4.NF.2: Comparing Fractions

Visual Models for Comparing Fractions

1. Fraction Strips

Create or print fraction strips of the same length to visually compare different fractions. For example, place a 2/3 strip next to a 3/4 strip to see that 3/4 is larger than 2/3.

2. Number Lines

Place fractions on a number line to compare their values. Fractions closer to 1 are larger than fractions closer to 0.

3. Area Models

Draw circles or rectangles of the same size and divide them according to the fractions you're comparing. Shade the appropriate portions to visually see which fraction represents more or less of the whole.

Strategies for Comparing Fractions

1. Common Denominators

Convert fractions to equivalent fractions with the same denominator, then compare the numerators.

Example: To compare 2/3 and 3/5

• Find a common denominator: 15
• Convert 2/3 to 10/15 (multiply numerator and denominator by 5)
• Convert 3/5 to 9/15 (multiply numerator and denominator by 3)
• Compare 10/15 and 9/15: Since 10 > 9, we know 2/3 > 3/5

2. Common Numerators

Convert fractions to equivalent fractions with the same numerator, then compare the denominators (smaller denominator means larger fraction).

Example: To compare 2/5 and 2/7

• The numerators are already the same (2)
• Compare the denominators: 5 and 7
• Since 5 < 7, and the numerators are the same, 2/5 > 2/7

3. Benchmark Fractions

Compare fractions to benchmark fractions like 0, 1/2, and 1.

Example: To compare 3/8 and 4/7

• 3/8 is less than 1/2 (since 4/8 = 1/2 and 3 < 4)
• 4/7 is greater than 1/2 (since 3.5/7 = 1/2 and 4 > 3.5)
• Therefore, 3/8 < 4/7

Everyday Applications

1. Cooking and Recipes

Compare ingredient amounts in recipes. For example, "Does this recipe call for more flour (3/4 cup) or sugar (2/3 cup)?"

2. Sharing Food

Compare portions when sharing food. For example, "Would you rather have 2/5 of the large pizza or 1/2 of the medium pizza?"

3. Measuring and Building

Compare measurements when building or crafting. For example, "Is 5/8 inch wider or narrower than 3/4 inch?"

When Your Child Struggles

1. Use Visual Models

If your child is having trouble comparing fractions numerically, use visual models like fraction strips or area models to help them see the differences.

2. Focus on One Strategy at a Time

Don't try to teach all comparison strategies at once. Start with the common denominator method, then introduce other strategies as your child becomes more comfortable.

3. Practice with Simple Fractions

Begin with fractions that are easy to compare, like 1/2 and 1/4, before moving on to more challenging comparisons.

4. Use Real-Life Examples

Connect fraction comparisons to real-life situations that your child can relate to, like sharing food or measuring ingredients.

5. Review Equivalent Fractions

If your child struggles with finding common denominators, review equivalent fractions first, as this is a foundational skill for comparing fractions.

5-Minute Activities

Activity 1: Fraction War

Play a card game where each player draws two cards to create a fraction (first card is numerator, second is denominator). The player with the larger fraction wins the round. Use the comparison symbols to record each comparison.

Activity 2: Fraction Sort

Create cards with various fractions and have your child sort them from least to greatest. Start with 5-6 fractions and gradually increase the difficulty.

Activity 3: Benchmark Challenge

Call out a fraction and have your child quickly tell you if it's less than 1/2, equal to 1/2, or greater than 1/2. Then do the same with benchmarks of 0 and 1.

Activity 4: Symbol Practice

Write pairs of fractions and have your child place the correct symbol (<, >, or =) between them. Include some equivalent fractions to practice using the equal sign.

Mid-Year Expectations

By the middle of the school year, your child should be able to:

• Compare fractions with the same denominator
• Compare fractions with the same numerator
• Use visual models to compare fractions
• Correctly use the symbols <, >, and = when comparing fractions
• Compare fractions to benchmark fractions like 0, 1/2, and 1

End-of-Year Expectations

By the end of the school year, your child should be able to:

• Compare fractions with different numerators and denominators using various strategies
• Find common denominators to compare fractions
• Justify their comparisons using visual models or numerical reasoning
• Order three or more fractions from least to greatest or greatest to least
• Apply fraction comparison skills to solve real-world problems

Signs of Mastery

Your child has mastered this standard when they can:

• Consistently and accurately compare fractions with different numerators and denominators
• Choose appropriate strategies for different types of fraction comparisons
• Explain their reasoning when comparing fractions
• Use precise mathematical language and symbols when comparing fractions
• Apply fraction comparison skills to solve complex real-world problems
• Order multiple fractions from least to greatest or greatest to least

Questions to Check Understanding:

• "Which is greater, 2/3 or 3/5? How do you know?"
• "How can you use a common denominator to compare 3/4 and 5/6?"
• "Is 7/8 closer to 1/2 or 1? How do you know?"
• "Place these fractions in order from least to greatest: 2/3, 3/8, 5/6, 1/2."

Below Grade Level

For students who need additional support with basic fraction concepts and simple fraction comparisons.

📥 Download Practice Worksheet

At Grade Level

For students who need practice with grade-level fraction comparison concepts.

📥 Download Grade Level Worksheet

Above Grade Level

For students ready for more challenging fraction comparison concepts and applications.

📥 Download Challenge Worksheet