Name Daily Spiral Review 4-1 - owlsharenest - home4+masters.pdf · Daily Spiral Review 4-1 27 marbles 6 books $6 ... 6 comics to each of her friends. If ... Which family pays the

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Topic 4 19

1. Melissa has 19 more stamps than George. If George has 24 stamps, how many stamps does Melissa have?A 33B 39C 43D 45

2. Madison’s hair was 10 inches long before she got it cut. She had 3 inches cut off. How many inches long is her hair now?A 3 inchesB 6 inchesC 7 inchesD 13 inches

3. Timothy gave the clerk a $20 bill for a book. The clerk gave him back $11 in change. How much did the book cost?A $10B $9C $8D $7

4. Andrew, Lynda, and Fiona each have 9 marbles. How many marbles do they have altogether?

5. Miguel is putting his books away on a bookcase. There are 5 shelves on the bookcase. Miguel has 30 books. How many books should Miguel put on each shelf so that each shelf has an equal number of books?

6. Tamika had $15 to spend at the fair. She played a game for $2, rode on the Ferris wheel for $3, and bought a sandwich for $4. How much money did she have left?

Daily Spiral Review

4-1Daily Spiral Review

4-1

Nat_AncTopic_4.indb 19 1/31/08 11:56:52 AM

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Topic 4 19

1. Melissa has 19 more stamps than George. If George has 24 stamps, how many stamps does Melissa have?A 33B 39C 43D 45

2. Madison’s hair was 10 inches long before she got it cut. She had 3 inches cut off. How many inches long is her hair now?A 3 inchesB 6 inchesC 7 inchesD 13 inches

3. Timothy gave the clerk a $20 bill for a book. The clerk gave him back $11 in change. How much did the book cost?A $10B $9C $8D $7

4. Andrew, Lynda, and Fiona each have 9 marbles. How many marbles do they have altogether?

5. Miguel is putting his books away on a bookcase. There are 5 shelves on the bookcase. Miguel has 30 books. How many books should Miguel put on each shelf so that each shelf has an equal number of books?

6. Tamika had $15 to spend at the fair. She played a game for $2, rode on the Ferris wheel for $3, and bought a sandwich for $4. How much money did she have left?

Daily Spiral Review


4-1

27 marbles

6 books

$6

Nat_AncTopic_4.indb 19 1/31/08 3:28:23 PM

© Pearson Education, Inc. 4

Problem of the DayJason bought 4 packages of pencils and 3 packages of pencil erasers. How many extra erasers did he have?

4-1

20

Topic 4

Problem of the Day 4-1Problem

of the Day

4-1

Nat_AncTopic_4.indb 20

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Topic 4 21

Quick Check

4-1Q

uick Check 4

-1

1. Yvette has 24 comics. She gives 6 comics to each of her friends. If she gives away all her comics, how many friends did she give comics to? Use the drawing to help you solve the problem.

6 6 6 6

A 4

B 5

C 6

D 7

2. Jackson gives away all 42 of his comics to 6 friends. If each friend receives the same number, how many comics does each friend receive? Use the drawing to help you solve the problem.

? ? ? ? ? ?

A 4

B 6

C 7

D 8

3. Writing to Explain Write a division problem that matches the drawing below. Explain your thinking.

? ? ? ? ?

24 comics 42 comics

60


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Topic 4 21

Quick Check

4-1Q

uick Check 4

-1

1. Yvette has 24 comics. She gives 6 comics to each of her friends. If she gives away all her comics, how many friends did she give comics to? Use the drawing to help you solve the problem.

6 6 6 6

A 4

B 5

C 6

D 7

2. Jackson gives away all 42 of his comics to 6 friends. If each friend receives the same number, how many comics does each friend receive? Use the drawing to help you solve the problem.

? ? ? ? ? ?

A 4

B 6

C 7

D 8

3. Writing to Explain Write a division problem that matches the drawing below. Explain your thinking.

? ? ? ? ?

24 comics 42 comics

60

See student samples to the right.


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22 Topic 4

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Meanings of DivisionWhen you divide, you separate things into equal groups.

Doris is making 8 box lunches, each with the same number of strawberries. She has a total of 32 strawberries. How many strawberries should go in each lunch?

What you think: Doris will have to place an equal number of strawberries in each box. She must put 32 strawberries into 8 equal groups. How many strawberries are in each group?

What you show: 8 equal groups

32 strawberries divided into 8 separate groups leaves 4 strawberries in each group.

What you write: 32 ! 8 " 4

32 is the dividend, the number that is being divided.

8 is the divisor, the number the dividend is being divided by.

4 is the quotient, or the answer to the division problem.

Each lunch should have 4 strawberries.

Draw pictures to solve each problem.

1. You put 15 marbles into 3 groups. How many marbles are in each group?

2. You need to put 20 ice cubes into 5 glasses. How many cubes should go into each glass?

Reteaching

4-1


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22 Topic 4

Rete

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Meanings of DivisionWhen you divide, you separate things into equal groups.

Doris is making 8 box lunches, each with the same number of strawberries. She has a total of 32 strawberries. How many strawberries should go in each lunch?

What you think: Doris will have to place an equal number of strawberries in each box. She must put 32 strawberries into 8 equal groups. How many strawberries are in each group?

What you show: 8 equal groups

32 strawberries divided into 8 separate groups leaves 4 strawberries in each group.

What you write: 32 ! 8 " 4

32 is the dividend, the number that is being divided.

8 is the divisor, the number the dividend is being divided by.

4 is the quotient, or the answer to the division problem.

Each lunch should have 4 strawberries.

Draw pictures to solve each problem.

1. You put 15 marbles into 3 groups. How many marbles are in each group?

2. You need to put 20 ice cubes into 5 glasses. How many cubes should go into each glass?

Reteaching

4-1

Sample answers:

5 marbles

4 cubes


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Practice 4-1

Topic 4 23

Practice

4-1Practice 4

-1

Meanings of DivisionDraw pictures to solve each problem.

1. There are 12 small gift bags. Each bag can hold 1 toy and some stickers. There are 36 stickers. If an equal number of stickers is put in each bag, how many stickers will be in each bag?

2. One egg carton holds 12 eggs. How many cartons are you able to fill with 60 eggs?

3. There are 21 students in Mr. Tentler’s class. The students divided themselves evenly into 3 groups. How many students are in each group?

4. Calvin read an 18-page chapter in his social studies book in 2 hours. If he read the same number of pages each hour, how many pages did he read per hour?

A 3 pages B 6 pages C 9 pages D 12 pages

5. Writing to Explain The class is planning a party. The pizza restaurant cuts each pizza into 8 slices. There are 32 students. How many pizzas does the class need to order for each student to have one slice? Explain.


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Practice 4-1

Topic 4 23

Practice

4-1Practice 4

-1

Meanings of DivisionDraw pictures to solve each problem.

1. There are 12 small gift bags. Each bag can hold 1 toy and some stickers. There are 36 stickers. If an equal number of stickers is put in each bag, how many stickers will be in each bag?

2. One egg carton holds 12 eggs. How many cartons are you able to fill with 60 eggs?

3. There are 21 students in Mr. Tentler’s class. The students divided themselves evenly into 3 groups. How many students are in each group?

4. Calvin read an 18-page chapter in his social studies book in 2 hours. If he read the same number of pages each hour, how many pages did he read per hour?

