1. Notes 1.1

2. Vocabulary Conjecture: an unproven statement that is based on truths
Inductive Reasoning: a process that includes looking for patterns and making conjectures
Counterexample: an example that shows that a conjecture is false

3. Example 1: Designing a Pattern
Sketch the next figure in the pattern.

4. Example 2: Describing a Number Pattern
Describe a pattern in the sequence of numbers. Predict the next two numbers.
a.) 5, 3, 1, -1, ___, ___
b.) 1, -4, 9, -16, ___, ___
c.) , ___, ___

5. Example 3: Make a Conjecture
Complete the conjecture.
Conjecture: The product of two consecutive even integers is divisible by ___________________ .

6. Example 4: Finding a Counterexample
Show that the conjecture is false by finding a counterexample.
Conjecture: All odd numbers are prime.

7. Exercises:
1.) Sketch the next figure in the pattern.

8. 2. ) Describe a pattern in the sequence of numbers
2.) Describe a pattern in the sequence of numbers. Predict the next two numbers.
a.) 1, 2, 6, 24, ___, ___
b.) 0, 3, 8, 15, 24, ___, ___

9. 3.) Show that the conjecture is false by finding a counterexample.
Conjecture: The square of the sum of two numbers is equal to the sum of the squares of two numbers. That is,
(a + b)2 = a2 + b2