MIRL Arithmetic 1

8/13/2019 MIRL Arithmetic 1

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www.MakeItRealLearning.com

Arithmetic I

Australia by the Numbers

Borrowing Money

Caring for Pets

Coins in the United States

Country Populations

Fruit Snacks

Sharing Snacks

Sharing Snacks #2

South Africa by the Numbers

Website Visitors

by Frank C. Wilson

Featuring real-world contexts:

Activity Collection


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2009 by Make It Real Learning Company

With the purchase of this workbook, license is granted for one (1) teacher to copy the

activities in this workbook for use in classes and professional development

workshops. Copying pages in this workbook for any other use is prohibited without

written consent from Make It Real Learning Company. For permissions, visit

www.MakeItRealLearning.comand complete the Contact Us form.


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Table of ontentsIntroduction ........................................................................................................................... 4

Activity Objectives ............................................................................................................... 5

Australia by the Numbers: Working with Number and Place Value ............................. 6Solutions ......................................................................................................................... 8

Borrowing Money: Working with Negative Integers ...................................................... 10

Solutions ........................................................................................................................ 12

Caring for Pets: Estimating by Rounding ........................................................................ 14

Solutions ........................................................................................................................ 16

Coins in the United States: Working with Money .......................................................... 18

Solutions ........................................................................................................................ 20

Country Populations: Using Bar Graphs ......................................................................... 22

Solutions ........................................................................................................................ 24

Fruit Snacks: Working with Averages .............................................................................. 26Solutions ........................................................................................................................ 28

Sharing Snacks: Dividing Whole Numbers ...................................................................... 30

Solutions ........................................................................................................................ 32

Sharing Snacks #2: Dividing Whole Numbers ................................................................ 34

Solutions ........................................................................................................................ 36

South Africa by the Numbers: Working with Number and Place Value ..................... 38

Solutions ........................................................................................................................ 40

Website Visitors: Using Bar Graphs ................................................................................. 42

Solutions ........................................................................................................................ 44

About the Author................................................................................................................. 46

Other Books in the Make It Real Learning Series ............................................................ 46


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Introduction

When am I ever going to use this? It is a question that has plagued teachers and

learners for decades. Now, with the help of the Make It Real Learning workbook

series, you can answer the question.

TheArithmetic Iworkbook focuses on real-world situations that may be effectively

analyzed using arithmetic concepts such as addition, subtraction, estimation,

division, bar graphs, etc. From figuring out how to determine the difference between

the populations of two countries to analyzing the number of visitors to a website,

learners get to use arithmetic in meaningful ways. Rest assured that each activity

integrates real world information not just realistic data. These are real companies

and countries (e.g. Webkinz, Australia, South Africa) and real world issues.

The mathematical objectives of each activity are clearly specified on the ActivityObjectives page following this introduction. Through the workbook series, we have

consistently sought to address the content and process standards of the National

Council of Teachers of Mathematics.

There are multiple ways to use the activities in a teaching environment. Many

teachers find that the activities are an excellent tool for stimulating mathematical

discussions in a small group setting. Due to the challenging nature of each activity,

group members are motivated to brainstorm problem solving strategies together. The

interesting real world contexts motivate them to want to solve the problems. The

activities may also be used for individual projects and class-wide discussions.

As a ready-resource for teachers, the workbook also includes completely worked out

solutions for each activity. To make it easier for teachers to assess student work, the

solutions are included on a duplicate copy of each activity.

We hope you enjoy the activities! We continue to increase the number of workbooks

in the Make It Real Learning workbook series. Please visit

www.MakeItRealLearning.comfor the most current list of activities. Thanks!

Frank C. WilsonAuthor


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Arithmetic I Activity Objectives

ctivity Title Mathematical ObjectivesAustralia by the Numbers: Working with

Number and Place Value (p. 6)

Convert numbers in words into numbers in digits and vice versa

Identify the place value of a given digit

Round numbers

Borrowing Money:Working with Negative Integers (p. 10)

Add and subtract positive and negative integers

Interpret the practical meaning of sums and differences of

integers

Caring for Pets:

Estimating by Rounding (p. 14)

Round numbers

Estimate the difference of two numbers

Estimate the product of two numbers

Coins in the United States:

Working with Money (p. 18)

Add whole numbers

Convert dollars to cents

Determine which of two sums has greater value

Country Populations:

Using Bar Graphs (p. 22)

Read data values from a bar graph

Round numbers to the nearest integer

Calculate the difference between two whole numbers

Calculate the sum of two whole numbersFruit Snacks:

Working with Averages (p. 26)

Find the average of a set of numbers

Predict unknown results based on averages

Sharing Snacks:

Dividing Whole Numbers (p. 30)

Divide a given number of items equally between a given

number of groups

Use long division to divide one integer by another

Interpret the practical meaning of a fraction

Sharing Snacks #2:

Dividing Whole Numbers (p. 34)

Use long division to divide one integer by another

Interpret the practical meaning of a fraction

Factor an integer into its prime factors

Convert a percent into a fraction

Determine the practical meaning of quotients and remainders

South Africa by the Numbers: Working

with Number and Place Value (p. 38)

Convert numbers in words into numbers in digits

Convert numbers in digits into numbers in words

Identify the place value of a given digit

Round numbers

Find the difference of two whole numbers

Website Visitors:

Using Bar Graphs (p. 42)

Read data values from a bar graph

Round numbers to the nearest integer

Calculate the sum and difference of two whole numbers


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Australia by the NumbersWorking with Numbers and Place Value

ustralia is the sixth largest country in geographical size. It is an island continent in the southern

hemisphere. The capital of Australia is Canberra. (Facts in this worksheet come from

www.australia.gov.auand www.abs.gov.au.)

1.As of July 2007, the population of Australia was estimated to be twenty one million people. Write that

number.21,000,000

2.Australia contains 7,682,300 square kilometers of land. What number is in the hundred thousands

place?

