Pam  00:01

Hey, fellow mathematicians! Welcome to the podcast where Math is Figure-Out-Able! I'm Pam. 

Kim  00:07

And I'm Kim. 

Pam  00:08

And you're listening to a MathStratChat episode where we talk about a problem that I've thrown out to social media every Wednesday evening, and people all around the world submit their strategies. We love hearing everyone hearing, seeing, reading everyone's thinking.

Kim  00:23

Okay, so this Wednesday, our problem was 16 times 75. We're curious, how would you solve it? Pause the podcast. Solve it however you want. The problem is 16 times 75. Solve it, and then come back to hear how we are solving it.

Pam  00:37

Okay, so I cannot unthink about the strategy used in last week's MathStratChat problem. 

Kim  00:43

Okay. 

Pam  00:44

So, I want to use your last strategy. Do you have anything else before I do that one? I feel like that should be the grand finale. Or it could be first.

Kim  00:53

I mean, I think that what you're going to share is maybe a little more efficient, so let me go first. And I'm going to say... Oh, I lied. Well, you know what I was going to do? I was going to go like, Five is Half of Ten. I was going to go ten 75s, five 75s. one 75. And it's fine, but then there's a lot of adding to do there, so I'm going to actually...

Pam  01:20

Let me just slow you down a little bit. You were going to do 10, 5, and 1 to get to sixteen 75s. Sorry, I had to say that out loud for my brain. Okay, mmhm

Kim  01:29

Yeah. 

Pam  01:30

But then, you have to add those parts. Yep.

Kim  01:31

Yeah. So, I don't love that one as much. And so, now, I kind of like two different things that we mentioned last week. And I don't know which one. 

Pam  01:39

Go for one of them, and I'll fill in the other. 

Kim  01:41

Okay, so I'm going to say flexible factoring for 16 is 4 times 4. And for 75 would be 25 times 3. So, I have 4 times 4 times 25 times 3. And I'm going to regroup the 4 times 25 to make it 100. So, I have 4 times 3 is 12, times 100 is 1,200.

Pam  02:05

Cool. I'm going to one-up your flexible factoring. 

Kim  02:08

Oh, okay. I like it.

Pam  02:10

Because I've been thinking about 75s lately. I don't know why. I'm not sure what's been happening in my work. But I'm realizing that I've been doubling 75 for a while and knowing that double 75 is 150.

Kim  02:24

Mmhm.

Pam  02:25

And I think I might base that on doubling 7.5 is 15. But I haven't quadrupled 75 a lot in my life. 

Kim  02:33

Oh, yeah. 

Pam  02:33

But I've started to play with quadrupling 75. And so, for this problem, I'm also going to factor that 16 into 4 times 4, but I'm going to leave the 75. So, I'm going to think about 4 times 4 times 75, and then regroup. I just drew parentheses around 4 times 75. 

Kim  02:52

Yeah.

Pam  02:52

Because that 4 times 75. If 2 times 75 is 150, then 4 times 75 is double that 150 or 300. So, now I've got 4 times 300, and that's also 1,200. 

Kim  03:02

Nice. Yeah, I like it. 

Pam  03:04

Cool. 

Kim  03:04

Yeah. 

Pam  03:05

And just for grins, we probably ought have also talk about that we could think about 75% of 16. 

Kim  03:11

Mmhm.

Pam  03:12

And 75% of 16 is 12, and then scale up to get that 1,200. 

Kim  03:16

Yeah. 

Pam  03:17

Just for completeness.

Kim  03:19

Lots of really cool strategies. I love when we have really rich problems, right, that make it worth re-looking at the problem. 

Pam  03:25

Yeah. 

Kim  03:25

That's fantastic.

Pam  03:26

Playing with different relationships is cool. 

Kim  03:27

Yeah. Okay, ya'll, we can't wait to see your strategies. And, you know, maybe you came up with something totally different than what we've been doing. Represent your thinking, take a picture of your work, and tell the world on social media. Invite everyone to join us. And while you're there, check out what other people did, like, and comment on their thinking. 

Pam  03:44

And tag me on Twitter, X, at @PWHarris. Or Instagram, PamHarris_math. Facebook, Pam Harris, author mathematics education. And use the hashtag MathStratChat. And check out the next MathStratChat problem that we'll... Did I just say that right? The MathStrat. The ChatMath. The MathStratChat problem that we'll post Wednesdays around 7pm Central Time, and then come back here to hear how we're thinking about the problem. Thanks for being part of the Math is Figure-Out-Able movement! Help us spread the word that Math is Figure-Out-Able!