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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)

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