Methods of Proof
Understand and apply different methods for proving mathematical statements, including direct proof, proof by contrapositive, and proof by contradiction.
About This Topic
Understand and apply different methods for proving mathematical statements, including direct proof, proof by contrapositive, and proof by contradiction.
Key Questions
- Compare the logical structure of a direct proof with a proof by contradiction.
- Explain the fundamental assumption made at the beginning of a proof by contradiction.
- Analyse the statement 'The square root of 2 is irrational' and outline the steps to prove it by contradiction.
Active Learning Ideas
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Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
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