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!