#MathStratChat - February 22, 2023

Pam: 0:00

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

Kim: 0:07

And I'm Kim.

Pam: 0:08

And this episode is a MathStratChat episode. MathStratChat is where I throw out a problem every Wednesday evening on Twitter, Facebook, Instagram, all social media. People from all around the world chat about the strategies they use. It is super to see everyone's thinking.

Kim: 0:23

Okay, so this Wednesday, our math problem was nineteen-twentieths minus three-fourths. How would you solve this problem? Pause the podcast, solve the problem any way you want. The problem is nineteen-twentieths minus three-fourths. Solve it, and then come back to here how we solve it.

Pam: 0:40

Alright, Kim, I think I'm going to go first today.

Kim: 0:44

Okay.

Pam: 0:45

Is it my turn. Can I go first?

Kim: 0:46

You can go first.

Pam: 0:47

Okay. So, I'm thinking about nineteen-twentieths minus three-fourths as the difference. Those feel like they're close to me. Nineteen-twentieths is feels close to $1.00 or 100 or a whole. And three-fourths... I'm thinking money, so that's why I said $1.00. And three-fourths also feels fairly close to$1.00, but I know it's a little bit less. And so, I think the how far apart those are is going to be a way to think about that.

Kim: 1:15

Yep.

Pam: 1:16

And for some reason, I'm playing around with dimes a lot lately. And so I was thinking in terms of dimes. So nineteen-twentieths, I can actually picture that in nickels, as one nickel away from the whole dollar. And that means it's $0.95, or 9 and a 1/2 dimes. So I just wrote down 9.5 out of 10, 9 and a 1/2 dimes. And I know that $0.75 is 7 and a 1/2 dimes. And one way I know that is because it's also 75 out of 100. And there's just this place value shift. So, if I could think about 75 out of 100, I can also think about 7.5 out of 10.

Kim: 1:53

Yeah.

Pam: 1:53

Which is 7 and a 1/2 dimes. And now, I'm looking at the difference between 9 and a 1/2 dimes and 7 and a 1/2 dimes, and that difference is just 2 dimes. And when I said 2 dimes right now, I literally wrote down 2 out of 10, 2 divided by 10.

Kim: 2:08

Yeah.

Pam: 2:08

So, 2 dimes. 2 dimes is like $0.20, and that's like 4 nickels, so I could write that as... Why am I? Ha! I was simplifying. And I just made it less simplified as four-twentieths. So, I could also think of it as one $0.20 chunk, which is a fifth of the dollar.

Kim: 2:26

Yeah.

Pam: 2:26

So, an equivalent if I needed an equivalent. Hey, if I need an equivalent, I could have gone up to four-twentieths. Up? Scale up? An equivalent four-twentieths or also one-fifth.

Kim: 2:37

It's so interesting to me because as I'm hearing you describe yours, I'm thinking there are so many similarities to what we did but just enough of a different bent on it that it would be fun to to compare papers and see like exactly what was the same. Because as you were describing the distance or the difference between the two numbers, I was nodding. Like,"Yep, that's exactly what I did." But my perspective wasn't the dimes. I was thinking percents again because you know I love them. And so...

Pam: 3:04

You're a percent kind of girl.

Kim: 3:05

I am. So, nineteen-twentieths to me is close to that whole that you were mentioning, but it's back 5%. So, it's 95%.

Pam: 3:15

You're an "Over" girl too, right? It' all about over.

Kim: 3:17

I know, right? That's all the things I love. So, I wrote down 95.

Pam: 3:21

Okay.

Kim: 3:22

Minus 75. So...

Pam: 3:24

Did you put percent after it when you wrote that down?

Kim: 3:26

I didn't.

Pam: 3:27

No, you're just. Because you know it, right? If you were...

Kim: 3:29

It's scratch paper for me.

Pam: 3:31

Sure. If you were, like, displaying your mathematical thinking as some sort of proof where you wanted people to be able to, if you wanted to communicate with people, you would have written in percent. But just a scratch, your okay. Yeah.

Kim: 3:41

Yeah. Well, but actually, I'm glad you mentioned that because I'm looking at my work now, and I wrote "95 minus 75". But then I wrote "equals twenty-hundredths". So, I'm going to put a percent there because that'll bug me later if I see it.

Pam: 3:56

Your kids will walk in there and see that.

Kim: 3:57

Like, "What, Mom?" So, then I wrote down twenty, one-hundredths, which is a fifth.

Pam: 4:05

You can just add. That 20% just screams probably one-fifth. Yeah, nice. How can you didn't use nickels?

Kim: 4:11

Oh, I don't like nickles. No nickles.

Pam: 4:16

Nickels are not your friends?

Kim: 4:20

You know, I think I actually... This is horrible. I work a little bit harder for nickels.

Pam: 4:25

Okay, okay.

Kim: 4:26

So, I'm going to say it here and now. I'm going to force myself to think more about nickels. It's not like I can't. I just... I can, and I just(unclear).

Pam: 4:37

And so, sometimes... I totally get it. I totally get it. Sometimes, you and I will play with relationships that aren't as... that don't come as slick for us, that they're not the first thing that we think about. I totally just realized I was leaning away from my microphone, and so our editor is going to be like, "Don't lean away from your microphone!" I'm back. I'm back to the. Sorry, about that. Sometimes we play around with relationships that don't come as slick to us, so that they then are more accessible to us. Because we recognize that we want to be dense, right? Like, we don't want to just kind of have it in the recesses that we could pull it up if we have to, but we'd like it to ping because there are times when boy that one to ping would be so super slick that we want that one to be at the forefront of our minds. And I think that's just kind of a evolution of, you know, once you own some things, then you want to own more. And it's fun! It's much more fun to play with the things the more that you own.

Kim: 5:33

Well, what's funny is that nineteen-twentieths is 19 nickels, which is $0.95, so it's not like it was so far off from. I just... Percents comes to mind.

Pam: 5:45

Well, and that's interesting because neither of us actually used nickel because we could have done nineteen-twentieths. But I have to reach a little harder for$0.75 to get to nickels.

Kim: 5:52

Yeah.

Pam: 5:53

Like... I'm thinking. What is that? 15?

Kim: 5:56

15.

Pam: 5:57

Is that 15 nickels? Oh, which totally. See, I should have thought percents. If I would have thought percents. That's funny. I was trying to go to nickels, and if I would have just thought about three-fourths being like the relationship of 3 to 4, three-fourths. I know 15 to 20. I own that three-fourths. That's funny. If I would have stayed in fractions and less in nickels, I would have had an easier time getting there. Okay, I don't know if that's interesting for anyone else but me, but it was for me to think about. Thanks for listening.

Kim: 6:29

We cannot wait to see your math strategy. I wonder if it was like one of ours or something entirely different. Represent your thinking, take a picture of your work or screenshot your phone, and tell the world on social media. And while you're there, check out what other people did on MathStratChat and comment on their thinking.

Pam: 6:45

Yeah, and tag me on Twitter at @PWHarris. Or on Instagram, PamHarris_math. And on Facebook, Pam Harris, author mathematics education. And use the hashtag MathStratChat. So, make sure you check out the next MathStratChat problem we post next Wednesday

at 7: 7:00

00 p.m. Central Time, and then pop back here to hear what we are 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!