Turn Around Facts: Easy Ways to Teach the Commutative Property

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Teaching Turn Around Facts

Teaching turn around facts is actually pretty fun because it is one of those skills where movement is hugely helpful for understanding. When we first begin working with turn around facts, we manipulate the numbers and manipulatives right there on the spot.

One way we do this is with interlocking cubes. I usually don’t give students too many cubes because, well, first graders will take as many cubes as possible and turn them into rockets or trains and send them on their way—basically anything but simply stack them!

Instead, I ask students to choose two colors and make two groups of cubes that equal 4. For example, they might stack 1 blue cube and 3 yellow cubes. We stand the stack up in front of us and say the fact:

3 + 1 = 4

Then we physically flip the entire stack upside down. Now we have:

1 + 3 = 4

We are actually turning the fact around!

How Turn Around Facts Help With Other Math Skills

Understanding turn around facts gives students a shortcut when learning addition facts. If a student already knows:

2 + 8 = 10

they don’t really have another fact to learn when they see:

8 + 2 = ?

They already know the answer is 10 because the addends have simply changed order.

This becomes especially helpful when one fact feels easier than the other. A student looking at 2 + 7 might think, 2…3, 4, 5, 6, 7, 8, 9 and count on seven more. But if they recognize that 2 + 7 is the turn around fact for 7 + 2, they can start with 7 and count on just two: 8, 9.

That’s a really concrete reason for learning the commutative property—it actually makes solving addition problems easier.

This understanding becomes useful later when students begin working with three addends, too. For example:

2 + 6 + 8

A student who understands that addends can change order can see the easier combination:

2 + 8 + 6 = 10 + 6 = 16

Now they’re using what they know about changing the order of addends to make an easier combination and solve the problem.

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Use Your Feet to Turn the Facts Around

One of my favorite ways to practice turn around facts was also the inspiration for one of my favorite lessons—and eventually one of my products.

We used our feet to practice!

I give students two numbers to tape to their shoes. They look down and read the addition fact shown on their feet. Then they physically switch the position of their feet to create the turn around fact. We repeat the activity with different facts, typically while moving around a circle.

It’s such a simple way to make the idea of turning a fact around something students can actually see and do instead of just looking at two equations on a page.

No matter which activity we’re doing, I always emphasize the same thing:

The numbers can change order, but the answer stays the same!

And I usually let students in on one more little secret: this works with multiplication, too—but NOT with subtraction or division!

Addends and Sums

When working with turn around facts, it is also a great time to introduce—or review—two important mathematical words. And, by the way, first graders love big math words! Big words are powerful, and kids love discovering that they know what they mean.

Students need to understand the words addend and sum.

An addend is a number being added in an addition problem. In the fact 3 + 7 = 10, 3 and 7 are the addends.

The sum is the answer when two or more numbers are added together. In 3 + 7 = 10, 10 is the sum.

This vocabulary fits perfectly with turn around facts because it gives us another way to describe exactly what is happening:

The addends change order, but the sum stays the same.

So when students turn 3 + 7 = 10 around to make 7 + 3 = 10, they aren’t just learning a math trick. They’re beginning to understand an important property of addition—and they have the mathematical vocabulary to explain it.

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Turn Around Facts with Shoes Activity

Once students understand what happens when we turn an addition fact around, they need lots of opportunities to practice seeing and creating those fact pairs.

The shoe activity inspired me to create my Turn Around Facts resource so students could continue working with the same visual idea. Students use shoe number cards to build an addition fact, then physically turn the shoes around and switch the addends to create its turn around fact.

The resource also includes an anchor chart, an Around the Room activity, recording pages, independent practice, and a Roll and Write activity, so students can work with the same concept in several different ways.

💚 Grab the Turn Around Facts Commutative Property Activities here!

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Turn Around Facts Practice Pages

And of course, plain old-fashioned practice on paper helps, too! I created a whole bunch of Turn Around Facts practice pages that I think are a little more fun than just writing numbers over and over. There are matching activities, cut-and-complete activities, dice and domino activities, and opportunities for students to complete and create turn around facts.

These are easy to pull out for independent practice, morning work, math centers, or anytime students need a little more practice with the commutative property. They’re also simple enough to leave for a substitute—something I appreciate even more now that I’m the sub! 😂

💚 Grab the Turn Around Facts Practice Pages here!

My Fact, Your Fact

Students love the infamous “I Have, Who Has?” games where they practice a skill such as time, money, or place value while playing with their classmates. I took the traditional game, twisted it a bit, and came up with my own version called My Fact, Your Fact—catchy, huh?

One student begins by saying, “My fact is 3 + 1. Who has my turn around fact?”

The player with 1 + 3 responds, “I have your turn around fact. It is 1 + 3.” That player then reads the fact on his or her card and asks who has the matching turn around fact.

The game continues around the class until everyone has had a turn and play returns to the student who started the game.

💚 Grab the My Fact, Your Fact Game here!

Seasonal Turn Around Facts Practice

I even made some seasonal turn around facts activities! Since this skill tends to be taught in the fall, I created some fall-themed practice activities as well as a set for Halloween.

Both give students another way to practice identifying and working with turn around facts while adding a little seasonal fun to math practice.

💚 Grab the Fall Turn Around Facts Activities here!

💚 Grab the Halloween Turn Around Facts Practice Pages here!

A FREE Turn Around Facts Activity

Those of you who have been following Boy Mama Teacher Mama for a while know that I love a good freebie and try to include at least one in every post. And if you’re new to the blog—now you know!

This freebie takes turn around facts one step further by using them together with number bonds, which is a logical next step in building number sense.

Students roll a die and use the number they roll to complete a number bond. Then they use the two parts of the number bond to write the corresponding turn around facts.

For example, if the whole is 6 and the two parts are 4 and 2, students can write:

4 + 2 = 6
2 + 4 = 6

Now students aren’t just memorizing that the addends can switch places. They’re seeing how the same two parts make the same whole, no matter which addend comes first.

💚 Grab the FREE Roll & Create Number Bonds with Turn Around Facts activity here!

Turn It Around!

Turn around facts may have a fancy mathematical name—the commutative property of addition—but the idea itself is pretty simple: the addends can change order, but the sum stays the same.

Give students plenty of opportunities to see it, build it, write it, and most importantly, actually turn it around! Flip those cubes, switch those shoes, trade places, play a game, and practice it on paper. Once students understand what is happening instead of simply memorizing two facts, they can begin using that understanding with number bonds, addition strategies, and other math skills down the road.