Mathematics · Year 7

Active learning ideas

Multiplying and Dividing Fractions

Fractions require concrete models because abstract operations often feel counterintuitive. Active tasks like shading grids or cutting paper let students see why two proper fractions multiplied together yield a smaller result, turning rules into visual evidence they can trust. Hands-on work reduces reliance on memorized steps and builds the proportional reasoning needed for later ratio and algebra topics.

• National Curriculum Attainment Targets
• KS3: Mathematics - Number

• 30–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Problem-Based Learning
• 35 min · Pairs

Area Model: Fraction Multiplication

Provide grid paper; students draw rectangles for each fraction, shade the first fully then overlay the second's fraction to show product. Pairs compare results and explain size reduction. Extend to multiply three fractions.

Explain why multiplying two proper fractions results in a smaller number.

Facilitation Tip

During Area Model: Fraction Multiplication, circulate and ask each pair to verbalize how the number of shaded cells in the overlap relates to the original fractions.

What to look for

Present students with the problem: 'A recipe requires 3/4 cup of sugar. You only want to make 1/3 of the recipe. How much sugar do you need?' Ask students to write down their calculation and the final answer.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 02

• Problem-Based Learning
• 45 min · Small Groups

Keep Change Flip Stations

Set up stations with division problems on cards; students solve using reciprocal method, record steps, and rotate. Small groups verify each other's work with visual checks like number lines. Include word problems at final station.

Analyze the 'keep, change, flip' method for dividing fractions.

Facilitation Tip

During Keep Change Flip Stations, stand at each station for 60 seconds to listen for the phrase ‘reciprocal of’ in students’ explanations.

What to look for

Pose the question: 'Imagine you have 5/8 of a chocolate bar and you want to share it equally among 3 friends. How much of the original chocolate bar does each friend receive?' Ask students to explain their method for solving this division problem.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 03

• Problem-Based Learning
• 30 min · Small Groups

Recipe Scaling Relay

Teams get recipe cards with fractions; one student multiplies or divides an ingredient then tags next teammate. Whole class debriefs errors and real-world accuracy. Adjust fractions for challenge.

Design a real-world problem that requires multiplying fractions.

Facilitation Tip

During Recipe Scaling Relay, time groups and emphasize that the final scaled recipe must be written in simplest form before passing it to the next station.

What to look for

Give each student a card with two fractions, e.g., 2/5 and 3/4. Ask them to perform one multiplication and one division calculation using these fractions. They should show their working for both.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Activity 04

• Problem-Based Learning
• 40 min · Pairs

Fraction Wall Builder

Students cut and assemble fraction strips to model multiplication as combining lengths and division as splitting. Individuals build then pair to test 'keep change flip' on walls. Share findings class-wide.

Explain why multiplying two proper fractions results in a smaller number.

What to look for

Present students with the problem: 'A recipe requires 3/4 cup of sugar. You only want to make 1/3 of the recipe. How much sugar do you need?' Ask students to write down their calculation and the final answer.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Teach division as repeated subtraction first using fraction bars so students see how many times one fraction fits into another. Avoid introducing the reciprocal method until students have physically partitioned strips and recorded their findings. For multiplication, connect the grid area to the word ‘overlap’ so students connect the visual to the numerical rule.

Students will confidently multiply and divide fractions using area models and the reciprocal method, explaining each step with clear language and visuals. They will justify their calculations by referencing the shaded overlap for multiplication and the ‘how many fit’ model for division. Missteps will be caught and corrected through peer discussion and teacher prompts during tasks.

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Watch Out for These Misconceptions

• During Area Model: Fraction Multiplication, watch for students who assume multiplying fractions always increases the value.

  Prompt students to compare the size of the overlap to the original rectangles and ask them to describe the relationship in words before calculating.

• During Keep Change Flip Stations, watch for students who divide numerators and denominators separately.

  Have students lay out fraction tiles for both fractions and physically group them to see how many of the divisor fit into the dividend.

• During Recipe Scaling Relay, watch for students who cancel terms before establishing equivalence.

  Place fraction tiles for both values side by side and ask students to explain how the tiles show whether cancellation is valid before they proceed.

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Methods used in this brief

• Problem-Based Learning