Teaching with Unifix Cubes: 5 Math Skills to Pair Them With (EP26)

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

Today we are going to talk about one of my favorite math manipulatives and all the different ways that you can use them in your classroom.

I’ve seen this topic discussed quite a bit in a few Facebook groups I’m in, so I did a little research before writing this episode. I wasn’t surprised by the most common answers. I felt like most people were going to say fraction tiles, base 10 blocks, or pattern blocks. But I was surprised that I could only find one other teacher who had the same answer as me.

My favorite manipulative is unifix cubes, so that tells me that either teachers don’t have them in their classroom, or they don’t know how to use them.

When I first started teaching fourth grade, I inherited probably 100 sets of these, but I never used them because I felt like they were more of a primary resource, and I just didn’t know how to use them with upper elementary lessons.

But that all changed back in 2018, when I had the honor and privilege of seeing Greg Tang, not once, but twice. If you’ve ever seen Greg Tang, then you know he uses unifix cubes to model a lot of different skills. And he really opened up my eyes to all the different ways that they can be used with upper elementary.

Once I saw how he used them, I started thinking about different skills that I could pair them with, and that’s what today’s episode is all about. So again, today, we’re going to discuss five different upper elementary skills that you can teach with unifix cubes.

Let me first start and tell you what sets them apart from other manipulatives like fraction tiles, base 10 blocks, or pattern blocks. I think the biggest thing that sets them apart is they are easy to pass out, they’re easy to collect, and they’re easy to count. They come in sets of 10, so it just makes all of those things much simpler.

Another thing that sets them apart is they are so easy to work with. Sometimes manipulatives can be frustrating if they keep moving around on you or they won’t fit together well, especially for those who struggle with fine motor skills.

And finally, because they’re so easy to work with, they are much less likely to end up on the floor or get lost. Fraction tiles and base 10 blocks are the worst for this. There are always pieces that fall on the floor or get left behind after cleaning up. But that rarely happens with unifix cubes.

So, let’s get to the different skills that you can teach using unifix cubes.

The first one is actually two skills: basic division and division with remainders. I’m going to start by explaining how to use them with division facts. I never use them with just division back since that was taught in third grade. But if you teach third grade, here’s how that would look.

Let’s say the problem is 20 ÷ 4. First, they will need to build one large set of 20 to represent the dividend. Just for fun, you can have them hold these up in the air and that way you can check that everyone has 20 to start with.

Then you can introduce the word dividend. This is a new term for them, so go through some examples of what the dividend could mean. Maybe these are 20 beads that we’re starting with when making necklaces. Maybe these are 20 coins that we’re dividing up into different groups. The sooner they can make a connection to what they’re doing the better.

Next, introduce the word divisor. Remember you are dividing by four, and they are going to put them in groups of four. To make the groups stand out a little bit more, you can have them take a dry erase marker and put a circle around them, and that’s going to help them see the connection to multiplication.

Once you’ve finished modeling the problem, then write the division equation 20 ÷ 4 = 5 and the related multiplication equation of 5 x 4 = 20 so they can see the connection between the two. So, that’s how third grade teachers can use them for division facts.

Let’s move on to fourth grade. Fourth grade teachers, you’re going to use them when you introduce dividing with remainders, and you’re going to follow the same steps. So, let’s say the problem is 19 ÷ 4. Start by having them put all 19 unifix cubes in one long stack, hold them up to check, name them as the dividend, then put them in groups of 4, and circle these groups of 4, but this time they’ll have 3 left over.

This is brand new to them because they are not used to having things left over. So, I found it helpful to have them label those remaining pieces with an R, and that way they didn’t accidentally circle them to make another equal group.

When they were finished modeling, they would have four circle groups of four with three left over that were labeled with an R. From there, we wrote both the division equation, which is 19 ÷ 4 = 4r3, and the multiplication equation to check, which is 4 x 4 + 3 = 19. Also, I do want to mention, if you have snap cubes, they will work just as well as unifix cubes will.

So, let’s move on to number two.

The second skill you can pair unifix cubes with is prime and composite numbers. Here’s what that lesson looked like for me. First, I had my students make a t-chart in their math notebooks. On one side, they labeled prime and wrote the definition, and the other side they labeled composite with the definition.

So, going into this, they knew the definitions of prime and composite, but we used the unifix cubes to explore the numbers that would fall into the prime and composite categories.

For this lesson, I gave each student 30 unifix cubes, and to make it easy, we went ahead and started with 30 as our first example. Their job essentially was to figure out, is 30 prime? Is there only one way to make equal groups with 30? Or is it composite? Are there multiple ways?

Once they built an array and found that factor pair, they recorded it and then they tried again, and they did this until they came up with all the factor pairs and all the different arrays that you could build with 30. That helped them determine whether it was prime or composite.

After they had some time to explore, we did come together as a group and we discussed all the different factor pairs. We wrote them on the t-chart. So, in this case, we would have written this on the composite side and recorded our factor pair t-chart to keep as a reference. So, 1 x 30, 2 x 15, 3 x 10, and 5 x 6.

We repeated this with the numbers 16, 9, 11 and 19. So, in the end, we had 30,16, and 9 under the composite side, and 11 and 19 under the prime side.

Alright, let’s move on to the third example. The third skill you can teach with unifix cubes is converting between mixed numbers and improper fractions.

This is a really effective way for them to practice naming a fraction greater than one as both a mixed number and improper fraction, and this will also prepare them for the next skill I’m recommending, which is subtracting mixed numbers with regrouping.

Let’s say you are modeling 2 ¾.  Here’s the best part about this. Every time they model the whole number, they will have to decide how many unifix cubes are going to represent the whole. So, let’s say the denominator is three, then each whole would be 3/3. If it’s five, then each whole would be 5/5.

