Mathematics · Year 6

Active learning ideas

Sharing in a Given Ratio

Active learning deepens proportional reasoning by letting students test abstract ideas with concrete objects and real choices. When ratios become about real transactions or exchanges, students see why the unitary method matters beyond the textbook.

• National Curriculum Attainment Targets
• KS2: Mathematics - Ratio and Proportion

• 20–45 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Inquiry Circle
• 40 min · Small Groups

Inquiry Circle: The Best Buy Challenge

Provide students with different sized packages of the same product (e.g., 300g for £2.40 and 500g for £3.50). In small groups, they must find the price per 100g for each to determine which is the 'best buy' and present their findings.

Explain how to determine the total number of parts when sharing in a ratio.

Facilitation Tip

During The Best Buy Challenge, give each group a calculator and a price list so they can focus on the method rather than mental arithmetic.

What to look for

Present students with a scenario: 'Sarah and Tom share 20 sweets in the ratio 3:2. How many sweets does each person get?' Ask students to show their working, focusing on identifying the total number of parts and the value of one part.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Activity 02

• Simulation Game
• 45 min · Pairs

Simulation Game: Currency Exchange

Set up a mock travel bureau where students must convert 'Travel Money' into different currencies using given exchange rates. They work in pairs to solve increasingly complex conversion problems for 'customers' (other students).

Analyze common errors when sharing quantities in a ratio and how to avoid them.

Facilitation Tip

Set a strict 3-minute timer for the Currency Exchange simulation to force quick calculations and peer correction.

What to look for

Pose the question: 'If two friends share £30 in the ratio 1:5, one friend gets £5 and the other gets £25. Is this correct? Explain why or why not, and what the correct answer should be.' Encourage students to articulate their reasoning about the total parts and the value of each part.

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Activity 03

• Think-Pair-Share
• 20 min · Pairs

Think-Pair-Share: Is it Proportional?

Present scenarios like 'the more you study, the higher your grade' or 'the more people painting a wall, the less time it takes.' Students discuss in pairs whether these are examples of direct proportion and why or why not.

Construct a problem that requires sharing a total amount in a specific ratio.

Facilitation Tip

After the Think-Pair-Share prompt, collect only the pairs who disagree to present first, creating natural debate and deeper reasoning.

What to look for

Give students a blank card. Ask them to write a word problem where a total amount (e.g., money, marbles, time) is shared in a ratio of 2:5. They must then solve their own problem, showing the steps clearly.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Teach the unitary method as a habit, not a trick. Model the language ‘First find one part, then scale up.’ Avoid shortcuts that skip the middle step, as this weakens proportional understanding. Research shows that collaborative problem-solving with immediate feedback builds stronger proportional reasoning than isolated worksheets.

Successful learners move from counting parts to calculating unit values and scaling up confidently. They can explain why dividing the total by the number of parts gives the value of one part and justify their answers with clear steps.

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Watch Out for These Misconceptions

• During The Best Buy Challenge, watch for students who pick the largest package because it has the same price as two smaller ones, ignoring the cost per unit.

  Have students calculate the price per gram or per item and present their findings to the class, forcing them to justify their choice with evidence.

• During Currency Exchange, watch for students who add or subtract the same amount to both parts of the ratio instead of scaling proportionally.

  Use the money or tokens in the simulation to physically group and split them, making the error visually impossible to ignore.

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Methods used in this brief

• Inquiry Circle
• Simulation Game
• Think-Pair-Share