Mathematics · Class 5

Active learning ideas

Improper Fractions and Mixed Numbers

Active learning works well for improper fractions and mixed numbers because students often struggle with abstract symbols. When they handle physical or visual materials, like strips or circles, they see how the same quantity can look different but mean the same thing. Moving, matching and converting turns confusion into clarity through repeated practice and discussion.

• CBSE Learning Outcomes
• NCERT: F-1.4

• 25–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Peer Teaching
• 30 min · Pairs

Fraction Strip Matching: Equivalents Game

Provide fraction strips for halves, thirds, and fourths. Pairs create improper fractions over one whole, then convert to mixed numbers using strips to verify equivalence. Groups share one match with the class, explaining steps.

Differentiate between an improper fraction and a mixed number.

Facilitation Tip

During Fraction Strip Matching, ask pairs to explain why a strip of 7 fourths equals 1 3/4 before they glue the match.

What to look for

Present students with five cards: three with mixed numbers (e.g., 3 1/2, 5 2/3, 1 7/8) and two with improper fractions (e.g., 11/4, 9/5). Ask students to hold up the card that is the improper fraction equivalent to a mixed number you call out, or vice versa.

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Activity 02

• Peer Teaching
• 40 min · Small Groups

Conversion Relay: Team Challenge

Divide class into small groups and line up. Give first student a mixed number to convert to improper; they pass answer to next for reverse conversion. First accurate team wins. Review errors as whole class.

Explain the process of converting a mixed number to an improper fraction and vice versa.

Facilitation Tip

In Conversion Relay, stand at the finish line to watch each team’s division steps on the board before they tag the next runner.

What to look for

On a small slip of paper, ask students to: 1. Write one mixed number and its equivalent improper fraction. 2. Write one improper fraction and its equivalent mixed number. 3. Draw a simple visual (like shaded circles or rectangles) to show why 5/2 is the same as 2 1/2.

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Activity 03

• Peer Teaching
• 35 min · Individual

Rope Measurement Models: Real-World Fractions

Use ropes or strings longer than one unit. Individuals mark improper fractions like 5/3, then convert to mixed by measuring wholes first. Pairs compare models and conversions on paper.

Construct a visual model that demonstrates the equivalence between an improper fraction and a mixed number.

Facilitation Tip

For Rope Measurement Models, assign each group a rope length so they must measure, cut and convert without pre-cut pieces.

What to look for

Pose the question: 'Imagine you have a pizza cut into 8 slices and you eat 10 slices from two pizzas. How can you write this amount as both an improper fraction and a mixed number? Explain your steps for each.' Facilitate a brief class discussion where students share their answers and reasoning.

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

Activity 04

• Peer Teaching
• 25 min · Whole Class

Circle Diagrams: Visual Conversions

Whole class draws circles for denominators. Shade improper fractions, regroup into wholes and remainders for mixed numbers. Discuss patterns in pairs before sharing on board.

Differentiate between an improper fraction and a mixed number.

Facilitation Tip

With Circle Diagrams, provide only blank circles and rulers so students plan their own wholes and fractions before shading.

What to look for

Present students with five cards: three with mixed numbers (e.g., 3 1/2, 5 2/3, 1 7/8) and two with improper fractions (e.g., 11/4, 9/5). Ask students to hold up the card that is the improper fraction equivalent to a mixed number you call out, or vice versa.

• Understand
• Apply
• Analyze
• Create
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Start with concrete models like fraction strips so students feel the size of fractions before symbols appear. Avoid rushing to rules; let students discover the conversion steps through guided questions. Research shows that drawing circles while talking about wholes and parts builds mental images stronger than memorised steps alone. Always connect back to real quantities so fractions stay meaningful, not just numbers on paper.

By the end of these activities, students will convert between mixed numbers and improper fractions without hesitation. They will explain their steps using correct mathematical language and visual models. Most importantly, they will confidently state that both forms represent the same amount, just written differently.

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Watch Out for These Misconceptions

• During Fraction Strip Matching, watch for students who add the whole number directly to the numerator without multiplying by the denominator.

  Have them lay out whole strips first, then add the fractional part. Ask: ‘How many full strips do you see? How many extra parts?’ to guide them toward the correct multiplication step.

• During Fraction Strip Matching, students may think mixed numbers and improper fractions are different sizes.

  Ask each pair to lay matching strips side by side and explain why 1 3/4 and 7/4 cover the same length. Their verbal comparison will show equivalence clearly.

• During Conversion Relay, watch for students who treat division as subtraction when converting improper fractions to mixed numbers.

  Have the team trace the division steps on the board: ‘How many times does the denominator fit into the numerator? What is left?’ Use number line jumps to show the quotient as wholes and remainder as the new numerator.

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Methods used in this brief

• Peer Teaching