Mathematics · Year 7 · Proportional Reasoning · Spring Term

Percentage Increase and Decrease

Calculating percentage changes and applying them to real-world problems like discounts or growth.

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

About This Topic

Percentage increase and decrease build on students' prior knowledge of finding percentages of amounts. Students learn to calculate a percentage change by first finding the percentage of the original amount, then adding or subtracting it. For example, a 20% increase on £50 adds £10 to reach £60. They apply these skills to real-world contexts, such as shop discounts, price rises, or population growth, and practise reversing changes to find original amounts.

This topic sits within proportional reasoning in the KS3 curriculum, linking number operations with ratio and rates of change. It strengthens problem-solving by requiring students to distinguish between a percentage of an amount and a percentage change, and to set up equations like original = final / (1 + change/100). These steps foster algebraic thinking early on.

Active learning suits this topic well. When students role-play shopping scenarios with price tags or track simulated savings growth over time, they grasp the multiplicative nature of percentages through tangible adjustments. Group challenges designing discount problems reveal misconceptions quickly and make abstract calculations concrete and relevant.

Key Questions

1. Analyze the difference between finding a percentage of an amount and a percentage change.
2. Explain how to calculate the original amount after a percentage change.
3. Design a problem involving a percentage increase or decrease.

Learning Objectives

• Calculate the new amount after a percentage increase or decrease.
• Determine the percentage change between two given amounts.
• Explain the steps required to find the original amount given a percentage change.
• Design a word problem that requires calculating a percentage increase or decrease in a real-world context.

Before You Start

Finding a Percentage of an Amount

Why: Students must be able to calculate a percentage of a number before they can calculate a percentage change.

Fractions and Decimals

Why: Understanding the relationship between fractions, decimals, and percentages is fundamental for all percentage calculations.

Key Vocabulary

Percentage Change	The measure of how much a quantity has changed relative to its original value, expressed as a percentage.
Percentage Increase	A calculation showing how much a value has gone up, expressed as a percentage of the original value.
Percentage Decrease	A calculation showing how much a value has gone down, expressed as a percentage of the original value.
Original Amount	The starting value before any percentage change has been applied.
New Amount	The value after a percentage increase or decrease has been applied.

Watch Out for These Misconceptions

Common Misconception

Percentage change means adding the percentage points directly to the original amount.

What to Teach Instead

Students often add 20 directly to 100 instead of 20% (£20). Hands-on price tag manipulations in groups show the correct multiplier effect, as they physically adjust and compare totals. Peer teaching reinforces the formula: new = original × (1 ± change/100).

Common Misconception

For decreases, subtract the percentage of the new amount, not the original.

What to Teach Instead

This leads to double-counting errors. Role-play shopping stations help, as students apply discounts sequentially and see why original-based subtraction works. Discussion clarifies the one-step method.

Common Misconception

Percentage increase and decrease are opposites and cancel exactly.

What to Teach Instead

A 50% increase followed by 50% decrease returns less than start. Growth tracking activities in pairs demonstrate this asymmetry visually through repeated multiplications, building intuition for non-linear changes.

Active Learning Ideas

Stations Rotation: Percentage Changes

Prepare stations with price tags showing original and sale prices. Students calculate increases or decreases, then reverse to find originals. Rotate groups every 10 minutes, discussing methods at each station. End with a class share-out.

45 min·Small Groups

Pair Challenge: Discount Design

Pairs create real-world problems, like clothing sales or wage rises, swapping with another pair to solve. They check answers using the reverse method. Teacher circulates to prompt equation setups.

30 min·Pairs

Whole Class: Growth Tracker

Display a table of yearly population growth percentages. Class predicts values after 3 years using calculators, then verifies step-by-step on board. Adjust for decreases like shrinking habitats.

35 min·Whole Class

Individual: Error Hunt

Provide worksheets with mixed calculations; students identify and correct errors in percentage changes. Follow with self-explanation of fixes.

20 min·Individual

Real-World Connections

• Retailers use percentage discounts to attract customers, for example, a 25% off sale on electronics in a store like Currys.
• Financial advisors calculate investment growth or losses using percentage changes, advising clients on the performance of their portfolios.
• Public transport providers adjust ticket prices based on inflation or operational costs, leading to percentage increases in fares for commuters.

Assessment Ideas

Exit Ticket

Provide students with two scenarios: 1) A price tag showing a £20 item is now £15. Ask: 'What is the percentage decrease?' 2) A savings account starts with £100 and grows by 5%. Ask: 'What is the new balance?'

Quick Check

Present students with a problem: 'A town's population increased from 50,000 to 55,000 in one year. Calculate the percentage increase.' Observe students' methods and identify common errors in calculation or concept.

Discussion Prompt

Pose the question: 'If a shopkeeper says an item is 'half price', is that the same as a 50% discount? Explain your reasoning.' Facilitate a class discussion comparing these two statements and their mathematical equivalence.

Frequently Asked Questions

How do you calculate the original price after a discount?

To find the original after, say, a 20% discount on a £80 sale price, divide by (1 - 0.20) or 0.80: £80 / 0.80 = £100. Students practise with real receipts, reinforcing the multiplier inverse. This reverse skill prevents common overestimation errors in proportional problems.

What is the difference between a percentage of an amount and a percentage change?

A percentage of an amount is static, like 20% of £100 is £20. A percentage change adds or subtracts that to/from the original for a new value. Activities like adjusting budgets clarify this, as students compute both and compare outcomes side-by-side.

How can active learning help students master percentage increase and decrease?

Active approaches like discount simulations or growth charts engage students kinesthetically. In small groups, they manipulate prices or predict changes, debating methods aloud. This reveals errors instantly, builds confidence through peer support, and connects maths to shopping or news, making multipliers intuitive over rote practice.

What real-world problems use percentage changes?

Discounts, tax, interest rates, population shifts, or profit margins apply daily. Students design problems from adverts, calculating sale prices or growth rates. This contextualises skills, showing relevance to careers in finance or data analysis, and motivates through familiar scenarios.