RATIO, PROPORTION, AND PERCENT - …mathandteaching.org/uploads/Modules/RP/RedCore RP1-SP.pdf ·...

Name ___________________________ Period __________ Date ___________

Ratio, Proportion, and Percent Unit (Student Pages) RP1 – SP

RP1.1 Sense Making with Percents • Convert fractions to decimals and percents. • Use sense-making strategies for finding percents. • Estimate percents of numbers.

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RP1.2 Percents and Equations • Use a linear model to solve percent problems. • Set up equivalent fractions to represent percent problems. • Practice sense-making strategies for solving percent problems.

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RP1.3 Vocabulary, Skill Builders, and Review 14

RP1 STUDENT PAGES

RATIO, PROPORTION, AND PERCENT Student Pages for Packet 1: Solving Percent Problems

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Solving Percent Problems

Ratio, Proportion, and Percent Unit (Student Pages) RP1 – SP0

WORD BANK (RP1)

Word Definition Picture or Example

equation

equivalent fractions

percent

percent of a number

ratio

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Solving Percent Problems 1.1 Sense-Making with Percents


SENSE-MAKING WITH PERCENTS

Ready (Summary) We will learn and apply sense-making strategies for finding percents of numbers.

Set (Goals)

• Convert fractions to decimals and percents.

• Use sense-making strategies for finding percents.

• Estimate percents of numbers.

Go (Warmup)

Complete the table. Use mental math to complete the table whenever possible. If another method is used, show the work clearly. Be prepared to explain your methods. Fraction Decimal Percent

1. 12

2. 25%

3. 710

4. 0.3333333…

5. 150%

6. 2.5%

7. 0.5% Sample

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PERCENTS OF CONTAINERS

Complete the problems. 1. About how full is each container? Give estimates using percents. Container A Container B Container C Container D

2. Suppose that each container holds 800 ounces of liquid when it is full. How many ounces

do you estimate to be in each container?

3. If these containers actually hold 900 ounces of liquid when full, how many ounces do you

estimate to be in each container?

The container below holds 600 ounces of liquid when it is full. Determine how many ounces of liquid would make the container: 4. 50% full __________ 5. 25% full __________ 6. 75% full __________ 7. 10% full __________ 8. 20% full __________ Sam

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PERCENTS OF OTHER ITEMS 1 A dollar is __________ cents. Find the following percents of a dollar. 1. 5% of a dollar is __________ cents. 2. 34% of a dollar is __________ cents.

3. 10% of a dollar is ___________ cents. 4. 76% of a dollar is __________ cents. 5. A meter is __________ centimeters. The rectangle below represents a meter stick. Write

some numbers on the meter stick to represent centimeters. The left edge of the meter stick represents 0 centimeters.

6. Write the letter on the meter stick above to indicate each percent of distance. A. 100% of the way C. 25% of the way

E. 5% of the way

G. 20% of the way

I. 80% of the way

B. 50% of the way D. 75% of the way F. 35% of the way H. 0% of the way J. 55% of the way

7. How are finding percents and finding centimeters on a meter stick related? ________________________________________________________________________ ________________________________________________________________________

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PERCENTS OF OTHER ITEMS 2

Complete each sentence. 1. Finding 100% of something is the same as finding __________ of it.

Therefore, 100% of $40 is __________.

2. Finding 50% of something is the same as finding __________ of it.

This is the same as dividing by__________. Therefore, 50% of $40 is __________.


This is the same as dividing by __________. Therefore, 25% of $40 is __________.


This is the same as dividing by__________. Therefore, 10% of $40 is __________.

5. Finding 10% can help you find other percents as well. Use your answer for 10% of $40 to find 20% of $40. Explain your strategy.

__________________________________________________________________ __________________________________________________________________

6. Find 5% of $40. Explain your strategy. __________________________________________________________________ __________________________________________________________________ Sam

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MONEY AND OTHER ITEMS

Use sense-making strategies to complete the tables.

