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Booklet 8 of 25

Family Letter for Unit 4

Chapter Pretest (3 pages)

Resources for Lessons 8.1 – 8.6 (6 pages/lesson)• Reteach 8.1 – 8.6• Practice 8.1 – 8.6• Enrichment 8.1 – 8.6• Problem Solving 8.1 – 8.6• Homework 8.1 – 8.6• English Learners 8.1 – 8.6

Chapter Test (2 pages)

Unit 4 Record Sheet

Chapter ResourcesGRADE 4, CHAPTER 8

Contents

Dear Family,

During the next few weeks, our math class will belearning about and practicing division of whole numbers.

You can expect to see work that provides practice with dividing numbers with up to four digits by one- andtwo-digit numbers.

As we use division to learn about prime and compositenumbers, you may wish to use this sample as a guide.

The number 2 is the only prime even number. The number 1 is neither prime nor composite.

During this unit, students should continue to practiceand memorize basic multiplication and division facts.

Sincerely,

Your Child’s TeacherCheck out Education Place ateduplace.com/kids/mw/ for e•Glossary, e•Word Games,test prep practice, and more.


prime number A whole number thathas only itself and 1 as factors.

composite number A whole numberthat has more than two factors.

divisible One number is divisible by another if the quotient is a wholenumber and the remainder is 0.

average The number found by dividingthe sum of a set of numbers by thenumber of addends.

Prime and Composite Numbers

You can use the factors of a number to tell if the number is prime or composite.

Unit 4 Family LetterCopyright © Houghton Mifflin Company. All rights reserved.

Examples of Prime Numbers

Prime Number Factors

2 1 and 2

5 1 and 5

13 1 and 13

Notice that each number has exactly two factors.

Examples of Composite Numbers

Composite Number Factors

4 1, 2, and 4

10 1, 2, 5, and 10

12 1, 2, 3, 4, 6, and 12

Notice that each number has more thantwo factors.

G4ELLFNLU04 8/1/05 5:09 PM Page 4

Name Date

Copyright © Houghton Mifflin Company. All rights reserved.

Chapter 8Pretest

Are You Ready?Divide. Check your answers.

Go on

1. 24 � 3

2. 42 � 6

3. 56 � 8

4. 72 � 9

Write a division fact for each picture.

5.

6.

Divide. Tell if there is a remainder.

7. 4��8�4� 8. 2��3�7� 9. 6��5�0�

Solve. Explain why your answer makes sense.

10. A van can hold 6 passengers. If 20 people need a ride tothe museum, how many vans are needed?

x xx

x x

x xx

x x

x xx

x x

x xx

x x

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Chapter 8Pretest

continued

1. 3��6�3� 2. 2��4�5� 3. 84 � 4 �

Divide. Check your answers.

4. 7��6�4� 5. 4�6�8�

6. 83 � 5 � 7. 99 � 6 �

Divide.

8. 15 � 3 9. 24 � 8 10. 54 � 6

150 � 3 240 � 8 540 � 6

1,500 � 3 2,400 � 8 5,400 � 6

11. 280 � 4 12. 300 � 6 13. 4,800 � 8

Check What You KnowDivide. Tell if there is a remainder.

Go on

4A08L2 6/29/05 4:50 PM Page 2

STOP

Name Date


Chapter 8Pretest

continuedEstimate. Write the basic fact you used.

14. 5��2�7� 15. 4��3�3�3�

16. 38 � 6 17. 500 � 8


18. Carly is placing postcards in a scrapbook. She can fit 4 postcards on a page. How many pages does Carlyneed for 26 postcards?

19. Sean has 30 days to work on a class project. How many full weeks does he have?

20. Andy buys as many $3-books as he can for $20. How much money does he have left over after he buysthe books?

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Model DivisionUse models to understand division.

Divide 13 into groups with 3 in each group.Use the counters below for Exercises 1–3.

1. Circle as many groups of 3 counters as you can.

How many groups of 3 are there?

2. How many are left over?

3. What is the quotient?

4. Draw a picture to show 10 divided equally into 2 groups.

5. How many are in each equal group?



Copyright © Houghton Mifflin Company. All rights reserved. Use with text pages 206–207.

Reteach8.1

Use money to find 14 � 5. Place 14 one-dollar bills in groups of 5.

Look at the picture.

It shows how to make as many groups of 5 as possible.

Ask yourself how many groups of 5 are there? You should count 2

Look at the one-dollar bills left over. Count them.

How many one-dollar bills are left over? 4

14 � 5 � 2 R4

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Practice8.1

Model DivisionUse base-ten blocks to complete the table.

6. Draw a picture to show 30 divided into 5 equal groups. Writea number sentence to show division.

7. Draw a picture to show 17 divided into groups of 4 in eachgroup. Write a number sentence to show division.

Test Prep

8. If you divide 20 one-dollar bills into 4equal groups how many one-dollarbills would be in each group?

A 4 C 5

B 3 D 1

9. Mr. Marris is building a birdhouse. Hehas 23 nails and 5 boards. Does hehave enough nails to hammer 4 nailsin each board? If so, how many nailswill he have left over?

Number Number of Number in Number NumberEqual Groups Each Group Left Sentence

14

29

35

75

25

63

2

7

5

9

7

9

8

0 14 � 2 � 7

1.

2.

3.

4.

5.

4C08L1 7/5/05 4:22 PM Page 1

1. 2.

3. 4.

5. 6.

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Picture Match-UpFor each picture, choose a division equation from the box thatrepresents the picture. Each equation will only be used once.Some equations may not be used.


Enrichment8.1

45 � 4 � 11 R1 64 � 3 � 21 R1 97 � 3 � 32 R1

67 � 3 � 22 R1 49 � 4 � 12 R1 81 � 2 � 40 R1

69 � 6 � 11 R3 64 � 6 � 10 R4 54 � 5 � 10 R4

76274-E-08-L1-L6 2/21/03 4:46 PM Page 1

Model DivisionUse base-ten blocks to model and solveeach problem.

1. Mrs. Murphy had 66 apples. She used6 apples in each pie she baked. Howmany pies did Mrs. Murphy bake?

2. Mr. Thomas picked several baskets ofstrawberries. He picked a total of 65strawberries. He equally divided thestrawberries into 3 containers. He ateany remaining strawberries. How manystrawberries did Mr. Thomas eat? Howcan you tell?

3. The grocery store had a total of 56oranges. The oranges were dividedevenly into bags of 5 oranges each.How many bags of oranges werethere? Were there any oranges leftover?

4. Write About It Explain how the modelof 54 � 5 is similar to 54 � 10.

Name Date


ProblemSolving

8.1

Show your work.

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Homework8.1

Problem Solving

5. Martin had 37 shells. He put them in 3 equal piles. How many shells wereleft over?

Show your work.



35

18

81

59

27 2 1 27 � 2 � 13 R113

6

5

7

9

1.

2.

3.

4.

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EnglishLearners

8.1

Write words from the box to fill the blanks.

6��1�2� This is a problem. In this problem you must

12 by 6. The number that must be divided, 12, is

called the . The number it must be divided by, 6,

is called the .

This division problem has been solved. The answer, 3, is called the

.

This division problem has 1 left over. This amount is called the

.

3 r14��1�2�

34��1�2�

Model Division Read this explanation.

In math, divide means “to separate into equalparts” or “to put in equal groups.”

The process of dividing is called division. Ina division problem, the process of dividing isshown in numbers. The total number beingdivided is called the dividend. The number of groups or portions the number is beingdivided into is called the divisor. The answer—the size of each portion or the number in eachgroup—is called the quotient. Any amount leftover when the equal portions are made iscalled the remainder.

divide division dividend divisor quotient remainder

2"

2"

2"2"

2" 2"

12 � 6 � 2

12 � 4 � 3

G4ELL081 7/23/05 2:51 PM Page 1

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Reteach8.2

Divide 25 � 2.

You can use dimes and pennies to show 25 cents.

Divide the money into 2 equal groups. Put 1 dime in each group.

Put two pennies in each group.There is one penny left over.

Count the dimes and pennies in one group. This is thequotient. The penny left over is the remainder.

Divide With Remainders

So, or 25 � 2 � 12 R1


1. 3�9�4� 2. 8�8�8� 3. 2�6�9�

4. 57 � 5 5. 46 � 2 6. 66 � 3

7. 23 � 2 8. 85 � 5 9. 47 � 4

12 R12��2�5��20�

05�4�

1

4R08L2 2/23/06 2:21 PM Page 2

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Divide With RemaindersDivide. Tell if there is a remainder.

1. 2�4�3� 2. 5�5�5 3. 4�4�9� 4. 4�4�6� 5. 3��3�6�

6. 5��5�4� 7. 4��4�7� 8. 2�6�5� 9. 7��7�8� 10. 3�6�6�

11. 42 � 2 � 12. 79 � 7 � 13. 64 � 3 � 14. 64 � 2 � 15. 22 � 2 �

16. 68 � 2 � 17. 51 � 9 � 18. 96 � 3 � 19. 73 � 7 � 20. 86 � 4 �

Algebra • Symbols Write ≥ or ≤ for each.

21. 20 � 5 24 � 4 22. 64 � 8 56 � 8 23. 12 � 6 14 � 2

24. 35 � 7 4 � 2 25. 48 � 4 84 � 4 26. 27 � 3 9 � 3

27. 43 � 2 15 � 3 28. 55 � 5 16 � 1 29. 56 � 8 81 � 9


Practice8.2

Test Prep

30. Find 67 � 3.

A 20 R1 C 21 R1

B 22 R1 D 23 R3

31. Marsha, Ashley, Peter and Dawn have45 pieces of candy to share equally.How many pieces will each get? Howmany are left over? Explain youranswers.

4C08L2 2/22/06 6:14 PM Page 2

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Division RiddlesDigit Detective needs help on a mission. He must organize thedividends, divisors, quotients, and remainders into 4 groups.The problem is that he doesn’t know which numbers arewhich. Your job is to help him solve these division riddles tofind each number. Then, organize the numbers into the fourgroups.


Enrichment8.2

1. Divide me by 3, and you’ll get aremainder of 2. My digits have a sumof 8 and a difference of 2. I am lessthan 6 � 6. What dividend am I?

