Definitions
A statement that can be written in the form "If p, then q."
What is a conditional statement?
The next number in the sequence 5, 9, 13, 17, ... (Justify with a conjecture).
What is 21? (The pattern is adding 4 to get the next vaue.)
The converse of the statement: "If an animal is a cardinal, then the animal is a bird."
What is "If an animal is a bird, then the animal is a cardinal"?
Give a counterexample for the following statement: "All numbers ending in 4 are divisible by 4."
Example responses: 14, 34, 54, ...
A statement formed by exchanging the hypothesis and conclusion of a conditional statement.
What is the converse?
The next letter in the sequence M, T, W, T, F ... (Justify with a conjecture).
What is S? (The pattern is using the first letter of the days of the week).
The inverse of the statement "If I like sports, then I like basketball."
What is "If I do not like sports, then I do not like basketball."
Give a counterexample for the following statement: "If a number is odd, then it is also prime."
Example responses: 9, 15, 21, 25, ...
An educated guess based on patterns or observations.
What is a conjecture?
The next number in the sequence 2, -8, 32, -128, ... (Justify with a conjecture).
What is -512? (The pattern is multiplying the previous number by -4 to get the next value).
The contrapositive of the statement: "If I went to the movies, then I got popcorn"?
What is "If I did not get popcorn, then I did not go to the movies"?
Give a counterexample for the following statement: "If the product of two numbers is negative, then the sum of those two numbers is negative."
Example responses: -5 and 7, -3 and 8, -2 and 4, ...
A statement formed by both exchanging and negating the hypothesis and conclusion of a conditional statement.
What is the contrapositive?
The next number in the sequence 2, 2, 4, 12, 48 ... (Justify with a conjecture).
What is 240? (The pattern is multiplying by the next consecutive number to get the next value).
The inverse of the statement "If I carry an umbrella, I will not get wet."
What is "If I do not carry an umbrella, I will get wet"?
Give a counterexample for the following statement: "If it is not Saturday, then we have to go to school."
Example response: If it is not Saturday, it could be Sunday, and we don't have to go to school!
A statement formed by negating the hypothesis and the conclusion of a conditional statement.
What is the inverse?
The next letter in the sequence A, D, G, J, M, ... (Justify with a conjecture).
What is P? (The pattern is skipping two letters alphabetically).
The contrapositive of the statement "If you are at home, then you are not at soccer practice."
What is "If you are at soccer practice, then you are not at home"?
Give a counterexample for the following statement: "Any number squared is bigger than the original number" (x2 > x)
Example responses: 1 * 1 = 1, 0.5 * 0.5 = 0.25, 1/3 * 1/3 = 1/9, ...