Understanding Percentages

Year Level

Year 9 Australian Curriculum (v9) Mathematics

Duration

60 minutes

Number of Students

20

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Learning Objectives

By the end of this lesson, students will be able to:

• Convert between percentages, decimals and fractions fluently.
• Calculate percentages of amounts using efficient strategies.
• Understand and calculate Goods and Services Tax (GST) on prices both before and after GST is added.
• Apply their knowledge in a real-world context by comparing prices with GST included and excluded in a mock shopping activity.
• Communicate their reasoning and explain calculations in the context of consumer arithmetic.

Curriculum References

• AC9M9N06: Use operations with rational numbers (including percentages, decimals and fractions) to solve problems using efficient calculation strategies.
• AC9M6N07: Solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts and GST.
• AC9M6N09: Use mathematical modelling to solve problems involving percentages in financial contexts, choose efficient strategies, and interpret solutions.
• AC9M7N09: Use mathematical modelling and representations to solve financial problems involving percentages, justifying choices made using digital tools.
  All adapted from Australian Curriculum v9 Content Descriptions for Years 6–9 Mathematics【2:AC9M7N06.md】【18:AC9M6N07.md】【4:AC9M9A01.md】【8:AC9M7N09.md】.

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Resources Needed

• Whiteboard and markers
• Student notebooks
• Calculators (optional)
• Printed mock shopping catalogues/lists showing product prices both including GST and excluding GST
• GST calculation worksheets
• Percentage, decimal and fraction conversion charts
• Digital tools or apps for calculation (optional)

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Lesson Structure

Introduction (10 minutes)

• Begin with a quick recap question: "What do we mean by 100%?" Confirm that 100% means the whole.
• Use visual models (e.g., 10x10 grid) to show how fractions, decimals and percentages relate (e.g., 0.25 = 25% = 1/4).
• Model a few conversions on the board:
  • Convert 0.3 to a percentage (30%)
  • Convert 3/5 to a percentage (60%)
  • Convert 45% to decimal (0.45)
• Explain the connection between them clearly and relate the conversions to everyday examples.

Activity 1: Converting Between Formats (10 minutes)

• Students work individually or in pairs with conversion charts and practice converting between decimals, percentages and fractions.
• Tasks include:
  • Convert 0.125, 0.4, 0.75 to percentages and fractions.
  • Convert 20%, 55%, 12.5% into decimals and simplified fractions.
• Teacher circulates, giving personalised feedback and affirming correct strategies.

Activity 2: Finding Percentages of Amounts (10 minutes)

• Demonstrate calculating percentages of amounts step-by-step:
  • Example: Find 25% of 160.
  • Explain quick methods (e.g., 25% is one quarter, so divide by 4).
• Provide practice problems:
  • Find 15% of 200.
  • Find 8% of 350.
• Students can use mental math, paper calculations or calculators.

Activity 3: Calculating GST Prices (15 minutes)

• Introduce GST (10%) as a real-world application of percentages.
• Show how to calculate:
  • Price before GST given price after GST.
  • Price after adding 10% GST.
• Example on the board:
  • Original price $50; GST = 10% of $50 = $5; Price after GST = $55
  • Price after GST $55; Price before GST = $55 ÷ 1.10 = $50
• Provide worksheet problems for practice.

Activity 4: Mock Shopping Task (15 minutes)

• Distribute mock shopping catalogues with items showing prices both including GST and excluding GST.
• Students work in pairs to:
  • Identify GST amount for each item.
  • Compare prices of similar products including and excluding GST.
  • Calculate price before GST for GST-included prices.
  • Discuss why GST is important in consumer purchases.
• Students prepare a short explanation for their calculations and decisions.

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Assessment

• Informal assessment during activities through observation and questioning.
• Collect worksheets for formative assessment of conversion and GST calculations.
• Evaluate students' explanation ability during the mock shopping task.

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Differentiation

• Provide conversion charts and calculation templates for students needing extra support.
• Challenge advanced students by:
  • Calculating GST for bulk purchases.
  • Exploring reverse GST problems with different GST rates.
  • Explaining real-world GST applications beyond retail, such as import taxes.

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Reflection and Closing (5 minutes)

• Discuss with students:
  • How percentages relate to decimals and fractions.
  • The importance of GST in pricing and consumer decisions.
• Quick quiz — matching decimals, fractions and percentages.
• Remind students to look for percentages in everyday life and consider what they represent.

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This lesson plan ensures alignment with the Australian Curriculum (v9) focusing on key Year 9 mathematics skills around percentages, decimals, fractions, and consumer arithmetic, specifically GST calculation and application, embedding practical and relevant financial literacy skills for students【2:AC9M7N06.md】【18:AC9M6N07.md】【8:AC9M7N09.md】.