In this example, the denominator is four, so they need to put four unifix cubes together to represent each whole number. So, they will make two sets of four to represent the whole number two, and then one set of three to represent the fraction three fourths.

Just like we did with division, talk about what this could mean. If you’re referring to pizza, it would be two whole pizzas and three-fourths of another one. If you’re talking about a candy bar, it would be two whole candy bars and three-fourths of another one. If you’re talking about money, it would be two whole dollars and three-fourths of another dollar.

To figure out the improper fraction, you can first have them count how many fourths are in the model, because remember, every unifix cube in this model represents ¼. I liked doing this to first introduce the term improper fraction because that number represents how many unit fractions there are. So, in 2 ¾, there are 11 fourths, and if they count them individually, they’ll see that.

But after a few examples of counting the unit fractions to determine the improper fraction, I moved on to writing it as a sum of fractions. So, instead of counting the fourths, they would write 4/4 + 4/4 + ¾ = 11/4. This is exactly what they have modeled in front of them, so it’s a very visual way to connect the two concepts.

You will find that many of them discover the shortcut of multiplying and adding when they model it this way, and I never like to tell them the shortcut up front. But if they discover it and they understand what it means, I’m okay with that.

One final thing before we move on to the next example. Make sure you use a variety of denominators in your examples. Do some that are thirds and fourths and fifths and sixths, so they always have to go back to the denominator and realize that the number of unifix cubes in the whole all depends on the denominator, and it can be different from one problem to the next.

All of that is so much easier to see when you use unifix cubes to model them versus pattern blocks, which is what I used to use when modeling these.

Alright, let’s move on to the fourth skill you can teach with unifix cubes, and that is subtracting mixed numbers with regrouping.

This was actually the very first lesson that I used unifix cubes with, and I noticed a difference immediately. I didn’t see the same mistakes that I often saw where when they would regroup, they would accidentally stick a one in front of the number. For example, if it was 2/5, they would make it 12/5. I was seeing them do the right thing, and here’s why.

Let’s say the problem is 3 and 2/5 – 1 and 4/5. First, they’re going to set up 3 and 2/5, so they’ll have three groups of 5/5, since the denominator is five, and then 2/5 leftover on the fraction side.

They will recognize that they don’t have enough on the fraction side to take away 4/5, and when they bring that whole number over to the fraction side to regroup, it will be crystal clear to them that they’re not adding 10 to the two to make it 12 like they would with whole numbers. They’re adding 5/5 to the 2/5 that are already there to get 7/5.

Really make sure to reinforce the fact that 3 and 2/5 is the same as 2 and 7/5. You didn’t change the value of the mixed number. You just needed to regroup to get more on the fraction side.

Now that they have 2 and 7/5, they can take away 1 and 4/5 to get their final answer.

This is such an effective way to teach this lesson, and the reason I could tell it was working is when we took the unifix cubes away, my students were solving these problems correctly. They weren’t making the same mistakes that I had seen in the past.

That’s when I knew I struck gold with this manipulative, and I wanted to tell everybody about it. I wrote a blog post about it. I’ve done an Instagram reel and an Instagram post about it. I’ve created a work mat to use along with this. I’ve also created task cards with unifix cubes, and more recently, I created a PowerPoint lesson that uses unifix cubes to teach subtracting mixed numbers.

All of those resources will be linked in the show notes and also a video that shows me working these problems from start to finish, just in case you need a visual.

My final idea for you today is to use unifix cubes to teach growing shape patterns. I used to dread teaching patterns. I don’t know why, but it was one of my least favorite lessons to teach. But once I started using unifix cubes, all of that changed. I went from dreading this lesson to really enjoying it and looking forward to it.

Here’s how I taught this lesson. I showed them a pattern with the first three or four figures in that pattern, and these figures were all made with unifix cubes. My students had to analyze those first three or four figures, and then I had them build the next figure. So, they didn’t build all three or all four, they just had to build the next one.

Once they had their figure built, I had them write a number pattern to match, which is helpful because it’s a way for them to check their answer. So, if they noticed that the first figure has five cubes, the second one has seven cubes, and the third one has nine, the figure that they built should have 11. They can see that 5, 7, 9, 11 pattern.

We then extended the pattern and found how many would be in the 8th or the 10th figure. I could tell they were having so much fun and they were doing exactly what we needed to do. They were analyzing a pattern, they were determining the rule, and they were extending the pattern. After we did five examples together, we then moved to the workbook and did a couple of examples there.

If you don’t have enough for your whole class, you can do this as a small group activity and it works just as well. I will put a link in the show notes to the task cards that I used for my whole group lesson, and that way you can print them and use them in small groups if that’s better for you.

So, to recap the five skills to teach with unifix cubes.

1. Basic division or division with remainders
2. Prime and composite numbers
3. Mixed numbers and improper fractions
4. Subtracting mixed numbers with regrouping
5. Shape patterns

I cannot wait for you guys to try using unifix cubes to teach these lessons. You are going to fall in love with this manipulative just like I did.

Before I let you go, let’s get to today’s teaching tip of the week.

This one is a classroom management tip when it comes to using unifix cubes in your lessons. As soon as you pass them out, they’re going to want to play with them. So, go ahead and let them play but only for one minute, just to get it out of their system.

When the time is up, they can hold up their creations to show them off. They can show their friends. They can show you. Then set the timer for one more minute, and that’s how much time they have to get them back to their sets of 10.

Yes, you’ll lose two minutes of instruction doing this, but this way they won’t have such an urge to play with them during your lesson. Well, friends, that is all for today’s episode. Have an awesome week, and I will see you next Tuesday!