# Equivalent Fractions

## Overview

Generate simple equivalent fractions by using visual fraction models and the number line.

This lesson is adapted from a lesson created by Engage NY: https://www.engageny.org/resource/grade-3-mathematics-module-5-topic-e-lesson-22/file/35446

The lesson image is Quarters by luca fruzza from the Noun Project.

# Introduction

Introduce Equivalent Fractions using the Number Rock Video: https://numberock.com/lessons/equivalent-fractions/

**Counting by Fractions Equal to Whole Numbers on the Number Line **

Materials: (S) Personal white board

*Note: This activity reviews the concept of naming equivalent fractions on the number line.*

T: (Project a number line partitioned into 12 thirds.) Count by thirds. (Write fractions as students count.)

Ask students to write the fractions equal to whole numbers in order from least to greatest.

**Practice**

Mr. Ramos wants to put a wire on the wall. He puts 9 nails equally spaced along the wire. Draw a number line representing the wire. Label it from 0 at the first nail of the wire to 1 at the last nail. Mark each fraction where Mr. Ramos puts each nail.

- Build a number bond with unit fractions to 1 whole.
- Write the fraction of the nail that is equivalent to \(\frac{1}{2}\) of the wire.

Let’s look at a model. These 3 wholes are the same. Name the shaded fraction as I point to the model.

Are these fractions equivalent? Work with your partner to use the number line to prove your answer. Be ready to share your thinking.

# We Do

Write the missing parts of the fractions:

Why does it take 2 copies of \(\frac{1}{8}\) to show the same amount as 1 copy of \(\frac{1}{4}\) ? Explain your answer in words and pictures.

How many sixths does it take to make the same amount as \(\frac{1}{3}\) ? Explain your answer in words and pictures.

Why does it take 10 copies of 1 sixth to make the same amount as 5 copies of 1 third? Explain your answer in words and pictures.