2. If you divide 48 by me, you’ll get noremainder. But if you divide 46 by me,you’ll get a remainder of 2. Whatdivisor am I?

3. Divide 56 or 71 by 5 and me as aremainder you’ll see. What remainderam I?

4. I am an odd number. When you divide38 by me, the remainder is 2. Whatdivisors could I be?

5. Divide me by 5 and you’ll get aremainder of 2. I am greater than 9 � 6, but less than 6 � 10. Whatdividend am I?

6. Add me to the product of the divisorand the quotient and you’ll get thedividend of 41. That is if the divisor was3 and the quotient was 13. Whatremainder am I?

7. Divide 98 by an odd number and you’llget me with a remainder of 8. Whatquotients can I be?

8. If you divide an even number by 2, Iwill be your remainder. What remainderam I?

Dividends Divisors

Quotients Remainders

4E08L2 2/22/06 7:49 AM Page 2

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Divide With RemaindersSolve.


1. Jordan has 42 files on his computer. Hesaved an equal number of files on 2disks. How many files are on each disk?

2. Jordan has 89 CDs in his collection. Hewants to organize them evenly into 4 cases. How many CDs will he put ineach case? How many will be leftover?

3. The music store displays CDs on 8 shelves and on the counter. Thesame number of CDs are displayed oneach shelf. If the store displays a totalof 83 CDs. How many CDs are on thecounter?

4. Randy spent $65 at the music store.He bought 5 CDs. How much did eachCD cost?

5. You Decide Harvey has 56 songsstored on his computer. He wants tosave them to 3 CDs. How manydifferent ways can he divide the songs?Explain how you found your answer.

ProblemSolving

8.2

Show your work.

4P08L2 1/20/04 9:53 PM Page 2

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Homework8.2

49 � 4

49 � 4 � 12 R1

Problem SolvingShow your work.


Multiply 1 ten � 4.Subtract 4 � 4.

Compare 0 � 4. Bring down 9 ones.Multiply 2 ones � 4.Subtract 9 � 8.Compare 1 � 4.

↓

1. 3�6�4� 2. 4�8�8� 3. 3�3�9� 4. 2�8�2�

5. 58 � 5 6. 35 � 3 7. 49 � 4 8. 77 � 7

Mental Math Write ≥ or ≤ for each �.

9. 24 � 8 � 12 � 2 10. 44 � 2 � 22 � 2 11. 54 � 6 � 72 � 9

12. Jan has 38 baseball caps. She wants toput them in groups of 3 caps each.How many groups of caps will shehave? Will she have any caps leftover? If so, how many?

14��4�9��4�

0

12 R14��4�9��4↓�

09� 8�

1

4H08L2 6/29/05 4:31 PM Page 2

Name Date


EnglishLearners

8.2

Match each picture to the definition that fits it.

1. a small copy of something

2. a tiny example of something not yet made

3. a style or design

4. a person serving as a subject for an artist

5. a person paid to display clothes by wearing them

Divide With RemaindersRead this information.

Model is a word with many meanings. It can be used as a noun, a verb, or an adjective. The dictionary entry below gives the noun meanings.

mod•el (mod´l) noun. 1. a small copy of something: This model of a racecar is 6 inches long. 2. a tiny example of something not yet made: Thebuilder showed the family a model of the house he planned to build. 3. astyle or design: This year’s model of the Speedycar is much better look-ing than last year’s model. 4. a person serving as a subject for an artist:Rhonda asked her friend Beth to be a model for a painting she wantedto make. 5. a person paid to display clothes by wearing them: Helen willbe a model in the fashion show tomorrow.

G4ELL082 7/23/05 2:51 PM Page 2

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Reteach8.3

Heather owns a trading-card shop. She is arranging 59 cards on a display. Each row ofthe display holds 5 cards. How many rows of cards will she need to display all the cards?

What is the question? One way to find the answer is to divide.

How many rows of cards will she need in the display?

What do you know? • She has 59 cards• Each row will hold 5 cards

Explanation: Eleven rows will hold 55 trading cards. Another row is needed for theextra 4 trading cards, so increase the quotient to the next whole number which is 12.The answer is 12 rows.

11 R45�5�9��5�

09�5�

4

Problem-Solving Application:Interpret Remainders

Solve each problem.

1. Brad collects trading cards. He has 68 cards in his collection. Hewants to store them in a book. Each page of the book holds 6cards. How many pages will Brad need to store all of his cards?

2. Complete the table to show how many pages Brad wouldneed if he only had 48 cards.

3. Maria is putting 93 football trading cards on display for 72days at the mall. How many full weeks will the cards be ondisplay?

4. Jim is arranging 69 basketball trading cards in 6 equal rows.Any cards left over will not be placed in the display. Howmany cards will not be in the display?

Page 1

6 cards

Page 2

12 cards

Page 3

Show your work.

4R08L3 6/30/05 5:00 PM Page 3

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Practice8.3

Problem-Solving Application:Interpret RemaindersSolve. Explain why your answer makes sense.

Show your work.

1. Gordan’s Pineapple Farm in Hawaii isshipping 69 pineapples in woodenboxes. Each box holds 6 pineapples.How many boxes are needed?

2. Ms. Ramon brought 26 pineappleshome from her vacation to Hawaii. Shedivided the pineapples into 3 equalpiles and ate the pineapples that wereleft over. How many pineapples did Ms.Ramon eat?

3. Mr. Kelly’s class has $65 to spend atthe pineapple farm. They decide to usetheir money to buy pineapples. Eachpineapple costs $3. How manypineapples can the class buy?

4. Mr. Jack’s class helps pack pineapplesin shipping boxes. The class is given94 pineapples to pack. Each shippingbox holds 9 pineapples. How manyboxes can the class fill?

5. At the grocery store, Alice is arrangingpineapples in the produce case. Sheputs 7 pineapples in each row, one ata time. What row does she put the29th pineapple in?

4P08L3 7/1/05 1:01 PM Page 3

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Problem-Solving Application:Interpret RemaindersProblem For a vacation, Mrs. Kluthrow and her family drove 478miles to Philadelphia to visit the museums and other historicalplaces. On the trip, Mrs. Kluthrow took 118 pictures. Of thepictures, 29 are photos of her children and the rest are photos ofthe places they visited.


Enrichment8.3

1. Mrs. Kluthrow divides the photos of hertwo children evenly between the twochildren. How many photos does eachchild get? Explain how you found youranswer.

2. Mrs. Kluthrow organized the photos ofthe places they visited into a photoalbum. If 4 photos can fit on each pageof the album, how many pages did Mrs.Kluthrow use? Explain how you foundyour answer.

3. Write a division problem in which theremainder is the answer to theproblem.

Show your work.

4E08L3 6/30/05 1:44 PM Page 3

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Problem-Solving Application:Interpret RemaindersProblem Peter has 58 photos to put in an album. He puts 5 photos on each page. How many pages will he need for all 58 photos?

1. For the above problem, what does thequotient of 58 � 5 tell you?

2. What is the remainder? How do youuse the remainder to find the answer?

3. How many pages does Peter need?

4. How many of the pages are full? Howdo you know?

ProblemSolving

8.3

Show your work.

4P08L3 7/1/05 9:56 AM Page 3

Name Date


Homework8.3

A basket holds 4 dinner rolls. How many baskets are needed to hold 47 dinnerrolls?

Another basket is needed to hold the 3 extra rolls, so 12 baskets are needed.


Solve each problem.

1. A florist received 69 roses. He wants toplace the roses in buckets of water.Each bucket holds 6 roses. How manybuckets will have 6 roses?

How many roses are left over?

How many buckets are needed for all the roses?

2. Ms. Dale bought 35 roses to give to herfriends. She divided the roses equallybetween her 3 friends and kept theleftover roses for herself. How manyroses did Ms. Dale keep?

11 R34��4�7��4�

07� 4�

3

How many baskets have 4 rolls? 11 basketsHow many rolls are left over? 3 rollsIs another basket needed? yes

Show your work.

4H08L3 6/29/05 4:31 PM Page 3

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EnglishLearners

8.3

Complete these paragraphs. Fill in the blanks with words from the boxes.

Mrs. Napoleon’s class is studying newspapers. Today

they are going to visit a to see how

newspapers are printed. There they will see a

of a printing press. After that, the students will

the newspaper office to see where the writers and editors work.

Mr. Ortega’s class is studying art. They are going to visit

a to see the famous paintings that are

there. They will also see an

of children’s art. After that, each child will be given a

with a picture of the museum on it. Each child

can send the card to a friend, or put it in a .

Problem-Solving Application:Interpret Remainders Read these definitions.

post card a card used for sending a short message through the mail

exhibit a display

on display being shown to people

tour to make a trip through a place for the purpose of seeing it

demonstration a show of how something works

scrapbook a book with blank pages for pasting pictures in

printing plant a building with machines that print words and pictures on paper

museum a building in which art or historic items are displayed

tour printing plant demonstration

on display museum exhibit scrapbook post card

G4ELL083 8/3/05 6:52 PM Page 3

Regroup In Division


1. 4��4�4� 2. 6��8�5� 3. 2��3�6� 4. 5��6�7�

5. 73 � 6 6. 88 � 8 7. 86 � 6

8. 48 � 3 9. 53 � 4 10. 87 � 6

Name Date


Reteach8.4

Divide 31 � 2. You can use play money to solve the problem. Show 31 using ten-dollar bills and one-dollar bills.

Divide the money into 2 equal groups. Start by moving the ten-dollar bills. You can place 1 ten-dollar bill in each group with 1 ten-dollarbill left over.

Exchange the remaining ten-dollar bill for 10 one-dollar bills. Place the one-dollar bills into the 2 equal groups with the ten-dollar bill. You will place 5 one-dollar bills in each group with 1 one-dollar bill left over.

Count the money in one of the groups. This is the quotient. The one-dollar bill left over is the remainder.

So, or 31 � 2 � 15R115R1

2��3�1��2�

11�10�

1

4R08L4 2/23/06 2:22 PM Page 4

Name Date

Regroup In DivisionDivide. Check your answers.

