In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 8, 2023.
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:
And I'm Kim.
Pam:
And this episode is a MathStratChat episode. What is MathStratChat? Every Wednesday evening, I throw out a math problem on Twitter, Facebook, Instagram, all the social media. People from all around the world chat about the strategies they use. It's super cool to see everyone's thinking.
Kim Montague:
So this Wednesday, our math problem was one fourth plus seven twentieths. How would you solve this problem? Pause the podcast, solve it any way you want. The problem again is one fourth plus seven twentieths. Solve it and then come on back to here how we solved it.
Pam:
Kim, Yeah,what did you get?
Kim:
I'm gonna go first if you don't mind. Okay. So, one fourth...
Pam:
Wait, wait, wait, wait, wait, did you I'm gonna, I'm gonna, I'm, I want to, I want to, I want to, good heavens!
Kim:
Words.
Pam:
[unclear] I want to guess what you're going to do. I'm betting that you did percentages.
Kim:
I didn't.
Pam:
You didn't? Oh, I can't wait! Okay.
Kim:
I thought about it. And I decided to try something different.
Pam:
Okay. I was just curious. All right.
Kim:
Yeah.
Pam:
Okay. What did you do?
Kim:
It's a good guess, though. Okay, so I went fourth. I was like, "Let's think about that in dimes, again."
Pam:
What?
Kim:
So I wrote down 2.5 dimes, 2.5 tenths. And the reason I kind of wanted to do the dimes thing is because I actually like seven twentieths in dimes because if it's seven twentieths, then it's also three and a half dimes.
Pam:
Because like seven nickels is three and a half dimes?
Kim:
Yeah. And so I just wrote down two and a half dimes plus three and a half dimes is six dimes, which is, well then he wrote down point six. So if we have to stay in fraction land, it's the same as six tenths, which is three fifths.
Pam:
Equivalent to three fifths. Nice. So I actually did dimes. When you said that, then I went ahead and flipped, and I'll do something else. Okay, because I just wanted to say why I did dimes. I'm thinking in terms of dimes. So as soon as I saw the 1/4, I was like two and a half dimes. So it was like pinging, it was like flashing in front of my eyes. And then I thought about the 7/20s. And I instantly said, "Oh, that's also going to be a half of a dime. So when I add the two half dimes together, I'll get a whole number of dimes." And that made me kind of happy to think about, so I was like, "Yeah, I'm going dimes." And then you shocked me by going dimes. It's okay, so I'm actually just gonna go nickels. So because the seven out of 20, that's seven nickels, because there's 20 nickels in a dollar. So then I just had to think about how many nickels were in a quarter. And that's five nickels. So that's 5/20ths. And seven twentieths is the same thing as or is equivalent to 12 twentieths. And I can think about those, that those 12 twentieths as 60 cents. Which is maybe kind of where you went. And if I had, so like that could be either six out of 10 or six dimes out of 10 dimes, or 60 pennies out of 100 dimes. And also the equivalent, if I'm thinking about 60 cents in terms of 20 cent chunks. So like 1/5 is a 20 cent chunk. And so how many 20 cent chunks are there in 60 cents? There are three of those 20 cent chunks out of 5 20 cent chunks. So three fifths.
Kim:
Yeah, nice. Okay, we can't wait to see your math strategy. I wonder if your strategy was like one of ours or something entirely different. Go ahead and represent your thinking by taking a picture of your work or screenshot on 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.
Pam: Yeah, tag me on Twitter:
@PW Harris or Instagram: Pam
Harris_math and Facebook:
Pam Harris, author, mathematics education. And don't forget to use the hashtag MathStratChat. And make sure you check out the MathStratChat problem we post every Wednesday at 7pm Central Time and 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