1. Do Now Look at each pattern or conjecture and determine whether each conjecture is valid. 1.2, 6, 14, 30, 62, 126 Conjecture: Each element is two more than two times the previous element. 2.Conjecture: If n is a real number, then –n is a negative number. *a real number can be positive or negative.

2. Proving a conjecture false Let’s look at number 2 from our do now… Conjecture: If n is a real number, then –n is a negative number. *a real number can be positive or negative. This conjecture is false. In order to prove it is false, we must provide a counterexample. A counterexample is a false example to show that a conjecture is not true. It can be a number, a drawing, or a statement that shows the necessary information.

3. Counterexample So…what could be a counterexample for number 2 in our do now…? Conjecture: If n is a real number, then –n is a negative number. *a real number can be positive or negative. FALSE. Counterexample: When n is -4, -n is –(-4) or 4, which is a positive number.

4. Always, sometimes, or never IMPORTANT! In order for a conjecture to be true, it has to be true ALWAYS. Ask yourself…are there any other options where this conjecture could be true? Example: If the area of a rectangle is 36 square feet, then the length is 9 feet and the width is 4 feet. This conjecture is false because you could have the following combinations for this rectangle: Length = 12 feet, width = 3 feet Length = 6 feet, width = 6 feet (meaning it’s a square, not just a rectangle) Length = 36 feet, width = 1 foot

5. Finding a counterexample On page 95 in your textbook, look at numbers 12 and 13. Work with a partner to complete these. Be ready to review as a class.