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
- Equivalent fractions: Fractions that represent the same amount or part of a whole.
- Multimedia Resource: https://www.media4math.com/library/42915/asset-preview
- Multimedia Resource: https://www.media4math.com/library/74765/asset-preview
- Numerator: The top number in a fraction, representing the number of parts.
- Multimedia Resource: https://www.media4math.com/library/42906/asset-preview
- Multimedia Resource: https://www.media4math.com/library/74783/asset-preview
- Denominator: The bottom number in a fraction, representing the total number of equal parts in the whole.
- Multimedia Resource: https://www.media4math.com/library/42907/asset-preview
- Multimedia Resource: https://www.media4math.com/library/74764/asset-preview
Multimedia Resources
- Math Definitions Collection: Fractions https://www.media4math.com/Definitions--Fractions
- Math Video Definitions Collection: Fractions https://www.media4math.com/MathVideoCollection--FractionsVocabulary
- Slideshow: Fraction Definitions https://www.media4math.com/library/slideshow/fraction-definitions
- Generating Equivalent Fractions Slide Show https://media4math.com/library/slideshow/generating-equivalent-fractions
- Examples of Generating Equivalent Fractions https://www.media4math.com/library/slideshow/examples-generating-equivalent-fractions
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.

- Multimedia Slideshow: Show the Fraction Definitions Slideshow (https://www.media4math.com/library/slideshow/fraction-definitions) and discuss how visual models represent equivalent 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.

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.

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.

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 \( \frac{2}{4} \).
![]() | ![]() |
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.

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.

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.
- Define equivalent fractions.
- Write an equivalent fraction for \( \frac{1}{2} \).
- Are \( \frac{3}{4} \) and \( \frac{6}{8} \) equivalent? Show your work.
- Locate \( \frac{2}{6} \) on a number line and mark its equivalent fraction.
- Explain why \( \frac{4}{8} \) and \( \frac{1}{2} \) are equivalent.
- Shade \( \frac{3}{6} \) of a rectangle. Is it equivalent to \( \frac{1}{2} \)? Why?
- Create an equivalent fraction for \( \frac{2}{3} \).
- Use a pizza example to show \( \frac{3}{6} \) equals \( \frac{1}{2} \).
- Identify the numerator and denominator of \( \frac{3}{4} \).
- Write two fractions equivalent to \( \frac{5}{10} \).
Answer Key
- Fractions representing the same value.
- Examples: \( \frac{2}{4}, \frac{4}{8} \).
- Yes; multiply numerator and denominator of \( \frac{3}{4} \) by 2 to get \( \frac{6}{8} \).
- Equivalent fraction: \( \frac{1}{3} \).
- Both represent half a whole.
- Yes, the shaded area matches. \( \frac{3}{6} \) simplifies to \( \frac{1}{2} \).
- Examples: \( \frac{4}{6}, \frac{6}{9} \).
- Draw two pizzas: one with 2 slices, the other with 4 slices. Shade 1 and 2 slices respectively to show equivalence.
- Numerator: 3, Denominator: 4.
- Examples: \( \frac{1}{2}, \frac{10}{20} \).