1. 3�4�0� 2. 5�6�8� 3. 6�9�3� 4. 4�8�4� 5. 2�7�3�

6. 2�9�6� 7. 4�8�7� 8. 2�3�7� 9. 3�4�9� 10. 3�7�6�

11. 54 � 4 � 12. 60 � 5 � 13. 83 � 7 � 14. 86 � 7 � 15. 45 � 4 �

16. 67 � 5 � 17. 49 � 3 � 18. 57 � 5 � 19. 88 � 8 � 20. 42 � 3 �

Algebra • FunctionsCopy and complete each table.


Practice8.4

Test Prep

33. Jason is trading baseball cards. He canget 1 pack of cards for 5 single cards.If Jason has 63 single cards to trade,how many packs can he get?

A 5 C 12

B 10 D 15

34. If you had 52 cookies to put into 4bags, how many cookies would go intoeach bag? How many will be left over?

Rule: y � x � 2

x

24

22

36

21.

22.

23.

24.

y

22

Rule: y � x � 5

x

55

65

25.

26.

27.

28.

y

9

19

Rule: y � x � 7

x

49

14

29.

30.

31.

32.

y

5

9

4P08L4 7/23/05 12:39 PM Page 4

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Remainder GameMaterials: two sets of number cards labeled 1–9, game board,game pieces

Number of Players: 1 or more

Rules of the game:

• Each player chooses a game piece and places it at the startsquare.

• Players take turns drawing 3 cards from the bag. The playerarranges the cards to make a division problem with a two-digitdividend and a one-digit divisor.

• The player solves the division problem and moves his or hergame piece the number of spaces as given below:

If the remainder equals 0—move your game piece 4 spaces.If the remainder equals 1 or 2—move your game piece 3 spaces.If the remainder equals 3 or greater—move your gamepiece 2 spaces.

• Play continues until someone reaches the finish space.


Enrichment8.4

4E08L4 7/25/05 12:54 PM Page 4

Regroup in DivisionSolve.

Name Date


ProblemSolving

8.4

1. Mrs. Rosenberg collected 84 leaves forher art class to use. If each studentuses 5 leaves to make a design, howmany designs will be made? Howmany leaves will be left over?

2. There are 52 sheets of drawing paper.The teacher wants to have as manysheets of paper as he can in 3 equalpiles. How many sheets will be in each pile?

3. There were 98 crayons in a container.Timothy divided the crayons equallyinto boxes of 8 crayons each. Howmany boxes were completely filled?

4. In art class, 67 drawings were made.All of the students except Carla made4 drawings. Carla made fewer than 4drawings. How many drawings didCarla make?

Show your work.

5. Reasoning Kip bought 4 paint sets at the craft store. Hegave the clerk $60. His change was $4. How much was eachpaint set? Explain how you found your answer.

4P08L4 2/22/06 7:31 PM Page 4

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Homework8.4

Problem Solving

15. Three friends made 44 cupcakes. Ifthey share the cupcakes evenly, howmany cupcakes will be left over?

Show your work.


4. 38 � 2 5. 79 � 6 6. 95 � 3

Algebra • FunctionsComplete each table.

x y

Rule: y � x � 4

44

84

7.

2410.

9.

8.

18

x y

Rule: y � x � 8

64

5

11.

2414.

13.

12.

9

1. 6�6�6

2. 5�7�1�

3. 53 � 4

Regroup the oneten left as 10ones.

41 � 3 � 13 R2

Check:

13 � 3 � 39

39 � 2 � 41

13 R23��4�1��3↓�

11� 9�

2

4H08L4 2/23/06 12:47 PM Page 4

Name Date


EnglishLearners

8.4

Complete the sentences below. Fill in the blanks with wordsin bold type.

1. To make sure that the votes have been counted correctly, two students will

the votes.

2. Edda Mae ordered pencils and pens for the office. They are almost gone, so she

must some soon.

3. The big show has been canceled. The ticket company will

money to everyone who bought a ticket.

4. Derek grouped the blocks in sets of 10 to solve the division problem. He must

some of the blocks in order to get the answer.

5. Sveta broke a flowerpot. She must it.

6. Keenan borrowed five dollars from his brother last week. Keenan has now earned

ten dollars, so he can his brother.

7. Greta does not like where the chairs and the tables have been placed. She will

the furniture so it looks better.

Regroup in DivisionRead the explanation and the definitions that follow.

The prefix re- usually means “back” or “again.” Knowing this can help you figure out the meanings of many words.

regroup to group again; to put into new groups

rearrange to arrange again; to arrange in a new way

repay to pay back; to pay people money you owe them

recount to count again

replace to put or give something in place of something that has been lost or broken

refund to give back money

reorder to order again

When you are dividing, youcan regroup ten as 10 ones to help you solve the problem.

G4ELL084 2/22/06 7:39 AM Page 4

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Reteach8.5

Divide Multiples of 10, 100, and 1,000.

Use basic facts and patterns to find each quotient.

1. 6 � 3 � 2. 8 � 2 � 3. 12 � 2 �

60 � 3 � 80� 2 � 120 � 2 �

600 � 30 � 800 � 2 � 1,200 � 2 �

6,000 � 300 � 8,000 � 2 � 1,200 � 20 �

4. 12 tens � 6 � tens �

5. 18 hundreds � 3 � hundreds �

6. 45 tens � 5 � tens �

7. 36 thousands � 9 � thousands �

8. 240 � 8 � 9. 160 � 4 � 10. 540 � 6 �

11. 150 � 3 � 12. 810 � 9 � 13. 2,400 � 6 �

You can use facts and patterns to help you divide mentally.

3,000 � 5 �

30 � 5 � 6 30 ones � 5 � 6 ones � 6

300 � 5 � 60 30 tens � 5 � 6 tens � 60

3,000 � 5 � 600 30 hundreds � 5 � 6 hundreds � 600

So, 3,000 � 5 � 600

4R08L5 1/21/04 5:21 PM Page 5

Name Date


Practice8.5

Divide Multiples of 10, 100, and 1,000Divide.

1. 8 � 2 � 2. 6 � 3 � 3. 5 � 1 �

80 � 2 � 60 � 3 � 50 � 1 �

800 � 2 � 600 � 3 � 500 � 1 �

8,000 � 2 � 6,000 � 3 � 5,000 � 1 �

4. 45 � 5 � 5. 10 � 2 � 6. 15 � 5 �

450 � 5 � 100 � 2 � 150 � 5 �

4,500 � 5 � 1,000 � 2 � 1,500 � 5 �

7. 480 � 6 � 8. 2,700 � 3 � 9. 600 � 2 �

10. 800 � 4 � 11. 6,300 � 9 � 12. 4,000 � 4 �

Algebra Equations Solve each equation.

13. 2,100 � 3 � n 14. 160 � 4 � x 15. 350 � 5 � y

16. 48 � 6 � q 17. 1,400 � 2 � p 18. 720 � 9 � c

Test Prep

19. Which number sentence is NOTcorrect?

A 240 � 4 � 60 C 2,800 � 4 � 700

B 250 � 5 � 50 D 700 � 2 � 1,400

20. Complete the problem.

16 � 2 �

160 � � 80

� 2 � 800

4C08L5 5/27/05 1:52 PM Page 5

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Quotient Mix-UpAt the math factory, there has been a big mix-up. Some of thequotients have been mismatched with a division problem.Look at each problem below. Write correct or incorrect besideeach number sentence. Write the correct answer to eachproblem beside each letter. Then write the letter above eachnumber in the saying below to find out a secret to doingdivision mentally.


Enrichment8.5

1. 1,200 � 4 � 30 A

2. 300 � 10 � 3,000 E

3. 2,700 � 3 � 90 F

4. 1,000 � 5 � 20 N

5. 6,400 � 8 � 80 O

6. 810 � 9 � 90 P

7. 320 � 8 � 40 R

8. 250 � 5 � 50 S

9. 3,600 � 9 � 40 T

10. 1,600 � 20 � 800 Z

90 300 400 400 30 40 200 50

800 900 80 30 40 800 50

76274-E-08-L1-L6 2/21/03 4:46 PM Page 5

Name Date


ProblemSolving

8.5Divide Multiples of 10, 100,and 1,000Solve.

1. The Yosemite waterfall has a height ofabout 2,400 feet. How many yards highis this? (Hint: There are 3 feet in ayard.)

2. A park had a total of 4,200 visitors lastweek. If the same number of visitorswere there each day, how many visitorswere at the park on Monday?

3. The number of people that go to thepark to swim is 3 times the number ofpeople that go to hike. If 270 peoplego to swim, how many people go tohike?

4. The snack bar sold $320 worth ofsport drinks to hikers. If each drinkcost $4, how many drinks did thesnack bar sell?

5. Patty hiked a total of 1500 miles. If shehiked 5 miles each day how many daysdid she hike?

Show your work.

76274-P-08-L1-L6 2/6/03 3:41 PM Page 5

5. 21 � 7 �

210 � 7 �

2,100 � 7 �

21,000 � 7 �

8. 350 � 5 �

4. 12 � 6 �

120 � 6 �

1,200 � 6 �

12,000 � 6 �

7. 420 � 7 �

3. 6 � 1 �

60 � 1 �

600 � 1 �

6,000 � 1 �

6. 3,600 � 6 �

1. 9 � 3 �

90 � 3 �

900 � 3 �

9,000 � 3 �

Name Date


Homework8.5

42 � 6 � 7

420 � 6 � 70

1 zero 1 zero

4,200 � 6 � 700

2 zeros 2 zeros

Problem Solving

12. A giant panda may eat up to 420 pounds of food in a week. Howmany pounds of food can a panda eatin 1 day?

Show your work.


2. 4 � 2 �

40 � 2 �

400 � 2 �

4,000 � 2 �

Solve each equation.

9. 2,500 � 5 � x 10. 180 � y � 20 11. 1,600 � n � 800

4H08L5 6/29/05 4:32 PM Page 5

Name Date


EnglishLearners

8.5

Match each phrase with its meaning.

1. a full week seven days in the future

2. 10 years ago seven days in a row

3. every week at least one time in a period of seven days

4. each of 10 years a date 10 years in the past

5. after one week every year in a period of 10 years

Divide Multiples of 10, 100, and 1,000Read these explanations.

