Lesson 3 Multiply Unit Fractions

- Let’s solve equations.

Warm-up Estimation Exploration: How Much is Shaded?

What is the area of the shaded region?

Diagram. Square, length and width, 1. Rectangle of length about 1 half and width about 1 fourth shaded.

Record an estimate that is:

too low	about right	too high

Activity 1 Notice Patterns in Expressions

Square, length and width, 1. Partitioned into 2 rows of 4 of the same size rectangles. 1 rectangle shaded. — A

Square, length and width, 1. Partitioned into 3 rows of 4 of the same size rectangles. 1 rectangle shaded. — B

Diagram. Square, length and width, 1. Partitioned into 4 rows of 4 of the same size rectangles. 1 rectangle shaded. — C

Diagram. Square, length and width, 1. Partitioned into 5 rows of 4 of the same size rectangles. 1 rectangle shaded. — D

Choose one of the diagrams and write a multiplication expression to represent the shaded region. How much of the whole square is shaded? Explain or show your thinking.
If the pattern continues, draw what you think the next diagram will look like. Be prepared to explain your thinking.

Activity 2 Write a Multiplication Equation

Problem 1

Write a multiplication equation to represent the area of the shaded piece.
Explain how the diagram represents the equation $\frac{1}{5} \times \frac{1}{3} = \frac{1}{15}$ .

Problem 2

Find the value that makes each equation true. Use a diagram, if it is helpful.

$\frac{1}{2} \times \frac{1}{6} = ?$
$\frac{1}{4} \times \frac{1}{6} = ?$

Practice Problem

Problem 1

Write an equation representing the shaded part of the diagram.
Explain how the diagram shows each part of your equation.