Hey, fellow mathematicians! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam Harris.
And I'm Kim Montague.
And this episode is a MathStratChat episode. MathStratChat is where I throw out a math problem on Twitter, Facebook, and Instagram every Wednesday, and people from all around the world chat about the strategies they use. It is cool to see everyone's thinking.
Okay, so this Wednesday, our math problem was 1 and a 1/2 minus 7/8. How would you solve this problem? Pause the podcast, solve the problem any way you want. The problem is 1 and a 1/2 minus 7/8. Solve it, and then come back to hear how we solved it.
Bam! Alright. Today, I'm going to go first.
Okeydoke.
So, to me, 1 and a 1/2 and 7/8 are very close together. 7/8 is almost 1. And then, we're just up 1 and a 1/2. So, I'm really thinking about 1 and a 1/2, kind of on a number line, and 7/8 kind of on a number line. And I'm thinking 7/8 is just 1/8 away from 1. And 1 and a 1/2 is just 1/2 away. So, I'm thinking about adding 1/8 and 1/2. And 1/2 is the same as 4/8. So, 1/8 and 4/8 is 5/8. But can I actually tell you what happened in my head when I added the 1/2 and the 1/8?
Yeah.
First thing I did was flop them. So, I wasn't thinking about 1/8 and a 1/2. I was thinking about 1/2, and 1/8. And I literally pictured a ruler in my head. So, on a ruler, if I'm thinking about where I am at 1/2, and then I go to just that next mark on a ruler. So, all of our international listeners right now are like, "What are you talking about?" So, you might have to go look at a customary ruler. But if you've dealt with customary measurements, then you often have to tell what those little
marks are. And it would be so much smarter if we were in metric because then they would just be a millimeter, but no. No, we have to do these funny things. So, that next mark would be an eighth. And if I think about that on a ruler, bam, that is just 5/8. I've dealt with it enough that I know that that's 5/8. Anyways, that's what I would do. What were you thinking about?
Nice. I was actually thinking about percentages. I don't know why. I have no idea.
Because that's you! That's such a you thing. You love percentages.
I do. Okay, so 1 and a 1/2 is 150%.
Okay.
And I know that 7/8 is at 87.5%.
How do you know that?
I must have known that an eighth is 12.5 percent.
Okay.
And so, I Have, You Need between 12.5 percent and 100% is 87.5%.
Okay, can we just. Like, how do you know that 12.5% is an eighth? How do you know that? I mean, maybe you just know it, but maybe for listeners.
You could half, half, half. So, half is 50%.
Half of that is?
Twenty-five percent and then, half of that is 12.5%.
So, that's an eighth 1/8 is 12.5%. Cool. Cool. Okay, so how do you know what 150% minus 87.5% is?
So, here's where I did a similar strategy. I found the distance between those two amounts. That's similar to what you were thinking, I think. And so, 87.5% to get to 100% is that 12.5%. And then, from 100 to 150% is another 50%. So, I actually left my answer as 37.5% . I don't know if that's legal, but I did. And so, then I would have to go back and think about that, and.
Well, hang on a second. How did you get?
Oh, sorry. 62.5%
There we go. Okay. (unclear)
I literally wrote 37.5%.
Three eighths, 5/8. What's the difference? It's all good. That's because you're such an Over girl. You were thinking, "I must have gone Over, so I need to go Under."
Probably. I don't know. I don't know. I did write 37.5% though.
That's funny. But so then you're kind of like. Could you leave an answer at 62.5% or do you have to switch it back into eighths? You know, I think that's an interesting question that teachers could kind of answer for themselves. Ideally, we would want kids to be able to switch back and forth flexibly between them. And as long as they can, then maybe we kind of don't care what they did for a particular problem. But yeah, what we want is the flexibility.
Yeah.
Cool.
Excellent.
Nice.
Alright, well we can't wait to hear what you did. Maybe you solved the problem like me, or maybe you solved the problem like Pam, or something entirely different. Represent your thinking. Take a picture of your work or screenshot your phone, and tell the world on social media. And while you're there, check out what other people did and comment on their thinking.
Yeah. And tag me on Twitter: @PWHarris. Or
PamHarris_math. Or Facebook: Pam Harris, author, mathematics education. And use the #MathStratChat. And make sure you check out the MathStratChat problem that we'll
00 p.m. Central time, and then pop 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! Let's keep spreading the word that Math is Figure-Out-Able!