Today it is December 1, 2003.

Six months ago it was June 1, 2003.

After one year it will be December 1 again.

If you are fifty years old, it means you have had a birthday in eachof 50 years.

If you go to the store every week, it means you go to the store atleast once every seven days.

If you work for a full week, you work all seven days in that week.

G4ELL085 7/26/05 3:09 PM Page 5

Estimate Quotients

Estimate. Write the basic fact you used.

1. 2��1�0�5� 2. 5��3�6�1�

Basic Fact: Basic Fact:

Estimate: Estimate:

3. 5��4�2�1� 4. 334 � 8


Estimate: Estimate:

5. 626 � 9 6. 373 � 6


Estimate: Estimate:

7. 131 � 3 8. 173 � 4


Estimate: Estimate:

Name Date


Reteach8.6

Estimate 82 � 3.

Look at the first digit in the number 82.

Think of a basic fact with 3 and a number that is close to the first digit of thedividend.

3 � 1 � 3 3 � 2 � 6 3 � 3 � 9 3 � 4 � 12 3 � 5 � 15

Choose 3 � 3 � 9, because 9 is close to 8.

To find the second digit in the number multiply 9 by 10. 9 � 10 � 90

Divide 90 � 3 � 30

So, 82 � 3 is about 30.

4R08L6 1/21/04 5:21 PM Page 6

Estimate QuotientsEstimate. Write the basic fact you used.

1. 2�1�7� 2. 3�2�8� 3. 5�3�1�

4. 3�3�3�1� 5. 4�1�8�4� 6. 7�1�7�7�

7. 9�5�0� 8. 4�3�3� 9. 3�2�2�4�

10. 31 � 3 � 11. 44 � 6 � 12. 13 � 6 �

13. 331 � 8 � 14. 213 � 5 � 15. 261 � 5 �

Decide whether the actual quotient is greater than or lessthan the estimate given. Write ≥ or ≤ for each.

16. 17 � 5 5 17. 23 � 4 5 18. 14 � 7 3

19. 47 � 5 8 20. 37 � 9 5 21. 10 � 2 4

Name Date


Practice8.6

Test Prep

22. Which is the best estimate of 132 ÷ 3?

A 30 C 50

B 40 D 60

23. Notebooks cost $4 each at the schoolstore. Chris has $15. How manynotebooks can he buy? Explain.

4C08L6 1/21/04 3:47 PM Page 6

Name Date

Estimate QuotientsFor each quotient given, write two division problems thatwould give the estimated quotient. The first one has beendone for you.

Estimated Quotient Division Problems

1. 30 246 � 8 192 � 6

2. 40

3. 8

4. 10

5. 7

6. 20

7. 9

8. 60

9. 5

10. 80

11. 4

12. 50


Enrichment8.6

4E08L6 6/30/05 1:44 PM Page 6

Estimate QuotientsThe Finley family took a vacation to the beach. Theystopped at the Sun N’ Fun Beach store to buy a fewsupplies. Use the table to answer problems 1–3.

Name Date


ProblemSolving

8.6

1. How many T-shirts can Maggie buywith 3 ten-dollar bills?

2. Mr. Finley bought sunscreen and somepostcards. He spent $19. How manypostcards did he buy?

3. Georgia has $42. She bought 3 T-shirts. How many pairs of sunglassescan she buy with the amount she hasleft over?

4. Four families went out for dinner. Thetotal food bill came to $327. Thefamilies also left a $40 tip for thewaitress. If each family spent the sameamount, about how much did eachfamily spend on dinner? Explain howyou found your answer.

Item Price

Sun N’ Fun Beach Store

sunscreen

postcard

sunglasses

T-shirt

$5

$2

$6

$7

Show your work.

4P08L6 7/1/05 9:56 AM Page 6

Name Date


Homework8.6

154 � 5

Use basic facts andmultiples of 10 to finda new dividend.

150 � 5

Think: 5 � 3 � 15

15 � 10 � 150

150 � 5 � 30

154 � 5 is about 30

Problem Solving

12. Jim used 29 beads to make a necklacefor his sister. The beads he used comein packages of 5 beads each. Abouthow many packages of beads did Jimuse?

Show your work.


1. 4�3�3� 2. 9�6�4�

3. 3�2�6� 4. 7�2�3�4�

5. 204 � 5 6. 26 � 8 7. 195 � 6

Decide whether the actual quotient is greater than or less thanthe estimate given. Write ≥ or ≤ for each �.

8. 27 � 3 � 4 9. 31 � 5 � 6 10. 24 � 3 � 7 11. 45 � 9 � 8

4H08L6 6/29/05 4:32 PM Page 6

Name Date


EnglishLearners

8.6

Some terms in the box tell about estimating. Others tellabout finding the exact amount. Write each term on any linein the web where it belongs.

Estimate QuotientsRead these explanations.

Estimate means “to use what you know to make a good guess atan answer.”

Find the exact amount means “to figure out the precise number.”

how much about how much guess calculate

how many about how many almost precisely

estimated quotient exact quotient possible certain

estimate

find the exact amount

G4ELL086 7/26/05 3:09 PM Page 6

Name Date


Chapter 8Test

1. 4��8�5� 2. 3��9�6� 3. 66 � 6 �


4. 8��6�2� 5. 3��5�7�

6. 77 � 6 � 7. 98 � 8 �

Divide.

8. 45 � 9 9. 42 � 7 10. 56 � 8

450 � 9 420 � 7 560 � 8

4,500 � 9 4,200 � 7 5,600 � 8

11. 480 � 6 12. 400 � 5 13. 7,200 � 9


Go on

76274-A-08-L1-L5 2/27/03 11:20 AM Page 4

STOP

Name Date


Chapter 8Test


14. 6��3�5� 15. 6��3�2�1�

16. 75 � 8 17. 700 � 8


18. Mark is displaying toy cars on shelves. He can fit 6 cars on each shelf. How many shelves does Mark needto display 25 cars?

19. Sarah’s birthday is in 40 days. How many full weeks is that?

20. Carlos buys as many $8-kites as he can for $35. How much money does he have left over after he buys the kites?

76274-A-08-L1-L5 2/27/03 11:20 AM Page 5

Class Date


Chapter 8 Chapter 9 Chapter 10 Chapter 11 Unit 4 Test

Student Pre- Chapter Pre- Chapter Pre- Chapter Pre- Chaptertest Test test Test test Test test Test Form A Form B

Unit 4Class Record

Unit 4 Assessment

76274-A-U4-CR 3/7/03 10:07 AM Page 1

Copyright © by Houghton Mifflin Company. All rights reserved.

Permission is hereby granted to teachers to reprint or photocopy classroom quantities of the pages or sheets in this work that carry a HoughtonMifflin copyright notice. These pages are designed to be reproduced by teachers for use in their classes with accompanying Houghton Mifflin materi-al, provided each copy made shows the copyright notice. Such copies may not be sold, and further distribution is expressly prohibited. Except asauthorized above, prior written permission must be obtained from Houghton Mifflin Company to reproduce or transmit this work or portions thereof inany form or by any electronic or mechanical means, including any information storage or retrieval system, unless expressly permitted by federal copy-right law. Address inquiries to School Permissions, 222 Berkeley Street, Boston, MA 02116.

Printed in the U.S.A.

Booklet 8 of 25


Chapter Pretest (3 pages)

Resources for Lessons 8.1 – 8.6 (6 pages/lesson)• Reteach 8.1 – 8.6• Practice 8.1 – 8.6• Enrichment 8.1 – 8.6• Problem Solving 8.1 – 8.6• Homework 8.1 – 8.6• English Learners 8.1 – 8.6

Chapter Test (2 pages)

Unit 4 Record Sheet

Chapter ResourcesGRADE 4, CHAPTER 8

Contents

Dear Family,

During the next few weeks, our math class will belearning about and practicing division of whole numbers.

You can expect to see work that provides practice with dividing numbers with up to four digits by one- andtwo-digit numbers.

As we use division to learn about prime and compositenumbers, you may wish to use this sample as a guide.

The number 2 is the only prime even number. The number 1 is neither prime nor composite.

During this unit, students should continue to practiceand memorize basic multiplication and division facts.

Sincerely,

Your Child’s TeacherCheck out Education Place ateduplace.com/kids/mw/ for e•Glossary, e•Word Games,test prep practice, and more.


prime number A whole number thathas only itself and 1 as factors.

composite number A whole numberthat has more than two factors.

divisible One number is divisible by another if the quotient is a wholenumber and the remainder is 0.

average The number found by dividingthe sum of a set of numbers by thenumber of addends.

Prime and Composite Numbers

You can use the factors of a number to tell if the number is prime or composite.

Unit 4 Family LetterCopyright © Houghton Mifflin Company. All rights reserved.

Examples of Prime Numbers

Prime Number Factors

2 1 and 2

5 1 and 5

13 1 and 13

Notice that each number has exactly two factors.

Examples of Composite Numbers

Composite Number Factors

4 1, 2, and 4

10 1, 2, 5, and 10

12 1, 2, 3, 4, 6, and 12

Notice that each number has more thantwo factors.

G4ELLFNLU04 8/1/05 5:09 PM Page 4

Name Date


Chapter 8Pretest

Are You Ready?Divide. Check your answers.

Go on

1. 24 � 3

2. 42 � 6

3. 56 � 8

4. 72 � 9

Write a division fact for each picture.

5.

6.


7. 4��8�4� 8. 2��3�7� 9. 6��5�0�


10. A van can hold 6 passengers. If 20 people need a ride tothe museum, how many vans are needed?

8; 8 � 3 � 247; 7 � 6 � 427; 7 � 8 � 568; 8 � 9 � 72

9 � 3 � 3

21

4 vans; explanations may vary.

18 R1 8 R2

20 � 5 � 4x xx

x x

x xx

x x

x xx

x x

x xx

x x

4A08L1 6/29/05 4:50 PM Page 1

Name Date


Chapter 8Pretest

continued

1. 3��6�3� 2. 2��4�5� 3. 84 � 4 �


4. 7��6�4� 5. 4�6�8�

6. 83 � 5 � 7. 99 � 6 �

Divide.

