# Equivalent Fractions

Design Guide

Designers for Learning - Adult Learning Zone

Project Requirements

Part 1: Lesson Description

Lesson Title

Abstract

Learner Audience / Primary Users

Educational Use

Language

Material Type

Keywords

Time Required for Lesson

Targeted Skills

Learning Objectives

College & Career Readiness Standards (CCRS) Alignment

Prior Knowledge

Required Resources

Part 2: Lesson

Instructional Strategies and Activities

Warm-Up

Introduction

Presentation / Modeling / Demonstration

Guided Practice

Evaluation

Application

Key Terms and Concepts

Part 3: Supplementary Resources & References

Supplementary Resources

References

## Part 1: Lesson Description

### Equivalent Fractions

Comparing and ordering fractions with different denominators.

### Abstract

The following math lesson focuses on developing a deeper understanding of the value of fractions and allows the students to compare and order fractions while making decisions in a shopping experience. Learners will be better prepared to perform basic operations (+,-,x,/) once they have completed this module.

### Educational Use

• Curriculum / Instruction

English

### Material Type

• Instructional Material
• Interactive

### Keywords

• Designers for Learning
• Fractions

30 minutes

### Targeted Skills

Key skills covered in this lesson include:

• Comparing fractions of prices
• Comparing fractions of time

### Learning Objectives

By the end of this lesson, the learner should be able to:

• Learners will be able to order fractions from least to greatest with 80% or better success. (4.NF.2)
• Learners will be able to compare fractions by creating similar denominators or numerators and choosing which fraction is greater with 80% or better success. (4.NF.1)
• Learners will apply their understanding of fractions by solving problems deciding which purchase is a better deal with a success rate of 80% or better.

### College & Career Readiness Standards (CCRS) Alignment

• Subject: Mathematics
• Domain or Strand:
• Domain: Numbers and Operations
• Strand: Fractions
• Standard Description:
• Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (4.NF.1)
• Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or

### Prior Knowledge

Learners should know that a fraction represents part of a whole and they should be able to draw a representation of a fraction.

### Required Resources

• Pencil
• Paper
• Lesson Plan
• Guided Learning Printable Page
• Printable Quiz
• Computer if you choose interactive activity
• Internet connection

• Lesson Author: Lisa Ramsey

## Part 2: Lesson

### Instructional Strategies and Activities

#### Warm-Up

Time: 5 minutes

Learners will begin by reviewing fractions and shading fraction ‘pies’ to compare fractions of the same denomination.

#### Introduction

Time: 5 minutes

Compare ½ pies and ⅓ pies from the warm up examples. Not all fractions have the same denominator and this makes it harder to compare fractions. In order to compare fractions accurately, we need to match fractions with the same denominators. This process can be shown by making a couple of changes to how we split the fractions.

#### Presentation / Modeling / Demonstration

Time: 10 minutes

Create equivalent fractions by multiplying the slices.

For instance:

¼ can be multiplied by 3/3 to create 3/12.

This allows us to compare it to ⅙ by multiplying the fraction by 2/2 to create 2/12.

We have not changed the portion of the rectangle shaded, we have just divided it into the same number of segments to make it easier to compare. If we look at the two fractions, we now see that 3/12 is more than 2/12.

2/12 is ‘equivalent’ to ⅙ and 3/12 is ‘equivalent’ to ¼. Equivalent fractions are equal in value to the original fraction.

This means that ⅙ is less than ¼.

#### Guided Practice

Time: 10 minutes

Guided Practice Worksheet

Learners will complete the worksheet using similar examples as above by finding equivalent fractions and comparing fractions with the same denominator.

Checking Inventory

Before we do some shopping of our own, let’s check and make sure we have our inventory straight.

1.Name an equivalent fraction for 3/4.

Next – Choose a number that is a multiple of 4. We will choose 12.

What do you need to multiply 4 by to get the answer of 12? ____

Multiply the numerator by the same number. The numerator of ¾ is the number 3.

3 x ___ = ____

Now compare your shaded group here with ¾ above. They should be the same amount. They are equivalent.

2.Find an equivalent fraction for 1/6. Draw diagrams below if you need them.

3.Find an equivalent fraction for 1/3. Draw diagrams below if you need them.

4.Find an equivalent fraction for 1/5. Draw diagrams below if you need them.

5.Compare the fractions 1/3 and 1/5. Change them both to equivalent fractions with the same denominator. Which fraction is a larger amount? Draw diagrams below if you need them.

#### Evaluation

Time: 5 minutes

Learners will complete quiz with 80% or better success.

Equivalent Fraction Quiz

Name two equivalent fractions for the fractions given below.

1.2/3

2.1/6

3.4/5

4.3/7

5.1/4

Compare the fractions below by using the symbols (, or =).

6.1/4  ____  2/3

7.1/2  ____  3/6

8.2/5  ____ 1/10

9.1/3  ____ 3/12

10.1/8  ____ 1/4

#### Application

Time: 10 minutes

“Is It a Deal???”

Learners will complete the worksheet comparing sale items by the fraction of the discount. Learners will write “Deal” across problems that are a deal and draw a large ‘x’ over problems that are not a deal.

Is It a Deal???

Look at the objects below and compare sale prices. Write “Deal” across the fraction that is the largest discount. Write an ‘x’ over the fraction that is smaller.

1.Armchair deal

Store A – 1/4 off                   Store B – 1/3 off

2.Shoes Deal

Store A – 1/5 off                  Store B – 1/2 off

3.Oil Change Deal

Store A – 1/6 off                   Store B – 2/5 off

4.Pizza Deal

Store A – 3/8 off                   Store B – 2/5 off

5.Shirt Deal

Store A – 2/3 off                   Store B – 5/6 off

### Key Terms and Concepts

Equivalent fractions - fractions that have the same value but do not have the same numerator and denominator.

## Part 3: Supplementary Resources & References

### Supplementary Resources

Printable Worksheets from lesson - separate attachment

For further practice:

Khan Academy - Equivalent Fractions https://youtu.be/U2ovEuEUxXQ

Math is Fun - Equivalent Fractions https://www.mathsisfun.com/equivalent_fractions.html

### References

http://www.helpwithfractions.com/math-homework-helper/equivalent-fractions.