Previously, students examined patterns in the multiplication table and used them to find products within 100 and to notice properties of multiplication—the commutative property, in particular. In this lesson, students analyze strategies for finding the area of rectangles to explore the distributive and associative properties. Students study gridded rectangles that have been decomposed into smaller parts and expressions that represent how the decomposition could help us find the area. Students see how the strategies, along with the diagrams and the expressions that represent them—can help us find the product of two numbers.

As students make sense of expressions and interpret them in terms of parts of area diagrams (MP1), they practice reasoning quantitatively and abstractly (MP2).