chapter resources • chapter 4

CHAPTER RESOURCES • Chapter 4Divide by 1-Digit Numbers

INCLUDES • School-Home Letter

• Vocabulary Game Directions

• Daily Enrichment Activities

• Reteach Intervention for every lesson

• Chapter 4 Test

• Chapter 4 Performance Task • Answer Keys and Individual Record Forms

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ContentsChapter 4 School-Home Letter (English) .......................................................4-1

Chapter 4 School-Home Letter (Spanish) ......................................................4-2

Vocabulary Game ..........................................................................................4-3

4.1 Reteach ..................................................................................................4-5

4.1 Enrich ......................................................................................................4-6

4.2 Reteach ..................................................................................................4-7

4.2 Enrich ......................................................................................................4-8

4.3 Reteach ..................................................................................................4-9

4.3 Enrich ....................................................................................................4-10

4.4 Reteach ................................................................................................ 4-11

4.4 Enrich ....................................................................................................4-12

4.5 Reteach ................................................................................................4-13

4.5 Enrich ....................................................................................................4-14

4.6 Reteach ................................................................................................4-15

4.6 Enrich ....................................................................................................4-16

4.7 Reteach ................................................................................................4-17

4.7 Enrich ....................................................................................................4-18

4.8 Reteach ................................................................................................4-19

4.8 Enrich ....................................................................................................4-20

Table of ContentsChapter Resources© Houghton Mifflin Harcourt Publishing Company

iii

4.9 Reteach ................................................................................................4-21

4.9 Enrich ....................................................................................................4-22

4.10 Reteach ..............................................................................................4-23

4.10 Enrich ..................................................................................................4-24

4.11 Reteach ...............................................................................................4-25

4.11 Enrich ...................................................................................................4-26

4.12 Reteach ..............................................................................................4-27

4.12 Enrich ..................................................................................................4-28

Chapter 4 Test .............................................................................................4-29

Chapter 4 Performance Task .......................................................................4-35

Answer Keys ................................................................................................4-40

Individual Record Forms ..............................................................................4-47

iv Table of ContentsChapter Resources© Houghton Mifflin Harcourt Publishing Company

School-HomeSchool-Home

LetterChapter

Tips

4

STEP 2

Think of 72 as 60 + 12. Break apart the model into two rectangles to show (60 + 12) ÷ 3.

3 60 12

Find 72 ÷ 3. Whenever possible, try to use division facts and multiples of ten when breaking your rectangle into smaller rectangles. In the problem at the left, 60 4 3 is easy to find mentally.

STEP 1

Draw a rectangle to model 72 ÷ 3.

3 72

This is how we will divide using the Distributive Property.

Use the Distributive Property to Divide

Dear Family,

During the next few weeks, our math class will be learning how to model division, and use the division algorithm to divide up to three-digit dividends by 1-digit divisors. The class will learn different methods to divide, including using models, repeated subtraction, and the standard division algorithm. We will also learn to divide with remainders.

You can expect to see homework that provides practice modeling division and using the division algorithm.

Here is a sample of how your child will be taught to model division using the Distributive Property.

Distributive Property The property that states that dividing a sum by a number is the same as dividing each addend by the number and then adding the quotients

multiple A number that is the product of a given number and a counting number

remainder The amount left over when a number cannot be divided evenly

?

72 4 3 = (60 ÷ 3) + (12 ÷ 3) = 20 + 4 = 24So, 72 ÷ 3 = 24.

STEP 3Each rectangle models a division.

4-1Chapter Resources© Houghton Mifflin Harcourt Publishing Company

para la casaCartaCartaCapítulo

Pistas

4

72 ÷ 3 = (60 ÷ 3) + (12 ÷ 3) = 20 + 4 = 24Por tanto, 72 ÷ 3 = 24.

?

PASO 3

Cada rectángulo representa una división.

PASO 2

Piensa en 72 como 60 + 12.Divide el modelo en dos rectángulos para

mostrar (60 + 12) ÷ 3.

3

Halla 72 ÷ 3. En la medida de lo posible, trata de usar operaciones de división y múltiplos de diez cuando dividas el modelo en rectángulos más pequeños. En el problema anterior, 60 ÷ 3 es fácil de hallar mentalmente.

PASO 1

Dibuja un rectángulo para representar 72 ÷ 3.

3

Así es como dividiremos usando la propiedad distributiva.

