Working with Percentages

Lesson 3 of 4: Functional Maths Foundations

Duration: 45 minutes

Class size: 2 students

Year Level: 10, NSW Curriculum-aligned

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Learning Objectives

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

• Understand percentages in context and calculate percentages of quantities.
• Apply percentage calculations to solve real-life problems such as discounts and sales.
• Develop fluency in converting between fractions, decimals and percentages relevant to everyday financial situations.
• Use estimation strategies to judge reasonableness of answers involving percentages.

This lesson aligns with the NSW Mathematics Stage 5 outcomes where students:

• Use mathematical modelling to solve financial and practical problems involving percentages.
• Apply understanding of percentages in problem-solving contexts, including discounts and sales.
• Develop proficiency in number calculations and financial literacy skills.

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Curriculum References

NSW Mathematics Syllabus Stage 5 (Year 10)

• MA5.4-9WM: Solve financial problems involving percentages, discounts, profit and loss.
• MA5.4-10SP: Use mathematical modelling to solve practical financial problems.
• Emphasis on functional mathematics foundations to connect maths concepts to real life.

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Lesson Outline

Time	Activity	Details
0-5 mins	Warm-up: Percentage Concept Recap	Brief Q&A to check prior knowledge of percentages. Encourage students to say how they understand “percentage” and recall key facts (e.g., percentage means per 100).
5-15 mins	Activity 1: Calculating Percentages - Basic Practice	- Use simple numbers to calculate percentages of quantities (e.g., 25% of 80, 15% of 200). - Students work individually with provided worksheet problems, then discuss solutions for feedback. - Emphasise relationship between fractions, decimals, and percentages.
15-30 mins	Activity 2: Real-Life Applications - Discounts and Sales	- Present real-life scenarios like a 30% sale on clothing, calculate sale price. - Students estimate and then calculate discounts. - Extend to questions like “If a shirt is $120 and there is a 15% discount, what is the sale price?” - Include problems with GST included and excluded to link financial literacy. - Students create their own real-life problems based on shopping or finances they are familiar with.
30-40 mins	Activity 3: Problem Solving & Discussion	- Students tackle a small set of multi-step problems involving percentages, discounts, and price increases. - Discuss with teacher the steps involved and reasoning. - Use practical examples (e.g., calculating tax, tipping, sales tax).
40-45 mins	Assessment & Reflection	- Oral questioning and quick worksheet quiz for formative assessment. - Students reflect on what they have learnt and describe how percentages are useful in real life. - Identify any areas needing review next lesson.

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Resources Needed

• Printed worksheets with percentage calculation questions and real-life discount problems.
• Calculators for accuracy checks (optional).
• Whiteboard or large paper for working through examples interactively.
• Everyday items photos or printouts labeled with prices to create realistic problems.

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Teaching Strategies

• Use scaffolding: begin with simple percentage calculations and extend to real-life problems.
• Use concrete contexts: relate percentages to shopping and finance to make maths relevant.
• Encourage student talk and reasoning: ask students to explain their thinking clearly.
• Use modelling: demonstrate calculations step-by-step before students practise independently.
• Build confidence with estimation to help students check answers realistically.

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Assessment Criteria

• Student accurately calculates percentages of given quantities.
• Student applies percentage concepts to solve discounts and sale price problems.
• Student estimates results and explains reasoning.
• Student creates simple real-life problems involving percentages.

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Extension Ideas

• Introduce compound percentage problems such as successive discounts.
• Explore percentage increase or decrease scenarios like tax increases or price changes over time.
• Use digital tools or apps to simulate shopping discounts.

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Notes for Teacher

• This lesson is designed for two students — ensure plenty of interaction and personalised feedback.
• Keep language clear, avoid jargon initially, focusing on foundational understanding.
• Use concrete examples from student interests where possible (e.g., favourite shops or hobbies).
• Assess understanding continuously with oral questions during activities.

This lesson builds directly on foundational maths skills and connects with students’ daily lives, in line with NSW curriculum expectations for Year 10 functional mathematics. It prepares students for the next and final lesson in the unit developing deeper financial problem solving with percentages.

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If you require, I can also quickly generate the worksheets or example problems tailored for this lesson.