Teaching Tips and Strategies for Multiplying Fractions (EP27)

Hey, everyone, and welcome to another episode of Elementary Math Chat!

Today is going to be another content-specific episode on multiplying fractions by a whole number and multiplying a fraction by a fraction. It has been a while since I’ve done a content-specific episode. My last one was on interpreting remainders back in episode 16. So, I’m well overdue for one of these, and I’m excited to share a few tips on multiplying fractions.

Let’s begin this one by breaking down the standards so we can understand exactly what it’s looking for. 

When I look at this standard, there are two things that stand out to me. Number one, it really wants you to focus on the fact that when you multiply a fraction by a whole number, or a fraction by a fraction, for that matter, we want students to understand that these are factors. They’re not going to be whole number factors, but they are factors since you’re multiplying two numbers to get a product.

The other thing that stands out is when you multiply a whole number by a fraction, you are combining equal groups just like they did with whole numbers, except this time, there’s a fraction involved. So, in a nutshell, this is really wanting you to teach for conceptual understanding, and do your best every lesson to connect what they’re about to learn with fractions to what they already know with whole numbers.

Alright, let’s kick things off with my first tip, and I’m going to start in fourth grade.

My first tip is for probably the first lesson you’ll teach in this unit where you express a fraction as the product of a whole number and a unit fraction. For example, 7/8 is seven groups of 1/8. This is a very different way of thinking about fractions because they’re used to thinking of 7/8 as seven out of eight equal parts. So, to all of a sudden think about it as a multiplication equation is really confusing. So, it’s important that you start this lesson out with fraction tiles.

The first thing I had them do was take their fraction tiles and model the fraction 7/8, and then I had them write it as a sum of unit fractions. They already knew how to do this; they learned it in the previous chapter. So, I’m building on their prior knowledge. 

So, they would write 7/8 = 1/8 + 1/8 + 1/8 and so on. It is a lot to write, and so I would kind of act a little annoyed like oh, 1/8 + 1/8 + 1/8…can anyone think of a shortcut, so we don’t have to write this repeated addition of 1/8? And of course, they’re gonna say yes, we can multiply! But I didn’t go straight to the multiplication.

I had them next write what we had modeled using the words groups of. 7/8 is 7 groups of 1/8. This is helpful because number one, it’s exactly what they have modeled in front of them. But number two, it reinforces the connection to multiplication.

So again, we started with repeated addition, then we wrote it as 7/8 is 7 groups of 1/8, and then finally, we ended by writing it as an equation with a multiplication sign. After a few examples, they’ll be able to do it without the models and without the extra steps. But this is a really good way to introduce this skill and connect it to their prior knowledge.

My second tip on multiplying fractions is when you are teaching them to name the multiples of fractions. So, this is where you’re counting by unit fractions and non-unit fractions. This was the second lesson I taught, and I really did like this lesson because it makes sense for them to start out with multiples of fractions. That’s how they learned it with whole numbers. They first learned to skip count 2, 4, 6, 8, 10, 12 before they learned to do multiplication. 

So, making those connections from the beginning I think is so important when you’re heading into fractions.

One of my favorite ways that I practiced naming multiples is using Round Robin and Rally Robin. Those are Kagan strategies that I talked about back in episode 20. But in case you’re not familiar with those, Rally Robin is where they named the multiples back and forth with a partner. So, let’s say they’re naming multiples of 1/4. One person would start by saying 1/4, their partner would say 2/4, and then they would say 3/4, and they keep going until you say stop.

When you do say stop, have them take the improper fraction that they ended on and change it to a mixed number as an extension. This is helpful because eventually, they’re going to have to change their answers that are improper fractions back to mixed numbers when they start multiplying fractions. So, it’s a good way to review that skill.

Then do the same thing with non-unit fractions like 2/3 or 3/4. So again, one person says 2/3, the other says 4/3, and then 6/3, and so on. This also works well in small groups using the Round Robin format. So, instead of going back and forth, they will go around your small group table and name the multiples of unit fractions or non-unit fractions. And then again, practice changing the improper fraction they end on to a mixed number.

Let’s move on to my third tip for multiplying fractions, and this one applies to the lesson where you teach them that two equations can be equal. For example, 2 x 3/5 = 6 x 1/5, and here’s a really good way to start this lesson. Either on your board or in your slides, put up a few whole number equations and have a missing factor. 

For example, you could write 3 x 4 = 2 x ____, so that would be 6. Another one you could write is 5 x 4 = 20 x ____. This is exactly what you’re about to teach them with fractions, so it’s a really strategic way to start your lesson.

So, let’s get to the main part of your lesson. One of my favorite ways to introduce a concept is using a work mat. I just love how you can take one skill, and you can write it in different ways, and you can model it and it can all be on one page. And so, I created one specifically for this lesson. The work mat also comes with a bonus 4-section activity mat that you can use in small groups. That will be linked in the show notes if you want to take a look.