Usar la propiedad distributiva para dividir

Querida familia,

Durante las próximas semanas, en la clase de matemáticas aprenderemos a representar la división y a usar el algoritmo de la división para dividir dividendos de hasta tres dígitos entre divisores de un dígito. Para ello, desarrollaremos diferentes métodos para dividir, incluyendo usar modelos, resta repetida y el algoritmo de la división estándar. También aprenderemos a dividir con residuos.

Llevaré a la casa tareas con actividades para representar la división y para usar el algoritmo de la división.

Este es un ejemplo de la manera como aprenderemos a representar la división usando la propiedad distributiva.

propiedad distributiva La propiedad que establece que dividir una suma entre un número es lo mismo que dividir cada sumando entre el número y luego sumar los cocientes

múltiplo Un número que es el producto de un número determinado y de un número positivo distinto de cero

residuo La cantidad sobrante cuando un número no se puede dividir en partes iguales

72 60 12

4-2Chapter Resources© Houghton Mifflin Harcourt Publishing Company

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Going Places with words

Pick It Word Boxcompatible numbersDistributive Propertydividenddivisormultiplepartial quotientquotientremainder

For 3 to 4 players

Materials

• 4 sets of word cards.

How to Play

1. Each player is dealt 5 cards. The remaining cards are a draw pile.

2. To take a turn, ask any player if he or she has a word that matches

one of your word cards.

3. If the player has the word, he or she gives the card to you, and you

must define the word.

• If you are correct, keep the card and put the matching pair in

front of you. Take another turn.

• If you are wrong, return the card. Your turn is over.

4. If the player does not have the word, he or she answers, “Pick it.”

Then you take a card from the draw pile.

5. If the card you draw matches one of your word cards, follow the

directions for Step 3 above. If it does not, your turn is over.

6. The game is over when one player has no cards left. The player

with the most pairs wins.

Chapter 4 196A

Chapter 4Vocabulary Game

4-3 Game DirectionsChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

150

150150

100100

30

Estimate Quotients Using Multiples

Find two numbers the quotient of 142 4 5 is between. Then estimate the quotient.

You can use multiples to estimate. A multiple of a number is the product of a number and a counting number.

Step 1 Think: What number multiplied by 5 is about 142? Since 142 is greater than 10 3 5, or 50, use counting numbers 10, 20, 30, and so on to find multiples of 5.

Step 2 Multiply 5 by multiples of 10 and make a table.

Counting Number 10 20 30 40

Multiple of 5 50 100 150 200

Step 3 Use the table to find multiples of 5 closest to 142.

20 3 5 =

30 3 5 =

142 is closest to , so 142 4 5 is about .

142 is between and .

Find two numbers the quotient is between. Then estimate the quotient.

1. 136 4 6

between and

about

2. 95 4 3

between and

about

3. 124 4 9

between and

about

4. 238 4 7

between and

about

Lesson 4.1Reteach

4-5 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

What did you do to find the missing word?

5 2 8 6 4 1 3 7

1. 342 4 8 about 50 E

2. 93 4 7 about 15 M

3. 125 4 6 about 12 I

4. 74 4 5 about 20 T

5. 275 4 4 about 70 E

6. 35 4 3 about 40 A

7. 481 4 9 about 18 T

8. 127 4 7 about 13 S

Estimating Quotients

Match each quotient with its best estimate. Then write the letter of the estimate on the appropriate blank to answer the question below.

Lesson 4.1Enrich

4-6 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

39

9 r3

2 r88

2

Use counters to find the quotient and remainder.

1. 6 q w 19

Divide. Draw a quick picture to help.

2. 3 q w 14

3. 39 4 4 4. 29 4 3

Remainders

Use counters to find the quotient and remainder.

9 q w 26

• Use 26 counters to represent the dividend, 26.

• Since you are dividing 26 by 9, draw 9 circles. Divide the 26 counters into 9 equal-sized groups.

• There are 2 counters in each circle, so the quotient is . There are 8 counters left over, so the remainder is . 9 q w 26

Divide. Draw a quick picture to help.

7 q w 66

• Use 66 counters to represent the dividend, 66.

• Since you are dividing 66 by 7, draw 7 circles. Divide 66 counters into 7 equal-sized groups.

• There are 9 counters in each circle, so the quotient is . There are 3 counters left over, so the remainder is .

7q w 66

Lesson 4.2Reteach


Name

9 r1

DIVISOR

QUOTIENT

DIVIDEND

REMAINDER

9. Use Exercises 1– 8 as models to write your own division number riddle.

Riddle Time

Use the clues to solve the riddles below. You will need to know the name for each part of a division equation. Use the division problem at the right as a reminder.

