Associative Property

Contributor: Meghan Vestal. Lesson ID: 11701

Were you ever told to watch who you associate with? In math addition, numbers don't care with whom they associate. Watch a video and work a worksheet to learn how this property makes addition easier!


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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The following image illustrates a mathematical problem. Compare and contrast the images on each side of the equal sign.

associative problem

  • Do you see what happened?

In math, there are rules we use with addition.

These rules are called properties of addition. The three rules of addition are:

  1. associative property
  2. commutative property
  3. distributive property

In this lesson, you will learn about the associative property of addition.

The image at the beginning of the lesson illustrates the associative property of addition. Based on what you see, what do you think this rule states? Discuss your thoughts with your parent or teacher.

The associative property states that when three or more numbers are added, it does not matter how the numbers are grouped or arranged; no matter how the parts are arranged, the sum will still be the same.

If you look at the image from the beginning of the problem, the first image shows three orange chips grouped with six blue chips. The second image shows the same three orange chips grouped with four yellow chips. You probably noticed that it does not really matter how the orange chips are grouped because the total is still the same on both sides: 13.

Mathematicians use the following equation to represent the associative property of addition:

A + (B + C) = (A + B) + C

Remember, parentheses show us what part of a problem needs to be solved first. This equation illustrates that it does not matter how the parentheses are arranged, or what numbers you add together first.

Look at the examples below to see what this equation looks like with numbers. For each example, add the numbers on both sides of the equal sign together.

  • 10 + (7 + 8) = (10 + 7) + 8
  • 2 + (4 + 6) = (2 + 4) + 6
  • 12 + (2 + 1) = (12 + 2) +1

You probably noticed that the only thing that changed in each problem was the placement of the parentheses that tell you which numbers to add first. Did you get the same sum on both sides of the equal sign for each problem? It did not matter how the numbers were grouped!

Take some time to review the associative property of addition and look at more examples by watching Associative Laws by Mathematics is Fun:

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When you are finished watching the video, explain the associative property of addition to your teacher or parent.

Then, move on to the Got It? section to practice adding with the associative property.

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