A 3 pages B 6 pages C 9 pages D 12 pages

5. Writing to Explain The class is planning a party. The pizza restaurant cuts each pizza into 8 slices. There are 32 students. How many pizzas does the class need to order for each student to have one slice? Explain.

3 stickersStudents’ drawings may vary.

5 cartonsStudents’ drawings may vary.

7 students

4 pizzas; Sample answer: How many groups of 8 slices are needed to have 32? 32 ! 8 " 4.


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Enrichment

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24 Topic 4

Enric

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Babysitting in the NeighborhoodJennifer babysits for some of the families in her neighborhood. She wants to decide how she can earn the most money. She has made a chart that shows how long she usually babysits for a family and how much she is paid for her job.

1. Which family pays the most per hour? What is the hourly rate?

2. Which family pays the least per hour?

3. Which would pay more, 8 hours of babysitting for the Oberlins or 7 hours of babysitting for the San Giacomos?

4. On one Friday night, Jennifer is asked to babysit for two different families. The Robinsons need her for 5 hours, and the Lings want her to babysit for 4 hours. If Jennifer can only take one job and wants to make the most money, which job should she take? How much will she earn?

5. On a different Friday night, the Roberts offer Jennifer a 5-hour babysitting job with a $4 tip, and the Robinsons offer Jennifer an 8-hour babysitting job. Which job should Jennifer take? How much more will she earn?

Family Hours Amount PaidRoberts 6 $30Robinsons 6 $24San Giacomos 8 $40Lings 5 $35Oberlins 7 $42

Reasoning


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24 Topic 4

Enric

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Babysitting in the NeighborhoodJennifer babysits for some of the families in her neighborhood. She wants to decide how she can earn the most money. She has made a chart that shows how long she usually babysits for a family and how much she is paid for her job.

1. Which family pays the most per hour? What is the hourly rate?

2. Which family pays the least per hour?

3. Which would pay more, 8 hours of babysitting for the Oberlins or 7 hours of babysitting for the San Giacomos?

4. On one Friday night, Jennifer is asked to babysit for two different families. The Robinsons need her for 5 hours, and the Lings want her to babysit for 4 hours. If Jennifer can only take one job and wants to make the most money, which job should she take? How much will she earn?

5. On a different Friday night, the Roberts offer Jennifer a 5-hour babysitting job with a $4 tip, and the Robinsons offer Jennifer an 8-hour babysitting job. Which job should Jennifer take? How much more will she earn?

Family Hours Amount PaidRoberts 6 $30Robinsons 6 $24San Giacomos 8 $40Lings 5 $35Oberlins 7 $42

Reasoning

The Lings pay the most per hour; $7

The Robinsons pay the least per hour; $4

8 hours of babysitting for the Oberlins would pay more: $48 ! $35 " $13 more

She should take the job with the Lings; $28

Jennifer should take the job with the Robinsons; $3 more


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Topic 4 25

1. Alexandra has 12 ! owers. She puts the same number of ! owers in each of her vases. How many ! owers will be in each vase?

A 3 B 4 C 8 D 12

2. Look at the array below. Which multiplication sentence describes the array?

A 3 ! 3 = 9B 5 ! 3 = 15C 3 ! 6 = 18D 5 ! 5 = 25

3. Keith planted 45 carrots in his garden. He planted them in 5 rows. Each row had the same number of carrot plants. How many carrot plants were in each row?

4. Jackson wants to buy a pair of sneakers that cost $106. So far, he has saved $57. How much more does Jackson have to save to buy the sneakers?

5. Put the numbers in order from least to greatest.9,856 9,865 9,964 9,846

6. Michelle wrote a basic multiplication fact, but she covered up some of the numbers. What multiplication fact did she write?

! = 25

Daily Spiral Review


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Topic 4 25

1. Alexandra has 12 ! owers. She puts the same number of ! owers in each of her vases. How many ! owers will be in each vase?

A 3 B 4 C 8 D 12

2. Look at the array below. Which multiplication sentence describes the array?

A 3 ! 3 = 9B 5 ! 3 = 15C 3 ! 6 = 18D 5 ! 5 = 25

3. Keith planted 45 carrots in his garden. He planted them in 5 rows. Each row had the same number of carrot plants. How many carrot plants were in each row?

4. Jackson wants to buy a pair of sneakers that cost $106. So far, he has saved $57. How much more does Jackson have to save to buy the sneakers?

5. Put the numbers in order from least to greatest.9,856 9,865 9,964 9,846

6. Michelle wrote a basic multiplication fact, but she covered up some of the numbers. What multiplication fact did she write?

! = 25

Daily Spiral Review


4-2

9,846 9,8569,865 9,964

5 ! 5 " 25

$49

9



26

Topic 4

Problem of the Day 4-2

4-2Problem of the DayProblem

of the Day

4-2

Lee and Amy fed their dog, Sox, 24 days in a row. Lee fed Sox two days more than Amy. How many days did each feed Sox? [Hint: Try, check, and revise.]


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Topic 4 27

Quick Check

4-2

1. Which number sentence below belongs in the fact family for 4, 5, and 20?

A 4 ! 5 " 20

B 5 # 4 " 25

C 20 $ 5 " 4

D 20 % 5 " 4

2. Which choice shows a related multiplication and division sentence?

A 2 # 5 " 10; 5 # 2 " 10

B 81 $ 9 " 9; 9 # 8 " 72

C 32 $ 8 " 4; 8 # 4 " 32

D 35 $ 5 " 7; 25 $ 5 " 5 Quick C

heck 4-2 3. Writing to Explain The shapes below stand for whole

numbers. What is the answer to the division problem? Explain how you found your answer.

# "

$ " ?


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Topic 4 27

Quick Check

4-2

1. Which number sentence below belongs in the fact family for 4, 5, and 20?

A 4 ! 5 " 20

B 5 # 4 " 25

C 20 $ 5 " 4

D 20 % 5 " 4

2. Which choice shows a related multiplication and division sentence?

A 2 # 5 " 10; 5 # 2 " 10

B 81 $ 9 " 9; 9 # 8 " 72

C 32 $ 8 " 4; 8 # 4 " 32

D 35 $ 5 " 7; 25 $ 5 " 5 Quick C

heck 4-2 3. Writing to Explain The shapes below stand for whole

numbers. What is the answer to the division problem? Explain how you found your answer.

# "

$ " ?



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Relating Multiplicationand DivisionMultiplication and division are related, just like addition andsubtraction are related.

This is the fact family for 5, 6, and 30:

5 ! 6 " 30 30 # 6 " 5

6 ! 5 " 30 30 # 5 " 6

Complete each fact family.

1. 2 ! " 10 2. 9 ! " 27

! " 10 ! " 27

10 # 5 " 27 # 3 "

10 # " 27 # "

3. 8 ! " 72 4. 6 ! " 48

! " 72 ! " 48

72 # 8 " 48 # 8 "

72 # " 48 # "

Write a fact family for each set of numbers.

5. 7, 4, 28

6. 5, 8, 40

7. Number Sense What multiplication facts are part of the factfamily for 12 # 3 " 4?

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28 Topic 4

Relating Multiplicationand DivisionMultiplication and division are related, just like addition andsubtraction are related.

