# The Craft of Word Problems

## CONTENTS OF CURRICULUM UNIT 04.05.04

## The Art of Interpreting Percent

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## Lesson 4

Goal: Students will appreciate that when the total numbers add up to100 one can easily calculate the decimal and percentages. When students have the opportunity to see the relationship between the fractions, decimals and percentage then they are able to transfer that knowledge to more difficult problems. Listed below are problems which I have solved and would be useful to solve with the students during the initiation portion of the lesson. For example, write 30 out of 100 as 30/100 = 0.30 = 30% ( For the problems involving pets in lesson assume that no student owns more than one pet)

### Part of a Whole as a Percentage, using Totals of 100

**
Table I Number Of Pets Owned By Students
**

- Number of students who own pet(s) 40
- Number of students who do not own pet(s) 60
- Total number of students 100

Problem 1.

A. What percent of the students own pets?

B. What percent of the students do not own pets?

Answers

A. 40/100 = 0.40 = 40%

B. 60/100 = 0.60 = 60%

**
Table II Number Of Pets Owned By Students
**

- Number of students who own dog(s) 30
- Number of students who own guinea pig(s) 25
- Number of students who own fish 15
- Number of students who own cat(s) 20
- Number of students who do not own pets 10

Problem 2.

A. What percent of students own dog(s)?

B. What percent of students own guinea pig(s)?

C. What percent of students own fish?

D. What percent of students own cat(s)?

E. What percent of students do not own pets?

Answers

A. 30/100 = 0.30 = 30%

B. 25/100 = 0.25 = 25%

C. 15/100 = 0.15 = 15%

D. 20/100 = 0.20 = 20%

E. 10/100 = 0.10 = 10%

Parts of a Whole as a Percentage, using Totals other than 100:

Once the students have an understanding of calculating percentages with totals equaling

100 then I will introduce totals of different amounts.

Table III Number of Students Who Attend Summer Camp

- Number of students who attend summer camp 60
- Number of students who do not attend summer camp 20
- Total number of students 80

Problem 3.

A. What percent of the students attend summer camp?

B. What percent of the students do not attend camp?

Answers

A.60/80 = 0.75 = 75%

B.20/80 = 0.25 = 25%

**
Table IV Number Of Pets Owned By Students
**

- Number of students who own dog(s) 35
- Number of students who own guinea pig(s) 40
- Number of students who own fish 25
- Number of students who own cat(s) 30
- Number of students who do not own pets 20
- Total number of students 150

Problem 4.

A What percent of students own dog(s)?

B What percent of students own guinea pig(s)?

C What percent of students own fish?

D What percent of students own cat(s)?

E What percent of students do not own pets?

Answers

A.35/150 = 0.23 = 23%

B.40/150 = 0.27 = 27%

C.25/150 = 0.17 = 17%

D.30/150 = 0.20 = 20%

E.20/150 = 0.13 = 13%

### Adding percent quantities

To solve percentage problems which require addition one must either: (1) Add the number of items and then calculate the percentage. or (2) Find the percentages and add them together.

Problem 5
*
*
Utilize Table IV, what percentage of the students own fish and cats?

(1) fish owners = 15 & cat owners = 20 therefore,15 + 20 = 35 and 35/100 = 35%

(2) fish owners = 15% & cat owners = 20% therefore, 15% + 20% = 35%

Problem 6 Utilize Table IV solve the following utilizing (1) formula:

A. What percent of the students own dogs or fish?

B. What percent of the students own dogs or cats?

C. What percent of the students own dogs, cats, or fish?

D. What percent of the students own guinea pigs, cats, & fish?

Answers

A. 30 + 15 = 45/100 = 45%

B. 30 + 20 = 50/100 = 50%

C. 30+20 +15 = 65/100=65%

D. 25 + 20 + 15 = 60/100 = 60%

Problem 7 Utilize Table IV to solve the following utilizing (2) formula:

A. What percent of the students own dogs or fish?

B. What percent of the students own dogs or cats?

C. What percent of the students own dogs, cats, or fish?

D. What percent of the students own guinea pigs, cats, or fish?

Answers

A. 30% + 15% = 45%

B. 30% + 20% = 50%

C. 30% +20% +15% = 65%

D. 25%+ 20%+15%=60%

**
Table V Number of Pets owned by Students
**

Number of students who own dog(s) 35

Number of students who own cat(s) 40

Number of students who own both dog(s) and cat(s) 25

Number of students who do not own any pets 50

Problem 8 A. What percent of the students own either a dog, cat, or both?

35 dogs + 40 cats =75 dogs/cats - 25 dogs/cats = 50 dogs/cats

Answer: 50/100 = 0.50 = 50%

B. What percent of the students own both dogs/cats = 25/100 = 0.25 = 25%

**
Table VI Chores Percentage
**

Clean up room 35%

Wash dishes 10%

Take out trash 15%

Walk the dog 20%

Feed the cat 8%

No chores 12%

Utilizing the formulas above solve the following problems, utilizing Table VI. For ease of calculations one must assume that each child only performs one chore.

Problem 9

A. What fraction/decimal of the students clean up room?

B. What fraction/decimal of the students wash dishes?

C. What fraction/decimal of the students take out the trash?

D. What fraction/decimal of the students walk the dog?

E. What fraction/decimal of the students feed the cat?

F. What fraction/decimal of the students have no chores?

G. What fraction/decimal of the students walk the dog and clean up room?

H. What percent/decimal of the students feed the cat and wash dishes?

I. What percent/decimal of the students take out the trash, feed the cat, and walk the dog?

**
Table VII Ice Cream Preferences of Students
**

Flavors Preference

Rocky Road 1/15

Chocolate Chip Cookie Dough 1/9

Mint Chocolate Chip 1/18

Vanilla 1/3

Strawberry 1/10

Chocolate 4/36

Coffee 2/9

Problem 10

A. What percentage of students prefer Rocky Road?

B. What percentage of students Chocolate Chip Cookie Dough?

C. What percentage of students Mint Chocolate Chip?

D. What percentage of students Vanilla?

E. What percentage of students Strawberry?

F. What percentage of students Chocolate?

G. What percentage of students Vanilla?