Florida B.E.S.T. MA.912.LT.4.6

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

The Standard

Apply methods of direct and indirect proof and determine whether a logical argument is valid.

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

Teacher's field guide

What Students Need to Do: Students write direct proofs and indirect proofs using definitions, algebra, and logical steps. They also decide whether a conclusion follows from given premises and explain why.
What Mastery Looks Like: Students organize a proof into justified steps and clearly state assumptions and conclusions. They choose direct proof or contradiction appropriately and can identify invalid reasoning with a counterexample or truth table.
Common Misconceptions: Students may assume a true conclusion makes an argument valid, even when it does not follow from the premises. They may also confuse a converse with the original statement or begin an indirect proof with the wrong negation.
How to Assess It: Use a two-part exit ticket: prove that the sum of two even integers is even, then test whether “If p, then q; q; therefore p” is valid.

Lesson moves

Give groups statement and reason cards to arrange into a direct proof that the sum of two odd integers is even.
Ask students to explain why a true conclusion does not always mean the argument used to reach it is valid.
Play Valid or Invalid with argument cards, requiring teams to name the rule used or provide a counterexample.
Analyze a courtroom claim by listing its premises, conclusion, hidden assumptions, and whether the conclusion follows logically.

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