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Learning Math/CS/Engineering Design with Robotics
1.2.1. Patterns in Numbers and the Commutative Property of Addition
Overview

In this lesson, students will learn how to recognize and apply the commutative property of addition.
Learning Objectives
  • Identify arithmetic patterns and explain them using properties of addition
Lesson Description

When numbers or objects are organized in a specific order, we call this order a pattern.

One pattern in addition is the identity property of addition. This property says that any number plus 0 will equal that number. For example,

4 + 0 = 4

Another pattern is the commutative property of addition. This property says that no matter the order you add two or more numbers, they will have the same sum. For example,

5 + 3 = 8

and

3 + 5 = 8

 
Vocabulary

pattern, identity property of addition, commutative property of addition

 
Example 1: Properties of Addition

In the addition table in the grid, we see that the row and column for the addend 0 are highlighted in a light orange. This shows that adding 0 to any number give us a sum which is just that number. This pattern is the identity property of addition.
Example 2: Cubes and the Commutative Property of Addition

Looking at the picture in the grid, we see two different groups of foam cubes. Both groups have 11 total cubes.

4 + 7 = 11

7 + 4 = 11

This illustrates that we can add 4 and 7 in any order and their sum is still 11. 
Example 3: Fruit and the Commutative Property of Addition

Looking at the picture in the grid, we see two different groups of pears and peaches. Both groups have 8 total fruits.

5 + 3 = 8

3 + 5 = 8

This illustrates that we can add 3 and 5 in any order and their sum is still 8. 

Note: After you click  Run , there will be a series of pop-up message boxes that guide you through this problem. To get to the next box, click anywhere in the grid area. Make sure that you click through all the pop-up boxes until the last one disappears. 
Example 4: Robots and the Commutative Property of Addition

As the robots drive, we see that Robot 1 moves 3 inches then 7 inches. Next, Robot 2 moves 7 inches then 3 inches. Robot 1 and Robot 2 both end at the position of 10 inches.

3 + 7 = 10

7 + 3 = 10

This illustrates that we can add 7 and 3 in any order and their sum is still 10. 
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