Download Review and 1.1 Patterns and Inductive Reasoning

“Our character is basically a composite of our habits. Because they
are consistent, often unconscious patterns, they constantly, daily,
express our character…”
-Stephen R. Covey
Review Examples
Multi - Step Equations :
1. 3  2t  5  12
2. 5a  15  9a  3a  29
Review Examples
Inequaliti es :
1. y  7  3  2 y
2. 15  6n  33
Review Examples
Slope :
1. Find the slope of the line through - 4,1 and 5,4 .
2. Find the slope of the line through - 2,1 and 6,-5
Review Examples
Squares and Square Roots :
1. 15 
2
4.
64 
2. - 9  
2
5.
3. - 4 
2
256 
Review Examples
Fractions and Percents :
2
1. What is of 20?
5
1
2. How many times does go into 9?
4
3. What is 18% of 300?
4. Twenty - four is what percent of 60?
Review Examples
Graphing :
1. Graph the line y  3 x  4.
2. Graph the line x  3y  6
Inductive Reasoning
Inductive reasoning is reasoning based on patterns you observe.
Examples:
Find the pattern of the sequence and show the next two terms or
symbols.
2, 4, 8, 16, …
1, 3, 7, 13, 21, …
Using Inductive Reasoning
A conjecture is a conclusion you reach using inductive reasoning.
Example 1:
Sum of odd numbers.
1
1+3
1+3+5
1+3+5+7
=1
=4
=9
= 16
= 12
= 22
= 32
= 42
What is the sum of the first 30
odd numbers?
The first 35 odd numbers?
Conjecture:
Using Inductive Reasoning
A conjecture is a conclusion you reach using inductive reasoning.
Example 2:
Sum of even numbers.
2
2+4
2+4+6
2+4+6+8
=2
=6
= 12
= 20
= 1(2)
= 2(3)
= 3(4)
= 4(5)
What is the sum of the first 30
even numbers?
The first 35 even numbers?
Conjecture:
Using Inductive Reasoning
A counterexample to a conjecture is an example where the conjecture
does not work.
Examples: Find a counterexample to the statements.
1) “If a number is divisible by 2, then it is also divisible by 6.”
2) “You can connect any three points to form a triangle.”
3) “The difference of two negative integers is negative.”
Review and 1.1 Patterns and Inductive
Reasoning
Section 1.1 page 6: 1-13 ODD, 19, 25-27, 30,
50, 53, 56-57
Terms: conjecture, counterexample
“Our character is basically a composite of our habits. Because they
are consistent, often unconscious patterns, they constantly, daily,
express our character…”
-Stephen R. Covey