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!