Chapter 2.1 – 2.2 “We have to reinvent the wheel every once in awhile, not because we need a lot of wheels, but because we need a lot of invention.” Bruce.

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Presentation transcript:

Chapter 2.1 – 2.2 “We have to reinvent the wheel every once in awhile, not because we need a lot of wheels, but because we need a lot of invention.” Bruce Joyce

Objectives Introduce and familiarize the students with inductive reasoning. Use inductive reasoning to find the next term in a number or picture pattern. Introduce and familiarize students with the deductive reasoning. Learn the relationship between inductive and deductive reasoning.

Inductive Reasoning The process of observing data, recognizing patterns, and making generalizing about those patterns. What are some real life examples? When you use inductive reasoning to make a generalization, the generalization is called a conjecture.

Example Make a conjecture about the rule for generating the sequence 2, 4, 7, 11,… The conjecture: If the pattern continues, you always add the next counting number to get the next term.

Investigation Shape ShiftersPg 96

Deductive Reasoning The process of showing that certain statements follow logically from agreed-upon assumptions and proven facts.

Example: Algebraic Proofs 3(2x + 1) + 2(2x + 1) + 7 = 42 – 5x 5(2x + 1) + 7 = 42 – 5x 5(2x + 1) = 35 – 5x 10x + 5 = 35 – 5x 10x = 30 – 5x 15x = 30 x = 2 Original Equation Combing Like Terms Subtraction property Distributive property Subtraction property Addition property Division property

Example Conjecture: If an obtuse angle is bisected, then two newly formed congruent angles are ___________.

Investigation Overlapping SegmentsPg 102

Closure In the investigation you used both inductive and deductive reasoning to convince yourself of the overlapping segments property. What is the relationship between inductive and deductive reasoning.

Objectives Introduce and familiarize the students with inductive reasoning. Use inductive reasoning to find the next term in a number or picture pattern. Introduce and familiarize students with the deductive reasoning. Learn the relationship between inductive and deductive reasoning.

Homework Sections 2.1 and 2.2