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 Lesson Plan: Equivalent Fractions

 

Lesson Objectives

  • Students will be able to explain the concept of equivalent fractions.
  • Students will be able to recognize and generate simple equivalent fractions.
  • Students will be able to model equivalent fractions using visual representations.

Common Core Standards

  • 3.NF.A.3.A - Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
  • 3.NF.A.3.B - Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent.

Prerequisite Skills

  • Understanding fractions and terminology
  • Ability to model fractions visually

Key Vocabulary

Multimedia Resources

 

 

Warm Up Activities

Choose from one or more of these activities.

Activity 1: Brief Review of Fraction Models

Introduce visual models for fractions and a brief introduction to equivalent fractions using this resource:

 https://www.media4math.com/library/43531/asset-preview

Activity 2: Fraction Sort Challenge

Objective: Help students recognize equivalent fractions using visual models.

Materials: Fraction strips or digital fraction tiles.

Instructions:

  1. Provide each student (or small groups) with a set of fraction strips or tiles.
  2. Call out a fraction, such as \( \frac{1}{2} \), and ask students to find all the equivalent fractions in their set, such as \( \frac{2}{4} \), \( \frac{3}{6} \), and \( \frac{4}{8} \).
  3. Have students explain how they know the fractions are equivalent.
  4. Optional: Use an interactive fraction tool online to visualize and confirm answers.

 

Fractions

 

Activity 3: Equivalent Fractions Number Line Race

Objective: Reinforce understanding of equivalent fractions by locating them on a number line.

Materials: Large number line on the board or individual number lines for students.

Instructions:

  1. Draw a number line from 0 to 1 on the board with fractions like \( \frac{1}{2} \), \( \frac{1}{4} \), and \( \frac{3}{4} \) marked.
  2. Call out a fraction, such as \( \frac{3}{6} \), and ask students to find and mark an equivalent fraction already on the number line.
  3. Have a discussion: Why is \( \frac{3}{6} \) the same as \( \frac{1}{2} \)?
  4. Repeat with different fractions and challenge students to explain their reasoning.

\[ \frac{3}{6} = \frac{1}{2} \]

 

Fractions

 

Activity 4: Fishing for Fractions

This interactive game has students finding fish with equivalent fractions. Use this game for students who are already familiar with equivalent fractions.

https://www.media4math.com/library/4845/asset-preview

 

 

 

Teach 

Define Equivalent Fractions

Use this slideshow to review fraction definitions. This also includes a definition for the term equivalent fraction:

https://www.media4math.com/library/slideshow/fraction-definitions

Follow up with this video definition of an equivalent fraction:

https://www.media4math.com/library/74765/asset-preview

Explain that equivalent fractions are different ways of representing the same value or amount. They may have different numerators and denominators, but they represent the same portion of a whole.

Use this slideshow to explain equivalent fractions in more detail:

 https://www.media4math.com/library/slideshow/equivalent-fractions

 

Identifying Equivalent Fractions

Use this resource to demonstrate how to tell if two fractions are equivalent:

https://www.media4math.com/library/43530/asset-preview

Use this resource to demonstrate equivalent fractions on a number line:

 https://www.media4math.com/library/43532/asset-preview

Procedures for Generating Equivalents

Introduce the concept of multiplying or dividing the numerator and denominator by the same non-zero number to generate equivalent fractions, using examples from Media4Math and Education.com. Provide examples and have students practice generating equivalent fractions using this method.

Use this slideshow to show examples of generating equivalent fractions:

 https://www.media4math.com/library/slideshow/examples-generating-equivalent-fractions

Example 1: Using Fraction Bars to Find Equivalent Fractions

Problem: Use fraction bars to find fractions equivalent to \( \frac{1}{3} \).

Solution:

  • Start with a fraction bar divided into 3 equal parts. Shade 1 part to represent \( \frac{1}{3} \).
  • Now, divide the same bar into 6 equal parts. Shade 2 parts—this still represents the same portion, so \( \frac{2}{6} \) is equivalent to \( \frac{1}{3} \).
  • Next, divide the bar into 9 equal parts. Shade 3 parts—this also covers the same section, so \( \frac{3}{9} \) is equivalent to \( \frac{1}{3} \).

\[ \frac{1}{3} = \frac{2}{6} = \frac{3}{9} \]

 

Fractions

 

Example 2: Multiplying to Find Equivalent Fractions

Problem: Find two equivalent fractions for \( \frac{4}{5} \) by multiplying the numerator and denominator by the same number.

Solution:

  • Multiply by 2: \[ \frac{4 • 2}{5 • 2} \ = \frac{8}{10} \]
  • Multiply by 3: \[ \frac{4 • 3}{5 • 3} \ = \frac{12}{15} \]

So, two equivalent fractions for \( \frac{4}{5} \) are:

\[ \frac{8}{10}, \quad \frac{12}{15} \]

Example 3: Simplifying to Find an Equivalent Fraction

Problem: Simplify \( \frac{18}{24} \) to its simplest form.