8. 15 � 3 9. 24 � 8 10. 54 � 6

150 � 3 240 � 8 540 � 6

1,500 � 3 2,400 � 8 5,400 � 6

11. 280 � 4 12. 300 � 6 13. 4,800 � 8

Check What You KnowDivide. Tell if there is a remainder.

Go on

550500

70 50 600

330300

990900

9 � 7 � 6363 � 1 � 64

16 � 5 � 8080 � 3 � 83

16 � 6 � 9696 � 3 � 99

17 � 4 � 68

21 22 R1 21

9 R1 17

16 R3 16 R3

4A08L2 6/29/05 4:50 PM Page 2

STOP

Name Date


Chapter 8Pretest


14. 5��2�7� 15. 4��3�3�3�

16. 38 � 6 17. 500 � 8


18. Carly is placing postcards in a scrapbook. She can fit 4 postcards on a page. How many pages does Carlyneed for 26 postcards?

19. Sean has 30 days to work on a class project. How many full weeks does he have?

20. Andy buys as many $3-books as he can for $20. How much money does he have left over after he buysthe books?

36 � 6 � 6 48 � 8 � 66 60

5; 25 � 5 � 5 80; 32 � 4 � 8

7 pages; explanations may vary.

4 weeks; explanations may vary.

$2; explanations may vary.

Estimatesmay vary.

76274-A-08-L1-L5 2/27/03 11:20 AM Page 3

Name Date

Model DivisionUse models to understand division.

Divide 13 into groups with 3 in each group.Use the counters below for Exercises 1–3.

1. Circle as many groups of 3 counters as you can.

How many groups of 3 are there?



4. Draw a picture to show 10 divided equally into 2 groups.

5. How many are in each equal group?




Reteach8.1

Use money to find 14 � 5. Place 14 one-dollar bills in groups of 5.

Look at the picture.

It shows how to make as many groups of 5 as possible.

Ask yourself how many groups of 5 are there? You should count 2

Look at the one-dollar bills left over. Count them.

How many one-dollar bills are left over? 4

14 � 5 � 2 R4

4

4 R1

5Picture shouldshow 2 groups

of 50

5

1

4R08L1 2/23/06 2:21 PM Page 1

Name Date


Practice8.1


6. Draw a picture to show 30 divided into 5 equal groups. Writea number sentence to show division.

7. Draw a picture to show 17 divided into groups of 4 in eachgroup. Write a number sentence to show division.

Test Prep

8. If you divide 20 one-dollar bills into 4equal groups how many one-dollarbills would be in each group?

A 4 C 5

B 3 D 1

9. Mr. Marris is building a birdhouse. Hehas 23 nails and 5 boards. Does hehave enough nails to hammer 4 nailsin each board? If so, how many nailswill he have left over?


14

29

35

75

25

63

2

7

5

9

7

9

8

0 14 � 2 � 7

1.

2.

3.

4.

5.

Answers may vary; 30 � 5 � 6

Answers may vary; 17 � 4 � 4 R1

Yes; 3 nails left overCC

4 1 29 � 7 � 4 R17 0 35 � 5 � 7

7 0 63 � 9 � 71

83 25 � 3 � 8 R1

3 75 � 8 � 9 R3

4C08L1 7/5/05 4:22 PM Page 1

1. 2.

3. 4.

5. 6.

Name Date

Picture Match-UpFor each picture, choose a division equation from the box thatrepresents the picture. Each equation will only be used once.Some equations may not be used.


Enrichment8.1

45 � 4 � 11 R1 64 � 3 � 21 R1 97 � 3 � 32 R1

67 � 3 � 22 R1 49 � 4 � 12 R1 81 � 2 � 40 R1

69 � 6 � 11 R3 64 � 6 � 10 R4 54 � 5 � 10 R4

54 � 5 � 10 R4 67 � 3 � 22 R1

49 � 4 � 12 R1 64 � 3 � 21 R1

45 � 4 � 11 R1 81 � 2 � 40 R1

76274-E-08-L1-L6 2/21/03 4:46 PM Page 1

Model DivisionUse base-ten blocks to model and solveeach problem.

1. Mrs. Murphy had 66 apples. She used6 apples in each pie she baked. Howmany pies did Mrs. Murphy bake?

2. Mr. Thomas picked several baskets ofstrawberries. He picked a total of 65strawberries. He equally divided thestrawberries into 3 containers. He ateany remaining strawberries. How manystrawberries did Mr. Thomas eat? Howcan you tell?

3. The grocery store had a total of 56oranges. The oranges were dividedevenly into bags of 5 oranges each.How many bags of oranges werethere? Were there any oranges leftover?

4. Write About It Explain how the modelof 54 � 5 is similar to 54 � 10.

Name Date


66; check students’models; 66 � 6 � 11

He ate 2 strawberries. He ate the leftoverstrawberries, and the remainder was 2.

There were 11 bags of orangesand 1 orange left over.

Answers will vary.

ProblemSolving

8.1

Show your work.

76274-P-08-L1-L6 2/6/03 3:41 PM Page 1

Name Date


Homework8.1

Problem Solving

5. Martin had 37 shells. He put them in 3 equal piles. How many shells wereleft over?

Show your work.



35

18

81

59

27 2 1 27 � 2 � 13 R113

6

5

7

9

1.

2.

3.

4.

5 535 � 6 � 5R5

3 318 � 5 � 3R3

8 359 � 7 � 8R3

9 0 81 � 9 � 9

1 shell

76274-H-08-L1-L6 2/6/03 1:37 PM Page 1

Name Date


EnglishLearners

8.1

Write words from the box to fill the blanks.

6��1�2� This is a problem. In this problem you must

12 by 6. The number that must be divided, 12, is

called the . The number it must be divided by, 6,

is called the .

This division problem has been solved. The answer, 3, is called the

.

This division problem has 1 left over. This amount is called the

.

3 r14��1�2�

34��1�2�

Model Division Read this explanation.

In math, divide means “to separate into equalparts” or “to put in equal groups.”

The process of dividing is called division. Ina division problem, the process of dividing isshown in numbers. The total number beingdivided is called the dividend. The number of groups or portions the number is beingdivided into is called the divisor. The answer—the size of each portion or the number in eachgroup—is called the quotient. Any amount leftover when the equal portions are made iscalled the remainder.

divide division dividend divisor quotient remainder

divisiondivide

dividenddivisor

quotient

remainder

2"

2"

2"2"

2" 2"

12 � 6 � 2

12 � 4 � 3

G4ELL081 7/23/05 2:51 PM Page 1

Name Date


Reteach8.2

Divide 25 � 2.

You can use dimes and pennies to show 25 cents.

Divide the money into 2 equal groups. Put 1 dime in each group.

Put two pennies in each group.There is one penny left over.

Count the dimes and pennies in one group. This is thequotient. The penny left over is the remainder.

Divide With Remainders

So, or 25 � 2 � 12 R1


1. 3�9�4� 2. 8�8�8� 3. 2�6�9�

4. 57 � 5 5. 46 � 2 6. 66 � 3

7. 23 � 2 8. 85 � 5 9. 47 � 4

11 R2

31 R1 11

23

34 R1

22

11 R1 17 11 R3

12 R12��2�5��20�

05�4�

1

4R08L2 2/23/06 2:21 PM Page 2

Name Date


1. 2�4�3� 2. 5�5�5 3. 4�4�9� 4. 4�4�6� 5. 3��3�6�

6. 5��5�4� 7. 4��4�7� 8. 2�6�5� 9. 7��7�8� 10. 3�6�6�

11. 42 � 2 � 12. 79 � 7 � 13. 64 � 3 � 14. 64 � 2 � 15. 22 � 2 �

16. 68 � 2 � 17. 51 � 9 � 18. 96 � 3 � 19. 73 � 7 � 20. 86 � 4 �

Algebra • Symbols Write ≥ or ≤ for each.

21. 20 � 5 24 � 4 22. 64 � 8 56 � 8 23. 12 � 6 14 � 2

24. 35 � 7 4 � 2 25. 48 � 4 84 � 4 26. 27 � 3 9 � 3

27. 43 � 2 15 � 3 28. 55 � 5 16 � 1 29. 56 � 8 81 � 9


Practice8.2

Test Prep

30. Find 67 � 3.

A 20 R1 C 21 R1

B 22 R1 D 23 R3

31. Marsha, Ashley, Peter and Dawn have45 pieces of candy to share equally.How many pieces will each get? Howmany are left over? Explain youranswers.

21 R1

10 R4

21

11

11 R3

11 R2

12 R1

32 R1

21 R1

11 R2

11 R1

32

12

22

11

34 5 R6 32 10 R3 21 R2

11 pieces; 1 piece left over.Explanations will vary.

≤

≤≤

≥≥

≤ ≤≥

≥

BB

4C08L2 2/22/06 6:14 PM Page 2

Name Date

Division RiddlesDigit Detective needs help on a mission. He must organize thedividends, divisors, quotients, and remainders into 4 groups.The problem is that he doesn’t know which numbers arewhich. Your job is to help him solve these division riddles tofind each number. Then, organize the numbers into the fourgroups.


Enrichment8.2

1. Divide me by 3, and you’ll get aremainder of 2. My digits have a sumof 8 and a difference of 2. I am lessthan 6 � 6. What dividend am I?

2. If you divide 48 by me, you’ll get noremainder. But if you divide 46 by me,you’ll get a remainder of 2. Whatdivisor am I?

3. Divide 56 or 71 by 5 and me as aremainder you’ll see. What remainderam I?

4. I am an odd number. When you divide38 by me, the remainder is 2. Whatdivisors could I be?

5. Divide me by 5 and you’ll get aremainder of 2. I am greater than 9 � 6, but less than 6 � 10. Whatdividend am I?

6. Add me to the product of the divisorand the quotient and you’ll get thedividend of 41. That is if the divisor was3 and the quotient was 13. Whatremainder am I?

7. Divide 98 by an odd number and you’llget me with a remainder of 8. Whatquotients can I be?

8. If you divide an even number by 2, Iwill be your remainder. What remainderam I?

35 4

1 3 or 9

57 2

2, 6, or 10 0Dividends Divisors

Quotients Remainders

35, 57

2, 6, 10

4, 3, 9

1, 2, 0

4E08L2 2/22/06 7:49 AM Page 2

Name Date

Divide With RemaindersSolve.


