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

20. 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, . . .

21. Thanks