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2.1 Reasoning                      August 30, 2012




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                  Sep 10­7:31 AM

HW pg. 75 #3­17                                      1
2.1 Reasoning                                                            August 30, 2012




   2-1 Inductive Reasoning
     Objectives:
      1. Describe patterns
      2. Use inductive reasoning to find the next term in a number or picture pattern.

    Draw the next 2 figures in the sequence below:




                                       Sep 3­1:15 PM

HW pg. 75 #3­17                                                                            2
2.1 Reasoning                     August 30, 2012




                  Sep 2­1:06 PM

HW pg. 75 #3­17                                     3
2.1 Reasoning                                                                      August 30, 2012

                                What is inductive reasoning?
           reaching a conclusion based on a pattern discovered through observation


                  Conjecture: an unproven statement that is based on observation



     Make a conjecture about the rule for the sequence below & find the next 2 terms:
      5, 10, 15, 20, __, __                                    You can add 5 to the last number to
                                                               get the next number in the sequence;
                                                               25, 30




     Make a conjecture about the rule for the sequence below & find the next 2 terms:
      1, ­1 ,  1, ­ 1  , __, __                            Multiply by -1/3 to get the
          3 9   27                                         next number in the sequence;
                                                                 1/81, -1/243




                                          Sep 15­12:26 PM

HW pg. 75 #3­17                                                                                       4
2.1 Reasoning                     August 30, 2012




                  Sep 9­1:57 PM

HW pg. 75 #3­17                                     5
2.1 Reasoning                                                             August 30, 2012




       Counterexample: a specific case when the conjecture is false


    The past 5 times that you have walked across your carpet barefoot and then touch the
    door knob on the front door you were shocked.
        a) What conclusion might you make about the next time you walk across
           the floor barefoot and touch the door knob?



         b) What counterexample would you need to find to disprove this
            conclusion?




                                      Sep 3­1:35 PM

HW pg. 75 #3­17                                                                             6
2.1 Reasoning                     August 30, 2012




                  Sep 9­1:59 PM

HW pg. 75 #3­17                                     7
2.1 Reasoning                     August 30, 2012




                  Sep 9­2:05 PM

HW pg. 75 #3­17                                     8
2.1 Reasoning                        August 30, 2012




                  Homework
                   pg. 75
                   #3-17




                     Sep 9­2:08 PM

HW pg. 75 #3­17                                        9

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2.1 notes

  • 1. 2.1 Reasoning August 30, 2012 B E L L W O R K Sep 10­7:31 AM HW pg. 75 #3­17 1
  • 2. 2.1 Reasoning August 30, 2012 2-1 Inductive Reasoning Objectives: 1. Describe patterns 2. Use inductive reasoning to find the next term in a number or picture pattern. Draw the next 2 figures in the sequence below: Sep 3­1:15 PM HW pg. 75 #3­17 2
  • 3. 2.1 Reasoning August 30, 2012 Sep 2­1:06 PM HW pg. 75 #3­17 3
  • 4. 2.1 Reasoning August 30, 2012 What is inductive reasoning? reaching a conclusion based on a pattern discovered through observation Conjecture: an unproven statement that is based on observation Make a conjecture about the rule for the sequence below & find the next 2 terms: 5, 10, 15, 20, __, __ You can add 5 to the last number to get the next number in the sequence; 25, 30 Make a conjecture about the rule for the sequence below & find the next 2 terms: 1, ­1 ,  1, ­ 1  , __, __ Multiply by -1/3 to get the 3 9   27 next number in the sequence; 1/81, -1/243 Sep 15­12:26 PM HW pg. 75 #3­17 4
  • 5. 2.1 Reasoning August 30, 2012 Sep 9­1:57 PM HW pg. 75 #3­17 5
  • 6. 2.1 Reasoning August 30, 2012 Counterexample: a specific case when the conjecture is false The past 5 times that you have walked across your carpet barefoot and then touch the door knob on the front door you were shocked. a) What conclusion might you make about the next time you walk across the floor barefoot and touch the door knob? b) What counterexample would you need to find to disprove this conclusion? Sep 3­1:35 PM HW pg. 75 #3­17 6
  • 7. 2.1 Reasoning August 30, 2012 Sep 9­1:59 PM HW pg. 75 #3­17 7
  • 8. 2.1 Reasoning August 30, 2012 Sep 9­2:05 PM HW pg. 75 #3­17 8
  • 9. 2.1 Reasoning August 30, 2012 Homework pg. 75 #3-17 Sep 9­2:08 PM HW pg. 75 #3­17 9