71. Teaching Fraction Operations

Brittany 0:00

What is your favorite fraction operation to teach? Adding, subtracting, multiplying, dividing?

Ellie 0:26

I think that it's actually dividing, because after I learned that you could divide fractions using common denominators, I kind of became fascinated

Brittany 0:37

Wait, what?

Ellie 0:38

What? You can divide fractions using common denominators.

Brittany 0:42

What?

Ellie 0:43

Yeah, one year, I had a student teacher, and her supervisor brought, or she actually sent me all of this information from a textbook that she had copied, and she's like, did you know you could do fraction division using common denominators? And I was like, No, I'd never seen that before. So from that moment on, I kind of became fascinated with that and how to show students both options, and then how to show fraction division with models so that they could understand that concept more clearly. But I can understand why many teachers don't like teaching any of the operations, especially fraction division.

Brittany 1:25

Yes.

Ellie 1:26

So if you're a math teacher, chances are you might approach fractions and fraction operations with a little apprehension. You're not alone. Many teachers find fractions challenging to teach, often due to the abstract nature of the concepts and the difficulty students face in understanding what is actually happening when they add, subtract, multiply, or divide fractions.

Brittany 1:48

Definitely. Welcome to the teaching Toolbox Podcast. I'm Brittany and I am here with my friend Ellie.

Ellie 1:58

Hello,

Brittany 1:58

and today we're going to explore the often daunting topic of teaching fraction operations. We're going to chat about why some teachers don't like teaching fraction operations, why it's important to teach fraction operations conceptually rather than just algorithmically, give you a few strategies for fitting in visual representations, and for how to fit in some fraction operation content every single day.

Ellie 2:31

Woo hoo.

Brittany 2:32

So Ellie, Why don't some teachers like teaching fraction operations?

Ellie 2:37

Well, while teaching fraction operations is often a really critical part of the math curriculum, many upper elementary and middle school teachers find challenges that make this topic kind of daunting, and there are several reasons for that. Fractions inherently involve abstract thinking, which can be difficult for students to grasp and for teachers to convey effectively if they just teach the steps or procedures.

Brittany 3:05

I know that a lot of teachers often feel unprepared because they don't have the resources or the professional development opportunities as well. I mean, how many of us had a course in teaching fraction concepts?

Ellie 3:19

Nope,

Brittany 3:20

no,

Ellie 3:21

we had one course in teaching math. That's it when I went to school. One course,

Brittany 3:27

yep,

Ellie 3:28

here's how to teach, not even how to teach math necessarily. Just here's a math course for people who are going to teach elementary school.

Brittany 3:36

Yeah, exactly.

Ellie 3:37

I was not in depth on fractions.

Brittany 3:38

So many teachers report a lack of in depth training focused on strategies for teaching fractions, including how to teach with manipulatives. I was never given a course on how to teach with manipulatives, either. So this can leave them feeling unequipped to handle students diverse learning needs. And we know students come to our grade levels with sometimes very varied backgrounds with fractions. Some schools also might not provide the necessary tools or manipulatives to facilitate hands on learning. So if there's no easy access to materials, teachers might rely solely on teaching algorithms. I know at sixth grade, we were not given manipulatives, except for the paper version that you photo copied and then cut up,

Ellie 4:27

right, right. So one result of students coming to a new grade level with varied backgrounds with fraction operations is that teachers somehow need to address the needs of the students who have gaps in their foundational understanding of fractions, as well as those who are ready for more advanced concepts. So that makes the whole process a little bit more difficult.

Brittany 4:48

And teachers often feel pressured to cover a lot of material in a very limited time, and that, of course, makes it difficult to individualize lessons to make sure all students achieve a solid understanding of fraction operations.

Ellie 5:03

Absolutely. I know I've seen lots of comments on social media, on Facebook with my kids don't understand fractions, but I have to keep moving. I have to get more things covered. So what am I supposed to do about this?

Brittany 5:15

Yeah, I just I have to go.

Ellie 5:18

Right. Well before we jump into some strategies, let's talk about why it is important to teach fraction operations conceptually, at least to begin with, instead of simply giving students the steps of the algorithm. Teaching fractions conceptually means focusing on helping students develop a deep understanding of what a fraction represents as part of a whole, rather than just memorizing procedures or algorithms by using visual models, real world examples and hands on activities to build a strong mental image of how fractions work and relate to each other, this helps students reason about fractions in different contexts.

Brittany 5:58

So why is conceptual understanding so important?

Ellie 6:01

It helps students develop deeper learning. Students who truly understand the concept of fractions can apply their knowledge to more complex problems and situations, not just the basic calculations. It also helps them to have flexibility in their thinking. Conceptual understanding allows students to reason through problems and solve them in different ways, rather than just following memorized steps, and it gives them transferable skills. A strong foundation in fractions is crucial for future math concepts like decimals, ratios, percentages and algebra.

Brittany 6:37

What are a few important aspects of conceptual teaching for fractions?

