Introducing the Associative Property of Addition

Introduction

In this lesson plan, you will find engaging activities for introducing the associative property of addition to your learner. They will also revisit the commutative property of addition which applies to adding two numbers, then relate it to adding three numbers with the associative property. These foundational concepts will help them understand how numbers can be grouped and ordered in addition.

Before beginning the lesson, your learner should be familiar with the commutative property of addition.

Key Concepts for Introducing the Associative Property of Addition

Here are a few concepts that are helpful to know for this lesson:

• Commutative Property of Addition: The commutative property of addition states that the order of addends does not change the sum. For example, 2 + 3 = 3 + 2.
• Associative Property of Addition: The associative property states that the way addends are grouped does not change the sum. For example, (2 + 3) + 4 = 2 + (3 + 4).
• Application to Addition but Not Subtraction: It's important that learners understand that these properties apply to addition but not to subtraction. In later grades, they will see that these properties also apply to multiplication but not to division.

Teaching Plan

The following activities will help your learner understand and apply the commutative property of addition.

Examples and visuals to support the lesson:

1. Revisiting the Commutative Property

• Begin by revisiting the commutative property of addition with two addends.
• Use practical examples and concrete materials to show that changing the order of addends does not affect the sum. For example: "I have one yellow car and four blue cars. How many cars do I have altogether?" Demonstrate that 1 + 4 and 4 + 1 both result in the same sum of 5 total cars.

Skill Check
I know that when adding two numbers, changing the order still gives the same total.

2. Introducing the Associative Property

• Since this is the first time your learner may be adding three addends, introduce the associative property by discussing equivalent number sentences using concrete materials.
• For example: "I have two red blocks, three blue blocks, and four green blocks. Whether I group (2 + 3) + 4 or 2 + (3 + 4), the total remains the same."
• Use concrete materials to show that the total is conserved regardless of which pair of addends are added first.
• Introduce the generalized statement: "When we add three numbers, the total will be the same whichever pair we add first."

Skill Check
I know that when I add three numbers, the total is the same no matter which numbers I add first.

3. Exploring Aggregation and Augmentation

• Explore commutativity in the context of aggregation (part-whole) stories: "I have three red cars, one yellow car, and four blue cars. How many cars do I have altogether? 3 + 1 + 4 = 1 + 3 + 4."
• Next, move the focus onto augmentation (joining) stories: "I had three red cars. On my birthday, my sister gave me one yellow car. The next day, my friends gave me four blue cars. How many cars do I have now? 3 + 1 + 4."
• Use the first-then-then-now story structure to illustrate commutativity with three addends, reordering the "thens" and switching one of the "thens" with the "first."
• Commutativity in the context of augmentation stories is often less intuitive for learners. Reordering the steps of the story using pictures can help them visualize the concept better.

Skill Check
I can use story problems to see that changing the order when adding three numbers still gives the same total.

4. Modeling the Associative Property

• Next, incorporate a variety of visual aids, such as part-whole models and number lines, to show the associative property.
• Transfer each pair of examples from the previous activity to part-part-part-whole structures. Compare each pair by asking your learner: "What’s the same?" "What’s different?" Emphasize that the sum remains the same even though the parts are in a different order.
• Use a number line to explore commutativity in situations where it looks less obvious. For example, show that adding 2 + 3 + 4 on a number line yields the same result whether you group (2 + 3) first or (3 + 4) first.

Skill Check
I can use part-whole models and number lines to see that adding three numbers in any order gives the same total.

5. Summary of Properties

By the end of these activities, your learner should understand the generalized statements:

• "If you change the order of the addends, the sum stays the same." (Commutative Property)
• "When we add three numbers, the total will be the same whichever pair we add first." (Associative Property)

Summary

By the end of this lesson plan, your learner will understand and know how to apply the associative property of addition and the commutative property of addition. They will also realize that these properties to addition but recognize that they do not apply to subtraction. This foundational knowledge will also prepare them for understanding these properties in multiplication in later grades.

Teaching Plan adapted from NCETM under OGL license v3.