Associative Property: Regrouping

Contributor: Erika Wargo. Lesson ID: 12102

Lining up in order counts with baseball batting order and standing in size place. But it doesn't matter in addition and multiplication; the numbers can line up any way they want and still work out!



learning style
personality style
Grade Level
Intermediate (3-5)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!


My three best friends came to my house for cake on my birthday. Emily arrived first, and put her neatly-packaged gift on the kitchen table. Next to arrive was Sean. He, too, brought a gift, wrapped in pretty blue paper, and placed it on the kitchen table. Finally, Sam arrived, and we had cake right after she placed her gift, which had a big red bow, on the kitchen table.

After we had cake I opened my presents. I started with Emily's, then Sam's, and last I opened Sean's. As it turned out, they all bought me the same thing: gift cards to my favorite store!

Would the outcome of what I received as gifts from my friends have been different if I opened them in a different order? What if they were not all grouped on the kitchen table? Why do you think the four of us associate with one another?

Discuss your answers with your parent or teacher.

There are four arithmetic operations in math: addition, subtraction, multiplication, and division.

Sometimes, problems can have more than one step, and have special characters in them, called, "parentheses" ( ). Parentheses separate a problem into parts and show us the order for doing the operations.

Operations also have certain properties, like the associative property that we cover in this lesson.

First, take a moment to think about what the word, "associate," means. Think about the story and the questions i the opening story. People associate with others who share common interests. Did you ever play a word association game, during which a person says a word and you say the first thing that pops into your head? For example, if I say, "ice cream," maybe you say, "cone," or "sprinkles," or perhaps your favorite flavor. These are all things that we associate, or group together, with ice cream.

Parentheses are used to show the associative property of addition and multiplication. This simply means the grouping of the numbers can change in the problem, but the answer will be the same. The associative property can also be thought of as having a combination of things, such as food. If you had a hamburger, fries, and a cookie, you may eat them in any order and still have the same result: the food will be gone and you won't be hungry anymore!

The associative property states that when you are adding or multiplying three or more numbers, it does not matter how you group the numbers (where you put the parentheses); your answer will always be the same.

Understanding and knowing how to use the associative property can help you solve math problems more quickly. If there are three numbers, you decide which two numbers to group together. Let's look at how this property works:

Associative Property of Addition

Let's begin with the problem 3 + 4 + 6 =

Suppose we want to add 3 + 4 first to get a total of 7, then add 7 to 6 to produce a sum of 13. We can also add 6 + 4 first to get 10, then add to get the sum of 13. Either way the numbers are grouped, the sum is the same.

Associate Property of Multiplication

Let's begin with the problem 4 x 5 x 2 =

We will begin by multiplying 4 x 5 first to get 20, then multiply 20 by 2, and the product is 40. Or, we can multiply 5 x 2 to get 10, then multiply 10 by 4, to get 40. Either way the factors are grouped, the product is the same.

Associate Property of Addition Associate Property of Multiplication
6 + (3 + 4) = 2x (4 x 5) =
(6 + 4) + 3 = (2 x 5) x 4 =


The associative property does not apply to division and subtraction, but parentheses are still used in problems involving those operations. You will learn more about order of operations in another lesson.

Let's go practice what you've learned in the Get It? section!

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