Lesson 12

Fractional Lengths

Lesson Narrative

This is the first of four lessons in which students use multiplication and division of fractions to solve geometric problems. In this lesson, they encounter problems involving fractional lengths. They use their understanding of the two interpretations of division—“how many groups?” and “how much in each group?”—to solve problems that involve multiplicative comparison (MP7).

In these geometry-themed lessons, students work with a wider range of fractions and mixed numbers, which gives them opportunities to choose their methods and tools for problem solving.

Learning Goals

Teacher Facing

  • Apply dividing by fractions to solve a problem about comparing lengths or measuring with non-standard units, and explain (orally and in writing) the solution method.
  • Interpret a question (in written language) about multiplicative comparison, e.g., “How many times as long?” and write a division equation to represent it.

Student Facing

Let’s solve problems about fractional lengths.

Required Preparation

You will need the Info Gap: How Many Would It Take? blackline master for this lesson. Make 1 copy for every 4 students, and cut them up ahead of time.

Consider preparing the objects mentioned in the Info Gap: How Many Would It Take? activity for students to verify their answers. These objects are: \(\frac34\)-inch square stickers, \(1\frac14\)-inch binder clips, and \(1\frac34\)-inch paper clips.

If the optional Comparing Paper Rolls activity is chosen, consider preparing the paper towel and toilet paper rolls as displayed in the image. 

Learning Targets

Student Facing

  • I can use division and multiplication to solve problems involving fractional lengths.

CCSS Standards

Building On