In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 11, 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.
And I'm Kim.
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.
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.
Okay, so I cannot unthink about the strategy used in last week's MathStratChat problem.
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.
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...
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
But then, you have to add those parts. Yep.
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.
Go for one of them, and I'll fill in the other.
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.
Cool. I'm going to one-up your flexible factoring.
Oh, okay. I like it.
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.
And I think I might base that on doubling 7.5 is 15. But I haven't quadrupled 75 a lot in my life.
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.
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.
Nice. Yeah, I like it.
And just for grins, we probably ought have also talk about that we could think about 75% of 16.
And 75% of 16 is 12, and then scale up to get that 1,200.
Just for completeness.
Lots of really cool strategies. I love when we have really rich problems, right, that make it worth re-looking at the problem.
Playing with different relationships is cool.
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.
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!