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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

Flow Chart Proofs

Objective

Students will be able to identify and apply properties of equality and properties of congruence, write flow chart 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 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

    Write the directions for making a sandwich in a flow chart.
     
    Teacher Note:
    You might want to have the ingredients to make a sandwich available in class.

    Development of Ideas

    Arrange in order the steps to solve an algebraic equation.
     
    Teacher Note:
    Have the students work in groups for problems 5, 6, and 7. Each group of students will need an envelope with the statements and reasons for each problem cut into strips and a copy of the flowchart template for each problem. The master copies follow the worksheet.
     
    Justify the steps to solve the algebraic equation in a flow chart format.
     
    Worksheet: Introduction to Flow Chart Proofs
     
    Justify geometric properties using a flow chart.
     
    Worksheet: Flow Chart Proofs

    Closure

    Describe the advantages and disadvantages of writing instructions for a task in a flow chart.
     
    Answer: An advantage of using flow charts is to be able to show different directions and logic pathways within the sequence of directions. A disadvantage is that the pathways can be confusing and difficult to see at first.
     
    Describe how deductive reasoning is used in flow charts.
     
    Answer: Flow charts show how deductive reasoning is developed by using the given statements, definitions, and theorems to demonstrate proofs and showing how the connections are made.

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