinking people. Take picture of your work and share it with us. We like to see what you're thinking and so does everybody else, so comment on their work too.
Unless it was like mine today. Ya'll, tag me on Twitter at @PWHarris. Or Instagram, PamHarris_math. Or Facebook, Pam Harris, author, mathematics education. And when you do, use the hashtag MathStratChat, then we can find it easier. And check out the next MathStratChat problem that we'll post somewhere around 7pm Central time on Wednesday, and then hop back here to hear how we're thinking about the problem. Ya'll, thanks for joining us as part of the Math is Figure-Out-Able movement. Help us keep spreading the word that Math is Figure-Out-Able!