1. Jordan has 42 files on his computer. Hesaved an equal number of files on 2disks. How many files are on each disk?

2. Jordan has 89 CDs in his collection. Hewants to organize them evenly into 4 cases. How many CDs will he put ineach case? How many will be leftover?

3. The music store displays CDs on 8 shelves and on the counter. Thesame number of CDs are displayed oneach shelf. If the store displays a totalof 83 CDs. How many CDs are on thecounter?

4. Randy spent $65 at the music store.He bought 5 CDs. How much did eachCD cost?

5. You Decide Harvey has 56 songsstored on his computer. He wants tosave them to 3 CDs. How manydifferent ways can he divide the songs?Explain how you found your answer.

ProblemSolving

8.2

Answers may vary. The CDsshould have a total of 56songs on them combined.

21 files

22 CDs; 1 CD

3 CDs

$13

Show your work.

4P08L2 1/20/04 9:53 PM Page 2

Name Date


Homework8.2

49 � 4

49 � 4 � 12 R1

Problem SolvingShow your work.


Multiply 1 ten � 4.Subtract 4 � 4.

Compare 0 � 4. Bring down 9 ones.Multiply 2 ones � 4.Subtract 9 � 8.Compare 1 � 4.

↓

1. 3�6�4� 2. 4�8�8� 3. 3�3�9� 4. 2�8�2�

5. 58 � 5 6. 35 � 3 7. 49 � 4 8. 77 � 7

Mental Math Write ≥ or ≤ for each �.

9. 24 � 8 � 12 � 2 10. 44 � 2 � 22 � 2 11. 54 � 6 � 72 � 9

12. Jan has 38 baseball caps. She wants toput them in groups of 3 caps each.How many groups of caps will shehave? Will she have any caps leftover? If so, how many?

21 R1 22 13 41

11 R3 11 R2 12 R1 11

≤ ≥ ≥

12 capsYes

2 caps

14��4�9��4�

0

12 R14��4�9��4↓�

09� 8�

1

4H08L2 6/29/05 4:31 PM Page 2

Name Date


EnglishLearners

8.2

Match each picture to the definition that fits it.

1. a small copy of something

2. a tiny example of something not yet made

3. a style or design

4. a person serving as a subject for an artist

5. a person paid to display clothes by wearing them

Divide With RemaindersRead this information.

Model is a word with many meanings. It can be used as a noun, a verb, or an adjective. The dictionary entry below gives the noun meanings.

mod•el (mod´l) noun. 1. a small copy of something: This model of a racecar is 6 inches long. 2. a tiny example of something not yet made: Thebuilder showed the family a model of the house he planned to build. 3. astyle or design: This year’s model of the Speedycar is much better look-ing than last year’s model. 4. a person serving as a subject for an artist:Rhonda asked her friend Beth to be a model for a painting she wantedto make. 5. a person paid to display clothes by wearing them: Helen willbe a model in the fashion show tomorrow.

G4ELL082 7/23/05 2:51 PM Page 2

Name Date


Reteach8.3

Heather owns a trading-card shop. She is arranging 59 cards on a display. Each row ofthe display holds 5 cards. How many rows of cards will she need to display all the cards?

What is the question? One way to find the answer is to divide.

How many rows of cards will she need in the display?

What do you know? • She has 59 cards• Each row will hold 5 cards

Explanation: Eleven rows will hold 55 trading cards. Another row is needed for theextra 4 trading cards, so increase the quotient to the next whole number which is 12.The answer is 12 rows.

11 R45�5�9��5�

09�5�

4

Problem-Solving Application:Interpret Remainders

Solve each problem.

1. Brad collects trading cards. He has 68 cards in his collection. Hewants to store them in a book. Each page of the book holds 6cards. How many pages will Brad need to store all of his cards?

2. Complete the table to show how many pages Brad wouldneed if he only had 48 cards.

3. Maria is putting 93 football trading cards on display for 72days at the mall. How many full weeks will the cards be ondisplay?

4. Jim is arranging 69 basketball trading cards in 6 equal rows.Any cards left over will not be placed in the display. Howmany cards will not be in the display?

12 pages

Page 1

6 cards

Page 2

12 cards

Page 3

Page 4

Page 5

Page 6

Page 7

Page 8

18 cards24 cards30 cards36 cards42 cards48 cards

10 full weeks

Show your work.

3 cards not in the display

4R08L3 6/30/05 5:00 PM Page 3

Name Date


Practice8.3


Show your work.

1. Gordan’s Pineapple Farm in Hawaii isshipping 69 pineapples in woodenboxes. Each box holds 6 pineapples.How many boxes are needed?

2. Ms. Ramon brought 26 pineappleshome from her vacation to Hawaii. Shedivided the pineapples into 3 equalpiles and ate the pineapples that wereleft over. How many pineapples did Ms.Ramon eat?

3. Mr. Kelly’s class has $65 to spend atthe pineapple farm. They decide to usetheir money to buy pineapples. Eachpineapple costs $3. How manypineapples can the class buy?

4. Mr. Jack’s class helps pack pineapplesin shipping boxes. The class is given94 pineapples to pack. Each shippingbox holds 9 pineapples. How manyboxes can the class fill?

5. At the grocery store, Alice is arrangingpineapples in the produce case. Sheputs 7 pineapples in each row, one ata time. What row does she put the29th pineapple in?

12 boxes

2 pineapples

21 pineapples

10 boxes

Row 5

4P08L3 7/1/05 1:01 PM Page 3

Name Date

Problem-Solving Application:Interpret RemaindersProblem For a vacation, Mrs. Kluthrow and her family drove 478miles to Philadelphia to visit the museums and other historicalplaces. On the trip, Mrs. Kluthrow took 118 pictures. Of thepictures, 29 are photos of her children and the rest are photos ofthe places they visited.


Enrichment8.3

1. Mrs. Kluthrow divides the photos of hertwo children evenly between the twochildren. How many photos does eachchild get? Explain how you found youranswer.

2. Mrs. Kluthrow organized the photos ofthe places they visited into a photoalbum. If 4 photos can fit on each pageof the album, how many pages did Mrs.Kluthrow use? Explain how you foundyour answer.

3. Write a division problem in which theremainder is the answer to theproblem.

14 photos; 29 � 2 � 14 R1. Each child got 14photos, and there was 1 photo left over.Because you can’t split 1 photo, I dropped

the remainder.

23 pages; I subtracted 118 � 29 � 89. Sinceeach page can hold 4 photos, I divided 89 �4 � 22 R1. Another page is needed for the 1

extra photo. So, I increased thequotient to 23.Answers may vary.

Show your work.

Explanationsmay vary.

4E08L3 6/30/05 1:44 PM Page 3

Name Date


Problem-Solving Application:Interpret RemaindersProblem Peter has 58 photos to put in an album. He puts 5 photos on each page. How many pages will he need for all 58 photos?

1. For the above problem, what does thequotient of 58 � 5 tell you?

2. What is the remainder? How do youuse the remainder to find the answer?

3. How many pages does Peter need?

4. How many of the pages are full? Howdo you know?

Possible answer: 58 photoswill fit evenly on 11 pageswith 3 photos left over.

11 pages; the whole number of thequotient is 11, so 11 pages are full.

3 photos; answers will vary.

12 pages

ProblemSolving

8.3

Show your work.

4P08L3 7/1/05 9:56 AM Page 3

Name Date


Homework8.3

A basket holds 4 dinner rolls. How many baskets are needed to hold 47 dinnerrolls?

Another basket is needed to hold the 3 extra rolls, so 12 baskets are needed.


Solve each problem.

1. A florist received 69 roses. He wants toplace the roses in buckets of water.Each bucket holds 6 roses. How manybuckets will have 6 roses?

How many roses are left over?

How many buckets are needed for all the roses?

2. Ms. Dale bought 35 roses to give to herfriends. She divided the roses equallybetween her 3 friends and kept theleftover roses for herself. How manyroses did Ms. Dale keep?

11 buckets

2 roses

Explanations mayvary.

11 R34��4�7��4�

07� 4�

3

How many baskets have 4 rolls? 11 basketsHow many rolls are left over? 3 rollsIs another basket needed? yes

3 roses

12 buckets

Show your work.

4H08L3 6/29/05 4:31 PM Page 3

Name Date


EnglishLearners

8.3

Complete these paragraphs. Fill in the blanks with words from the boxes.

Mrs. Napoleon’s class is studying newspapers. Today

they are going to visit a to see how

newspapers are printed. There they will see a

of a printing press. After that, the students will

the newspaper office to see where the writers and editors work.

Mr. Ortega’s class is studying art. They are going to visit

a to see the famous paintings that are

there. They will also see an

of children’s art. After that, each child will be given a

with a picture of the museum on it. Each child

can send the card to a friend, or put it in a .

Problem-Solving Application:Interpret Remainders Read these definitions.

post card a card used for sending a short message through the mail

exhibit a display

on display being shown to people

tour to make a trip through a place for the purpose of seeing it

demonstration a show of how something works

scrapbook a book with blank pages for pasting pictures in

printing plant a building with machines that print words and pictures on paper

museum a building in which art or historic items are displayed

tour printing plant demonstration

printing plantdemonstration

tour

on display museum exhibit scrapbook post card

museumon display exhibit

post cardscrapbook

G4ELL083 8/3/05 6:52 PM Page 3

Regroup In Division


1. 4��4�4� 2. 6��8�5� 3. 2��3�6� 4. 5��6�7�

5. 73 � 6 6. 88 � 8 7. 86 � 6

8. 48 � 3 9. 53 � 4 10. 87 � 6

Name Date


Reteach8.4

Divide 31 � 2. You can use play money to solve the problem. Show 31 using ten-dollar bills and one-dollar bills.

Divide the money into 2 equal groups. Start by moving the ten-dollar bills. You can place 1 ten-dollar bill in each group with 1 ten-dollarbill left over.

