Year 8 synthesis

Objective. Solve mixed problems spanning the complete Year 8 programme.

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

Learn: the key idea

Year 8 synthesis develops a connected mathematical idea rather than an isolated trick. Combine ideas, test conjectures and communicate complete solutions. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

A taxi charges £3 plus £7 per mile. Find the cost of 5 miles.

1 $Identify the known information, the unknown and any conditions.$
2 $Choose a diagram, table, graph or algebraic representation that exposes the structure.$
3 $Apply the relevant rule one justified step at a time, keeping exact values where useful.$
4 $Check by substitution, inverse reasoning or estimation. The result is £38.$

Answer: £38

Concept mastery

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

Complete a practice set to see your concept breakdown here.

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. A common error in year 8 synthesis is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

Your progress

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