Name Daily Spiral Review 4-1 · 2018. 1. 14. · Daily Spiral Review 4-1 Topic 4 29 1. Steve uses 6...

Name©

Pea

rson

Edu

catio

n, In

c. 5

Daily Spiral Review

4-1

Topic 4 29

1. Steve uses 6 balls of yarn to knit a sweater. Knitting a blanket takes 15 times as many balls of yarn. Which equation can Steve use to ! nd b, the number of balls of yarn he needs to knit a blanket? A 6 ! 15 " b B 6 # 15 " b C 6 ! b " 15 D 6 # b " 15

2. Meg buys 12 bags of sun" ower seeds. Each bag has 58 seeds. How many seeds does Meg buy?A 696B 686C 174D 116

3. After waking up, it takes Cheyenne 35 minutes to get ready to leave for school. She takes 20 minutes to walk to school. If Cheyenne wakes up at 7:15 A.M., at what time does she arrive at school?A 7:40 A.M.B 7:55 A.M.C 8:00 A.M.D 8:10 A.M.

4. A building has 8 same-sized apartments. The area of 1 apartment is 725 square feet. Let t be the total area of the 8 apartments.a. Draw a picture to describe t.

b. Write an equation that you could use to ! nd t.

c. What is the value of t?

5. For the 2004–05 school year, the state of Texas spent about thirty-eight billion dollars on education. Write this amount of money in standard form.

6. Last year, Handy Hardware Store sold 45,078 bolts and 5,011,542 nails. How many more nails did the store sell than bolts?

Daily Spiral Review

4-1

30428_T04_029_29 29 1/31/08 8:41:24 PM

www.inmatesearch.mobi

Name©

Pea

rson

Edu

catio

n, In

c. 5

Daily Spiral Review

4-1

Topic 4 29

1. Steve uses 6 balls of yarn to knit a sweater. Knitting a blanket takes 15 times as many balls of yarn. Which equation can Steve use to ! nd b, the number of balls of yarn he needs to knit a blanket? A 6 ! 15 " b B 6 # 15 " b C 6 ! b " 15 D 6 # b " 15

2. Meg buys 12 bags of sun" ower seeds. Each bag has 58 seeds. How many seeds does Meg buy?A 696B 686C 174D 116

3. After waking up, it takes Cheyenne 35 minutes to get ready to leave for school. She takes 20 minutes to walk to school. If Cheyenne wakes up at 7:15 A.M., at what time does she arrive at school?A 7:40 A.M.B 7:55 A.M.C 8:00 A.M.D 8:10 A.M.

4. A building has 8 same-sized apartments. The area of 1 apartment is 725 square feet. Let t be the total area of the 8 apartments.a. Draw a picture to describe t.

b. Write an equation that you could use to ! nd t.

c. What is the value of t?

5. For the 2004–05 school year, the state of Texas spent about thirty-eight billion dollars on education. Write this amount of money in standard form.

6. Last year, Handy Hardware Store sold 45,078 bolts and 5,011,542 nails. How many more nails did the store sell than bolts?

Daily Spiral Review

4-1

4,966,464

$38,000,000,000

725 ! 8 " t

5,800 square feet

725 725 725 725 725 725 725 725

t " total area

30428_T04_029_29 29 3/18/08 1:52:27 PM

© Pearson Education, Inc. 5

At the theater, the price of a ticket was $7.50 in 2001, $8.00 in 2003, $8.50 in 2005, and $9.00 in 2007. If the pattern continues, in what year will the price reach $10.00? Explain.

Problem of the Day

4-1

4-1Problem of the DayProblem of the Day 4-1

30

Topic 4

30428_T04_030_30 30

1/31/08 8:41:31 PM

Name

Topic 4 31

© P

ears

on E

duca

tion,

Inc.

5Q

uick Check 4

-1

Use mental math to find the quotients.

1. 480 ! 6

A 8

B 80

C 800

D 8,000

2. 36,000 ! 4

A 9

B 90

C 900

D 9,000

3. A company has 5,400 bottles of shampoo to be packed into 9 boxes. How many bottles of shampoo will be in each box?

A 6,000

B 600

C 60

D 6

4. Writing to Explain The Ruiz family took a summer trip. In 4 days, they drove 1,600 miles. If they drove an equal number of miles each day, how many miles did they drive each day? Describe the basic fact you use to find your answer and how many zeros you add from the dividend.

Quick Check

4-1

30428_T04_031_31 31 1/31/08 8:41:38 PM

Name

Topic 4 31

© P

ears

on E

duca

tion,

Inc.

5

Quick C

heck 4-1


1. 480 ! 6

A 8

B 80

C 800

D 8,000

2. 36,000 ! 4

A 9

B 90

C 900

D 9,000

3. A company has 5,400 bottles of shampoo to be packed into 9 boxes. How many bottles of shampoo will be in each box?

A 6,000

B 600

C 60

D 6

4. Writing to Explain The Ruiz family took a summer trip. In 4 days, they drove 1,600 miles. If they drove an equal number of miles each day, how many miles did they drive each day? Describe the basic fact you use to find your answer and how many zeros you add from the dividend.

Quick Check

4-1

See student samples at the right.

30428_T04_031_31 31 3/18/08 1:52:45 PM

Number of bundles 12

Number of newspapersper bundle 9

Arlo’s Newspaper Delivery

Name

© P

ears

on E

duca

tion,

Inc.

5

Reteaching

4-1Dividing Multiples of 10 and 100You can use math facts and patterns to help you divide mentally.

Find each quotient. Use mental math.

1. 32 ! 8 " 2. 320 ! 8 " 3. 3,200 ! 8 " 4. 32,000 ÷ 8 =

5. 56 ! 7 " 6. 560 ! 7 " 7. 5,600 ! 7 " 8. 56,000 ÷ 7 =

9. 15 ! 3 " 10. 150 ! 3 " 11. 1,500 ! 3 " 12. 15,000 ÷ 3 =

13. Number Sense Explain how dividing 720 by 9 is like dividing 72 by 9.

Arlo has a newspaper delivery job. He wants to wrap each of his newspapers in a plastic bag to protect them from the rain. The newspapers are in bundles.

Use mental math to answer the following questions.

14. How many bags will he use for 5 bundles?

15. How many bags will he use for 7 bundles?

16. How many bags will he use for all 12 bundles?

What is 480 ! 6?

You already know that 48 ! 6 " 8.

480 has one more zero than 48, soplace one more zero in the quotient.

480 ! 6 " 80.

What is 60,000 ! 6?

60 ! 6 " 10

60,000 has three more zeros than6, so place three zeros in the quotient.

60,000 ! 6 " 10,000.

Rete

achi

ng 4-1

32 Topic 4

30428_T04_032-034_32 32 1/31/08 8:41:46 PM

Number of bundles 12

Number of newspapersper bundle 9

Arlo’s Newspaper Delivery

Name

© P

ears

on E

duca

tion,

Inc.

5

Reteaching

4-1Dividing Multiples of 10 and 100You can use math facts and patterns to help you divide mentally.

Find each quotient. Use mental math.

1. 32 ! 8 " 2. 320 ! 8 " 3. 3,200 ! 8 " 4. 32,000 ÷ 8 =

5. 56 ! 7 " 6. 560 ! 7 " 7. 5,600 ! 7 " 8. 56,000 ÷ 7 =

9. 15 ! 3 " 10. 150 ! 3 " 11. 1,500 ! 3 " 12. 15,000 ÷ 3 =

13. Number Sense Explain how dividing 720 by 9 is like dividing 72 by 9.

Arlo has a newspaper delivery job. He wants to wrap each of his newspapers in a plastic bag to protect them from the rain. The newspapers are in bundles.


14. How many bags will he use for 5 bundles? 15. How many bags will he use for 7 bundles? 16. How many bags will he use for all 12 bundles?

What is 480 ! 6?

You already know that 48 ! 6 " 8.

480 has one more zero than 48, soplace one more zero in the quotient.

480 ! 6 " 80.

What is 60,000 ! 6?

60 ! 6 " 10

60,000 has three more zeros than6, so place three zeros in the quotient.

60,000 ! 6 " 10,000.

Rete

achi

ng 4-1

32 Topic 4

You divide 72 by 9. For 720, you add azero for the ones place.

63 bags45 bags

108 bags

400404

8

5

80

50

800

500

4,000

8,000

5,000

30428_T04_032-034_32 32 3/18/08 1:52:58 PM

Sections of vehicles ............. 4Vehicles for sale ............ 1,200Rows per section ................10

Dealership Vehicle Storage

Name©

Pea

rson

Edu

catio

n, In

c. 5

Dividing Multiples of 10 and 100Use mental math to find each quotient.

10. If a bike race covers 120 mi over 6 days and the cyclists ride the same distance each day, how many miles does each cyclist ride each day?


11. If the vehicles are divided evenly between the sections, how many vehicles are in each section?

12. If the vehicles are divided evenly between the rows in each section, how many vehicles are in each row?

13. Algebra If 160,000 ! n " 4, find n.

14. Find 32,000 ! 8 mentally.

A 4,000 B 400 C 40 D 4

15. Explain It Solve the equation n # 50 " 5,000. Explain your solution.

1. 27 ! 9 "

4. 24 ! 4 "

7. 720 ! 9 "

2. 270 ! 9 "

5. 240 ! 4 "

8. 140 ! 7 "

3. 2,700 ! 9 "

6. 2,400 ! 4 "

9. 2,100 ! 3 "

Practice 4-1

Practice

4-1

Topic 4 33

30428_T04_032-034_33 33 1/31/08 8:41:49 PM

Sections of vehicles ............. 4Vehicles for sale ............ 1,200Rows per section ................10

Dealership Vehicle Storage

Name©

Pea

rson

Edu

catio

n, In

c. 5

Dividing Multiples of 10 and 100Use mental math to find each quotient.

10. If a bike race covers 120 mi over 6 days and the cyclists ride the same distance each day, how many miles does each cyclist ride each day?


11. If the vehicles are divided evenly between the sections, how many vehicles are in each section?

12. If the vehicles are divided evenly between the rows in each section, how many vehicles are in each row?

13. Algebra If 160,000 ! n " 4, find n.

14. Find 32,000 ! 8 mentally.

A 4,000 B 400 C 40 D 4

15. Explain It Solve the equation n # 50 " 5,000. Explain your solution.

1. 27 ! 9 "

4. 24 ! 4 "

7. 720 ! 9 "

2. 270 ! 9 "

5. 240 ! 4 "

8. 140 ! 7 "

3. 2,700 ! 9 "

6. 2,400 ! 4 "

9. 2,100 ! 3 "

Practice 4-1

Practice

4-1

Topic 4 33

n! 100; Sample answer: Divide each side by 50.

3 30

6

80

60

20 700

600

300

20 mi

300 vehicles

30 Vehicles40,000

30428_T04_032-034_33 33 3/18/08 1:53:00 PM

© P

ears

on E

duca

tion,

Inc.

5

Mental Math

Fun and Relaxation1. Ten friends won the grand prize in the raffle. They won

2,000 music CDs. Use mental math to find out how many CDs each of the friends receives if they divide the prize equally.

2. If Jasmine roller skates 280 miles in 7 weeks and skates the same distance each week, how many miles does she skate each week?

3. Four sisters are going on a camping trip. They need to divide up their supplies equally to carry in their backpacks. If they want to bring along 120 energy bars, how many will each sister carry?

4. The Green family has a movie rental plan of 900 movies per year. Mr. and Mrs. Green rent a certain number of movies, and their children Tyrone and Tina divide the remaining movies in half. How many movies can each of the children rent per year?

5. If Kevin writes 850 words in his blog from Monday through Friday, and he writes the same number of words each day, how many words does he write each day?

Enrichment

4-1

DVD Rentals

NameNumber of

Movies

Mr. Green 300

Mrs. Green 380

Tyrone

Tina

Name

34 Topic 4

Enric

hmen

t 4-1

30428_T04_032-034_34 34 1/31/08 8:41:51 PM

© P

ears

on E

duca

tion,

Inc.

5

Mental Math

Fun and Relaxation1. Ten friends won the grand prize in the raffle. They won

2,000 music CDs. Use mental math to find out how many CDs each of the friends receives if they divide the prize equally.

2. If Jasmine roller skates 280 miles in 7 weeks and skates the same distance each week, how many miles does she skate each week?

3. Four sisters are going on a camping trip. They need to divide up their supplies equally to carry in their backpacks. If they want to bring along 120 energy bars, how many will each sister carry?

4. The Green family has a movie rental plan of 900 movies per year. Mr. and Mrs. Green rent a certain number of movies, and their children Tyrone and Tina divide the remaining movies in half. How many movies can each of the children rent per year?

5. If Kevin writes 850 words in his blog from Monday through Friday, and he writes the same number of words each day, how many words does he write each day?

Enrichment

4-1

DVD Rentals

NameNumber of

Movies

Mr. Green 300

Mrs. Green 380

Tyrone

Tina

Name

34 Topic 4

Enric

hmen

t 4-1

200 CDs

40 miles per week

30 bars

110 movies each

170 words each day

30428_T04_032-034_34 34 3/18/08 1:53:03 PM

40 !C

30 !C

20 !C

10 !C

Human

40 !C

30 !C

20 !C

10 !C

Fish

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 35

Daily Spiral Review

4-2

1. A school’s Parent-Teacher Club raises $280 by washing cars. Each car wash costs $4. How many cars did the club wash?A 7B 70C 700D 7,000

2. In basketball, if a player makes a basket from behind a certain line, the basket is worth 3 points. Last year, a team made 392 of its 3-point baskets. How many points did the team earn last year from 3-point baskets?A 1,176B 1,086C 976D 395

3. Mr. Lopez buys shoes for his two children, Maria and Juan. Maria’s shoes cost $28.35 with tax. Juan’s shoes cost $30.97 with tax. How much did Mr. Lopez pay for Maria’s and Juan’s shoes?A $57.05B $58.22C $59.32D $68.05

4. A ! our mill produces the same amount of ! our every hour. At the end of 8 hours, the mill has produced 48,000 pounds of ! our. How many pounds of ! our does the mill produce in 1 hour?

5. In the year 2000, San Antonio, Texas, had a population of 1,144,646. What is this population rounded to the nearest hundred thousand?

6. This thermometer shows the normal temperature of a healthy adult human.

The temperature of a fish could be 19˚C lower. Mark the fish’s temperature on the thermometer below.

