Florida B.E.S.T. MA.912.LT.4.7
The Standard
Identify and give examples of undefined terms; axioms; theorems; proofs, including proofs using mathematical induction; and inductive and deductive reasoning.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students classify mathematical terms and statements as undefined terms, axioms, theorems, or proofs. They distinguish pattern-based inductive reasoning from deductive reasoning and recognize the parts of a proof by mathematical induction.
What Mastery Looks Like
- Given a short list, students correctly label undefined terms, axioms, theorems, and proofs, then justify each choice. They can compare inductive and deductive arguments and complete a proof by induction using a base case and an inductive step.
Common Misconceptions
- Students may think an undefined term is meaningless or that an axiom must be proved. They may treat repeated examples as proof, confuse pattern-based reasoning with mathematical induction, or skip the base case.
How to Assess It
- Exit ticket: Label “point,” “through two points there is exactly one line,” and “vertical angles are congruent” as an undefined term, axiom, or theorem. Then explain why checking three cases does not prove a claim for all cases.
Lesson moves
Ways to Teach It
Give pairs a card set with points, lines, axioms, theorems, and proof excerpts; students sort the cards and defend one placement.
Have students respond to the prompt, “A pattern works for 20 cases, so is it proved for every case?” and compare reasoning.
Run an induction relay: teams complete the base case, induction hypothesis, and step for n + 1 for the sum of the first n odd numbers.
Examine a store’s claim based on three customer reviews, then identify the unsupported generalization and rewrite a valid conditional argument.
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Related Standards
- MA.912.LT.1.3
Apply mathematical induction in a variety of applications.
- MA.912.LT.4
Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.
- MA.912.LT.4.6
Apply methods of direct and indirect proof and determine whether a logical argument is valid.
- MA.912.LT.4.8
Construct proofs, including proofs by contradiction.
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