# Lesson 7

Divide to Multiply Unit Fractions

### Lesson Purpose

The purpose of this lesson is for students to solve problems involving multiplication of whole numbers by unit fractions and represent the problems with equations and diagrams.

### Lesson Narrative

In this lesson students interpret situations and solve problems that involve products of a whole number and a fraction. Students solve story problems in a way that makes sense to them and match stories with diagrams and expressions. They work with expressions and flexibly interpret a diagram to extend their understanding of the relationship between fractions and multiplication and division. For example, consider this image:

It shows $$4 \div 3$$ because there are 4 whole squares divided into 3 equal parts with 1 of those parts shaded. It also shows $$\frac{4}{3}$$ as there are 4 pieces shaded and each is $$\frac{1}{3}$$ of a unit rectangle. It shows the multiplication expression $$4 \times \frac{1}{3}$$ because there are 4 groups of $$\frac{1}{3}$$ shaded. It shows the multiplication expression $$\frac{1}{3} \times 4$$ since there is a total of 4, and $$\frac{1}{3}$$ of that is shaded.

• Engagement
• MLR8

Activity 1: How Far Did They Run?

### Learning Goals

Teacher Facing

• Connect division to multiplication of a whole number by a unit fraction.

### Student Facing

• Let’s solve problems about multiplying whole numbers by unit fractions.

### Required Materials

Materials to Copy

• Match the Situation

### Required Preparation

Activity 2:

• Create a set of cards from the blackline master for each group of 2.

Building Towards

### Lesson Timeline

 Warm-up 10 min Activity 1 20 min Activity 2 15 min Lesson Synthesis 10 min Cool-down 5 min

### Teacher Reflection Questions

Which student responses did you anticipate from today’s lesson? Which student responses surprised you in today’s lesson?

### Suggested Centers

• Target Measurements (2–5), Stage 5: Fractions of Angles (Addressing)
• Compare (1–5), Stage 5: Fractions (Supporting)

### Print Formatted Materials

For access, consult one of our IM Certified Partners.