Problem-Solving Strategy: Look for a pattern

Problem-Solving Strategy: Look for a pattern

Objective: Solve problems by looking for a pattern.

2-6 Problem-Solving Strategy: Look for a Pattern

ExampleSara 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.

2-6 Problem-Solving Strategy: Look for a Pattern

ExampleSara 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 worked1st 30 min 32nd 30 min 43rd 30 min 64th 30 min 9

2-6 Problem-Solving Strategy: Look for a Pattern

ExampleSara 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 worked1st 30 min 32nd 30 min 43rd 30 min 64th 30 min 9

Plan Look for a pattern.

2-6 Problem-Solving Strategy: Look for a Pattern

ExampleSara 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 worked1st 30 min 32nd 30 min 4 increased by 13rd 30 min 64th 30 min 9

Plan Look for a pattern.

2-6 Problem-Solving Strategy: Look for a Pattern

ExampleSara 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 worked1st 30 min 32nd 30 min 4 increased by 13rd 30 min 6 increased by 24th 30 min 9

Plan Look for a pattern.

2-6 Problem-Solving Strategy: Look for a Pattern

ExampleSara 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 worked1st 30 min 32nd 30 min 4 increased by 13rd 30 min 6 increased by 24th 30 min 9 increased by 3

Plan Look for a pattern.

2-6 Problem-Solving Strategy: Look for a Pattern

ExampleSara 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 worked1st 30 min 32nd 30 min 4 increased by 13rd 30 min 6 increased by 24th 30 min 9 increased by 3

Plan Look for a pattern. The difference between numbers increases by 1 each time.

2-6 Problem-Solving Strategy: Look for a Pattern

Solve Problems worked: 3 4

Time worked: 1hr

2-6 Problem-Solving Strategy: Look for a Pattern

Solve Problems worked: 3 4 6 9

Time worked: 1hr 2hr

2-6 Problem-Solving Strategy: Look for a Pattern

Solve Problems worked: 3 4 6 9 13 18

Time worked: 1hr 2hr 3hr

2-6 Problem-Solving Strategy: Look for a Pattern

Solve Problems worked: 3 4 6 9 13 18 24 31

Time worked: 1hr 2hr 3hr 4hr

2-6 Problem-Solving Strategy: Look for a Pattern

Solve Problems worked: 3 4 6 9 13 18 24 31

Time worked: 1hr 2hr 3hr 4hr3 + 4 + 6 + 9 + 13 + 18 + 24 + 31 =

Problems worked: 3 4 6 9 13 18 24 31

Time worked: 1hr 2hr 3hr 4hr3 + 4 + 6 + 9 + 13 + 18 + 24 + 31 = 108 problems

2-6 Problem-Solving Strategy: Look for a Pattern

Solve

Problems worked: 3 4 6 9 13 18 24 31

Time worked: 1hr 2hr 3hr 4hr3 + 4 + 6 + 9 + 13 + 18 + 24 + 31 = 108 problems

2-6 Problem-Solving Strategy: Look for a Pattern

Solve

Examine Do the number of problems worked each half hour follow the pattern?

63, 48, 35, 24, . . . . . .

2-6 Problem-Solving Strategy: Look for a Pattern

Write a rule to find the successive terms in the pattern.

63, 48, 35, 24, . . . . . .

2-6 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.

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.

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

2-6 Problem-Solving Strategy: Look for a Pattern

Find a pattern for the following numbers.

1, 3, 5, 8, 11, 15, 19, . . . . . .

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, . . .

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, . . . . . . 12, 13, 13, __

12

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, __, __, __

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