This is the fact family for 5, 6, and 30:

5 ! 6 " 30 30 # 6 " 5

6 ! 5 " 30 30 # 5 " 6

Complete each fact family.

1. 2 ! " 10 2. 9 ! " 27

! " 10 ! " 27

10 # 5 " 27 # 3 "

10 # " 27 # "

3. 8 ! " 72 4. 6 ! " 48

! " 72 ! " 48

72 # 8 " 48 # 8 "

72 # " 48 # "


5. 7, 4, 28

6. 5, 8, 40

7. Number Sense What multiplication facts are part of the factfamily for 12 # 3 " 4?

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5

25 2

2 5

33 9

99

39

9 88

8 6

6 86

9 89

4 ! 7 " 28; 7 ! 4 " 28; 28 # 7 " 4; 28 # 4 " 7

40 # 5 " 8; 40 # 8 " 5; 8 ! 5 " 40; 5 ! 8 " 40

3 ! 4 " 12 and 4 ! 3 " 12


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Topic 4 29

Relating Multiplicationand DivisionComplete each fact family.

1. 7 ! " 42 2. 9 ! " 36

! " 42 ! " 36

42 # 6 " 36 # 4 "

42 # " 36 # "


3. 6, 3, 18

4. 5, 5, 25

5. Reasoning Why does the fact family for 81 and 9 have only two number sentences?

6. Which number sentence completes the fact family?

9 ! 6 " 54 54 # 9 " 6 54 # 6 " 9

A 9 ! 9 " 81 B 6 ! 9 " 54 C 6 ! 6 " 36 D 8 ! 6 " 48

7. Writing to Explain Find two ways to divide 16 evenly. Explain.

Practice

4-2Practice 4

-2


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Topic 4 29

Relating Multiplicationand DivisionComplete each fact family.

1. 7 ! " 42 2. 9 ! " 36

! " 42 ! " 36

42 # 6 " 36 # 4 "

42 # " 36 # "


3. 6, 3, 18

4. 5, 5, 25

5. Reasoning Why does the fact family for 81 and 9 have only two number sentences?

6. Which number sentence completes the fact family?

9 ! 6 " 54 54 # 9 " 6 54 # 6 " 9

A 9 ! 9 " 81 B 6 ! 9 " 54 C 6 ! 6 " 36 D 8 ! 6 " 48

7. Writing to Explain Find two ways to divide 16 evenly. Explain.

Practice

4-2Practice 4

-2

Sample answer: The related facts have the same numbers; 9 ! 9 " 81 and 81 # 9 " 9.

5 ! 5 " 25; 25 # 5 " 5

6 ! 3 " 18; 3 ! 6 " 18; 18 # 6 " 3; 18 # 3 " 6

Sample answer: 16 # 2 " 8; 16 # 8 " 2

6 47 4 9

767

99 4

6


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30 Topic 4

Just the Fact(or)s Some numbers have several factors. Complete the following to find all of the factors of 12. The first one is done for you.

1.

2.

3.

4.

5. There are 6 numbers that are factors of 12. What are they?

12

2 groups

6 in a group

12

in a group

4 groups

12

groups

4

12

12 in a group

1 group

Enrichment

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Visual Thinking


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Just the Fact(or)s Some numbers have several factors. Complete the following to find all of the factors of 12. The first one is done for you.

1.

2.

3.

4.

5. There are 6 numbers that are factors of 12. What are they?

12

2 groups

6 in a group

12

in a group

4 groups

12

groups

4

12

12 in a group

1 group

Enrichment

4-2En

richm

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Visual Thinking

12, 6, 4, 3, 2, 1

3

in a group

3


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Topic 4 31 Topic 4 31

1. Last year, there were 420 students at Madison Elementary. This year, 190 more students enrolled. How many students attend Madison Elementary now? A 230B 380C 510D 610

2. There were 213 people in the audience at Erika’s recital. 29 were children. How many adults were at the recital? A 184B 204C 232D 242

3. To visit their grandmother, James’s family drove 347 miles and then stopped to have lunch. The entire trip is 568 miles. How many more miles does James’s family have to drive? A 221 milesB 226 milesC 279 milesD 915 miles

4. Find the missing digits in the problem below. Rewrite the subtraction sentence.

Use the table for problems 5 and 6.

Number of Books ReadClass 4A 1,008Class 4B 994Class 4C 1,056

5. The fourth-grade students at Milton Elementary kept track of the number of books they read. Which class read the greatest number of books?

6. How many more books did Class 4A read than Class 4B?

917! 2??

705

Daily Spiral Review

4-3

Daily Spiral Review 4-3


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Topic 4 31 Topic 4 31

1. Last year, there were 420 students at Madison Elementary. This year, 190 more students enrolled. How many students attend Madison Elementary now? A 230B 380C 510D 610

2. There were 213 people in the audience at Erika’s recital. 29 were children. How many adults were at the recital? A 184B 204C 232D 242

3. To visit their grandmother, James’s family drove 347 miles and then stopped to have lunch. The entire trip is 568 miles. How many more miles does James’s family have to drive? A 221 milesB 226 milesC 279 milesD 915 miles

4. Find the missing digits in the problem below. Rewrite the subtraction sentence.

Use the table for problems 5 and 6.

Number of Books ReadClass 4A 1,008Class 4B 994Class 4C 1,056

5. The fourth-grade students at Milton Elementary kept track of the number of books they read. Which class read the greatest number of books?

6. How many more books did Class 4A read than Class 4B?

917! 2??

705

Daily Spiral Review

4-3


917 ! 212 " 705

Class 4C

14



Problem of the DayProblem of the Day 4-3

Problem of the Day

4-3

32

Topic 4

4-3

Write two fact families for the product 48.


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Topic 4 33

Quick Check

4-3

Topic 4 33

1. For breakfast, 4 campers share bananas, grapefruit, and cantaloupe. They have 16 sections of grapefruit and 8 slices of cantaloupe. Which number sentence below shows the number of sections of grapefruit each camper will get?

A 16 ! 4 " 4

B 8 ! 4 " 2

C 0 ! 4 " 0

D 4 ! 0 " 0

3. Which number sentence shows how many people can have one slice of pie that is divided into 12 slices?

A 12 ! 0 " 0

B 12 ! 1 " 12

C 12 ! 4 " 3

D 12 ! 6 " 2

2. Look back at Exercise 1. Jerome ate all of the cantaloupe. Which number sentence below shows the number of cantaloupe slices Jerome ate?

A 8 ! 1 " 8

B 1 ! 8 " 8

C 16 ! 1 " 16

D 1 ! 16 " 16

Quick C

heck 4-3

4. Writing to Explain Luke has a foot-long sandwich that is cut into 6 pieces. How many people can have a piece of sandwich? Write a number sentence to show how many people can have a piece of sandwich. Explain your answer.


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Topic 4 33

Quick Check

4-3

Topic 4 33

1. For breakfast, 4 campers share bananas, grapefruit, and cantaloupe. They have 16 sections of grapefruit and 8 slices of cantaloupe. Which number sentence below shows the number of sections of grapefruit each camper will get?

A 16 ! 4 " 4

B 8 ! 4 " 2

C 0 ! 4 " 0

D 4 ! 0 " 0

3. Which number sentence shows how many people can have one slice of pie that is divided into 12 slices?

A 12 ! 0 " 0

B 12 ! 1 " 12

C 12 ! 4 " 3

D 12 ! 6 " 2

2. Look back at Exercise 1. Jerome ate all of the cantaloupe. Which number sentence below shows the number of cantaloupe slices Jerome ate?

