Lesson 7
Divide to Multiply Unit Fractions
Lesson Purpose
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.
CCSS Standards
Lesson Timeline
Warmup  10 min 
Activity 1  20 min 
Activity 2  15 min 
Lesson Synthesis  10 min 
Cooldown  5 min 
Teacher Reflection Questions
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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Additional Resources
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