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MathidiaMathematics Academy
Financial mathematics and modelling
Lesson 75 of 75
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Year 9 synthesis

Objective. Solve unfamiliar problems spanning the full Key Stage 3 curriculum.

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

Learn: the key idea

Year 9 synthesis questions combine multiple Key Stage 3 topics into a single unfamiliar problem, requiring pupils to decide which methods to apply and in what order, rather than practising one isolated skill. A typical synthesis question might require forming an equation from a worded context, solving it algebraically, and then interpreting the numerical result back within the original real-world setting, such as cost, geometry or probability. Success depends on reading the whole problem carefully first, identifying what is known and what is being asked, and breaking the problem into smaller manageable stages before attempting any calculation. Checking that a final answer makes sense in the original context, such as a sensible age, length, or price, is an important final step.

Worked example

A rectangular garden has a length that is 3 m more than its width. Its perimeter is 26 m. Find the garden's width and length as a multi-step synthesis problem.

Diagram of a rectangle
  1. 1Let the width be w, so the length is w + 3.
  2. 2The perimeter formula gives 2(w + (w + 3)) = 26.
  3. 3Simplify inside the brackets: 2(2w + 3) = 26, so 4w + 6 = 26.
  4. 4Subtract 6 and divide by 4: 4w = 20, so w = 5, giving length = 8.

Answer: Width = 5 m, length = 8 m

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 sometimes dive into calculating with the first numbers they see without reading the whole problem and planning the order of steps, which causes them to use the wrong method entirely. Always read the full problem and plan the required stages before starting any calculation.

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