A 8 ! 1 " 8

B 1 ! 8 " 8

C 16 ! 1 " 16

D 1 ! 16 " 16

Quick C

heck 4-3

4. Writing to Explain Luke has a foot-long sandwich that is cut into 6 pieces. How many people can have a piece of sandwich? Write a number sentence to show how many people can have a piece of sandwich. Explain your answer.



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34 Topic 4

Special QuotientsThere are special rules for dividing numbers by 1 and by 0.

Rule: A number divided by 1 is that number.

Examples: 4 ! 1 " 4 55 ! 1 " 55

Rule: A number divided by itself (except 0) is 1.

Examples: 17 ! 17 " 1 135 ! 135 " 1

Rule: Zero divided by a number (except 0) is 0.

Examples: 0 ! 4 " 0 0 ! 15 " 0

Rule: You cannot divide a number by zero.

Examples: 7 ! 0 cannot be done. 12 ! 0 cannot be done.

1. 0 ! 2 " 2. 4 ! 4 "

3. 0 ! 7 " 4. 9 ! 9 "

5. 0 ! 3 " 6. 10 ! 10 "

7. 0 ! 11 " 8. 11 ! 1 "

Compare. Use >, <, or " for each .

9. 6 ! 6 3 ! 3 10. 7 ! 1 8 ! 8

11. 0 ! 5 3 ! 1 12. 0 ! 4 0 ! 9

13. 5 ! 5 0 ! 5 14. 7 ! 7 9 ! 9

15. 8 ! 1 0 ! 8 16. 9 ! 9 9 ! 1

17. 0 ! 12 12 ! 1 18. 0 ! 11 0 ! 15

19. Number Sense If a ! 4 " 0, what do you know about a?


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34 Topic 4

Special QuotientsThere are special rules for dividing numbers by 1 and by 0.

Rule: A number divided by 1 is that number.

Examples: 4 ! 1 " 4 55 ! 1 " 55

Rule: A number divided by itself (except 0) is 1.

Examples: 17 ! 17 " 1 135 ! 135 " 1

Rule: Zero divided by a number (except 0) is 0.

Examples: 0 ! 4 " 0 0 ! 15 " 0

Rule: You cannot divide a number by zero.

Examples: 7 ! 0 cannot be done. 12 ! 0 cannot be done.

1. 0 ! 2 " 2. 4 ! 4 "

3. 0 ! 7 " 4. 9 ! 9 "

5. 0 ! 3 " 6. 10 ! 10 "

7. 0 ! 11 " 8. 11 ! 1 "

Compare. Use >, <, or " for each .

9. 6 ! 6 3 ! 3 10. 7 ! 1 8 ! 8

11. 0 ! 5 3 ! 1 12. 0 ! 4 0 ! 9

13. 5 ! 5 0 ! 5 14. 7 ! 7 9 ! 9

15. 8 ! 1 0 ! 8 16. 9 ! 9 9 ! 1

17. 0 ! 12 12 ! 1 18. 0 ! 11 0 ! 15

19. Number Sense If a ! 4 " 0, what do you know about a?

0

a ! 0

11010

101

<<>!

>< !

> !

!


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Practice 4-3

Practice

4-3Practice 4

-3

Topic 4 35

Special Quotients1. 0 ! 10 " 2. 7 ! 1 " 3. 8 ! 8 "

4. 9 ! 9 " 5. 0 ! 5 " 6. 5 ! 1 "

7. 1!4" 8. 8!0" 9. 3!3" 10. 1!6"

11. Number Sense If x ! 9 " 1, how do you know what x is? Explain.

12. Kenneth has 22 math problems to do for homework. He has 12 problems done. How many more problems does he have left? If he completes 1 problem every minute, how many more minutes does he have to work?

13. There are 8 people who would like to share a box of granola bars that contains 8 bars. How many granola bars does each person get if they share equally?

14. Which is the quotient of 20 ! 20?

A 20 B 2 C 1 D 0

15. Writing to Explain Write a rule for the following number sentence: 0 ! 7 " 0.


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Practice

4-3Practice 4

-3

Topic 4 35

Special Quotients1. 0 ! 10 " 2. 7 ! 1 " 3. 8 ! 8 "

4. 9 ! 9 " 5. 0 ! 5 " 6. 5 ! 1 "

7. 1!4" 8. 8!0" 9. 3!3" 10. 1!6"

11. Number Sense If x ! 9 " 1, how do you know what x is? Explain.

12. Kenneth has 22 math problems to do for homework. He has 12 problems done. How many more problems does he have left? If he completes 1 problem every minute, how many more minutes does he have to work?

13. There are 8 people who would like to share a box of granola bars that contains 8 bars. How many granola bars does each person get if they share equally?


A 20 B 2 C 1 D 0

15. Writing to Explain Write a rule for the following number sentence: 0 ! 7 " 0.

51

61040170

x ! 9; Sample answer: Any number divided by itself equals 1.

10; 10 min

1 granola bar

Sample answer: The rule for 0 " 7 ! 0 is that when 0 is divided by any number (except 0) the answer is 0.


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36 Topic 4

Analyze ThisAn analogy is often used to show the relationship between pairs of items.

1. How are the drawings of the rectangles related?

2. How are the drawings of the triangles related?

3. Draw the missing item in the following analogies.

a.

b.

c.

d.

is to as is to

is to as is to

is to as is to

Reasoning


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is to as is to

36 Topic 4

Analyze ThisAn analogy is often used to show the relationship between pairs of items.

1. How are the drawings of the rectangles related?

2. How are the drawings of the triangles related?

3. Draw the missing item in the following analogies.

a.

b.

c.

d.

is to as is to

is to as is to

is to as is to

Reasoning

Sample answer: The rectangles are related by size, from larger to smaller.

Sample answer: The triangles are relatedby size, from larger to smaller.


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Topic 4 37

1. Elizabeth is baking cookies for her birthday party. She has invited 12 people to her party. She wants each guest to have 2 cookies.How many cookies does she need to bake for her guests?A 20B 22C 24D 26

2. There were 32 students going on a ! eld trip. Each van could carry 8 students. Which number sentence is in the same fact family as 32 ! 8 " ?A 4 # " 32B 32 # 8 " C # 4 " 8D 8 # 8 "

3. In which number sentence does 5 make the equation true?A 3 # 2 " B # 6 " 42C 9 # " 45D # 3 " 18

4. Complete the fact family below.

4 # " 20

# 4 " 20

! 5 " 4

20 ! " 5


# 6 " 42

# 7 " 42

42 ! 7 "

! 6 " 7

6. Arthur, Jorge, and Dylan collected 328 cans for recycling altogether. Arthur collected 105 and Jorge collected 112. How many did Dylan collect?

