Florida B.E.S.T. MA.912.LT.4

MA.912.LT.4 is a B.E.S.T. standard. These are the benchmarks under it.

• MA.912.LT.4.1

  Translate propositional statements into logical arguments using propositional variables and logical connectives.

• MA.912.LT.4.10

  Judge the validity of arguments and give counterexamples to disprove statements.

• MA.912.LT.4.2

  Determine truth values of simple and compound statements using truth tables.

• MA.912.LT.4.3

  Identify and accurately interpret “if…then,” “if and only if,” “all” and “not” statements. Find the converse, inverse and contrapositive of a statement.

• MA.912.LT.4.4

  Represent logic operations, such as AND, OR, NOT, NOR, and XOR, using logical symbolism to solve problems.

• MA.912.LT.4.5

  Determine whether two propositions are logically equivalent.

• MA.912.LT.4.6

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

• MA.912.LT.4.7

  Identify and give examples of undefined terms; axioms; theorems; proofs, including proofs using mathematical induction; and inductive and deductive reasoning.

• MA.912.LT.4.8

  Construct proofs, including proofs by contradiction.

• MA.912.LT.4.9

  Construct logical arguments using laws of detachment, syllogism, tautology, contradiction and Euler Diagrams.

01

What Students Need to Do

Students translate claims into symbols and use logical connectives, truth tables, and equivalences to analyze them. They test arguments for validity and prove claims directly, by contrapositive, or by contradiction.

02

What Mastery Looks Like

Students correctly build and read truth tables, test argument validity, and identify equivalent statements. They choose a suitable proof method and justify each step, or disprove a claim with a counterexample.

03

Common Misconceptions

Students often confuse a statement with its converse, inverse, or contrapositive. They may treat a true conclusion as proof that an argument is valid. They may also use several examples as proof of a general claim instead of giving a logical argument.

04

How to Assess It

Exit ticket: Complete the truth table for [(p → q) ∧ p] → q, then state whether it is a tautology. Explain how the table supports modus ponens.

1. 01

   Give pairs proposition cards and connective cards, then have them build compound statements and verify each with a truth table.

2. 02

   Ask students to explain why a valid argument can have false premises but cannot have true premises and a false conclusion.

3. 03

   Play Truth Table Relay: teams complete one row at a time, then check whether the assigned argument form is valid.

4. 04

   Analyze a short advertisement, identify its premises and conclusion, then judge the reasoning and check whether the premises are true.