 ### Commutative Property

The commutative property of addition is illustrated with images of blocks. Rearranging the blocks indicates that the total number of blocks does not change when the order is changed. Students use this property to learn how addition statements can be rewritten.

In the problems in this lesson, students are given an addition statement and rewrite it using the commutative property.

### Associative Property

The associative property of addition is illustrated with addition of three digits. The three digits are added in different orders to illustrate that the final result is not affected by the ways in which the individual numbers are associated for addition.

In the problems in this lesson, students are shown one way to solve an addition of three single-digit numbers. They select a different way to solve the same problem, using the associative property.

### Using Properties to Simplify Mental Calculations

In this lesson, the associative and commutative properties are used to illustrate easy ways to add three digits mentally. By associating two digits that sum to 10 or a multiple of ten, the remaining step in addition is easier to do mentally.

In the problems in this lesson, students are given problems requiring the addition of three numbers that are either one digit or two digits. These problems all include two numbers whose sum is ten or a multiple of ten. The student must add the digits mentally, and the addition becomes easier when the strategy taught in the lesson is used.

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