Daily Spiral Review


4-4


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Topic 4 37

1. Elizabeth is baking cookies for her birthday party. She has invited 12 people to her party. She wants each guest to have 2 cookies.How many cookies does she need to bake for her guests?A 20B 22C 24D 26

2. There were 32 students going on a ! eld trip. Each van could carry 8 students. Which number sentence is in the same fact family as 32 ! 8 " ?A 4 # " 32B 32 # 8 " C # 4 " 8D 8 # 8 "

3. In which number sentence does 5 make the equation true?A 3 # 2 " B # 6 " 42C 9 # " 45D # 3 " 18


4 # " 20

# 4 " 20

! 5 " 4

20 ! " 5


# 6 " 42

# 7 " 42

42 ! 7 "

! 6 " 7

6. Arthur, Jorge, and Dylan collected 328 cans for recycling altogether. Arthur collected 105 and Jorge collected 112. How many did Dylan collect?

Daily Spiral Review

4-4


111

7

55

420

66

42




Problem of the Day

4-4

38

Topic 4

4-4

If x ÷ y = x and n ÷ n = y, then what do you know about y?


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Topic 4 39

Quick Check

4-4Q

uick Check 4

-4

1. Jamal has 35 model airplanes in his collection. He displays his models on 7 shelves in his room. If there are an equal number of planes on each shelf, how many planes are displayed on each shelf?

A 5

B 7

C 28

D 42

3. Lincoln bought 36 tomato plants. He planted an equal number of plants in 4 rows. How many plants are in each row?

A 6

B 7

C 8

D 9

2. Sandra ran a total of 14 miles last week. She ran every day. She ran the same number of miles each day. How many miles did she run each day?

A 28 miles

B 7 miles

C 2 miles

D There is not enough information to answer this question.

4. Writing to Explain Write a multiplication sentence and a division sentence that represent the model below. Explain how you found your answer.


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Topic 4 39

Quick Check

4-4Q

uick Check 4

-4

1. Jamal has 35 model airplanes in his collection. He displays his models on 7 shelves in his room. If there are an equal number of planes on each shelf, how many planes are displayed on each shelf?

A 5

B 7

C 28

D 42

3. Lincoln bought 36 tomato plants. He planted an equal number of plants in 4 rows. How many plants are in each row?

A 6

B 7

C 8

D 9

2. Sandra ran a total of 14 miles last week. She ran every day. She ran the same number of miles each day. How many miles did she run each day?

A 28 miles

B 7 miles

C 2 miles

D There is not enough information to answer this question.

4. Writing to Explain Write a multiplication sentence and a division sentence that represent the model below. Explain how you found your answer.



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40 Topic 4

Using Multiplication Facts to Find Division FactsDarren is laying a tile floor in the hallway. The pattern for the floor is shown to the right.

First, use Darren’s tile floor to write a multiplication story for 4 ! 8 " 32.

Second, use Darren’s tile floor to write a division story for 32 # 4 " 8.

Use the data in the table to write a multiplication or a division story for each number fact. Solve.

1. 4 ! 6

2. 12 # 4

Darren’s tile floor has 4 rows with 8 pieces of tile in each row. How many pieces of tile are there in all?

Darren has 32 small triangles. He needs 4 for each shaded square. How many shaded squares can he make with the small triangles?

Building Supplies Number in a BoxFasteners 6Bolts 12


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40 Topic 4

Using Multiplication Facts to Find Division FactsDarren is laying a tile floor in the hallway. The pattern for the floor is shown to the right.

First, use Darren’s tile floor to write a multiplication story for 4 ! 8 " 32.

Second, use Darren’s tile floor to write a division story for 32 # 4 " 8.

Use the data in the table to write a multiplication or a division story for each number fact. Solve.

1. 4 ! 6

2. 12 # 4

Darren’s tile floor has 4 rows with 8 pieces of tile in each row. How many pieces of tile are there in all?

Darren has 32 small triangles. He needs 4 for each shaded square. How many shaded squares can he make with the small triangles?

Building Supplies Number in a BoxFasteners 6Bolts 12

There are 6 fasteners in a box. How many fasteners are in 4 boxes? 24 fasteners

There are 4 sizes of bolts in each box of 12. How many of each size bolt are in each box?3 bolts of each size

Sample answers are given for 1-2


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Topic 4 41

Using Multiplication Facts to Find Division FactsSolve.

1. 12 ! 3 " 7. 63 ! 9 "

2. 20 ! 5 " 8. 36 ! 4 "

3. 50 ! 10 " 9. 48 ! 6 "

4. 27 ! 9 " 10. 32 ! 8 "

5. 6 ! 2 " 11. 25 ! 5 "

6. 16 ! 8 " 12. 18 ! 2 "

Use the data in the table to write a multiplication story for the number fact. Solve.

13. 2 # 6 "


A 14 B 9 C 6 D 4

15. Writing to Explain Write a division story for 12 and 3.

First Aid KitSupply Number in Kit

Bandages 4Cleanser Pads 6Cotton Balls 12


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Practice

4-4Practice 4

-4

Topic 4 41

Using Multiplication Facts to Find Division FactsSolve.

1. 12 ! 3 " 7. 63 ! 9 "

2. 20 ! 5 " 8. 36 ! 4 "

3. 50 ! 10 " 9. 48 ! 6 "

4. 27 ! 9 " 10. 32 ! 8 "

5. 6 ! 2 " 11. 25 ! 5 "

6. 16 ! 8 " 12. 18 ! 2 "

Use the data in the table to write a multiplication story for the number fact. Solve.

13. 2 # 6 "


A 14 B 9 C 6 D 4

15. Writing to Explain Write a division story for 12 and 3.

First Aid KitSupply Number in Kit

Bandages 4Cleanser Pads 6Cotton Balls 12

Answers will vary; 12

445332

798459

Check students’ stories.


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42 Topic 4

Tables That RuleBelow are some tables. Dewey, Corrie, and Isaac each try to guess the rule. If the rule is correct, write yes. If the rule is incorrect, write the correct rule. Complete each table.

1. Dewey says, “The rule for this table is divide by 4.”

2. Corrie says, “The rule for this table is multiply by 2, then subtract 1.”

3. Isaac says, “The rule for this table is add 1.”

Dewey’s 16 32 56 48 12 18 24 30 n

Table 8 16 28

Corrie’s 7 2 6 4 12 3 10 5 11 n

Table 13 3 11

Isaac’s 2 9 6 4 3 5 8 7 9 n

Table 3 24 15 9

Patterns


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42 Topic 4

Tables That RuleBelow are some tables. Dewey, Corrie, and Isaac each try to guess the rule. If the rule is correct, write yes. If the rule is incorrect, write the correct rule. Complete each table.

1. Dewey says, “The rule for this table is divide by 4.”

2. Corrie says, “The rule for this table is multiply by 2, then subtract 1.”

3. Isaac says, “The rule for this table is add 1.”

Dewey’s 16 32 56 48 12 18 24 30 n

Table 8 16 28

Corrie’s 7 2 6 4 12 3 10 5 11 n

Table 13 3 11

Isaac’s 2 9 6 4 3 5 8 7 9 n

Table 3 24 15 9

Patterns

24 6 9 12 15 !n2!

7 23 5 19 9 21 2n–1

6 12 21 18 24 3n– 3

The correct rule for the table is divide by 2.

Yes

The correct rule is multiply by 3, then subtract 3.


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Topic 4 43

1. Luz had $13.12 in her purse. She gave $0.33 to her niece. How much money does she have in her purse now?A $33.00B $13.89C $12.79D $10.12

2. Megan has 8 classes each day. How many classes does she have in 12 days?A 48B 72C 86D 96

3. Mr. Farina is 42 years old. He is 7 times older than his daughter. How old is his daughter?A 6B 7C 8D 9

4. What temperature does the thermometer show?

100

80

90

30

70

60

40

50

20

10

0

F

5. Doug read 67 pages on Tuesday, 43 pages on Wednesday, and 54 pages on Thursday. About how many pages did he read? Round your answer to the nearest ten.

