# Lesson 9 Explain Equivalence

• Let’s talk about how we know whether two fractions are equivalent.

## Warm-up Number Talk: Familiar Numbers

Find the value of each expression mentally.

## Activity 1 Pointed Discussion

Andre, Lin, and Clare are representing on a number line.

• Andre said, “Oh, no! We’ll need to partition the line into 100 equal parts and count 70 parts just to mark one point!”

• Lin said, “What if we mark instead? We could partition the line into just 10 parts and count 7 parts.”

• Clare said, “What if we partition the line into 5 parts and mark ?

Do you agree with any of them? Explain or show your reasoning.

## Activity 2 How Do You Know?

Around the room you will find six posters, each showing either two or three fractions.

With your group, visit at least two posters: one with two fractions and one with three fractions.

1. For the set of 2 fractions:

• Explain or show how you know the fractions are equivalent.

• Write a new equivalent fraction on a sticky note and add it to the poster. Think of a fraction that hasn’t already been written by someone else.

• We visited poster , which shows and .

• New equivalent fraction:

2. For the set of 3 fractions:

• Identify 2 fractions that are equivalent. Explain your reasoning.

• We visited poster , which shows , , and .

## Problem 1

Explain why the fractions and are equivalent.