In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 15, 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.
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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's that? Well, every Wednesday evening, I throw out a MathStratChat problem on Twitter, Facebook, Instagram, all of a social media, and people from around the world chat about the strategies they use. It's super cool to see everyone's thinking.Kim:
I was listening (unclear) forgot to talk.Pam:
[Pam laughs] Hey, Kim! You're up!Kim:
(unclear) Oh, heavens.Pam:
Hey, it's usually me, so there you go.Kim:
This Wednesday, our problem is one-twentieth plus three-fourths.Pam:
Well, that was one of our problems.Kim:
Oh, gosh. I don't even know.Pam:
We might have had multiple problems.Kim:
One-twentieth plus three-fourths. If you want to pause the podcast, solve the problem any way you want, and then come back and hear how we solved it.Pam:
Alright. So, Kim, I'm going to go first. We've been using time to solve problems, but I'm going to guess on this one that you might not. So, I'm going to go ahead and do a solution with time.Kim:
We'll see. We'll see what was in your head.Kim:
Okay, so I'm thinking about one-twentieth plus three-fourths as a twentieth of an hour. Twentieth of an hour. So, if I want to find one-twentieth of an hour, I'm thinking about 60 divided by 20. That's 3. So, it's like a 3 minute chunk. So, it's like 3 out of... Well, now I got to think for a second. It's a 3 minute chunk. I know what my head was just doing. So, that's like 3 minutes. 3 minutes out of the 60 minutes. Is that right?Kim:
Yes. 3 minutes out of the 60 minutes. I was trying to think about how many 3 minute chunks there were, and there's 20 of them, which is why it's one-twentieth. I'm okay.Kim:
Alright, so 3 minutes out of the 60 minutes. And then, I'm thinking about 3 quarters of an hour. That's like 45 minutes out of the 60 minutes. So, 3 minutes plus 45 minutes is 48 minutes out of 60 minutes. And honestly, I just sort of stopped there, so I don't know that I did anything to simplify or to find an equivalent fraction without repeated factors in the numerator and denominator. I just sort of left it 48/60.Kim:
Which is okay, right? Your answer is absolutely correct. 48/60 is a solution to this problem. And I think people get really, really hung up on... You know, maybe even teachers who said like, "That would not be correct." But we would say it's absolutely correct, right?Pam:
Do you want to have me go, and then you can maybe think about if you were forced to pull out common factors how you would do that? Or do you want to?Pam:
Yeah, you go (unclear).Kim:
(unclear). Okay. Alright. Cool. You are absolutely correct that I did not think about time for this one, and I don't really know why I didn't. I think probably because when I glanced at the numbers, I was like, "Oh, that screams percents to me." You know, I do like the percents.Pam:
You are a percent girl. It's true.Kim:
We should make a shirt. "Are you a percent girl?"Kim:
Or am I an Over girl? I don't know.Pam:
I think you're a percent, Over girl. An Over, percent girl? Is that a comma? It's got to have a comma in between those percent "comma". Okay, alright, alright I'll stop.Kim:
Okay, so a 1/20 I know is 5%. How do I know that? I don't know how I know that. Because 5 is 20%. Because there are twenty 5% in a 100%. So, 1/20 would be just one of those 5%. I'm not sure that that made sense. But anyway, 1/20 is 5%. And I know that three-fourths is 75% because I know 1/4 is 25%. So, then, I just had 5% plus 75%, which is 80%. And I also know that 80% is the equivalent to 4/5 because I know that every 1/5 is 20%, so then 4/5 would be 80%. So, I say four-fifths.Pam:
So, your answer is four-fifths because you had to... You felt like since the problem was given in fractions, you might end up back in fractions. Yeah. But you can also sort of think of it as 80%. Cool.Kim:
I'll tell you what I actually did, and then I'll tell you what I wish I would have done once I had 48/60. And I was listening to you talk while I was trying to.Kim:
Yeah, because I was trying to multitask and thinking about all that simultaneously. Right, that's one of the hallmarks of your brain having to do more activities when you're trying to hang on to things simultaneously.Kim:
So, I literally just cut stuff in half. I found an equivalent 24/30, and then 12/15. And then, from there I divided by 3, and I got the equivalent 4/5. But then, I thought to myself, "Duh, 48/60." There's four 12s in 48. And five 12s in 60. So, that would also be equivalent to four-fifths. But interesting, when you said 80% was right about when I had gotten to four-fifths. And I was like, (unclear). It was the 80% that got me. I was like, "Is that 80%?" Like, I was sort of picturing a clock, and I was picturing where the hand would be on 48 minutes, and trying to like make 80% jump out, and it didn't really. Like, I don't know. Do you know what I mean? Like, when I look at a...Kim:
Yeah. I don't know this 48/60 screams 80% without just a little bit more thinking to it.Pam:
Yeah, yeah. Especially not visually, I didn't really (unclear). I didn't see 8 chunks of things. I guess I could see eight 6 minute chunks. That's just not really a chunk we see on a clock, right?Kim:
Right. It's so focused on 5 minutes, and 10 minutes, and 1 minute.Pam:
Okay. Well, we can't wait to hear your strategy. And I wonder if it 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 what you were thinking about for this problem. While you're there, check out what other people did and comment on their thinking.Pam:
Yeah, when you do tag me on Twitter at @PWHarris. Or Instagram, PamHarris_math. Or Facebook, Pam Harris, author mathematics education. You can also on Facebook look at Math is Figure-Out-Able. That shows up now. And use the hashtag MathStratChat. So, make sure you check out the next MathStratChat problem. We'll post next Wednesday at 7:00 p.m., around then anyway. 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, so keep spreading the word that Math is Figure-Out-Able!