1.1 Patterns and Inductive Reasoning. Inductive Reasoning Watching weather patterns develop help forcasters… Predict weather.. They recognize and… Describe.

1.1 Patterns and Inductive Reasoning

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

Visual Patterns

• Can you predict and sketch the next figure in these patterns?

Number Patterns

• Describe a pattern in the number sequence and predict the next number.

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.

Sketch the next figure in the pattern….

How many squares are in the next figure?

Mixed Review

Mixed Review

(-2,1)

(4,0)

(3,-2)

(-1,-3)

Assignment 1.1