6. Which is worth more, 49 pennies or 5 dimes?

Daily Spiral Review


4-5


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Topic 4 43

1. Luz had $13.12 in her purse. She gave $0.33 to her niece. How much money does she have in her purse now?A $33.00B $13.89C $12.79D $10.12

2. Megan has 8 classes each day. How many classes does she have in 12 days?A 48B 72C 86D 96

3. Mr. Farina is 42 years old. He is 7 times older than his daughter. How old is his daughter?A 6B 7C 8D 9

4. What temperature does the thermometer show?

100

80

90

30

70

60

40

50

20

10

0

F

5. Doug read 67 pages on Tuesday, 43 pages on Wednesday, and 54 pages on Thursday. About how many pages did he read? Round your answer to the nearest ten.

6. Which is worth more, 49 pennies or 5 dimes?

Daily Spiral Review


4-5

5 dimes

55°F

160




Problem of the Day

4-5

44

Topic eat 4

4-5The athletic department supplies oranges during soccer games. If each member of the team eats about 3 oranges each game and there are 48 players in all, abouthow many oranges should be supplied for 9 games?


1/31/08 11:57:19 AM

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Topic 4 45

Quick Check

4-5Q

uick Check 4

-5

5. Writing to Explain 48 people are invited to Jill’s older sister’s graduation dinner. At dinner, 8 people will sit at each table. How many tables are there? Draw a picture to explain your answer.

1. Mr. Perkins has 18 songs. He has an equal number of rockabilly songs, country songs, and rock songs. How many of each kind of song does he have?

A 21

B 20

C 6

D 3

3. Carl is planting seeds. He has 36 seeds that he wants to plant in 6 rows. Which shows the number of seeds that will go into each row?

A 360

6 66666

B 1 11111

6

C 6 6 6 6 6 6

36

D 10 1010101010

60

2. Lee has 99 golf balls. He has 9 colors of golf balls, and an equal number of each color. Which number sentence shows how many of each color he has?

A 9 ! 1 " 9

B 9 ! 9 " 1

C 99 ! 11 " 9

D 99 ! 9 " 11

4. Shauna has an art collection. She has 9 paintings that are each worth the same amount. The total amount the paintings are worth is $81. How much is each painting worth?

A $729

B $90

C $10

D $9


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Topic 4 45

Quick Check

4-5Q

uick Check 4

-5

5. Writing to Explain 48 people are invited to Jill’s older sister’s graduation dinner. At dinner, 8 people will sit at each table. How many tables are there? Draw a picture to explain your answer.

1. Mr. Perkins has 18 songs. He has an equal number of rockabilly songs, country songs, and rock songs. How many of each kind of song does he have?

A 21

B 20

C 6

D 3

3. Carl is planting seeds. He has 36 seeds that he wants to plant in 6 rows. Which shows the number of seeds that will go into each row?

A 360

6 66666

B 1 11111

6

C 6 6 6 6 6 6

36

D 10 1010101010

60

2. Lee has 99 golf balls. He has 9 colors of golf balls, and an equal number of each color. Which number sentence shows how many of each color he has?

A 9 ! 1 " 9

B 9 ! 9 " 1

C 99 ! 11 " 9

D 99 ! 9 " 11

4. Shauna has an art collection. She has 9 paintings that are each worth the same amount. The total amount the paintings are worth is $81. How much is each painting worth?

A $729

B $90

C $10

D $9



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46 Topic 4

Reteaching

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4-5

Step 1: Read/Understand

• Find the information the problem gives you. [There are 24 bottles of water and 8 backpacks.]

• Find the information the problem wants you to figure out. [The number of bottles in each backpack]

Step 2: Plan and Solve

• Draw a picture to help you visualize the problem.

24 in all

• Figure out which operation you need to use. [Division]

• Write an equation. [24 ! 8 " ?] Solve.[? " 3 bottles]

Step 3: Check

• Check your answer by using the inverse operation. [I used division to solve the problem, so I need to use multiplication to check my answer. If 8 divides into 24 three times, then 8 # 3 should equal 24. 8 # 3 " 24. The answer checks.]

46 Topic 4

Problem Solving: Draw a Picture and Write an Equation Read the question and follow the steps to solve.Bryan has 24 bottles of water. He and his friends have 8 backpacks. If he puts the same number of bottles into each backpack, how many bottles will be in each?

1. Strategy Practice Joeli has 10 quarters. She wants to buy postcards to mail to her friends. Each postcard costs 2 quarters. How many postcards can she buy?

• What does the question tell you?

• What does the question ask you to find?

• Write an equation. Solve and check.

Solve the following problems. Draw a picture to help.

2. Mack has 36 photos. His album can fit 9 photos per page. How many pages will he need to use?

3. There are 3 buses taking 96 students on a field trip. If each bus has the same number of students, how many students are on each bus?

? ? ? ? ? ? ? ?


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Reteaching

4-5Re

teac

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4-5

Step 1: Read/Understand

• Find the information the problem gives you. [There are 24 bottles of water and 8 backpacks.]

• Find the information the problem wants you to figure out. [The number of bottles in each backpack]

Step 2: Plan and Solve

• Draw a picture to help you visualize the problem.

24 in all

• Figure out which operation you need to use. [Division]

• Write an equation. [24 ! 8 " ?] Solve.[? " 3 bottles]

Step 3: Check

• Check your answer by using the inverse operation. [I used division to solve the problem, so I need to use multiplication to check my answer. If 8 divides into 24 three times, then 8 # 3 should equal 24. 8 # 3 " 24. The answer checks.]

46 Topic 4

Problem Solving: Draw a Picture and Write an Equation Read the question and follow the steps to solve.Bryan has 24 bottles of water. He and his friends have 8 backpacks. If he puts the same number of bottles into each backpack, how many bottles will be in each?

1. Strategy Practice Joeli has 10 quarters. She wants to buy postcards to mail to her friends. Each postcard costs 2 quarters. How many postcards can she buy?

• What does the question tell you?

• What does the question ask you to find?

• Write an equation. Solve and check.

Solve the following problems. Draw a picture to help.

2. Mack has 36 photos. His album can fit 9 photos per page. How many pages will he need to use?

3. There are 3 buses taking 96 students on a field trip. If each bus has the same number of students, how many students are on each bus?

? ? ? ? ? ? ? ?

4

32

Joeli has 10 quarters, each postcard costs 2 quartersHow many can she buy?

10 ! 2 " 5She can buy 5 postcards.


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Practice

4-5Practice 4

-5

Topic 4 47

Problem Solving: Draw a Picture and Write an Equation

5. Mrs. Lopez is 54 and has a daughter who is six years more than a third of her age. Draw a picture to help find which expression below shows how old Mrs. Lopez’s daughter is.

A 54 ! 6 " 3 B 54 " 3 ! 6 C 54 " 6 ! 3 D 54 ! 3 " 6

6. Writing to Explain Jillian wants to organize her CD collection into wooden crates. Each crate holds 8 CDs. Jillian has 48 CDs. How can she use a picture to figure out how many crates she needs?

