Proof by Exhaustion

• Identify proof by exhaustion accurately in a familiar context.

  Activities — Modelled example on the board · Paired talk task · Mini whiteboard check

  Assessment — Exit ticket of four short items

• Identify proof by exhaustion independently in an unfamiliar context.

  Activities — Independent worksheet · Card sort · Concept-check quiz

  Assessment — Marked worksheet with a marking scheme

• Explain proof by exhaustion accurately in a familiar context.

  Activities — Modelled example on the board · Paired talk task · Mini whiteboard check

  Assessment — Exit ticket of four short items

• Explain proof by exhaustion independently in an unfamiliar context.

  Activities — Independent worksheet · Card sort · Concept-check quiz

  Assessment — Marked worksheet with a marking scheme

• Explain the reasoning behind proof by exhaustion using correct vocabulary.

  Activities — Talk-through with a partner · Write a model answer · AI Tutor Socratic session

  Assessment — Extended written response, levelled

• Calculate proof by exhaustion accurately in a familiar context.

  Activities — Modelled example on the board · Paired talk task · Mini whiteboard check

  Assessment — Exit ticket of four short items

• Calculate proof by exhaustion independently in an unfamiliar context.

  Activities — Independent worksheet · Card sort · Concept-check quiz

  Assessment — Marked worksheet with a marking scheme

• Compare proof by exhaustion accurately in a familiar context.

  Activities — Modelled example on the board · Paired talk task · Mini whiteboard check

  Assessment — Exit ticket of four short items

• Compare proof by exhaustion independently in an unfamiliar context.

  Activities — Independent worksheet · Card sort · Concept-check quiz

  Assessment — Marked worksheet with a marking scheme

• Explain the reasoning behind proof by exhaustion using correct vocabulary.

  Activities — Talk-through with a partner · Write a model answer · AI Tutor Socratic session

  Assessment — Extended written response, levelled

• Algebraic ProofUnit
• CounterexamplesUnit
• MatricesDomain

• Counterexamples
• Algebraic Proof
• Problem Solving

Students treat proof by exhaustion as a rule to memorise rather than a relationship to understand.

Correction — Anchor the rule in a visual model first, then abstract it — the model is the explanation.

Learners apply the correct method to proof by exhaustion but ignore the context or units.

Correction — Require an answer sentence with units on every applied question.