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MathidiaMathematics Academy
Mathematical reasoning and modelling
Lesson 73 of 75
Standard practice

Multi-step modelling

Objective. Select and connect methods in unfamiliar situations.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Multi-step modelling means breaking an unfamiliar real-world problem into smaller mathematical steps, choosing which method fits each stage, and connecting the results together to reach a final answer. It often requires combining skills from different topics, such as percentages, ratio or geometry, within one extended question. Reading carefully to identify what each sentence tells you, and what the question ultimately asks for, is key to planning the right sequence of steps. Example: finding the cost of tiling a floor requires calculating the area first, then applying a price per square metre, two connected but distinct stages.

Worked example

A rectangular garden measuring 8 m by 5 m is to be covered with turf costing £3 per square metre. Use multi-step modelling to find the total cost of the turf.

£3.00
Money illustration for £3
  1. 1Find the area of the garden: 8 × 5.
  2. 2This gives an area of 40 square metres.
  3. 3Multiply the area by the cost per square metre: 40 × £3.
  4. 4The total cost of the turf is £120.

Answer: £120

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

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Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

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Common mistake. Pupils often attempt the final calculation immediately without identifying the smaller steps needed first; always plan out each stage of the problem on paper before starting any single calculation.

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