Commutative Property

Contributor: Meghan Vestal. Lesson ID: 11702

Do you know what a "commuter" (not "computer") is? Do you know someone who travels to work, from one place to another? Numbers in addition can travel, too. Watch a video and play some games and learn!


Arithmetic, Operations and Algebraic Thinking, Rules and Properties

learning style
personality style
Lion, Beaver
Grade Level
Primary (K-2), Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

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What do people do when they commute to work?

Properties of addition describe rules that tell us how to add numbers.

In the first Related Lesson of this series, found in the right-hand sidebar, you learned about the associative property of addition. Tell your teacher or parent what the associative property of addition says.

The associative property has to do with the way numbers are grouped. According to the associative property, when you have three or more numbers being added, it does not matter how the numbers are grouped together by parentheses because the sum will always be the same.

In this lesson, you will learn about the commutative property of addition. The commutative property of addition states that you can move around the numbers in an addition problem and still get the same sum. In other words, it does not matter in what order you add numbers together. Mathematicians use the following formula to represent the commutative property of addition:

A + B = B + A

In the equation above, you can see the that letters on the right side of the equal sign are the same as those on the left, just simply flipped.

Look at the numerical examples below. Add the numbers on both sides of the equal sign, and see if the sides are balanced:

  • 20 + 10 = 10 + 20
  • 9 + 11 = 11 + 9
  • 16 + 8 + 12 = 12 + 16 + 8

For each problem, including the problem with three numbers, the numbers moved, or changed places. Despite swapping places, you should have found that both sides of the equal sign had the same sum, meaning the equation is balanced.

Commutative sounds like the word "commute," and the terms have a similar meaning. Earlier in the lesson, you should have said that people who commute to work travel back and forth between their work and home. How does the concept of commuting to work relate to the commutative property of addition? Tell your teacher or parent.

You can easily remember the commutative property of addition because it is so similar to commuting to work. When people commute to work, they are moving back and forth between different places. With the commutative property of addition, the numbers are moving back and forth between different places.

Review what you have learned about the commutative property of addition by watching Commutative Laws by Mathematics is Fun:

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When you are finished watching the video, tell your teacher or parent which other operation you can apply the commutative property to.

Then, move on to the Got It? section to practice solving problems with the commutative property of addition.

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