# Ep 51: Fractions, a Clock Model Pt 2

June 08, 2021 Pam Harris Episode 51
Math is Figure-Out-Able with Pam Harris
Ep 51: Fractions, a Clock Model Pt 2
Chapters
Math is Figure-Out-Able with Pam Harris
Ep 51: Fractions, a Clock Model Pt 2
Jun 08, 2021 Episode 51
Pam Harris

We've had so much fun talking about fractions! In this episode Pam and Kim do another Problem String to demonstrate the effectiveness of a clock model.
Talking Points:

• What denominators work well for a clock model?
• Problems that work with both money and a clock model
• Today's students need the experience from learning with a clock model

We've had so much fun talking about fractions! In this episode Pam and Kim do another Problem String to demonstrate the effectiveness of a clock model.
Talking Points:

• What denominators work well for a clock model?
• Problems that work with both money and a clock model
• Today's students need the experience from learning with a clock model

Pam Harris:

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 we're here to suggest that mathematizing is not about mimicking or rote memorizing. It's about

reasoning:

about creating and using mental relationships. That mathematics class can be less like it has been for so many of us, and more like mathematicians working together, learning together. We answer the question, if not algorithms, then what? Alright, y'all on Facebook, we got a really cool message from Amanda Mctavish Watson, who said, "I got a teacher-appreciation card from a young lady this week that said, 'Thank you for helping me THINK math' made me cry. Honestly, I always praise my girls for thinking math. It's not a favorite for many girls and men dominate the STEM world. So here's one for Pam Harris and teaching kids to THINK math, rather than do math". Amanda I love that. Thank you so much for sharing that. That is amazing. Super cool. Super cool that your student recognized you during appreciation week when we got this, it was a little while ago, but we're so appreciative that you sent that on. And way to change these young women's lives. That's excellent, excellent, excellent.

Kim Montague:

I love, love, love when people share what they're doing and how their kids are thinking based on what they're learning from you. It's so fantastic to hear.

Pam Harris:

I think math not do math, yah.

Kim Montague:

Yeah. Okay. So in the last episode, we introduced the idea of a clock model for adding and subtracting fractions. It is such a great tool. And we asked for which denominators would this model be helpful? We asked y'all to think about what those would be.

Pam Harris:

So pause, if you haven't thought about it. Pause first. Okay, go ahead.

Kim Montague:

All right. So that would be anything that is a factor of 60. Right? Thinking about minutes.

Pam Harris:

Clock model, minutes, that sort of makes sense. So with money, we get 100 - factors of 100. And with clock, we get 60 - factors of 60. Totally cool. When we started talking about fractions, I quoted a dear friend and colleague Garland Linkenhoger, who said, if you really understand fraction equivalence, you do not need any rules for fraction operations, you can just reason your way through the operations. So true. So cool. Garland, I appreciate you throwing that out for me years ago. Let's get right at continuing to do that.

Kim Montague:

So today, let's do another problem string to help build equivalence using addition and subtraction. Are you ready?

Pam Harris:

I'm on the hotseat, alright.

Kim Montague:

Alright. So you're thinking about a clock model today. And I'm gonna ask you the first problem, which is three fourths minus 1/3.

Pam Harris:

3/4s minus 1/3. So instantly, I'm thinking not money, because 1/3 money yuck. Clock, nice, I can think about a third of an hour. So that's going to be really brilliant. So let's see the first thing that comes to mind... I'm going to do minutes first, even though actually five minute chunks came to mind first, but I'm going to do minutes in an attempt to kind of keep everybody with us today. Okay, so I could think about well, and actually, in our last episode, we promised that we would do fractions that were more than unit fractions. So I'm just going to remind you, that in the last episode, if you haven't listened to that one, go check it out, because we really talked about unit fractions, and today we're going to talk about how we can think about non unit fractions. So three fourths, that's a non unit fraction, the numerator is not one - three fourths. So I can think about 1/4 on a clock. And then I can think about three of those one fourths. And so that sort of puts me at 1/4 is 15 minutes. So three of those one fourths would be 45 minutes, so I just wrote 45/60, 45 minutes out of the 60 minutes. And 1/3 I can think of on a clock is a third of an hour. 60 divided by three is 20. So that's like 20 minutes out of the 60 minutes. So 20/60s, so now I've got 45/60 minus 20/60, 45 minus 20 is 25. So 25/60. So that would be one way of solving the problem three fourths minus 1/3. I'd like to do another way. For fun, and this is actually the way that came to mind first. I'm going to use five minute chunks. So where are the five minute chunks. just to review a little bit, five minute chunks are sort of the numbers on the clock. Every time that minute hand goes to one that's five minutes to two, that's 10 minutes, right, another five minute chunk. Three, that's 15 minutes, 3 5 minute chunks. So I'm gonna think about three fourths of an hour in terms of five minute chunks, three fourths of an hour's is over there on the nine. And so that's nine out of 12 so that's like nine twelfths. And then that 1/3 we decided was on the 20 minutes, or the four, so that's four twelfths and so 9/12 minus 4/12 is five twelfths. I can kind of ask myself 5/12, where am I on a clock? 5/12 that's like 25 minutes, right? Hey, that's what we got when we did minutes, we got 25 sixtieths. 25 minutes out of 60 minutes. So 5/12 and 25/60 is sure enough the same place on the clock. Equivalent. Bam!