What I love about the work mat is it’s super simple, and it’s organized into three parts. The top part is where they write the equations. The middle section is where they model with fraction tiles, and then in the bottom, there is a fill-in-the- blank statement where they write it in words. Let me walk you through a quick example.

Let’s say they start off by modeling three groups of ¾. They would do that on one side and then write the equation 3 x ¾. Then they would separate those fraction tiles into unit fractions. So, nine groups of ¼, and in the equation side, they would write 9 x ¼ at the bottom. Then they would fill in the blanks and say that 3 groups of 3/4 is the same as 9 groups of 1/4.

I know you may be thinking, man, that means every student needs nine fourths, and only four-fourths come in a student set. So, if you don’t have enough, there are a couple of things you can do. You can print off a few printable fraction tiles, and that way you can give them more than they would get in a typical set. Or you can have them pull up the digital fraction tiles to model. 

But if you don’t want to do that, another option is to glue this work mat in their notebooks and have them draw the fraction tiles instead.

I did have enough to give everyone a large amount because we had a ton of extra fraction tiles. Our math coach did us a huge favor, and she organized them by fractions. So, all the half pieces were in one container, and all the thirds were in another. So, my teammates and I went up and grabbed the entire tub of sixths and eighths I think is what we use for this lesson. So, that would be my recommendation if you have enough extras.

Hey, fourth grade teachers. I’m interrupting this episode for a brief moment because state testing is right around the corner, and I know you might be feeling a little anxious and unsure about the best way to prepare your students. That’s why I want to make sure you know about my all-inclusive test prep kit with everything you’ll need the week before state testing.

This kit includes four interactive PowerPoint lessons, plus an editable choice board with printable and digital activities included. This means you’re getting four sets of boom cards, four independent practice worksheets, and four partner worksheets, plus a few extras to make your test prep week a breeze. All you have to do is make the copies because the rest has been done for you.

For more information, visit the show notes and click on Test Prep Kit or head to krejcicreations.com/testprep. Alright, let’s head back to the episode.

Let’s move on to my fourth tip for multiplying fractions, and this one is for when you actually start multiplying a fraction by a whole number.

This is a tip I learned from Greg Tang, and it is such a clever way to start this lesson. Start by writing this phrase on the board: 2 groups of 5 dogs equals ____, and keep everything in word form except the two and the five. You want those to stand out. Your students are going to answer with 10 dogs.

Repeat with a similar phrase like 3 groups of 7 apples equals _____. They will answer with 21 apples.

Then move to a phrase like 4 groups of 3 eighths equals _____. In this third example, I changed what they were grouping to be a fraction. But it’s still in word form, so they may not even notice, and so they will follow the pattern and answer with 12 eighths.

Now, take that same statement 4 groups of 3 eighths and write it as 4 x 3 eighths and the only thing you want to keep in word form is the eighths. They will once again answer with 12 eighths.

Then you’re going to write it one final time without any words, so you’re giving them the multiplying a whole number by a fraction equation: 4 x 3/8 = _____.

By now they’ve seen the pattern. They’ve discovered that the denominator is what you’re grouping, so it’s always part of the answer, just like the dogs and the apples were in the first few examples. So, I can pretty much guarantee you that they’re going to get that last one correct. They’ll know that 4 x 3/8 = 12/8.

This is also something to keep in mind if you have students start struggling with this concept later on. Go back to this whole idea of putting it in word form, and I think it’ll help them figure out what they’re doing wrong.

This seems like a pretty simple and straightforward concept, but a common mistake I saw often is when they multiplied a fraction by a whole number, they would change it to an improper fraction. So, I always made a point to show both of these side by side and addressed how they are not the same thing. 5 x 1/4 is not the same thing as 5¼.

I think a lot of them discover the shortcut for changing a mixed number to an improper fraction, and so sometimes they stick a multiplication sign in between the five and the four, so I’m pretty sure that’s why they’re making that mistake. The most frustrating part is that if they ever see something like 5 x ¼ on a multiple-choice test, don’t you think Choice A is going to be 21/4? It always is. It’s a huge distractor. So, even if you’re not seeing this mistake, I would address it early.

One thing that did help my students, and I actually noticed one of my girls doing this on her own, is to circle the whole number with the numerator, like put a horizontal circle around it, because that’s what you’re really multiplying, and the denominator gets written underneath it. Don’t you love it when you learn things from your students that you can pass on to others? So that’s a great tip if you have some students struggling with this.

Now, I know in fifth grade that you teach students to put a one under the whole number, and that makes sense for you. But I do not recommend doing that for fourth grade because it really takes the focus off the meaning behind combining equal groups of the fractions. So, save that one for fifth grade.