6

3. The coastline of Australia is 36,735 kilometers long. Round this number to the nearest thousand.

37,000

4. The distance from the north end of Australia to the south end is approximately three thousand two

hundred kilometers. Write that number.

3200

5. European settlers came to Australia in 1788. Write this number in words.

One thousand seven hundred eighty eight

6. The population of the city of Cabrerra is 320,000. What number is in the ten thousands place?

2

7.Although other people were already living in Australia, Captain James Cook is believed to be the first

European to discover Australia. He made is discovery in 1770. Write this number in words.

One thousand seven hundred seventy


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8. Europeans originally shipped prisoners to Australia but stopped doing so in 1868. Round this number to

the nearest ten.

1870

9.Australia produces many different things including water heaters. In May 2008, Australia made 48,613

water heaters (Source: www.abs.gov.au). Write this number in words.

Forty eight thousand six hundred thirteen

10. In June 2008, Australia made 55,345 water heaters. Round this number to the nearest hundred.

55,300

11. There were 531,600 short-term visitors who came to Australia in July 2008. What number is in the

hundred thousands place?

5

12. There were 483,500 short-term visitors who left Australia in July 2008. Write this number in words.

Four hundred eighty three thousand five hundred

13. Rounded to the nearest thousand, how many more short-term visitors came than short-term visitors

who left Australia in July 2008?

531,600

483,500

48,100

Rounded to the nearest thousand, 48,000 more short-term visitors came than short-term visitors who

left in July 2008.

14.The population of Australia is expected to increase to at least 30,900,000 people by 2056. Rounded to

the nearest million, what is the projected population of Australia?

7


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Australia by the NumbersWorking with Numbers and Place Value

ustralia is the sixth largest country in geographical size. It is an island continent in the southern

hemisphere. The capital of Australia is Canberra. (Facts in this worksheet come from

www.australia.gov.auand www.abs.gov.au.)

1.As of July 2007, the population of Australia was estimated to be twenty one million people. Write that

number.21,000,000

2.Australia contains 7,682,300 square kilometers of land. What number is in the hundred thousands

place?

6

3. The coastline of Australia is 36,735 kilometers long. Round this number to the nearest thousand.

37,000

4. The distance from the north end of Australia to the south end is approximately three thousand two

hundred kilometers. Write that number.

3200

5. European settlers came to Australia in 1788. Write this number in words.

One thousand seven hundred eighty eight

6. The population of the city of Cabrerra is 320,000. What number is in the ten thousands place?

2

7.Although other people were already living in Australia, Captain James Cook is believed to be the first

European to discover Australia. He made is discovery in 1770. Write this number in words.

One thousand seven hundred seventy


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8. Europeans originally shipped prisoners to Australia but stopped doing so in 1868. Round this number to

the nearest ten.

1870

9.Australia produces many different things including water heaters. In May 2008, Australia made 48,613

water heaters (Source: www.abs.gov.au). Write this number in words.

Forty eight thousand six hundred thirteen

10. In June 2008, Australia made 55,345 water heaters. Round this number to the nearest hundred.

55,300

11. There were 531,600 short-term visitors who came to Australia in July 2008. What number is in the

hundred thousands place?

5

12. There were 483,500 short-term visitors who left Australia in July 2008. Write this number in words.

Four hundred eighty three thousand five hundred

13. Rounded to the nearest thousand, how many more short-term visitors came than short-term visitors

who left Australia in July 2008?

531,600

483,500

48,100

Rounded to the nearest thousand, 48,000 more short-term visitors came than short-term visitors who

left in July 2008.

14.The population of Australia is expected to increase to at least 30,900,000 people by 2056. Rounded to

the nearest million, what is the projected population of Australia?

31,000,000

9


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Borrowing MoneyWorking with Negative Integers

lthough it is often best to avoid borrowing money to buy the things you want, sometimes it is

necessary to borrow money. Using the mathematical concepts of negative integers, addition, and

subtraction, we can figure out how much money to borrow to buy the thing we need.

In the United States in 2008, a pack of 12 pencils cost 89 cents, a single ball-point pen cost 79 cents, and

a 80-page paper notebook cost 99 cents (Source: www.officedepot.com).

1. In cents, how much money will it take to buy the pack of pencils, the pen, and the notepad?89

79

99

267

+

It will take 267 cents to buy all three items.

2.A student wants to buy all three items but only has $1.80 (180 cents). How much money does he need

to borrow?

We need to figure out the difference between 180 cents and 267 cents. That is, we need to find180 267 . Since 180 is smaller than 267, the answer will be a negative number. To solve the problem,

we find 267 180 and place a negative sign on the result to show that we are borrowing money.267

180

87

So 180 267 87 = . The student will need to borrow 87 cents.

3. The student in Exercise 2 decides that she needs two pens instead of one. How much money will she

need to borrow to buy the pack of pencils, the two pens, and the pad of paper?

From Exercise 2 we know that the student had to borrow 87 cents to buy the first three items. To buy

another pen, she will need to borrow an additional 79 cents. We need to find 87 79 . To do this, we

factor out the negative sign and find 87 79+ .

( )87 79 87 79

166

= +

=

She will need to borrow 166 cents ($1.66).


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4.Before going to the store, the students grandfather gives her five dollars (500 cents) as a birthday gift.

If the student uses the money from her grandfather to make up the additional amount of money she

needed to buy the pack of pencils, two pens, and pad of paper, how many cents will she have left over?

She needed to borrow 166 cents but now she has 500 cents.166

500

+ is equal to

500

166

334

5.Why does it make sense to use negative numbers to represent borrowed money?

Negative numbers are often used for quantities that are below a certain level. For example, when the

temperature is two degrees below zero, we write 2 . With money, 0 cents represents having no money.

Since borrowing money takes us below this level, it makes sense to use negative numbers.

6.What is the difference in meaning between ( )5cents 10 cents + and 5 cents 10 cents + ?

