# 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

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

• What denominators work well for a clock model?
• Example Problem String with non-unit fractions and mixed numbers
• Should we insist on the most simplified fraction answer?
• 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. And I'm Kim. 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, very cool.

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:

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

Pam Harris:

Yeah. 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 3/4 minus 1/3.

Pam Harris:

3/4 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 go ahead and 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.

Kim Montague:

Okay.

Pam Harris:

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 3/4, 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 20/60. So now I've got 45/60 minus 20/60. 45 minus 20 is 25, so 25/60. That would be one way of solving the problem 3/4 minus 1/3.

Kim Montague:

Nice.

Pam Harris:

I'd like to do another way, for fun. And this is actually the way that came to mind first.

Kim Montague:

Nice. Alright, here we go. 3/4 minus a sixth. Ok. I'm going to use five minute chunks. So where are the five minute chunks? Just to review a little bit, five minute chunks

Pam Harris:

Kim Montague:

That's good. Alright.

Pam Harris:

Bring it on!

Kim Montague:

Pam Harris:

Yeah. And I'm sort of, I'm looking back. You guys Yeah. Okay, cool. Now I'm going to go ahead and do can't look back, unless you're writing along with me. But I had five minute chunks. So four and and a fourth is like four and - 3 and 55/60 or 3and 11/12. And sure enough, those put me at the 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 4 and 3/12. I'm supposed to subtract a third. A third is like at the four o'clock, so that's four five minute chunks out of 12 five minute chunks, 4/12. So I've got 4 and 3/12 minus 4/12. So again, I'm sort of at 4 and 3/12. I'm going to subtract 3/12 to get at 4. I've got to subtract one more twelfth. What is 4 minus 1/12? That would be 3 and 11/12. same place on the clock, right? 55 minutes and the 11 minute - yeah, yeah, we're good.

Kim Montague:

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

Pam Harris: