This lesson is to extend the work students did with the distributive property in a previous lesson to situations in which one of the quantities is represented by a variable, as in . As they did before, students begin by using rectangular diagrams to represent these relationships, reinforcing the idea that the work they do with expressions with variables is an extension of the work they did with numbers.

Students see that the distributive property can arise when we represent the area of a rectangle in two different ways: as a product of its length and width or as the sum of the areas of two smaller rectangles that form the larger one. In making connections between expressions and quantities in a diagram, students engage in abstract and quantitative reasoning (MP2). This dual representation emphasizes the idea of equivalent expressions as two different ways of writing the same quantity.