Daily Spiral Review

4-2

30428_T04_035_35 35 1/31/08 8:41:59 PM

40 !C

30 !C

20 !C

10 !C

Human

40 !C

30 !C

20 !C

10 !C

Fish

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 35

Daily Spiral Review

4-2

1. A school’s Parent-Teacher Club raises $280 by washing cars. Each car wash costs $4. How many cars did the club wash?A 7B 70C 700D 7,000

2. In basketball, if a player makes a basket from behind a certain line, the basket is worth 3 points. Last year, a team made 392 of its 3-point baskets. How many points did the team earn last year from 3-point baskets?A 1,176B 1,086C 976D 395

3. Mr. Lopez buys shoes for his two children, Maria and Juan. Maria’s shoes cost $28.35 with tax. Juan’s shoes cost $30.97 with tax. How much did Mr. Lopez pay for Maria’s and Juan’s shoes?A $57.05B $58.22C $59.32D $68.05

4. A ! our mill produces the same amount of ! our every hour. At the end of 8 hours, the mill has produced 48,000 pounds of ! our. How many pounds of ! our does the mill produce in 1 hour?

5. In the year 2000, San Antonio, Texas, had a population of 1,144,646. What is this population rounded to the nearest hundred thousand?

6. This thermometer shows the normal temperature of a healthy adult human.

The temperature of a fish could be 19˚C lower. Mark the fish’s temperature on the thermometer below.

Daily Spiral Review

4-2

6,000 pounds

1,100,000

30428_T04_035_35 35 3/18/08 1:53:14 PM


Problem of the Day

4-2

Tortoises can weigh up to 500 lb. Turtles can weigh up to 1,500 lb. How many times the maximum weight of a tortoise is the maximum weight of a turtle?

Problem of the Day 4-2

36

Topic 4

4-2Problem of the Day

30428_T04_036_36 36

1/31/08 8:42:06 PM

Name

Topic 4 37

© P

ears

on E

duca

tion,

Inc.

5Q

uick Check 4

-2Quick Check

4-2

1. Use rounding to estimate the quotient. 415 ! 8

A 5

B 6

C 50

D 60

2. Use compatible numbers to estimate the quotient. 435 ! 7

A 70

B 60

C 7

D 6

3. A school held a food drive. The 8 classrooms collected 307 cans of food. Each classroom collected about the same number. About how many cans of food did each classroom collect?

A 30

B 40

C 42

D 45

4. Writing to Explain Tarek is dividing his 483 baseball cards among his 5 younger cousins. About how many baseball cards could he give each of his cousins? Use compatible numbers and rounding to overestimate and underestimate. Explain your work.

30428_T04_037_37 37 1/31/08 8:42:13 PM

Name

Topic 4 37

© P

ears

on E

duca

tion,

Inc.

5

Quick C

heck 4-2

Quick Check

4-2

1. Use rounding to estimate the quotient. 415 ! 8

A 5

B 6

C 50

D 60

2. Use compatible numbers to estimate the quotient. 435 ! 7

A 70

B 60

C 7

D 6

3. A school held a food drive. The 8 classrooms collected 307 cans of food. Each classroom collected about the same number. About how many cans of food did each classroom collect?

A 30

B 40

C 42

D 45

4. Writing to Explain Tarek is dividing his 483 baseball cards among his 5 younger cousins. About how many baseball cards could he give each of his cousins? Use compatible numbers and rounding to overestimate and underestimate. Explain your work.


30428_T04_037_37 37 3/18/08 1:53:35 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Rete

achi

ng 4-2

Reteaching

4-2

38 Topic 4

Estimating QuotientsThere are several ways to adjust whole numbers to estimate quotients.

Example:

There are 216 students. The school has 8 classrooms. How many students will be in each classroom?

Estimate 216 ! 8.

Estimate each quotient. You may use any method.

1. 411 ! 2 2. 162 ! 4

3. Number Sense If you estimate 342 ! 7 by using 350 ! 7 " 50, is 50 greater than or less than the exact answer? How did you decide? Is 50 an overestimate or an underestimate?

Rounding

You can use rounding to estimate a quotient.

Round 216 to the nearest hundred.

In this case, 216 rounds to 200.

200 ! 8 " 25

25 students per room is an underestimate, because 216 was rounded down to 200.

Compatible Numbers

You can use compatible numbers to estimate a quotient.

Change 216 to a compatible number for 8.

Compatible numbers for 8 are numbers divisible by 8, such as 160, 240, and 320. Choose 240, because it is the closest compatible number to 216.

240 ! 8 " 30

30 students per class is an overestimate, because 216 was rounded up to 240.

Multiplication

You can use multiplication to estimate a quotient.

Think: 8 times what number is about 216?

8 # 25 " 200

8 # 30 " 240

216 is between 200 and 240. So a good estimate is a little more than 25 and a little less than 30 students per classroom.

30428_T04_38-40_38 38 1/31/08 8:47:44 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Rete

achi

ng 4-2

Reteaching

4-2

38 Topic 4

Estimating QuotientsThere are several ways to adjust whole numbers to estimate quotients.

Example:

There are 216 students. The school has 8 classrooms. How many students will be in each classroom?

Estimate 216 ! 8.

Estimate each quotient. You may use any method.

1. 411 ! 2 2. 162 ! 4

3. Number Sense If you estimate 342 ! 7 by using 350 ! 7 " 50, is 50 greater than or less than the exact answer? How did you decide? Is 50 an overestimate or an underestimate?

Rounding

You can use rounding to estimate a quotient.

Round 216 to the nearest hundred.

In this case, 216 rounds to 200.

200 ! 8 " 25

25 students per room is an underestimate, because 216 was rounded down to 200.

Compatible Numbers

You can use compatible numbers to estimate a quotient.

Change 216 to a compatible number for 8.

Compatible numbers for 8 are numbers divisible by 8, such as 160, 240, and 320. Choose 240, because it is the closest compatible number to 216.

240 ! 8 " 30

30 students per class is an overestimate, because 216 was rounded up to 240.

Multiplication

You can use multiplication to estimate a quotient.

Think: 8 times what number is about 216?

8 # 25 " 200

8 # 30 " 240

216 is between 200 and 240. So a good estimate is a little more than 25 and a little less than 30 students per classroom.

400 ! 2 " 200 160 ! 4 " 40

It is greater, because you rounded 342 up to 350. So, 50 is an overestimate.

30428_T04_38-40_38 38 3/18/08 2:00:37 PM

NamePractice 4

-2Practice

4-2

Topic 4 39

Estimating QuotientsEstimate each quotient. Tell which method you used.

1. 195 ! 4

2. 283 ! 5

3. 766 ! 8

4. 179 ! 2

5. $395.20 ! 5

6. $31.75 ! 8

7. $247.80 ! 5

8. Reasoning If you use $63.00 ! 9 to estimate $62.59 ! 9, is $7.00 greater than or less than the exact answer? Explain.

11. Which is the closest estimate for 213 ! 4?

A 50 B 40 C 30 D 20

12. Explain It Explain how to estimate 524 ! 9.

9. A band played 3 concerts and earned a total of $321.00. The band earned about the same amount for each concert. Estimate how much the band earned each night.

10. At a department store, a woman’s total was $284.00 for 7 items. Estimate the average cost per item.

© P

ears

on E

duca

tion,

Inc.

5

30428_T04_38-40_39 39 1/31/08 8:47:46 PM

NamePractice 4

-2Practice

4-2

Topic 4 39

Estimating QuotientsEstimate each quotient. Tell which method you used.

1. 195 ! 4

2. 283 ! 5

3. 766 ! 8

4. 179 ! 2

5. $395.20 ! 5

6. $31.75 ! 8

7. $247.80 ! 5

8. Reasoning If you use $63.00 ! 9 to estimate $62.59 ! 9, is $7.00 greater than or less than the exact answer? Explain.

11. Which is the closest estimate for 213 ! 4?

A 50 B 40 C 30 D 20

12. Explain It Explain how to estimate 524 ! 9.

9. A band played 3 concerts and earned a total of $321.00. The band earned about the same amount for each concert. Estimate how much the band earned each night.

10. At a department store, a woman’s total was $284.00 for 7 items. Estimate the average cost per item.

© P

ears

on E

duca

tion,

Inc.

5

50609090$80$4$50

MultiplicationRoundingRoundingCompatible numbers

Multiplication

RoundingCompatible numbers

Greater than; 9 ! 7 " 63, which is greater than $62.59.

About $100 each night

About $40.00

Sample answer: Round 524 to 500, 9 to 10, and divide: 500 # 10 " 50.

Sample answers for 1–8.

30428_T04_38-40_39 39 3/18/08 2:00:39 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Estimation

Working Hard 1. Janelle earned $889 in 3 months for babysitting. If she was

paid the same amount for each month, about how much did she earn per month?

2. Roberto is collecting stuffed toys to donate to 8 different charities. He wants to donate about the same amount to each charity. If Roberto collected 711 stuffed toys, about how many should he donate to each charity?

3. Julia is packing her paperweight collection into 7 boxes. She wants to put about the same number in each box. If Julia has 500 paperweights in her collection, about how many should she pack in each box?

4. Tony is testing a new type of sneaker for his mother’s company. He will wear the sneaker for 6 days while he jogs on the beach for about the same distance each day. If Tony jogs 70 miles in 6 days, about how many miles does he jog each day?

5. Marissa is saving for a laptop computer. She deposited $391 into her bank account over 5 months. If she deposited the same amount into her account each month, about how much did she deposit each month?

6. The laptop computer that Marissa is saving for in Problem 5 costs $625. If she continues to deposit the same amount into her account each month, about how many more months will it take before she can purchase the computer?

40 Topic 4

Enrichment

4-2En

richm

ent 4

-2

30428_T04_38-40_40 40 1/31/08 8:47:48 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Estimation

Working Hard 1. Janelle earned $889 in 3 months for babysitting. If she was

paid the same amount for each month, about how much did she earn per month?

2. Roberto is collecting stuffed toys to donate to 8 different charities. He wants to donate about the same amount to each charity. If Roberto collected 711 stuffed toys, about how many should he donate to each charity?

3. Julia is packing her paperweight collection into 7 boxes. She wants to put about the same number in each box. If Julia has 500 paperweights in her collection, about how many should she pack in each box?

4. Tony is testing a new type of sneaker for his mother’s company. He will wear the sneaker for 6 days while he jogs on the beach for about the same distance each day. If Tony jogs 70 miles in 6 days, about how many miles does he jog each day?

5. Marissa is saving for a laptop computer. She deposited $391 into her bank account over 5 months. If she deposited the same amount into her account each month, about how much did she deposit each month?

6. The laptop computer that Marissa is saving for in Problem 5 costs $625. If she continues to deposit the same amount into her account each month, about how many more months will it take before she can purchase the computer?

40 Topic 4

Enrichment

4-2En

richm

ent 4

-2

About $300

About 90

About 70

About 12

About $80

About 3 more months

30428_T04_38-40_40 40 3/18/08 2:00:42 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Daily Spiral Review

4-3Daily Spiral Review

4-3

Topic 4 41

1. Last summer, 137 kids signed up for swim lessons at City Pool. Each of the 7 swim teachers had about the same number of kids. About how many kids did each teacher have?A About 13 B About 14 C About 20 D About 30

2. A scientist studies a sample that weighs 1 ounce, which is about 28 grams. About how many grams would be in a 48 ounce sample? A About 80 grams B About 600 grams C About 1,500 gramsD About 2,800 grams

3. The state of Texas is 268,601 square miles in area. Rhode Island is 1,545 square miles. How much larger is Texas than Rhode Island? A 267,144 square miles B 267,056 square miles C 156,055 square milesD 114,101 square miles

4. A crew of house painters uses 814 gallons of paint to paint 9 buildings. They used about the same amount of paint for each. About how many gallons of paint did they use on each building?

5. Logan puts a wallpaper border along the top edge of the 4 walls of a rectangular room. The room is 10 feet long and 12 feet wide. If there are no breaks in the border, how long is it?

6. There are 40,000 people at a football game. The seats are set up in 8 equal sections. How many people can sit in each section?

30428_T04_041_41 41 1/31/08 8:42:20 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Daily Spiral Review


4-3

Topic 4 41

1. Last summer, 137 kids signed up for swim lessons at City Pool. Each of the 7 swim teachers had about the same number of kids. About how many kids did each teacher have?A About 13 B About 14 C About 20 D About 30

2. A scientist studies a sample that weighs 1 ounce, which is about 28 grams. About how many grams would be in a 48 ounce sample? A About 80 grams B About 600 grams C About 1,500 gramsD About 2,800 grams

3. The state of Texas is 268,601 square miles in area. Rhode Island is 1,545 square miles. How much larger is Texas than Rhode Island? A 267,144 square miles B 267,056 square miles C 156,055 square milesD 114,101 square miles

4. A crew of house painters uses 814 gallons of paint to paint 9 buildings. They used about the same amount of paint for each. About how many gallons of paint did they use on each building?

5. Logan puts a wallpaper border along the top edge of the 4 walls of a rectangular room. The room is 10 feet long and 12 feet wide. If there are no breaks in the border, how long is it?

6. There are 40,000 people at a football game. The seats are set up in 8 equal sections. How many people can sit in each section?

44 feet

about 90 gallons

5,000

30428_T04_041_41 41 3/18/08 1:53:47 PM


Bamboo sometimes grows 3 ft each day. How many days could it take for this plant to grow to its greatest possible height of about 98 ft?

Problem of the Day

4-3

4-3Problem of the DayProblem of the Day 4-3

42

Topic 4

30428_T04_042_42 42

1/31/08 8:42:26 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Quick Check

4-3Q

uick Check 4

-3

1. Samantha has 45 books. She can pack 7 in each box. How many boxes can she completely fill? How many books will be left?

A 6 boxes; 3 books

B 6 boxes; 2 books

C 7 boxes; 0 books

D 7 boxes; 3 books

2. Dana invited 35 people to a party. Bottled soda comes in packages of 6 bottles. How many packages must Dana buy to have enough soda for each guest to have 1 bottle?

A 4

B 5

C 6

D 7

3. There are 48 students going on a field trip. Each van holds 10 students. If every van but the last one is full, how many students will be in the last van?

