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Lesson Plan: Lesson plans were written by Maryland mathematics educators and could be used when teaching the concepts.

Goal 2 Geometry, Measurement, And Reasoning

Expectation 2.2 The student will apply geometric properties and relationships to solve problems using tools and technology when appropriate.

Indicator 2.2.3 The student will use inductive or deductive reasoning.

Lesson Content

Two-Column Proofs

Objective

Students will be able to identify and apply properties of equality and properties of congruence, write two-column proofs for organizing deductive arguments, and validate properties of geometric figures and explain the processes used.

Approximate Time

50-minute lesson

Prerequisite Concepts Needed

Students will need to be able to analyze conditional statements.

Materials Needed

Lesson Structure

    Essential Questions

    How can deductive reasoning be used to validate conjectures?
     
    What methods can be used to organize a deductive argument?

    Warm-Up/Opening Activity

    Develop a flow chart proof and a paragraph proof for solving an algebraic equation.

    Development of Ideas

    Construct a two-column proof for solving an equation.
     
    Worksheet: Introduction to Two-Column Proofs
     
    Justify geometric properties using a two-column proof format.
     
    Worksheet: Two-Column Proofs

    Closure

    Compare and contrast flow-chart proofs and two-column proofs.
     
    Answer: Flow-chart proofs and two-column proofs both organize statements and reasons together but flow-chart proofs allow multiple pathways and connections as where two-column proofs are always linear in reasoning.

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