1 1 Patterns and Inductive Reasoning Inductive Reasoning

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