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2022 G-RL-1-3

Page history last edited by Brigit Minden 11 months, 3 weeks ago

G.RL.1.3

G.RL.1.3 Assess the validity of a logical argument and give counterexamples to disprove a statement.

In a Nutshell

Determining the validity of a conditional statement further extends students’ understanding of deductive and inductive reasoning. Being able to provide a counterexample as to why a conditional statement is false will assist students in their geometry course when categorizing polygons, among other concepts. Deciding if an argument follows the correct form of logical reasoning helps students assess its validity.

Student Actions	Teacher Actions
Develop mathematical reasoning by deciding the truth values of conditional statements using logical reasoning and providing counterexamples for false statements. Develop the ability to communicate mathematically by writing or verbalizing relevant counterexamples for conditional statements with a truth value of false.	Facilitate meaningful mathematical discourse by leading classroom discussions in which students will compare and analyze responses from fellow students as to the validity of a conditional statement. Elicit and use evidence of student thinking by having students give their responses, either verbal or written to situations involving conditional statements.
Key Understandings	Misconceptions
A conditional statement is true when both the hypothesis and conclusion are true. A conditional statement is false when the hypothesis is true and the conclusion is false. Only one valid counterexample is needed to prove a statement false. A biconditional statement is formed when a true conditional statement is combined with its true converse.	Students do not understand that only one counterexample is needed to prove a statement false. Students believe that theorems are always bi-conditionals. Students think that all related statements will have the same truth value every time. Students believe that one example will prove a statement to be true in general.
Knowledge Connections
Prior Knowledge	Leads to
Apply probability concepts to real-world situations to make informed decisions. (A1.D.2.4)	Identify and use the mathematical model that is most appropriate to solve problems. (A2.A.2.4) Evaluate reports by making inferences, justifying conclusions, and determining appropriateness of data collection methods. Show how graphs and data can be distorted to support different points of view. (A2.D.2.1) Identify and explain misleading conclusions and graphical representations of data sets. (A2.D.2.2)