In this lesson, students solve multiplicative comparison problems involving fractional lengths. Familiarity with questions such as “How many groups?” and “What fraction of a group?” helps students answer questions such as “How many objects of this length are in that length?” and “What fraction of this height is that height?”

In the main activity, an Information Gap routine, students practice identifying and asking for information that they need in order to solve geometric problems. The context involves the lengths and widths of objects. Two optional activities that follow allow students to practice interpreting other situations involving fractional lengths and using multiplication and division to find unknown values.

Now that students have at their disposal an algorithm for dividing fractions, they encounter a wider range of numbers than in earlier lessons. In working with fractions—including mixed numbers—with various denominators and larger values, they have opportunities to be strategic in how they approach problems based on the numbers involved.