Problem Solving Skills: Find a Pattern

1. Section 2-9
Problem Solving Skills: Find a Pattern

2. Essential Question
• How do you recognize and extend
patterns to solve problems?
• Where you’ll see this:
• Law enforcement, part-time jobs

3. Vocabulary
1. Look for a Pattern:
2. Sequence:
3. Term (of a Pattern):

4. Vocabulary
1. Look for a Pattern: A strategy that is used to
help solve problems, where the same thing
is done over and over
2. Sequence:
3. Term (of a Pattern):

5. Vocabulary
1. Look for a Pattern: A strategy that is used to
help solve problems, where the same thing
is done over and over
2. Sequence: A set of numbers arranged in a
pattern
3. Term (of a Pattern):

6. Vocabulary
1. Look for a Pattern: A strategy that is used to
help solve problems, where the same thing
is done over and over
2. Sequence: A set of numbers arranged in a
pattern
3. Term (of a Pattern): Each value in a
sequence, often described by where in a
sequence it is (first term, second term, etc.)

7. Vocabulary
1. Look for a Pattern: A strategy that is used to
help solve problems, where the same thing
is done over and over
2. Sequence: A set of numbers arranged in a
pattern
3. Term (of a Pattern): Each value in a
sequence, often described by where in a
sequence it is (first term, second term, etc.)
Notation:

8. Vocabulary
1. Look for a Pattern: A strategy that is used to
help solve problems, where the same thing
is done over and over
2. Sequence: A set of numbers arranged in a
pattern
3. Term (of a Pattern): Each value in a
sequence, often described by where in a
sequence it is (first term, second term, etc.)
Notation: t1 = first term, t 2 = second term, etc.

9. Exercise
Find the multiples of 3 that are between 40
and 65.

10. Exercise
Find the multiples of 3 that are between 40
and 65.
How do you identify multiples of 3?

11. Exercise
Find the multiples of 3 that are between 40
and 65.
How do you identify multiples of 3?
Divisible by 3

12. Exercise
Find the multiples of 3 that are between 40
and 65.
How do you identify multiples of 3?
Divisible by 3
Digits add up to a number divisible by 3

13. Exercise
Find the multiples of 3 that are between 40
and 65.
How do you identify multiples of 3?
Divisible by 3
Digits add up to a number divisible by 3
Find first, then add 3

14. Exercise
Find the multiples of 3 that are between 40
and 65.
How do you identify multiples of 3?
Divisible by 3
Digits add up to a number divisible by 3
Find first, then add 3
42,

15. Exercise
Find the multiples of 3 that are between 40
and 65.
How do you identify multiples of 3?
Divisible by 3
Digits add up to a number divisible by 3
Find first, then add 3
42, 45,

16. Exercise
Find the multiples of 3 that are between 40
and 65.
How do you identify multiples of 3?
Divisible by 3
Digits add up to a number divisible by 3
Find first, then add 3
42, 45, 48,

17. Exercise
Find the multiples of 3 that are between 40
and 65.
How do you identify multiples of 3?
Divisible by 3
Digits add up to a number divisible by 3
Find first, then add 3
42, 45, 48, 51,

18. Exercise
Find the multiples of 3 that are between 40
and 65.
How do you identify multiples of 3?
Divisible by 3
Digits add up to a number divisible by 3
Find first, then add 3
42, 45, 48, 51, 54,

19. Exercise
Find the multiples of 3 that are between 40
and 65.
How do you identify multiples of 3?
Divisible by 3
Digits add up to a number divisible by 3
Find first, then add 3
42, 45, 48, 51, 54, 57,

20. Exercise
Find the multiples of 3 that are between 40
and 65.
How do you identify multiples of 3?
Divisible by 3
Digits add up to a number divisible by 3
Find first, then add 3
42, 45, 48, 51, 54, 57, 60,

21. Exercise
Find the multiples of 3 that are between 40
and 65.
How do you identify multiples of 3?
Divisible by 3
Digits add up to a number divisible by 3
Find first, then add 3
42, 45, 48, 51, 54, 57, 60, 63

22. Example 1
The sequence 7, 10, 13, 16, ... represents
the number of seats in consecutive rows of a
theatre. How many seats are there in the
10 th row? 50th row? Explain how you found
your answer, including the “what” you did
and “why” you did it.

23. Example 1
The sequence 7, 10, 13, 16, ... represents
the number of seats in consecutive rows of a
theatre. How many seats are there in the
10 th row? 50th row? Explain how you found
your answer, including the “what” you did
and “why” you did it.
What pattern exists?

24. Example 1
The sequence 7, 10, 13, 16, ... represents
the number of seats in consecutive rows of a
theatre. How many seats are there in the
10 th row? 50th row? Explain how you found
your answer, including the “what” you did
and “why” you did it.
What pattern exists?
Adding 3 to the previous term

25. Example 1
The sequence 7, 10, 13, 16, ... represents
the number of seats in consecutive rows of a
theatre. How many seats are there in the
10 th row? 50th row? Explain how you found
your answer, including the “what” you did
and “why” you did it.
What pattern exists?
Adding 3 to the previous term
Does this pattern help us find the 10th and
50th terms?

