In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 18, 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.
Hey, fellow mathematicians! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam. And this episode is a MathStratChat episode. What isKim:
And I'm Kim. MathStratChat? Well, every Wednesday evening, I throw out a math problem on social media, Twitter, Facebook, Instagram. People from all around the world chat about the strategies they use. We love seeing everyone's thinking. Sure, do. So, this Wednesday, our math problem was 2 minus 8.9. How would you solve this problem? Pause the podcast, solve it any way you want. The problem was 2 minus 8 and 9/10. Solve it, and then come back to hear how we solved it.Pam:
Alright, so we got a little integer work going on here.Kim:
Yeah, we do.Pam:
Nice. Nice. Hey, I'm just going to point out one quick thing. YouKim:
Yeah. might notice that whenever we use decimals, Kim is really particular to say the problem in point language and in tenths language. So 8.9 and 8 and 9/10. And we think that that makes sense. We think that students ought to hear both. So, we'll just throw that out there. Alright, Kim. I'm curious. How were you thinking about 2 subtract 8.9? Okay, so the first thing I did was start a number line. And I put 2 on kind of the right side, and then I made a jump of to subtract 8. And I did mark down where 0 would be, just to kind of orient myself. But when I jumped back 8, then I landed on negative 6. And then, I knew I still needed to remove $0.90, or 0.9, or nine-tenths. So, then I made one more jump back of a smaller jump of 0.9, and I landed on negative 6.9.Pam:
So, a jump back of 0.9 is negative 6.9. That's not negative 5.1 or some weird(unclear) back that direction.Kim:
Can you... How did you know that 2 minus 8 was negative 6? I know you said 0 was in there, but can you just like say that out loud?Kim:
Yeah. So, if I had gone from 2 to 0, then that would bePam:
Cool. So, you sort of could think about that 0 in there as a jump of minus 2. And then, if I went from 2 to negative 6, then that would be another amount of minus 6. So, minus 2 and minus 6 was minus 8. kind of being helpful.Kim:
Yeah, it's kind of a benchmark to make sure that I'm on the right track.Pam:
Yeah, totally. So, I'm a little curious that you didn't use an Over strategy. That would typically be your go to.Kim:
It would be. You know what? And I think it's because I'm less familiar with integer work. I mean, I obviously can, and I have a few strategies. But it's been a little while. And so, I think what happens is when I'm less in it, maybe I revert to a simpler strategy.Pam:
A less sophisticated strategy?Kim:
Yeah. So, I'll just go. I'll play with an Over strategy then. So, 2 subtract 8.9 is really close to 2 subtract 9. So, 2 subtract 9, if I kind of think about 2 to 0 is two, then I got to subtract 7 more. So, I'm at negative 7. 2 subtract 9 is negative 7. But I've subtracted a bit too much, so I need to adjust a 2 by a tenth to the right. And that would also be negative 6.9. Yeah.Kim:
I actually like your strategy better. I wish thought about that. It didn't even occur to me to be perfectly honest with you when I saw the 8.9.Pam:
Well, so listeners might find it interesting that this is a very typical thing. That when students do something new, they sort of go into a more difficult number system, or all of a sudden the numbers get bigger, or smaller, or more fractiony, more decimaly... In some way they're more complicated. Students will often revert back, or people will often revert to something less sophisticated.Kim:
Something they feel solid in. "Yep, I'm confident." But then quickly be able to kind of pull in those other strategies that they had developed with easier number systems.Kim:
So, that's a thing to know and to just sort of expect. That's going to happen. Yeah.Kim:
Okay, we can't wait to see your strategies. I wonder if yours was like mine, or Pam's, or something entirely different. Represent your thinking, take a picture of your work, or screenshot your phone, and tell the world on social media. While you're there, check out what other people did and comment on their thinking.Pam:
While you were talking, I've totally looking at that problem wondering about a different. I was asking myself,"Well, what's more sophisticated that you weren't thinking about, Pam?" I'll just mentioned listeners. See, it's good that you listened to the whole thing. I was thinking about constant difference. So, I'll just throw that out there and see if anybody wants to play with that.Kim:
Alright, while you're doing it, tag me on Twitter:@PWHarris. On Instagram:
@Pam Harris_math. And at Facebook: Pam Harris, author mathematics education. And use the hashtag MathStratChat. So, make sure you check out the MathStratChat problem we post next Wednesday at 7:00 p.m., Central Time, and then pop back here to 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!