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

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