1 / 53

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.

tammy
Download Presentation

PATTERNS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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 ?

More Related