1. Inductive and Deductive Reasoning
1.1 Notes
Inductive and Deductive Reasoning

2. Warm-up: What’s the next term in the sequence?
What are the next three terms in the sequence?
3, 12, 48, 192, 768, ______ , ______, ______

3. Vocabulary
Inductive Reasoning: the process of arriving at a general conclusion based on observations of specific examples.
Conjectures or Hypotheses: conclusions drawn from inductive reasoning, educated guesses
Counterexample: a case for which a conjecture is false. One counterexample is needed to prove a conjecture false.
Find a counterexample to the conjecture:
The sum of two two-digit numbers is a three digit number.

4. Strong vs. Weak Inductive Argument
Strong Example:
Weak Example

5. Inductive Reasoning: More than one Solution!
2, 4, ?
What is the next number in this sequence?
We need to know one more number to decide.
What do you see?

6. Finding the Next Figure in a Visual Sequence
Describe two patterns in this sequence of figures. Use the pattern to draw the next figure.

7. Deductive Reasoning
Deductive Reasoning: the process of proving a specific conclusion from one or more general statements. A conclusion that is proved to be true by deductive reasoning is called a theorem.
You’re playing Scrabble with Mr. Flood and he tells you, “You have to remove those 5 letters. You can’t use TEXAS as a word.”
General Statement: All proper names are prohibited in Scrabble.
Conclusion:

8. Using Inductive and Deductive Reasoning
Select any 4 numbers between 1 and 100, and do the following:
Multiply the number by 6. Add 8 to the product. Divide the sum by 2. Subtract 4 from the quotient.
Write a conjecture that relates the results of this process to the original number selected. 4 7 11
100
Mult by 6
Add 8
Divide by 2
Subtract 4

9. 1.1 HW
Ready to go on MATH XL