This document discusses making logical arguments and general conclusions from observations. It explains that while repeated observations of specific examples can lead to general principles, these principles do not always apply to all cases. Applying general conclusions as rules to new specific examples may not always yield accurate predictions, as the available data is limited and exceptions may exist.

1. August 2011

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