( )5 10cents cents + means we borrowed 5 cents and then borrowed an additional 10 cents. Since

5 10 15+ = , the total amount of money borrowed was 15 cents. That is,

( )5 10 15cents cents cents + = .

5 cents 10 cents + means we borrowed 5 cents and then earned 10 cents. Since 5 10 10 5 + = , the

total amount of money left over after paying back the borrowed money was 5 cents. That is,,

5 cents 10 cents 5cents + = .

7. The United States government borrows money to pay for things. The total amount of money borrowed

is called the national debt. As of September 5, 2008, the national debt was approximately $9,669,799

million dollars (Source: www.treasurydirect.gov). The approximate number of people living in the

United States on the same date was 305 million. If every person in the United States gave $1 to pay

towards that national debt, what would be the new debt amount?

We need to add 305 to 9,669,799. Since more money is borrowed than we are paying back, the

answer will be a negative number. We find ( ) ( )305 9,669,799 305 9,669,799+ = +

.9,669,799

305

9,669,494

So ( )305 9,669,799 9,669,494+ = . The new national debt amount would be $9,669,494 million

dollars.

11


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Borrowing MoneyWorking with Negative Integers

lthough it is often best to avoid borrowing money to buy the things you want, sometimes it is

necessary to borrow money. Using the mathematical concepts of negative integers, addition, and

subtraction, we can figure out how much money to borrow to buy the thing we need.

In the United States in 2008, a pack of 12 pencils cost 89 cents, a single ball-point pen cost 79 cents, and

a 80-page paper notebook cost 99 cents (Source: www.officedepot.com).

1. In cents, how much money will it take to buy the pack of pencils, the pen, and the notepad?89

79

99

267

+

It will take 267 cents to buy all three items.

2.A student wants to buy all three items but only has $1.80 (180 cents). How much money does he need

to borrow?

We need to figure out the difference between 180 cents and 267 cents. That is, we need to find180 267 . Since 180 is smaller than 267, the answer will be a negative number. To solve the problem,

we find 267 180 and place a negative sign on the result to show that we are borrowing money.267

180

87

So 180 267 87 = . The student will need to borrow 87 cents.

3. The student in Exercise 2 decides that she needs two pens instead of one. How much money will she

need to borrow to buy the pack of pencils, the two pens, and the pad of paper?

From Exercise 2 we know that the student had to borrow 87 cents to buy the first three items. To buy

another pen, she will need to borrow an additional 79 cents. We need to find 87 79 . To do this, we

factor out the negative sign and find 87 79+ .

( )87 79 87 79

166

= +

=

She will need to borrow 166 cents ($1.66).


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4.Before going to the store, the students grandfather gives her five dollars (500 cents) as a birthday gift.

If the student uses the money from her grandfather to make up the additional amount of money she

needed to buy the pack of pencils, two pens, and pad of paper, how many cents will she have left over?

She needed to borrow 166 cents but now she has 500 cents.166

500

+ is equal to

500

166

334

5.Why does it make sense to use negative numbers to represent borrowed money?

Negative numbers are often used for quantities that are below a certain level. For example, when the

temperature is two degrees below zero, we write 2 . With money, 0 cents represents having no money.

Since borrowing money takes us below this level, it makes sense to use negative numbers.

6.What is the difference in meaning between ( )5cents 10 cents + and 5 cents 10 cents + ?

( )5 10cents cents + means we borrowed 5 cents and then borrowed an additional 10 cents. Since

5 10 15+ = , the total amount of money borrowed was 15 cents. That is,

( )5 10 15cents cents cents + = .

5 cents 10 cents + means we borrowed 5 cents and then earned 10 cents. Since 5 10 10 5 + = , the

total amount of money left over after paying back the borrowed money was 5 cents. That is,,

5 cents 10 cents 5cents + = .

7. The United States government borrows money to pay for things. The total amount of money borrowed

is called the national debt. As of September 5, 2008, the national debt was approximately $9,669,799

million dollars (Source: www.treasurydirect.gov). The approximate number of people living in the

United States on the same date was 305 million. If every person in the United States gave $1 to pay

towards that national debt, what would be the new debt amount?

We need to add 305 to 9,669,799. Since more money is borrowed than we are paying back, the

answer will be a negative number. We find ( ) ( )305 9,669,799 305 9,669,799+ = +

.9,669,799

305

9,669,494

So ( )305 9,669,799 9,669,494+ = . The new national debt amount would be $9,669,494 million

dollars.

13


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Caring for PetsEstimating by Rounding

etSmart, Inc. (PETM) sells products and services to meet the needs of pets. As of 2008, the company

had 1043 stores in the United States and Canada (Soure: www.petsmart.com). The products and

prices in this worksheet come from the companys online catalog.

1. A 6-pound bag of Blue Buffalo Puppy Food Formula cost $15.99. A 30-pound bag of the puppy food

cost $42.99. Round each of the prices to the nearest dollar and then estimate how much more the 30-

pound bag costs than the 6-pound bag.

We round 15.99 to 16 and 42.99 to 43.

43

16

27

The 30-pound bag costs approximately $27 more than the 6-pound bag.

2.The cost of the 6-pound bag of puppy food in Exercise 1 was approximately $2.67 per pound. The cost

of the 30-pound bag of puppy food was approximately $1.43 per pound. Round each price per pound to

the nearest $0.10 and estimate the difference in the price per pound of the two bags.

2.70

1.40

1.30

The price per pound for the 30-pound back is about $1.30 less than the price per pound for the 6-

pound bag.

3. Is it less expensive to buy four 6-pound bags or one 30-pound bag?

Each 6-pound bag costs about $16 and each 30-pound bag costs about $43. We need to figure out if4 16 is more or less than 43.

16

4

64

Since $64 is more than $43, it is less expensive to buy one 30-pound bag.

