Mathematics · Year 9 · Financial Mathematics and Proportion · Term 4

Percentage Increase and Decrease

Students will calculate percentage increases and decreases, applying them to various contexts like sales and growth.

• ACARA Content Descriptions
• AC9M9N04

About This Topic

Percentage increase and decrease build essential skills for handling change in quantities, such as sales discounts or population growth. Students calculate new values using multipliers: add the percentage as a decimal for increases (original × (1 + p/100)) and subtract for decreases (original × (1 - p/100)). They investigate why a 10% increase followed by a 10% decrease yields less than the original amount, since 1.1 × 0.9 = 0.99, a net 1% loss. This reveals the compounding effect of successive percentage changes.

Aligned with AC9M9N04 in the Australian Curriculum, this topic strengthens proportional reasoning within financial mathematics and proportion. Students analyze impacts on initial values and construct real-world problems, like successive price hikes or salary adjustments, to apply concepts flexibly.

Active learning suits this topic well. When students compute changes on price tags in small groups or simulate investment growth across multiple rounds, they spot patterns in multipliers firsthand. Peer discussions clarify why changes do not reverse symmetrically, turning potential confusion into shared insight.

Key Questions

1. Why is a 10 percent increase followed by a 10 percent decrease not the same as the original price?
2. Analyze the impact of successive percentage changes on an initial value.
3. Construct a problem involving a percentage increase or decrease in a real-world context.

Learning Objectives

• Calculate the new price after a percentage increase or decrease, applying the correct multiplier.
• Explain why successive percentage changes, such as a discount followed by a price increase, do not result in the original value.
• Compare the net effect of different sequences of percentage changes on an initial amount.
• Construct a word problem involving a real-world scenario that requires calculating successive percentage changes.
• Analyze the impact of a given percentage increase or decrease on a specific financial quantity.

Before You Start

Calculating Percentages of Amounts

Why: Students need to be able to find a percentage of a number before they can calculate percentage increases or decreases.

Fractions, Decimals, and Percentages

Why: Understanding the equivalence and conversion between these number forms is essential for using multipliers correctly.

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 value; in percentage change, it represents the original amount plus or minus the percentage change as a decimal.
Successive Percentage Changes	Applying more than one percentage change one after another to a value, where each change is calculated on the result of the previous one.

Watch Out for These Misconceptions

Common Misconception

A 10% increase followed by a 10% decrease returns to the original value.

What to Teach Instead

Multipliers show 1.1 × 0.9 = 0.99, a 1% net loss since the decrease applies to a larger amount. Pair computations on various starting values reveal this pattern quickly. Group sharing of examples corrects the additive thinking error.

Common Misconception

Percentage decrease is calculated on the new value after change.

What to Teach Instead

Percentages always base on the original amount unless specified. Hands-on price tag adjustments in small groups, comparing original versus adjusted calculations, highlight the consistent original base. Discussion reinforces formula application.

Common Misconception

All percentage changes are additive.

What to Teach Instead

Changes multiply, not add, as each applies to the updated value. Relay activities where students pass updated totals demonstrate compounding visually. Class graphing of results solidifies the multiplicative model.

Active Learning Ideas

Pairs: Multiplier Match-Up

Provide cards with percentage changes (e.g., +20%, -10%) and initial values. Pairs match sequences to final outcomes, compute using multipliers, and predict results before calculating. Discuss patterns in why successive changes compound differently.

25 min·Pairs

Small Groups: Shop Sale Simulation

Groups receive store inventory lists with original prices. Apply successive percentage changes from customer scenarios, like 15% off then 10% tax. Record final prices and present one misleading 'sale' to the class.

40 min·Small Groups

Whole Class: Growth Chain Relay

Line up students; first computes a percentage increase on a starting value and passes to next for a decrease. Chain continues with class-chosen percentages. Graph results to analyze net change after 5-6 steps.

35 min·Whole Class

Individual: Problem Creator

Each student constructs a real-world problem with successive percentage changes, like phone plan costs. Swap with a partner to solve and verify using multipliers. Share one class example.

20 min·Individual

Real-World Connections

• Retailers use percentage increases and decreases daily for sales, discounts, and marking up wholesale prices. For example, a clothing store might offer a 20% off sale on all items, then later increase the price of a returned item to its original value.
• Financial advisors calculate the impact of percentage changes on investments over time. A portfolio might experience a 5% growth one quarter, followed by a 3% loss the next, requiring calculations of the net change.
• Economists track inflation using percentage increases in the Consumer Price Index. This affects the purchasing power of money, influencing decisions about wages and the cost of goods like housing or fuel.

Assessment Ideas

Exit Ticket

Provide students with a starting price of $50. Ask them to calculate the final price after a 10% increase followed by a 10% decrease. Then, ask them to write one sentence explaining why the final price is not $50.

Quick Check

Present students with two scenarios: Scenario A: A $100 item is increased by 20%, then decreased by 20%. Scenario B: A $100 item is decreased by 20%, then increased by 20%. Ask students to calculate the final price for each scenario and identify which scenario results in a higher final price.

Discussion Prompt

Pose the question: 'Imagine a shop owner increases the price of a popular video game by 15% due to high demand, and then a month later, they put it on sale for 15% off. Is the sale price the same as the original price? Why or why not?' Facilitate a class discussion using student responses.

Frequently Asked Questions

Why does a 10% increase and 10% decrease not equal the original amount?

The increase raises the value first (e.g., $100 to $110), so the 10% decrease applies to $110 ($11 off), resulting in $99. Multipliers confirm: 1.1 × 0.9 = 0.99. Students grasp this through repeated pair calculations on different originals, seeing the consistent net loss pattern emerge.

What real-world contexts teach percentage increase and decrease?

Use sales promotions (20% off then 10% GST), population growth (2% yearly increase over years), or salary rises (5% then 3% adjustment). Students construct problems from news articles on inflation or discounts. Small group simulations with props like price tags connect math to daily financial choices effectively.

How can active learning help students master percentage changes?

Active tasks like group price simulations or relay computations let students apply multipliers repeatedly, spotting why successive changes compound. Peer teaching in discussions corrects errors live, while graphing chains visualizes net effects. This builds fluency faster than worksheets, as tangible contexts make abstract multipliers intuitive and memorable.

How to address errors in successive percentage calculations?

Common pitfalls include additive thinking or wrong bases. Start with visual multiplier strips students adjust physically. Follow with paired verifications using formulas, then whole-class error analysis from sample problems. This scaffolds from concrete manipulation to abstract reasoning, ensuring AC9M9N04 proficiency.