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PATTERNS

PATTERNS. PATTERNS. There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic. PATTERNS. There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic.

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PATTERNS

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  1. PATTERNS

  2. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic

  3. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic Lets begin with Linear patterns. They are probably the easiest to recognize because the change is related to slope of a line.

  4. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic

  5. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic

  6. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic

  7. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic EXAMPLE #1 : What pattern is shown in the graph ?

  8. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic EXAMPLE #1 : What pattern is shown in the graph ?

  9. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic EXAMPLE #1 : What pattern is shown in the graph ?

  10. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic EXAMPLE #1 : What pattern is shown in the graph ?

  11. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic Geometric patterns can be represented numerically and generalized algebraically.

  12. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic Geometric patterns can be represented numerically and generalized algebraically.

  13. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks…

  14. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks…

  15. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #1

  16. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #2 Build #1

  17. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #3 Build #2 Build #1

  18. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… The number changing in each build is the number of rows of two. Build #3 Build #2 Build #1

  19. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #3 Build #2 Build #1

  20. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. nth term 4. Quadratic Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

  21. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

  22. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

  23. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

  24. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

  25. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

  26. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression 1st Find the difference for each consecutive term 14 – (-1) = 15 39 – 14 = 25 74 – 39 = 35 119 – 74 = 45

  27. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression Since the differences are NOT CONSTANT, we need to find the difference between the differences we just found…

  28. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

  29. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

  30. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

  31. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

  32. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression

  33. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #3 : What is the tenth term of the pattern below ?

  34. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #3 : What is the tenth term of the pattern below ? The difference is constant, so a linear pattern.

  35. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #3 : What is the tenth term of the pattern below ? The difference is constant, so a linear pattern. The pattern is decreasing so coefficient will be negative.

  36. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #3 : What is the tenth term of the pattern below ?

  37. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #3 : What is the tenth term of the pattern below ?

  38. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #3 : What is the tenth term of the pattern below ?

  39. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #4 : Write the first five terms of the pattern from the given expression below.

  40. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #4 : Write the first five terms of the pattern from the given expression below. Just start plugging in values for “n” starting with 1…

  41. Nth term Patterns - look at the difference between the terms - if the differences are constant, the expression is linear - if the differences are not constant, look at the differences between the differences - if the second differences are constant, then the expression will be a quadratic expression EXAMPLE #4 : Write the first five terms of the pattern from the given expression below. Just start plugging in values for “n” starting with 1…

  42. EXAMPLE #5 : What function does the pattern below represent ?

  43. EXAMPLE #5 : What function does the pattern below represent ? First differences are not constant…

  44. EXAMPLE #5 : What function does the pattern below represent ?

  45. EXAMPLE #5 : What function does the pattern below represent ?

  46. EXAMPLE #5 : What function does the pattern below represent ?

  47. EXAMPLE #5 : What function does the pattern below represent ?

  48. EXAMPLE #5 : What function does the pattern below represent ?

  49. EXAMPLE #5 : What function does the pattern below represent ?

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