Unit 3 Lesson 1.1/2.3: Inductive & Deductive Reasoning

Lesson GoalsIdentify when inductive or deductive reasoning is used.

ESLRs: Becoming Competent Learners, Complex Thinkers, and Effective Communicators

ESLRs: Becoming Competent Learners, Complex Thinkers, and Effective Communicators

Inductive Reasoning

Looking for a pattern and making a conjecture based on the pattern.

Starts with specific casesStates a general ruleExamples

Number sequencesWeather reportsStock market recommendationsPoll results

An unproven statement based on observation

3

Inductive Reasoning

What is the next number in the sequence?

5432?

Rule:

17, 15, 12, 8,

subtract consecutive integers

Inductive Reasoning

Sketch the next figure.

Rule: a 90o counterclockwise turn

Inductive ReasoningDetermine the date for Labor Day in 2012.The first Labor Day in 1882 was September 5th.The second Labor Day in 1883 was September 5th .Labor Day in 2005 was September 5th.Labor Day in 2011 was September 5th.

September 3, 2012

Inductive Reasoning

Was the price of Google stock more or less than $480.22 on June 24, 2011?

Date Closing Price

June 16, 2011 $ 500.37June 17, 2011 $ 485.02June 20, 2011 $ 484.58June 21, 2011 $ 493.00June 22, 2011 $ 487.01June 23, 2011 $ 480.22

June 24, 2011$474.88

Inductive Reasoning

16 163 9

1882 1883 2005 2011 2012

Sept 5 Sept 5 Sept 5 Sept 5

16 17 20 21 22 23 24

$500.37 $485.02 $484.58 $493.00 $487.01 $4

1627

Sept 3

$4780.2 42 .88

317, 15, 12, 8,

48, 16, , ,

A CONJECTURE is an unproven statement.unproven

Inductive Reasoning

Write a conjecture based on the pattern.

The sum of any three consecutive integers is _________________________3 times the middle number. now the right side

First describe the left side of the equations

3 4 5 4 3 7 8 9 8 3 4 5 6 5 3 8 9 10 9 3 5 6 7 6 3 9 10 11 10 3 6 7 8 7 3 10 11 12 11 3

The sum of any three consecutive integers is _________________________3 times the middle number.

example

Write a conjecture based on the pattern.

4 5 6 5 3 3 4 5 4 3

5 6 7 6 3 6 7 8 7 3

7 8 9 8 3 8 9 10 9 3

9 10 11 10 3 10 11 12 11 3

1 2 3 1n n n n

Deductive Reasoning

DEDUCTIVE REASONING Using facts, definitions, and previously accepted properties (rules) to write a logical argument.• Starts with a general rule• Applicable to specific cases

Because oranges are fruit and all fruit grow on trees, oranges must grow on trees.

You Try

Jill and Bob are friends. Jill likes to dance, cook and write. Bob likes to dance and cook. Therefore, Bob must also like to write.

InductiveThe conclusion is based on a pattern of previous examples.

Decide whether inductive or deductive reasoning is used to reach the conclusion.

All squares are rectangles. Rectangles have four sides. Therefore, all squares have four sides.

You Try

DeductiveThe conclusion is based on specific facts.

Decide whether inductive or deductive reasoning is used to reach the conclusion.

Sue heard Kelly’s mom say that every Monday isFamily Game Night at their house. Today is Tuesday.Sue reasons that Kelly might have played Monopoly

last night.

You Try

DeductiveThe conclusion is based on the rules at Kelly’s house.

Decide whether inductive or deductive reasoning is used to reach the conclusion.

Jennifer leaves for school at 7:00 a.m. and is on time. Jennifer assumes, then, that she will always be on time if she leaves at 7:00 a.m.

You Try

InductiveThe conclusion is based past experience.

Decide whether inductive or deductive reasoning is used to reach the conclusion.

The football team easily won the first two games of the season. The team will probably be league champions this year.

You Try

InductiveThe conclusion is based on a limited observation.

Decide whether inductive or deductive reasoning is used to reach the conclusion.

Summary

In your own words describe inductive and deductive reasoning.What is a conjecture?Give an example of how you may have used inductive/deductive reasoning in your own experiences.

Today’s Assignment

p. 6: 1-6, 11, 30, 31, 44p. 91: 2, 21, 22, 33-35

p. 6: 1-6, 11, 30, 31, 44

p. 91: 2, 21, 22, 33-35