A 7

B 8

C 9

D 10

4. Writing to Explain For a cookout, Amelia is serving hamburgers. She has invited 35 people. Hamburger buns come in packages of 8. Hamburgers come in packages of 4. If each person will eat 1 hamburger with a bun, how many packages of hamburgers does she need? How many packages of buns does she need? How many buns and hamburgers will be left over?

Topic 4 43

30428_T04_043_43 43 1/31/08 8:42:34 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Quick Check

4-3Q

uick Check 4

-3

1. Samantha has 45 books. She can pack 7 in each box. How many boxes can she completely fill? How many books will be left?

A 6 boxes; 3 books

B 6 boxes; 2 books

C 7 boxes; 0 books

D 7 boxes; 3 books

2. Dana invited 35 people to a party. Bottled soda comes in packages of 6 bottles. How many packages must Dana buy to have enough soda for each guest to have 1 bottle?

A 4

B 5

C 6

D 7

3. There are 48 students going on a field trip. Each van holds 10 students. If every van but the last one is full, how many students will be in the last van?

A 7

B 8

C 9

D 10

4. Writing to Explain For a cookout, Amelia is serving hamburgers. She has invited 35 people. Hamburger buns come in packages of 8. Hamburgers come in packages of 4. If each person will eat 1 hamburger with a bun, how many packages of hamburgers does she need? How many packages of buns does she need? How many buns and hamburgers will be left over?

Topic 4 43


30428_T04_043_43 43 3/18/08 1:54:09 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

44 Topic 4

Rete

achi

ng 4-3

Reteaching

4-3Problem Solving: ReasonablenessAfter you solve a problem, check to see if your answer is reasonable. Also check that you answered the right question.

Example: 74 students are going to a special class dinner where they will be seated 8 to a table. Will 9 tables be enough?

Reasonableness The answer is close to 9 tables.76 ! 8 " 9 R2

Answering the right question All students must have seats, so there must be one more table to hold the remaining 2 students, making 10 tables in all.

Tell whether each answer is reasonable.

1. Kendra wants to paste 500 photographs into an album, 6 photos to a page. She figures that she will need about 100 pages.

2. Hwong has 39 muffins. If each of his guests will eat 2 muffins, Hwong figures that he can serve muffins to 19 guests.

Tell whether each answer answers the right question.

3. Ivan has a piece of lumber 104 inches long. He is sawing it into 12-inch lengths to make fence posts. He says he can get about 9 fence posts out of the board.

30428_T04_044-046_44 44 1/31/08 8:42:41 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

44 Topic 4

Rete

achi

ng 4-3

Reteaching

4-3Problem Solving: ReasonablenessAfter you solve a problem, check to see if your answer is reasonable. Also check that you answered the right question.

Example: 74 students are going to a special class dinner where they will be seated 8 to a table. Will 9 tables be enough?

Reasonableness The answer is close to 9 tables.76 ! 8 " 9 R2

Answering the right question All students must have seats, so there must be one more table to hold the remaining 2 students, making 10 tables in all.

Tell whether each answer is reasonable.

1. Kendra wants to paste 500 photographs into an album, 6 photos to a page. She figures that she will need about 100 pages.

2. Hwong has 39 muffins. If each of his guests will eat 2 muffins, Hwong figures that he can serve muffins to 19 guests.

Tell whether each answer answers the right question.

3. Ivan has a piece of lumber 104 inches long. He is sawing it into 12-inch lengths to make fence posts. He says he can get about 9 fence posts out of the board.

Six times 100 is 600, much more space than Kendra needs. Since 500 is between 480 (6 ! 80) and 540 (6 ! 90), she needs between 80 and 90 pages.

This is reasonable, since 2 ! 19 " 38.

Although 104 # 12 is closer to 9 than to 8, each post must be a full 12 inches, and therefore any remainder must be thrown away. Ivan can only make 8 posts.

30428_T04_044-046_44 44 3/18/08 1:54:19 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 45

Practice 4-3

Practice

4-3Problem Solving: ReasonablenessSolve.

1. One tray holds eight sandwiches. If there are 30 sandwiches in all, how many trays are needed?

2. There are 53 students on a field trip. One chaperone is needed for every 6 students. How many chaperones are needed?

Mrs. Favicchio has 72 students in her science class. The table shows how many students can use each item of lab supplies she is ordering.

3. How many packets of pH paper does she need to order?

4. How many cases of test tubes does she need to order?

5. Algebra A loaf of banana bread serves 6 guests. There will be 47 guests attending the faculty breakfast. Which expression shows how many loaves are needed to serve them all?

A 47 divided by 6 is 7 R 5, so 7 loaves are needed.

B 47 divided by 6 is 7 R 5, so 8 loaves are needed.

C 47 plus 6 is 53, so 53 loaves are needed.

D 47 minus 6 is 41, so 41 loaves are needed.

6. Explain It You are in line at an amusement park. You count 34 people in front of you. Each rollercoaster fits 11 people. How many rollercoasters must run before you can get on? Explain.

Lab Supplies

Item Number of Students

Packet of pH paper 10

Case of test tubes 5

Case of petri dishes 4

30428_T04_044-046_45 45 1/31/08 8:42:43 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 45

Practice 4-3

Practice

4-3Problem Solving: ReasonablenessSolve.

1. One tray holds eight sandwiches. If there are 30 sandwiches in all, how many trays are needed?

2. There are 53 students on a field trip. One chaperone is needed for every 6 students. How many chaperones are needed?

Mrs. Favicchio has 72 students in her science class. The table shows how many students can use each item of lab supplies she is ordering.

3. How many packets of pH paper does she need to order?

4. How many cases of test tubes does she need to order?

5. Algebra A loaf of banana bread serves 6 guests. There will be 47 guests attending the faculty breakfast. Which expression shows how many loaves are needed to serve them all?

A 47 divided by 6 is 7 R 5, so 7 loaves are needed.

B 47 divided by 6 is 7 R 5, so 8 loaves are needed.

C 47 plus 6 is 53, so 53 loaves are needed.

D 47 minus 6 is 41, so 41 loaves are needed.

6. Explain It You are in line at an amusement park. You count 34 people in front of you. Each rollercoaster fits 11 people. How many rollercoasters must run before you can get on? Explain.

Lab Supplies

Item Number of Students

Packet of pH paper 10

Case of test tubes 5

Case of petri dishes 4

4 trays9

3 rides must go by, and you will get on the fourth one.

8

15

30428_T04_044-046_45 45 3/18/08 1:54:21 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

46 Topic 4

Enric

hmen

t 4-3

Enrichment

4-3Place Your OrdersMr. Christie has 37 students in his cake-decorating class. He is ordering supplies. The table shows how many students can use each item he buys.

Cake Decorating ItemNumber of

Students it Will Serve

Box of pastry bags 4

Box of icing tips 7

Box of figurines 3

1. Use the table to find out how many boxes of icing tips Mr. Christie needs to order.

2. Use the table to find out how many boxes of figurines Mr. Christie needs to order.

3. Ten more students joined the cake-decorating class. Use the table to find out how many boxes of pastry bags Mr. Christie needs to order.

4. Mr. Christie is ordering cartons of gingerbread house kits for 45 of his students. Each carton has enough kits for 6 students. How many cartons of gingerbread house kits does Mr. Christie need to order?

5. In the final class, each of Mr. Christie’s 47 students will bake 3 cakes. All the cakes will be displayed in cases that can hold 15 cakes. How many cases will be needed to display all the cakes?

Decision-Making

30428_T04_044-046_46 46 1/31/08 8:42:45 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

46 Topic 4

Enric

hmen

t 4-3

Enrichment

4-3Place Your OrdersMr. Christie has 37 students in his cake-decorating class. He is ordering supplies. The table shows how many students can use each item he buys.

Cake Decorating ItemNumber of

Students it Will Serve

Box of pastry bags 4

Box of icing tips 7

Box of figurines 3

1. Use the table to find out how many boxes of icing tips Mr. Christie needs to order.

2. Use the table to find out how many boxes of figurines Mr. Christie needs to order.

3. Ten more students joined the cake-decorating class. Use the table to find out how many boxes of pastry bags Mr. Christie needs to order.

4. Mr. Christie is ordering cartons of gingerbread house kits for 45 of his students. Each carton has enough kits for 6 students. How many cartons of gingerbread house kits does Mr. Christie need to order?

5. In the final class, each of Mr. Christie’s 47 students will bake 3 cakes. All the cakes will be displayed in cases that can hold 15 cakes. How many cases will be needed to display all the cakes?

Decision-Making

6 boxes

13 boxes

12 boxes

8 cartons

10 cases

30428_T04_044-046_46 46 3/18/08 1:54:24 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Daily Spiral Review


4-4

Topic 4 47

1. A baker makes 75 muf! ns. How many boxes of 4 muf! ns can the baker completely ! ll?A 18 B 19 C 21 D 22

2. Maria, Cho, and Kelly live in an apartment. They spend $180 for a new couch. If they split the cost equally, how much does each girl owe? A $90 B $80 C $60 D $30

3. Ricky buys a big box of crayons. Inside the big box are 4 small boxes. Each small box holds the same number of crayons. Which do you need to know to ! nd the total number of crayons Ricky buys?A The width of a crayonB The length of a crayon C The cost of a small box of

crayons D How many crayons are in a

small box

4. The Texas coast is 367 miles long. One day, 30 school groups pick up trash along the coast. Each group cleans up a different part of the coastline. Each group’s part is the same length, a whole number of miles. a. What is the greatest number of

whole miles of coast that any one group could clean up?

b. What is the length of the coast that NONE of the groups cleaned?

5. A carpenter buys 144 boxes of nails. Each box has 36 nails. How many nails does the carpenter buy?

6. Fill in the boxes to make the number sentences true.

6 ! " 48

48 # " 8

30428_T04_047_47 47 1/31/08 8:42:53 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Daily Spiral Review


4-4

Topic 4 47

1. A baker makes 75 muf! ns. How many boxes of 4 muf! ns can the baker completely ! ll?A 18 B 19 C 21 D 22

2. Maria, Cho, and Kelly live in an apartment. They spend $180 for a new couch. If they split the cost equally, how much does each girl owe? A $90 B $80 C $60 D $30

3. Ricky buys a big box of crayons. Inside the big box are 4 small boxes. Each small box holds the same number of crayons. Which do you need to know to ! nd the total number of crayons Ricky buys?A The width of a crayonB The length of a crayon C The cost of a small box of

crayons D How many crayons are in a

small box

4. The Texas coast is 367 miles long. One day, 30 school groups pick up trash along the coast. Each group cleans up a different part of the coastline. Each group’s part is the same length, a whole number of miles. a. What is the greatest number of

whole miles of coast that any one group could clean up?

b. What is the length of the coast that NONE of the groups cleaned?

5. A carpenter buys 144 boxes of nails. Each box has 36 nails. How many nails does the carpenter buy?

6. Fill in the boxes to make the number sentences true.

6 ! " 48

48 # " 8

5,184

7 miles

68

12 miles

30428_T04_047_47 47 3/18/08 1:54:34 PM


Tetsuo has $20 to buy some balls for his soccer team. If each ball costs $6, how many can he buy? How much money will he have left?

4-4Problem of the DayProblem

of the Day

4-4


48

Topic 4

30428_T04_048_48 48

1/31/08 8:43:01 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Quick Check

4-4Q

uick Check 4

-4

Use play money or draw diagrams to help you divide.

1. 448 ! 7

A 50

B 54

C 60

D 64

2. A school made $492 on ticket sales for a volleyball game. The money from ticket sales is divided evenly among 6 school sports. How much money did each sport receive from the volleyball ticket sales?

A $85

B $82

C $80

D $78

3. Writing to Explain Manuela agreed to pay her 4 grandsons $180 for helping her with yard work for the day. If her grandsons divide the money equally, how much will each of them earn? Draw bills to help you divide.

Topic 4 49

30428_T04_049_49 49 1/31/08 8:43:08 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Quick Check

4-4Q

uick Check 4

-4

Use play money or draw diagrams to help you divide.

1. 448 ! 7

A 50

B 54

C 60

D 64

2. A school made $492 on ticket sales for a volleyball game. The money from ticket sales is divided evenly among 6 school sports. How much money did each sport receive from the volleyball ticket sales?

A $85

B $82

C $80

D $78

3. Writing to Explain Manuela agreed to pay her 4 grandsons $180 for helping her with yard work for the day. If her grandsons divide the money equally, how much will each of them earn? Draw bills to help you divide.

Topic 4 49


30428_T04_049_49 49 3/18/08 1:54:54 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Reteaching

4-4Connecting Models and SymbolsDivide 138 equally into 3 groups.

50 Topic 4

Rete

achi

ng 4-4

Use models to help you divide.

1. 4 !"" 76 2. 2 !"" 94 3. 5 !"" 130

4. 7 !"" 238 5. 6 !"" 426 6. 3 !"" 264

7. Algebra If n ! 3 " 57, what is the value of n?

What You Think

What You Think

Step 1: You can model 138 as 13 groups of 10 plus 8 ones.130 ! 3 " 40, so each group will get 4 groups of 10.40 # 3 " 120130 $ 120 " 10, so there is 1 group of 10 left.

Step 2: There is 1 group of 10 plus 1 group of 8 ones left. You can model 18 as 18 ones. 18 ! 3 " 6, so each group will also get 6 ones. There is nothing left.

What You Write

43 !""" 1 3 8 $1 2

1

What You Write

4 63 !""" 1 3 8 $1 2

1 8$1 8

0138 ! 3 " 46

30428_T04_050-052_50 50 1/31/08 8:43:19 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Reteaching

4-4Connecting Models and SymbolsDivide 138 equally into 3 groups.

50 Topic 4

Rete

achi

ng 4-4

Use models to help you divide.

1. 4 !"" 76 2. 2 !"" 94 3. 5 !"" 130

4. 7 !"" 238 5. 6 !"" 426 6. 3 !"" 264

7. Algebra If n ! 3 " 57, what is the value of n?

What You Think

What You Think

Step 1: You can model 138 as 13 groups of 10 plus 8 ones.130 ! 3 " 40, so each group will get 4 groups of 10.40 # 3 " 120130 $ 120 " 10, so there is 1 group of 10 left.

Step 2: There is 1 group of 10 plus 1 group of 8 ones left. You can model 18 as 18 ones. 18 ! 3 " 6, so each group will also get 6 ones. There is nothing left.

