Comparing Fractions Fun

Grade Level

3rd Grade

Duration

45 minutes

Standards

Common Core State Standards – Mathematics

• CCSS.MATH.CONTENT.3.NF.A.3b: Understand two fractions as equivalent if they are the same size or the same point on a number line.
• CCSS.MATH.CONTENT.3.NF.A.3c: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
• CCSS.MATH.CONTENT.3.NF.A.3d: Compare two fractions with the same numerator or the same denominator by reasoning about their size.

Learning Objectives

By the end of the lesson, students will be able to:

• Understand how to compare fractions with either the same numerator or denominator based on size reasoning.
• Use visual fraction models and manipulatives to support their understanding of comparing fractions.
• Accurately determine which fraction is greater or if two fractions are equivalent.
• Verbally explain and write comparisons using inequality symbols (<, >, =).

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Materials Needed

• Fraction strips or fraction circles (1 set per student or pair)
• Whiteboards and dry erase markers (one per student)
• Pre-made fraction comparison cards (fractions sharing the same numerator or denominator)
• Comparison symbols cut-outs (<, >, =)
• Exit ticket worksheet (3 questions comparing fractions)
• Chart paper or projector for modeling examples
• Timer or clock

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Lesson Plan Outline

1. Introduction & Review (5 minutes)

• Engage Students: Begin by asking students if they’ve ever shared a pizza or pie and noticed how slices might be bigger or smaller. Use this relatable example to prime their thinking about fractions.
• Quickly review fractions as parts of a whole using a visual aid (fraction strips or circles).
• Introduce today’s goal: Comparing fractions with the same numerator or the same denominator.

2. Direct Instruction & Modeling (10 minutes)

• Display two fractions with the same denominator (e.g., 3/8 and 5/8). Use fraction strips to show these visually.
• Pose the question: Which is larger? Why? Highlight that when denominators are the same, the fraction with the larger numerator is bigger.
• Write it symbolically: 3/8 < 5/8. Explain the meaning of the inequality symbol.
• Repeat with two fractions with the same numerator (e.g., 3/5 and 3/9). Use fraction strips again.
• Ask: Which fraction is larger? Lead students to observe that when numerators are the same, the smaller denominator means bigger pieces (so 3/5 > 3/9).
• Emphasize reasoning rather than rote memorization.

3. Hands-On Activity: Fraction Comparisons with Manipulatives (15 minutes)

• Setup: Students work in pairs or individually with fraction strips or circles.
• Distribute sets of fraction comparison cards (with pairs of fractions that share either the same numerator or denominator).
• Students will:
  • Use fraction strips to represent the two fractions on the card.
  • Decide which fraction is larger or if they are equal.
  • Place the appropriate inequality symbol cut-out between two cards.
• Teacher circulates, asks probing questions to encourage reasoning:
  • "How do your fraction strips look different?"
  • "Why do you think this fraction is bigger?"
• After 10 minutes, randomly select 2-3 pairs to share their reasoning with the class for peer learning.

4. Guided Practice on Whiteboards (8 minutes)

• Display 3 fraction comparison problems on the board.
• Students will:
  • Draw or write the fractions.
  • Use reasoning to compare fractions (same numerator or denominator).
  • Write the correct inequality symbol.
• Teacher provides immediate feedback and reinforces correct reasoning.

5. Exit Ticket (7 minutes)

• Hand out a short exit ticket with 3 fraction comparison questions requiring students to:
  • Compare fractions.
  • Circle the larger fraction or write the correct inequality symbol between pairs.
• Exit ticket includes:
  1. Fractions with the same denominator (e.g., 4/7 and 6/7)
  2. Fractions with the same numerator (e.g., 5/8 and 5/12)
  3. An opportunity to explain which fraction is larger in one sentence.
• Collect exit tickets for informal assessment of understanding.

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Assessment & Differentiation

• Formative: Observe students during hands-on activity and guided practice; listen for reasoning and check for correct usage of symbols
• Summative: Exit ticket answers will show individual student mastery
• Differentiation:
  • For struggling students – provide fraction strips with fewer pieces and simplified fractions (e.g., halves, thirds, fourths)
  • For advanced students – incorporate fractions that require reasoning with both numerator and denominator differences (e.g., 3/4 vs. 2/3), and ask for justification

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Closing Reflection (Optional)

Ask students one last question: "If you had to explain to a friend how to tell which fraction is bigger when numerators or denominators are the same, what would you say?" This can be a think-pair-share or a quick verbal response.

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Teacher’s Tip: Using physical manipulatives like fraction strips transforms abstract fraction concepts into tangible comparisons, making learning memorable and fun for young students!