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

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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.

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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 workednumber of problems worked 1 st 30 min3 2 nd 30 min4 3 rd 30 min6 4 th 30 min9

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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 workednumber of problems worked 1 st 30 min3 2 nd 30 min4 3 rd 30 min6 4 th 30 min9 Plan Look for a pattern.

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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 workednumber of problems worked 1 st 30 min3 2 nd 30 min4increased by 1 3 rd 30 min6 4 th 30 min9 Plan Look for a pattern.

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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 workednumber of problems worked 1 st 30 min3 2 nd 30 min4increased by 1 3 rd 30 min6increased by 2 4 th 30 min9 Plan Look for a pattern.

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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 workednumber of problems worked 1 st 30 min3 2 nd 30 min4increased by 1 3 rd 30 min6increased by 2 4 th 30 min9increased by 3 Plan Look for a pattern.

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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 workednumber of problems worked 1 st 30 min3 2 nd 30 min4increased by 1 3 rd 30 min6increased by 2 4 th 30 min9increased by 3 Plan Look for a pattern. The difference between numbers increases by 1 each time.

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2-6 Problem-Solving Strategy: Look for a Pattern Solve Problems worked: 3 4 Time worked: 1hr

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2-6 Problem-Solving Strategy: Look for a Pattern Solve Problems worked: Time worked: 1hr 2hr

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2-6 Problem-Solving Strategy: Look for a Pattern Solve Problems worked: Time worked: 1hr 2hr 3hr

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2-6 Problem-Solving Strategy: Look for a Pattern Solve Problems worked: Time worked: 1hr 2hr 3hr 4hr

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2-6 Problem-Solving Strategy: Look for a Pattern Solve Problems worked: Time worked: 1hr 2hr 3hr 4hr =

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Problems worked: Time worked: 1hr 2hr 3hr 4hr = 108 problems 2-6 Problem-Solving Strategy: Look for a Pattern Solve

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Problems worked: Time worked: 1hr 2hr 3hr 4hr = 108 problems 2-6 Problem-Solving Strategy: Look for a Pattern Solve ExamineDo the number of problems worked each half hour follow the pattern?

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

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

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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.

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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

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

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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,...

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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

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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, __, __, __

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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

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