The purpose of this activity is for students to compare different methods to find the value of a product of mixed numbers. First, they solve problems in a way that makes sense to them. Then they compare an area diagram, which students have seen in earlier lessons, with a more abstract diagram like those students examined in the Warm-up. Then they compare both diagrams with another strategy that renames the mixed numbers as fractions, and then uses the method they generalized in previous lessons to find the product of any two fractions.

In a later unit, students learn how to add fractions with unlike denominators. The number choices in this activity allow students to find the sum of the partial products with reasoning and sense making. It is acceptable if students express a product as an expression with the sum of the partial products.

• Display both diagrams.