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 Shifters Pg 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 Segments Pg 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