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Repeated
  Observations            General Conclusion
(The 5 dogs I saw today   (All dogs will bark at me)
    barked at me)
Apply To
  Take General
                            Specific
   Principles
                           Examples
(I know that all dogs
                        (This dog is going
     bark at me)
                          to Bark at me)
   Natural Numbers (Counting
    Numbers)
     ◦ Whole numbers, (No parts of numbers
       included, no fractions or decimals)
     ◦ Numbers Starting at 0, 1, 2, 3….
     ◦ The numbers you count with!

               Find the next 3 natural numbers

           2, 9, 16, 23…
Explain how you found them. Can you tell me
the rule?
Write an expression for the Rule
a n
   Exponent
   What does the
    “exponent” tell you                Base- a
    to do?
                                       Exponent- n
An exponent tells you how many
times you multiply the base times
itself.

73 means you multiply 7 times
itself 3 times or 7x7x7=
   Premise         An assumption. A rule or
                     idea you think is true

   Conclusion      Use reasoning to test, and
                     what you find is the
                     conclusion

   Logical Argument       A Statement arguing
                            your case that includes
                            the Premise and
                            Conclusion
   Can you always make an accurate General
    Conclusion based on the data you have?
    (chords in a circle example)


       Why not?
          It is not Possible to find EVERY
          number in a sequence in a Number
          Pattern, Because Numbers are
          INFINITE.. They go on forever
Create a Rule




                                Test that rule…
See a pattern                   then test some
                                more. Sometimes
                                the rule doesn’t
                                hold up

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Solving problems by inductive reasoning

  • 2. Repeated Observations General Conclusion (The 5 dogs I saw today (All dogs will bark at me) barked at me)
  • 3. Apply To Take General Specific Principles Examples (I know that all dogs (This dog is going bark at me) to Bark at me)
  • 4. Natural Numbers (Counting Numbers) ◦ Whole numbers, (No parts of numbers included, no fractions or decimals) ◦ Numbers Starting at 0, 1, 2, 3…. ◦ The numbers you count with! Find the next 3 natural numbers 2, 9, 16, 23… Explain how you found them. Can you tell me the rule? Write an expression for the Rule
  • 5. a n  Exponent  What does the “exponent” tell you  Base- a to do?  Exponent- n An exponent tells you how many times you multiply the base times itself. 73 means you multiply 7 times itself 3 times or 7x7x7=
  • 6. Premise  An assumption. A rule or idea you think is true  Conclusion  Use reasoning to test, and what you find is the conclusion  Logical Argument  A Statement arguing your case that includes the Premise and Conclusion
  • 7. Can you always make an accurate General Conclusion based on the data you have? (chords in a circle example)  Why not? It is not Possible to find EVERY number in a sequence in a Number Pattern, Because Numbers are INFINITE.. They go on forever
  • 8. Create a Rule Test that rule… See a pattern then test some more. Sometimes the rule doesn’t hold up