# 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 3, 2024

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 3, 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 **00:01

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

**Kim **00:08

And I'm business Kim.

**Pam **00:09

(laughs) Business Kim?

**Kim **00:12

You said don't laugh, so I'm I'm in business mode right now. Okay, ya'll, this past Wednesday, the problem was 44 times 55. And we are curious, how are you solving this problem? Pause the podcast, solve it, come on back to here how we're going to solve it. The problem is 44 times 55.

**Pam **00:15

And this episode is a straight laced MathStratChat episode with no laughing, no fun whatsoever, where we are going to chat very seriously about our math strategies because 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, best part, comment on each other's thinking. Oh my gosh, Kim. There's so many things I want to play with right now.

**Kim **00:51

Yeah, I know.

**Pam **00:53

Alright, do you want to play first because then I can just play after?

**Kim **00:56

I will if you want.

**Pam **00:57

Or should I go?

**Kim **00:58

You sound very eager, and (unclear).

**Pam **01:00

I'm kind of eager. (unclear).

**Kim **01:01

Go! Do it! Yes!

**Pam **01:02

So, I'm thinking about 44 as 4 times 11, and I'm thinking about 55 as 5 times 11. So, 4 times 5 is 20. And 11 times 11 is 121. And now, I just have 20 times 121. And so, 2 times 121 is 242 times that leftover 10. And so, that would be 2,420. Bam!

**Kim **01:28

Yeah. I like it.

**Pam **01:29

Flexible factoring for the win.

**Kim **01:31

Very nice. I'm going to mess with 55s.

**Pam **01:35

Okay.

**Kim **01:36

I'm going to go four 55s is 220. I know you're going to ask me how I know. Mmm, how do I know that? I feel like I know that. I guess... No, I didn't think about 2 (unclear).

**Pam **01:45

I mean, it's really.

**Kim **01:46

It's kind of (unclear).

**Pam **01:47

Four 55s and four 5s is pretty.

**Kim **01:50

Yeah, I was saying I definitely didn't do two 55s. I guess I might have four 50s. I don't really think about it too long, I guess, to know, so... I'm going to call it four 50s and four 5s.

**Pam **02:00

Okay.

**Kim **02:00

Maybe. So, anyway, four 55s is is 220, which means then that fourty 55s is 2,200. So, I have 22 tens and 22 hundreds. And 220 and 2,200 is 2,420.

**Pam **02:16

Bam!

**Kim **02:18

I like that problem.

**Pam **02:19

That was almost too easy.

**Kim **02:21

Yeah.

**Pam **02:21

Okay, I'm feeling like there should be a difference of squares in here, though.

**Kim **02:25

Go for it.

**Pam **02:25

Am I right, though? I don't know. Let me think. Is that... So, 44 is kind of like 50 minus 6.

**Kim **02:33

Mmhm.

**Pam **02:34

And 55 is like 50 plus 5.

**Kim **02:37

Mmhm.

**Pam **02:38

So, 50 times 50 is that 2,500? And then, minus six 50s plus five 50s is one, negative 50. So, minus 50. And then, minus 6 times plus 5 is negative 30. So, I end up with 2,500 minus 80. And 2,500 minus 80 is 2,420. Ooh! And I got a difference of squares off the... Yes! Bam!

**Kim **02:41

Mmhm. Nice!

**Pam **03:07

I'm so happy! It's a good day. It's a good day. Because Kim? Yes, Kim, math is a good day because when somebody brought up the difference of squares as a strategy, I had a hard time not only recognizing when it might be a thing to consider, but then really thinking about how to make it work. And so, I've gotten better. And I'm not even sure I can describe my thinking. But I've gotten better at thinking about the fact that you're kind of trying to split the difference. Like, you're trying to think about a number in between the two factors. So, it's 44 and 55. And you're thinking about a number that's in between-ish. And here's the kicker, you have to know the square of that number.

**Kim **03:45

Yeah.

**Pam **03:46

I think. Or it's not as good of a strategy. So, when I was able to say, well, 50 is kind of in between 44 and 55, then how does 50 relate to 44 and 55? Oh, and sure enough, it's just 1 apart? And then, I can... Yeah. So, again, I had to know. I guess I should say. So, on my paper, I had 50 minus 6, that quantity, times the quantity 50 plus 5.

**Kim **04:09

Mmhm.

**Pam **04:09

And then, I could kind of use binomial, polynomial multiplication to think about that you're using the distributive property, and then it just sort of falls out really nicely.

**Kim **04:17

And not long ago you and I were actually talking about which squares were worth owning.

**Pam **04:22

Oh, yeah.

**Kim **04:22

Like, committing to spending the time to have that experience in order to own, so maybe this particular strategy would lend itself to more people as they know more squares.

**Pam **04:36

Yeah, I think you have to know enough. Well, because I just kind of said it only works if you know the square of that first number. So, the more squares you have experience with, that you own, then the more often this one might pop out. Yeah, it makes sense.

**Kim **04:50

Alright, everyone, we want to see what you're thinking. Solve the problem if you haven't already and you listened to ours first. Major, major no no. But go ahead and go to MathStratChat posts and share the world what you're thinking, and check out what other people have done while you're there.

**Pam **05:06

Yeah, and if you'll tag me, I'll comment back. And use the hashtag MathStratChat. And make sure you check out our next MathStratChat problem that we'll post next Wednesday around 7pm Central Time, and then come back here to hear what we're thinking about the problem. We love having you as part of the Math is Figure-Out-Able movement. Thanks for keeping spreading the word that Math is Figure-Out-Able!