What You Write

43 !""" 1 3 8 $1 2

1

What You Write

4 63 !""" 1 3 8 $1 2

1 8$1 8

0138 ! 3 " 46

19 47 26

34 71 88

171

30428_T04_050-052_50 50 3/18/08 1:55:07 PM

4

!

!

3 61

6

3

!

!

6 21

2

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 51

Practice

4-4Practice 4

-4

Connecting Models and SymbolsAfter mowing lawns for one week, John put the money he earned on the table. There were four $100 bills, three $10 bills, and five $1 bills.

1. If John’s brother borrowed one of the $100 bills and replaced it with ten $10 bills,

a. how many $100 bills would there be?

b. how many $10 bills would there be?

2. If John needed to divide the money evenly with two other workers, how much would each person receive?

3. If John needed to divide the money evenly with four other workers, how much would each person receive?

Complete each division problem. You may use play money or draw diagrams to help.

4. 5.

6. If $644.00 is divided equally among 7 people, how much will each person receive?

A $82.00 B $92.00 C $93.00 D $103.00

7. Explain It Write a story problem using two $100 bills, nine $10 bills, and seven $1 bills.

30428_T04_050-052_51 51 1/31/08 8:43:21 PM

4

!

!

3 61

6

3

!

!

6 21

2

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 51

Practice

4-4

Practice 4-4

Connecting Models and SymbolsAfter mowing lawns for one week, John put the money he earned on the table. There were four $100 bills, three $10 bills, and five $1 bills.

1. If John’s brother borrowed one of the $100 bills and replaced it with ten $10 bills,

a. how many $100 bills would there be? b. how many $10 bills would there be?

2. If John needed to divide the money evenly with two other workers, how much would each person receive?

3. If John needed to divide the money evenly with four other workers, how much would each person receive?

Complete each division problem. You may use play money or draw diagrams to help.

4. 5.

6. If $644.00 is divided equally among 7 people, how much will each person receive?

A $82.00 B $92.00 C $93.00 D $103.00

7. Explain It Write a story problem using two $100 bills, nine $10 bills, and seven $1 bills.

4

Three $100 bills

Sample answer: Karl borrowed $297from his sister. He pays her $33 eachweek. How many weeks will it take Karlto pay $297?

3

21

611

0

45

51

211

0

Thirteen $10 bills

$145

$87

30428_T04_050-052_51 51 3/18/08 1:55:10 PM

$100! !

! " # 2 "$5

$10 $5

$100 !

!

!

!" # 3 "$100

$100 $20

$10

$100

! !!

" # 4 "

$100

$100$100

$20

$20$20

$100

$10

!!

!! " # 5 "

$10

$50 $20$20

$20

$20

!$50

!

! !

" # 6 "

$100$100

$100$100

$20$10

$100 !

!!

! " # 7 "$100

$50$50$50

$100$20

$20

Name

© P

ears

on E

duca

tion,

Inc.

5

Algebra

Follow the Money TrailEach trail below has money that you collect as you walk. At the end of each trail, the total amount of money is divided by a divisor. You receive the quotient.

1.

2.

3.

4.

5.

6.

Enrichment

4-4En

richm

ent 4

-4

52 Topic 4

30428_T04_050-052_52 52 1/31/08 8:43:24 PM

$100! !

! " # 2 "$5

$10 $5

$100 !

!

!

!" # 3 "$100

$100 $20

$10

$100

! !!

" # 4 "

$100

$100$100

$20

$20$20

$100

$10

!!

!! " # 5 "

$10

$50 $20$20

$20

$20

!$50

!

! !

" # 6 "

$100$100

$100$100

$20$10

$100 !

!!

! " # 7 "$100

$50$50$50

$100$20

$20

Name

© P

ears

on E

duca

tion,

Inc.

5

Algebra

Follow the Money TrailEach trail below has money that you collect as you walk. At the end of each trail, the total amount of money is divided by a divisor. You receive the quotient.

1.

2.

3.

4.

5.

6.

Enrichment

4-4En

richm

ent 4

-4

52 Topic 4

$120 $60

$330 $110

$460 $115

$250 $50

$480 $80

$490 $70

30428_T04_050-052_52 52 3/18/08 1:55:13 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Daily Spiral Review 4-5

Daily Spiral Review

4-5

Topic 4 53

1. The 4 businesses in a shopping center each pay an equal share of the center’s electric bill. This month, they used 852 kilowatt-hours of electricity. How many kilowatt-hours must each business pay for?A 210 kilowatt-hours B 213 kilowatt-hoursC 240 kilowatt-hoursD 243 kilowatt-hours

2. Dakota has 416 baseball cards in 7 boxes. Each box has about the same number of cards. About how many cards are in each box? A 80 B 60 C 50 D 40

3. D’Andre is 13 years old. How many days old is D’Andre? (Include 3 leap days.)A 1,350B 4,635C 4,648D 4,748

4. There are 6 salespeople at Good Folks Used Car Lot. Last year, they each sold the same number of cars. Together, they sold 534 cars. How many cars did each salesperson sell?

5. The table shows the area of the four oceans.

List the oceans in order from greatest area to least area.

6. Does the shape below have any lines of symmetry? If so, draw each line of symmetry. If not, write no lines of symmetry.

Ocean Area (square kilometers)

Arctic 14,056,000Atlantic 76,762,000Indian 68,556,000Pacific 155,557,000

30428_T04_53_53 53 1/31/08 8:47:55 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5


Daily Spiral Review

4-5

Topic 4 53

1. The 4 businesses in a shopping center each pay an equal share of the center’s electric bill. This month, they used 852 kilowatt-hours of electricity. How many kilowatt-hours must each business pay for?A 210 kilowatt-hours B 213 kilowatt-hoursC 240 kilowatt-hoursD 243 kilowatt-hours

2. Dakota has 416 baseball cards in 7 boxes. Each box has about the same number of cards. About how many cards are in each box? A 80 B 60 C 50 D 40

3. D’Andre is 13 years old. How many days old is D’Andre? (Include 3 leap days.)A 1,350B 4,635C 4,648D 4,748

4. There are 6 salespeople at Good Folks Used Car Lot. Last year, they each sold the same number of cars. Together, they sold 534 cars. How many cars did each salesperson sell?

5. The table shows the area of the four oceans.

List the oceans in order from greatest area to least area.

6. Does the shape below have any lines of symmetry? If so, draw each line of symmetry. If not, write no lines of symmetry.

Ocean Area (square kilometers)

Arctic 14,056,000Atlantic 76,762,000Indian 68,556,000Pacific 155,557,000

89

Pacific, Atlantic, Indian, Arctic

30428_T04_53_53 53 3/18/08 2:00:55 PM



of the Day

4-5

54

Topic 4


Five friends stood in line. Jamie was fourth in line. Jose stood right behind Ned. Les was not third or last. Alice was also in line. In what order did the friends stand?

30428_T04_054_54 54

1/31/08 8:43:32 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Quick Check

4-5Q

uick Check 4

-5

1. Where will the first digit of the quotient be placed in the following problem? Use compatible numbers.

7 !"" 372

A ones place

B tens place

C hundreds place

D thousands place

2. Kelly wants to divide 496 cards into 4 groups. Complete the calculation to find how many cards will be in each group.

4 !"" 496

A 12

B 14

C 114

D 124

3. Writing to Explain Juan is sorting school newsletters. There are 9 classrooms in the fifth grade. Each classroom has the same number of students. He has 240 newsletters. How many newsletters will each classroom get? Will he have any leftover? Show your work.

Topic 4 55

30428_T04_055_55 55 1/31/08 8:43:39 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Quick Check

4-5Q

uick Check 4

-5

1. Where will the first digit of the quotient be placed in the following problem? Use compatible numbers.

7 !"" 372

A ones place

B tens place

C hundreds place

D thousands place

2. Kelly wants to divide 496 cards into 4 groups. Complete the calculation to find how many cards will be in each group.

4 !"" 496

A 12

B 14

C 114

D 124

3. Writing to Explain Juan is sorting school newsletters. There are 9 classrooms in the fifth grade. Each classroom has the same number of students. He has 240 newsletters. How many newsletters will each classroom get? Will he have any leftover? Show your work.

Topic 4 55


30428_T04_055_55 55 3/18/08 1:55:32 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Dividing by 1-Digit DivisorsFind 362 ! 5.

Step 1: To decide where to place the first digit in the quotient, compare the first digit of the dividend with the divisor.

3 " 5, so the first digit in the quotient will not go in the hundreds place.

Now, compare the first two digits of the dividend with the divisor.

36 # 5, so the first digit in the quotient will go in the tens place.

Step 2: Divide the tens. Use multiplication facts and compatible numbers. Think 5 $ ? % 35.

Write 7 in the tens place of the quotient.Multiply. 5 $ 7 % 35

75 !"" 3 6

&3 5 1

Subtract. 36 & 35 % 1Compare. 1 " 5Bring down the ones.

Step 3: Divide the ones. Use multiplication facts and compatible numbers. Think 5 $ ? % 10.

Write 2 in the ones place of the quotient.Multiply. 5 $ 2 % 10

7 2R25 !""" 3 6 2 &3 5

1 2!1 0

2Subtract. 12 & 10 % 2Compare. 2 " 5There are no more digits to bring down, so 2 is the remainder.

Step 4: Check by multiplying.

5 $ 72 % 360 ' 2 % 362

Rete

achi

ng 4-5

56 Topic 4

Reteaching

4-5

Divide. Check by multiplying.

1. 8 !"" 863 2. 7 !"" 249 3. 5 !"" 365

4. 8 !"" 448 5. 2 !"" 499 6. 6 !"" 396

7. Number Sense How can you tell before you divide 425 by 9 that the first digit of the quotient is in the tens place?

30428_T04_056-058_56 56 1/31/08 8:43:46 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Dividing by 1-Digit DivisorsFind 362 ! 5.

Step 1: To decide where to place the first digit in the quotient, compare the first digit of the dividend with the divisor.

3 " 5, so the first digit in the quotient will not go in the hundreds place.

Now, compare the first two digits of the dividend with the divisor.

36 # 5, so the first digit in the quotient will go in the tens place.

Step 2: Divide the tens. Use multiplication facts and compatible numbers. Think 5 $ ? % 35.

Write 7 in the tens place of the quotient.Multiply. 5 $ 7 % 35

75 !"" 3 6

&3 5 1

Subtract. 36 & 35 % 1Compare. 1 " 5Bring down the ones.

Step 3: Divide the ones. Use multiplication facts and compatible numbers. Think 5 $ ? % 10.

Write 2 in the ones place of the quotient.Multiply. 5 $ 2 % 10

7 2R25 !""" 3 6 2 &3 5

1 2!1 0

2Subtract. 12 & 10 % 2Compare. 2 " 5There are no more digits to bring down, so 2 is the remainder.

Step 4: Check by multiplying.

5 $ 72 % 360 ' 2 % 362

Rete

achi

ng 4-5

56 Topic 4

Reteaching

4-5

Divide. Check by multiplying.

1. 8 !"" 863 2. 7 !"" 249 3. 5 !"" 365

4. 8 !"" 448 5. 2 !"" 499 6. 6 !"" 396

7. Number Sense How can you tell before you divide 425 by 9 that the first digit of the quotient is in the tens place?

107 R7 35 R4 73

56 249 R1 66

4 < 9

30428_T04_056-058_56 56 3/18/08 1:55:45 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Dividing by 1-Digit DivisorsFind each quotient.

The Paez family lives in Louisville, Kentucky, and has decided to take a road trip for their summer vacation.

9. How many miles will the Paez family drive each day if they decide to take 5 days to drive 865 mi to Dallas?

10. The Paez family decides they want to drive 996 mi to Boston in 6 days. How many miles will they drive each day?

11. Reasonableness If a staff of 9 people had to clean a hotel with 198 rooms, how many rooms would each person have to clean if they divided the rooms equally?

A 29 B 25 C 23 D 22

12. Explain It Explain how to check the quotient from a division problem.

1. 2 !"" 586

5. 5 !"" 642

2. 3 !"" 565

6. 6 !"" 354

3. 5 !"" 718

7. 9 !"" 210

4. 4 !"" 599

8. 8 !"" 927

Practice 4-5

Practice

4-5

Topic 4 57

30428_T04_056-058_57 57 1/31/08 8:43:48 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Dividing by 1-Digit DivisorsFind each quotient.

The Paez family lives in Louisville, Kentucky, and has decided to take a road trip for their summer vacation.

9. How many miles will the Paez family drive each day if they decide to take 5 days to drive 865 mi to Dallas?

10. The Paez family decides they want to drive 996 mi to Boston in 6 days. How many miles will they drive each day?

11. Reasonableness If a staff of 9 people had to clean a hotel with 198 rooms, how many rooms would each person have to clean if they divided the rooms equally?

A 29 B 25 C 23 D 22

12. Explain It Explain how to check the quotient from a division problem.

1. 2 !"" 586

5. 5 !"" 642

2. 3 !"" 565

6. 6 !"" 354

3. 5 !"" 718

7. 9 !"" 210

4. 4 !"" 599

8. 8 !"" 927

Practice 4-5

Practice

4-5

Topic 4 57

173 mi each day

293 188 R1 143 R3 149 R3

Sample answer: You need to multiply the quotient by the divisor and then add the remainder. This should equal the dividend.

166 mi

128 R2 59 23 R3 115 R7

30428_T04_056-058_57 57 3/18/08 1:55:48 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Estimation

At the Amusement ParkThe chart below shows in seconds how long certain rides at the amusement park take to complete a specific number of revolutions. In the exercises below, estimate first to find how long one revolution will take. Then find the actual time per revolution.

1. Ferris wheel

2. Roller coaster

3. Merry-go-round

4. Swiss slalom

RideNumber of

RevolutionsTime

(seconds)

Ferris wheel 5 515

Roller coaster 4 832

Merry-go-round 3 609

Swiss slalom 7 840

Enrichment

4-5En

richm

ent 4

-5

58 Topic 4

30428_T04_056-058_58 58 1/31/08 8:43:51 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Estimation

At the Amusement ParkThe chart below shows in seconds how long certain rides at the amusement park take to complete a specific number of revolutions. In the exercises below, estimate first to find how long one revolution will take. Then find the actual time per revolution.