Kim Montague:

Nice. All right, here we go. Three fourths minus a sixth.

Pam Harris:

Kim Montague:

That's good. All right.

Pam Harris:

Bring it on!

Kim Montague:

One more problem, you're on a roll. What is 11/12 minus 5/6.

Pam Harris:

11/12 minus five sixths. Y'all on a clock model it's just screaming at me. But I'll go ahead and talk through

Kim Montague:

Pam Harris:

4 and a fourth, subtract a third. So we promised you guys a mixed number, we wanted to make sure we got at least one of those in there. And really nothing changes, I'm still going to use a clock to help me think about what's going on. Let's see. So four and a fourth. It's almost like I've got four hours and a quarter of an hour. And I'm going to subtract a third of an hour. Hmm. I'm thinking about that. I yeah, it's screaming at me, I'm going to do minutes first, even though the twelfths are screaming at me, I've gotten much better at the 12ths at the five minute chunks over time. I'm going to do minutes first. So I've got sort of four hours and a quarter is four hours and 15 minutes. So I'm going to write four and 15/60. Subtract a third of an hour, a third of an hour is like 20 minutes out of 60 minutes. So I've got four and 15/60 minus 20/60. I'm thinking about that on a number line. I couldn't do it on a clock, I could think about - nah I'm gonna do it on a number line. 4 and 15/60 and if I subtract 20/60, I'm gonna subtracts 15/60 first and land on the four and now I've got to subtract another 5/60 or five minutes. And so four hours minus five minutes. That's like three hours and 55/60, that would be one way to solve that problem. 3 and 55/60, right?

Kim Montague:

Yeah.

Pam Harris:

Yeah. Okay, cool. Now I'm going to go ahead and do five minute chunks. So four and and a fourth is like four and - a fourth of an hour is like on the 15. So that's like the three o'clock or three five minute chunks out of 12 five minute chunks. So four and three twelfths. I'm supposed to subatract a third. A third is like at the four o'clock, so that's four five minute chunks out of 12 five minute chunks. Four twelfths. So I've got four and 3/12 minus four twelfths. So again, I'm sort of at four and three twelfths. I'm going to subtract three twelfths to get at four. I've got to subtract one more twelfth. What is four minus 1/12? That would be three and 11/12.

Kim Montague:

Nice.

Pam Harris:

Yeah. And I'm sort of I'm looking back. You guys can't look back, unless you're writing along with me. But I had three and 55/60 or three and 11 twelfths. And sure enough, those put me at the same place on the clock right? 55 minutes and the 11 minute - yeah, yeah, we're good.

Kim Montague:

All right, so great. So we today used, actually last week or the week before, used money to work with denominators that were factors of 100. And then we've been working with a clock to create equivalence with factors of 60. But what about when there's denominators that are both factors of 100 and 60?

Pam Harris:

Bam.

Kim Montague:

Right? Well, that's when we give kids choice, right?

Pam Harris:

teaching fractions:

do work with the money model and the clock model to help your students create both relationships, the relationships with money and time and the relationships with equivalencies with common denominators. So we get it, we get it, but it is all the more important to do this kind of work. Alright, fabulous. Remember to join us on MathStratChat on Facebook, Twitter, Instagram on Wednesday evenings, as we explore interesting problems with the world.

Kim Montague:

If you're enjoying the podcast, and you find it helpful, please rate it and give us a review. That way more people can find it wherever they get podcasts.

Pam Harris:

So if you're interested to learn more math, and you want to help yourself and students develop as mathematicians that don't miss the Math is Figure-Out-Able Podcast because math is figure-out-able.