Comparing Fractions

Curriculum Alignment

Grade Level: 3rd Grade
Standards: Common Core State Standards (CCSS) - Mathematics
Domain: Number and Operations - Fractions
Standard: CCSS.MATH.CONTENT.3.NF.A.3
Objective: Use models to recognize, compare, and generate simple equivalent fractions and determine which fraction is greater or less than another.

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Lesson Objectives

By the end of this 30-minute lesson, students will be able to:

1. Use visual fraction models (such as bars and circles) to compare two fractions.
2. Identify if two fractions are equivalent using fraction models.
3. Determine which fraction is greater or less than another fraction based on the model.

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Materials Needed

• Large visual fraction models (paper cut-outs, magnetic models, or laminated visuals)
• Whiteboard and markers
• Student fraction strips or fraction circle sets (one set per student)
• Mini whiteboards and dry erase markers for students
• Guided worksheet for practice
• A “Comparing Fractions” anchor chart

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Warm-Up (5 Minutes)

Activity Title: Quick Fractions Refresher

1. Start by asking students: “Who remembers what a fraction is? What does the top number mean? What about the bottom number?” Encourage brief responses.
2. Draw a simple fraction model on the board (e.g., a circle divided into 4 equal parts, with 2 shaded) and ask: “What fraction is shaded here?”
3. Guide students to say: “2 out of 4, or 2/4.”
4. Repeat with 1 or 2 other examples using different shapes (e.g., bar models) to refresh students' memory of fractions.

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Introduction to Comparing Fractions (5 Minutes)

Discuss and Demonstrate:

1. Show a bar model divided into 4 parts with 2 shaded (representing 2/4), and another bar model divided into 6 parts with 3 shaded (representing 3/6). Ask students: “Which is bigger?”
2. Place the models side by side under a magnet board or visualizer, and then adjust them to the same width to show that 2/4 = 3/6. Explain that even though they look different, the size of the shaded part tells us they are equivalent.
3. Next, demonstrate two fractions that are not equivalent. For example, compare 2/3 and 3/4. Use different colors to shade each model, placing them side by side and visually demonstrating which represents a greater value. Emphasize the importance of comparing fraction sizes with the same whole.

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Hands-On Group Practice (10 Minutes)

Activity Title: Fraction Models Team Challenge

1. Setup: Split the 11 students into small groups of 2 or 3. Provide each group with fraction strips or fraction circle pieces.
2. Instructions: Give each group two fractions to compare (e.g., 1/2 vs. 1/4, 2/3 vs. 3/4). Students will physically build the fraction comparisons using the strips or circle pieces.
3. Once students have constructed their models, ask: “Which fraction is bigger? Why? Are they equal?” Groups will share their findings with the class.
4. Rotate through another round of two fractions to compare. Ensure diverse fractions are used (e.g., 3/6 vs. 1/3, 4/8 vs. 5/8).

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Individual Practice (5 Minutes)

Activity Title: Mini Whiteboard Fractions

1. Hand out a mini whiteboard and marker to each student. Give them fractions to compare (e.g., “Write which fraction is greater: 1/3 or 2/6.”).
2. Provide about 15–20 seconds for each problem. Then, ask everyone to hold up their whiteboards simultaneously, showing their answers.
3. For incorrect answers, choose another student to explain their thinking and demonstrate the correct answer using a fraction model at the front of the class.

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Wrap-Up and Exit Ticket (5 Minutes)

Closing Discussion: Ask the students:

• “When we compare fractions, why do we use models instead of just looking at the numbers?”
• “Can two fractions look different but be the same size? Why?”

Exit Ticket Activity:
Hand out a quick worksheet with 2 fraction comparison questions:

1. Compare 1/2 and 3/4 using a fraction model. Circle the larger fraction.
2. Are 2/4 and 4/8 equivalent? Draw a model to prove your answer.

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Differentiation and Extensions

• For Advanced Students: Challenge them to generate their own pairs of fractions for comparison and justify their reasoning without models.
• For Struggling Students: Pair them with a peer for additional support. Use simpler fractions (e.g., 1/2 vs. 1/4) and emphasize visual aids.
• Extension Activity: Introduce the idea of a common denominator to check their comparisons mathematically.

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Assessment

• Observe students’ participation during the hands-on group challenge.
• Review their mini whiteboard responses for understanding.
• Use exit tickets to evaluate individual comprehension.

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Teacher's Reflection

• Were the fraction models effective in helping students compare fractions?
• Were students actively engaged during the team practice?
• Did most students demonstrate understanding on their exit tickets?

Let’s make fraction comparisons a visual and interactive adventure!