1. Ferris wheel

2. Roller coaster

3. Merry-go-round

4. Swiss slalom

RideNumber of

RevolutionsTime

(seconds)

Ferris wheel 5 515

Roller coaster 4 832

Merry-go-round 3 609

Swiss slalom 7 840

Enrichment

4-5En

richm

ent 4

-5

58 Topic 4

Estimate: 100 sec per revolutionActual time per revolution ! 103 sec




Sample answer:

Sample answer:

Sample answer:

Sample answer:

30428_T04_056-058_58 58 3/18/08 1:55:50 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5


Daily Spiral Review

4-6

Topic 4 59

1. Ms. Sanchez buys boxes to pack up 169 books. Each box holds 9 books. How many boxes should Ms. Sanchez buy?A 25 B 19 C 18 D 11

2. The members of a softball team put their names in a hat. Then the coach picks one name to see who will bring snacks to the next game.

What are the chances that the person who brings snacks to the next game has a name that starts with the letter M?

A 1 out of 9 B 2 out of 3 C 4 out of 9 D 5 out of 4

3. The tallest mountain measured from the bottom of the ocean is Mauna Kea, in Hawaii. Mauna Kea is 33,474 feet tall, but only 13,796 feet of its height is above sea level. How many feet of Mauna Kea are below sea level?A 19,678 feetB 20,322 feetC 46,160 feetD 47,270 feet

4. A ! ower shop sells vases of mixed ! owers. Each vase includes 3 roses. If the shop uses 882 roses, how many vases of mixed ! owers do they sell?

5. The average distance from the Sun to the planet Neptune is 2,795,080,000 miles. Write this distance in word form.

6. Julia rents an apartment that costs $845 each month. How much rent will she owe for a year?

Mari Paula

DavidMike Meg

Zoë

Juan Mina Pablo

30428_T04_059_59 59 1/31/08 8:43:58 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5


Daily Spiral Review

4-6

Topic 4 59

1. Ms. Sanchez buys boxes to pack up 169 books. Each box holds 9 books. How many boxes should Ms. Sanchez buy?A 25 B 19 C 18 D 11

2. The members of a softball team put their names in a hat. Then the coach picks one name to see who will bring snacks to the next game.

What are the chances that the person who brings snacks to the next game has a name that starts with the letter M?

A 1 out of 9 B 2 out of 3 C 4 out of 9 D 5 out of 4

3. The tallest mountain measured from the bottom of the ocean is Mauna Kea, in Hawaii. Mauna Kea is 33,474 feet tall, but only 13,796 feet of its height is above sea level. How many feet of Mauna Kea are below sea level?A 19,678 feetB 20,322 feetC 46,160 feetD 47,270 feet

4. A ! ower shop sells vases of mixed ! owers. Each vase includes 3 roses. If the shop uses 882 roses, how many vases of mixed ! owers do they sell?

5. The average distance from the Sun to the planet Neptune is 2,795,080,000 miles. Write this distance in word form.

6. Julia rents an apartment that costs $845 each month. How much rent will she owe for a year?

Mari Paula

DavidMike Meg

Zoë

Juan Mina Pablo

Two billion seven hundred

ninety-five million eighty thousand

294

$10,140

30428_T04_059_59 59 3/18/08 1:55:58 PM



Nicole has 7 United States coins worth 53¢. What are the 7 coins?


of the Day

4-6

60

Topic 4

30428_T04_060_60 60

1/31/08 8:44:05 PM

5 books

Name©

Pea

rson

Edu

catio

n, In

c. 5

Quick Check

4-6Q

uick Check 4

-6

Find the quotient.

1. 7 !"" 756

A 108

B 118

C 128

D 180

2. There are 360 people on a tour. They are divided into 3 equal groups. How many tourists are in each group?

A 119

B 120

C 121

D 122

3. Writing to Explain Mary is shipping books to a school. If she has 108 books and 5 books fit in one box, how many boxes will she need? Show your work and explain.

Topic 4 61

30428_T04_061_61 61 1/31/08 8:44:13 PM

5 books

Name©

Pea

rson

Edu

catio

n, In

c. 5

Quick Check

4-6Q

uick Check 4

-6

Find the quotient.

1. 7 !"" 756

A 108

B 118

C 128

D 180

2. There are 360 people on a tour. They are divided into 3 equal groups. How many tourists are in each group?

A 119

B 120

C 121

D 122

3. Writing to Explain Mary is shipping books to a school. If she has 108 books and 5 books fit in one box, how many boxes will she need? Show your work and explain.

Topic 4 61


30428_T04_061_61 61 3/18/08 1:56:20 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Reteaching

4-6

62 Topic 4

Zeros in the QuotientFind 816 ! 4.

Find each quotient. Check your answers by multiplying.

1. 8 !"" 640 2. 3 !"" 322 3. 4 !"" 908

4. 15 !"" 225 5. 6 !"" 624 6. 6 !"" 965

7. Explain It Is 593 ! 6 a little less than 10, a little more than 10, a little less than 100, or a little more than 100? Explain.

Step 1: Compare the first digit of the dividend with the divisor. 8 " 4, so the first digit in the quotient will go in the hundreds place.

Divide the hundreds. Think 4 # ? $ 8.

Write 2 in the hundreds place of the quotient. Multiply. 4 # 2 $ 8

24 !"" 8 1

%8 0 1

Subtract. 8 % 8 $ 0

Compare. 0 & 4

Bring down the tens.

Step 2: Compare.1 & 4

You cannot divide the tens, so place 0 in the tens place of the quotient.

Bring down the ones.

2 04 !""" 8 1 6

%8 0 1 6

Step 3: Compare.16 " 4

Divide the ones. Think4 # ? $ 16.

Write 4 in the ones place of the quotient.

Multiply. 4 # 4 $ 16

Subtract. 16 % 16 $ 0

Compare. 0 & 4

There are no more digits to bring down, so the problem is done.

2 0 44 !""" 8 1 6

%8 0 1 6 % 1 6 0

Step 4: Check by multiplying. 4 # 204 $ 816

Rete

achi

ng 4-6

30428_T04_062-064_62 62 1/31/08 8:44:20 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Reteaching

4-6

62 Topic 4

Zeros in the QuotientFind 816 ! 4.

Find each quotient. Check your answers by multiplying.

1. 8 !"" 640 2. 3 !"" 322 3. 4 !"" 908

4. 15 !"" 225 5. 6 !"" 624 6. 6 !"" 965

7. Explain It Is 593 ! 6 a little less than 10, a little more than 10, a little less than 100, or a little more than 100? Explain.

Step 1: Compare the first digit of the dividend with the divisor. 8 " 4, so the first digit in the quotient will go in the hundreds place.

Divide the hundreds. Think 4 # ? $ 8.

Write 2 in the hundreds place of the quotient. Multiply. 4 # 2 $ 8

24 !"" 8 1

%8 0 1

Subtract. 8 % 8 $ 0

Compare. 0 & 4

Bring down the tens.

Step 2: Compare.1 & 4

You cannot divide the tens, so place 0 in the tens place of the quotient.

Bring down the ones.

2 04 !""" 8 1 6

%8 0 1 6

Step 3: Compare.16 " 4

Divide the ones. Think4 # ? $ 16.

Write 4 in the ones place of the quotient.

Multiply. 4 # 4 $ 16

Subtract. 16 % 16 $ 0

Compare. 0 & 4

There are no more digits to bring down, so the problem is done.

2 0 44 !""" 8 1 6

%8 0 1 6 % 1 6 0

Step 4: Check by multiplying. 4 # 204 $ 816

Rete

achi

ng 4-6

A little less than 100; 593 ! 6 " 98 R5 & 100.

80 107 R1 227

15 104 160 R5

30428_T04_062-064_62 62 3/18/08 1:56:32 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Zeros in the QuotientFind each quotient. Check your answers by multiplying.

1. 490 ! 7 " 2. 326 ! 3 "

3. 916 ! 3 " 4. 720 ! 2 "

9. If there are 505 seats in an auditorium divided equally into 5 sections, how many seats are in each section?

10. A book company publishes 749 copies of a novel and distributes them to 7 bookstores. If each bookstore were to receive the same number of copies, how many copies would be sent to each store?

11. In one year, Dolores and Tom’s four children saved $420 by recycling cans. When they divided the money equally, how much money did each child receive?

A $50 B $100 C $105 D $1,500

12. Explain It Explain why estimating before you divide 624 ! 6 helps you place the first digit in the quotient.

5. 2 !"" 941 6. 9 !"" 982 7. 7 !"" 740 8. 5 !"" 703

Practice 4-6Practice

4-6

Topic 4 63

30428_T04_062-064_63 63 1/31/08 8:44:23 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Zeros in the QuotientFind each quotient. Check your answers by multiplying.

1. 490 ! 7 " 2. 326 ! 3 "

3. 916 ! 3 " 4. 720 ! 2 "

9. If there are 505 seats in an auditorium divided equally into 5 sections, how many seats are in each section?

10. A book company publishes 749 copies of a novel and distributes them to 7 bookstores. If each bookstore were to receive the same number of copies, how many copies would be sent to each store?

11. In one year, Dolores and Tom’s four children saved $420 by recycling cans. When they divided the money equally, how much money did each child receive?

A $50 B $100 C $105 D $1,500

12. Explain It Explain why estimating before you divide 624 ! 6 helps you place the first digit in the quotient.

5. 2 !"" 941 6. 9 !"" 982 7. 7 !"" 740 8. 5 !"" 703

Practice 4-6Practice

4-6

Topic 4 63

101 seats

470 R1 109 R1 105 R5 140 R3

Sample answer: By estimating you will know if the answer will be in the hundreds, tens, or ones.

107 copies

70305 R1

108 R2360

30428_T04_062-064_63 63 3/18/08 1:56:34 PM

Length of bridge: 252 ft



Name

© P

ears

on E

duca

tion,

Inc.

5

Decision Making

Is the Bridge Safe?The Davis Construction Company follows certain rules for building safe bridges: The distance between the bridge’s supports, called the span, must not be more than 100 ft. The chart at the right shows how to classify bridges as very safe, safe, or unsafe. Find the span length of each bridge below. Then tell whether the bridge is very safe, safe, or unsafe.

1.

2.

3.

Length of Span Rating

0 to 50 ft very safe

51 to 100 ft safe

101 ft or more unsafe

Bridge Safety Ratings

Enric

hmen

t 4-6

Enrichment

4-6

64 Topic 4

30428_T04_062-064_64 64 1/31/08 8:44:25 PM




Name

© P

ears

on E

duca

tion,

Inc.

5

Decision Making

Is the Bridge Safe?The Davis Construction Company follows certain rules for building safe bridges: The distance between the bridge’s supports, called the span, must not be more than 100 ft. The chart at the right shows how to classify bridges as very safe, safe, or unsafe. Find the span length of each bridge below. Then tell whether the bridge is very safe, safe, or unsafe.

1.

2.

3.

Length of Span Rating

0 to 50 ft very safe

51 to 100 ft safe

101 ft or more unsafe

Bridge Safety Ratings

Enric

hmen

t 4-6

Enrichment

4-6

64 Topic 4

63 ft; Safe

42 ft; Very safe

133 ft; Unsafe

30428_T04_062-064_64 64 3/18/08 1:56:37 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Daily Spiral Review

4-7

Topic 4 65

Daily Spiral Review 4

-7

1. A company puts up a billboard every 4 miles along 432 miles of highway. How many billboards does the company put up?

A 10 B 18 C 108 D 180

2. During a sale, a grocery store gives every third customer a free loaf of bread. If the store gets 910 customers, how many loaves of bread does the store give away for free?

A 340 B 330 C 304 D 303

3. Which button has a letter with a pair of parallel lines?

A B C D

4. A pet store can put no more than 5 ! sh in each tank. What is the least number of tanks the store needs to hold 354 ! sh?

5. Write six billion, sixty-seven million, four hundred four thousand, thirteen in standard form.

6. The Turner family saves $42 each month. How much have the Turners saved after 15 months?

K

GRH

30428_T04_065_65 65 1/31/08 8:44:33 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Daily Spiral Review

4-7

Topic 4 65


1. A company puts up a billboard every 4 miles along 432 miles of highway. How many billboards does the company put up?

A 10 B 18 C 108 D 180

2. During a sale, a grocery store gives every third customer a free loaf of bread. If the store gets 910 customers, how many loaves of bread does the store give away for free?

A 340 B 330 C 304 D 303

3. Which button has a letter with a pair of parallel lines?

A B C D

4. A pet store can put no more than 5 ! sh in each tank. What is the least number of tanks the store needs to hold 354 ! sh?

5. Write six billion, sixty-seven million, four hundred four thousand, thirteen in standard form.

6. The Turner family saves $42 each month. How much have the Turners saved after 15 months?

K

GRH

71

6,067,404,013

$630

30428_T04_065_65 65 3/18/08 1:56:47 PM




of the Day

4-7

66

Topic 4

Wesley started with his favorite number. Then he subtracted 7 from it. He multiplied this difference by 3 and then added 5. Finally, he divided this number by 11. His end result was 1. What was Wesley’s favorite number?

30428_T04_066_66 66

1/31/08 8:44:41 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Quick C

heck 4-7

Quick Check

4-71. Which of the following is a factor pair of 28?

A 4, 6

B 3, 8

C 3, 9

D 4, 7

2. Jared’s grandfather is 72. Which of the following lists all of the factors of 72?

A 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

B 1, 2, 4, 6, 8, 9, 12, 16, 36, 48, 72

C 1, 2, 4, 6, 8, 9, 12, 18, 36

D 2, 4, 6, 8, 9, 12, 18, 36, 72

3. Writing to Explain There are 128 students in the fifth grade at Oak Elementary School. List all the factors of 128.

Topic 4 67

30428_T04_067_67 67 1/31/08 8:44:49 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Quick C

heck 4-7

Quick Check

4-71. Which of the following is a factor pair of 28?

A 4, 6

B 3, 8

C 3, 9

D 4, 7

2. Jared’s grandfather is 72. Which of the following lists all of the factors of 72?

A 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

B 1, 2, 4, 6, 8, 9, 12, 16, 36, 48, 72

C 1, 2, 4, 6, 8, 9, 12, 18, 36

D 2, 4, 6, 8, 9, 12, 18, 36, 72

3. Writing to Explain There are 128 students in the fifth grade at Oak Elementary School. List all the factors of 128.

Topic 4 67


30428_T04_067_67 67 3/18/08 1:57:08 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Rete

achi

ng 4-7

Reteaching

4-7

68 Topic 4

Understanding FactorsYou can use the divisibility rules to find the factors of a number.

