Lesson Plan: Proof by Contradiction Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to describe what proof by contradiction is and use it to determine whether a conjecture is true or false.


Students will be able to

  • determine the negation of the statement that is being set out to prove,
  • use algebraic methods to prove by contradiction that a statement is true (that the negation is false),
  • recall standard proofs, such as the irrationality of root 2 or the infinity of primes,
  • discern errors in proofs related to proof by contradiction and make amendments or changes to accurately prove a statement using proof by contradiction.


Students should already be familiar with

  • mathematical proofs such as by deduction, exhaustion, and counter example,
  • algebraic methods,
  • properties of numbers such as rational and irrational numbers, multiples, factors, prime numbers, odd and even numbers, and squared and cubed numbers.


Students will not cover

  • proof by deduction, exhaustion, counter example, or mathematical induction.

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