**Pam **00:00

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

**Kim **00:06

And I'm Kim Montague.

**Pam **00:07

And this episode 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. Hey, Kim. How's it going? Hi!

**Kim **00:25

So our problem... Well, I just saw the problem, and so I started thinking right away. So, our problem this week is...

**Pam **00:30

Cheater, cheater, pumpkin eater.

**Kim **00:31

I know. 48 times 62. How would you solve this problem? Pause it, podcast and solve it however you want. The problem is 48 times 62. I actually started writing the problem down, and... I know. Good gravy, people probably think that I'm a mess.

**Pam **00:49

But you are a mess.

**Kim **00:50

It's a little bit true. Okay. So, when I... I'm going to go first. When I see 48 times 62, the first thing I thought of and wrote down is 50 times 62.

**Pam **00:59

Mmm, mmhm.

**Kim **01:00

So, I'm going to then write down 100 times 62 because to find 50 times 62, I want to find 100 times 62. Now, I probably could have Double Halved at that point, but whatever. So, I'm going to say 100 times 62 is 6200. So, then that means that 50 times 62 is half of that, so that's 3100.

**Pam **01:24

Nice.

**Kim **01:25

That's two 62s too much, which is 124. And so, I'm going to start with 3100. And I'm going to go back on a number line. Actually, that's not true. I'm going to say 3100 minus 124 is equivalent to 3000 minus 24.

**Pam **01:48

Mmhm.

**Kim **01:50

And then, I can play I Have, You Need. And so, that is 2976.

**Pam **01:55

Nice. That's interesting when you were doing the subtraction, because I was thinking about 3100 minus 100 is 3000. And then, minus 24. But I think you kind of shifted. Is that right?

**Kim **02:07

Yeah, yeah.

**Pam **02:08

Yeah, cool. Nice.

**Kim **02:09

Alright, what you got?

**Pam **02:10

Well, interesting. My first thought was we've been doing the difference of perfect square, so I wonder if this one would... Not perfect just squares. I wonder if this one would also. But then I was like, "48, and 62. How far apart are those?" So, I'm doing this live. So, I think they're 14 apart. So, if they're 14... No? Am I crazy? Yeah. Yeah, right? 48, 62. 14? Yes?

**Kim **02:38

Oh, they're 14 apart. I'm sorry. I thought you were thinking about... Oh. Then, you and I are thinking about it differently. Oh, perfect. Okay, go ahead. Sorry.

**Pam **02:46

Okay.

**Kim **02:46

That's not what I was thinking about. So.

**Pam **02:48

Well, there you go. So, then I was thinking, maybe if I went up 7 from 48, then that would be 55. So, it was like, is that in the middle of those two? So, is 48, 55 minus 7? And 62, 55 plus 7? And I think that's right. Yeah? Yeah. So, then I'm not so happy because now I've got to square 55. And that's not making me very happy at all to do the difference of squares because I don't know the square of 55. I could figure the square of 55, but do I really want to? So, now you have me wondering if there's a different total that would be even better? Or is there? What were you thinking about?

**Kim **03:36

No, I'm not with my brain today because I was thinking I was totally looking at 48 and thinking 52 and 62, and thinking... Oh, sorry. 48 and thinking 50 and 62 and thinking 50. But that's clearly, clearly not.

**Pam **03:51

Gotcha, gotcha.

**Kim **03:52

Why am I here, Pam? Oh.

**Pam **03:56

Alergies are high. That's a good excuse. That's a good excuse. Yeah, so I don't know. I might say I'm not so excited about difference of squares for this problem. It did have me start to wonder about like if there was something with 100. But I don't think so. Because usually, when you're trying to do this square thing, you're trying to find a number that's in the middle, so you can add the same. You can add the same to that to the number and subtract the same from that number. Because then you just have this nice square. Do you have something friendly for squaring 55. Somebody's out there yelling right now, "Just do blank for squaring 55!" I mean, I can think...

**Kim **04:36

Oh, but it's very interesting like side conversation that...

**Pam **04:41

What's that?