What are the factors of 92?

Possible Factor Test of Divisibility Result of Test Factors Found

1 Is 92 a whole number?

Yes. Therefore it is divisible by 1.

92 ! 1 " 921 and 92 are factors.

2 Is 92 an even number?



3 Is the sum of the digits divisible by 3?

No. Therefore it is not divisible by 3.

3 is not a factor.

4 Are the last 2 digits divisible by 4?



5 Is the last digit 5 or 0?


5 is not a factor.

6 Is it divisible by both 2 and 3?


6 is not a factor.



9 is not a factor.

10 Is the last digit 0? No. Therefore it is not divisible by 10.

10 is not a factor.

The factors of 92 are 1, 2, 4, 23, 46, and 92.

Find all the factors of each number.

1. 12 2. 35

3. 45 4. 49

5. Number Sense Is 2,340 divisible by 90? How do you know?

30428_T04_068-070_68 68 1/31/08 8:44:57 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Rete

achi

ng 4-7

Reteaching

4-7

68 Topic 4

Understanding FactorsYou can use the divisibility rules to find the factors of a number.

What are the factors of 92?

Possible Factor Test of Divisibility Result of Test Factors Found

1 Is 92 a whole number?



2 Is 92 an even number?





3 is not a factor.

4 Are the last 2 digits divisible by 4?



5 Is the last digit 5 or 0?


5 is not a factor.

6 Is it divisible by both 2 and 3?


6 is not a factor.



9 is not a factor.

10 Is the last digit 0? No. Therefore it is not divisible by 10.

10 is not a factor.

The factors of 92 are 1, 2, 4, 23, 46, and 92.

Find all the factors of each number.

1. 12 2. 35

3. 45 4. 49

5. Number Sense Is 2,340 divisible by 90? How do you know?

Yes. It is divisible by 9 and 10, because the sum of the digits is divisible by 9, and the last digit is 0.

1, 2, 3, 4, 6, 12 1, 5, 7, 351, 3, 5, 9, 15, 45 1, 7, 49

30428_T04_068-070_68 68 3/18/08 1:57:21 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Practice 4-7

Practice

4-7

Topic 4 69

Understanding FactorsList all the factors of each number.

1. 36

2. 90

3. 84

Number Sense A number is divisible by 4 if the last two digitsare divisible by 4. Write yes on the line if the number is divisible by 4 and no if it is not.

4. 324 5. 634 6. 172

7. A class of 80 students is graduating from elementary school. The teachers need help figuring out how to line up the students for the ceremony. One row of 80 students would be too long. What other ways could the students be arranged for the ceremony?

8. A number is divisible by another number when the after division by that number is 0.

9. Number Sense What factor pair is missing for 45 if you already know 1 and 45, 5 and 9?

A 7 and 6 B 8 and 6 C 3 and 15 D. 4 and 12

10. Explain It Explain how to find all the factor pairs of 40.

30428_T04_068-070_69 69 1/31/08 8:44:59 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Practice 4-7

Practice

4-7

Topic 4 69

Understanding FactorsList all the factors of each number.

1. 36

2. 90

3. 84

Number Sense A number is divisible by 4 if the last two digitsare divisible by 4. Write yes on the line if the number is divisible by 4 and no if it is not.

4. 324 5. 634 6. 172

7. A class of 80 students is graduating from elementary school. The teachers need help figuring out how to line up the students for the ceremony. One row of 80 students would be too long. What other ways could the students be arranged for the ceremony?

8. A number is divisible by another number when the after division by that number is 0.

9. Number Sense What factor pair is missing for 45 if you already know 1 and 45, 5 and 9?

A 7 and 6 B 8 and 6 C 3 and 15 D. 4 and 12

10. Explain It Explain how to find all the factor pairs of 40.

1, 2, 3, 4, 6, 9, 12, 18, 361, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 901, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Yes No Yes

2 rows of 40, 4 rows of 20, 5 rows of 16, 8 rows of 10

remainder

Sample answer: Follow the rules for divisibility of 2, 3, 4, 5, 6, 9, and 10, and check if the number is divisible by 7 and 8.

30428_T04_068-070_69 69 3/18/08 1:57:24 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Enric

hmen

t 4-7

Algebra

Enrichment

4-7

70 Topic 4

Finding Factors

1. Fill in the chart to find all the factor pairs of 16. Then list the factor pairs of 16.

Try Is It a Factor? Factor Pair

1

2

3

4

5

6

7

8

9

10



1

2

3

4

5

6

7

8

9

10

30428_T04_068-070_70 70 1/31/08 8:45:02 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Enric

hmen

t 4-7

Algebra

Enrichment

4-7

70 Topic 4

Finding Factors



1

2

3

4

5

6

7

8

9

10



1

2

3

4

5

6

7

8

9

10

Yes, 1 is a factor of every whole number.

Yes, 16 is even.

No. Since 1 ! 6 " 7, it is not divisible by 3.

Yes; 16 is divisible by 4.

No, because 16 does not end in 0 or 5.

No, because 16 is not divisible by both 2 and 3.No.

Yes; 16 is divisible by 8.


No, because the last digit of 16 is not 0.

1 and 16

2 and 8

4 and 4

8 and 2

Yes, 1 is a factor of every whole number.

No, 21 is not even.

Yes, 2 ! 1 " 3 and is divisible by 3.

No; 21 is not divisible by 4.

No, because 21 does not end in 0 or 5.

No, because 21 is not divisible by both 2 and 3.

Yes.

No; 21 is not divisible by 8.


No, because the last digit of 21 is not 0.

1 and 21

3 and 7

7 and 3

30428_T04_068-070_70 70 3/18/08 1:57:26 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 71

1. Dan sets up 24 tables in equal rows for a big party. Each row must have at least 5 tables. Which list shows all the different ways that Dan can set up the tables in equal rows? A 1 ! 2, 2 ! 3, 3 ! 4, 4 ! 6B 1 ! 2, 3 ! 4, 6 ! 8, 12 ! 24C 1 ! 24, 2 ! 12, 3 ! 8, 4 ! 6 D 1 ! 24, 2 ! 12, 3 ! 8, 4 ! 6,

5 ! 5

2. Which best explains how to change 3 5 _ 9 into an improper fraction?A Add 9 and 3. Then multiply

the sum by 5. Then write the product over the old denominator, 9.

B Add 3 and 5. Then multiplythe sum by 9. Then write the product over the old denominator, 9.

C Multiply 3 by 5. Then add 9 to the product. Then write the sum over the old denominator, 9.

D Multiply 9 by 3. Then add 5 to the product. Then write the sum over the old denominator, 9.

3. A rancher has 112 sheep. He puts a group of 28 sheep in each of his ! elds. How many ! elds does the farmer have?A 4 B 7 C 37 D 48

4. List all the factors of 96.

5. A sign shop charges $4 per letter to print a message on a banner. How much does the shop charge for a banner with the message “Big Sale Today”?

6. Plot and label a point on this number line to show 0.7.

0 1

Daily Spiral Review

4-8

Daily Spiral Review

4-8

30428_T04_071_71 71 1/31/08 8:45:10 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 71

1. Dan sets up 24 tables in equal rows for a big party. Each row must have at least 5 tables. Which list shows all the different ways that Dan can set up the tables in equal rows? A 1 ! 2, 2 ! 3, 3 ! 4, 4 ! 6B 1 ! 2, 3 ! 4, 6 ! 8, 12 ! 24C 1 ! 24, 2 ! 12, 3 ! 8, 4 ! 6 D 1 ! 24, 2 ! 12, 3 ! 8, 4 ! 6,

5 ! 5

2. Which best explains how to change 3 5 _ 9 into an improper fraction?A Add 9 and 3. Then multiply

the sum by 5. Then write the product over the old denominator, 9.

B Add 3 and 5. Then multiplythe sum by 9. Then write the product over the old denominator, 9.

C Multiply 3 by 5. Then add 9 to the product. Then write the sum over the old denominator, 9.

D Multiply 9 by 3. Then add 5 to the product. Then write the sum over the old denominator, 9.

3. A rancher has 112 sheep. He puts a group of 28 sheep in each of his ! elds. How many ! elds does the farmer have?A 4 B 7 C 37 D 48

4. List all the factors of 96.

5. A sign shop charges $4 per letter to print a message on a banner. How much does the shop charge for a banner with the message “Big Sale Today”?

6. Plot and label a point on this number line to show 0.7.

0 1

Daily Spiral Review

4-8

Daily Spiral Review

4-8

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

$48

0.7

30428_T04_071_71 71 3/18/08 1:57:37 PM




of the Day

4-8

72

Topic 4

Martha has 6 coins that are quarters, dimes, and nickels. She has a total of $0.80. What combination of coins does she have?

30428_T04_072_72 72

1/31/08 8:45:17 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 73

Interactive Learning Recording Sheet 9

Prime and Composite Numbers

Number Factor Pair(s) Prime or Composite?

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Interactive Learning Recording Sheet

9

30428_T04_073_73 73 1/31/08 8:45:25 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 73

Interactive Learning Recording Sheet 9

Prime and Composite Numbers

Number Factor Pair(s) Prime or Composite?

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Interactive Learning Recording Sheet

9

1 ! 21 ! 31 ! 4, 2 ! 21 ! 51 ! 6, 2 ! 31 ! 71 ! 8, 2 ! 41 ! 9, 3 ! 31 ! 10, 2 ! 51 ! 111 ! 12, 2 ! 6, 3 ! 41 ! 131 ! 14, 2 ! 71 ! 15, 3 ! 51 ! 16, 2 ! 8, 4 ! 41 ! 171 ! 18, 2 ! 9, 3 ! 61 ! 191 ! 20, 2 ! 10, 4 ! 5

primeprime

compositeprime

compositeprime

compositecompositecomposite

primecomposite

primecompositecompositecomposite

primecomposite

primecomposite

30428_T04_073_73 73 3/18/08 1:57:55 PM

96

Name

© P

ears

on E

duca

tion,

Inc.

5

Qui

ck C

heck

4-8

Quick Check

4-8

74 Topic 4

1. Which of the following numbers is a prime number?

A 106

B 121

C 168

D 211

2. Which of the following numbers is a composite number?

A 83

B 96

C 103

D 131

3. Writing to Explain A tree farm planted 96 new trees. Draw a factor tree to find the prime factorization of 96.

30428_T04_074_74 74 1/31/08 8:45:32 PM

96

Name

© P

ears

on E

duca

tion,

Inc.

5

Qui

ck C

heck

4-8

Quick Check

4-8

74 Topic 4

1. Which of the following numbers is a prime number?

A 106

B 121

C 168

D 211

2. Which of the following numbers is a composite number?

A 83

B 96

C 103

D 131

3. Writing to Explain A tree farm planted 96 new trees. Draw a factor tree to find the prime factorization of 96.


30428_T04_074_74 74 3/18/08 1:58:06 PM

1 ! 3 " 3 1 ! 8 " 8

2 ! 4 " 8

Name©

Pea

rson

Edu

catio

n, In

c. 5

Prime and Composite NumbersNumbers such as 2, 3, 5, 7, and 11 are prime numbers. A prime number has only two factors, itself and 1. A whole number that has more than two factors is called a composite number.

3 is an example of a prime number.Its only factors are 1 and 3.

To find the prime factorization of a number, you can use afactor tree.

You can also use divisibility rules to tell whether a number is prime or composite. In the example above, 12 is an even number, so it is divisible by 2. Therefore, 12 is a composite number.

Write whether each number is prime or composite.

1. 17 2. 47

Find the prime factorization.

3. 28

4. Number Sense The prime factorization ofa number is 2 ! 3 ! 3. What is the number?

8 is a composite number.Its factors are 1, 2, 4, and 8.

Reteaching

4-8

Topic 4 75

Reteaching 4-8

Find the prime factorization of 12. 12 Think of two numbers whose product

is 12. You can use 2 ! 6 or 3 ! 4.

2 is prime. 2 ! 6 6 is not prime, so keep dividing.

2 ! 2 ! 3 All the factors are prime, so you can stop dividing.

The prime factorization of 12 is 2 ! 2 ! 3.

30428_T04_075-076_75 75 1/31/08 8:45:39 PM

1 ! 3 " 3 1 ! 8 " 8

2 ! 4 " 8

Name©

Pea

rson

Edu

catio

n, In

c. 5

Prime and Composite NumbersNumbers such as 2, 3, 5, 7, and 11 are prime numbers. A prime number has only two factors, itself and 1. A whole number that has more than two factors is called a composite number.

3 is an example of a prime number.Its only factors are 1 and 3.

To find the prime factorization of a number, you can use afactor tree.

You can also use divisibility rules to tell whether a number is prime or composite. In the example above, 12 is an even number, so it is divisible by 2. Therefore, 12 is a composite number.

Write whether each number is prime or composite.

1. 17 2. 47

Find the prime factorization.

3. 28

4. Number Sense The prime factorization ofa number is 2 ! 3 ! 3. What is the number?

8 is a composite number.Its factors are 1, 2, 4, and 8.

Reteaching

4-8

Topic 4 75

Reteaching 4-8

Find the prime factorization of 12. 12 Think of two numbers whose product

is 12. You can use 2 ! 6 or 3 ! 4.

2 is prime. 2 ! 6 6 is not prime, so keep dividing.

2 ! 2 ! 3 All the factors are prime, so you can stop dividing.


Prime

2!2!7

Prime

18

30428_T04_075-076_75 75 3/18/08 1:58:19 PM

NamePr

actic

e 4-8

© P

ears

on E

duca

tion,

Inc.

5

Practice

4-8Prime and Composite NumbersWrite whether each number is prime or composite.

1. 21 2. 36 3. 31

4. 87 5. 62 6. 23

Use factor trees to find the prime factorization of each number.

7. 44 8. 63

9. 13 10. 54

11. Number Sense Audrey says that the prime factorization of 42 is 21 ! 2. Is she correct? If not, tell why.

12. Is 4,564,282 prime or composite? Explain how you determined your answer.

13. Which of the following is a prime number?

A 105 B 27 C 19 D 9

14. Explain It Does it matter what two factors you select to complete a factor tree? Explain.

76 Topic 4

30428_T04_075-076_76 76 1/31/08 8:45:41 PM

NamePr

actic

e 4-8

© P

ears

on E

duca

tion,

Inc.

