Associative Property Lesson for Kids

Instructor: Trisha Fyfe

Trisha has taught college and K-12 English, reading, writing, and math. She has a master's degree in teaching.

Did you know that you can sometimes move numbers around in math problems, but the answer doesn't change? Let's look at why this happens as we explore the associative property in this lesson.

Cookies for Sale!

You are selling cookies at a bake sale to earn money for a new bike. Two of your neighbors come just as you open. You're off to a good start! Sam from next door buys 1 butter cookie and 2 lemon cookies. Mary from down the street buys 4 sugar cookies. How many cookies have you sold so far?

You sold 1 butter cookie and 2 lemon cookies to Sam, so that's 1 + 2. Then you add Sam's cookies to Mary's 4 cookies, to get 1 + 2 + 4. That's 7 cookies total. Pretty good!

When we add (1 + 2) + 4, we get 7 cookies
Associative Property Cookie Example 1

Different Groupings

Now, let's switch things around. Maybe Sam hates lemons and buys only 1 butter cookie. Mary buys the 2 lemon cookies and 4 sugar cookies. Did the total number of cookies you sold change? Let's find out.

First, Mary. She buys 2 lemon and 4 sugar cookies, 2 + 4. Add those cookies to Sam's 1 cookie, 2 + 4 + 1, and you get 7 cookies, just like before.

When we add 1 + (2 + 4), we still get 7 cookies because of the associative property
associative property cookie example 2

The Associative Property of Addition

Why wasn't the total different in the second example? Because of the associative property of addition, which says that even if we change the groupings of the numbers we are adding, the total will always be the same.

Take a look at the associative property in our bake sale example: (1 + 2) + 4 = 1 + (2 + 4). It doesn't matter which grouping (operation inside the parentheses) we complete first. The answer is the same both times.

Funny Little Marks: Parentheses ( )

Notice the parentheses, ( ). Have you seen these in math before? In math, we complete the operations (addition, subtraction, multiplication, or division) inside the parentheses first. Parentheses group together numbers that we need to work with before any other numbers.

The Associative Property of Multiplication

The associative property also applies to multiplication. The associative property of multiplication says if we change the groupings of the numbers we are multiplying, the total will always be the same. Every time, I promise! Let's take a deeper look.

Try this:

(4 x 5) x 6 = ?

If you got 120, great job! Let's explore the steps.

First, complete the operations inside the parentheses. Remember we always do this step first.

4 x 5 = 20

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