Exchange the remaining ten-dollar bill for 10 one-dollar bills. Place the one-dollar bills into the 2 equal groups with the ten-dollar bill. You will place 5 one-dollar bills in each group with 1 one-dollar bill left over.

Count the money in one of the groups. This is the quotient. The one-dollar bill left over is the remainder.

So, or 31 � 2 � 15R1

11 14 R2

13 R214 R1 18

12 R1

11

16 13 R1 14 R3

15R12��3�1��2�

11�10�

1

4R08L4 2/23/06 2:22 PM Page 4

Name Date


1. 3�4�0� 2. 5�6�8� 3. 6�9�3� 4. 4�8�4� 5. 2�7�3�

6. 2�9�6� 7. 4�8�7� 8. 2�3�7� 9. 3�4�9� 10. 3�7�6�

11. 54 � 4 � 12. 60 � 5 � 13. 83 � 7 � 14. 86 � 7 � 15. 45 � 4 �

16. 67 � 5 � 17. 49 � 3 � 18. 57 � 5 � 19. 88 � 8 � 20. 42 � 3 �

Algebra • FunctionsCopy and complete each table.


Practice8.4

Test Prep

33. Jason is trading baseball cards. He canget 1 pack of cards for 5 single cards.If Jason has 63 single cards to trade,how many packs can he get?

A 5 C 12

B 10 D 15

34. If you had 52 cookies to put into 4bags, how many cookies would go intoeach bag? How many will be left over?

Rule: y � x � 2

x

24

22

36

21.

22.

23.

24.

y

22

Rule: y � x � 5

x

55

65

25.

26.

27.

28.

y

9

19

Rule: y � x � 7

x

49

14

29.

30.

31.

32.

y

5

9

48

13 R2

13 R3

21 R3

12

15 R3

18 R1

11 R6

21

16 R1

12 R2

25 R1

11 R1

13 R2

1244

1118

73563

2

1145

1395

16 R1 11 R2 11 14

13 R1

C

36 R1

13 cookies in eachbag; none left over

4P08L4 7/23/05 12:39 PM Page 4

Name Date

Remainder GameMaterials: two sets of number cards labeled 1–9, game board,game pieces

Number of Players: 1 or more

Rules of the game:

• Each player chooses a game piece and places it at the startsquare.

• Players take turns drawing 3 cards from the bag. The playerarranges the cards to make a division problem with a two-digitdividend and a one-digit divisor.

• The player solves the division problem and moves his or hergame piece the number of spaces as given below:

If the remainder equals 0—move your game piece 4 spaces.If the remainder equals 1 or 2—move your game piece 3 spaces.If the remainder equals 3 or greater—move your gamepiece 2 spaces.

• Play continues until someone reaches the finish space.


Enrichment8.4

4E08L4 7/25/05 12:54 PM Page 4

Regroup in DivisionSolve.

Name Date


ProblemSolving

8.4

1. Mrs. Rosenberg collected 84 leaves forher art class to use. If each studentuses 5 leaves to make a design, howmany designs will be made? Howmany leaves will be left over?

2. There are 52 sheets of drawing paper.The teacher wants to have as manysheets of paper as he can in 3 equalpiles. How many sheets will be in each pile?

3. There were 98 crayons in a container.Timothy divided the crayons equallyinto boxes of 8 crayons each. Howmany boxes were completely filled?

4. In art class, 67 drawings were made.All of the students except Carla made4 drawings. Carla made fewer than 4drawings. How many drawings didCarla make?

16 designs; 4 leavesleft over

17 sheets

12 boxes

3 drawings

Show your work.

5. Reasoning Kip bought 4 paint sets at the craft store. Hegave the clerk $60. His change was $4. How much was eachpaint set? Explain how you found your answer.

$14; subtract to find the total cost of the 4 paintsets, then divide to find the cost of each paint set.

4P08L4 2/22/06 7:31 PM Page 4

Name Date


Homework8.4

Problem Solving

15. Three friends made 44 cupcakes. Ifthey share the cupcakes evenly, howmany cupcakes will be left over?

Show your work.


4. 38 � 2 5. 79 � 6 6. 95 � 3

Algebra • FunctionsComplete each table.

2 cupcakes

19 13 R1 31 R2

13 R1

x y

Rule: y � x � 4

44

84

7.

2410.

9.

8.

18

x y

Rule: y � x � 8

64

5

11.

2414.

13.

12.

9

11 8

40

72

3

21

72

6

1. 6�6�6

2. 5�7�1�

3. 53 � 4

Regroup the oneten left as 10ones.

41 � 3 � 13 R2

Check:

13 � 3 � 39

39 � 2 � 41

13 R23��4�1��3↓�

11� 9�

2

11

14 R1

4H08L4 2/23/06 12:47 PM Page 4

Name Date


EnglishLearners

8.4

Complete the sentences below. Fill in the blanks with wordsin bold type.

1. To make sure that the votes have been counted correctly, two students will

the votes.

2. Edda Mae ordered pencils and pens for the office. They are almost gone, so she

must some soon.

3. The big show has been canceled. The ticket company will

money to everyone who bought a ticket.

4. Derek grouped the blocks in sets of 10 to solve the division problem. He must

some of the blocks in order to get the answer.

5. Sveta broke a flowerpot. She must it.

6. Keenan borrowed five dollars from his brother last week. Keenan has now earned

ten dollars, so he can his brother.

7. Greta does not like where the chairs and the tables have been placed. She will

the furniture so it looks better.

Regroup in DivisionRead the explanation and the definitions that follow.

The prefix re- usually means “back” or “again.” Knowing this can help you figure out the meanings of many words.

regroup to group again; to put into new groups

rearrange to arrange again; to arrange in a new way

repay to pay back; to pay people money you owe them

recount to count again

replace to put or give something in place of something that has been lost or broken

refund to give back money

reorder to order again

recount

reorderrefund

regroup

rearrange

repay

replace

When you are dividing, youcan regroup ten as 10 ones to help you solve the problem.

G4ELL084 2/22/06 7:39 AM Page 4

Name Date


Reteach8.5

Divide Multiples of 10, 100, and 1,000.

Use basic facts and patterns to find each quotient.

1. 6 � 3 � 2. 8 � 2 � 3. 12 � 2 �

60 � 3 � 80� 2 � 120 � 2 �

600 � 30 � 800 � 2 � 1,200 � 2 �

6,000 � 300 � 8,000 � 2 � 1,200 � 20 �

4. 12 tens � 6 � tens �

5. 18 hundreds � 3 � hundreds �

6. 45 tens � 5 � tens �

7. 36 thousands � 9 � thousands �

8. 240 � 8 � 9. 160 � 4 � 10. 540 � 6 �

11. 150 � 3 � 12. 810 � 9 � 13. 2,400 � 6 �

You can use facts and patterns to help you divide mentally.

3,000 � 5 �

30 � 5 � 6 30 ones � 5 � 6 ones � 6

300 � 5 � 60 30 tens � 5 � 6 tens � 60

3,000 � 5 � 600 30 hundreds � 5 � 6 hundreds � 600

So, 3,000 � 5 � 600

2 6

600

60

2

9

30

50

40

90

90

400

20

90

4

6 600

4,000

60

4

40

400

4,000

20

20

20

4R08L5 1/21/04 5:21 PM Page 5

Name Date


Practice8.5


1. 8 � 2 � 2. 6 � 3 � 3. 5 � 1 �

80 � 2 � 60 � 3 � 50 � 1 �

800 � 2 � 600 � 3 � 500 � 1 �

8,000 � 2 � 6,000 � 3 � 5,000 � 1 �

4. 45 � 5 � 5. 10 � 2 � 6. 15 � 5 �

450 � 5 � 100 � 2 � 150 � 5 �

4,500 � 5 � 1,000 � 2 � 1,500 � 5 �

7. 480 � 6 � 8. 2,700 � 3 � 9. 600 � 2 �

10. 800 � 4 � 11. 6,300 � 9 � 12. 4,000 � 4 �

Algebra Equations Solve each equation.

13. 2,100 � 3 � n 14. 160 � 4 � x 15. 350 � 5 � y

16. 48 � 6 � q 17. 1,400 � 2 � p 18. 720 � 9 � c

Test Prep

19. Which number sentence is NOTcorrect?

A 240 � 4 � 60 C 2,800 � 4 � 700

B 250 � 5 � 50 D 700 � 2 � 1,400

20. Complete the problem.

16 � 2 �

160 � � 80

� 2 � 800

4404004,00099090080200

2202002,000550500900

5505005,000330300300

700 1,000

n = 700 x = 40 y = 70

q = 8 p = 700 c = 80

D8

21,600

4C08L5 5/27/05 1:52 PM Page 5

Name Date

Quotient Mix-UpAt the math factory, there has been a big mix-up. Some of thequotients have been mismatched with a division problem.Look at each problem below. Write correct or incorrect besideeach number sentence. Write the correct answer to eachproblem beside each letter. Then write the letter above eachnumber in the saying below to find out a secret to doingdivision mentally.


Enrichment8.5

1. 1,200 � 4 � 30 A

2. 300 � 10 � 3,000 E

3. 2,700 � 3 � 90 F

4. 1,000 � 5 � 20 N

5. 6,400 � 8 � 80 O

6. 810 � 9 � 90 P

7. 320 � 8 � 40 R

8. 250 � 5 � 50 S

9. 3,600 � 9 � 40 T

10. 1,600 � 20 � 800 Z

90 300 400 400 30 40 200 50

800 900 80 30 40 800 50

300incorrect30incorrect900incorrect200incorrect800incorrect90correct40correct50correct400incorrect80incorrect

P A T T E R N S

O F Z E R O S

76274-E-08-L1-L6 2/21/03 4:46 PM Page 5

Name Date


ProblemSolving

8.5Divide Multiples of 10, 100,and 1,000Solve.

1. The Yosemite waterfall has a height ofabout 2,400 feet. How many yards highis this? (Hint: There are 3 feet in ayard.)

2. A park had a total of 4,200 visitors lastweek. If the same number of visitorswere there each day, how many visitorswere at the park on Monday?

3. The number of people that go to thepark to swim is 3 times the number ofpeople that go to hike. If 270 peoplego to swim, how many people go tohike?

