# Math is Figure-Out-Able!

Math teacher educator Pam Harris and her cohost Kim Montague answer the question: If not algorithms, then what? Join them for ~15-30 minutes every Tuesday as they cast their vision for mathematics education and give actionable items to help teachers teach math that is Figure-Out-Able. See www.MathisFigureOutAble.com for more great resources!

## Math is Figure-Out-Able!

# #MathStratChat - January 24, 2024

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 24, 2024.

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.

Twitter: @PWHarris

Instagram: Pam Harris_math

Facebook: Pam Harris, author, mathematics education

Want more? Check out the archive of all of our #MathStratChat posts!

**Pam **00:00

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

**Kim **00:07

And I'm Kim Montague.

**Pam **00:08

And this is a MathStratChat episode, where we chat about our math strategies. Every Wednesday evening, I throw out a math problem on social media and people from around the world chat about the strategies they use and comment on each other's thinking.

**Kim **00:21

Okay, so this week, our math problem was four-sixteenths times two-fifths. And we're wondering how you would solve this problem. Pause the podcast. Solve it however you want. The problem is four-sixteenths times two-fifths. Solve it, and then come back to here how we're going to solve it.

**Pam **00:37

Bam! Alright, I'm going to go first.

**Kim **00:39

Go for it.

**Pam **00:41

So, I'm going to find four-sixteenths is equivalent to one-fourth.

**Kim **00:46

Okay.

**Pam **00:47

So, I'm thinking about one-fourth of two-fifths. And I'm going to think about one-fourth of anything as a half of that thing times a half of that thing. So, a half of two-fifths is one-fifth. Half of 2 anythings is 1 of those things, so a half of the two-fifths is one-fifth. Now, I have to find a half of one-fifth. Now, I could go a couple directions. I'm going to choose to go a half of 1/5 is thinking about what a fifth looks like in respect to the whole. And if I cut that fifth in half, I think I would have a piece called a tenth.

**Kim **01:23

Yep.

**Pam **01:24

That's one way to think of it. Can I think of it in another way real quick?

**Kim **01:26

Sure.

**Pam **01:27

So, I can also think about a half of a fifth as... And this is tricky because let me tell you what I'm writing. I'm writing 0.5 divided by, the fraction bar, fifths. Or I could have written the little tiny fraction one-half, and then the big fraction bar, five or fifths one-half. It's a half of a fifth. And then, I could say, a half of a fifth, I could scale that to make a tenth. And then, that's also one-tenth. A couple different ways of thinking about it.

**Kim **01:57

Yeah.

**Pam **01:58

Yeah.

**Kim **01:59

Very cool.

**Pam **02:00

Cool. Alright. What are you thinking about?

**Kim **02:01

So, you know, I love the fractions, and the percents. But what I don't force myself to do quite as much is decimals. So, I'm going to go decimals because I recognize these both are nice decimals. So, I wrote down 25/100 times 0.4.

**Pam **02:16

Mmhm.

**Kim **02:18

Four-tenths. So, then, that's nice because it's got to 25 times 4. So, I wrote down 100. And then, I'm scaling that down. Three 10s. So, thousandth... No. 10, 20... Yeah, a 1,000. To get 0.1.

**Pam **02:37

Oh, that's why you said a thousand. I was like, "Wait, what are you..." Gotcha.

**Kim **02:42

Yeah. And then, I scaled it. I scaled it down three-tenths.

**Both Pam and Kim **02:42

(unclear) (unclear).

**Kim **02:48

Found a tenth of it.

**Pam **02:49

Yeah.

**Kim **02:50

Yeah.

**Pam **02:50

That's funny you said a tenth, and I said divided by 10.

**Kim **02:52

Yeah.

**Pam **02:53

Yeah, nice. You know what I thought maybe you were going to do. When you were saying that, I wrote down what you were doing, so I could follow your thinking. And when you had 0.25 times 0.4. I wondered if you were going to Double and Halve. So...

**Kim **03:06

Oh, yeah.

**Pam **03:06

...point 0.25 would be... I double that to a half, 0.5. And then, I would have to halve 0.4, which is 0.2.

**Kim **03:14

Mmhm.

**Pam **03:15

And then, I could do that again. So, double the half, the 0.5, to 1 times halve the point to 2 to 0.1. And 1 times 0.1 is 0.1 or one-tenth.

**Kim **03:25

Yeah. (unclear)

**Pam **03:28

I wouldn't have thought of that, Kim, if you hadn't said put it in decimals.

**Kim **03:31

Well, and I was going to say, I don't know that I as much think about Double Halve with fractions. Although, it's certainly doable.

**Pam **03:38

Yeah.

**Kim **03:39

But I think I naturally gravitate towards it more in decimals.

**Pam **03:44

Well, that's interesting because...

**Kim **03:45

(unclear) look for. Yeah.

**Pam **03:46

Like, as you say one-fourth of two-fifths, I could double the one-fourth to get one-half and halve the two-fifths to get one-fifth. And then, right there, I think I'd stop, and I'd think about a half of a fifth.

**Kim **03:58

But then, if you have a fifth, you can halve that to get a tenth. And double. Yeah, you think you'd stop? I think once you said it, I was like, "Oh, no, I would keep going."

**Pam **04:07

Well, you could keep going, but notice where you are. You're at a half of a fifth. Like.

**Kim **04:11

Yeah.

**Pam **04:12

(unclear).

**Kim **04:12

But you know what? I just switched my brain to decimals when you were saying it.

**Pam **04:16

Oh, that's interesting.

**Kim **04:17

So weird. (unclear).

**Pam **04:18

So, it's funny to me because once I have a half of a fifth, half times one-fifth. You said, "But you can keep going." But if you double the half to get 1, then you have to halve the fifth. You have to do the thing that you (unclear).

**Kim **04:32

I mean, if it's a thing to do. Like I just... I don't know. Because we were talking about a half of the fifth as a tenth just a second ago.

**Pam **04:40

Mmhm.

**Kim **04:41

I didn't really think about it.

**Pam **04:42

Yeah, makes sense.

**Both Pam and Kim **04:43

Yeah.

**Kim **04:44

Alright.

**Pam **04:44

Fun! That was a good one.

**Kim **04:45

Fun. Fraction's are fun. Alright, we can't wait to see what you're thinking. Did you think about decimals, or fractions, or percents? Share your strategy, take a picture, and tell the world on social media. And while you're checking out what you did, check out what other people did and comment on their thinking.

**Pam **05:00

Okay. While they're checking out what you did? While you're posting what you did.

**Kim **05:03

While you're posting what you did. Alright. So many words.

**Pam **05:07

Tag me and use the hashtag MathStratChat and make sure that you check out the next MathStratChat problem that we'll post Wednesday around 7pm, and then come back here to hear how we're thinking about the problem. Ya'll, we love having you as part of the Math is Figure-Out-Able movement. Thanks for spreading the word that Math is Figure-Out-Able!