EOCT Practice '''

1
EOCT Practice ?...

• If two angles are congruent, then the angles are
  vertical angles. Which diagram provides a
  counterexample for the statement?

2
Mathematical Argument JustificationInductive
Reasoning

• GPS
• MM1G2a
• EQ
• How do we use conjecture, inductive reasoning,
  deductive reasoning, counterexamples indirect
  proof as appropriate?

3
Vocabulary

• Conjecture An unproven statement that is based
  on observations.
• Inductive Reasoning The process of looking for
  a pattern and using that pattern to make a
  generalization.
• Counterexample An example that shows a
  conjecture to be false. You only need one to
  prove that a conjecture is not true.

4
Example 1Describe a visual pattern

• Describe how to sketch the next figure in the
  pattern. Then sketch the next figure.

5
Guided Practice

• Sketch the next figure in the pattern.

6
Example 2Describe a number pattern

• Describe the pattern in the numbers 2, 8, 32,
  128, and write the next three numbers in the
  pattern.

7
Guided Practice

• Describe the pattern in the numbers. Then give
  the next number in the pattern.
• 1, 5, 9, 13,
• 1, 3, 9, 27, 81,

8
Example 3Make and test a conjecture

• Make and test a conjecture about the product of
  any two odd integers.
• Solution
• Step 1 Find a pattern using a few groups of
  small numbers.
• 3 x 13 39 5 x 9 45 7 x 21 147 11 x 15
  165
• Conjecture The product of any two odd integers
  is odd.
• Step 2 Test your conjecture using other
  numbers.
• 17 x 19 323 23 x 31 713

9
Guided Practice

• Make and test a conjecture about the product of
  any two even integers.
• Make and test a conjecture about the sum of an
  even integer and an odd integer.

10
Example 4Find a counterexample

• Find a counterexample to show that the conjecture
  is false.
• Conjecture All odd numbers are prime.

11
Guided Practice

• Find a counterexample to show that the conjecture
  is false.
• Conjecture The difference of two positive
  numbers is always positive.

12
Brain Teaser for the Day

• A man is trapped in a room. The room has only two
  possible exits two doors. Through the first door
  there is a room constructed from magnifying
  glass. The blazing hot sun instantly fries
  anything or anyone that enters. Through the
  second door there is a fire-breathing dragon. How
  does the man escape?

13

• He waits until night time and goes through the
  first door.