Lesson Plan: Understanding Equivalent Fractions


Lesson Summary

In this 50-minute lesson, students will explore the concept of equivalent fractions using visual models, interactive activities, and multimedia resources. Students will learn to recognize and generate equivalent fractions and explain their equivalence using fraction bars, circles, and number lines. The lesson includes a warm-up, detailed instruction, review, and a 10-question quiz with an answer key.

Lesson Objectives

  • Recognize and generate equivalent fractions.
  • Explain why fractions are equivalent using visual models.

Common Core Standards

  • CCSS.Math.Content.4.NF.1: Explain why a fraction \( \frac{a}{b} \) is equivalent to a fraction \( \frac{n \times a}{n \times b} \) 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.

Prerequisite Skills

  • Basic understanding of fractions.
  • Multiplication of whole numbers.

Key Vocabulary

Multimedia Resources


Warm Up Activities

Choose from one or more of these activities:

  • Calculator Activity: Write three fractions on the board: \( \frac{1}{2}, \frac{2}{4}, \frac{3}{6} \). Provide calculators to each student or group. Ask students to divide the numerator by the denominator for each fraction and observe the results. Discuss how the decimal representation confirms equivalence. The Desmos scientific calculator provides access to a fraction calculator.

 

Fractions

 

 

Fractions

 

  • Hands-on Activity: Use fraction bars or circles to find equivalent fractions like \( \frac{1}{2} \) and \( \frac{2}{4} \). Encourage students to record and explain their findings.

 

Fractions

 


Teach

Introduction: Use fraction bars and circles to demonstrate that fractions are equivalent if they represent the same portion of a whole, even if the numerator and denominator are different.

  • Equivalent Fractions on a Number Line: Draw a number line from 0 to 1. Mark \( \frac{1}{2} \) and subdivide the segment into quarters to show \( \frac{2}{4} \). Highlight how these points align.
  • Area Models: Draw a rectangle divided into two equal parts. Shade one part to represent \( \frac{1}{2} \). Redraw the same rectangle divided into four parts and shade two parts to show \( \frac{2}{4} \).

Use the following slide show to review equivalent fractions:

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

Example 1: Using Fraction Bars

Place a fraction bar for \( \frac{1}{2} \) next to a fraction bar for \( \frac{2}{4} \). Discuss how the lengths are the same, demonstrating equivalence.

 

Fractions

 

Example 2: On a Number Line

Mark \( \frac{2}{3} \) on a number line. Subdivide the same section into six equal parts and mark \( \frac{4}{6} \). Highlight how the two fractions align perfectly, showing they are equivalent.

 

Fractions

 

Example 3: Real-world Application: Sharing Pizzas

Draw two pizzas, one cut into 2 slices and the other into 4 slices. Shade 1 slice in the first pizza and 2 slices in the second. Ask students if the amount eaten is the same, guiding them to see how \( \frac{1}{2} \) equals \( \frac{2}{4} \).

 

Equivalent FractionsEquivalent Fractions

 

Example 4: Generating Equivalent Fractions

Generate fractions equivalent to \( \frac{1}{2} \) and \( \frac{1}{3} \). 

Multiply the numerator and denominator by the same factor:

 

Fraction

Factor = 2

Factor = 3

Factor = 4

\( \frac{1}{2} \)

\( \frac{1•2}{2•2} \) = \( \frac{2}{4} \)

\( \frac{1•3}{2•3} \) = \( \frac{3}{6} \)

\( \frac{1•4}{2•4} \) = \( \frac{4}{8} \)

\( \frac{1}{3} \)

\( \frac{1•2}{3•2} \) = \( \frac{2}{6} \)

\( \frac{1•3}{3•3} \) = \( \frac{3}{9} \)

\( \frac{1•4}{3•4} \) = \( \frac{4}{12} \)

 


Review

Summarize the key points and reinforce how equivalent fractions are represented using various models. Use real-world examples like pizza slices to illustrate equivalence.

Example 1: Using Area Models

  • Shade \( \frac{3}{6} \) of a rectangle. Divide into two equal parts to show \( \frac{1}{2} \). Ask students to explain why the shaded area remains unchanged.

 

Fractions

 

Example 2: Real-world Example

  • A cup is \( \frac{3}{4} \) filled with milk. This is equivalent to six \( \frac{1}{8} \)-cup measurements of milk. Have students determine a method to confirm this equivalence.

 

Fractions

 

Additional Review

To review equivalent fractions have students play these interactive games:

Pizza Party (Level 1). In this game students can input equivalent fractions: https://www.media4math.com/library/37600/asset-preview

Pizza Party (Level 2). In this game students must input fractions in simplest form: https://www.media4math.com/library/37601/asset-preview

 


Quiz

Directions: Answer the following questions.

  1. Define equivalent fractions.
  2. Write an equivalent fraction for \( \frac{1}{2} \).
  3. Are \( \frac{3}{4} \) and \( \frac{6}{8} \) equivalent? Show your work.
  4. Locate \( \frac{2}{6} \) on a number line and mark its equivalent fraction.
  5. Explain why \( \frac{4}{8} \) and \( \frac{1}{2} \) are equivalent.
  6. Shade \( \frac{3}{6} \) of a rectangle. Is it equivalent to \( \frac{1}{2} \)? Why?
  7. Create an equivalent fraction for \( \frac{2}{3} \).
  8. Use a pizza example to show \( \frac{3}{6} \) equals \( \frac{1}{2} \).
  9. Identify the numerator and denominator of \( \frac{3}{4} \).
  10. Write two fractions equivalent to \( \frac{5}{10} \).

Answer Key

  1. Fractions representing the same value.
  2. Examples: \( \frac{2}{4}, \frac{4}{8} \).
  3. Yes; multiply numerator and denominator of \( \frac{3}{4} \) by 2 to get \( \frac{6}{8} \).
  4. Equivalent fraction: \( \frac{1}{3} \).
  5. Both represent half a whole.
  6. Yes, the shaded area matches. \( \frac{3}{6} \) simplifies to \( \frac{1}{2} \).
  7. Examples: \( \frac{4}{6}, \frac{6}{9} \).
  8. Draw two pizzas: one with 2 slices, the other with 4 slices. Shade 1 and 2 slices respectively to show equivalence.
  9. Numerator: 3, Denominator: 4.
  10. Examples: \( \frac{1}{2}, \frac{10}{20} \).