1. 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

2. 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, …

3. Using Inductive Reasoning
A conjecture is a conclusion you reach using inductive reasoning.
Example:
Sum of odd numbers. 1
1 + 3
= 1
= 4
= 9
= 16
= 12
= 22
= 32
= 42
What is the sum of the first 30 odd numbers?
The first 35 odd numbers?
Conjecture:

4. Using Inductive Reasoning
A conjecture is a conclusion you reach using inductive reasoning.
Example:
Sum of even numbers. 2
2 + 4
= 2
= 6
= 12
= 20
= 1(1 +1)
= 2(2+1)
= 3(3+1)
= 4(4+1)
What is the sum of the first 30 even numbers?
The first 35 even numbers?
Conjecture:

5. Using Inductive Reasoning
A counterexample to a conjecture is an example where the conjecture does not work.
Example:
Find a counterexample to the statements.
“If a number is divisible by 2, then it is also divisible by 6.”
“You can connect any three points to form a triangle.”

6. Practice: Inductive Reasoning Worksheet
1.1 Patterns and Inductive Reasoning
Practice: Inductive Reasoning Worksheet
Terms: inductive reasoning, 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

7. Review Examples

8. Review Examples

9. Review Examples

10. Review Examples

11. Review Examples

12. Review Examples