Percentage Increase and DecreaseActivities & Teaching Strategies
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.
Learning Objectives
- 1Calculate the new value after a given percentage increase or decrease, expressing the answer to an appropriate degree of accuracy.
- 2Compare the effect of a percentage increase versus a percentage decrease on an original quantity, explaining the difference in outcomes.
- 3Justify the use of a single multiplier to represent successive percentage changes, demonstrating efficiency over sequential calculations.
- 4Predict the final value of a quantity after multiple successive percentage changes, such as two consecutive discounts.
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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.
Prepare & details
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.
Setup: Groups at tables with matrix worksheets
Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template
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.
Prepare & details
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.
Setup: Groups at tables with matrix worksheets
Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template
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.
Prepare & details
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.
Setup: Groups at tables with matrix worksheets
Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template
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.
Prepare & details
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.
Setup: Groups at tables with matrix worksheets
Materials: Decision matrix template, Option description cards, Criteria weighting guide, Presentation template
Teaching This Topic
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%).
What to Expect
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.
These activities are a starting point. A full mission is the experience.
- Complete facilitation script with teacher dialogue
- Printable student materials, ready for class
- Differentiation strategies for every learner
Watch Out for These Misconceptions
Common MisconceptionDuring Card Sort: Increase or Decrease Scenarios, watch for students who assume a 10% increase followed by a 10% decrease returns to the original amount.
What to Teach Instead
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.
Common MisconceptionDuring Card Sort: Increase or Decrease Scenarios, watch for students who confuse the multiplier for a 25% increase as 0.25 or 25.
What to Teach Instead
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.
Common MisconceptionDuring Multiplier Chain Relay, watch for students who add successive percentage changes (e.g., +10% then +20% = +30%).
What to Teach Instead
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.
Assessment Ideas
After Card Sort: Increase or Decrease Scenarios, present the scenario 'A jacket costs $80. It is first discounted by 10%, then by an additional 20% off the sale price. Calculate the final price using multipliers and write one sentence explaining why the final discount is not 30%.' Collect responses to assess both calculation and reasoning.
During Multiplier Chain Relay, 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 using calculations from your relay.' Facilitate a class discussion comparing different approaches and justifications.
After Price Tracker Simulation, 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 to assess individual understanding.
Extensions & Scaffolding
- Challenge: Ask students to design a two-step discount scenario where the final price is less than a 30% single discount, then prove their scenario mathematically.
- Scaffolding: Provide a template for the Reverse Percentage Challenge with partially completed calculations to guide students toward the correct multiplier.
- Deeper exploration: Have students research and present on how compound interest or inflation uses the same multiplicative method, comparing linear vs. exponential growth.
Key Vocabulary
| Percentage Increase | A calculation that determines how much a quantity has grown relative to its original value, expressed as a percentage. |
| Percentage Decrease | A calculation that determines how much a quantity has shrunk relative to its original value, expressed as a percentage. |
| Multiplier | A single number used to efficiently calculate a percentage change. For example, multiplying by 1.10 represents a 10% increase. |
| Successive Percentage Change | Applying one percentage change after another to a quantity, where the second change is calculated on the new, already changed value. |
Suggested Methodologies
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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