# 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

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.

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:

For the set of 3 fractions:

Identify 2 fractions that are equivalent. Explain your reasoning.

We visited poster , which shows , , and .

## Practice Problem

## Problem 1

Explain why the fractions