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.
• “How can you use Lin’s diagram to see the value of each part of Han’s diagram?”
• Record the partial products on the diagrams as selected students explain.
• Write an expression to show the sum of the partial products and invite a student to explain how they reasoned to add the fractions.
• If no students mention the distributive property, consider writing the product of as and relating the partial products in this equation to both diagrams.
• “How is Jada’s way the same and different from the other strategies?”
• “We have talked about three ways to multiply mixed numbers so that you can use a strategy that makes sense to you in the next activity.”

The purpose of this activity is for students to continue to make sense of strategies for multiplying 2 mixed numbers. The previous activity introduced a variety of strategies for students to consider applying. In this activity, they have the option of choosing any 3 of the 4 problems to solve, and then reflect on the different strategies.

• Invite selected students to share and explain the strategy they used and why they chose that strategy.
• “What was most challenging? Why?”