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Lesson Plan: Mathematical Logic and Proof Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to prove mathematical statements by deductive reasoning or by exhaustion or disprove them using a counterexample.
Objectives
Students will be able to
- understand how to mathematically prove a statement,
- prove algebraic or geometric statements by
- a direct proof,
- exhaustion,
- prove a mathematical statement is not true via a counterexample.
Prerequisites
Students should already be familiar with
- algebraic techniques such as
- expanding parentheses,
- completing the square,
- factoring polynomial expressions up to degree 3,
- writing even numbers as and odd numbers as ,
- geometric techniques such as
- finding the equation of a line between two points,
- proving two lines are perpendicular or parallel,
- constructing circles given three points on them.
Exclusions
Students will not cover
- proof by induction,
- proof by contraposition.
