Conjectures and Counterexamples

Patterns and Inductive Reasoning

Multiple Choice

Inductive Reasoning means...

• Guessing
• Testing and observing patterns to make conjectures
• Explaining why
• Ura nok seblu!

Multiple Choice

How would you describe this pattern's rule?

16, 11, 6, 1

• Add 5

• Subtract 3

• Subtract 5

• Subtract 6

Multiple Choice

What number belongs in the blank?

18,24,___,36,42

• 28

• 31

• 30

• 35

Multiple Choice

How many squares are in Step 5?

• 30

• 31

• 32

• 33

• 34

Multiple Choice

How many squares are in Figure 4?

• 10

• 11

• 12

• 13

• 14

Multiple Choice

How many counters would come next?

• 5

• 7

• 9

• 11

Multiple Choice

Complete the conjecture.
The sum of two negative numbers is ___________.

• positive
• negative
• odd
• even

Multiple Choice

Find the next number in the sequence.
1, -1, 2, -2, 3, ___

• 4
• -4
• 3
• -3

Multiple Choice

Which of the following conjectures is false?

• The product of two even numbers is even.
• The sum of two even numbers is even.
• The product of two odd numbers is odd.
• The sum of two odd numbers is odd.

Multiple Choice

For a conjecture to be true, it must be true...

• in most cases.

• in all cases.

• on Thursday mornings.

• at least once.

Multiple Choice

Which is a counterexample to the following statement?

If an angle is obtuse, then it is $$125\degree$$ .

• $$90\degree$$  

• $$57\degree$$  

• $$160\degree$$  

• $$180\degree$$  

Multiple Choice

Which of the following provide a counterexample to the claim:

"If two angles are supplementary, then they are not congruent."

• $$40\degree\ and\ \ 140\degree$$

• $$80\degree\ and\ \ 80\degree$$

• $$30\degree\ and\ \ 150\degree$$

• $$90\degree\ and\ \ 90\degree$$

Multiple Choice

Which is a counterexample to the following statement?

If you add two numbers, then the sum is odd.

• 2+5=7

• 3+2=5

• 1+8=9

• 2+4=6

Multiple Choice

Which is a counterexample to the following statement?

If an animal is brown, then it is a dog.

• Squirrel

• Chocolate lab

• White rabbit

• Blue jay

NOW LET'S PUT IT ALL TOGETHER AND PRACTICE A FEW MORE!

Multiple Choice

Which is a counterexample of: The difference of two numbers is less than the greater number.

• (5) - (2) = 3

• (-5) - (4) = -9

• (2) - 0 = 2

• (3) - (3) = 0

Multiple Choice

Which number is a counterexample to the following statement? :

All numbers that are divisible by 2 are divisible by 4

• 0

• 12

• 28

• 42

Multiple Choice

Used to prove that a conjecture is false.

• Counterexample

• Inductive Reasoning

• Concluding statement

• Conjecture

Multiple Choice

How would you describe this pattern's rule?

65, 62, 59, 56, 53, 50

• Subtract 2

• Subtract 3

• Subtract 4

• Add 3

Multiple Choice

What are the next two numbers in this pattern?

12, 17, 22, 27, ___, ___

• 32, 37

• 30, 37

• 30, 33

• 32, 35

Multiple Choice

Where would the next red square be?

• bottom left

• top right

• top left

• bottom right

Multiple Choice

What are the missing numbers in this pattern?

23, 33, ___, 53, ___, 73

• 32, 62

• 42, 63

• 43, 63

• 42, 62

Multiple Choice

Find the next term in the sequence:

A, D, G, J, _____

• L

• M

• P

• K

Multiple Choice

What is a conjecture?

• A statement believed to be true based on observations.

• An example which disproves an hypothesis.

• the performance of tricks that are seemingly magical

Multiple Choice

The type of reasoning where a person makes conclusions based on observations and patterns is called...

• Inductive reasoning

• Deductive reasoning

• Conjecture

• Experiments

Multiple Choice

In which hand is the Statue of Liberty's torch?

• Left

• Right