26. Example 1
t1 = 7

27. Example 1
t1 = 7 = 7 + 3(1 − 1)

28. Example 1
t1 = 7 = 7 + 3(1 − 1)
t 2 = 7 + 3(2 − 1)

29. Example 1
t1 = 7 = 7 + 3(1 − 1)
t 2 = 7 + 3(2 − 1)
t n = 7 + 3( n − 1)

30. Example 1
t1 = 7 = 7 + 3(1 − 1)
t 2 = 7 + 3(2 − 1)
t n = 7 + 3( n − 1)
t10 = 7 + 3(10 − 1)

31. Example 1
t1 = 7 = 7 + 3(1 − 1)
t 2 = 7 + 3(2 − 1)
t n = 7 + 3( n − 1)
t10 = 7 + 3(10 − 1) = 7 + 3(9)

32. Example 1
t1 = 7 = 7 + 3(1 − 1)
t 2 = 7 + 3(2 − 1)
t n = 7 + 3( n − 1)
t10 = 7 + 3(10 − 1) = 7 + 3(9) = 7 + 27

33. Example 1
t1 = 7 = 7 + 3(1 − 1)
t 2 = 7 + 3(2 − 1)
t n = 7 + 3( n − 1)
t10 = 7 + 3(10 − 1) = 7 + 3(9) = 7 + 27 = 34

34. Example 1
t1 = 7 = 7 + 3(1 − 1)
t 2 = 7 + 3(2 − 1)
t n = 7 + 3( n − 1)
t10 = 7 + 3(10 − 1) = 7 + 3(9) = 7 + 27 = 34
t50 = 7 + 3(50 − 1)

35. Example 1
t1 = 7 = 7 + 3(1 − 1)
t 2 = 7 + 3(2 − 1)
t n = 7 + 3( n − 1)
t10 = 7 + 3(10 − 1) = 7 + 3(9) = 7 + 27 = 34
t50 = 7 + 3(50 − 1) = 7 + 3(49)

36. Example 1
t1 = 7 = 7 + 3(1 − 1)
t 2 = 7 + 3(2 − 1)
t n = 7 + 3( n − 1)
t10 = 7 + 3(10 − 1) = 7 + 3(9) = 7 + 27 = 34
t50 = 7 + 3(50 − 1) = 7 + 3(49) = 7 + 147

37. Example 1
t1 = 7 = 7 + 3(1 − 1)
t 2 = 7 + 3(2 − 1)
t n = 7 + 3( n − 1)
t10 = 7 + 3(10 − 1) = 7 + 3(9) = 7 + 27 = 34
t50 = 7 + 3(50 − 1) = 7 + 3(49) = 7 + 147 = 154

38. Example 1
t1 = 7 = 7 + 3(1 − 1)
t 2 = 7 + 3(2 − 1)
t n = 7 + 3( n − 1)
t10 = 7 + 3(10 − 1) = 7 + 3(9) = 7 + 27 = 34
t50 = 7 + 3(50 − 1) = 7 + 3(49) = 7 + 147 = 154
There are 34 seats in the tenth row and 154
seats in the fiftieth row.

39. Example 1
Knowing that I needed to find the tenth and fiftieth
terms, I knew I needed to find an equation that could
take me directly to those terms. I realized that I
could add three to each term, as the difference from
one term to the next was three. It would take me
very long to get to the answer using this method. I
was able to use an explicit formula to go directly to
each term.

40. Example 2
A machine in a factory sorts gumballs to be
placed in bags. In the first bag, it placed 17
blue gumballs. In the next bag, it placed 25
blue gumballs. In the third bag, it placed 33
blue gumballs. It follows this pattern up to
ten bags, then on the eleventh bag, it goes
back to 17 blue gumballs. What is the total
number of blue gumballs it needs for every
grouping of ten consecutive bags? Explain
how you found your answer, including the
“what” you did and “why” you did it.

41. Example 2
t1 = 17 t 2 = 25 t 3 = 33

42. Example 2
t1 = 17 t 2 = 25 t 3 = 33
Add 8 for each term.

43. Example 2
t1 = 17 t 2 = 25 t 3 = 33
Add 8 for each term.
t 4 = 33 + 8

44. Example 2
t1 = 17 t 2 = 25 t 3 = 33
Add 8 for each term.
t 4 = 33 + 8 = 41

45. Example 2
t1 = 17 t 2 = 25 t 3 = 33
Add 8 for each term.
t 4 = 33 + 8 = 41
49, 57, 65, 73, 81, 89

46. Example 2
t1 = 17 t 2 = 25 t 3 = 33
Add 8 for each term.
t 4 = 33 + 8 = 41
49, 57, 65, 73, 81, 89
17 + 25 + 33 + 41 + 49 + 57 + 65 + 73 + 81 + 89

47. Example 2
t1 = 17 t 2 = 25 t 3 = 33
Add 8 for each term.
t 4 = 33 + 8 = 41
49, 57, 65, 73, 81, 89
17 + 25 + 33 + 41 + 49 + 57 + 65 + 73 + 81 + 89
= 530

48. Example 2
t1 = 17 t 2 = 25 t 3 = 33
Add 8 for each term.
t 4 = 33 + 8 = 41
49, 57, 65, 73, 81, 89
17 + 25 + 33 + 41 + 49 + 57 + 65 + 73 + 81 + 89
= 530 blue gumballs

49. Example 2
Since I needed to know the total number of
blue gumballs for ten consecutive bags, I
needed to know how many blue gumballs
would be in each bag. I was given the first
three amounts, and found that, by
subtracting one bag’s number by the
previous bag’s number, there were eight
more blue gumballs in each bag. I added
eight to the third bag, then the fourth, and
so on until I had all ten bags. I then added
these ten numbers together to find the total
for the ten bags, which is 530 blue
gumballs.

50. Problem Set

51. Problem Set
p. 92 #1-25
“If you think you can win, you can win. Faith
is necessary to victory.” - William Hazlitt