Mathematics · Year 11

Active learning ideas

Compound Interest and Depreciation

Active learning turns abstract repeated percentage changes into concrete experiences. Students manipulate multipliers, compare timelines, and debate outcomes, which builds durable understanding beyond textbook formulas.

• National Curriculum Attainment Targets
• GCSE: Mathematics - Number
• GCSE: Mathematics - Ratio, Proportion and Rates of Change

• 30–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Decision Matrix
• 45 min · Small Groups

Savings Simulator: Group Challenges

Provide groups with calculators and scenario cards detailing initial amounts, rates, and periods. Students apply multipliers step-by-step to compute compound interest, then graph results. Groups present one key insight, such as doubling time at different rates.

Compare compound interest to simple interest over extended periods.

Facilitation Tip

During Savings Simulator, circulate with colored tokens to physically show how each group’s pile grows faster than the last when compound interest is applied.

What to look for

Present students with a scenario: 'An item costs £500 and depreciates by 10% each year. What is its value after 3 years?' Ask students to show their multiplier calculation and final answer on a mini-whiteboard.

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

Activity 02

• Decision Matrix
• 30 min · Pairs

Depreciation Relay: Pairs Race

Pairs receive asset cards with starting values and annual depreciation multipliers. One student calculates one period, passes to partner for the next, racing against other pairs to 10 years. Debrief compares straight-line versus compound models.

Explain why a multiplier is an efficient tool for calculating percentage changes.

Facilitation Tip

For Depreciation Relay, station a timer at each card set so pairs race against the clock while ensuring they use the multiplier under one each round.

What to look for

Pose the question: 'Imagine you have two savings accounts, one offering 3% simple interest and another offering 3% compound interest, both for 20 years. Which would you choose and why?' Facilitate a class discussion comparing the long-term outcomes.

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

Activity 03

• Decision Matrix
• 35 min · Whole Class

Multiplier Match-Up: Whole Class

Distribute cards with percentage changes, multipliers, and scenarios. Students match them in a class mingle, then verify calculations on boards. Discuss efficiencies of multipliers over repeated division/multiplication.

Analyze the long-term financial implications of different interest rates or depreciation values.

Facilitation Tip

In Multiplier Match-Up, give every student a card with a starting value and percentage change so the whole class can simultaneously pair multipliers to scene cards on the board.

What to look for

Give each student a card with a different initial investment amount and interest rate. Ask them to calculate the value after 5 years using compound interest and write one sentence explaining why this method is beneficial for long-term savings.

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

Activity 04

• Decision Matrix
• 50 min · Small Groups

Investment Debate: Small Groups Prep

Assign groups simple versus compound interest scenarios over 20 years. They calculate outcomes, prepare arguments for best choice, and debate. Vote on most convincing evidence with supporting maths.

Compare compound interest to simple interest over extended periods.

What to look for

Present students with a scenario: 'An item costs £500 and depreciates by 10% each year. What is its value after 3 years?' Ask students to show their multiplier calculation and final answer on a mini-whiteboard.

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

A few notes on teaching this unit

Teach multipliers as a mathematical shortcut first, then anchor them in real contexts. Avoid rushing to the formula—let students derive the power rule by chaining small multipliers over several rounds. Research shows concrete–abstract–abstract sequences work best for percentage change, so move from physical tokens to tables to pure multipliers.

Success looks like students confidently selecting the correct multiplier, explaining why compound interest outpaces simple interest over time, and using decreasing multipliers correctly for depreciation scenarios.

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Watch Out for These Misconceptions

• During Savings Simulator, watch for students who keep adding the same percentage of the original amount instead of the new total.

  Have peers in each group rebuild their token pile using the new total after each round and compare the growth curve to a simple interest timeline laid beside it.

• During Depreciation Relay, watch for students who subtract a fixed amount each year rather than applying a decreasing multiplier.

  Pause the relay and ask each pair to sort their asset value cards in descending order, then ask them to explain why the gaps between cards shrink over time when using the correct multiplier.

• During Multiplier Match-Up, watch for students who think multipliers can only be used for one period and resist raising them to a power.

  Ask students to chain three identical multipliers on a mini-whiteboard and then prompt them to write the single equivalent multiplier as a power, verifying with calculators.

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Methods used in this brief

• Decision Matrix