Lesson 11 Generate Equivalent Fractions

- Let’s generate equivalent fractions.

Warm-up Number Talk: Something Times 8

Find the value of each expression mentally.

$2 \times 8$
$6 \times 8$
$10 \times 8$
$12 \times 8$

Activity 1 Show Equivalence

Problem 1

The diagram represents 1.

Diagram. Rectangle partitioned into 4 equal parts, 2 shaded.

What fraction does the shaded part of the diagram represent?
Jada says it represents $\frac{4}{8}$ . Tyler is not so sure.
Do you agree with Jada? If so, explain or show how you would convince Tyler that Jada is correct. If not, show your reasoning.

Problem 2

Each diagram represents 1.

Show that the shaded part of this diagram represents both $\frac{1}{3}$ and $\frac{2}{6}$ .
Show that the shaded part represents both $\frac{6}{8}$ and $\frac{3}{4}$ .
Show that the shaded part represents both $\frac{6}{6}$ and $\frac{2}{2}$ .

Activity 2 More Than One Name

Problem 1

Each diagram represents 1. Write two fractions to represent the shaded part of each diagram.

Problem 2

Here’s another diagram.

Diagram. 2 rectangles partitioned into 2 equal parts. Total for each, 1. 3 of 4 parts shaded.

What fraction does the shaded part of the diagram represent?
Write another fraction that it represents.

Practice Problem

Problem 1

Write as many fractions as you can that represent the shaded part of each diagram.