8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 1/34

Problem-Solving Strategy: Look 

for a pattern

Objective: Solve problems by looking

for a pattern.

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 2/34

5-Minute Check 

Solve each equation.

1. n = 9 ± (-1)

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 3/34

5-Minute Check 

Solve each equation.

1. n = 9 ± (-1) 10

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 4/34

5-Minute Check 

Solve each equation.

1. n = 9 ± (-1)

2. x = -3 ± (21)

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 5/34

5-Minute Check 

Solve each equation.

1. n = 9 ± (-1)

2. x = -3 ± (21) -24

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 6/34

5-Minute Check 

Solve each equation.

1. n = 9 ± (-1)

2. x = -3 ± (21)3. T = -8 ± (-3)

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 7/34

5-Minute Check 

Solve each equation.

1. n = 9 ± (-1)

2. x = -3 ± (21)3. T = -8 ± (-3) -5

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 8/34

5-Minute Check 

Solve each equation.

1. n = 9 ± (-1)

2. x = -3 ± (21)3. T = -8 ± (-3)

Simplify.

4. 8m ± (-6m)

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 9/34

5-Minute Check 

Solve each equation.

1. n = 9 ± (-1)

2. x = -3 ± (21)3. T = -8 ± (-3)

Simplify.

4. 8m ± (-6m) 14m

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 10/34

5-Minute Check 

Solve each equation.

1. n = 9 ± (-1)

2. x = -3 ± (21)3. T = -8 ± (-3)

Simplify.

4. 8m ± (-6m)

5. -15c ± 17c

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 11/34

5-Minute Check 

Solve each equation.

1. n = 9 ± (-1)

2. x = -3 ± (21)3. T = -8 ± (-3)

Simplify.

4. 8m ± (-6m)

5. -15c ± 17c -32c

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 12/34

2-6 Problem-Solving Strategy:

Look for a PatternExample

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 willshe have done in 4 hours.

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 13/34

2-6 Problem-Solving Strategy:

Look for a PatternExample

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 willshe 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

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 14/34

2-6 Problem-Solving Strategy:

Look for a PatternExample

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 willshe 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.

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 15/34

2-6 Problem-Solving Strategy:

Look for a PatternExample

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 willshe 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.

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 16/34

2-6 Problem-Solving Strategy:

Look for a PatternExample

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 willshe 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.

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 17/34

2-6 Problem-Solving Strategy:

Look for a PatternExample

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 willshe 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.

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 18/34

2-6 Problem-Solving Strategy:

Look for a PatternExample

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 willshe 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.

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 19/34

2-6 Problem-Solving Strategy:

Look for a PatternSolve Problems worked: 3 4

Time worked: 1hr 

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 20/34

2-6 Problem-Solving Strategy:

Look for a PatternSolve Problems worked: 3 4 6 9

Time worked: 1hr 2hr 

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 21/34

2-6 Problem-Solving Strategy:

Look for a PatternSolve Problems worked: 3 4 6 9 13 18

Time worked: 1hr 2hr 3hr 

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 22/34

2-6 Problem-Solving Strategy:

Look for a PatternSolve Problems worked: 3 4 6 9 13 18 24 31

Time worked: 1hr 2hr 3hr 4hr 

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 23/34

2-6 Problem-Solving Strategy:

Look for a PatternSolve Problems worked: 3 4 6 9 13 18 24 31

Time worked: 1hr 2hr 3hr 4hr 

3 + 4 + 6 + 9 + 13 + 18 + 24 + 31 =

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 24/34

Problems worked: 3 4 6 9 13 18 24 31

Time worked: 1hr 2hr 3hr 4hr 

3 + 4 + 6 + 9 + 13 + 18 + 24 + 31 =

108 problems

2-6 Problem-Solving Strategy:

Look for a PatternSolve

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 25/34

Problems worked: 3 4 6 9 13 18 24 31

Time worked: 1hr 2hr 3hr 4hr 

3 + 4 + 6 + 9 + 13 + 18 + 24 + 31 =

108 problems

2-6 Problem-Solving Strategy:

Look for a PatternSolve

Examine Do the number of problems worked each half 

hour follow the pattern?

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 26/34

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

2-6 Problem-Solving Strategy:

Look for a Pattern

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

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 27/34

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.

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 28/34

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.

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 29/34

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

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 30/34

2-6 Problem-Solving Strategy:

Look for a Pattern

Find a pattern for the following numbers.

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

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 31/34

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, . . .

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 32/34

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

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 33/34

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, __, __, __ 

8/3/2019 Pre Algebra Lesson 2 6

http://slidepdf.com/reader/full/pre-algebra-lesson-2-6 34/34

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