Florida B.E.S.T. MA.912.LT.4.8

MathGrades 9–12Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.

The Standard

Construct proofs, including proofs by contradiction.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students turn a mathematical claim into a sequence of statements supported by clear reasons. They choose a direct approach or assume the claim is false and derive an impossible result.
What Mastery Looks Like: A student writes a complete chain of justified statements using definitions, properties, and known results. In a contradiction proof, the student states the negation, identifies the contradiction, and connects it back to the original claim.
Common Misconceptions: Students may use the claim itself as a reason, which creates circular logic. They often prove the converse instead of the given claim. In contradiction proofs, they may negate the claim incorrectly or reach a surprising result that is not logically impossible.
How to Assess It: Give this exit ticket: Prove by contradiction that if n² is odd, then n is odd. Require each statement to include a reason.

Lesson moves

Use colored cards to arrange shuffled statements and reasons into a proof, then remove one card and explain the resulting gap.
Ask students to write how assuming a claim is false can show it must be true, using an odd-number example.
Run a proof-error hunt where pairs mark the first unjustified step in four short proofs and repair it.
Give a scheduling scenario with conflicting constraints, and have students prove that no proposed schedule can satisfy every condition.

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