MathIsimple
Lesson 2-1

Equivalent Fractions Deep Dive

Master equivalent fractions using fraction walls and cross-multiplication verification. Learn to find equivalent fractions through scaling and visual models.

Learning Scenario: Fraction Wall Construction

Scenario: You're helping build a fraction wall for your classroom! A fraction wall shows different fractions that represent the same amount. For example, 1/2, 2/4, and 3/6 all represent the same portion of a whole.

Your task is to find all the equivalent fractions that can be built using the same-sized blocks. This will help you understand that different fractions can represent the same value!

What Are Equivalent Fractions?

Equivalent fractions are different fractions that represent the same value or amount. They look different but are equal.

Examples:

  • • 1/2 = 2/4 = 3/6 = 4/8
  • • 2/3 = 4/6 = 6/9 = 8/12
  • • 1/4 = 2/8 = 3/12 = 4/16
Fraction Wall Method

A fraction wall is a visual tool that shows equivalent fractions by stacking equal-sized blocks.

How to Build:

  • • Start with a whole block
  • • Divide into equal parts
  • • Stack to show equivalence
  • • Compare different fractions
Step-by-Step Learning
1

Understanding Fraction Walls

A fraction wall shows equivalent fractions by using blocks of the same size. Each row represents a different denominator.

Example: For 1/2, you can use 2 blocks of 1/2 each, or 4 blocks of 1/4 each, or 6 blocks of 1/6 each. All represent the same amount!

2

Cross-Multiplication Verification

To verify if two fractions are equivalent, multiply the numerator of the first by the denominator of the second, and vice versa.

Example: Is 2/3 = 4/6? Check: 2 × 6 = 12 and 3 × 4 = 12. Since both equal 12, they are equivalent!

3

Scaling Up and Down

To find equivalent fractions, multiply or divide both the numerator and denominator by the same number.

Example: 1/2 = ?/6. Since 2 × 3 = 6, multiply 1 × 3 = 3. So 1/2 = 3/6.

Interactive Activities

Activity 1: Fraction Wall Builder

Build a fraction wall showing equivalent fractions for 1/2:

  • • Use blocks to represent 1/2
  • • Find fractions equal to 1/2
  • • Try: 2/4, 3/6, 4/8, 5/10
  • • Verify with cross-multiplication

Activity 2: Equivalent Fraction Finder

Find equivalent fractions for 2/3:

  • • What is 2/3 equal to in sixths?
  • • What is 2/3 equal to in ninths?
  • • What is 2/3 equal to in twelfths?
  • • Check your answers!
Practice Problems

Problem Set 1: Basic Equivalence

1. Find 3 fractions equivalent to 1/4

2. Find 3 fractions equivalent to 3/5

3. Find 3 fractions equivalent to 2/7

Problem Set 2: Verification

4. Is 3/4 = 6/8? Verify your answer.

5. Is 2/5 = 4/10? Verify your answer.

6. Is 1/3 = 3/9? Verify your answer.

Common Mistakes to Avoid

❌ Adding to numerator and denominator

Wrong: 1/2 + 1/1 = 2/3 (This is NOT equivalent!)

Correct: 1/2 = 2/4 (Multiply both by 2)

❌ Only changing one number

Wrong: 1/2 = 2/2 (This changes the value!)

Correct: 1/2 = 2/4 (Change both numerator and denominator by the same factor)

Key Takeaways

Equivalent fractions represent the same value but look different

Use fraction walls to visualize equivalent fractions

Cross-multiplication is a reliable way to verify equivalence

Always multiply or divide both numerator and denominator by the same number