1. My divisor is 5. I am greater than 4 3 5. I am less than 5 3 5. My remainder is 1. What dividend am I?

2. My divisor is 9. I am greater than 7 3 9. I am less than 8 3 9. My remainder is 7. What dividend am I?

3. My divisor is 8. I am less than 30. I am greater than 3 3 8. My remainder is 5. What dividend am I?

4. My divisor is 6. I am less than 60. I am greater than 8 3 6. I have no remainder. What dividend am I?

5. My dividend is 50. My remainder is 1. I am an odd number. What divisor am I?

6. My dividend is 8 times as large as my divisor. I am an even number less than 15. What quotient am I?

7. My remainder is 8. My dividend is 80. I am a 1- digit number. What divisor am I?

8. My dividend is 24. I am 2 more than my quotient. I have no remainder. What divisor am I?

Lesson 4.2Enrich

4 ) ‾ 37


Name

4 _ 8 remainder divisor

8

1. There are 35 students going to the zoo.

Each van can hold 6 students. How

many vans are needed?

2. Sue has 55 inches of ribbon. She wants

to cut the ribbon into 6 equal pieces.

How long will each piece be?

7 4 _ 8

4

7

7 r4

7 r4

7 r4

7 r4

Interpret the Remainder

When you solve a division problem with a remainder, the way you interpret the remainder depends on the situation and the question.

Way 1: Write the remainder as a fraction. Callie has a board that is 60 inches long. She wants to cut 8 shelves of equal length from the board and use the entire board. How long will each shelf be?

Divide. 60 4 8

The remainder, 4 inches, can be divided into 8 equal parts.

Write the remainder as a fraction.

Each shelf will be inches long.

Way 2: Drop the remainder. Callie has 60 beads. She wants to make 8 identical bracelets and use as many beads as possible on each bracelet. How many beads will be on each bracelet?

Divide. 60 4 8

The remainder is the number of beads left over. Those beads will not be used. Drop the remainder.

Callie will use beads on each bracelet.

Way 3: Add 1 to the quotient. Callie has 60 beads. She wants to put 8 beads in each container. How many containers will she need?

Divide. 60 4 8

The answer shows that Callie can fill 7 containers but will have 4 beads left over. She will need 1 more container for the 4 leftover beads. Add 1 to the quotient. Callie will need containers.

Way 4: Use only the remainder. Callie has 60 stickers. She wants to give an equal number of stickers to 8 friends. She will give the leftover stickers to her sister. How many stickers will Callie give to her sister?

Divide. 60 4 8

The remainder is the number of stickers left over. Use the remainder as the answer. Callie will give her sister stickers.

Lesson 4.3Reteach


Name

Remainder Questions

Read each scenario. Use the scenario to write questions that would have the given answers.

1. There are 52 students in the fourth grade. Each minivan can hold

6 students. The students are going on a field trip.

8

9

4

2. Six friends are going on a hike. Becky made 64 ounces of trail mix.

10 4 __ 6

4

3. Why is it important to read division problems

carefully before giving the answer?

Lesson 4.3Enrich


Name

Use basic facts and place value to find the quotient.

1. 280 4 4

What division fact can you use?

280 = tens

28 tens 4 4 5 tens

280 4 4 5

2. 1,800 4 9

What division fact can you use?

1,800 5 hundreds

18 hundreds 4 9 5 hundreds

1,800 4 9 5

3. 560 4 7 5 4. 180 4 6 5

5. 1,500 4 5 5 6. 3,200 4 4 5

8

24

24 4 3

80

80

80

8

24

Divide Tens, Hundreds, and Thousands

You can use base-ten blocks, place value, and basic facts to divide.

Divide. 240 4 3

Use base-ten blocks. Use place value.

Step 1 Draw a quick picture to show 240.

Step 1 Identify the basic fact to use.

Use .

Step 2 You cannot divide 2 hundreds into 3 equal groups. Rename 2 hundreds as tens.

240 5 tens

Step 2 Use place value to rewrite 240 as tens.

240 5 tens

Step 3 Separate the tens into 3 equal groups to divide.

There are 3 groups of tens.Write the answer.

240 4 3 5

Step 3 Divide.

24 tens 4 3 5 tens

5

Write the answer.

240 4 3 5

Lesson 4.4Reteach


Name

7. Stretch Your Thinking Find the sum of the six answers to the riddles. Write your own riddle so that the answer is this sum.