Solution:

  • Find the greatest common factor (GCF) of 18 and 24.
  • The GCF of 18 and 24 is 6.
  • Divide both numerator and denominator by 6: \[ \frac{18 ÷ 6}{24 ÷ 6} \ = \frac{3}{4} \]

So, the simplest form of \( \frac{18}{24} \) is:

\[ \frac{3}{4} \]

Example 4: Real-World Example – Measuring Cups

Problem: You have a measuring cup that only has markings for \( \frac{1}{4} \) cup increments. You need to measure \( \frac{2}{8} \) cup of flour. Can you use your measuring cup?

Solution:

  • To compare the fractions, simplify \( \frac{2}{8} \): \[ \frac{1•2}{4•2} = \frac{1}{4} \]
  • Since \( \frac{2}{8} \) simplifies to \( \frac{1}{4} \), you can use the \( \frac{1}{4} \) cup measurement.

Thus, \( \frac{2}{8} \) and \( \frac{1}{4} \) are equivalent.

\[ \frac{2}{8} = \frac{1}{4} \]

Example 5: Real-World Example – Fuel Efficiency

Problem: A car's fuel efficiency is listed as \( \frac{24}{32} \) miles per gallon. A different manual lists it as a simpler fraction. What is the equivalent fraction in simplest form?

Solution:

  • Find the greatest common factor (GCF) of 24 and 32.
  • The GCF of 24 and 32 is 8.
  • Divide both the numerator and denominator by 8: \[ \frac{24 ÷ 8}{32 ÷ 8} \ = \frac{3}{4} \]

So, the simplified and equivalent fraction for \( \frac{24}{32} \) is:

\[ \frac{3}{4} \]

 

 

Review 

Introduce this math game to review equivalent fractions:

https://www.media4math.com/library/4845/asset-preview

Review equivalent fractions with this worksheet:

https://www.media4math.com/library/37046/asset-preview

Example 1: Identifying Equivalent Fractions

Problem: Which of the following fractions is equivalent to \( \frac{3}{5} \)?

A) \( \frac{6}{10} \)    B) \( \frac{9}{15} \)    C) \( \frac{12}{20} \)    D) All of the above

Solution:

  • Multiply the numerator and denominator of \( \frac{3}{5} \) by 2: \[ \frac{3 • 2}{5 • 2} \ = \frac{6}{10} \]
  • Multiply by 3: \[ \frac{3 • 3}{5 • 3} \ = \frac{9}{15} \]
  • Multiply by 4: \[ \frac{3 • 4}{5 • 4} \ = \frac{12}{20} \]

Since all three fractions match the given choices, the correct answer is:

D) All of the above

Review Example 2: Simplifying a Fraction Using GCF

Problem: Simplify \( \frac{36}{48} \) to its lowest terms.

Solution:

  • Find the greatest common factor (GCF) of 36 and 48.
  • The factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  • The factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
  • The GCF of 36 and 48 is 12.
  • Divide both the numerator and denominator by 12: \[ \frac{36 ÷ 12}{48 ÷ 12} \ = \frac{3}{4} \]

So, the simplest form of \( \frac{36}{48} \) is:

\[ \frac{3}{4} \]

Example 3: Real-World Example – Painting a Wall

Problem: James is painting a wall and has completed \( \frac{6}{9} \) of the job. His friend tells him that he has finished an equivalent fraction of the wall in thirds. How much of the wall has his friend completed?

Solution:

  • Find the greatest common factor (GCF) of 6 and 9.
  • The GCF of 6 and 9 is 3.
  • Divide both the numerator and denominator by 3: \[ \frac{6 ÷ 3}{9 ÷ 3} \ = \frac{2}{3} \]

So, James's friend has completed:

\[ \frac{2}{3} \]

of the painting job.

Multimedia Resources

 

 

Quiz

Distribute a 10-question quiz (see below) for students to complete independently. This will assess their understanding of recognizing and generating equivalent fractions. 

  1. Which fraction is equivalent to 3/6? 
    a) 1/2
    b) 2/3
    c) 1/3
    d) 2/4
  2. Generate an equivalent fraction for 5/10. 
  3. Are 4/8 and 3/6 equivalent fractions? Explain your reasoning using a visual model. 
  4. Write two equivalent fractions for 1/4.
  5. Which fraction is not equivalent to 2/3? 
    a) 4/6
    b) 6/9
    c) 8/12
    d) 5/7
  6. Generate an equivalent fraction for 7/14 by multiplying the numerator and denominator by the same number. 
  7. Represent the equivalent fractions 3/6 and 1/2 using visual models.
  8. Explain why 6/12 and 1/2 are equivalent fractions.
  9. Which pair of fractions is not equivalent? 
    a) 2/4 and 1/2
    b) 3/9 and 1/3
    c) 5/10 and 1/2
    d) 4/8 and 2/4
    e) All fraction pairs are equivalent.
  10. Generate an equivalent fraction for 3/9 by dividing the numerator and denominator by the same number. 

Answer Key

  1. a) 1/2
  2. Accept any fraction that simplifies to 1/2.
  3. Yes, they are equivalent fractions because 4/8 and 3/6 represent the same portion of a whole. 
  4. Accept any pair of fractions that simplify to 1/4.
  5. c and d.
  6. Accept any fraction that simplifies to 1/2.
  7. Check student's work.
  8. Both fractions in simplest form are 1/2.
  9. e.
  10. Accept any fraction that simplifies to 1/3.