P


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4.A carton of Whiskas CatMilk Plus cost $1.39 and a carton of CatSip Milk for Cats cost $1.19. Round

each of the prices to the nearest $0.10. Then predict whether it is less expensive to buy six cartons of

Whiskas CatMilk Plus or eight cartons of CatSip Milk for Cats.

Each carton of CatMilk Plus costs about $1.40 and each carton of CatSip Milk costs about $1.20.

1.40

6

8.40

1.20

8

9.60

It will be less expensive to buy the six cartons of the Whiskas CatMilk Plus ($8.40 versus $9.60).

5. An Avian Adventures Chiquita Dometop Bird Cage cost $369.99 and a Midwest Small and Medium

Parrot Bird Cage cost $149.99. Round each price to the nearest $10 and estimate how much it would

cost to buy both cages.

The first cage will cost about $370 and the second cage will cost about $150.

+

370

150

520

It will cost about $520 to buy both cages.

6.Suppose PetSmart sells 12 of the dometop bird cages given in Exercise 5. Estimate in two different ways

the amount of money the company will earn.

We need to estimate 12 369.99 .

One way to find an estimate is to round 12 down to 10 and round 369.99 up to 400. Then we can use

mental math to find the estimate: =10 400 4000 . We estimate the company will make around $4000

by selling the cages

Another way is to round 369.99 to 370 and then multiply 370 by 12.

370

12

740

370

4440

We estimate the company will make approximately $4440 selling the cages.

15


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Caring for PetsEstimating by Rounding

etSmart, Inc. (PETM) sells products and services to meet the needs of pets. As of 2008, the company

had 1043 stores in the United States and Canada (Soure: www.petsmart.com). The products and

prices in this worksheet come from the companys online catalog.

1. A 6-pound bag of Blue Buffalo Puppy Food Formula cost $15.99. A 30-pound bag of the puppy food

cost $42.99. Round each of the prices to the nearest dollar and then estimate how much more the 30-

pound bag costs than the 6-pound bag.

We round 15.99 to 16 and 42.99 to 43.

43

16

27

The 30-pound bag costs approximately $27 more than the 6-pound bag.

2.The cost of the 6-pound bag of puppy food in Exercise 1 was approximately $2.67 per pound. The cost

of the 30-pound bag of puppy food was approximately $1.43 per pound. Round each price per pound to

the nearest $0.10 and estimate the difference in the price per pound of the two bags.

2.70

1.40

1.30

The price per pound for the 30-pound back is about $1.30 less than the price per pound for the 6-

pound bag.

3. Is it less expensive to buy four 6-pound bags or one 30-pound bag?

Each 6-pound bag costs about $16 and each 30-pound bag costs about $43. We need to figure out if4 16 is more or less than 43.

16

4

64

Since $64 is more than $43, it is less expensive to buy one 30-pound bag.

P


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4.A carton of Whiskas CatMilk Plus cost $1.39 and a carton of CatSip Milk for Cats cost $1.19. Round

each of the prices to the nearest $0.10. Then predict whether it is less expensive to buy six cartons of

Whiskas CatMilk Plus or eight cartons of CatSip Milk for Cats.

Each carton of CatMilk Plus costs about $1.40 and each carton of CatSip Milk costs about $1.20.

1.40

6

8.40

1.20

8

9.60

It will be less expensive to buy the six cartons of the Whiskas CatMilk Plus ($8.40 versus $9.60).

5. An Avian Adventures Chiquita Dometop Bird Cage cost $369.99 and a Midwest Small and Medium

Parrot Bird Cage cost $149.99. Round each price to the nearest $10 and estimate how much it would

cost to buy both cages.

The first cage will cost about $370 and the second cage will cost about $150.

+

370

150

520

It will cost about $520 to buy both cages.

6.Suppose PetSmart sells 12 of the dometop bird cages given in Exercise 5. Estimate in two different ways

the amount of money the company will earn.

We need to estimate 12 369.99 .

One way to find an estimate is to round 12 down to 10 and round 369.99 up to 400. Then we can use

mental math to find the estimate: =10 400 4000 . We estimate the company will make around $4000

by selling the cages

Another way is to round 369.99 to 370 and then multiply 370 by 12.

370

12

740

370

4440

We estimate the company will make approximately $4440 selling the cages.

17


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Working with Money

oins commonly used in the United States include the penny, nickel, dime, quarter, and half-dollar.

The penny is worth 1 cent, the nickel is worth 5 cents, the dime is worth 10 cents, the quarter is

worth 25 cents and the half-dollar is worth 50 cents.

1. In 2008, a Kit Kat candy bar cost 89 cents (Source: www.safeway.com). If you have four dimes, six

nickels, and one quarter, do you have enough money to buy the candy bar?

We need to figure out how much money you have.

Four dimes: 10 10 10 10 40cents cents cents cents cents+ + + =

Six nickels: 5 5 5 5 5 5 30cents cents cents cents cents cents cents+ + + + + =

One quarter: 25 cents

Total amount of money:40

30

25

95

+

You have 95 cents. Since the candy bar costs 89 cents, you have enough money to buy the candy bar.

2. One dollar is the same as 100 cents. You have three dollars and 20 cents and use the money to buy

three 89-cent candy bars. How much money is left over?

Since one dollar is the same as 100 cents, three dollars is the same as 300 cents. The person has 320

cents.320

89

231

231

89

142

142

89

53

After buying three 89-cent candy bars, 53 cents is left over.

C


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3.Which has greater value: two quarters, a dime, and eight pennies or seven dimes and a nickel?

25

25

10

8

68

+

10

10

10

10

1010

10

5

75

+

Seven dimes and a nickel equal 75 cents. Two quarters, a dime, and eight pennies equal 68 cents. The

seven dimes and a nickel have greater value.

4. If you have a half-dollar, four quarters, two dimes, one nickel, and eight pennies, how much more

money do you need to be able to buy three 89 cent candy bars?

89

89

89

267

+

You need 267 cents.50

25

25

2525

10

10

5

8

183

+

You have 183 cents.

