Understanding Percentages

Year Level

Year 9 Australian Curriculum (v9) Mathematics

Duration

60 minutes

Number of Students

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】.

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)

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.

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.

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.

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.

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】.