Mathematics · Year 7 · Proportional Reasoning · Term 2

Percentage Increase and Decrease

Students will calculate percentage changes and apply them to financial scenarios like discounts and interest.

• ACARA Content Descriptions
• AC9M7N07

About This Topic

Percentage increase and decrease require students to calculate changes relative to an original amount, a core part of proportional reasoning in Year 7 Mathematics. Students find percentage increases, such as a 15% pay rise, and decreases, like a 20% discount on clothing. They apply these to financial contexts, including sales tax and simple interest, and explore why a percentage increase followed by the same percentage decrease does not return to the original value. For example, a 10% increase on $100 yields $110, but a 10% decrease on $110 results in $99.

This topic connects to earlier work on ratios and fractions while laying groundwork for compound growth in later years. Students analyze successive percentage changes, such as repeated discounts, and construct real-world problems involving discounts or taxes. These skills foster financial literacy and critical thinking about everyday economic decisions.

Active learning benefits this topic greatly because students often struggle with the changing base in multi-step calculations. Hands-on tasks with price tags or savings trackers make abstract percentages concrete, encourage peer explanations during group problem-solving, and reveal patterns through repeated trials, building confidence and deeper understanding.

Key Questions

1. Justify why a percentage increase followed by the same percentage decrease does not return to the original value.
2. Analyze the impact of successive percentage changes on an initial amount.
3. Construct a problem involving a real-world discount or tax calculation.

Learning Objectives

• Calculate the new value after a percentage increase or decrease is applied to an initial amount.
• Explain why successive percentage changes of the same value do not result in the original amount.
• Analyze the impact of multiple successive percentage changes on a starting value.
• Construct a word problem that requires calculating a discount or sales tax.
• Compare the final amounts resulting from different sequences of percentage changes.

Before You Start

Calculating Percentages

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

Fractions and Decimals

Why: Understanding the relationship between fractions, decimals, and percentages is fundamental to performing these calculations accurately.

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.
Original Value	The starting amount or quantity before any percentage change is applied.
Successive Percentage Changes	Applying multiple percentage increases or decreases one after another, where each change is calculated on the new amount from the previous step.

Watch Out for These Misconceptions

Common Misconception

A percentage increase followed by the same percentage decrease returns to the original amount.

What to Teach Instead

The base changes after the first operation, so decreases apply to a larger amount. Group discussions of concrete examples, like $100 becoming $110 then $99, help students visualize this. Peer teaching reinforces the concept through shared explanations.

Common Misconception

Percentage changes always add or subtract directly from the original.

What to Teach Instead

Each change uses the current value as the new base. Hands-on simulations with manipulatives, such as adjusting stacks of money, clarify sequential effects. Collaborative problem-solving uncovers errors in real time.

Common Misconception

Successive percentages multiply directly without considering order.

What to Teach Instead

Order matters because percentages compound on updated amounts. Station activities with varied sequences allow trial and error, while whole-class sharing highlights patterns and corrects assumptions.

Active Learning Ideas

Shopping Spree: Discount Calculations

Provide catalogs or printed store flyers with prices. In small groups, students select items, apply successive discounts like 20% off then 10% off, and calculate final prices. Groups present one purchase scenario, justifying steps to the class.

45 min·Small Groups

Savings Challenge: Interest Tracker

Give each pair a starting savings amount. They apply quarterly interest rates, such as 2% per quarter for four quarters, recording changes on a shared chart. Pairs compare results and discuss why the amount grows nonlinearly.

30 min·Pairs

Stations Rotation: Percentage Scenarios

Set up stations for wage increases, price drops, tax additions, and mixed changes. Students rotate, solving two problems per station with calculators and recording justifications. Debrief as a whole class on common patterns.

50 min·Small Groups

Problem Construction: Real-Life Builds

Individually, students create a financial scenario with at least two percentage changes, such as a sale followed by tax. They swap with a partner for solving and feedback, then revise based on peer input.

35 min·Pairs

Real-World Connections

• Retailers use percentage discounts to attract customers during sales events, like a 25% off all shoes at a department store in Melbourne.
• Banks calculate simple interest on savings accounts using percentage rates, such as a 3% annual interest on a student's first $1000 saved.
• Government bodies apply Goods and Services Tax (GST) as a percentage added to the price of many goods and services, impacting consumer costs across Australia.

Assessment Ideas

Quick Check

Present students with a scenario: 'A video game costs $60. It is on sale for 15% off. What is the sale price?' Ask students to show their calculation steps and final answer on a mini-whiteboard.

Discussion Prompt

Pose the question: 'If you get a 10% pay rise one year and a 10% pay cut the next, are you earning the same amount as when you started? Explain your reasoning using an example.' Facilitate a class discussion to explore the changing base value.

Exit Ticket

Give each student a card with a starting price (e.g., $200) and two percentage changes (e.g., +20%, -10%). Ask them to calculate the final price and write one sentence about whether the final price is higher or lower than the original.

Frequently Asked Questions

Why doesn't a 10% increase and 10% decrease return to the original price?

After a 10% increase on $100, the new amount is $110, so the 10% decrease subtracts $11, resulting in $99. Students grasp this through visual models like number lines or price tag adjustments. Repeated examples in pairs build intuition for non-reversibility in percentages.

How to teach percentage discounts and taxes in Year 7?

Start with single-step calculations using real receipts, then add successive changes like discount plus GST. Use spreadsheets for tracking to show patterns. Encourage students to create their own shopping problems, promoting ownership and application to Australian contexts like 10% GST.

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

Active approaches like discount simulations with store flyers or interest trackers make the changing base tangible. Small group rotations allow peer correction during successive calculations, while constructing problems deepens justification skills. These methods turn abstract math into relatable finance, boosting engagement and retention over lectures.

What real-world examples for successive percentage changes?

Use scenarios like a 25% discount followed by 10% off clearance items, or 5% annual wage increases over years. Simple interest on savings provides positive growth examples. Students analyze impacts on budgets, connecting to Australian consumer math like superannuation basics, through collaborative case studies.