Money Find 10% Find 5% Find 15% Find 20%

1. $30

2. $16

3. $150

4. $500

Items Find 10% Find 5% Find 50% Find 25%

5. 80 games

6. 40 balloons

7. 120 students

8. 12 cars

More Money Find 1% Find 100% Find 33 13

% Find 66 23

%

9. $60

10. $1,000

11. $150

12. $1

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PERCENTS BIG AND SMALL

Use sense-making strategies to complete the tables. Money Find 10% Find 1% Find 0.5% Find 2.5%

1. $600

2. $12

3. $880

4. $10,000

Items Find 100% Find 200% Find 150% Find 110%

5. 30 marbles

6. 500 paper clips

7. 300 students

8. 10 chairs

More Money Find 1% Find 0.5% Find 1.5% Find 150%

9. $100

10. $36

11. $360

12 $8

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ESTIMATING PERCENTS

Estimate 19% of $61.87 in two different ways. Method 1 Method 2

Answer (to nearest penny): Which method was closer?

Compute each problem.

1. Find 1.1% of $99.99. Estimate: Answer (to nearest penny):

2. Find 16% of $68.95. Estimate: Answer (to nearest penny):

3. Find 121% of $207. Estimate: Answer (to nearest penny):

4. Find 0.48% of $319. Estimate: Answer (to nearest penny): Sam

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Solving Percent Problems 1.2 Percents and Equations


PERCENTS AND EQUATIONS

Ready (Summary) Use a visual model and sense-making strategies to solve percent problems.

Set (Goals)

• Use a linear model to solve percent problems.

• Set up equivalent fractions to represent percent problems.

• Practice sense-making strategies for solving percent problems.

Go (Warmup)

Solve each problem. Be prepared to share your strategy. Remember to include units in your answer.

1. What is 30% of 100 cm?




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USING STRIPS TO SOLVE PERCENT EQUATIONS

A B Use the strips to complete the table.

Words Equivalent Fractions (Equation)

1. 30% of 80 is 24.

2. 60 48 =

100 80

3. 40% of 80 is _______.

4. 25 = 100 80

x

%

%

0

100

0

80

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FINDING 20%

Cut off and use the strip at the bottom of the page to set up an equation with equivalent fractions to represent each problem and find the answers.

1. What is 20% of

60?

2. What is 20% of

140?

3. What is 20% of

400?

4. What is 20% of

64?

part 20whole 100 60

x = =

x = _____

part = = whole 100

0

60

0

140

0

400

0

64

0%

100%

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FINDING 85%


1. What is 85% of

60?

2. What is 85% of

140?

3. What is 85% of

400?

4. What is 85% of

64?

part 85whole 100 60

x = =

x = _____

part = = whole 100

0

60

0

140

0

400

0

64

0%

100%

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MORE STRIPS AND PERCENT EQUATIONS


1. What percent of

80 is 32?

2. 30% of what

amount is 15?

3. What % of 220 is

11?

4. 60% of 180 is

what amount?

part whole 100

= =

x = _____

0

80

0

0

220

0

180

0%

100%

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MORE STRIPS AND PERCENT EQUATIONS (continued) Cut off and use the strip at the bottom of the page to set up an equation with equivalent fractions to represent each problem and find the answers.

5. What is 40% of

50?

6. 50 is 25% of

what?

7. What is 15% of

400?

8. 100 is 20% of

what?

= =part

whole

0

0

0

0

0%

100%

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Solving Percent Problems 1.3 Vocabulary, Skill Builder, and Review


FOCUS ON VOCABULARY (RP1) Unscramble the words to reveal words from the word bank. Then write their definitions or give examples.

Example: irfcaotn fraction: (example) 12

and 103

are examples of fractions.

1. tirao ______________________________________________________________ __________________________________________________________________ 2. neecprt fo a unemrb __________________________________________________ __________________________________________________________________ 3. oqetuain __________________________________________________________ __________________________________________________________________ 4. eqietulvan rfcniato ___________________________________________________ __________________________________________________________________ 5. eptencr ___________________________________________________________ __________________________________________________________________

Word Bank

equation equivalent fraction

percent

percent of a number

ratio

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SKILL BUILDER 1

Find each missing fraction, decimal, or percent. Use mental strategies whenever possible.

