Patterns and Inductive ReasoningGeometryMrs. King

Unit 1, Lesson 1

Definition

Inductive Reasoning: reasoning based on patterns you observe

Example #1

Find the next two terms of the number sequence: 1, 2, 3, 4, …

5, 6

Describe the pattern you observed.

Example #2

Find the next two terms of the number sequence: 9, 6, 3, …

0, -3

Describe the pattern you observed.

Example #3

Find the next two terms of the number sequence: 2, 4, 8, 16, …

32, 64

Describe the pattern you observed.

Example #4

What are the next two terms in the sequence Monday, Tuesday, Wednesday, …?

A. Saturday, SundayB. Friday, SaturdayC. Friday, ThursdayD. Thursday, Friday

Example #5What are the next two terms in the sequence? 

A.  

B. 

C.

D.

Definition

Conjecture: a conclusion reached by inductive reasoning

The price of overnight shipping was $8.00 in 2000, $9.50 in 2001,

and $11.00 in 2002. Make a conjecture about the price in 2003.

Write the data in a table. Find a pattern.

2000

$8.00

2001 2002

$9.50 $11.00

Each year the price increased by $1.50.

A possible conjecture is that the price in 2003 will increase by $1.50.

If so, the price in 2003 would be $12.50.

Definition

Counterexample: a example for which the conjecture is incorrect

Find a counterexample for each conjecture.

1. A number is always greater than its reciprocal.Sample counterexamples:

2. If a number is divisible by 5, then it is divisible by 10.Sample counterexample:

25 is divisible by 5 but not by 10.

1 is not greater than = 1.11

is not greater than 2.12

Homework

Patterns and Inductive Reasoning in Student Practice Packet(Page 2, #1-10)