5

Practice

4-8Prime and Composite NumbersWrite whether each number is prime or composite.

1. 21 2. 36 3. 31

4. 87 5. 62 6. 23

Use factor trees to find the prime factorization of each number.

7. 44 8. 63

9. 13 10. 54

11. Number Sense Audrey says that the prime factorization of 42 is 21 ! 2. Is she correct? If not, tell why.

12. Is 4,564,282 prime or composite? Explain how you determined your answer.

13. Which of the following is a prime number?

A 105 B 27 C 19 D 9

14. Explain It Does it matter what two factors you select to complete a factor tree? Explain.

76 Topic 4

Composite Composite PrimeComposite Composite Prime

2!2!11 3!3!71!13 2!3!3!3

Sample answer: Audrey is not correct. Since21 can be divided by 7 or 3, 21 is not prime.

Composite; It ends with an even number, so it is divisible by 2.

No; the prime factors will always end up at the bottom of the tree.

30428_T04_075-076_76 76 3/18/08 1:58:21 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Enrichment 4

-8

Number Sense

Enrichment

4-8

Topic 4 77

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

10

20

30

40

50

60

70

80

90

100

Homework HelperBeth has been studying prime and composite numbers. Help her complete her homework problems.

1. Step 1 Find a factor pair for 36.

Step 2 Write each factor that is not prime as a product.

Step 3 Continue until all branches of the “tree” end in prime numbers.

2. The Greek mathematician Eratosthenes invented a sieve to find prime numbers. Use the chart and directions to circle all the prime numbers from 1 to 100.

Step 1 Cross out 1 because it is not prime.

Step 2 Circle 2, the smallest even prime. Then cross out every multiple of 2, or every second number.

Step 3 Circle 3, the smallest odd prime. Then cross out every multiple of 3, or every third number.

Step 4 Circle the next prime number, 5. Then cross out every multiple of 5, or every fifth number.

Step 5 Continue these steps, circling all the prime numbers and crossing out their multiples, until you reach 100. When you are finished, you should have 25 circled prime numbers.

30428_T04_077_77 77 1/31/08 8:45:50 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Enrichment 4

-8

Number Sense

Enrichment

4-8

Topic 4 77

1

11

21

31

41

51

61

71

81

91

2

12

22

32

42

52

62

72

82

92

3

13

23

33

43

53

63

73

83

93

4

14

24

34

44

54

64

74

84

94

5

15

25

35

45

55

65

75

85

95

6

16

26

36

46

56

66

76

86

96

7

17

27

37

47

57

67

77

87

97

8

18

28

38

48

58

68

78

88

98

9

19

29

39

49

59

69

79

89

99

10

20

30

40

50

60

70

80

90

100

Homework HelperBeth has been studying prime and composite numbers. Help her complete her homework problems.

1. Step 1 Find a factor pair for 36.

Step 2 Write each factor that is not prime as a product.

Step 3 Continue until all branches of the “tree” end in prime numbers.

2. The Greek mathematician Eratosthenes invented a sieve to find prime numbers. Use the chart and directions to circle all the prime numbers from 1 to 100.

Step 1 Cross out 1 because it is not prime.

Step 2 Circle 2, the smallest even prime. Then cross out every multiple of 2, or every second number.

Step 3 Circle 3, the smallest odd prime. Then cross out every multiple of 3, or every third number.

Step 4 Circle the next prime number, 5. Then cross out every multiple of 5, or every fifth number.

Step 5 Continue these steps, circling all the prime numbers and crossing out their multiples, until you reach 100. When you are finished, you should have 25 circled prime numbers.

X X X X X XX XX X X X

X X X XX XX XX XX X X X X XX X

XX X X X X

X X X X XX XX XX X X X X XX X XX X X X

X XX X X X X XX XX X X X X X X

One Way Another Way 36 36

6 ! 6 2 ! 18

2 ! 3 ! 2 ! 3 2 ! 2 ! 9

2 ! 2 ! 3 ! 3

30428_T04_077_77 77 3/18/08 1:58:32 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

78 Topic 4

1. In a game, each player draws a number. If the number is prime, the player gets 5 points. The table shows four players and the numbers they draw.

Game ResultsPlayer NumberAngel 38Cory 31Maria 30Rachel 35

Which player gets 5 points?

A Angel B Cory C Maria D Rachel

2. A baker makes 84 loaves of bread, but she burns 4 of them. What fraction of the loaves does the baker burn?

A 1 ___ 88

B 1 ___ 80

C 1 ___ 21

D 1 ___ 20

3. Use a factor tree to ! nd the prime factorization of 164.

4. Kevin buys a car. His car payment is $248 per month. After 55 payments, how much has Kevin paid?

5. The clock shows the time when Kelly left for school.

Kelly takes 15 minutes to walk to school. What time is it when she gets to school?

Daily

Spi

ral R

evie

w

4-9

Daily Spiral Review

4-9

30428_T04_078_78 78 1/31/08 8:45:59 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

78 Topic 4

1. In a game, each player draws a number. If the number is prime, the player gets 5 points. The table shows four players and the numbers they draw.

Game ResultsPlayer NumberAngel 38Cory 31Maria 30Rachel 35

Which player gets 5 points?

A Angel B Cory C Maria D Rachel

2. A baker makes 84 loaves of bread, but she burns 4 of them. What fraction of the loaves does the baker burn?

A 1 ___ 88

B 1 ___ 80

C 1 ___ 21

D 1 ___ 20

3. Use a factor tree to ! nd the prime factorization of 164.

4. Kevin buys a car. His car payment is $248 per month. After 55 payments, how much has Kevin paid?

5. The clock shows the time when Kelly left for school.

Kelly takes 15 minutes to walk to school. What time is it when she gets to school?

Daily

Spi

ral R

evie

w

4-9

Daily Spiral Review

4-9


8:03 A.M.

$13,640

164

4

2 2

41

2 41

164

82 2

30428_T04_078_78 78 3/18/08 1:58:43 PM


Topic 4 7

9


4-9Problem of the DayThe Prado family is traveling 1,700 miles in 3 days to visit relatives. They drove 652 miles the first day. They want to drive the same distance each of the last two days. How far should they drive each day?

Problem of the Day

4-9

30428_T04_79-83_79 79

1/31/08 8:48:04 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

80 Topic 4

Quick Check

4-9Q

uick

Che

ck 4-9

3. Writing to Explain Gretchen is packing books in boxes to move. She has 118 books, and each box holds 6 books. How many boxes will she need to move all the books? Draw a picture and write an equation to solve.

1. Which equation can you use to solve the following problem?

Aaron has 186 photographs. Each page in his photo album holds 8 photographs. How many pages in his photo album will his photographs fill completely?

A 8 ! 186 " p

B 186 # 8 ! p

C 186 $ 8 ! p

D 8 ! 186p


A group of 168 students is on a field trip. They are doing a ropes course at a local camp. If 8 students can start the ropes course together at one time, in how many groups must the students go through the course?

A g ! 168 # 8

B g ! 168 $ 8

C 168 " g ! 8

D 168 # g ! 8

30428_T04_79-83_80 80 1/31/08 8:48:06 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

80 Topic 4

Quick Check

4-9Q

uick

Che

ck 4-9

3. Writing to Explain Gretchen is packing books in boxes to move. She has 118 books, and each box holds 6 books. How many boxes will she need to move all the books? Draw a picture and write an equation to solve.


Aaron has 186 photographs. Each page in his photo album holds 8 photographs. How many pages in his photo album will his photographs fill completely?

A 8 ! 186 " p

B 186 # 8 ! p

C 186 $ 8 ! p

D 8 ! 186p


A group of 168 students is on a field trip. They are doing a ropes course at a local camp. If 8 students can start the ropes course together at one time, in how many groups must the students go through the course?

A g ! 168 # 8

B g ! 168 $ 8

C 168 " g ! 8

D 168 # g ! 8


30428_T04_79-83_80 80 3/18/08 2:01:10 PM

? racks

10 test tubes

4

test tubes per rack

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 81

Reteaching

4-9Reteaching 4

-9

Problem Solving: Draw a Picture and Write an EquationMr. Rodriguez needs to store 10 test tubes in racks that hold 4 test tubes apiece. How many racks does he need?

Draw a picture.

Write an equation. Let r be the number of test-tube racks needed.

10 ! 4 " r

Solve the problem. r " 2 R 2

Think: R 2 means that 2 test tubes are still left. Since they must be in a rack, one more rack is needed.

Write the answer in a Mr. Rodriguez will need complete sentence. three test-tube racks.

Explain It Mr. Rodriguez could also use racks that hold three test tubes or racks that hold five test tubes. Which racks should he use if he wants each rack completely filled? Explain.

30428_T04_79-83_81 81 1/31/08 8:48:08 PM

? racks

10 test tubes

4

test tubes per rack

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 81

Reteaching

4-9Reteaching 4

-9

Problem Solving: Draw a Picture and Write an EquationMr. Rodriguez needs to store 10 test tubes in racks that hold 4 test tubes apiece. How many racks does he need?

Draw a picture.

Write an equation. Let r be the number of test-tube racks needed.

10 ! 4 " r

Solve the problem. r " 2 R 2

Think: R 2 means that 2 test tubes are still left. Since they must be in a rack, one more rack is needed.

Write the answer in a Mr. Rodriguez will need complete sentence. three test-tube racks.

Explain It Mr. Rodriguez could also use racks that hold three test tubes or racks that hold five test tubes. Which racks should he use if he wants each rack completely filled? Explain.

He should use the racks that hold 5 testtubes, because 10 is evenly divisible by 5.

30428_T04_79-83_81 81 3/18/08 2:01:13 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

82 Topic 4

Practice

4-9Pr

actic

e 4-9

Problem Solving: Draw a Picture and Write an EquationDraw a picture and write an equation. Then solve.

1. Tommy paid $39 to fill up the gas tank in his car. If one gallon of gas costs $3, how many gallons of gas did Tommy put in?

2. To prepare for the brunch, Ivana needs to place 8 muffins in each basket. If she has 115 muffins, how many baskets will she need?

3. Write a Problem Write a real-world problem that you can solve by writing an equation. The answer to the problem must be 6.

4. Geometry The perimeter is the distance around an object. The perimeter of a square is 84 centimeters. What is the length of one side of the square?

A 75 cm B 42 cm C 21 cm D 14 cm

5. Explain It A perfect score on a quiz is 100. Mrs. Frisoli gives students 1 point for putting their name on the paper. If there are only 9 questions on the quiz, how much is each question worth? Explain how you found your answer.

30428_T04_79-83_82 82 1/31/08 8:48:11 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

82 Topic 4

Practice

4-9Pr

actic

e 4-9

Problem Solving: Draw a Picture and Write an EquationDraw a picture and write an equation. Then solve.

1. Tommy paid $39 to fill up the gas tank in his car. If one gallon of gas costs $3, how many gallons of gas did Tommy put in?

2. To prepare for the brunch, Ivana needs to place 8 muffins in each basket. If she has 115 muffins, how many baskets will she need?

3. Write a Problem Write a real-world problem that you can solve by writing an equation. The answer to the problem must be 6.

4. Geometry The perimeter is the distance around an object. The perimeter of a square is 84 centimeters. What is the length of one side of the square?

A 75 cm B 42 cm C 21 cm D 14 cm

5. Explain It A perfect score on a quiz is 100. Mrs. Frisoli gives students 1 point for putting their name on the paper. If there are only 9 questions on the quiz, how much is each question worth? Explain how you found your answer.

Check students’ diagrams. 39 ! 3 " g; g " 13; 13 gallons of gas

Check students’ diagrams. 115 ! 8 " b; b " 14 R 3; 15 baskets

Answer will vary. Check students’ work.

100 # 1 " 99. 99 ! 9 " 11. Each question is worth 11 points.

30428_T04_79-83_82 82 3/18/08 2:01:15 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 83

Enrichment

4-9Enrichm

ent 4-9

Kayak TripThree sisters are going on a kayaking trip in the mountains. They will carry their supplies in their kayaks. If the sisters divide up the supplies below equally, how many of each item will each sister carry? How many will be left over?

1. 131 bottles of juice

2. 295 energy bars

3. 467 food packets

4. 691 packs of matches

5. The sisters plan to finish a trip of 351 miles in 13 days. How many miles will they paddle each day?

6. The sisters took 868 photos on their kayak trip. If their photo albums each hold 75 photos, how many albums will they fill completely? How many photos will be in the last album?

7. The sisters used up 769 minutes on their cell phone plan. If their plan allows for 2,500 minutes and they divide up the remaining minutes, how many minutes will each sister have?

Number Sense

30428_T04_79-83_83 83 1/31/08 8:48:13 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4 83

Enrichment

4-9Enrichm

ent 4-9

Kayak TripThree sisters are going on a kayaking trip in the mountains. They will carry their supplies in their kayaks. If the sisters divide up the supplies below equally, how many of each item will each sister carry? How many will be left over?

1. 131 bottles of juice

2. 295 energy bars

3. 467 food packets

4. 691 packs of matches

5. The sisters plan to finish a trip of 351 miles in 13 days. How many miles will they paddle each day?

6. The sisters took 868 photos on their kayak trip. If their photo albums each hold 75 photos, how many albums will they fill completely? How many photos will be in the last album?

7. The sisters used up 769 minutes on their cell phone plan. If their plan allows for 2,500 minutes and they divide up the remaining minutes, how many minutes will each sister have?

Number Sense

43 bottles apiece; 2 bottles left over

98 energy bars apiece; 1 bar left over

155 packets apiece; 2 extra packets

230 packs apiece; 1 pack left over

27 miles each day

11 photo albums will be full; there will be 43 photos in the twelfth album.

577 minutes

30428_T04_79-83_83 83 3/18/08 2:01:18 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Topic 4 Multiple-Choice Test

1. If the money shown is to be divided among 5 people, what should be the first step? (4-4)

A Exchange the $50 bill for two $20 bills and ten $1 bills.

B Exchange the ! ve $10 bills for ! fty $1 bills.

C Exchange the $50 bill for ! fty $1 bills.

D Exchange the $50 bill for ! ve $10 bills.

2. If $900 is divided evenly by 9 people, how many dollars does each person get? (4-1)

A $10

B $100

C $1,000

D $10,000

3. If 327 is divided by 6, where should the first digit of the quotient be placed? (4-5)

A Because 6 is greater than 3, it should be placed in the tens place.

