# 1.1 – Induction: The Search for Rules and Patterns

Objectives

• Define induction and observe how it is used in everyday life and in science.
• Identify patterns and use induction to form general rules or conjectures.
• Make conjectures about triangular and geometric number patterns.
• Build patterns and make conjectures about those patterns.
• Explore the geometric property of symmetry, and use the property to identify lines of symmetry in images.

Key Terms

• Induction – a way of thinking that uses observations to form a general rule.
• Conjecture – a statement that appears to be correct based on observation but has not been proven or disproven; a guess.
• observe the shapes
• find a pattern
• decide how that pattern will continue
• Sierpinski Triangle – a pattern made by removing smaller triangles from a larger one.
• Grouping – a way to organize information.  It simplifies information and makes it easier to understand.
• Symmetry – the quality of being made up of exactly similar parts facing each other or around an axis.

Notes

• Patterns can repeat or grow
• Repeat: {1, 2, 3, 1, 2, 3, 1, 2, 3, …}  <== the numbers 1, 2, & 3 repeat (forever)
• Grow: {2, 4, 8, 16, 32, 64, …}  <== the numbers keep doubling (forever)