1.1 patterns and inductive reasoning. inductive reasoning watching weather patterns develop help...
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Inductive Reasoning• Watching weather patterns
develop help forcasters…• Predict weather..• They recognize and…• Describe patterns.• They then try to make
accurate predictions based on the patterns they discover.
• Inductive reasoning – reasoning from detailed facts to general principles
Patterns & Inductive Reasoning
• In Geometry, we will• Study many
patterns…• Some discovered by
others….• Some we will
discover…• And use those
patterns to make accurate predictions
Using Inductive Reasoning
• Look for a Pattern • (Looks at several examples…use pictures
and tables to help discover a pattern)• Make a conjecture.• (A conjecture is an unproven “statement”
based on observation…it might be right or wrong…discuss it with others…make a new conjecture if necessary)
How do you know your conjecture is True or False?
• To prove a conjecture is TRUE, you need to prove it is ALWAYS true (not always so easy!)
• To prove a conjecture is FALSE, you need only provide a SINGLE counterexample.
• A counterexample is an example that shows a conjecture is false.
Decide if this conjecture is TRUE or FALSE.
• All people over 6 feet tall are good basketball players.
• This conjecture is false (there are plenty of counterexamples…even here at CHS)
• A full moon occurs every 29 or 30 days.• This conjecture is true. The moon revolves
around Earth once approximately every 29.5 days.