Mathematics · Year 5

Active learning ideas

Finding Percentages of Amounts

Active learning works for finding percentages because concrete, hands-on steps let students build fluency before moving to abstract calculations. Breaking percentages into familiar fractions (half, quarter, tenth) helps students see the connections and reduces cognitive load while they practise with real objects and shared strategies.

• National Curriculum Attainment Targets
• KS2: Mathematics - Fractions, Decimals and Percentages

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

Activity 01

• Decision Matrix
• 30 min · Pairs

Pairs: Discount Deals

Provide pairs with shopping lists showing items priced £10 to £50 and discounts of 10%, 25%, or 50%. Students calculate savings, total new costs, then swap lists to check partner's work. Discuss efficient strategies like halving for 50%.

Justify why finding 50% of an amount is equivalent to dividing it by two.

Facilitation Tip

During Discount Deals, circulate and listen for pairs that justify their choice of 10%, 25% or 50% by naming the fraction it represents.

What to look for

Present students with a list of calculations, such as 'Find 50% of 80', 'Find 10% of £150', and 'Find 25% of 40'. Ask students to write down their answers and show one step of their working for each.

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

Activity 02

• Decision Matrix
• 35 min · Small Groups

Small Groups: Percentage Relay

Divide class into teams of four. First student calculates 10% of a given amount on whiteboard, next does 25%, third 50%, fourth checks all. Teams compete for speed and accuracy, rotating roles.

Predict the outcome of finding 10% of £250.

Facilitation Tip

Set a visible timer for each leg of the Percentage Relay so groups focus on speed and accuracy simultaneously.

What to look for

Pose the question: 'Imagine you have £200. How would you find 25% of it? Explain your method using either fractions or decimals, and then tell us why your method works.'

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

Activity 03

• Decision Matrix
• 25 min · Whole Class

Whole Class: Prediction Challenge

Display amounts like £200 or 80 sweets. Students predict silently then share 10% or 25% estimates via mini-whiteboards. Reveal correct calculations together, vote on best mental methods.

Design a strategy to find 25% of a number using both fractions and decimals.

Facilitation Tip

In the Prediction Challenge, invite students to hold up whiteboards only when they can show how they reached 10%, 25% or 50% in two different ways.

What to look for

Give each student a card with a different amount of money and a percentage (e.g., £70 and 10%, £120 and 25%). Ask them to calculate the value and write one sentence explaining how they found their answer.

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

Activity 04

• Decision Matrix
• 20 min · Individual

Individual: Strategy Design

Each student picks an amount and designs two ways to find 25%, one with fractions, one with decimals. They test on three examples, then pair-share to refine.

Justify why finding 50% of an amount is equivalent to dividing it by two.

Facilitation Tip

For Strategy Design, provide squared paper so students can sketch their steps and annotate each move with numbers and arrows.

What to look for

Present students with a list of calculations, such as 'Find 50% of 80', 'Find 10% of £150', and 'Find 25% of 40'. Ask students to write down their answers and show one step of their working for each.

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

A few notes on teaching this unit

Teach this topic by starting with quantities students can manipulate—coins, metre sticks, packets of sweets—so they see 10% as one tenth of a strip or 25% as one quarter of a circle. Avoid rushing to the written algorithm; let students articulate the steps in their own words first. Research shows that when students verbalise the link between fractions and percentages, their transfer to new contexts improves.

By the end of these activities, students should confidently choose and justify a method to find 10%, 25% or 50% of any whole-number amount. They will explain why dividing by 10 gives 10%, why halving twice gives 25%, and how to check answers with another strategy.

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Watch Out for These Misconceptions

• During Discount Deals, watch for students who subtract 10 from the price instead of calculating one tenth.

  Have them lay out ten £1 coins (or ten 10p coins) and physically remove one coin to see that 10% is one coin out of ten; this visual count corrects the subtraction error immediately.

• During Percentage Relay, watch for students who try to find 25% by dividing by four without halving twice.

  Give each group a strip of paper and have them halve it once to show 50%, then halve again to show 25%; this reinforces the two-halves process and helps peers spot the pattern.

• During Discount Deals, watch for students who claim percentages only work with money.

  Swap the price tags for length or mass labels (e.g., 200 cm of ribbon or 400 g of flour) and ask them to measure 10% using a ruler or scale; this generalises the concept beyond coins.

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Methods used in this brief

• Decision Matrix