267183

84

You need 84 cents more.

19


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Working with Money

oins commonly used in the United States include the penny, nickel, dime, quarter, and half-dollar.

The penny is worth 1 cent, the nickel is worth 5 cents, the dime is worth 10 cents, the quarter is

worth 25 cents and the half-dollar is worth 50 cents.

1. In 2008, a Kit Kat candy bar cost 89 cents (Source: www.safeway.com). If you have four dimes, six

nickels, and one quarter, do you have enough money to buy the candy bar?

We need to figure out how much money you have.

Four dimes: 10 10 10 10 40cents cents cents cents cents+ + + =

Six nickels: 5 5 5 5 5 5 30cents cents cents cents cents cents cents+ + + + + =

One quarter: 25 cents

Total amount of money:40

30

25

95

+

You have 95 cents. Since the candy bar costs 89 cents, you have enough money to buy the candy bar.

2. One dollar is the same as 100 cents. You have three dollars and 20 cents and use the money to buy

three 89-cent candy bars. How much money is left over?

Since one dollar is the same as 100 cents, three dollars is the same as 300 cents. The person has 320

cents.320

89

231

231

89

142

142

89

53

After buying three 89-cent candy bars, 53 cents is left over.

C


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3.Which has greater value: two quarters, a dime, and eight pennies or seven dimes and a nickel?

25

25

10

8

68

+

10

10

10

10

1010

10

5

75

+

Seven dimes and a nickel equal 75 cents. Two quarters, a dime, and eight pennies equal 68 cents. The

seven dimes and a nickel have greater value.

4. If you have a half-dollar, four quarters, two dimes, one nickel, and eight pennies, how much more

money do you need to be able to buy three 89 cent candy bars?

89

89

89

267

+

You need 267 cents.50

25

25

2525

10

10

5

8

183

+

You have 183 cents.

267183

84

You need 84 cents more.

21


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Country PopulationsUsing Bar Graphs

here are nearly 200 different countries in the world. Each country has a different number of people

living in it. The bar graph shows the number of people living in six different countries in 2005

(Source: World Health Organization).

1. Rounded to the nearest million, how many people live in Egypt?

There are 74 million people that live in Egypt.

2. Estimate how many more people live in the Philippines than in Egypt. Round your answer to the

nearest million.

There are 74 million people in Egypt and 83 million people in the Philippines.83

74

9

There are 9 million more people living in the Philippines than in Egypt.

T


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3. The bar for Viet Nam is almost twice as tall as the bar for Ethiopia. Does this mean that the population

of Viet Nam is two times bigger than the population of Ethiopia? Explain.

No. The population of Viet Nam is a little bit more than 84 million. The population of Ethiopia is a

little bit more than 77 million. The number that is two times bigger than 77 million is found by adding

77 million to 77 million.77

77154

+

Since the population of Viet Nam is not 154 million, the population is of Viet Nam is not twice as big

as the population of Ethiopia.

4. Is the combined population of Turkey and Germany greater than the combine population of Egypt and

Ethiopia?

The population of Turkey is a little bit more than 73 million and the population of Germany is a little

bit less than 83 million. We add 73 million to 83 million to estimate their combined population.73

83

156

+

The combined population of Germany and Turkey is about 156 million people.

The population of Egypt is about 74 million and the population of Ethiopia is a little bit more than 77

million. We add 74 million to 77 million to estimate their combined population.74

77

151

+

The combined population of Egypt and Ethiopia is about 151 million people. This is smaller than thecombined population of Germany and Turkey.

5. How much bigger is the combined population of Germany and Turkey than the population of the

Philippines?

In (4), we saw that the combined population of Germany and Turkey was about156 million people. The

population of the Philippines is about 83 million people.

156

83

73

The combined population of Germany and Turkey has about 73 million more people than the

population of the Philippines.

23


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Country PopulationsUsing Bar Graphs

here are nearly 200 different countries in the world. Each country has a different number of people

living in it. The bar graph shows the number of people living in six different countries in 2005

(Source: World Health Organization).

1. Rounded to the nearest million, how many people live in Egypt?

There are 74 million people that live in Egypt.

2. Estimate how many more people live in the Philippines than in Egypt. Round your answer to the

nearest million.

There are 74 million people in Egypt and 83 million people in the Philippines.83

74

9

There are 9 million more people living in the Philippines than in Egypt.

T


25/46

3. The bar for Viet Nam is almost twice as tall as the bar for Ethiopia. Does this mean that the population

of Viet Nam is two times bigger than the population of Ethiopia? Explain.

No. The population of Viet Nam is a little bit more than 84 million. The population of Ethiopia is a

little bit more than 77 million. The number that is two times bigger than 77 million is found by adding

77 million to 77 million.77

77154

+

Since the population of Viet Nam is not 154 million, the population is of Viet Nam is not twice as big

as the population of Ethiopia.

4. Is the combined population of Turkey and Germany greater than the combine population of Egypt and

Ethiopia?

The population of Turkey is a little bit more than 73 million and the population of Germany is a little

bit less than 83 million. We add 73 million to 83 million to estimate their combined population.73

83

156

+

The combined population of Germany and Turkey is about 156 million people.

The population of Egypt is about 74 million and the population of Ethiopia is a little bit more than 77

million. We add 74 million to 77 million to estimate their combined population.74

77

151

+

The combined population of Egypt and Ethiopia is about 151 million people. This is smaller than thecombined population of Germany and Turkey.

5. How much bigger is the combined population of Germany and Turkey than the population of the

Philippines?

In (4), we saw that the combined population of Germany and Turkey was about156 million people. The

population of the Philippines is about 83 million people.

156

83

73

The combined population of Germany and Turkey has about 73 million more people than the

population of the Philippines.

25


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Fruit Snacks

Working with Averages

any people enjoy eating fruit snacks. Kirkland Signature Fruit Snacks are made from seven

different fruit juices (Source: package labeling). A father opened five bags of the Fruit Snacks,

counted the number of pieces in each bag, and recorded the results in the table.