1. When divided by 5, I am 60. When divided by 6, I am 50. What number am I?






Dividend Riddles

Solve each riddle.

Lesson 4.4Enrich


Name

Use compatible numbers to estimate the quotient.

1. 3 q w 252

2. 6 q w 546

3. 4 q w 2,545

4. 5 q w 314

5. 2 q w 1,578

6. 8 q w 289

216 2 180 5 36 240 2 216 5 24

2124

4030

18

180 4 6 5 30 240 4 6 5 40

40

Estimate Quotients Using Compatible Numbers

6 12 18 24 30 36 42 48 54

Compatible numbers are numbers that are easy to compute mentally. In division, one compatible number divides evenly into the other. Think of the multiples of a number to help you find compatible numbers.

Estimate. 6 q w 216

Step 1 Think of these multiples of 6:

Find multiples that are close to the first 2 digits of the dividend. tens and tens are both close to tens . You can use

either or both numbers to estimate the quotient.

Step 2 Estimate using compatible numbers.

216 4 6 216 4 6

So, 216 4 6 is between and .

Step 3 Decide whether the estimate is closer to 30 or 40.

216 is closer to 240, so use as the estimate.

Lesson 4.5Reteach


Estimate A B C

1. 70

2. 80

3. 90

4. 40

5. 100

6. 400

7. 200

8. 700

9. 300

10. 120

11. 50

12. 20

13. 900

14. 150

15. 60

408 � 7

332 � 5

410 � 2

2,384 � 5

2,663 � 5

628 � 8

115 � 4

8,250 � 9

256 � 6

3 251

9 350

4 1,584

2 532

8 274

6 909

342 � 5

423 � 8

593 � 6

3,006 � 8

221 � 7

5,740 � 8

189 � 3

8 545

8 628

4 767

4 198

3 296

5 1,126

6 3,411

8 1,040

816 � 9

477 � 7

538 � 9

712 � 3

1,742 � 9

483 � 4

317 � 5

2,992 � 4

182 � 5

9 780

4 849

2 289

6 141

7 5,026

7 881

Name

16. What strategy did you use to help you choose the best match?

17. Stretch Your Thinking Create three of your own division expressions as estimates for Exercise 15. Circle the choice that has the best estimate.

Make the Best Estimate

One of the division expressions in columns A, B, and C is the best match for the Estimate column. Circle the best choice for each.

Lesson 4.5Enrich


Name

(60 4 6) (18 4 6)

3

13

10

Lesson 4.6Reteach

Division and the Distributive Property

Divide. 78 4 6

Use the Distributive Property and quick pictures to break apart numbers to make them easier to divide.

Step 1 Draw a quick picture to show 78.

Step 2 Think about how to break apart 78. You know 6 tens 4 6 5 10, so use 78 5 60 1 18. Draw a quick picture to show 6 tens and 18 ones.

Step 3 Draw circles to show 6 tens 4 6 and 18 ones 4 6. Your drawing shows the use of the Distributive Property. 78 4 6 5 1

Step 4 Add the quotients to find 78 4 6.

78 4 6 5 (60 4 6) 1 (18 4 6)

5 1

5

Use quick pictures to model the quotient.

1. 84 ÷ 4 = 2. 54 ÷ 3 = 3. 68 ÷ 2 =

4. 65 ÷ 5 = 5. 96 ÷ 8 = 6. 90 ÷ 6 =


Name

True or Not True?

The Associative Property of Multiplication states that when you change the grouping of factors, the product remains the same: (3 3 4) 3 5 5 12 3 5, or 60, and 3 3 (4 3 5) 5 3 3 20, or 60.

Is the Associative Property also true for division? Complete Exercises 1–4.

1. (8 4 4) 4 1 5 and 8 4 (4 4 1) 5

2. (10 4 2) 4 1 5 and 10 4 (2 4 1) 5

3. When you changed the grouping in Exercises 1 and 2,

what happened to the quotient?

4. Now use the numbers 2, 4, and 8 to write and evaluate

a division expression. Then change the grouping of the

numbers and evaluate the new expression.

5. When you changed the grouping in Exercise 3, what

happened to the quotient?

6. Is the Associative Property true for division?

Explain.

Lesson 4.6Enrich


Name

6 r3

Use repeated subtraction to divide.

