Lesson Plans ~ Mathematics CLG 2.2.3 ~ Coordinate Proofs ~ 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.

Coordinate Proofs

The student will use analytic geometry to write coordinate proofs involving midpoint, slope and distance.

50-minute lesson

Students will need to be able to calculate distance, slope, and midpoint on a coordinate plane.

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
Use the Pythagorean Theorem to find the distance between A(5, 3) and B(-4, 1).
Development of Ideas
Recall the distance, slope, and midpoint formulas. Place geometric figures on a coordinate plane so that calculations are simplified. Justify geometric properties using coordinate proofs. Worksheet: Introduction to Coordinate Proofs Worksheet: Coordinate Proofs
Closure
Describe the advantages and disadvantages of coordinate proofs. Answer: The advantages of coordinate proofs is that they can be generalized to all possible contexts and they incorporate the use of algebraic reasoning. A disadvantage is that you have to be sure that you are selecting a diagram that does include all possible cases for the given statements. Describe when and why you might want to double the coordinates of a figure when using a coordinate proof. Answer: Sometimes doubling the coordinates will allow the use of fractions to be easier to use in the problem.

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