1.What was the average number of pieces in each bag?

14 13 12 14 13 66

5 5

13.2pieces

+ + + +=

=

The average number of pieces in each bag is 13.2 pieces.

2.Which is greater: the average number of green pieces in each bag or the average number of orange

pieces in each bag?

5 3 3 6 6 23

5 5

4.6 green pieces

+ + + +=

=

4 4 4 4 4 20

5 5

4orange pieces

+ + + +=

=

The average number of green pieces in each bag is greater than the average number of orange pieces?

3. The number of yellow pieces in each bag was less than the number of pieces of every other color. What

was the average number of yellow pieces in each bag?

1 2 0 2 1 6

5 5

1.2yellow pieces

+ + + +=

=

MBag #1 14 pieces 4 red, 5 green, 4 orange, 1 yellow

Bag #2 13 pieces 4 red, 3 green, 4 orange, 2 yellow





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4. Is it likely that there is exactly 1 red piece in a bag of Fruit Snacks?

To answer the question we first find the average number of red pieces in each bag.

4 4 5 2 2 17

5 5

3.4 red pieces

+ + + +=

=

Since the average number of red pieces is 3.4 pieces, it is unlikely that there is exactly 1 red piece in a

bag of Fruit Snacks.

5. Using the results from Exercises 1 through 4, predict the number of pieces of each color in an unopened

bag of Fruit Snacks.

On average there were 1.2 yellow pieces, 4.6 green pieces, 4 orange pieces, and 3.4 red pieces. Since it

doesnt make sense to talk about less than a whole piece, we round each of the amounts. We predict

that there is 1 yellow piece, 5 green pieces, 4 orange pieces, and 3 red pieces in an unopened bag. This

adds up to 13 pieces in the bag which is close to the average of 13.2 pieces.

6. After predicting the number of Fruit Snacks in an unopened bag, the father opened up a sixth bag of

Fruit Snacks. It contained 1 yellow piece, 5 green pieces, 4 orange pieces, and 4 red pieces. How

accurate was the prediction in Exercise 5?

The sixth bag contained the exact number of yellow, green and orange pieces predicted and contained

one red piece more than predicted. There were 14 pieces in the bag.

7.When the sixth bag is included with the first five bags, what is the average number of pieces in each

bag?

1

3

14 13 12 14 13 14 80

6 6

13 pieces

+ + + + +=

=

The average number of pieces is 1313 pieces .

27


28/46

Fruit Snacks

Working with Averages

any people enjoy eating fruit snacks. Kirkland Signature Fruit Snacks are made from seven

different fruit juices (Source: package labeling). A father opened five bags of the Fruit Snacks,

counted the number of pieces in each bag, and recorded the results in the table.

1.What was the average number of pieces in each bag?

14 13 12 14 13 66

5 5

13.2pieces

+ + + +=

=

The average number of pieces in each bag is 13.2 pieces.

2.Which is greater: the average number of green pieces in each bag or the average number of orange

pieces in each bag?

5 3 3 6 6 23

5 5

4.6 green pieces

+ + + +=

=

4 4 4 4 4 20

5 5

4orange pieces

+ + + +=

=

The average number of green pieces in each bag is greater than the average number of orange pieces?

3. The number of yellow pieces in each bag was less than the number of pieces of every other color. What

was the average number of yellow pieces in each bag?

1 2 0 2 1 6

5 5

1.2yellow pieces

+ + + +=

=

MBag #1 14 pieces 4 red, 5 green, 4 orange, 1 yellow






29/46


30/46

Sharing SnacksDividing Whole Numbers

rs. Mays makes Trio Natural Bars, a natural fruit and nut bar. The 34 oz. box has 20 bars in it;

five bars are blueberry, five bars are strawberry, five bars are cranberry, and five bars are tropical

(Source: package labeling).

1.A group of five friends will share the box of bars. If each friend gets the same number of bars, how

many bars will each friend get? To find the answer, draw the bars that each friend gets.

Each friend gets four bars.

M

S

TC

B

C

C C

B

B

B

B

S

S

SS

T

T

T

T

C

S

TC

B

CCC C

B B B B S S S S

T T T T


31/46

2. If 6 friends share the box of 20 bars and each friend gets the same number of bars, how many bars will

each friend get and how many bars will be left over?

We can figure out the answer by dividing 20 by 6 and finding the quotient and remainder.

36 20

182

Each friend gets three bars. There are two bars left over.

3. Three of the friends like the tropical and blueberry bars the best. If the 10 tropical and blueberry bars

are divided evenly between the three friends, how many bars does each friend get and how many are

left over?

33 10

9

1

Each friend gets three bars. There is one bar left over.

4. Four friends like the strawberry and blueberry bars the best. If the 10 strawberry and blueberry bars are

divided evenly between the four friends, how many bars does each friend get and how many are left

over?

24 10

8

2

Each friend gets two bars. There are two bars left over.

5. If each friend gets two bars and there are four bars left over, how many friends are in the group?

Since we started with 20 bars and there are 4 left over, 16 bars were given out (20 4 16 = ). Thesesixteen bars are divided into groups of two bars.

8

2 16

16

0

There are eight groups of two bars. Since each friend gets two bars, there are eight friends in the group.

31


32/46

Sharing SnacksDividing Whole Numbers

rs. Mays makes Trio Natural Bars, a natural fruit and nut bar. The 34 oz. box has 20 bars in it;

five bars are blueberry, five bars are strawberry, five bars are cranberry, and five bars are tropical

(Source: package labeling).

1.A group of five friends will share the box of bars. If each friend gets the same number of bars, how

many bars will each friend get? To find the answer, draw the bars that each friend gets.

Each friend gets four bars.

M

S

TC

B

C

C C

B

B

B

B

S

S

SS

T

T

T

T

C

S

TC

B

CCC C

B B B B S S S S

T T T T


33/46



We can figure out the answer by dividing 20 by 6 and finding the quotient and remainder.