1. 30 4 4 2. 24 4 5 3. 47 4 7

4 q w 27

24 ___ 23 1

24 ___ 19 1

24 ___ 15 1

24 ___ 11 1

24 ___ 7 1

24 ___ 3 1

Divide Using Repeated Subtraction

You can use repeated subtraction to divide. Use repeated subtraction to solve the problem.

Nestor has 27 shells to make bracelets. He needs 4 shells for each bracelet. How many bracelets can he make?

Divide. 27 4 4

Write 4 q w 27 .

Step 1

Subtract the divisor until the remainder is less than the divisor. Record a 1 each time you subtract. So, Nestor can make 6 bracelets. He will have 3 shells left.

Step 2

Count the number of times you subtracted the divisor, 4.

4 is subtracted six times with 3 left.

27 4 4

Lesson 4.7Reteach


Name

1. There are 51 fourth-graders going on

a field trip. One group of 16 students

rides in one van. A second group of

16 students rides in a second van. A

third group of 16 students rides in a

third van. The 3 students who are left

ride in a car.

Find the quotient. 51 4 8

2. Kate bakes 144 cookies for a bake

sale. She places 3 cookies in one

bag, 3 cookies in a second bag, and

so on, until there are no cookies left.

She has 48 bags of 3 cookies each.

Find the quotient. 144 4 9

3. Describe how the given situations helped you solve

the division problems.

Subtraction Situations

Each situation below involves repeated subtraction. Read each situation. Use the given information to solve the related division problem. Explain your reasoning.

Lesson 4.7Enrich


Name

3 12320100

4 q w 492 2 400

_

92 2 80

_

12 2 12 _

0

80 12400

100

4 _4924002

92

80 12400

100 20

4 _9280212

80 12400

100 20 3

4 _12122

0

100 3 100

100 3

3

3 1

3 q w 6 5 7

Partial quotients

100 3 4 100

20 3 4 20

3 3 4 1 3 123

Divide Using Partial Quotients

You can use partial quotients to divide.

Divide. 492 4 4

Step 1 Subtract greater multiples of the divisor. Repeat if needed.

Step 2 Subtract lesser multiples of the divisor. Repeat until the remaining number is less than the divisor.

Step 3 Add the partial quotients.

Use rectangular models to record partial quotients.

1 1 5

Divide. Use partial quotients. Divide. Use rectangular models to record the partial quotients.

1. 2. 852 4 6 5

Lesson 4.8Reteach


Name

#5#3#2

458 41 129 236 625

243 284 29 149 355 163

813 152 85 120 339 925

2. Could any letter be delivered to all three mailboxes? Explain your reasoning.

Special Delivery

Mailbox #2 only accepts letters with numbers that can be evenly divided by 2.Mailbox #3 only accepts letters with numbers that can be evenly divided by 3.Mailbox #5 only accepts letters with numbers that can be evenly divided by 5.

1. Deliver the letters by writing each number below the correctmailbox. Some letters will be undeliverable.

Lesson 4.8Enrich


Name

1 6

1

16 r1

Model Division with Regrouping

You can use base-ten blocks to model division with regrouping.

Use base-ten blocks to find the quotient 65 4 4.

Step 1 Show 65 with base-ten blocks.

Step 2 Draw 4 circles to represent dividing 65 into 4 equal groups. Share the tens equally among the 4 groups.

Step 3 Regroup leftover tens as ones.

Step 4 Share the ones equally among the 4 groups.

There are ten(s) and one(s) in

each group with left over.

So, the quotient is .

Divide. Use base-ten blocks.

1. 37 4 2 2. 74 4 3 3. 66 4 5

Lesson 4.9Reteach


Name

KEY: A D E L O T U V W

13 23 r1 28 r1 17 r4 23 19 r1 17 r2 16 r2 12 r4

Riddle: The more I dry, the wetter I get. What am I?

1 2 3 4 5 6

7. Stretch Your Thinking Make up a new division problem for Exercise 2 so that when using the quotient and the key, the result will be the answer to this riddle: “What is the difference between SHELL and SHALL?”

1. 78 4 6 2. 58 4 3 3. 92 4 4

4. 88 4 7 5. 57 4 2 6. 89 4 5

Division Drying

To find the answer to the riddle, complete each division. Then use the KEY to find the answer to the riddle.

Lesson 4.9Enrich


Name

3 q w 763

2 6

__

16 2 15

__

13 2 12

__

1

3 q w 763

2 6

__

16 2 15

_

1

25

25 254

2 3 q w 763

2 6

_

16

3 q w 763 254 r1

3 q w 763

2 6

__

16 2 15

_

13

2 3 q w 763

2 6

_

1

Divide.

