Comparing Best Buys

Lesson Objectives

By the end of the lesson, students will:

1. Understand how to determine the "best buy" using unit cost comparison.
2. Develop problem-solving skills to compare deals and prices in real-world contexts.
3. Confidently complete differentiated tasks, using mathematical reasoning to justify decisions.

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Curriculum Alignment

Key Stage 3: Mathematics National Curriculum for England

• Ratio, Proportion and Rates of Change:
  • Solve problems involving direct proportion, including best-buy problems (NCETM core content).
  • Develop fluency in using unit ratios and proportional reasoning in practical scenarios.

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Lesson Outline (60 Minutes)

Starter Activity (10 minutes)

1. Engage with Real-World Context:

   • Present students with two similar items in contrasting packaging (e.g., crisps, drinks).
   • Ask: “If you were shopping, which one would you buy? Why?”
   • Write their initial responses on the board and steer discussion towards the importance of determining value for money.

2. Interactive Warm-Up:

   • Display simple examples on the board (e.g., "6 apples for £1.80, or 10 apples for £2.50").
   • Ask pairs to calculate the unit price for each option and share their answers.
   • Introduce the concept of "best buy" by identifying the deal with the lower unit cost.

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Main Teaching and Guided Practice (25 minutes)

1. Modelling the Concept (10 minutes):

   • Explicitly teach how to calculate the unit cost: [ \text{Unit cost} = \frac{\text{Total cost}}{\text{Number of units}} ]
   • Use concrete, age-appropriate examples (e.g., price of snacks, items students might encounter shopping).
   • Work through examples step-by-step, ensuring all students are confident:
     • Example 1: £5 for 12 cans of drink.
     • Example 2: £3.50 for an 8-pack.
   • Include conversions for comparison when units differ (e.g., grams vs kilograms).

2. Guided Questions (5 minutes):

   • Pose questions for the whole class:
     • "If two items have the same price but different quantities, how do we decide which is the better deal?"
     • "What happens if you don’t compare like-for-like measurements?"

3. Think-Pair-Share (10 minutes):

   • Distribute mini whiteboards to pairs. Provide additional examples for students to calculate best buys.
   • Encourage collaboration, and circulate to check understanding.
   • Use misconceptions as opportunities for teaching points (e.g., forgetting to compare equivalent units).

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Independent Practice (20 minutes)

Differentiated Worksheets:

1. Beginner Worksheet (Green):

   • Straightforward unit price comparisons, e.g., "3 chocolate bars for £2.10 versus 5 chocolate bars for £3.40."
   • Simple, consistent units (e.g., no conversions).

2. Intermediate Worksheet (Amber):

   • More varied pricing structures requiring unit price calculations and some conversions, e.g., "1.5L of juice for £2.25 or 2.25L for £3.60."
   • Includes a mix of litres, grams, and packs of items.

3. Challenge Worksheet (Red):

   • Real-life shopping scenarios with multiple items to compare.
   • Open-ended tasks requiring students to justify their choice of best buy in paragraph form.
   • For example: "You have £10. Compare deals for two different brands of coffee and choose which would save you money in the long run."

Encourage students to move between worksheets if they complete one level early or demonstrate confidence with a particular skill.

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Plenary (5 minutes)

1. Class Discussion:

   • Revisit the starter question: "How can you decide which product is the best buy?"
   • Ask students to explain which maths skills helped them.

2. Exit Question:

   • Pose a single-question challenge (e.g., "A 1kg bag of rice costs £1.90. A 2kg bag costs £3.60. Which is better value?"). Students write their answer as they leave.

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Resources Needed

• Interactive whiteboard.
• Mini whiteboards and pens for pair activities.
• Differentiated worksheets (photocopied and distributed).
• Everyday shopping examples for the starter (e.g., branded vs non-branded snack packs).

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Differentiation and Inclusion

1. Scaffolding: Green worksheet provides simpler calculations for students requiring additional support. Paired working helps with confidence.
2. Stretch and Challenge: Red worksheet encourages higher-order thinking and reasoning. Able students can move quickly into these open-ended problems.
3. EAL Support: Use visuals and real-life examples to make concepts accessible.
4. SEND Considerations: Break tasks into manageable chunks. Provide templates for calculations if necessary.

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Teacher Reflection

• Did students confidently calculate unit prices across all ability levels?
• Were misconceptions about proportional reasoning addressed effectively?
• Did all students engage in higher-level reasoning skills through discussion or practice?