Patterns and Inductive Reasoning
Conditional Statements
Biconditionals and Definitions
Deductive Reasoning
100
Find a pattern for the sequence. Use the pattern to show the next two terms. 5, 11, 18, 26, …
What is 35 and 45?
100
Identify the hypothesis and conclusion of the statement: If a number is divisible by 2, then the number is even.
What is "a number is divisible by 2" (hypothesis) and "the number is even" (conclusion).
100
When can you write a biconditional statement?
What is when both the conditional and the converse statements are true.
100

My mother is Irish. Everyone from Ireland has blonde hair. 

What can you conclude?

What is my mother has blonde hair

200
Find a pattern for the sequence. Use the pattern to show the next two terms. 1, 4, 9, 16, 25, 36...
What is 49 and 64?
200
Identify the hypothesis and conclusion of the conditional. The dog will bark if a stranger walks by the house.
What is "the dog will bark" (conclusion) and "a stranger walks by the house" (hypothesis).
200
What are the two conditional statements that form this biconditional? A ray is an angle bisector if and only if it divides an angle into two congruent angles.
What is "If a ray is an angle bisector, then it divides an angle into two congruent angles" and "If a ray divides an angle into two congruent angles, then it is an angle bisector."
200

All of our snowstorms come from the north. It's starting to snow.

What can you conclude?

What is the storm is coming from the north.

300
Find a pattern for the sequence. Use the pattern to show the next two terms. 1/4, 1/16, 1/64...
What is 1/256 and 1/1024?
300
Determine if the conditional is true or false. If it is false, find a counterexample. If the figure has four congruent angles, then the figure is a square.
What is false (counterexample: rectangle)?
300
Write the converse of the conditional statement below. Then write the biconditional statement or a counterexample. If a number is even, then it is divisible by 2.
What is "If a number is divisible by 2, then it is even." True.
300

Maximillian is a shelter dog. All shelter dogs are happy.

What can you conclude?

What is Maximillian is happy.
400
Find one counterexample to show that the conjecture is false. Angle 1 and Angle 2 are supplementary, so one of the angles is acute.
What is two right angles?
400
Write the sentence as a conditional. Two complementary angles form a right angle.
What is "If two angles are complementary, then they form a right angle"?
400
Write the statement as a biconditional. An equilateral triangle is a triangle with three congruent angles.
What is "A figure is an equilateral triangle if and only if it is a triangle with three congruent sides."
400

Elephants have cells in their bodies, and all cells have DNA.

What can you conclude?

What is all elephants have DNA

500
Find one counterexample to show that the conjecture is false. The product of two positive numbers is greater than either number.
What is the product of two (positive) fractions?
500
Without looking at your notes, what are two other ways you can write a conditional statement?
What is "q if p" and "p implies q"?
500
Write the converse of the conditional statement below. Then write the biconditional statement or a counterexample. If x > 5, then the absolute value of x is > 5.
What is "If the absolute value of x is > 5, then x > 5." False. Counterexample: x = -10.
500

Acute angles are less than 90 degrees. This angle is 40 degrees. 

What can you conclude?

What is it must be an acute angle

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