**Kim **04:42

We were talking about square numbers. My seventh grader is... Like, he's really good about predicting. And, you know, he's finding. He's using formula to find the hypotenuse. And so, that's a conversation. But anyway. So, it was the distance between... I don't know. It was like 3 and 4, and so 3.5. And he was like, "It's got to be whatever's right in the middle." And so, he's tinkering with that. Like, I'm super excited about the fact that he's like, "Why isn't it right in the middle?"

**Pam **05:12

Nice.

**Kim **05:13

Keep messing with it, buddy.

**Pam **05:14

Alright, while you were talking, I was thinking about squaring 55. So, I wrote down a ratio table. I wrote 1 to 55. 10 times 55 is 550, so five times 55 is half of that. Half of 550 is 225. Now, that I have 5 of them, I can scale that up to get 50 of them. That's 2,250. I already had the 5. Bam. So, I add the 5 and the 50 together, so that's 2,250 plus 225, which is 2,475. Is that right? Yeah.

**Kim **05:48

I don't know because I was thinking about something else I want to do.

**Pam **05:50

So, I think that's 55 times itself. Yes. So, now I'm going to have the 55 times 55 is 2,475. The insides add out. And subtract 49. And so now I've going to do 2,479 subtract 49... No. I didn't get what you got. I wonder where I get... Shoot 55. Well, I don't know that we have to figure that out on live.

**Kim **06:20

You want to figure while I tell you the thing I was just thinking about?

**Pam **06:22

Well, maybe? Yeah, I'll work with that. What were you thinking about?

**Kim **06:26

Well, so I was wondering about, you know, the... For some reason, 48 just makes me feel like 4 times 12. And so I thought, "Are there any factors that are nice?" 62 is kind of funky because (unclear).

**Pam **06:43

(unclear) That's a nice thought.

**Kim **06:44

Yeah, so I wrote 4 times 12 times 2 times 31. And 4 times 2 is 8 times 12 is 96. And so, then you have 96 times 31. Which is really close to 100 times 31. So, the factoring was pretty quick. The thinking about 100 times 31 was pretty quick. So. And 4 times 31 is 124. So, I actually ended up with the same subtraction that I did with my other strategy.

**Pam **07:09

I still can't find my error.

**Kim **07:11

Oh, you want to say it again?

**Pam **07:12

Well, I did 55 times 55 wrong.

**Kim **07:15

Okay.

**Pam **07:15

But I'm not sure how.

**Kim **07:17

Okay, so one 55.

**Pam **07:18

So, I thought about 55s, and I did ten 55s is 550.

**Kim **07:21

Mmhm.

**Pam **07:22

Five 550s is half of that. Is... OH! Half of 550 is not 225 it's 275.

**Kim **07:29

Way to relook at your work! Behavior of a mathematician.

**Pam **07:31

Is that right? 275?

**Kim **07:32

Yeah.

**Pam **07:33

I finally got it right?

**Kim **07:34

Yeah.

**Pam **07:34

Okay, so 50 of them is 2,750. Add the 5, and so add the 2,750 and the 275, and that is... I can do it. That's 3,025. Okay. So, now 55 times 55 is 3,025. I need to subtract 49. That's almost like your 3000 subtract 24. That's kind of interesting. And so, then I would end up with 2,976. Okay, bam. I feel better. Thank you. So, yeah. I halved 550 wrong. Way to go, Pam. It's alright.

**Kim **08:09

We should Double Halve more.

**Pam **08:10

Probably, probably. Kim, you're up.

**Kim **08:15

Oh, sorry. We get excited about our own work. But we really can't wait to see what you guys are thinking about, so join us on MathStratChat and let us know how you think about the problems. And be a good sport and comment on other people's thinking.

**Pam **08:29

Yeah, we post our problems on Wednesdays at 7pm Central time. When you answer, tag me and use the hashtag MathStratChat. And join us here to hear how we're thinking about the problem. And notice, it's okay if you make a mistake because somebody can point it out or somebody can say, "Mmm," and then you could get a chance to rethink just like I did today. Ya'll, thank you for being part of the Math is Figure-Out-Able movement!