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!
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 28, 2022.
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.
Pam:
Hey, fellow mathematicians. Welcome to the podcast where Math is Figure-Out-Able. I'm Pam Harris.
Kim:
And I'm Kim Montague.
Pam:
And this episode is a MathStratChat episode. What is MathStratChat? Well, every Wednesday evening, I throw out a math problem on Twitter, Facebook, Instagram, any social media we can think of, and people from around the world chat about the strategies they used. It is super cool to see everyone's thinking.
Kim:
Okay, so this Wednesday, our problem was 121 minus 88. How would you solve this problem? Pause the podcast, and solve the problem any way you want. The problem is 121 minus 88. Solve it, and then come back to hear how we solved it.
Pam:
Alright, Kim, I'm going to go first today.
Kim:
Okiedoke.
Pam:
So, this is one of my purposely planned problems to pull out a cool strategy that I like, so (unclear).
Kim:
Wait, wait, wait. Can I think about it for just a second? I think I know what you're going to say.
Pam:
Okay.
Kim:
(unclear).
Pam:
Okay.
Kim:
Okay. Alright.
Pam:
Are you saying you want to go first?
Kim:
Well, when you said, super cool strategy. No, I don't want to go first. I just I think I know what you might say now, and I didn't think about it that way. But I wanted a chance to.
Pam:
Okay, okay.
Kim:
Sorry, go ahead.
Pam:
Because we believe in that, right? Like, if I just tell it to you, and you haven't had a chance to think about it, your brain doesn't engage in the same way, doesn't have a chance to make those neural connections stronger in the same way.
Kim:
Yeah, thank you for that.
Pam:
Okay, cool. Are you ready, then?
Kim:
Yep.
Pam:
Okay. 121 is eleven 11s.
Kim:
Mmhmm.
Pam:
11 times 11 is 121. And 88 is eight 11s. So, I'm thinking about eleven 11s, subtract eight 11s, is three 11s. I just totally spit when I said that three. I don't know why I did that all over the desk. Yuck!. So, then three 11s is 33. So, I think the difference is 33. Yeah. Is that what you thought I might do?
Kim:
I did because when you said, "I wrote this for a super cool strategy to come out," I think you said something about that last week.
Pam:
Mmhmm.
Kim:
And when I first looked at this problem, it never even occurred to me, and so I wanted to think for a second about that 121.
Pam:
Cool.
Kim:
So, anywho.
Pam:
Nice.
Kim:
That's not what I did, obviously.
Pam:
Ooh, so I'm going to guess. I think I know what you did.
Kim:
Okay.
Pam:
I bet you used the Over strategy.
Kim:
I actually didn't. Is that so weird?
Pam:
What?!
Kim:
I mean, we do play I Have, You Need a lot, and (unclear).
Pam:
You could have.
Kim:
Yeah, but I didn't.
Pam:
Alright, what did you do?
Kim:
It is so weird. This is the dumbest reason too. When I was a kid, my favorite subtraction problem was 12 minus 8. I don't know why. I know it's so random. Completely random.
Pam:
That's random. Okay, you know what's actually the randomest thing is that you know what your favorite subtraction problem was.
Kim:
Well, it was because I thought that was really helpful(laughs). I know.
Pam:
Alright, all you listeners out there. How many of you have a favorite subtraction problem? I think you should post that on for other stuff. So anyway. social media. Tell us about it. What is your favorite? I don't think I had a favorite subtraction problem. Alright.
Kim:
So, I kind of read the problem left to right, and so I thought about it like twelve 10s minus eight 10s.
Pam:
Hang on. Hang on. When you say left to right. I'm sorry, I'm interrupting you. It's almost like you wrote it vertically, kind of like in a traditional algorithm kind of way.
Kim:
Oh, I didn't.
Pam:
You didn't.
Kim:
Is that so weird. I didn't. No, I wrote it horizontally.
Pam:
Okay, but you're thinking sort of big to small? Is that a way to say that? Left to right?
Kim:
Yes.
Pam:
Okay. Alright. Keep going. I'm sorry to interrupt.
Kim:
So, twelve 10s minus eight 10s, would be 40, but I know it's not going to be 40. I know it's going to be 30 something because of the 1 in the 121 and the 8 in 88. And so, then, I did think about 11 and 8 is a difference of 3, And so I knew it was 33. But I really wanted to think about that 12 and 8.
Pam:
So, you're saying twelve 10s minus eight 10s. You're like, it's going to be 40. But then, when you looked at the other two, that's sort of last numbers in each of the numbers.
Kim:
Yep.
Pam:
Yeah. Then you were like,"Well, there's a 1 and an 8. Oh, no. I've got to grab a 10." Or something. "It's going to be 10 less, so it's actually not..." Okay. And that's how you got 30.
Kim:
Yeah.
Pam:
And then 11 minus 8 was 3.
Kim:
Yeah.
Pam:
I don't think I would have done that in this problem.
Kim:
Huh.
Pam:
Every once in a while.
Kim:
Maybe you don't like 12 minus 8.
Pam:
Well, it definitely didn't ping for me quite like that. Every once in a while, I will subtract left to right or greatest to least, and then kind of when I hit that spot where it's like, "Oh, nope. It's not going to work out." In fact, maybe it's worth saying that often you or I... You and I? Both of us will add and subtract left to right.
Kim:
Sure.
Pam:
Especially if there's no need to do any of those hiccups. Especially if you just can add up the magnitudes and sort of think about them left to right. That would probably be our first strategy for all those problems. But when there is a hiccup, often we'll do a different strategy.
Kim:
Yeah, yep.
Pam:
Yeah, I think that's worth saying. Cool.
Kim:
Very good.
Pam:
Nice strategy.
Kim:
Thanks. Alright. We can't wait to see your math strategies. I wonder if you were like either of us and did what we did. Represent your thinking, and take a picture of your work, or screenshot your phone, and tell the world on social media. And while you're there, would you check out what other people did and comment on their thinking? That would be fantastic.
Pam:
Yeah, we love it when you comment on other people's thinking. It encourages everybody to join in, and we can spread the word more and more. So, while you're there, tag me
on Twitter:
@PWHarris. Or Instagram: Pam Harris_math. Or
Facebook:
Pam Harris, author mathematics education. And use the #MathStratChat, so other people can find it. Make sure you check out our next MathStratChat problem that will post on Wednesdays at 7pm Central Time, and then pop back here to hear how we're thinking about the problem. We love having you as part of the Math is Figure-Out-Able movement. Let's keep spreading the word that Math is Figure-Out-Able!
