When teaching fractions, kids need lots of visuals and concrete manipulatives to help build their understanding. But there’s one visual representation that we use a lot that actually builds some misconceptions about fractions. Today we’re going to investigate the visual aid that you should not be using to teach fractions.

Watch the video or read the transcript below:

Now, there are a lot of visuals that we can use, and I want you to take a look at your standards because there are standards that specifically call out using visual models. Here’s an example from third grade.

About third grade, fourth grade, fifth grade, you typically will have some mention of this. It just says visual fraction models. Well, if you dig a little deeper, it gives information about what visual fraction models they’re talking about.

It talks about using a tape diagram, a number line, the area model. But there’s one visual type that we tend to use a lot that is not referenced, and that is representing fractions as part of a set.

Fractions As Part Of A Set

Yes, we do this often. We show fractions as multiple things and then one of them colored in.

This example showing one-third was really, really typical in textbooks for a long time. There would be three things, we would color in one of those three, and the issue is that kids start to see it as two separate things.

I get one out of the three. Which is a way to view fractions, but it’s more of a ratio view, which needs to come later, in the middle grades, when they’re developing their understanding of ratios.

And the hardest part is that if this is the visual of one-third that kids have, and then we ask them to add one-half to it, this visual helps facilitate the number one wrong answer to one-third plus one-half.

The number one wrong answer is two-fifths. And kids think it is because this visual helps facilitate it. If I have one out of three and then I get one out of two, I got two out of five. That’s what that visual is showing kids, right?

The other hard part, too, is when they go to compare. Right, if I’m trying to compare one-third to one-half and talk about when do I get more, which one’s greater, all of that kind of stuff, it’s hard to do that because their visual is telling them that they get the same. If I get one out of three, and then I get one out of two, I still get one. It does not matter to me.

That visual there is helping facilitate the understanding that I get one. And it’s the same sized one. The problem with this visual is that it isn’t giving kids the same sized whole, and that’s why we want to move towards showing fractions as part of a whole, by using tape diagrams, using the number line, using the area model, because you’re using the same whole.

Fractions As Part Of A Whole

Then when you slice a whole into thirds and a half and you’re trying to add one-third plus one-half, kids can see, I don’t have the same size pieces, so I can’t add them together. We tell kids all the time, you have to have like denominators. Well, like denominators gives us the same size pieces, the same units to work in, right?

Just like with whole numbers, you can’t add tens and tenths together, right? You have to have the same size units. You can’t add thirds and halves.

We need to have something that’s the same sized units to be able to add them together.

And the visual when you put fractions as part of a whole helps kids realize when it is the same size and when it’s not. When you do it as part of a set, it’s really, really muddy water in there, and it’s hard for kids to understand why they can’t use that. It looks like they’re the same size. But they’re really not. And again, it helps with comparison, right?

When I’m showing one-third versus one-half, it’s way easier to tell what one-half is, I get more, it’s larger than one-third. So there are lots of great fraction visuals, but the one I want you to avoid is part of a set. It needs to come later after they’ve developed their understanding of what fractions are. So I hope that this has helped you build your math mind so you can go build the math minds of your students.

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