In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 4, 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.Kim:
And I'm Kim.Pam:
And this episode is a MathStratChat episode. What is 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. That's why it's MathStratChat. It's super to see everyone's thinking.Kim:
Okay, so this Wednesday, our math problem was 25.6 minus 12.8. How would you solve this problem? Pause the podcast, solve the problem any way you want. The problem was 25.6 minus 12.8. Solve it, and then come back to hear how we solved it.Pam:
Alright, Kim, you're up. What were you thinking?Kim:
Well, so when I looked at this problem, I kind of ignored the decimals a little bit, and I saw 256 minus 128. And I just know that 128 is half of 256. And so, I knew that it was going to be 12.8 is the answer,Pam:
Because 12.8 is also half of 25.6.Kim:
How do you know that 128 is half of 256? Do you know how you know that?Kim:
That's a good question? I don't know how I know that. I mean.Pam:
I have a wonder.Kim:
I wonder if it's because you have played around with lots of doubles, and you've doubled a lot. And I also wonder if you've paid attention at all to powers of 2 in like computing. So, we'll often have 128k something.Kim:
Like 256 gigs.Kim:
So, those are typical powers of 2 that we deal with a lot. So, maybe that's why.Kim:
Could be, I definitely double and half a lot. Just in routine. Yeah, and we suggest that with students, right? That a thing mathy people do is play with doubles and play with halves. So, a thing you can do to bring that out is to just play with doubles and play with halves with your students and yourself, and get your brain sort of thinking in terms of doubles and halves. Yeah, that's kind of an important thing to do. What did you do?Pam:
Well, interesting to me. I'm looking at getting a new cell phone, new mobile phone. And I was looking at different memory amounts that I could get in the new phone. And those are definitely. Like, 128 and 256 were choices.Kim:
Maybe that's why I know it. I just got a new phone too.Pam:
Ah, well there you go.Kim:
Very well be it. Absolutely. So, stick with that for a second because that's where my brain went. So, my brain thought about 256. And the reason it's a number that we deal with in sort of memory size and computers is because it's a power of 2. So, 256 is 2^8. And 128 is 2^7. So, I literally wrote down 2^8 minus 2^7 is 2^7. Which is a little bit of a weird look. You might look at 2^8 minus 2^7 and think the answer should be 2^1 But that's not right. And so, we kind of have to understand that, you know, what does it mean to have to get from 2^7 to 2^8? What is that relationship? You have to double it. You literally double 2^7 to get 2^8. And so, what's the relationship between them? Well, 2^7 is half of 2^8. And so, I was thinking about halves. And so, 25.6 minus 12.8 is 12.8. It's that other half. Yeah?Kim:
Amazing, yeah. That's great. Very nice.Pam:
Okay, we can't wait to see your math strategies. I wonder if you were like Pam, or you were like me, or something completely different.Pam:
Are you ridiculing my strategy a little bit?Kim:
Not at all. Nope. It's brilliant. Represent your thinking, and take a picture of your work, and tell the world on social media. While you're there, check out what other people are doing and comment on their thinking.Pam:
Yeah, and tag me on Twitter: @PWHarris. Or onInstagram:
Pam Harris_math. And on Facebook: at Pam Harris, author, mathematics education. And make sure you use the hashtag MathStratChat and check out the MathStratChat problem we'll post next Wednesday at 7:00 pm 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!