1. Problem-Solving Strategy: Look for a pattern
Objective: Solve problems by looking for a pattern.

2. 2-6 Problem-Solving Strategy: Look for a Pattern
Example
Sara was trying to finish all her math homework on Friday. She did 3 problems the first 30 minutes, 4 problems the next 30 minutes, 6 problems the next 30 minutes, 9 problems the next 30 minutes, and so forth. If she continues to work at this rate, how many problems will she have done in 4 hours.

3. 2-6 Problem-Solving Strategy: Look for a Pattern
Example
Sara was trying to finish all her math homework on Friday. She did 3 problems the first 30 minutes, 4 problems the next 30 minutes, 6 problems the next 30 minutes, 9 problems the next 30 minutes, and so forth. If she continues to work at this rate, how many problems will she have done in 4 hours.
Explore
Sara worked 30 min per problem set.
Time worked number of problems worked
1st 30 min 3
2nd 30 min 4
3rd 30 min 6
4th 30 min 9

4. 2-6 Problem-Solving Strategy: Look for a Pattern
Example
Sara was trying to finish all her math homework on Friday. She did 3 problems the first 30 minutes, 4 problems the next 30 minutes, 6 problems the next 30 minutes, 9 problems the next 30 minutes, and so forth. If she continues to work at this rate, how many problems will she have done in 4 hours.
Explore
Sara worked 30 min per problem set.
Time worked number of problems worked
1st 30 min 3
2nd 30 min 4
3rd 30 min 6
4th 30 min 9
Plan
Look for a pattern.

5. 2-6 Problem-Solving Strategy: Look for a Pattern
Example
Sara was trying to finish all her math homework on Friday. She did 3 problems the first 30 minutes, 4 problems the next 30 minutes, 6 problems the next 30 minutes, 9 problems the next 30 minutes, and so forth. If she continues to work at this rate, how many problems will she have done in 4 hours.
Explore
Sara worked 30 min per problem set.
Time worked number of problems worked
1st 30 min 3
2nd 30 min 4 increased by 1
3rd 30 min 6
4th 30 min 9
Plan
Look for a pattern.

6. 2-6 Problem-Solving Strategy: Look for a Pattern
Example
Sara was trying to finish all her math homework on Friday. She did 3 problems the first 30 minutes, 4 problems the next 30 minutes, 6 problems the next 30 minutes, 9 problems the next 30 minutes, and so forth. If she continues to work at this rate, how many problems will she have done in 4 hours.
Explore
Sara worked 30 min per problem set.
Time worked number of problems worked
1st 30 min 3
2nd 30 min 4 increased by 1
3rd 30 min 6 increased by 2
4th 30 min 9
Plan
Look for a pattern.

7. 2-6 Problem-Solving Strategy: Look for a Pattern
Example
Sara was trying to finish all her math homework on Friday. She did 3 problems the first 30 minutes, 4 problems the next 30 minutes, 6 problems the next 30 minutes, 9 problems the next 30 minutes, and so forth. If she continues to work at this rate, how many problems will she have done in 4 hours.
Explore
Sara worked 30 min per problem set.
Time worked number of problems worked
1st 30 min 3
2nd 30 min 4 increased by 1
3rd 30 min 6 increased by 2
4th 30 min 9 increased by 3
Plan
Look for a pattern.

8. 2-6 Problem-Solving Strategy: Look for a Pattern
Example
Sara was trying to finish all her math homework on Friday. She did 3 problems the first 30 minutes, 4 problems the next 30 minutes, 6 problems the next 30 minutes, 9 problems the next 30 minutes, and so forth. If she continues to work at this rate, how many problems will she have done in 4 hours.
Explore
Sara worked 30 min per problem set.
Time worked number of problems worked
1st 30 min 3
2nd 30 min 4 increased by 1
3rd 30 min 6 increased by 2
4th 30 min 9 increased by 3
Plan
Look for a pattern. The difference between numbers increases by 1 each time.

9. 2-6 Problem-Solving Strategy: Look for a Pattern
Solve
Problems worked: 3 4
Time worked: hr

10. 2-6 Problem-Solving Strategy: Look for a Pattern
Solve
Problems worked:
Time worked: hr 2hr

11. 2-6 Problem-Solving Strategy: Look for a Pattern
Solve
Problems worked:
Time worked: hr 2hr hr

12. 2-6 Problem-Solving Strategy: Look for a Pattern
Solve
Problems worked:
Time worked: hr 2hr hr hr

13. 2-6 Problem-Solving Strategy: Look for a Pattern
Solve
Problems worked:
Time worked: hr 2hr hr hr =

14. 2-6 Problem-Solving Strategy: Look for a Pattern
Solve
Problems worked:
Time worked: hr 2hr hr hr =
108 problems

15. 2-6 Problem-Solving Strategy: Look for a Pattern
Solve
Problems worked:
Time worked: hr 2hr hr hr =
108 problems
Examine
Do the number of problems worked each half hour follow the pattern?

16. 2-6 Problem-Solving Strategy: Look for a Pattern
Write a rule to find the successive terms in the pattern.
63, 48, 35, 24,

17. 2-6 Problem-Solving Strategy: Look for a Pattern
Write a rule to find the successive terms in the pattern.
63, 48, 35, 24,
The number decreased by 15, then 13, then 11, so the next number should decrease by 9 and then by 7. The number subtracted decreases by two each time.

18. 2-6 Problem-Solving Strategy: Look for a Pattern
The pattern of numbers, 1, 1, 2, 3, 5, 8, , is called the Fibonacci sequence. The terms of the sequence are called the Fibonacci numbers. List the first ten Fibonacci numbers.

19. 2-6 Problem-Solving Strategy: Look for a Pattern
The pattern of numbers, 1, 1, 2, 3, 5, 8, , is called the Fibonacci sequence. The terms of the sequence are called the Fibonacci numbers. List the first ten Fibonacci numbers.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55

20. 2-6 Problem-Solving Strategy: Look for a Pattern
Find a pattern for the following numbers.
1, 3, 5, 8, 11, 15, 19,

21. 2-6 Problem-Solving Strategy: Look for a Pattern
Find a pattern for the following numbers.
1, 3, 5, 8, 11, 15, 19,
Pattern: +2, +2, +3, +3, +4, +4, +5, +5, . . .

22. 2-6 Problem-Solving Strategy: Look for a Pattern
Find the number that should be in the blank space.
1, 24, 2, 23, 3, 22, 4, , 13, 13, __ 12

23. 2-6 Problem-Solving Strategy: Look for a Pattern
Find the number that should be in the blank spaces.
1, 4, 10, 20, 35, 56, __, __, __

24. 2-6 Problem-Solving Strategy: Look for a Pattern
Find the number that should be in the blank spaces.
1, 4, 10, 20, 35, 56, __, __, __
84, 120