Lesson objective: Understand that algebraic expressions can represent both a “recipe” and a quantity (that we may or may not be able to name with a number).

Students bring prior knowledge of properties of operations on numerical expressions from 5.OA. This prior knowledge is extended to algebraic expressions as students write algebraic expressions which describe the perimeter of picture frames. A conceptual challenge students may encounter is understanding that algebraic expressions might look different if a different "recipe" was used to create them, but these different-looking expressions can still describe the same situation and have the same value.

The concept is developed through work with algebra tiles, which allow students to make a connection between concrete numeric representations and abstract algebraic representations.

This work helps students deepen their understanding of equivalence because they will see that equivalent expressions may look different, but they represent the same value (in this case, equivalent expressions represent the same perimeter of a picture frame.)

Students engage in Mathematical Practice 2 (Students** **reason abstractly and quantitatively) as they represent the perimeter of the picture frame symbolically and understand that different variable expressions represent the same value for the perimeter. Representing the frame with algebra tiles helps students make a transition from a concrete representation in which all lengths are known to an abstract representation in which some lengths are unknown.

**Key vocabulary:**

- expression
- equivalent
- value

**Special materials needed:**