B Because 6 is less than 3, it should be placed in the tens place.

C Because 6 is greater than 3, it should be placed in the hundreds place.

D Because 6 is less than 3, it should be placed in the hundreds place.

4. Using estimation, about how much is 155 ! 9? (4-2)

A 7

B 9

C 12

D 16

5. The table shows the boxes of cookies sold by students as a school fundraiser. Marc sold 3 times the amount that Karen did. How many boxes of cookies did Karen sell? (4-6)

Student BoxesMarc 408Karen ?Mia 97

A 204 C 136

B 173 D 121

Topi

c 4

M

ultip

le-C

hoic

e Te

st

$10 $10$10

$10$10

$50

84 Topic 4

Mark the best answer.

30428_T04_084-86_84 84 1/31/08 8:46:06 PM

Name

© P

ears

on E

duca

tion,

Inc.

5

Topic 4 Multiple-Choice Test

1. If the money shown is to be divided among 5 people, what should be the first step? (4-4)

A Exchange the $50 bill for two $20 bills and ten $1 bills.

B Exchange the ! ve $10 bills for ! fty $1 bills.

C Exchange the $50 bill for ! fty $1 bills.

D Exchange the $50 bill for ! ve $10 bills.

2. If $900 is divided evenly by 9 people, how many dollars does each person get? (4-1)

A $10

B $100

C $1,000

D $10,000

3. If 327 is divided by 6, where should the first digit of the quotient be placed? (4-5)

A Because 6 is greater than 3, it should be placed in the tens place.

B Because 6 is less than 3, it should be placed in the tens place.

C Because 6 is greater than 3, it should be placed in the hundreds place.

D Because 6 is less than 3, it should be placed in the hundreds place.

4. Using estimation, about how much is 155 ! 9? (4-2)

A 7

B 9

C 12

D 16

5. The table shows the boxes of cookies sold by students as a school fundraiser. Marc sold 3 times the amount that Karen did. How many boxes of cookies did Karen sell? (4-6)

Student BoxesMarc 408Karen ?Mia 97

A 204 C 136

B 173 D 121

Topi

c 4

M

ultip

le-C

hoic

e Te

st

$10 $10$10

$10$10

$50

84 Topic 4


30428_T04_084-86_84 84 3/18/08 1:58:55 PM

Name

Topic 4 87

Topic 4Free-Response Test



1. 56 ! 8

2. 480 ! 6

3. 49,000 ! 7

4. 81,000 ! 9

Use rounding to estimate each quotient.

5. 412 ! 5

6. 545 ! 8

7. 404 ! 11

8. 797 ! 51

Use compatible numbers to estimate each quotient.

9. 357 ! 18

10. 1,056 ! 75

11. 331 ! 80

12. 436 ! 90

Divide.

13. 6 !"" 360

14. 12 !"" 480

15. 32 !"" 160

16. 11 !"" 121

Find each quotient.

17. 4 !"" 156

18. 2 !"" 81

19. 3 !"" 99

20. 4 !"" 34

21. 7 !"" 50

22. 3 !"" 57

23. 3 !"" 110

24. 2 !"" 97

25. 3 !"" 130

© P

ears

on E

duca

tion,

Inc.

5

30428_T04_87-88_87 87 1/31/08 8:48:22 PM

Name

Topic 4 87




1. 56 ! 8

2. 480 ! 6

3. 49,000 ! 7

4. 81,000 ! 9

Use rounding to estimate each quotient.

5. 412 ! 5

6. 545 ! 8

7. 404 ! 11

8. 797 ! 51

Use compatible numbers to estimate each quotient.

9. 357 ! 18

10. 1,056 ! 75

11. 331 ! 80

12. 436 ! 90

Divide.

13. 6 !"" 360

14. 12 !"" 480

15. 32 !"" 160

16. 11 !"" 121

Find each quotient.

17. 4 !"" 156

18. 2 !"" 81

19. 3 !"" 99

20. 4 !"" 34

21. 7 !"" 50

22. 3 !"" 57

23. 3 !"" 110

24. 2 !"" 97

25. 3 !"" 130

© P

ears

on E

duca

tion,

Inc.

5

400 ! 5 " 80

560 ! 8 " 70

400 ! 10 " 40

800 ! 50 " 16

360 ! 18 " 20

1,050 ! 75 " 14

320 ! 80 " 4

450 ! 90 " 5

60

40

511

3940 R1

338 R2

7 R1

19

36 R248 R1

43 R1

7

80

7,000

9,000

30428_T04_87-88_87 87 3/18/08 2:01:29 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4Performance Assessment

Topic 4Perform

ance Assessment Topic 4 89

Use the data in the table for 1 and 2.

1. How many shelves are needed for the new releases if each shelf holds 8 videos?

2. Half of the action movies are on DVD and the other half are on VHS. How many action DVDs does the video store have?

3. A three-digit number is divided by a one-digit number. The quotient is a two-digit number. What can you say about the dividend and the divisor? Give an example.

4. The Quade family drove 920 miles in 3 days. They drove the same number of miles the first 2 days and then drove 50 miles the third day. Explain how to find the number of miles they drove on each of the first two days.

5. Four families went out for dinner. The total food bill came to $327. The families also left a $50 tip for the waiter. If each family spent the same amount, about how much did each family spend on dinner? Explain how you found your answer.

Video Store Movies

Comedy 512Drama 378Action 456Horror 392

New Releases 425

30428_T04_089_89 89 1/31/08 8:46:19 PM

Name©

Pea

rson

Edu

catio

n, In

c. 5

Topic 4Performance Assessment

Topic 4Perform

ance Assessment Topic 4 89

Use the data in the table for 1 and 2.

1. How many shelves are needed for the new releases if each shelf holds 8 videos?

2. Half of the action movies are on DVD and the

other half are on VHS. How many action DVDs does the video store have?

3. A three-digit number is divided by a one-digit number.

The quotient is a two-digit number. What can you say about the dividend and the divisor? Give an example.

4. The Quade family drove 920 miles in 3 days. They drove the same number of miles the first 2 days and then drove 50 miles the third day. Explain how to find the number of miles they drove on each of the first two days.

5. Four families went out for dinner. The total food bill came to $327. The families also left a $50 tip for the waiter. If each family spent the same amount, about how much did each family spend on dinner? Explain how you found your answer.

Video Store Movies

Comedy 512Drama 378Action 456Horror 392

New Releases 425

54 shelves

228 action DVDs

The hundreds digit of the dividend is less than the divisor. 510 ! 6 " 85

Subtract 50 miles from the total and divide by two: (920 # 50) ! 2 " 435 miles.

I added the food bill to the tip ($327 $ $50 " 377). Then I rounded $377 to $400 and divided by 4. Each family spent about $100.

30428_T04_089_89 89 3/18/08 1:59:10 PM

Name

90 Topic 4

© P

ears

on E

duca

tion,

Inc.

5

Cumulative Test Topics 1–4


Cum

ulat

ive

Test

Topi

cs 1

– 4

1. Write 80 + 6 + 0.03 + 0.001 in standard form.

A 8.6031

B 86.031

C 86.301

D 86.31

2. What is the value of the digit 3 in 23,457?

A Three

B Three hundred

C Three thousand

D Thirty thousand

3. Which shows the numbers ordered from least to greatest?

A 31,240; 30,408; 31,703

B 30,408; 31,240; 31,703

C 31,703; 31,240; 30,408

D 30,408; 31,703; 31, 240

4. What is the value of the digit 7 in 43.78?

A Seven tenths

B Seven hundredths

C Seven thousandths

D Seventy thousandths

5. Which shows five billion, two hundred thirty-six million, four thousand, one hundred seven in standard form?

A 5,236,004,107

B 5,236,004,017

C 5,236,404,107

D 5,236,400,107

6. Which shows the decimals ordered from least to greatest?

A 0.4, 0.05, 0.61, 0.007

B 0.007, 0.4, 0.05, 0.61

C 0.05, 0.61, 0.007, 0.4

D 0.007, 0.05, 0.4, 0.61

7. Which shows forty and seventy-two thousandths in standard form?

A 47. 002

B 40.72

C 4.72

D 40.072

8. Express 230.02 in word form.

A Two hundred thirty and two tenths

B Two hundred three and two hundredths

C Two hundred thirty and two hundredths

D Two hundred three and two tenths

30428_T04_090-093_90 90 1/31/08 8:46:27 PM

Name

90 Topic 4

© P

ears

on E

duca

tion,

Inc.

5

Cumulative Test Topics 1–4


Cum

ulat

ive

Test

Topi

cs 1

– 4

1. Write 80 + 6 + 0.03 + 0.001 in standard form.

A 8.6031

B 86.031

C 86.301

D 86.31

2. What is the value of the digit 3 in 23,457?

A Three

B Three hundred

C Three thousand

D Thirty thousand

3. Which shows the numbers ordered from least to greatest?

A 31,240; 30,408; 31,703

B 30,408; 31,240; 31,703

C 31,703; 31,240; 30,408

D 30,408; 31,703; 31, 240

4. What is the value of the digit 7 in 43.78?

A Seven tenths

B Seven hundredths

C Seven thousandths

D Seventy thousandths

5. Which shows five billion, two hundred thirty-six million, four thousand, one hundred seven in standard form?

A 5,236,004,107

B 5,236,004,017

C 5,236,404,107

D 5,236,400,107

6. Which shows the decimals ordered from least to greatest?

A 0.4, 0.05, 0.61, 0.007

B 0.007, 0.4, 0.05, 0.61

C 0.05, 0.61, 0.007, 0.4

D 0.007, 0.05, 0.4, 0.61

7. Which shows forty and seventy-two thousandths in standard form?

A 47. 002

B 40.72

C 4.72

D 40.072

8. Express 230.02 in word form.

A Two hundred thirty and two tenths

B Two hundred three and two hundredths

C Two hundred thirty and two hundredths

D Two hundred three and two tenths

30428_T04_090-093_90 90 3/18/08 1:59:21 PM

Benc

hmar

k Te

st 1

Topi

cs 1

–4

Benchmark Test 1Topics 1–4

1. What is the standard form of 2,000,000 ! 300,000 ! 6,000 ! 400 ! 20 ! 1?

A 2,306,421

B 2,360,421

C 2,364,021

D 2,634,210

2. What is 10,483,190 in word form?

A Ten billion, four hundred eighty-three million, one hundred ninety thousand

B Ten million, four hundred eighty-three, one hundred ninety

C Ten million, four hundred thousand eighty-three, one hundred ninety

D Ten million, four hundred eighty-three thousand, one hundred ninety

3. What is the value of the underlined digit in the number 57,035,189?

A Seven billion

B Seven thousand

C Seven

D Seven million

Name

© P

ears

on E

duca

tion,

Inc.

5

94 Topic 4


4. Jorge sorts mail to be delivered into cubby holes. The shaded parts of the grid below show the cubby holes that have mail in them.

Which decimal is equivalent to the number of cubby holes that have mail?

A 0.57

B 1.057

C 1.57

D 2.57

30428_T04_094-104_FSD_94 94 1/31/08 8:46:45 PM

Benc

hmar

k Te

st 1

Topi

cs 1

–4

Benchmark Test 1Topics 1–4

1. What is the standard form of 2,000,000 ! 300,000 ! 6,000 ! 400 ! 20 ! 1?

A 2,306,421

B 2,360,421

C 2,364,021

D 2,634,210

2. What is 10,483,190 in word form?

A Ten billion, four hundred eighty-three million, one hundred ninety thousand

B Ten million, four hundred eighty-three, one hundred ninety

C Ten million, four hundred thousand eighty-three, one hundred ninety

D Ten million, four hundred eighty-three thousand, one hundred ninety

3. What is the value of the underlined digit in the number 57,035,189?

A Seven billion

B Seven thousand

C Seven

D Seven million

Name

© P

ears

on E

duca

tion,

Inc.

5

94 Topic 4


4. Jorge sorts mail to be delivered into cubby holes. The shaded parts of the grid below show the cubby holes that have mail in them.

Which decimal is equivalent to the number of cubby holes that have mail?

A 0.57

B 1.057

C 1.57

D 2.57

30428_T04_094-104_FSD_94 94 3/18/08 1:59:44 PM

Benchmark Test 1

Topics 1–

4

Benchmark Test 1 Report

NAEP Mathematics Objectives

Test Items

Number Correct

Check ( ) if OK

Student Book Lessons MDIS*

Number Properties and Operations1) Number Sense

a) Use place value to model and describe integers and decimals.

1, 2, 3

3

1–1 F10, F13

e) Recognize, translate between, or apply multiple representations of rational numbers (fractions, decimals, and percents) in meaningful contexts.

4, 5, 6

3

1–3 H22, H24, H25

j) Order or compare rational numbers including very large and small integers, and decimals and fractions close to zero.

7, 8, 9

3

1–2, 1–4 F12, H28, H29

2) Estimation

b) Make estimates appropriate to a given situation by: identifying when estimation is appropriate, determining the level of accuracy needed, selecting the appropriate method of estimation, or analyzing the effect of an estimation method on the accuracy of results.

10, 11, 12

3

2–2, 2–3, 3–3, 4–2

F11, G15, G45, G46, G67, H26, H27, H53, H56

c) Verify solutions or determine the reasonableness of results in a variety of situations including calculator and computer results.

13, 14, 15

3

4–3 J35

3) Number Operations

a) Perform computations with rational numbers.

16, 17, 18, 19, 20, 21

6

2–1, 2–5, 2–6, 2–7, 3–4, 3–5, 3–6, 3–7, 4–4, 4–5, 4–6

G11, G19, G20, G52, G53, G55, G56, G58, G62, G68, G69, G70, G71, H54, H55, H57

*MDIS (Scott Foresman • Addison Wesley enVisionMATH™ Math Diagnosis and Intervention System)

Topic 4 103

Name©

Pea

rson

Edu

catio

n, In

c. 5

30428_T04_094-104_FSD_103 103 1/31/08 8:47:04 PM

Name Daily Spiral Review 4-1 · 2018. 1. 14. · Daily Spiral Review 4-1 Topic 4 29 1. Steve uses 6...

Documents

Transcript of Name Daily Spiral Review 4-1 · 2018. 1. 14. · Daily Spiral Review 4-1 Topic 4 29 1. Steve uses 6...