#2.2 Inductive and Deductive Reasoning

Find the next two numbers in the pattern:

2, 5, 11, 23, 47, ...

• 84, 182

• 81, 176

• 95, 191

• 76, 162

Find the next two terms in the pattern:

A, Z, B, Y, C, ...

• X, D

• D, X

• E,W

• W, E

Tags

CCSS.4.OA.C.5

Make a conjecture about the product of three negative numbers.

• The product of three negative numbers is always positive.

• The product of three negative numbers is always negative.

• The product of three negative numbers is never negative.

• The product of three negative numbers is sometimes positive.

Tags

CCSS.7.NS.A.2

CCSS.7.NS.A.3

What is a counterexample?

• A specific case for which a conjecture is false.

• A specific case for which a conjecture is true.

• An example of a true statement.

• An example of the converse statement.

What is a conjecture?

• A statement that has been proven true.

• An unproven statement based on observations.

• A statement that has been proven false.

• An unproven statement that is assumed false.

What can you conclude from this information?

"If you go swimming, then you will get wet.

You went swimming."

• You got wet.

• You did not get wet.

• No conclusion possible.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.6

What can you conclude from this information?

"If you study, then you will pass the test. If you pass the test, then you will pass the course."

• You did not study.

• You did not pass the course.

• If you study, then you will pass the course.

• You passed the test.

What conclusion can you make from this information?

If a straight angle is bisected, then each angle is 90º.

If an angle is 90º, then it is a right angle.

• If a straight angle is bisected, then each angle is a right angle.

• If a straight angle is bisected, then the angle measures 180°

• If an angle is 90º, then it is a straight angle.

• If an angle is 90º, then the angle was bisected.

Tags

CCSS.HSG.CO.C.9

Is this Inductive or Deductive reasoning?

"This weekend, the sun was shining and it did not rain. So, the next time the sun is shining, you know it will not rain."

• Inductive. You are assuming a pattern will continue.

• Deductive. It is a fact that when the sun is shining it does not rain.

Is this inductive or deductive reasoning?

"The product of two even integers is always even. Because 92 and 14 are even numbers, the product is even."

• Inductive. You are assuming a pattern will continue.

• Deductive. The conjecture is based on the fact that 92 x 14 = 1288.