1. Terrence has 16 trophies and he wants to put an equal number on 4 shelves. How many trophies will he have on each shelf?

3. Lisa has 45 megabytes of space left on her flash drive. She has 5 files that are the same size that will fill up the space. How many megabytes is each file?

2. Jody is making a sculpture of her dog. If the sculpture is 6 inches long and her dog is 7 times as long as the sculpture, how long is Jody’s dog?

4. A store is displaying boxes of a new video game in 7 rows. If the store has 49 copies of the game how many games are in each row?


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Topic 4 47

Practice

4-5Practice 4

-5

Topic 4 47

Problem Solving: Draw a Picture and Write an Equation

5. Mrs. Lopez is 54 and has a daughter who is six years more than a third of her age. Draw a picture to help find which expression below shows how old Mrs. Lopez’s daughter is.

A 54 ! 6 " 3 B 54 " 3 ! 6 C 54 " 6 ! 3 D 54 ! 3 " 6

6. Writing to Explain Jillian wants to organize her CD collection into wooden crates. Each crate holds 8 CDs. Jillian has 48 CDs. How can she use a picture to figure out how many crates she needs?

1. Terrence has 16 trophies and he wants to put an equal number on 4 shelves. How many trophies will he have on each shelf?

3. Lisa has 45 megabytes of space left on her flash drive. She has 5 files that are the same size that will fill up the space. How many megabytes is each file?

2. Jody is making a sculpture of her dog. If the sculpture is 6 inches long and her dog is 7 times as long as the sculpture, how long is Jody’s dog?

4. A store is displaying boxes of a new video game in 7 rows. If the store has 49 copies of the game how many games are in each row?

She can draw a picture of her 48 CDs, and divide the picture into groups of 8. That will tell her that she needs 6 wooden crates to hold all of her CDs.

16 ! 4 " 4 trophies

45 ! 5 " 9 megabytes

6 # 7 " 42 inches

49 ! 7 " 7 games

Trophies per shelf

16 Trophies

? ? ??

45 Megabytes

Megabytes per !le

? ? ???

? Length of Dog

Dog

Sculpture

666666

6

6

49 Games

Games in one row

?????? ?


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Enrichment

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48 Topic 4

Just the Facts Write each missing number. Then, write a related multiplication fact.

Missing Number Related Fact

1. 27 ! 3 "

2. 48 ! 6 "

3. 32 ! 8 "

4. 18 ! 3 "

5. 63 ! 9 "

Choose from the missing numbers you found above to make these sentences true.

6. There are pints in 3 quarts.

7. There are legs on an octopus.

8. There are days in a week.

9. A baseball game lasts innings.

10. A dog has legs.

Number Sense


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48 Topic 4

Just the Facts Write each missing number. Then, write a related multiplication fact.

Missing Number Related Fact

1. 27 ! 3 "

2. 48 ! 6 "

3. 32 ! 8 "

4. 18 ! 3 "

5. 63 ! 9 "

Choose from the missing numbers you found above to make these sentences true.

6. There are pints in 3 quarts.

7. There are legs on an octopus.

8. There are days in a week.

9. A baseball game lasts innings.

10. A dog has legs.

Number Sense

98467

687

94

3 ! 9 " 278 ! 6 " 484 ! 8 " 326 ! 3 " 189 ! 7 " 63


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Topic 4 49

Topic 4M

ultiple-Choice Test

1. Pauline puts 3 stickers on every letter she mails. So far, she has used 27 stickers. Which number sentence can be used to find the number of letters she has mailed so far? (4-4)

A 27 ! 3 " 9

B 27 # 3 " 24

C 27 $ 3 " 30

D 27 % 3 " 162

2. Gus picked 12 sunflowers to share equally among his 4 sisters. How can he find how many flowers to give each sister? (4-1)

A Add the number of ! owers 4 times.

B Divide the number of ! owers by 4.

C Subtract the number of ! owers from 4.

D Multiply the number of ! owers by 4.

3. Renee dives for 48 wands over the course of 12 dives. Which number sentence is NOT in the same fact family as the others? (4-2)

A 12 % 4 " 48

B 4 % 12 " 48

C 48 ! 12 " 4

D 48 ! 4 " 4

4. In which number sentence does 9 make the equation true? (4-4)

A 9 ! " 3

B 16 ! " 2

C 18 ! " 2

D 18 ! " 9

5. Four monkeys at the zoo share 20 bananas. How many bananas does each monkey get? (4-1)

20 bananas

? ? ? ?

Bananas each monkey gets

A 24

B 16

C 5

D 4

Mark the best answer.

Topic 4 Multiple-Choice

Test


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Topic 4 49

Topic 4M

ultiple-Choice Test

1. Pauline puts 3 stickers on every letter she mails. So far, she has used 27 stickers. Which number sentence can be used to find the number of letters she has mailed so far? (4-4)

A 27 ! 3 " 9

B 27 # 3 " 24

C 27 $ 3 " 30

D 27 % 3 " 162

2. Gus picked 12 sunflowers to share equally among his 4 sisters. How can he find how many flowers to give each sister? (4-1)

A Add the number of ! owers 4 times.

B Divide the number of ! owers by 4.

C Subtract the number of ! owers from 4.

D Multiply the number of ! owers by 4.

3. Renee dives for 48 wands over the course of 12 dives. Which number sentence is NOT in the same fact family as the others? (4-2)

A 12 % 4 " 48

B 4 % 12 " 48

C 48 ! 12 " 4

D 48 ! 4 " 4

4. In which number sentence does 9 make the equation true? (4-4)

A 9 ! " 3

B 16 ! " 2

C 18 ! " 2

D 18 ! " 9

5. Four monkeys at the zoo share 20 bananas. How many bananas does each monkey get? (4-1)

20 bananas

? ? ? ?

Bananas each monkey gets

A 24

B 16

C 5

D 4


Topic 4 Multiple-Choice

Test


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Topic 4Free-Response Test

Topi

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Draw pictures to help you divide.

1. Matthew has 12 baseball cards. He wants to put the same number on each of four pages. How many cards should be on each page?

2. Amanda has 18 teddy bears. She puts them into equal groups on 3 shelves. How many bears are on each shelf?

3. Mrs. Sanchez has 25 screwdrivers. She puts them in 5 equal rows. How many screwdrivers are in each row?


4. 4, 6, 24

5. 3, 9, 27

6. 5, 8, 40

Give each answer.


Name

52 Topic 4

Topic 4Free-Response Test

Topi

c 4

Free

-Res

pons

e Te

st

© P

ears

on E

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tion,

Inc.

4

Draw pictures to help you divide.

1. Matthew has 12 baseball cards. He wants to put the same number on each of four pages. How many cards should be on each page?

2. Amanda has 18 teddy bears. She puts them into equal groups on 3 shelves. How many bears are on each shelf?

3. Mrs. Sanchez has 25 screwdrivers. She puts them in 5 equal rows. How many screwdrivers are in each row?


4. 4, 6, 24

5. 3, 9, 27

6. 5, 8, 40

Give each answer.

Students should draw 4 pages with 3 cards on each page.

6

5

4 ! 6 " 246 ! 4 " 2424 # 6 " 424 # 4 " 6

3

Students should draw 3 shelves with 6 bearson each.