1. 2 q w 531 2. 4 q w 628 3. 9 q w 349 4. 7 q w 794

Place the First Digit

Divide. 763 4 3 5

Step 1 Estimate. Then divide the hundreds.

Think: 3 3 1 hundred 5 3 hundreds 3 3 2 hundreds 5 6 hundreds 3 3 3 hundreds 5 9 hundreds

3 3 3 hundreds is too large. Use 2 hundreds as an estimate.

Divide 7 hundreds by 3.

Multiply. 3 3 2 hundreds

Subtract.

Step 2 Bring down the tens digit. Then divide the tens. Bring down

the 6.

Divide 16 tens by 3.

Multiply. 3 3 5 tens Subtract.

Step 3 Bring down the ones digit. Then divide the ones.

Bring down the 3.

Divide 13 ones by 3.

Multiply. 3 3 4 ones Subtract.

Step 4 Check to make sure that the remainder is less than the divisor. Write the answer.

1 , 3

Lesson 4.10Reteach


Name

How Many Digits?

Circle how many digits will be in the quotient. Find the quotient to check that you are correct. Then, look at the riddle below. To answer the riddle, write the letter of the number you circled on the line above the exercise number.

What can run but cannot walk?

7 2 5 3 8 1 6 4

1. 346 4 2 5

1 5 P 2 5 R 3 5 N

2. 108 4 9 5

1 5 T 2 5 A 3 5 C

3. 652 4 4 5

1 5 L 2 5 I 3 5 H

4. 210 4 5 5

1 5 R 2 5 S 3 5 N

5. 120 4 8 5

1 5 S 2 5 C 3 5 W

6. 162 4 6 5

1 5 G 2 5 E 3 5 J

7. 420 4 7 5

1 5 C 2 5 M 3 5 E

8. 444 4 4 =

1 5 K 2 5 E 3 5 I

Lesson 4.10Enrich


Name

127 3 6

_

762 1 4

_

766

12 6 q w 766

2 6

__

16 212

_

46

127 6 q w 766

2 6

_

16 212

_

46 2 42 _

4

1 6 q w 766

2 6

_

16

12

6 q w 766 2 6 ______

16

212 ______ 4

127 r4 6 q w 766

Divide and check.

1. 4 q w 868 2. 2 q w 657 3. 7 q w 8,473

Divide by 1-Digit Numbers

Divide. 766 4 6 5

Step 1 Use place value to place the first digit.Think: 7 hundreds can be shared among 6 groups without regrouping.

1 6 q w 766

_

Step 2 Bring down the tens digit. Then divide the tens. Bring down

the 6.

Divide 16 tens by 6.

Multiply. 6 3 2 tens Subtract.

Step 3 Bring down the ones digit. Then divide the ones.

Bring down the 6.

Divide 46 ones by 6.

Multiply. 6 3 7 ones Subtract.

Step 4 Check to make sure that the remainder is less than the divisor. Write the answer.

4 , 6

Step 5 Use multiplication and addition to check your answer.

Lesson 4.11Reteach

12 127


Name

What flies around all day but never goes anywhere?

1 2 3 4 5 6 7 8

G F E L A N S T

What Is Left Over ?

Find the “leftover” in each situation. Then use the code key to see

which letters match each of your answers. Write the letters in order

of the exercises to find the answer to the riddle.

1. Jude puts 6 lemons in each bag. If he has 170 lemons,how many will be left over?

2. Selena has a piece of ribbon that is 130 inches long. If shewants to make bracelets that are 9 inches long, how many inches of ribbon will be left over?

3. Justin prepares 229 hamburgers for a company picnic. Ifbuns come in packages of 8, how many will be left over?

4. Mrs. Bradley has $204 to divide equally between her 7 grandchildren. How many dollars will she have left over?

5. Mr. White has 115 tulips for bouquets. He puts 9 tulips ineach bouquet. How many tulips will be left over?

Lesson 4.11Enrich


39 39 39 39

156

156

72 84

Name

4

4

39

students

84

72 and 84

72

1. Miranda has 180 beads for making jewelry. She buys 240 more beads. She wants to store the beads in a case with 6 sections. She wants to put the same number of beads in each section. How many beads should Miranda put in each section?

2. All 203 students at Polk School eat lunch at the same time. One day 19 students were absent. If 8 students sit at each table in the lunchroom, how many tables were used that day at lunch?

