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Unit 3, Lesson 12

Represent Division of Unit Fractions by Whole Numbers

Grade 5

Warm-up

Estimation Exploration: How Much Is Shaded?

How much is shaded?

Diagram. 4 equal sized parts. About 1 fifth of 1 part shaded. Total length, 1.

Record an estimate that is:

too low	about right	too high

Are You Ready for More?

Activity 1

Diagrams, Equations, Situations

Priya and Mai use these diagrams to find the value of .

Priya’s diagram

Diagram. 12 equal parts. 1 part shaded. Total length, 1.

Mai’s diagram

Diagram. 3 equal parts. 1 of the 3 parts partitioned into 4 equal parts with 1 shaded. Total length, 1.

How are the diagrams alike?
How are they different?
Find the value that makes the equation true.
Han draws this diagram to represent . How does his diagram show ? Explain or show your reasoning.
Find the value that makes the equation true. Explain or show your reasoning.

Activity 2

Noah's Work

Find the value of . Explain or show your reasoning.
Noah is trying out Mai’s diagram for this problem. Here is his work.

, because I divided into 2 equal parts and of is shaded in.
1. What questions do you have for Noah?
2. Noah’s equation is incorrect. How can Noah revise his explanation?

Activity 3

Look for Patterns

Find the value that makes each equation true. Use a diagram if it is helpful.
What patterns do you notice?
How would you find the value of divided by any whole number? Explain or show your reasoning.