Lesson objective: Understand that the distributive property applies to algebraic expressions.

Students bring prior knowledge of using the distributive property with numeric expressions from 3.OA.B.5. This prior knowledge is extended to variable expressions as students identify equivalent expressions which describe the perimeter of a rectangle. A conceptual challenge students may encounter is understanding that when one dimension of the rectangle is unknown, it is still possible to use the distributive property to write equivalent variable expressions for the rectangle's perimeter.

The concept is developed through work with a rectangle which has its side lengths labeled. This representation is used to show how different grouping strategies result in different looking expressions, and that the distributive property is evident in the relationship between two of the resulting expressions.

This work helps students deepen their understanding of equivalence because expressions describing the perimeter of a rectangle are shown to be equivalent through applying the distributive property just as it is applied to numeric expressions.

Students engage in Mathematical Practice 7 (look for and make use of structure) as they write and examine equivalent expressions for the perimeter of a rectangle. Through comparing equivalent expressions for the rectangle's perimeter, students see that the distributive property can be used to relate the equivalent expressions.

**Key vocabulary:**

- distributive property
- equivalent
- expression
- multiply
- perimeter