# 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 - August 21, 2024

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 21, 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 mathers! Welcome to the podcast where Math is Figure-Out-Able! I'm Pam.

**Kim **00:06

And I'm Kim.

**Pam **00:07

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 **00:19

Okay, so this Wednesday, our math problem was 1.4 times 4.5. How would you solve this problem? Pause the podcast, solve however you want, and then come back to hear how we solved 1.4 times 4.5.

**Pam **00:32

Bam.

**Kim **00:33

And you know, I just said "solved". We haven't solved it yet. Like, we haven't solved the problems yet. So. It's not like we have it pre-solved.

**Pam **00:41

No.

**Kim **00:41

What do you want to do? Or you want me to go first?

**Pam **00:44

You go first.

**Kim **00:45

Okay, so 1.4 times 4.5 looks pretty yucky, but if I double...

**Pam **00:53

Hey, Kim, before you start doing something.

**Kim **00:55

Yeah.

**Pam **00:55

Can you ish this one? I was listening to a podcast with Jo Boaler on it, and her brand new book, "Ish".

**Kim **01:00

Mmhm.

**Pam **01:01

And I wonder if you just have like some approximate. Like, is there some...

**Kim **01:06

Yeah. So, like, 1 and a 1/2?

**Pam **01:09

one and a half, 4 and a 1/2s.

**Kim **01:10

Mmhm.

**Pam **01:11

So, you can kind of like think about. Yeah. It just kind of gives you an idea of where we should be if we're kind of in the ballpark.

**Kim **01:18

Mmhm

**Pam **01:19

Okay, alright.

**Kim **01:19

Yeah.

**Pam **01:19

Okay, go ahead. I didn't mean to interrupt you. Sorry.

**Kim **01:21

No, it's okay. So, if I double 4.5, then I have twice the size, but I only want half of them, so I'm going to go 0.7 times 9.

**Pam **01:37

So, half of 1.4 was 0.7. Okay, I got it. Mmhm, mmhm.

**Kim **01:41

So, 7 times 9 is 63, so 0.7 times nine is 6.3.

**Pam **01:49

Okay, which is like 6 and a bit is about is one 4.5. And about half of that. So, that feels like it's kind of in the ballpark.

**Kim **01:58

Yep.

**Pam **01:59

Yeah, cool. I have no idea if this is going to be any good, but I'm going to think about 1.4s. So, I'm in a ratio table, and I (unclear) 4 and a 1/2 of them.

**Kim **02:09

Okay. Oh, yeah.

**Pam **02:10

Got one 1.4. Two, 1.4s would be 2.8. So, four, 1.4s would be double that. Double 28, I know it's 56. So, 5.6. Because I've just doubled 28 a lot. So, so far, I have four 1.4s, but I need four and a half, 1.4s. So, make it a half 1.4. And half of 1.4 is 0.7. So, now I'm going to add the 4 and the 1/2 together to get 4 and a 1/2. And I'm going to add the 5.6 and the 0.7 together. But actually, they're just screaming at me 56 and 7. And 56 and 7 is 63, so 6.3.

**Kim **02:51

You know what I heard you do is what I do also is you for each layer, kind of each piece that you did.

**Pam **02:58

Mmhm.

**Kim **02:58

You go in and out, back and forth between whole and decimal, whole and decimal, whole and decimal.

**Pam **03:02

I did this time, yeah.

**Kim **03:04

Yeah, and I don't know if you do that all the time, but it's something that I do as well. And it's almost like you're thinking, like you're checking the reasonableness all throughout, instead of what a lot of teachers will say is like extract the decimal, pretend it's not there, do all the work, and then throw it back in at the end.

**Pam **03:22

Mmhm, mmhm.

**Kim **03:23

And instead, you're like, "Well, I want to think about the whole numbers because I own those. I know them. That's kind of where my brain's going." But then, it almost sounded like you went back to what the actual amount would be, kind of each stage of the game, like each layer that you did.

**Pam **03:39

Yeah.

**Kim **03:40

It's noteworthy.

**Pam **03:41

Can I do one more just for fun?

**Kim **03:43

Sure.

**Pam **03:44

I wondered what would happen if I thought about 1.4, 4.5s. So, while you were talking, I was kind of listening.

**Kim **03:54

Fair, fair. I do it too.

**Pam **03:57

So, I've got one 4.5, and then I need 0.4, 4.5s. So, I thought to myself I'm going to think about 0.1, 4.5s. So, 0.1, 4.5s just mean I'm dividing by 10. So, 0.1 correlates to 0.4, 45/100. But I need 0.4 of them, so I got to quadruple that. And I could have doubled it and doubled it again. But I can quadruple 45 because I know double 45 is 90 and double 90 is 180.

**Kim **04:27

Mmhm.

**Pam **04:28

So, I'm thinking 0.4, 4.5s is 1.8. I had to kind of jury rig the decimal point there. So, now I'm adding the 1 to 0.4 and the 4.5 to 1.8. And now I'm not so happy. Like, I can do that. That would be what? 5.5 plus 0.8. Yeah, 6.3. That took me... I had to jury.... I had to think about that addition a little more than I wanted to.

**Kim **04:52

What if you did one 4.5.

**Pam **04:56

Yeah.

**Kim **04:56

And then you did half of 4.5. Which is pretty nice. And then you went...

**Pam **05:04

(unclear)

**Kim **05:04

Hmm?

**Pam **05:04

Why half?

**Kim **05:05

Because instead of 0.4, you're going to do 0.5.

**Pam **05:09

Okay.

**Kim **05:09

And then back up the tenth. So, you did the tenth and quadrupled.

**Pam **05:13

Yeah.

**Kim **05:14

I think the numbers would have been nice if you did half of the 4.5, and then backed up the tenth.

**Pam **05:20

Because it'd be 2.25.

**Kim **05:22

Mmhm. And then you're at 6.75

**Pam **05:24

6.75. And you're going to get rid of 0.45. Oh, that is nice.

**Kim **05:28

Yeah.

**Pam **05:29

That's a nice. When you said, "And then subtract." I was like, "Bleh, subtract." But (unclear).

**Kim **05:33

Yeah, but it was a nice one.

**Pam **05:34

Yeah, the 6.75 minus 0.45 is 6.3. That subtracts pretty nicely. Man, it's fun to play. That was playful. Cool.

**Kim **05:42

Yeah. Alright, we cannot wait to see what you do every week when Pam throws out a problem on MathStratChat. So, join us and let us know how you think about the problems, and be sure to comment on other people's strategies.

**Pam **05:52

When you just said, "throw out", I was like, "Throw up. Not throw up. Throw out."

**Kim **05:57

Don't do either.

**Pam **05:57

Ya'll, we throw out the problems on Wednesdays around 7pm. And when you answer, tag me and use the hashtag MathStratChat, then join us here to hear how we're thinking about the problem. We love having you as part of the Math is Figure-Out-Able movement because Math is Figure-Out-Able!