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8.1 – Finding Patterns

Objectives

  • Identify real-world patterns that repeat themselves.
  • Find the missing term in a pattern of pictures, letters, or numbers.

 

Key Terms

  • Pattern – A consistent or characteristic form, style, or method used to connect various objects or ideas.
    Ex. 2, 6, 18, 54, …

 

Notes

  • When you look for a pattern, you are searching for repeating colors, shapes, words, letters, or numbers.

 

  • Questions to Ask Yourself About a Pattern
    • Is a certain number added or subtracted at each step to get the next number?
    • Is each number multiplied or divided by a certain number?
    • Are different numbers, which themselves form a pattern, added to each number?
    • Are a few of the above cases happening?

 

  • Sometimes a list of numbers forms a sequence that can be described by an algebraic function.
    • 1, 3, 5, 7, … y=2x-1
    • 1, 3, 9, 27, 81, 243 … y=3^x

 

  • Finding the pattern often starts with looking for a rule that will explain how you get from one term in the list to the next.
    • 1, 3, 5, 7, … add 2 each step
    • 1, 3, 9, 27, 81, 243, … multiply by 3 each step

 

  • Example: Which number is the next number in the following pattern?
    • 2, -3, 4, -5, _____
    • Pattern: + – + – … and numbers increase by 1
      • Answer: 6

 


  • Sierpinski Triangle Patterns

SierpinskiTriangle-ani-0-7 Sierpinski Triangle Patter

 


  • Money Investment Patterns
    • You won $1 Million dollars and plan to invest the money.  Would you have more money if you took the $1 Million up front or received $50,000 each year for 20 years?
      • If you invest the $1 Million up front, your money could grow with interest over the next 20 years; so, you would end up having more money this way!
      • If you only invest $50,000 each year, your money won’t grow as fast, as the interest base is much less than $1 Million.
      • Remember: investments that compound have exponential growth!
      • Exponential growth is a geometric sequence.

 

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