36 20

182

Each friend gets three bars. There are two bars left over.

3. Three of the friends like the tropical and blueberry bars the best. If the 10 tropical and blueberry bars

are divided evenly between the three friends, how many bars does each friend get and how many are

left over?

33 10

9

1

Each friend gets three bars. There is one bar left over.

4. Four friends like the strawberry and blueberry bars the best. If the 10 strawberry and blueberry bars are

divided evenly between the four friends, how many bars does each friend get and how many are left

over?

24 10

8

2

Each friend gets two bars. There are two bars left over.

5. If each friend gets two bars and there are four bars left over, how many friends are in the group?

Since we started with 20 bars and there are 4 left over, 16 bars were given out (20 4 16 = ). Thesesixteen bars are divided into groups of two bars.

8

2 16

16

0

There are eight groups of two bars. Since each friend gets two bars, there are eight friends in the group.

33


34/46

Sharing Snacks #2Dividing Whole Numbers

box of Tigers Milk peanut butter nutrition bars contains 24 bars. Each bar contains 6 grams of

protein and 30% of the recommended Daily Value for Vitamin B12 (Source: package labeling).

1.A group of nine friends will share the box of nutrition bars. If each friend gets the same number of

bars, how many bars will each friend get and how many will be left over?

We figure out the answer by dividing 24 by 9 and finding the quotient and remainder.

29 24

18

6

Each friend gets two bars. There are six bars left over.

2. One of the friends wants to get at least 20 grams of protein by eating the Tigers Milk bars. What is the

minimum number of whole bars she must eat? (She doesnt want to waste any portion of a bar.)

36 20

18

2

If she eats 3 and2

6bars, she gets 20 grams of protein. However, since she doesnt want to waste any

portion of a bar, she needs to eat four bars.



45 24

20

4

Each friend gets four bars. There are four bars left over.


35/46

4. Each bar contains 15% of the recommended Daily Value of Vitamin A and 10% of the recommended

Daily Value of Vitamin C. How many bars will a person have to eat to get at least 100% of the

recommended daily value of both vitamins?

615 100

90

10

1010 100

100

0

We pick the larger of the quotients. To get at least 100% of both vitamins, the person needs to eat 10

bars.

5. If a person eats enough bars to get 100% of the recommended Daily Value for Vitamin C, what

percentage of the recommended Daily Value for Vitamin B12 did the person get? (Hint: Each bar

contains 30% of the recommended Daily Value for Vitamin B12.)

From (4), we know that the person ate 10 bars. Since each bar contains 30% of the recommended Daily

Value, we multiply 30% by 10 to get 300%. If the person eats enough bars to get 100% of the Daily

Value of Vitamin C, the person gets 300% of the Daily Value of Vitamin B12.

6. For what group sizes can the bars be divided equally among the group without any bars being left over?

Explain.

The number 24 has factors 1, 2, 3, 4, 6, 8, 12, and 24. The bars may be divided evenly among anygroup of 1, 2, 3, 4, 6, 8, 12, or 24 members.

If the group has 1 person, the person gets 24 bars.

If the group has 2 people, each person gets 12 bars.






If the group has 24 people, each person gets 1 bar.

7.When the 24 bars are divided among a group of 13 people, how many bars are left over?

113 24

13

11

There are 11 bars left over.

35


36/46

Sharing Snacks #2Dividing Whole Numbers

box of Tigers Milk peanut butter nutrition bars contains 24 bars. Each bar contains 6 grams of

protein and 30% of the recommended Daily Value for Vitamin B12 (Source: package labeling).

1.A group of nine friends will share the box of nutrition bars. If each friend gets the same number of

bars, how many bars will each friend get and how many will be left over?

We figure out the answer by dividing 24 by 9 and finding the quotient and remainder.

29 24

18

6

Each friend gets two bars. There are six bars left over.

2. One of the friends wants to get at least 20 grams of protein by eating the Tigers Milk bars. What is the

minimum number of whole bars she must eat? (She doesnt want to waste any portion of a bar.)

36 20

18

2

If she eats 3 and2

6bars, she gets 20 grams of protein. However, since she doesnt want to waste any

portion of a bar, she needs to eat four bars.



45 24

20

4

Each friend gets four bars. There are four bars left over.


37/46

4. Each bar contains 15% of the recommended Daily Value of Vitamin A and 10% of the recommended

Daily Value of Vitamin C. How many bars will a person have to eat to get at least 100% of the

recommended daily value of both vitamins?

615 100

90

10

1010 100

100

0

We pick the larger of the quotients. To get at least 100% of both vitamins, the person needs to eat 10

bars.

5. If a person eats enough bars to get 100% of the recommended Daily Value for Vitamin C, what

percentage of the recommended Daily Value for Vitamin B12 did the person get? (Hint: Each bar

contains 30% of the recommended Daily Value for Vitamin B12.)

From (4), we know that the person ate 10 bars. Since each bar contains 30% of the recommended Daily

Value, we multiply 30% by 10 to get 300%. If the person eats enough bars to get 100% of the Daily

Value of Vitamin C, the person gets 300% of the Daily Value of Vitamin B12.

6. For what group sizes can the bars be divided equally among the group without any bars being left over?

Explain.

The number 24 has factors 1, 2, 3, 4, 6, 8, 12, and 24. The bars may be divided evenly among anygroup of 1, 2, 3, 4, 6, 8, 12, or 24 members.

If the group has 1 person, the person gets 24 bars.







If the group has 24 people, each person gets 1 bar.

7.When the 24 bars are divided among a group of 13 people, how many bars are left over?

113 24

13

11

There are 11 bars left over.

37


38/46

South Africa by the NumbersWorking with Numbers and Place Value

South Africa lies on the southern tip of the African continent. It is an island continent in the southern

hemisphere. The legislative capital of South Africa is Cape Town. (Facts in this worksheet come from

www.statssa.gov.zaand from en.wikipedia.org.)

