School Improvement in Maryland

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

Practice with Proofs

Objective

Students will be able to identify and apply properties of equality and properties of congruence, perform a variety of methods 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 interpret and 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

    Rewrite conjectures in if-then form.

    Development of Ideas

    Investigate the relationship between an if-then statement and the given information and then prove information in a deductive proof.
     
    Practice simple proofs.
     
    Worksheet: Practice with Proofs

    Closure

    What are the important elements in any proof?
     
    Answer: Every proof must have givens and what is to be proved as well as logical reasoning to get from one to the other.
     
    Compare and contrast flow-chart, paragraph, and two-column proofs.
     
    Answer: All proofs use given statements and logical reasoning to prove statements. Flow-chart proofs allow multiple connects and pathways, paragraph proofs use sentences to demonstrate logical reasoning, and two-column proofs use a linear structure to go from given statements to what is to be proved.

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