Ellie 6:43

Well, one would be using visual representations, using tools like fraction bars, number lines, area models ,and pictures to visually represent fractions and demonstrate how they relate to a whole. And using manipulatives also supports diverse learning styles. This would provide multiple representations of concepts by teaching fraction operations in many different ways, like orally, visually, with pictures and diagrams, and physically with manipulatives. Students with different learning types and choices can find a way that the material works for them and a way in which they understand the material. Conceptual teaching is also a bridge for struggling learners. Students who find the regular methods challenging, usually benefit from manipulatives' tangible nature, which makes ideas less abstract and intimidating and more accessible. And then we have real world connections, applying fractions to everyday situations like sharing pizza, and measuring ingredients or dividing time to make the concepts more relatable.

Brittany 7:45

I think students also enjoy that active learning, where they get to engage in hands on activities like cutting, using manipulatives, playing fraction games to solidify their understanding as well.

Ellie 7:58

Yes, absolutely. And then there's building intuition - encouraging students to reason about the size of fractions without just relying on calculations. For example, students can be taught to think about easy benchmark fractions, like one half, in order to start estimating their answers to an addition or subtraction problem, so they can tell if their answer is reasonable, to see if it even makes sense.

Brittany 8:22

Yeah, that's great. Most of the time, the students in our middle school classes come to us with background knowledge about fractions, at least, we hope they have something, and some of that knowledge is correct and some of it's not, but it's a great foundation for them to learn the next operation or to use the operations and other math contexts, like solving equations with fractions, finding area or perimeter with fractions, working with ratios and more. But often students background knowledge is shaky, sometimes incorrect for whatever reason, and knowing that we have to move on in our curriculum and that we can't spend a ton of time re-teaching the concepts students should already know, we end up feeling like really stuck, like we talked about earlier. Do we just give them calculators that are fraction friendly and hope that they enter numbers correctly, just so they can get a correct answer? Or do we ignore the fact that we have to move on and just re teach and re teach and re teach until they've got it?

Ellie 9:30

Right, that's really tough. And I do see a lot of comments that just say, just give them a calculator. They're going to use calculators eventually. Just give them a calculator. But one of the difficult, very difficult things about that is, if it's a word problem, and the problem is not written out, it doesn't say three and three fourths divided by two thirds, and you just have those numbers in the problem, that does not help them understand what to put in the calculator, right? How do they know which number goes first? How do they know whether they're dividing or multiplying or whatever. So they need to have more of a conceptual understanding, and the calculator doesn't help that,

exactly.

So I don't think we do either of those things. Just give them a calculator, you know, or just re teaching and re teaching, because we know there's no time for that either. There are quite a few strategies that we can use to work fraction basics and fraction operation practice into our classes on a daily basis. And so one of the first strategies is to make sure you have some fraction strips on hand. These can be sets of manipulatives your school might purchase, or if they don't have anything for you, you can print sets of fraction strips and laminate them so they're handy to either put up on your board for students to see, or for students to grab themselves and use. Any time a fraction problem pops up during your regular instruction, whether it's converting from an improper fraction to a mixed number, or adding or multiplying fractions, be ready with the fraction strips, or be ready to draw the fractions so students can see what's happening. And it doesn't have to be for every single problem, but if you know there's a fraction problem coming, and there was a fraction problem in the homework, if you're ready with those things, it's easy to just incorporate that. And the more they see representations, the more likely they are to then draw their own representations, or just grab the fraction strips and use them. The more you can show students different ways to combine fractions, the more flexible their thinking becomes with fractions and with math in general. For example, if students are trying to solve the problem one and three eighths plus three fourths, using the fraction strips can first help them see that three fourths is equivalent to six eighths, so we've got an equivalent fraction there. And then they can also see that taking two of those eighths from the three eighths and combining it with the three fourths gives them another one whole with 1/8 left over for a total of two and 1/8 and that's obviously much easier to see if you have the visuals in front of you, rather than just listening to me. And that type of fraction, strip movement or manipulative movement, can be shown next to the actual work for the problem, the algorithmic type of work there. It takes a little more time, but if you're prepared to show those representations on a regular basis, students will get better at fractions and faster with their work, which ends up speeding things up as the year goes by, and new topics that use fractions come up, and then you don't have to re teach that again, because you've kind of been incorporating it the whole time.

I was actually just helping a fourth grade teacher remotely with some fraction math problems, and had to draw diagrams to show the difference between 1/4 divided by 4 and 4 divided by 1/4 but I think it really helped them to clarify what they wanted from their students when I kind of showed them the diagrams of what it would look like.

Yeah, it just makes it so much clearer. And I think that a lot of us did not learn to do that. A lot of teachers didn't necessarily learn to do that. And so when they're looking at those problems, they don't they don't know what they're looking for.

Yeah,

So whether you love or dislike, we can't say hate here.

No no

teaching fraction operations. We. Hope you heard some ideas that you can add to your fraction teaching toolbox. But if you'd like to learn more about teaching fractions, join the wait list for the free fraction training that Ellie has, and we'll link that in the show notes. We hope you have a great day, and we'll talk to you later. Bye.

Bye.