Students should draw 5 rows with 5 screwdrivers in each row.

3 ! 9 " 279 ! 3 " 2727 # 3 " 927 # 9 " 3

5 ! 8 " 408 ! 5 " 4040 # 5 " 840 # 8 " 5


Name

© P

ears

on E

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Inc.

4

Your class is going to work in 4 small groups to make jewelry for a craft fair. Each group will be given one of the boxes of materials below.

Box A25 strings45 round beads40 square beads

Box B18 strings72 round beads81 square beads

Box C42 strings49 round beads63 square beads

Box D24 strings36 round beads48 square beads

Each group will have a different number of students. The students in each group will share the materials equally with nothing left over. Decide how many students will be in each group. (Hint: Think about basic facts of multiplication. There is only one possible answer for each box of materials.)

1. Make and complete a table like the one below.

Group/Box Number of Students

Strings for each student

Rounds beads for each student

Square beads for each student

A

B

C

D

2. In which group did each student get the most strings?

3. In which group did each student get the fewest strings?

4. In which group did each student get the most round beads?

5. Pretend that you are in Group B. Describe the jewelry you would make with your materials.

Topic 4Performance Assessment

Topi

c 4

Pe

rform

ance

Ass

essm

ent

54 Topic 4


Name

© P

ears

on E

duca

tion,

Inc.

4

Your class is going to work in 4 small groups to make jewelry for a craft fair. Each group will be given one of the boxes of materials below.

Box A25 strings45 round beads40 square beads

Box B18 strings72 round beads81 square beads

Box C42 strings49 round beads63 square beads

Box D24 strings36 round beads48 square beads

Each group will have a different number of students. The students in each group will share the materials equally with nothing left over. Decide how many students will be in each group. (Hint: Think about basic facts of multiplication. There is only one possible answer for each box of materials.)

1. Make and complete a table like the one below.

Group/Box Number of Students

Strings for each student

Rounds beads for each student

Square beads for each student

A

B

C

D

2. In which group did each student get the most strings?

3. In which group did each student get the fewest strings?

4. In which group did each student get the most round beads?

5. Pretend that you are in Group B. Describe the jewelry you would make with your materials.

Topic 4Performance Assessment

Topi

c 4

Pe

rform

ance

Ass

essm

ent

54 Topic 4

5 5 9 8 9 2 8 9 7 6 7 9 6 4 6 8

CB

A

See below.


Name©

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Cum

ulative TestTopics 1

–4

Topic 4 55

1. Which of the following is another way to write the numeral 12,663?

A one-thousand, two hundred sixty three

B twelve thousand, sixty-three

C twelve thousand, six hundred sixty-three

D twelve thousand, six hundred sixty

2. Mike bought school supplies for $3.92. He paid with a $5 bill. How much change did he get back?

A $1.08

B $2.18

C $2.07

D $1.92

3. The table shows the number of magazines sold at a bookstore.

Magazines SoldJanuary 291February 425March 377

Which is the best estimate of the total magazines sold?

A 900

B 1,000

C 1,100

D 1,200

4. Each train has 8 wheels.

How many wheels are there altogether?

A 82 C 17

B 72 D 1

5. Ava has 14 dog treats to share equally among 7 puppies. How can she find how many treats to give each puppy?

A Add the number of treats 7 times.

B Divide the number of treats by 7.

C Subtract the number of treats from 7.

D Multiply the number of treats by 7.

6. There are 1,102 marbles in a bag. There are 3,908 marbles in a different bag. How many marbles are there in both bags?

A 41,010

B 5,010

C 5,000

D 4,000

Cumulative TestTopics 1– 4


Name©

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Edu

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Cum

ulative TestTopics 1

–4

Topic 4 55

1. Which of the following is another way to write the numeral 12,663?

A one-thousand, two hundred sixty three

B twelve thousand, sixty-three

C twelve thousand, six hundred sixty-three

D twelve thousand, six hundred sixty

2. Mike bought school supplies for $3.92. He paid with a $5 bill. How much change did he get back?

A $1.08

B $2.18

C $2.07

D $1.92

3. The table shows the number of magazines sold at a bookstore.

Magazines SoldJanuary 291February 425March 377

Which is the best estimate of the total magazines sold?

A 900

B 1,000

C 1,100

D 1,200

4. Each train has 8 wheels.

How many wheels are there altogether?

A 82 C 17

B 72 D 1

5. Ava has 14 dog treats to share equally among 7 puppies. How can she find how many treats to give each puppy?

A Add the number of treats 7 times.

B Divide the number of treats by 7.

C Subtract the number of treats from 7.

D Multiply the number of treats by 7.

6. There are 1,102 marbles in a bag. There are 3,908 marbles in a different bag. How many marbles are there in both bags?

A 41,010

B 5,010

C 5,000

D 4,000

Cumulative TestTopics 1– 4


Benchmark Test 1

Topics 1–4Benchmark Test 1

Topics 1–4Name

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1. What is the place-value position of the 4 in 754,361?

A Hundred thousands

B Ten thousands

C Thousands

D Hundreds

2. What is the value of the 7 in 278,146,359?

A 700,000,000

B 70,000,000

C 7,000,000

D 700,000

3. What is 8 ones, 6 tenths, and 4 hundredths written with a dollar sign and decimal point?

A $8.64

B $81.64

C $86.40

D $864.00

4. Look at the model below.

What is this number in standard form?

A 230,314

B 23,041

C 3,241

D 2,314

Topic 4 59


Benchmark Test 1

Topics 1–4Benchmark Test 1

Topics 1–4Name

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4


1. What is the place-value position of the 4 in 754,361?

A Hundred thousands

B Ten thousands

C Thousands

D Hundreds

2. What is the value of the 7 in 278,146,359?

A 700,000,000

B 70,000,000

C 7,000,000

D 700,000

3. What is 8 ones, 6 tenths, and 4 hundredths written with a dollar sign and decimal point?

A $8.64

B $81.64

C $86.40

D $864.00

4. Look at the model below.

What is this number in standard form?

A 230,314

B 23,041

C 3,241

D 2,314

Topic 4 59


Benc

hmar

k Re

port

68 Topic 4

Name

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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) Identify the place value and actual value of digits in whole numbers.

1, 2, 3

3

1-1, 1-2, 1-5

F7, F10, F12, H13

b) Represent numbers using models such as base 10 representations, number lines, and two-dimensional models.

4, 5, 6

3

1-1 F7

c) Compose or decompose whole quantities by place value (e.g., write whole numbers in expanded notation using place value: 342 = 300 + 40 + 2).

7, 8, 9

3

1-1, 1-2 F7, F10, F12

j) Order or compare whole numbers, decimals, or fractions.

10, 11, 12

3

1-3, 1-5 F9, F11, H13

2) Estimation

b) Make estimates appropriate to a given situation with whole numbers, fractions, or decimals by: selecting the appropriate method of estimation (e.g., rounding).

13, 14, 15

3

1-4, 2-2 F8, G7, G8, G15

3) Number and Operations

a) Add and subtract: whole numbers. 16, 17, 18

3

2-4, 2-5, 2-6

G12, G13, G16, G17, G18, G19, G20

b) Multiply whole numbers: no larger than two-digit by two-digit with paper and pencil computation.

19, 20, 21

3

3-4, 3-5, 3-6

G28, G29, G30, G31, G32, G33

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


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