Notes 1.1

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

Example 1: Designing a Pattern Sketch the next figure in the pattern. 1 2 3

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.) , ___, ___

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

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

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

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, ___, ___

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