Mathematics · Class 1

Active learning ideas

Multiplying Fractions and Mixed Numbers

Active learning works well for multiplying fractions and mixed numbers because students often struggle with abstract rules. When they use physical or visual tools, they see clearly how numerators and denominators interact, building confidence before moving to symbols.

• CBSE Learning Outcomes
• NCERT: Class 7, Chapter 2, Fractions and Decimals

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Plan-Do-Review
• 25 min · Pairs

Pairs Activity: Fraction Strips Multiplication

Provide each pair with fraction strips. Students represent two fractions, then layer strips to show the product by finding overlapping shaded sections. Pairs record the result and compare with direct multiplication.

Analyze how multiplying fractions differs from adding them.

Facilitation Tip

During the Fraction Strips Multiplication activity, have pairs layer strips to show how multiplying fractions scales the area, not the length.

What to look for

Present students with a problem like 'Calculate 2/3 of 3/4'. Ask them to write down the steps they followed and the final answer. Review their work to identify common errors in numerator/denominator multiplication.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 02

• Plan-Do-Review
• 35 min · Small Groups

Small Groups: Pizza Sharing Model

Groups draw pizzas on grid paper, shade fractions for each factor, then shade the overlapping area for the product. Discuss why the product area is smaller. Convert mixed numbers using the same method.

Construct a visual model to represent the multiplication of two fractions.

Facilitation Tip

For the Pizza Sharing Model, encourage groups to draw and shade pizzas to connect real-life sharing with fraction multiplication.

What to look for

Give each student a card with a mixed number multiplication problem, e.g., '1 and 1/2 multiplied by 2'. Ask them to show their work, including the conversion of the mixed number, and write the final product. Collect these to gauge individual understanding of the process.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 03

• Plan-Do-Review
• 30 min · Whole Class

Whole Class: Number Line Relay

Mark fractions on class number lines. Teams race to plot factors, multiply by jumping the product distance, and explain steps aloud. Teacher notes common steps on board.

Evaluate the impact of multiplying a fraction by a whole number.

Facilitation Tip

In the Number Line Relay, place visible fraction markers so students can see how multiplying moves them closer to zero.

What to look for

Pose the question: 'Why is the product of two fractions less than 1 always smaller than either of the original fractions?' Facilitate a class discussion where students can share their reasoning, perhaps using visual models they created.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 04

• Plan-Do-Review
• 20 min · Individual

Individual: Visual Diary

Students create personal journals with drawings of fraction multiplications, including mixed numbers. They label numerators, denominators, and explain 'of' in sentences.

Analyze how multiplying fractions differs from adding them.

Facilitation Tip

Ask students to label their Visual Diaries with clear steps and drawings to reinforce the conversion process.

What to look for

Present students with a problem like 'Calculate 2/3 of 3/4'. Ask them to write down the steps they followed and the final answer. Review their work to identify common errors in numerator/denominator multiplication.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

A few notes on teaching this unit

Start with concrete models before introducing symbols. Many students confuse multiplying fractions with adding them, so avoid rushing to rules. Use peer teaching to allow students to explain their thinking, which helps correct misconceptions early. Research shows that students who draw or use physical tools retain concepts longer than those who only memorise steps.

Students will confidently multiply fractions and mixed numbers using visual models and conversion steps. They will explain why the product of two fractions less than one is smaller than the factors, showing understanding through discussion and written work.

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Watch Out for These Misconceptions

• During the Number Line Relay activity, watch for students multiplying mixed numbers without converting to improper fractions. Have them use the number line to see why direct multiplication does not fit. Ask them to convert the mixed number first and then multiply to clarify the process.

  During the Pizza Sharing Model activity, watch for students assuming the product is larger than the factors. Have groups compare their shaded pizzas to see that the shaded area shrinks when multiplying two fractions less than one. Ask them to explain how the model shows this change.

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Methods used in this brief

• Plan-Do-Review