Mathematics · Year 8 · Numbers and the Power of Proportion · Term 1

Percentage Increase and Decrease

Students will calculate percentage increases and decreases, and apply them to real-world scenarios like discounts and interest.

• ACARA Content Descriptions
• AC9M8N03

About This Topic

Percentage increase and decrease help students model real changes in quantities, from price discounts to population growth. In Year 8 Mathematics, aligned with AC9M8N03 in the Australian Curriculum, students calculate these changes using multipliers, reverse them to find original amounts, and apply them to scenarios like successive discounts or simple interest. This topic sits within the Numbers and the Power of Proportion unit, building proportional reasoning from earlier fraction and decimal work. Students tackle key questions: they differentiate percentage of a number from percentage change, justify steps to recover originals, and predict final values after multiple adjustments.

These concepts develop algebraic habits and financial literacy, as students connect calculations to everyday decisions like sales tax or savings growth. Visualising multipliers as scaling factors strengthens understanding, while successive changes reveal why percentages do not simply add. This prepares students for advanced modelling in later years.

Active learning benefits this topic through contextual, collaborative tasks. When students handle real price tags in market simulations or build percentage strips from paper, they internalise multipliers intuitively. Group challenges with successive discounts make reversal strategies concrete, boosting confidence and retention over rote practice.

Key Questions

1. Differentiate between calculating a percentage of a number and calculating a percentage increase.
2. Justify the steps involved in finding the original amount after a percentage change.
3. Predict the final price of an item after multiple percentage discounts are applied.

Learning Objectives

• Calculate the new amount after a percentage increase or decrease using decimal multipliers.
• Explain the inverse relationship between percentage increase and decrease when finding an original value.
• Compare the final price of an item after sequential percentage discounts versus a single combined discount.
• Justify the steps taken to determine the original price of an item given its price after a percentage change.

Before You Start

Calculating a Percentage of a Number

Why: Students must be able to find a fraction of a quantity to understand how to calculate the amount of increase or decrease.

Fractions, Decimals, and Percentages

Why: Students need to understand the equivalence and conversion between these forms to work with percentage multipliers.

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 number used to multiply a quantity. For percentage changes, multipliers like 1.15 (for 15% increase) or 0.85 (for 15% decrease) simplify calculations.
Original Amount	The starting value before any percentage increase or decrease is applied.
Successive Discounts	Applying multiple percentage discounts one after another, where each discount is calculated on the reduced price, not the original.

Watch Out for These Misconceptions

Common Misconception

A percentage increase or decrease is the same as finding that percentage of the original amount.

What to Teach Instead

Percentage change uses a multiplier: original × (1 ± percent/100). Visual aids like percentage strips in pairs help students see scaling, not just addition or subtraction, clarifying the distinction through manipulation and comparison.

Common Misconception

Percentages from successive changes can be added or subtracted directly.

What to Teach Instead

Successive changes multiply multipliers, for example 1.1 × 0.9 for 10% increase then 10% decrease. Relay races where teams compute step-by-step expose this, as incorrect addition leads to team errors, prompting collaborative correction.

Common Misconception

To reverse a percentage increase, subtract that percentage from the new amount.

What to Teach Instead

Divide by the multiplier or subtract the percentage of the original, which is smaller. Puzzle-solving in small groups with price tags reinforces the correct formula through trial and verification, building procedural fluency.

Active Learning Ideas

Market Stall: Successive Discounts

Price everyday items with AUD tags. Groups apply two successive discounts, such as 20% then 10%, and calculate final prices using calculators. Rotate roles: seller quotes, buyer verifies, accountant records multipliers. Discuss predictions versus actuals.

45 min·Small Groups

Reverse Price Puzzle: Pairs Challenge

Provide final sale prices after known percentage decreases. Pairs work backwards using the formula original = final / (1 - percent/100), then verify by reapplying change. Swap puzzles with another pair for peer checking.

30 min·Pairs

Interest Growth Relay: Whole Class

Divide class into teams. Each student calculates one step of compound interest over years, passes baton with updated amount. First team to correct final amount wins. Debrief multipliers.

35 min·Whole Class

Percentage Strip Builder: Individual Start

Students cut and label strips for 100 units, shade percentages, then extend or shrink for increases/decreases. Combine in pairs to model successive changes visually.

25 min·Individual

Real-World Connections

• Retailers use percentage decreases to offer discounts on clothing and electronics during sales events like Black Friday. Customers benefit by paying less for desired items.
• Banks and financial institutions use percentage increases to calculate simple interest on savings accounts or loans. This allows money to grow over time or the cost of borrowing to be determined.
• Real estate agents often calculate potential property value increases based on market trends and renovation costs. This helps sellers set appropriate asking prices.

Assessment Ideas

Quick Check

Present students with a scenario: 'A video game console originally cost $500 and is now on sale for $400. What is the percentage decrease?' Ask students to show their calculation using a multiplier and write the percentage decrease.

Exit Ticket

Give students two problems: 1. Calculate the price of a $60 shirt after a 25% discount. 2. A jacket is now $90 after a 10% increase. What was the original price? Students write their answers and one sentence explaining their method for the second problem.

Discussion Prompt

Pose the question: 'If an item is discounted by 20% and then by another 20%, is that the same as a 40% discount? Why or why not?' Facilitate a class discussion where students use examples to justify their reasoning.

Frequently Asked Questions

How do you calculate the original price after a percentage discount?

Use the formula: original = final price / (1 - discount percent/100). For a 20% discount on a $50 final price, divide 50 by 0.8 to get $62.50. Practice with real receipts helps students justify steps and check by reapplying the discount, aligning with AC9M8N03 reversal skills.

What are real-world examples of percentage increase and decrease?

Discounts on school uniforms, GST increases on purchases, or bank interest on savings accounts. Students can track supermarket specials over a week, calculate percentage changes from original prices, and predict costs after multiple offers. This connects math to consumer decisions in Australia.

How can active learning help students master percentage changes?

Hands-on tasks like discount market stalls or visual strip models make multipliers tangible. In small groups, students negotiate prices and verify calculations, turning abstract formulas into collaborative problem-solving. This approach addresses key questions on differentiation and prediction, improving engagement and deepens proportional understanding over worksheets.

How to differentiate percentage of a quantity from percentage change?

Percentage of finds part of original, like 20% of 100 is 20. Percentage change scales it, like 20% increase makes 120. Use paired sorting activities with cards showing both types; discussion reveals patterns. This targets the unit's key question and builds foundational clarity.