So, that takes care of the fourth grade skills. We ended up not multiplying fractions by a mixed number because when we dug deep into the standard, we couldn’t find any proof that we needed to teach this skill, which was kind of a relief because we felt like in the past when we taught that skill, it was really confusing for them, and they kind of forgot everything they had learned about multiplying fractions by a whole number. So, my last few years, we kept it simple and we just did a fraction by a whole number.

Let’s move on to fifth grade. Now, it has been a while since I’ve taught fifth grade, but there are two things I remember being extremely helpful with multiplying fractions.

As I mentioned earlier, in fifth grade, when you multiply a fraction by a whole number, you teach them to put a one under the whole number and make it a fraction times a fraction. I really wanted to make sure that they understood why we put a one under the whole number. Why not a two? Why not a three? Why not the same number as the whole number? 

I felt like if I didn’t address this, they wouldn’t understand what they were doing, and they might put a one on top of the whole number as the numerator instead.

So, what I did is I started out with a number talk, and I put a whole bunch of fractions on the board, but I made sure that all of the numerators were the same. It was only the denominators that changed, and we practiced going through and reading them.

So, let’s say they all had a numerator of two. We would read two fifths, two-fourths, two thirds, two halves, and then I had one that said two over one. So, we went through and read them, and they knew how to read all of them, except they did not know how to read the two over one. 

Some of them would say two over one, and while literally, that’s what’s written, they had a hard time telling me what that meant. They could tell me that two-fifths was two out of five equal parts. They could tell me that two-thirds was two out of three equal parts, but it was pretty clear that they didn’t understand what the one meant.

So, then I showed them a picture of these fractions. They already knew what the other fractions were going to look like, but when they got to the two wholes, they could clearly see that two over one meant two wholes. They weren’t broken into smaller pieces. They were in one whole piece.

This is like when you take a pizza out of the oven and you haven’t cut it yet. It’s one whole pizza. Once you cut it, then those pieces become fractions. But until you do so, it’s one whole pizza, and that’s why whole numbers have a denominator of one.

After that, we went through a few more examples of looking at some visuals of whole numbers and then practiced writing them with a denominator of one and reading them out loud. You know, four over one means four wholes, three over one means three wholes, and so on.

Another helpful tip was a little rhyme I made up, and this one is for multiplying fractions, and they would repeat each line after me. It goes like this, and you have to clap along when you do this. Multiplying fractions is no problem. So, then they would say multiplying fractions is no problem. Top times top and bottom times bottom. 

That’s the first part of the rhyme, and I love it because it reminds them of how simple this concept is. It also helps them when they have a mixed number because they’ll have to write it as an improper fraction to get a top and a bottom.

Now the second part of the rhyme is, reduce to get those numbers down, crisscross or up and down. When we said this part, I had them do the crisscross and the up and down motions as well. This is going to remind them to simplify either a numerator and denominator from the two different fractions or within the same fraction.

So, from start to finish:

Multiplying fractions is no problem

Top times top and bottom times bottom

Reduce to get those numbers down

Crisscross or up and down

Now, of course, I think it’s extremely important to draw and shade models of multiplying fractions, and that way they can see proof of how their answers get smaller. I always reminded them that when they multiply two fractions, they are finding part of a part. So, of course, it made sense that their answers were getting smaller. Just like when they multiplied a fraction by a whole number, their answer also got smaller. 

I’m sure that’s the way most teachers teach this skill, but I wanted to mention it just in case.

So, those are my teaching tips for multiplying fractions. Hopefully, you gained a few ideas and some tips that you can try with your students.

Alright, well, let’s wrap up with today’s teaching tip of the week.

Today’s tip is an idea for a small group activity that involves two of my favorite things: task cards and puzzles. Here’s how it works.

Let’s say you have six students at your small group table. Each pair will need a stack of task cards and then one puzzle, and you’ll want to make sure you have three different puzzles so they don’t see each other’s puzzle. When they get to your small group table, the puzzles will be inside of a Ziploc bag, and their goal is to put the puzzle back together. They do this by solving task cards.

So, for every task card that they answer correctly, they get to pull a piece of the puzzle out of the bag. Then once they have all the pieces out, they are finished solving the task cards and they can work together to put the puzzle back together.

As far as the puzzles go, I always found 8 to 10 pieces was the perfect amount, and I will put a link in the show notes to some really simple but fun puzzles that you can print that have 8 to 10 pieces. This is an activity that my students always enjoyed, and you know I’m a fan of task cards, but sometimes it’s nice to mix things up. Adding in this puzzle element is the perfect way to do so.

Well, friends, that is all for today’s episode. Have a great week, and I will see you next Tuesday!