Compare And Resize

Overview

This one-to-one Year 10 lesson strengthens proportional reasoning through authentic supermarket and recipe contexts. The student connects ratios, equivalent rates and unit prices, then communicates a recommendation using calculations, tables and diagrams.

Learning intentions

• WALT identify and represent proportional relationships.
• WALT calculate and compare unit prices accurately.
• WALT use scale factors to resize a recipe.
• WALT justify a decision using mathematical evidence and clear representations.

Success criteria

• I can find a unit price and compare products fairly.
• I can use a scale factor to resize every ingredient in a recipe.
• I can record my working in a table or diagram.
• I can explain why one option is better value, not simply state an answer.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers: alignment with textbook content to provide relevant challenge.
• Mathematical practices: representing relationships, calculating accurately, communicating reasoning and evaluating the reasonableness of an answer.
• Key competencies: thinking; using language, symbols and texts; managing self; relating to others.

Lesson structure (60 minutes)

1. 0–7 min · Hook and diagnostic. Open with the supermarket comparison hook and show two differently sized products, such as six yoghurt pouches for $4.80 and ten pouches for $7.50. Ask, “Which is better value, and how can we prove it?” The student makes an initial choice, explains their instinct, and completes two quick calculations: cost per item and the ratio of quantity to price.

2. 7–17 min · Build the concept. Use the unit-price teaching slides to model unit price as total cost ÷ number of units, then represent the same comparison in a ratio table and a double number line. Explicitly distinguish “more product” from “better value”. The student copies the table, identifies the constant rate, and checks the result by multiplying the unit price back by the quantity.

3. 17–32 min · Supermarket investigation. Distribute the supermarket value and recipe worksheet and provide selected supermarket flyers or displayed product images. The student compares three pairs with different package sizes, including one special offer, recording package size, total price, unit price and a recommendation. Prompt: “What must stay the same for this comparison to be fair?” Ask the student to draw either a ratio table or a bar model for one comparison.

4. 32–45 min · Recipe scaling. Return to the recipe scaling instruction slide and introduce a recipe for four servings, such as 240 g flour, 180 ml milk, 2 eggs and 30 g butter. Ask the student to resize it for six servings using the scale factor (6 ÷ 4 = 1.5). The student completes the recipe section of the supermarket value and recipe worksheet, showing the scale factor, a table of original and new quantities, and a diagram or annotated recipe card. Discuss which quantities are exact and which may require a practical decision, such as eggs.

5. 45–53 min · Explain and challenge. The student explains one supermarket comparison and the recipe scaling to the teacher as their “partner”, using the completed table or diagram. Use the explanation prompts: “The relationship is proportional because…”, “The unit rate tells me…”, and “My recommendation is justified by…”. Ask one challenge question: “If the recipe serves ten people, what changes, and how could you check your answer?”

6. 53–60 min · Plenary and exit check. Display the final check slide and ask the student to solve: “A 750 g cereal box costs $6.60. A 1.2 kg box costs $9.36. Which has the lower price per 100 g?” Finish with the exam command words reference mat available as a support for the written justification. The student records the calculation, recommendation and one sentence explaining how proportional reasoning helped.

Resources

• the complete proportional reasoning slide deck
• the supermarket value and recipe worksheet
• Supermarket flyers or teacher-prepared product images with prices and quantities
• Calculator
• Ruler and coloured pens or highlighters
• Whiteboard and markers
• Recipe ingredients or recipe cards, if available
• the exam command words reference mat

Assessment

• During the diagnostic, check whether the student compares total prices or correctly calculates a common unit rate.
• Review the worksheet for accurate division, equivalent ratios, scale factors, labelled tables or diagrams, and a justified recommendation.
• Use the final cereal question as an exit check. Note whether the student converts units consistently, calculates price per 100 g, and explains the proportional relationship in words.

Differentiation

• For support, use friendly numbers first, provide a partially completed ratio table, and prompt with “What is one unit?” and “What is the multiplier from the original quantity?”
• Allow the student to use a calculator after setting up the calculation, while requiring an estimate before calculating.
• Use colour coding: one colour for quantity, one for price and one for the constant unit rate. Read all written instructions aloud and allow oral explanation before recording.
• For extension, ask the student to compare a bulk offer with a discount, calculate the effective unit price, and identify when an apparently proportional situation is not proportional, such as a fixed delivery fee.