Mathematics · Year 8

Active learning ideas

Percentage Increase and Decrease

Active learning works well for percentage increase and decrease because students often confuse the mechanics of calculating changes with the meaning behind them. Hands-on activities like sorting, simulating, and relaying help students build correct mental models by making abstract processes concrete and visible.

• National Curriculum Attainment Targets
• KS3: Mathematics - Number
• KS3: Mathematics - Ratio, Proportion and Rates of Change

• 25–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Decision Matrix
• 30 min · Pairs

Card Sort: Increase or Decrease Scenarios

Prepare cards with real-world problems like '£50 phone with 20% VAT increase' or '£80 jacket with 25% sale decrease'. In pairs, students sort into increase/decrease piles, calculate new amounts using multipliers, then swap and check calculations. Discuss efficiencies of the multiplier method.

Analyze the impact of a percentage increase versus a percentage decrease on an original value.

Facilitation Tip

During the Card Sort, circulate and ask groups to explain their reasoning for categorizing each scenario as an increase or decrease before they write the calculations.

What to look for

Present students with a scenario: 'A jacket costs $80. It is first discounted by 10%, then by an additional 20% off the sale price. Calculate the final price.' Ask students to show their working using multipliers and to write one sentence explaining why the final discount is not 30%.

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

Activity 02

• Decision Matrix
• 40 min · Small Groups

Multiplier Chain Relay

Divide small groups into teams. Each member applies one percentage change from a chain (e.g., +10%, -5%, +20%) to a starting amount, passes to the next. Teams predict and verify final amounts, then compare multiplier products. Extend to justify predictions.

Justify the use of a multiplier for efficient percentage change calculations.

Facilitation Tip

For the Multiplier Chain Relay, provide each group with a different starting value to ensure varied outcomes and deeper discussion during the class debrief.

What to look for

Pose the question: 'If you invest 1000 and it increases by 5% in year one and decreases by 5% in year two, is your final amount more than, less than, or equal to your original 1000? Explain your reasoning using calculations.' Facilitate a class discussion comparing different approaches and justifications.

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

Activity 03

• Decision Matrix
• 45 min · Small Groups

Price Tracker Simulation

Provide item prices; small groups apply successive changes over 'months' (e.g., inflation +3%, then discount -2%). Record on tables, predict trends, and graph results. Whole class shares one surprising outcome and explains with multipliers.

Predict the outcome of successive percentage changes on an initial quantity.

Facilitation Tip

In the Price Tracker Simulation, have students record their calculations on a whiteboard so peers can see how discounts compound over time.

What to look for

Give each student a card with a different starting value and a percentage change (e.g., 'Increase 50 by 15%', 'Decrease 200 by 25%'). Ask them to calculate the new value using a multiplier and write down the multiplier they used.

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

Activity 04

• Decision Matrix
• 25 min · Individual

Reverse Percentage Challenge

Individuals start with final prices and work backwards to originals using inverse multipliers (e.g., divide by 1.20 for 20% increase reversal). Pairs peer-review, then share strategies for successive reverses.

Analyze the impact of a percentage increase versus a percentage decrease on an original value.

Facilitation Tip

During the Reverse Percentage Challenge, ask students to present their method for reversing a 35% decrease to a partner before sharing with the whole class.

What to look for

Present students with a scenario: 'A jacket costs $80. It is first discounted by 10%, then by an additional 20% off the sale price. Calculate the final price.' Ask students to show their working using multipliers and to write one sentence explaining why the final discount is not 30%.

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

A few notes on teaching this unit

Start with concrete examples using money or familiar quantities to anchor the concept. Avoid teaching formulas in isolation; instead, connect multipliers to the idea of scaling up or down by parts of a whole. Research shows that students grasp multiplicative reasoning better when they see percentages as operations (like ×1.25) rather than isolated steps (×25% + 100%).

Students will confidently apply multipliers and percentage calculations to real-life contexts, recognizing that percentage changes depend on the current amount, not just the original. They will articulate why successive changes are multiplicative, not additive, and justify their reasoning with calculations.

---

Watch Out for These Misconceptions

• During Card Sort: Increase or Decrease Scenarios, watch for students who assume a 10% increase followed by a 10% decrease returns to the original amount.

  Have groups test their assumption using the provided £100 card and record the steps on the sort sheet, then compare outcomes in a class vote before correcting the misconception.

• During Card Sort: Increase or Decrease Scenarios, watch for students who confuse the multiplier for a 25% increase as 0.25 or 25.

  Provide pairs with price cards labeled with original and final amounts, and ask them to identify the correct multiplier (1.25) by comparing the increase to the original on their sort cards.

• During Multiplier Chain Relay, watch for students who add successive percentage changes (e.g., +10% then +20% = +30%).

  Pause the relay and have groups multiply their multipliers (1.10 × 1.20) to find the total change, then justify why addition is incorrect using their recorded calculations.

---

Methods used in this brief

• Decision Matrix