Florida B.E.S.T. MA.912.LT.4.9
The Standard
Construct logical arguments using laws of detachment, syllogism, tautology, contradiction and Euler Diagrams.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use given statements to reach valid conclusions through detachment and syllogism. They test arguments using tautologies, contradictions, and Euler diagrams.
What Mastery Looks Like
- A student can identify premises, reach a valid conclusion, and name the reasoning used. The student can check a claim with logical cases or an Euler diagram and explain why an invalid argument fails.
Common Misconceptions
- Students often affirm the consequent, treating "If p, then q" and q as proof of p. They may chain statements backward or read overlap in an Euler diagram as full inclusion. They may call a statement a tautology because one example is true, or confuse a contradiction with any false statement.
How to Assess It
- Exit ticket: From "All squares are rectangles," "All rectangles are quadrilaterals," and "WXYZ is a square," derive a conclusion and name each inference. Draw nested Euler circles, then classify p ∨ ¬p and p ∧ ¬p as tautology or contradiction.
Lesson moves
Ways to Teach It
Use labeled hoops and student name cards to model set relationships, then have groups state conclusions supported by the Euler diagram.
Ask students to explain why "If it rains, streets are wet; streets are wet; therefore it rained" is invalid.
Run a logic relay where teams sort cards into detachment, syllogism, tautology, contradiction, or invalid, then defend one choice.
Have students analyze school club eligibility rules, draw an Euler diagram, and write a valid conclusion from two stated conditions.
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Related Standards
- MA.912.LT.4.1
Translate propositional statements into logical arguments using propositional variables and logical connectives.
- 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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