1. PATTERNS

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

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

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

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

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

15. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #DescriptionProcess# of blocks 1 1 row of 2 plus 1 1(2)+13 Build #1

16. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #DescriptionProcess# of blocks 1 1 row of 2 plus 1 1(2)+13 2 2 rows of 2 plus 1 2(2)+15 Build #1 Build #2

17. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #DescriptionProcess# of blocks 1 1 row of 2 plus 1 1(2)+13 2 2 rows of 2 plus 1 2(2)+15 3 3 rows of 2 plus 1 3(2)+17 Build #1 Build #2 Build #3

18. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #DescriptionProcess# of blocks 1 1 row of 2 plus 1 1(2)+13 2 2 rows of 2 plus 1 2(2)+15 3 3 rows of 2 plus 1 3(2)+17 Build #1 Build #2 Build #3 The number changing in each build is the number of rows of two.

19. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th term 4. Quadratic Let’s create a table to see the relationship between each build and the number of blocks… Build #DescriptionProcess# of blocks 1 1 row of 2 plus 1 1(2)+13 2 2 rows of 2 plus 1 2(2)+15 3 3 rows of 2 plus 1 3(2)+17 Build #1 Build #2 Build #3

20. PATTERNS There are 4 types of patterns : 1. Geometric 2. Linear 3. n th 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 1 st 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…

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

44. First differences are not constant…

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