1.As of October 2001, the population of South Africa was estimated to be forty-four million eight

hundred nineteen thousand seven hundred seventy eight. Write that number.

44,819,778

2. South Africa contains 1,221,037 square kilometers of land. What number is in the hundreds place?

0

3. South Africa mines gold. In August 2007, South African gold sales totaled 3,243,200,000 Rand. (The

Rand is the basic unit of money in South Africa like the dollar is the basic unit of money in the United

States.) Write that number in words.

Three billion two hundred forty three million two hundred thousand

4. The coast of South Africa is 2798 kilometers long. Round this number to the nearest thousand.

3000

5. Cape Town, South Africa, typically receives 627 millimeters of precipitation each year. Round this

number to the nearest ten.

630

6. South Africa grows about nine million tons of maize (corn) each year. Write that number.

9,000,000

7. The estimated population of South Africa in 2008 was 43,786,115. What is the number in the ten

thousands place?

8


39/46


40/46

South Africa by the NumbersWorking with Numbers and Place Value

South Africa lies on the southern tip of the African continent. It is an island continent in the southern

hemisphere. The legislative capital of South Africa is Cape Town. (Facts in this worksheet come from

www.statssa.gov.zaand from en.wikipedia.org.)

1.As of October 2001, the population of South Africa was estimated to be forty-four million eight

hundred nineteen thousand seven hundred seventy eight. Write that number.

44,819,778

2. South Africa contains 1,221,037 square kilometers of land. What number is in the hundreds place?

0

3. South Africa mines gold. In August 2007, South African gold sales totaled 3,243,200,000 Rand. (The

Rand is the basic unit of money in South Africa like the dollar is the basic unit of money in the United

States.) Write that number in words.

Three billion two hundred forty three million two hundred thousand

4. The coast of South Africa is 2798 kilometers long. Round this number to the nearest thousand.

3000

5. Cape Town, South Africa, typically receives 627 millimeters of precipitation each year. Round this

number to the nearest ten.

630

6. South Africa grows about nine million tons of maize (corn) each year. Write that number.

9,000,000

7. The estimated population of South Africa in 2008 was 43,786,115. What is the number in the ten

thousands place?

8


41/46


42/46

Website Visitors

Using Bar Graphs

Webkinz are stuffed animal toys that come with a secret code. By logging on to the Webkinz website, the

toy owner can name the pet and explore the Webkinz World online. The website has great games and

activities that many kids enjoy (Source: www.webkinz.com).

The number of people visiting the Webkinz website changes each month. The bar graph below

shows the number of unique online visitors to the site from March 2008 through August 2008 (Source:

www.compete.com).

1. How many visitors to the Webkinz website were there in June?

There were 6.8 million visitors in June.

2. How many more people visited the website in April than in February?

In April, 7.5 million people visited the website. In February, 6.9 million people visited the website.7.5

6.9

0.6

There were 0.6 million more visitors in April than in February.


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3. In what month did the smallest number of people visit the website?

In July, 6.5 million people visited the website. This is smallest number of people visiting the website for

the months shown.

4.What is the difference in the largest number of people and the smallest number of people visiting thewebsite?

There were 7.5 million people who visited the website in April and 6.5 million who visited the website

in June.7.5

6.5

1.0

The difference between the largest and smallest number of people visiting the website was 1 million.

5. Find the average number of people visiting the website each month between January and July.

Round your answer to the nearest 0.1 million people.

We find the average by adding up the number of people visiting each month and dividing by the total

number of months.

6.6

6.9

7.37.5

6.8

6.8

6.5

48.4

+

Since there are seven months shown on the graph, we divide 48.4 million by 7.

6.97 48.4

42

64

63

1

Rounded to the nearest 0.1 million, the average number of visitors to the site was 6.9 million.

43


44/46

Website Visitors

Using Bar Graphs

Webkinz are stuffed animal toys that come with a secret code. By logging on to the Webkinz website, the

toy owner can name the pet and explore the Webkinz World online. The website has great games and

activities that many kids enjoy (Source: www.webkinz.com).

The number of people visiting the Webkinz website changes each month. The bar graph below

shows the number of unique online visitors to the site from March 2008 through August 2008 (Source:

www.compete.com).

1. How many visitors to the Webkinz website were there in June?

There were 6.8 million visitors in June.

2. How many more people visited the website in April than in February?

In April, 7.5 million people visited the website. In February, 6.9 million people visited the website.7.5

6.9

0.6

There were 0.6 million more visitors in April than in February.


45/46


46/46

bout the uthorFrank Wilson earned his B.S. and M.S. degrees in mathematics from Brigham

Young University. He spent six years serving as an officer in the United StatesAir Force before returning to civilian life. He has taught students math at the

United States Air Force Academy, Park College, Green River Community

College, and Chandler-Gilbert Community College. In addition to teaching,

Frank is a popular author and workshop presenter. His college mathematics

textbooks (Finite Mathematics, Finite Mathematics and Applied Calculus, Brief

Applied Calculus, and Applied Calculus) are used at colleges and universities

across the United States. Finite Mathematics and Applied Calculus was selected

by the Textbook and Academic Authors Association as the winner of the 2007

TEXTY Textbook Excellence award for mathematics. Franks picture book on

measurement, Measure Up! A Bug Contest, is popular among teachers and

children alike.

Frank lives with his wife and five living children in Queen Creek, Arizona.

Other Books in the Make It Real Learning ctivity Series Calculus I Exponential and Logarithmic Functions I

Fractions, Percents, Decimals I Fractions, Percents, Decimals II Linear Functions I Linear Functions II Periodic and Piecewise Functions I Polynomial, Power, Logistic, Rational Functions I Quadratic Functions I Sets, Probability, Statistics I

Visit www.MakeItRealLearning.comfor the most current listing of titles.

Documents

MIRL Arithmetic 1