4. The snack bar sold $320 worth ofsport drinks to hikers. If each drinkcost $4, how many drinks did thesnack bar sell?

5. Patty hiked a total of 1500 miles. If shehiked 5 miles each day how many daysdid she hike?

800 yards

600 visitors

90 people

80 drinks

300 days

Show your work.

76274-P-08-L1-L6 2/6/03 3:41 PM Page 5

5. 21 � 7 �

210 � 7 �

2,100 � 7 �

21,000 � 7 �

8. 350 � 5 �

4. 12 � 6 �

120 � 6 �

1,200 � 6 �

12,000 � 6 �

7. 420 � 7 �

3. 6 � 1 �

60 � 1 �

600 � 1 �

6,000 � 1 �

6. 3,600 � 6 �

1. 9 � 3 �

90 � 3 �

900 � 3 �

9,000 � 3 �

Name Date


Homework8.5

42 � 6 � 7

420 � 6 � 70

1 zero 1 zero

4,200 � 6 � 700

2 zeros 2 zeros

Problem Solving

12. A giant panda may eat up to 420 pounds of food in a week. Howmany pounds of food can a panda eatin 1 day?

Show your work.


2. 4 � 2 �

40 � 2 �

400 � 2 �

4,000 � 2 �

3303003,000

2202002,000

6

60

600

6,000

2

20200

2,000

3

30

300

3,000

600 60 70

x � 500 y � 9 n � 2

60 pounds

Solve each equation.

9. 2,500 � 5 � x 10. 180 � y � 20 11. 1,600 � n � 800

4H08L5 6/29/05 4:32 PM Page 5

Name Date


EnglishLearners

8.5

Match each phrase with its meaning.

1. a full week seven days in the future

2. 10 years ago seven days in a row

3. every week at least one time in a period of seven days

4. each of 10 years a date 10 years in the past

5. after one week every year in a period of 10 years

Divide Multiples of 10, 100, and 1,000Read these explanations.

Today it is December 1, 2003.

Six months ago it was June 1, 2003.

After one year it will be December 1 again.

If you are fifty years old, it means you have had a birthday in eachof 50 years.

If you go to the store every week, it means you go to the store atleast once every seven days.

If you work for a full week, you work all seven days in that week.

G4ELL085 7/26/05 3:09 PM Page 5

Estimate Quotients

Estimate. Write the basic fact you used.

1. 2��1�0�5� 2. 5��3�6�1�


Estimate: Estimate:

3. 5��4�2�1� 4. 334 � 8


Estimate: Estimate:

5. 626 � 9 6. 373 � 6


Estimate: Estimate:

7. 131 � 3 8. 173 � 4


Estimate: Estimate:

Name Date


Reteach8.6

Estimate 82 � 3.

Look at the first digit in the number 82.

Think of a basic fact with 3 and a number that is close to the first digit of thedividend.

3 � 1 � 3 3 � 2 � 6 3 � 3 � 9 3 � 4 � 12 3 � 5 � 15

Choose 3 � 3 � 9, because 9 is close to 8.

To find the second digit in the number multiply 9 by 10. 9 � 10 � 90

Divide 90 � 3 � 30

So, 82 � 3 is about 30.

2 � 5 � 10 5 � 7 � 35

60

70

9 � 7 � 6370

8 � 4 � 3240

50

3 � 4 �12 4 � 4 � 16

6 � 6 � 36

4040

5 � 8 � 4080

4R08L6 1/21/04 5:21 PM Page 6


1. 2�1�7� 2. 3�2�8� 3. 5�3�1�

4. 3�3�3�1� 5. 4�1�8�4� 6. 7�1�7�7�

7. 9�5�0� 8. 4�3�3� 9. 3�2�2�4�

10. 31 � 3 � 11. 44 � 6 � 12. 13 � 6 �

13. 331 � 8 � 14. 213 � 5 � 15. 261 � 5 �

Decide whether the actual quotient is greater than or lessthan the estimate given. Write ≥ or ≤ for each.

16. 17 � 5 5 17. 23 � 4 5 18. 14 � 7 3

19. 47 � 5 8 20. 37 � 9 5 21. 10 � 2 4

Name Date


Practice8.6

Test Prep

22. Which is the best estimate of 132 ÷ 3?

A 30 C 50

B 40 D 60

23. Notebooks cost $4 each at the schoolstore. Chris has $15. How manynotebooks can he buy? Explain.

3 � 10 � 30 6 � 7 � 42 6 � 2 � 12

8 � 4 � 32 5 � 4 � 20 5 � 5 � 25

He can buy 3notebooks.

B

≤

≤≤ ≥

≥ ≥

8 � 2 � 16 9 � 3 � 27 6 � 5 � 30

3 � 11 � 33 4 � 4 � 16 7 � 2 � 14

5 � 9 � 45 4 � 8 � 32 3 � 7 � 21

9 6

5 8 70

110 40 20

8

10 7 2

40 40 50

4C08L6 1/21/04 3:47 PM Page 6

Name Date

Estimate QuotientsFor each quotient given, write two division problems thatwould give the estimated quotient. The first one has beendone for you.

Estimated Quotient Division Problems

1. 30 246 � 8 192 � 6

2. 40

3. 8

4. 10

5. 7

6. 20

7. 9

8. 60

9. 5

10. 80

11. 4

12. 50


Enrichment8.6

Answers may vary.

4E08L6 6/30/05 1:44 PM Page 6

Estimate QuotientsThe Finley family took a vacation to the beach. Theystopped at the Sun N’ Fun Beach store to buy a fewsupplies. Use the table to answer problems 1–3.

Name Date


ProblemSolving

8.6

1. How many T-shirts can Maggie buywith 3 ten-dollar bills?

2. Mr. Finley bought sunscreen and somepostcards. He spent $19. How manypostcards did he buy?

3. Georgia has $42. She bought 3 T-shirts. How many pairs of sunglassescan she buy with the amount she hasleft over?

4. Four families went out for dinner. Thetotal food bill came to $327. Thefamilies also left a $40 tip for thewaitress. If each family spent the sameamount, about how much did eachfamily spend on dinner? Explain howyou found your answer.

Item Price

Sun N’ Fun Beach Store

sunscreen

postcard

sunglasses

T-shirt

$5

$2

$6

$74 T-shirts

7 postcards

First add $327 � $40 to findthe total bill that wasdivided between the 4families. Then estimate.$367 is close to $360.$360 � 4 is $90. Each familyspent about $90 on dinner.

3 pairs of sunglasses

Show your work.

4P08L6 7/1/05 9:56 AM Page 6

Name Date


Homework8.6

154 � 5

Use basic facts andmultiples of 10 to finda new dividend.

150 � 5

Think: 5 � 3 � 15

15 � 10 � 150

150 � 5 � 30

154 � 5 is about 30

Problem Solving

12. Jim used 29 beads to make a necklacefor his sister. The beads he used comein packages of 5 beads each. Abouthow many packages of beads did Jimuse?

Show your work.


1. 4�3�3� 2. 9�6�4�

3. 3�2�6� 4. 7�2�3�4�

5. 204 � 5 6. 26 � 8 7. 195 � 6

Decide whether the actual quotient is greater than or less thanthe estimate given. Write ≥ or ≤ for each �.

8. 27 � 3 � 4 9. 31 � 5 � 6 10. 24 � 3 � 7 11. 45 � 9 � 8

8;4 � 8 � 32

7;9 � 7 � 63

9;9 � 3 � 27

30;7 � 3 � 21

40;5 � 4 � 20

3;8 � 3 � 24

30;6 � 3 � 18

≤≥≥ ≥

6 packages

4H08L6 6/29/05 4:32 PM Page 6

Name Date


EnglishLearners

8.6

Some terms in the box tell about estimating. Others tellabout finding the exact amount. Write each term on any linein the web where it belongs.

Estimate QuotientsRead these explanations.

Estimate means “to use what you know to make a good guess atan answer.”

Find the exact amount means “to figure out the precise number.”

how much about how much guess calculate

how many about how many almost precisely

estimated quotient exact quotient possible certain

estimate

find the exact amount

estimatedquotient

about howmuch

about howmany

guess how much

certainhow many

exact quotient

calculate

precisely

almost

possible

G4ELL086 7/26/05 3:09 PM Page 6

Name Date


Chapter 8Test

1. 4��8�5� 2. 3��9�6� 3. 66 � 6 �


4. 8��6�2� 5. 3��5�7�

6. 77 � 6 � 7. 98 � 8 �

Divide.

8. 45 � 9 9. 42 � 7 10. 56 � 8

450 � 9 420 � 7 560 � 8

4,500 � 9 4,200 � 7 5,600 � 8

11. 480 � 6 12. 400 � 5 13. 7,200 � 9


Go on

21 R1

550

80 80 800

500

660600

770700

32 11

7 � 8 � 5656 � 6 � 62

7 R6 19

19 � 3 � 57

12 � 6 � 7272 � 5 � 77

12 � 8 � 9696 � 2 � 98

12 R5 12 R2

76274-A-08-L1-L5 2/27/03 11:20 AM Page 4

STOP

Name Date


Chapter 8Test


14. 6��3�5� 15. 6��3�2�1�

16. 75 � 8 17. 700 � 8


18. Mark is displaying toy cars on shelves. He can fit 6 cars on each shelf. How many shelves does Mark needto display 25 cars?

19. Sarah’s birthday is in 40 days. How many full weeks is that?

20. Carlos buys as many $8-kites as he can for $35. How much money does he have left over after he buys the kites?

6; 36 � 6 � 69

5 shelves; explanations may vary.

5 weeks; explanations may vary.

$3; explanations may vary.

72 � 8 � 9 72 � 8 � 990

50; 30 � 6 � 5

Estimatesmay vary.

76274-A-08-L1-L5 2/27/03 11:20 AM Page 5

Class Date


Chapter 8 Chapter 9 Chapter 10 Chapter 11 Unit 4 Test

Student Pre- Chapter Pre- Chapter Pre- Chapter Pre- Chaptertest Test test Test test Test test Test Form A Form B

Unit 4Class Record

Unit 4 Assessment

76274-A-U4-CR 3/7/03 10:07 AM Page 1

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