Lesson objective: Understand that the commutative and associative properties apply to algebraic expressions just as they do to numeric expressions.

Students bring prior knowledge of the associative and commutative properties from 3.OA.D.8. This prior knowledge is extended to algebraic expressions as students use the properties to simplify an algebraic sum. A conceptual challenge students may encounter is understanding that using the properties to rewrite an algebraic expression results in an expression which looks different than the original expression but which still represents the same value.

The concept is developed through work with an algebraic expression describing the sum of the heights of three children, which is simplified using the commutative and associative properties to produce an equivalent sum-of-heights expression.

This work helps students deepen their understanding of equivalence because students see that the original expression and the rewritten expression are equivalent since they both represent the same quantity.

Students engage in Mathematical Practice 7 (look for and make use of structure) as they apply the associative and commutative properties to algebraic expressions which describe the sum of the heights of three students; these properties are applied to the algebraic expressions in the same way they are applied to numeric expressions.

**Key vocabulary:**

- associative property
- commutative property
- equivalent
- expression