Fraction Decimal Percent

1. 50%

2. 0.25

3. 34

4. 18

5. 0.375

6. 0.625

7. 33 1/3%

8. 23

9. 19

10. 29

11. 0.444444…

12. 16

13. 26

14. 56

15. 32

16. 125% Sample

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SKILL BUILDER 2 Compute.

1.

23

+ 114

2. 7 1 8 6−

3. 2 1 35 2• 4. 31 5

7÷

5. 2 2

6+

112

6. 15

9−

79

7. - 2

3•

910

8. - 3

4÷

13

9. 78+

512

10. 7 2

7− 3 5

6

11. 2 3

4•

15

12. 6 2

3÷

89

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SKILL BUILDER 3

Example: Find 51

2% of 600.

Estimate first:

10% of 600 is 60.

5% of 600 is 30.

Strategy 1: Use benchmark percents

1% of 600 = 6

5% of 600 → 5(6) =30

1

2% of 600 →

1

2(6) = 3

So 51

2% of 600 = 30+3 = 33

Strategy 2: Use fractions

51

2% = =

15 112100 200

11 600

33200 1

• =

Strategy 3: Use decimals

51

2% = 0.055

600

0.055

300030000

33.000

×

+

Estimate and compute each problem.

1. Find 17% of $54. Estimate first: Compute:




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SKILL BUILDER 4

Estimate and compute each problem.

1. Find 25 12

% of $120.

Estimate first: Compute:

2. Find 1.8% of $28.


3. Find 8 14

% of $50.


4. Find 6.05% of $72.




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SKILL BUILDER 5

Cut off and use the strip at the bottom of the page to set up an equation with equivalent fractions to represent each problem. Then use the strips to find the missing number or percent.

1. What percent of

60 is 48?

2. 56 is 40% of

what?

3. What percent is

22.5 of 90?

4. 19 is 95% of

what?

= =part

whole

0

0

0

0

0 100%

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TEST PREPARATION (RP1) Show your work on a separate sheet of paper and choose the best answer. 1. What is 40% of 60 people? A. 6 people B. 24 people C. 25 people D. 100 people

2. What is 150% of 40 apples? A. 190 apples B. 110 apples C. 60 apples D. 20 apples

3. What is 8.5% of $80? A. $0.68 B. $6.80 C. $68 D. $680

4. Change 18

to a decimal.

A. 0.125 B. 0.18 C. 1.25 D. 1.8

5. Change 1333

% to a decimal

A. 0.3 B. 0.33 C. 0.33333… D. 1.3

6. Choose the equation that represents this question:

What percent of 50 is 25?

A. 25100 50 x = B. 25 50

100 =

x C. 25

100 50 x = D. 50

100 25 x =

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KNOWLEDGE CHECK (RP1)

Show your work on a separate sheet of paper and write your answers on this page. 1.1 Sense–Making with Percents Use sense-making strategies to find the following percents.

Amount Find 10% Find 5% Find 15% Find 20%

1. $42

2. 760 Stickers

3. Find 71% of $880 in two different ways. 2.1 Percents and Equations Use paper strips if needed. Write an equation with equivalent fractions to solve each problem. 4. What is 30% of 80?

5. What percent of 90 is 36?

%

%

0

100

0

80 %

%

0

100

0

36 Sample

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Solving Percent Problems


Home-School Connection (RP1)

Here are some questions to review with your young mathematician. 1. Complete the table.

Find 10% Find 5% Find 50% Find 25%

240 students

2. What percent of 140 is 7? 3. Find 17% of 430 in two different ways. Parent (or Guardian) signature ____________________________

SELECTED COMMON CORE STATE STANDARDS FOR MATHEMATICS

Selected Common Core Standards for Mathematics 6.RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the

quantity); solve problems involving finding the whole, given a part and the percent. FIRST PRINTING DO NOT DUPLICATE © 2011

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RATIO, PROPORTION, AND PERCENT - …mathandteaching.org/uploads/Modules/RP/RedCore RP1-SP.pdf ·...

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