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MathidiaMathematics Academy
Proof, modelling and Year 10 synthesis
Lesson 71 of 75
Introduction

Algebraic proof

Objective. Prove parity, divisibility and consecutive-integer results.

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

Learn: the key idea

Algebraic proof is developed here as connected GCSE mathematics, not a memorised shortcut. Construct arguments, test assumptions and connect GCSE methods. The lesson moves from a precise representation and key definitions to fluent procedure, linked reasoning and an unfamiliar application. Learners compare possible methods, state restrictions and assumptions, preserve exact values where appropriate, and justify accuracy, notation and units before evaluating whether the result is mathematically and contextually reasonable.

Worked example

Prove n(n+1) is even. State the key fact.

Prove n(n+1) is even
Illustrated card showing Prove n(n+1) is even
  1. 1Translate the information into a labelled diagram, table, graph or algebraic statement and identify every constraint.
  2. 2Select the most efficient GCSE method, explain why its conditions apply, and keep exact values until approximation is requested.
  3. 3Carry out each transformation on a separate justified line, tracking signs, units, domains and required accuracy.
  4. 4Verify with substitution, an inverse method, estimation or a second representation. The checked result is one of consecutive integers is even.

Answer: one of consecutive integers is even

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. A common error in algebraic proof is applying a familiar rule before checking its conditions, domain or direction. Name the structure first, retain exact values, and test the final result against every original constraint.

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