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Page history last edited by Brenda Butz 3 years, 9 months ago

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

In a Nutshell

Determining if the validity of a  statement is sometimes true, always true, or never true is a further extension of conditional statements.  Understanding what makes a statement false and the use of a counterexample for concrete examples will assist students later when discussing the different types of polygons, especially quads. Deciding if an argument follows the correct form helps students assess its validity.

Student Actions

Teacher Actions

  • Develop mathematical reasoning: Students will decide the truth values of conditional statements using logical reasoning and provide counterexamples for false statements.

  • Develop the ability to communicate mathematically: Students will provide counterexamples for conditional statements with a truth value of false.
  • Teachers will facilitate meaningful mathematical discourse by leading classroom discussions. In these discussions students will compare and analyze responses from fellow students.

  • Teachers will elicit and use evidence of student thinking by having students give their responses to questions asked about conditional statements

Key Understandings


  • Students understand how to determine truth value of a given statement and its different forms.

  • Students understand how to provide a relevant counterexample to prove statements false.

  • Students understand the relationship between bi-conditionals, definitions and theorems.

  • Students understand that one counterexample proves a statement to be false.

  • 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.

  • Students believe that one example will prove a statement to be true in general.

OKMath Framework Introduction

Geometry Grade Introduction




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