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.

• Year 5
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the value of simple percentages (10%, 25%, 50%) of given whole numbers and amounts of money.
2. Explain the mathematical relationship between finding 50% of a number and dividing it by two.
3. Compare the results of finding 10% of a number using division and multiplication by a decimal.
4. Design a strategy to find 25% of a quantity using both fractional and decimal representations.

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%.

Prepare & details

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.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

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

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.

Prepare & details

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.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

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

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.

Prepare & details

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.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

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

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.

Prepare & details

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.

Setup: Groups at tables with matrix worksheets

Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Discount Deals, give each pair a quick-check slip with three items: 10% of 80, 25% of 60, 50% of 90. Collect slips and look for correct calculations and at least one noted step.

Discussion Prompt

During Percentage Relay, after the final leg, ask two groups to share their methods for 25% of 120; listen for explanations that mention halving twice and verify they connect to the fraction one quarter.

Exit Ticket

After Strategy Design, students hand in their annotated sketches; assess whether each sketch shows a clear path to 10%, 25% or 50% and includes at least one check (e.g., doubling or adding halves).

Extensions & Scaffolding

• Challenge: Prompt early finishers to find 5% of an amount by first finding 10% and halving the result, then extend to 15% by adding 10% and 5%.
• Scaffolding: Provide a strip of paper pre-marked into tenths for students who still count individual squares; let them fold or mark to locate 10% and 25%.
• Deeper exploration: Ask pairs to create a mini-poster showing three different objects (e.g., a 2-metre rope, 120 sweets, 300 ml juice) and the percentage strips they would use to find 10%, 25% and 50% of each.

Key Vocabulary

Percentage	A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, '%'. For example, 50% means 50 out of 100.
Decimal	A decimal is a number that uses a decimal point to separate the whole number part from the fractional part. For example, 0.5 is the decimal equivalent of 50%.
Fraction	A fraction represents a part of a whole. For example, 1/2 is the fraction equivalent of 50%.
Equivalent	Equivalent means having the same value or amount. For example, 50%, 0.5, and 1/2 are equivalent.