Finding the Best Buy

National Curriculum Links

• KS4 Mathematics (Year 10 – GCSE Foundation / Higher)
• Number – Fractions, Decimals and Percentages:
  • Solve problems involving percentage change, including original value problems and simple interest.
• Ratio and Proportion:
  • Use ratio notation, including reduction to simplest form.
  • Solve problems involving direct and inverse proportion, including graphical and algebraic representations.
• Problem Solving:
  • Apply maths in real-life contexts and multi-step problems.

The lesson aligns with the programme of study for KS4 under the theme of applying mathematics to everyday contexts, including interpreting and comparing measurements and costs.

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Lesson Overview

• Duration: 60 minutes
• Class size: 25
• Topic: Best Buy – Comparing Value for Money Using Ratios and Unit Pricing
• Prior Knowledge Required:
  • Understanding of ratios, decimals, percentages
  • Basic multiplication and division
  • Familiarity with real-world contexts (shopping / money)

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Learning Objectives

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

1. Calculate unit prices by dividing total price by amount (weight, volume, quantity).
2. Compare products using unit prices to identify the better value purchase ("Best Buy").
3. Apply ratio and proportional reasoning to real-life scenarios involving shopping.
4. Interpret and explain the findings clearly, justifying their choice.

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Resources Needed

• Whiteboard and markers
• Worksheets with real-life shopping scenarios (food, drink, technology, etc.)
• Calculators
• Product price labels / pictures for class demonstration
• Mini whiteboards and pens for group activities
• Projector (optional) to display examples

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Lesson Structure

1. Introduction (10 minutes)

• Engage: Start with an interactive question—
  “If you had £3 and some snacks to buy, how do you decide which is the best value?”
• Show two products of different sizes and prices (e.g., 500g bag of crisps for £1.99, 250g bag for £1.20).
• Ask students to estimate which is the better buy and then discuss why simply looking at the price can be misleading.
• Introduce the concept of unit price, explaining it as the cost per 100g, litre, or item, which allows fair comparison.
• Write the key definition on the board:

  Unit Price = Total Price ÷ Quantity (weight, volume, number)

• Link this to the curriculum by highlighting how this applies ratio and proportion in real-life contexts.

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2. Guided Activity (15 minutes)

• Teacher Demonstration:

  • Walkthrough calculating the unit price of three products, e.g., milk bottles of different volumes and prices, sweets sold by weight, packs of toilet rolls, etc.
  • Use both decimals and fractions interchangeably, showing flexibility with form.
  • Show how to write the ratio price per 100g or per litre for easy comparison.

• Group Task:

  • Divide students into 5 groups, each with a worksheet containing a different set of products and prices.
  • Each group calculates unit prices for their products and decides the best buy.
  • Encourage clear written explanations justifying their answer referencing their calculations.

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3. Independent Practice (20 minutes)

• Worksheet exercises:

  • Varied questions: find unit prices, compare, then pick best buy.
  • More complex examples: multi-step problems involving percentage discounts or special offers (e.g., buy one get one half price).
  • At least one problem requires students to calculate the total price after discount and then find unit price to compare.

• Circulate to support students needing help with dividing decimals and working with percentages.

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4. Formative Assessment & Discussion (10 minutes)

• Quick quiz (5 questions) on mini whiteboards:
  • Calculate unit price for given products.
  • Identify best buy between two options.
• Invite several students to explain their reasoning aloud to the class.
• Address any misconceptions (e.g., forgetting to adjust units, errors with decimals).

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5. Plenary (5 minutes)

• Recap key points:
  • How unit price helps shop smarter.
  • Importance of careful calculations for real-life decisions.
• Ask students:
  “How can these skills help you outside school?”
• Set a short review homework: find two similar products at home or online and compare their unit prices, bringing their conclusion to the next lesson.

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Assessment and Differentiation

• Formative assessment: Mini whiteboard quiz and group explanations give immediate insights.
• Differentiation:
  • Support for weaker pupils via one-to-one or paired work with scaffolded worksheets.
  • Challenge tasks include percentage discounts and multi-step reasoning for higher ability students.
  • Extension task: convert units (e.g., grams to kilograms) if time permits.

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Teacher Notes

• Emphasise that unit prices allow fair comparisons regardless of packaging sizes.
• Use real brands and common products relevant to students’ experiences to increase engagement.
• Highlight the relevance of ratio, proportion, and decimals as key GCSE skills.
• Encourage students to articulate mathematical reasoning using correct terms, e.g., “The unit price is calculated by dividing the total price by the quantity in grams.”
• Be mindful of different calculator skills and ensure all students understand inputs clearly.

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This lesson equips Year 10 students with functional numeracy skills fully aligned to the National Curriculum, empowering them to interpret and act on everyday maths problems meaningfully and confidently.