Support Math I Unit Three Day 1

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Support Math I Unit Three Day 1

• Standard
• Students will use conjecture, Inductive
  Reasoning, Deductive Reasoning, Counterexamples,
  and Indirect Proof as appropriate

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Inductive Reasoning

• Inductive reasoning is the process of arriving at
  a conclusion based on a set of observations.
• It is not a valid method of proof.
• Just because a person observes a number of
  situations in which a pattern exists doesn't mean
  that that pattern is true for all situations.

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Inductive Reasoning

• Example
• After seeing many people outside walking their
  dogs, one may observe that every dog that is a
  poodle is being walked by an elderly person. The
  person observing this pattern could inductively
  reason that poodles are owned by elderly people.

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Conjecture

• Conjecture is what you call the observation you
  make using Inductive Reasoning. An educated
  guess.
• Conjecture
• All elderly people own poodles

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Counterexample

• Example that is opposite of your conjecture.
• Old Mr. Smith owns a pitbull.

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Inductive Reasoning

• Use Inductive Reasoning
• Andres is talks in class on Monday, Tuesday,
  Wednesday, and Thursday
• Conjecture Andres will talk in class every day.
• Counterexample Andres didnt talk Friday

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Inductive Reasoning

• Use Inductive Reasoning
• Sam made 90 on the first test, 90 on the second
  test, 90 on the third test, and 90 on the fourth
  test.
• Conjecture Sam will make a 90 on the all tests.
• Counterexample Sam made a 100 on the sixth test.

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Inductive Reasoning

• Use Inductive Reasoning
• Sesar drinks milk for lunch on Monday, Tuesday,
  Wednesday, and Thursday.
• Conjecture Sesar drinks milk every day for
  lunch.
• Counterexample Sesar drank orange juice on
  Friday.

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Inductive Reasoning

• Use Inductive Reasoning
• Jerico listens to Brittany Spears in class on
  Monday, Tuesday, Wednesday, and Thursday.
• Conjecture Jerico always listens to Brittany
  Spears in class.
• Counterexample Jerico listened to Jimmy Buffett
  on Friday.

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Deductive Reasoning

• Deductive reasoning, unlike inductive reasoning,
  is a valid form of proof. It is, in fact, the way
  in which geometric proofs are written. Deductive
  reasoning is the process by which a person makes
  conclusions based on previously known facts.

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Deductive Reasoning

• An instance of deductive reasoning might go
  something like this
• A person knows that all the men in a certain room
  are bakers, that all bakers get up early to bake
  bread in the morning.
• Jim is in that specific room.
• Knowing these statements to be true, a person
  could deductively reason that Jim gets up early
  in the morning.

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Deductive Reasoning

• Use Deductive Reasoning
• Every time a batter reaches first base, the next
  batter hits a double.
• Every time a batter hits a double, the runner on
  first scores.
• Jon reaches first base.
• What can you deduce about Jon?
• Jon scores.

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Deductive Reasoning

• Use Deductive Reasoning
• When the sun shines, the grass grows. When the
  grass grows, it needs to be cut.
• The sun shines.
• What can you deduce about the grass?
• It needs to be cut.

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Deductive Reasoning

• Use Deductive Reasoning
• Jim is a barber. Everybody who gets his hair cut
  by Jim gets a good haircut.
• Austin got a good haircut.
• What can you deduce about Austin?
• Nothing.
• Just because Austin got a good haircut does not
  mean that Jim cut his hair.

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Deductive Reasoning

• Use Deductive Reasoning
• All dogs are mammals, and all mammals are
  vertebrates.
• Shaggy is a dog.
• What can be deduced about Shaggy?
• Shaggy is a mammal and a vertebrate.

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Deductive Reasoning

• Use Deductive Reasoning
• Why is the following example of deductive
  reasoning faulty?
• Given Khaki pants are comfortable. Comfortable
  pants are expensive.
• Adrian's pants are not khaki pants.
• Deduction Adrian's pants are not expensive.
• Simply because Adrian's pants are not khaki does
  not mean that they are not comfortable.
• Also, even if they are not comfortable, this
  would not necessarily mean that they are not
  expensive. There could be comfortable pants that
  are not khakis, and expensive pants that are not
  comfortable.

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Inductive Reasoning
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Deductive Reasoning
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Inductive or Deductive

• Given 2, 5, 8, 11
• the next number is 14
• Inductive

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Inductive or Deductive

• The weather is warm and we always go swimming
  when the weather is warm.
• We will go swimming
• Deductive

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Inductive or Deductive

• It has been warm everyday this week.
• It will be warm next week.
• Inductive

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Inductive or Deductive

• Dominic is a poodle
• Poodles are dogs
• Dominic is a dog.
• Deductive

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Inductive or Deductive

• Mr. Appelman is a teacher.
• All teachers are mean.
• Mr. Appelman is mean.
• Deductive.