Standard 4 : Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.



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General Information

Number: MA.912.LT.4
Title: Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
Strand: Logic and Discrete Theory

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.LT.4.1: Translate propositional statements into logical arguments using propositional variables and logical connectives.
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.
Clarifications:
Clarification 1: Instruction focuses on recognizing the relationships between an “if…then” statement and the converse, inverse and contrapositive of that statement.

Clarification 2: Within the Geometry course, instruction focuses on the connection to proofs within the course.

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.
Clarifications:
Clarification 1: Within the Geometry course, proofs are limited to geometric statements within the course.
MA.912.LT.4.9: Construct logical arguments using laws of detachment, syllogism, tautology, contradiction and Euler Diagrams.
MA.912.LT.4.10: Judge the validity of arguments and give counterexamples to disprove statements.
Clarifications:
Clarification 1: Within the Geometry course, instruction focuses on the connection to proofs within the course.


Related Access Points

This cluster includes the following access points.

Access Points

Access Point Number Access Point Title
MA.912.LT.4.AP.3: Identify and accurately interpret “if…then,” “if and only if,” “all” and “not” statements.
MA.912.LT.4.AP.10: Select the validity of an argument or give counterexamples to disprove statements.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Lesson Plans

Name Description
Basic Definitions in Geometry:

A set of basic definitions in geometry (line segment, ray, angle, perpendicular lines, and parallel lines) is addressed. The notation used in naming each defined term is also emphasized.

Musical Chairs with Words and a Ball:

This lesson introduces students to concepts and skills that they will use throughout the year. Students will learn that the terms point, and line are considered "undefined." Students will play musical chairs while learning to develop precise definitions of circle, angle, parallel line, and perpendicular line, using counterexamples at different classroom stations. Students will identify models, use notation, and make sketches of these terms.

Sage and Scribe - Points, Lines, and Planes:

Students will practice using precise definitions while they draw images of Points, Lines, and Planes. Students will work in pairs taking turns describing an image while their partner attempts to accurately draw the image.