Mathematics · Year 5

Active learning ideas

Understanding Percentages as Fractions and Decimals

Active learning helps students grasp percentages as fractions and decimals because it turns abstract symbols into visual and tactile experiences. Shading hundred squares or matching cards makes equivalences concrete, which builds confidence in converting between forms.

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

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

Activity 01

• Problem-Based Learning
• 30 min · Pairs

Hundred Square Shading: Percentage Equivalences

Provide hundred squares for pairs to shade given percentages, such as 40%. Students write the matching fraction and decimal, then explain to their partner. Extend by creating their own examples for peers to solve.

Explain how the term 'percent' relates to the concept of a hundred.

Facilitation Tip

During Hundred Square Shading, circulate with a checklist to note which students still count squares one by one instead of using the 10 x 10 grid structure.

What to look for

Provide students with three cards: one with '40%', one with '2/5', and one with '0.4'. Ask them to write one sentence explaining how these three representations are equivalent and to draw a simple bar model showing 40%.

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

Activity 02

• Problem-Based Learning
• 25 min · Small Groups

Matching Game: Percent-Fraction-Decimal

Prepare cards with percentages, fractions, and decimals. In small groups, students match sets like 75%, 3/4, 0.75. Discuss mismatches and record correct equivalences in maths journals.

Construct a visual representation to show 25% as a fraction and a decimal.

Facilitation Tip

In the Matching Game, stand back during peer explanations and listen for students who justify their matches with hundred square shading or decimal place value.

What to look for

Display a hundred square grid on the board, with 30 squares shaded. Ask students to write down the percentage, fraction, and decimal that this shaded area represents. Discuss their answers, focusing on any misconceptions.

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

Activity 03

• Problem-Based Learning
• 45 min · Small Groups

Real-Life Discounts: Shop Simulation

Set up a class shop with priced items. Small groups apply percentage discounts, like 20% off, calculating new prices as fractions and decimals. Share strategies in a whole-class debrief.

Analyze why 100% represents a whole quantity and how to express it as a fraction and decimal.

Facilitation Tip

For Real-Life Discounts, prepare a timer so teams feel urgency to convert prices correctly before the next customer arrives.

What to look for

Pose the question: 'If you see a sign that says 'Save 100%', what does that mean for the price of the item? Explain your answer using the terms 'whole', 'fraction', and 'decimal'.

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

Activity 04

• Problem-Based Learning
• 20 min · Small Groups

Conversion Relay: Team Challenge

Divide class into teams. Each student converts a percentage to fraction or decimal on a whiteboard, passes to next teammate. First accurate team wins; review all answers together.

Explain how the term 'percent' relates to the concept of a hundred.

Facilitation Tip

In Conversion Relay, rotate teams every minute to keep all students engaged and prevent one student from dominating the conversions.

What to look for

Provide students with three cards: one with '40%', one with '2/5', and one with '0.4'. Ask them to write one sentence explaining how these three representations are equivalent and to draw a simple bar model showing 40%.

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

A few notes on teaching this unit

Teach this topic by starting with hundred squares to ground the concept of 100%. Move to matching games to build fluency, then apply skills in a shop simulation to show relevance. Avoid rushing to abstract rules; instead, let students discover patterns through guided exploration. Research shows that visual models followed by hands-on practice lead to stronger retention of fraction-decimal-percentage relationships.

Successful learning looks like students fluently converting between percentages, fractions, and decimals without hesitation. They should explain equivalences using hundred squares or real-life examples and correct peers’ misconceptions during discussions.

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Watch Out for These Misconceptions

• During Hundred Square Shading, watch for students who assume percentages must be whole numbers only.

  Provide one card with a decimal percentage like 37.5% and ask students to shade exactly 37.5 squares, then discuss why the decimal aligns with the hundredths place in the decimal form.

• During Hundred Square Shading, watch for students who believe 100% means more than a whole.

  Have students fully shade the hundred square and label it with 100%, 100/100, and 1.0, then prompt them to explain why shading 101 squares would represent 101%, which is over a whole.

• During Conversion Relay, watch for students who think the larger the percentage, the larger the decimal beyond 100%.

  Include a card with 150% and ask teams to convert it, then plot it on a number line to see how decimals increase correspondingly up to and beyond 1.

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Methods used in this brief

• Problem-Based Learning