Teacher Guide: Comparing & Equivalent Fractions

🎯 Learning Objective 10-15 min lesson

Students will: Compare fractions with the same numerator or same denominator using reasoning and visual models. Identify equivalent fractions using number lines, area models, and explain WHY fractions are equivalent.

Important: Allowed denominators are 2, 3, 4, 5, 6, 8, 10, and 12. For comparing (MA.3.FR.2.1), include fractions greater than 1. For equivalent fractions (MA.3.FR.2.2), fractions are limited to ≤ 1.

Clarification: Students should identify and explain equivalent fractions using visual support, not generate them through multiplication/division procedures. Focus on understanding, not procedures.

📦 Materials Needed

Fraction strips or tiles
Number lines (0 to 2, marked in various denominators)
Fraction circles or rectangles for area models
Rulers (connect fractions to measurement)
Student worksheets

⚠️ Common Misconceptions to Address

Misconception #1: Larger Denominator = Larger Fraction

Students think 1/8 > 1/4 because 8 > 4. They don't understand that larger denominators mean SMALLER pieces.

How to Address:

Use fraction strips! Show: "If I cut a pizza into 8 pieces vs. 4 pieces, which piece is bigger?" The more cuts, the smaller each piece.

Misconception #2: Only Comparing Numerators

Students compare 3/4 and 3/8 by only looking at numerators: "They both have 3, so they're equal."

How to Address:

Emphasize: "Same number of pieces, but what SIZE are the pieces?" 3 big pieces (fourths) vs. 3 small pieces (eighths). Use visual models to show the difference.

Misconception #3: Equivalent Means "The Same Numbers"

Students think 1/2 and 2/4 can't be equal because they have different numbers.

How to Address:

Use area models and number lines. Show 1/2 of a rectangle and 2/4 of the same rectangle. "They cover the same amount!" Different names for the same amount of space.

📝 Lesson Steps

1

Compare Fractions with Same Denominator (3 min)

Show fraction strips: 2/6 and 5/6. Ask: "Which is more? How do you know?"

SAY THIS:

"When fractions have the same denominator, the pieces are the same size. So we just compare how many pieces: 5 pieces is more than 2 pieces. 5/6 > 2/6."

2

Compare Fractions with Same Numerator (3 min)

Show: 2/4 and 2/8. Ask: "Both have 2 pieces. Are they equal?"

SAY THIS:

"When fractions have the same numerator, we have the same NUMBER of pieces, but the SIZE is different. Fourths are bigger pieces than eighths. 2 big pieces is more than 2 small pieces. So 2/4 > 2/8."

Use fraction strips to physically show 2/4 is longer than 2/8.

3

Use Number Lines to Compare (3 min)

Draw number lines from 0 to 1. Plot 3/4 and 3/6 on separate number lines aligned together.

SAY THIS:

"The fraction that's farther to the right is greater. We can see 3/4 is farther right than 3/6, so 3/4 > 3/6. The number line helps us compare by position."

4

Introduce Equivalent Fractions (3 min)

Show 1/2 and 2/4 using area models (same-sized rectangles).

SAY THIS:

"Look—1/2 of this rectangle and 2/4 of this rectangle cover the SAME amount of space! They're called equivalent fractions. Different names, same amount."

Also show on a number line: 1/2 and 2/4 land at the same point.

5

Practice Identifying Equivalents (2 min)

Using fraction strips or number lines, have students find fractions equivalent to 1/2:

2/4 = 1/2 (show with strips)
3/6 = 1/2 (show on number line)
4/8 = 1/2 (verify with area model)

6

Independent Practice

Distribute worksheets. Remind students to use visual models (draw number lines, shade rectangles) to support their comparisons and find equivalents.

🧠 Key Strategies to Teach

Same Denominator Strategy

Same-sized pieces → just compare how many. More pieces = greater fraction.

Same Numerator Strategy

Same number of pieces → compare piece SIZE. Smaller denominator = bigger pieces = greater fraction.

Number Line Strategy

Plot both fractions. Farther right = greater. Same position = equivalent.

Area Model Strategy

Shade same-sized shapes. Same shaded area = equivalent fractions.

💻 IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Compare fractions with same denominator Compare fractions with same numerator Compare fractions using models Compare fractions on number lines Identify equivalent fractions Equivalent fractions on number lines

🏠 Differentiation

For struggling students: Focus on unit fractions first (1/2, 1/3, 1/4). Use physical fraction manipulatives before pictures. Limit to denominators 2, 3, 4, 6 initially.

For advanced students: Include fractions greater than 1 for comparisons. Challenge with ordering three or more fractions. Explore patterns in equivalent fractions.

For home: Send fraction strips home. Parents can use food (pizza, pie, chocolate bars) to show equivalent parts.