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G-RL-1-1

Page history last edited by Tashe Harris 6 years, 2 months ago

G.RL.1.1 Understand the use of undefined terms, definitions, postulates, and theorems in logical arguments/proofs.

In a Nutshell

Geometry is built upon a system of statements called undefined terms, definitions, postulates and theorems. The undefined terms of point, line and plane are the starting points for understanding all of the geometric relationships. Postulates are statements that are accepted as true without formal proof. Theorems are statements that are proven and can be used in subsequent proofs.

Student Actions	Teacher Actions
Develop Mathematical Reasoning: Students will apply definitions, postulates and theorems appropriately when given diagrams or mathematical relationships. Develop the ability to communicate mathematically: Students will communicate terminology in their own words in multiple representations (pictorially, written, and verbal)	Teachers will pose purposeful questions that require students to explain their thought processes. Teachers will utilize a variety of correct answers given by students to encourage them to develop multiple pathways through meaningful discourse. Teachers will elicit and use evidence of student thinking by having students present proofs that are correct but show different methods of proving the same given statement.
Key Understandings	Misconceptions
Students understand how to decide if a definition, postulate or theorem applies in a specific situation. Students understand using definitions to identify relationships within diagrams. Students understand the correct vocabulary to use when describing a geometric problem. Students understand the step by step process of writing a proof by showing their explanation and defending each step of the process.	Students believe definitions need to be proven. Students use the prove statement as a given statement. Students do not understand subtle differences in some definitions for example, the difference between a segment and a line, or a line and a ray. Students think there is only one correct way to write every proof. Students think proofs must be two-column proofs.