# Lesson 10

The Distributive Property, Part 2

### Lesson Narrative

The purpose of this lesson is to extend the work with the distributive property in the previous lesson to situations where one of the quantities is represented by a variable, as in $$2(x+3) = 2x + 2\boldcdot3$$. Students use the same rectangle diagrams as before to represent these situations, reinforcing the idea that the work they do with expressions is simply an extension of the work they previously did with numbers. They see that the distributive property can arise out of writing areas of rectangles in two different ways, which emphasizes the idea of equivalent expressions as being two different ways of writing the same quantity.

### Learning Goals

Teacher Facing

• Generate algebraic expressions that represent the area of a rectangle with an unknown length.
• Justify (orally and using other representations) that algebraic expressions that are related by the distributive property are equivalent.

### Student Facing

Let's use rectangles to understand the distributive property with variables.

### Student Facing

• I can use a diagram of a split rectangle to write different expressions with variables representing its area.