Problem Solving • Multistep Division Problems

There are 72 third graders and 84 fourth graders going on a field trip. An equal number of students will ride on each of 4 buses. How many students will ride on each bus?

Read the Problem Solve the Problem

What do I need to find?

I need to find the number of who will ride on each bus.

I can model the number of students in all

using a bar diagram.

I can model the number of buses and

divide to find the number of students on

each bus.

What information do I need to use?

There are third graders and

fourth graders. There will be

buses.

How will I use the information?

I will make a bar diagram for each step. I

will add to find the total number

of students. I will divide by to find how

many students will ride on each bus.

So, students will ride on each bus.

Lesson 4.12Reteach


Name

It’s a Riddle!

Solve each problem. Look for the answer in the riddle below and write the letter of the problem on the line. Not all letters will be used.

Which city has no people?

5 7 5 16 30 108 175 16 175 30 17

C Maria takes 24 photos at the circus and 72 photos on her vacation. If each page in her scrapbook can hold 6 photos, how many pages can Maria fill?

I Carmen and Wayne sell 25 birdhouses at a craft fair. They share the money equally. If each birdhouse costs $14, how much money will Carmen and Wayne each receive?

R José uses 3 flowers for each corsage he makes. He has orders for 18 corsages each from two different stores. How many flowers will he need?

L Mr. Davis sells sleeping bags. He has 30 red sleeping bags and 26 green sleeping bags to put on shelves. Each shelf can hold 8 sleeping bags. How many shelves can he fill?

Y Taren makes 62 chocolate chip cookies and 74 oatmeal cookies. If she places 8 cookies on a plate for the bake sale, how many plates will Taren need?

T Keisha bought 10 bags of apples. There are 15 apples in each bag. If Keisha repacks the apples into 5 bags, how many apples will be in each bag?

N Chan and his two sisters make and sell jewelry. They sell each piece of jewelry for $9 and agree to share the money equally. If they sell 38 pieces of jewelry in all, how much money will each person receive?

E Linh orders 16 blueberry muffins and 24 cranberry muffins from a bakery. The bakery places 8 muffins in each package. How many packages will Linh have to pick up?

Lesson 4.12Enrich


Chapter 4 TestPage 1

1. Kelli and her family went to the beach for vacation. They

drove 293 miles in 7 hours to get there. If they drove the

same number of miles each hour, about how many miles

did they drive each hour? Select the numbers the quotient

is between.

A B C D E

40 50 60 70 80

2. Between which two numbers is the quotient of 88 ÷ 5?

Write the numbers in the boxes.

5 10 15 20 25

The quotient is between and .

3. Look at the model. What division does it show?

÷ r

4. For 4a–4d, choose Yes or No to tell whether the division

sentence has a remainder.

4a. 32 ÷ 4 Yes No

4b. 41 ÷ 3 Yes No

4c. 65 ÷ 4 Yes No

4d. 36 ÷ 9 Yes No

Chapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

Chapter 4 Test4-29


5. The harbormaster decides how many trips the ferry needs to

make for 37 cars. The ferry can carry 8 cars at a time. What is

the best way to interpret the remainder of 37 ÷ 8 so that all

cars can cross the harbor?

6. Kira makes 93 greeting cards for a craft fair. She sells the

cards in packs of 5. How many full packs of greeting cards

does Kira make?

packs

7. A kennel is moving 160 dogs to a new facility. Each dog

has its own crate. The facility manager rents 17 trucks. Each

truck holds 9 dogs in their crates.

Part A

Write a division problem that can be used to find the number

of trucks needed to carry the dogs in their crates. Then solve.

Part B

What does the remainder mean in the context of the problem?

Part C

How can you use your answer to determine if the facility manager

rented enough trucks? Explain.

8. Solve.

4,500 ÷ 9 =


Name

Chapter 4 Test4-30


9. Which quotients are equal to 600? Mark all that apply.

A 1,200 ÷ 2 C 2,400 ÷ 4 E 420 ÷ 7

B 180 ÷ 3 D 3,000 ÷ 5 F 6,000 ÷ 3

10. Liz estimated 228 ÷ 7 to be between 30 and 40. Which basic

facts did she use to help her estimate? Mark all that apply.

A 20 ÷ 5 B 21 ÷ 7 C 28 ÷ 7 D 30 ÷ 5

11. Amanda and her four sisters divided 1,021 stickers equally.

About how many stickers did each girl receive?

12. For numbers 12a–12d, choose Yes or No to show how to use

the Distributive Property to break apart the dividend to find

the quotient 128 ÷ 4.

