In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 19, 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.
Hey fellow mathematicians. Welcome to the podcast where Math is Figure-Out-Able. I'm Pam.Kim Montague:
And I'm Kim.Pam Harris:
And this episode is a MathStratChat episode. What is MathStratChat? Every Wednesday evening, I throw out a math problem on Twitter, Facebook and Instagram. People from all around the world chat about the strategies they use. It's super cool to see everyone's thinking.Kim Montague:
It's so fun. Okay, so this Wednesday, our problem was three fourths of nine. How would you solve this problem? Go ahead and pause the podcast. Solve the problem any way you want. Remember, the problem was three fourths of nine, solve it and then come back to here how we solve it. Ready? Go.Pam Harris:
All right. So three fourths of nine, three fourths of nine.Kim Montague:
I'm gonna go first.Kim Montague:
Okay, sounds great.Pam Harris:
So I'm not sure I would do this, except I've got last week's problem ringing in my head. So last week, we decided that three fourths of 10 was 7.5. And I have dealt with three fourths of eight a lot. I just know that three fourths of eight is six. So I could talk about how I know that half of eight is four. And I just know three fourths of eight. So really, I just know it's six, but if it's four and two, then that's six. So I know that there's this linear relationship, this constant rate of change relationship that's between that if I'm dealing with percents are three fourths of. And so if I'm thinking about three fourths of nine, if I know three fourths of eight is six, and three fourths of 10 is 7.5, then three fourths of nine is, since nine is right in between eight and 10, that three fourths of it is going to be right in between six and 7.5. So then I have to ask myself, what's right in the middle of six and seven and a half? Well, there's sort of one and a half is the difference there. And half of one and a half, is point seven five. I'm actually kind of thinking about that in money. It's like a buck 50 and half of that is 75 cents. And so six and 75 cents is 6.75, or six and 0.75. So that is fourths of nine.Kim Montague:
So, I've been trying not to laugh, because I'm smiling, because I did almost exactly the same.Pam Harris:
Is that yours? No way.Kim Montague:
Yes. Okay.Pam Harris:
We never do the same.Kim Montague:
I know that's so funny, right? Because the eight, I just thought about what I knew about the eight and ten also and nine being right in the middle. But I will say that another one pinged for me, right kind of at the very end when I was like, "Oh, yeah, I know, three fourths of three." And so I don't know why it came to me that I know three fourths of three instead of three fourths of nine.Pam Harris:
Wait a minute. I'm not sure I know three fourths of three. What's three fourths of three?Kim Montague:
I don't know why I know that. It's $2.25. I think it's because it's money.Pam Harris:
Huh? Well, let me think for a second. So three So if three fourths of three is two and a quarter, $2.25, then fourths of, you've got me thinking in terms of quarters, three fourths of 12 quarters. And then there's the three fourths of 12 is really nice. That's nine. And so nine you could just scale up by three to get three fourths of nine. quarters is two and a quarter, 2.25. Okay, so I can buy your three quarters of, three fourths of three. I was trying to say fourths and quarters at the same time. And three times two and a quarter is?Kim Montague:
(unclear) Yeah, like I said that on purpose, two and one quarter, three of those would be six and three quarters. It's a way of thinking about that.Kim Montague:
Nice. All right. So we've shared a couple strategies. We purposely decided not to share all the different ways that we can think about the problem. So we'll leave it at that.Kim Montague:
Yeah. So we can't wait to see your strategy. And I wonder if your strategy was like one of ours 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 in what other people did and comment on their thinking.Pam Harris:
Yeah, so tag me on Twitter at PW Harris or Instagram Pam Harris_math or on Facebook, Pam Harris, author, mathematics education, and make sure you use the hashtag MathStratChat. And make sure you check out the MathStratChat problem that we post next Wednesday 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