12a. (100 ÷ 4) + (28 ÷ 4) Yes No

12b. (103 ÷ 4) + (25 ÷ 4) Yes No

12c. (64 ÷ 4) + (64 ÷ 4) Yes No

12d. (12 ÷ 4) + (28 ÷ 4) Yes No

13. There are 48 people waiting for a fishing tour. Each boat

holds 12 people. Rodney used the work below to find the

number of boats needed. Explain how Rodney’s work can be

used to find the number of boats needed.

12 q w 48 −12

_

36 −12

_

24 −12

_

12 −12

_

0


Name

Chapter 4 Test4-31


14. A science show brings along everything it needs for a show

in big trucks.

Part A

The science show sets up chairs in rows with 8 seats in each

row. How many rows will need to be set up if 456 people are

expected to attend the show?

rows

Part B

Can the rows be divided into a number of equal sections?

Explain how you found your answer.

Part C

The lizards in the show eat about 250 crickets per week.

About how many crickets do the lizards eat each day?

Explain.

15. Sylvia plans to place 617 stamps in an album. Each page of

the album holds 5 stamps. She uses division to find out how

many full pages she will have. In what place is the first digit

of the quotient?


Name

Chapter 4 Test4-32


16. Which model matches each expression? Write the letter in the box next to the model.

180900

12040 800

18060 1200

120600

17. Diego bought 488 frozen yogurt bars in 4 different flavors for a party. He bought the same number of each flavor. How many of each flavor did he buy?

bars of each flavor

18. Use partial quotients. Fill in the blanks.

100 × 7

7 × 7 +

7 q w 749 –

–

A 120 ÷ 40 B 180 ÷ 90 C 120 ÷ 60 D 180 ÷ 60


Name

Chapter 4 Test4-33


19. Ethan needs to divide these base-ten blocks into 3 equal groups.

Draw or describe the model to show how many are in each

group.

20. Jake wants to distribute 543 marbles equally among 7 of his

friends. In which place is the first digit of the quotient? Choose

the word that makes the sentence true.

The first digit of the quotient is in the

ones

tens

hundreds

thousands

place.

21. Chad bought 8 dozen note pads for his office. The note pads

were divided equally into 6 boxes. How many note pads are in

each box?

note pads

22. There are 126 seats in a meeting room. There are 9 seats in

each row. There are 90 people seated, filling up full rows of

seats. How many rows are empty?

rows


Name

4-34 Chapter 4 Test

Name Chapter 4

Helping Hands

Matt, Carlos, and Tavon are helping make repairs to their school building during the summer. Their math teacher, Mr. Johnson, is in charge of the repairs and makes sure the boys get some extra math practice while they help out.

1. A delivery of lumber arrives at the school. Mr. Johnson asks Carlos to show the deliverymen to the classroom that has a number equal to the quotient of 5,286 4 3. How many digits will the classroom number have? Explain your mathematical reasoning.

2. Mr. Johnson and the boys are helping paint the school. Mr. Johnson asks Tavon to follow these instructions.

Divide 2,430 by 9. Then divide that quotient by 6. Take two cans of paint to the classroom that has the same number as the final quotient.

Choose two different methods to find the answer. Explain your choices and then find the number of the classroom where Tavon should take the cans of paint.

Name

4-35 Chapter 4 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company

3. Mr. Johnson asked Carlos to take garbage bags to another floor using these instructions.

Find how many 7s are in 1,762. The remainder is the number of garbage bags you will take. The quotient is the classroom number.

How can Carlos use partial products to find the information he needs? Show and explain your mathematical thinking.

4. Matt had instructions to take a box of nails to a classroom that has a number equal to the remainder of the division 2,960 ÷ 9. Matt took the nails to classroom 17. Without performing calculations, tell whether Matt was correct. Explain your mathematical thinking.


Chapter 4Divide by 1-Digit Numbers

Helping HandsCOMMON CORE STANDARDS

4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MP2 Reason abstractly and quantitatively.

MP4 Model with mathematics.

PURPOSE To assess the ability to divide up to four-digit numbers by one-digit numbers

TIME 25–30 minutes

GROUPING Individuals

MATERIALS• Performance Task, paper, pencil

• Grid paper, base-ten blocks (optional)

PREPARATION HINTS • Review basic division with students before assigning the task.

• Review partial products with students before assigning the task.

• Review vocabulary, including quotient, remainder, distributive.

IMPLEMENTATION NOTES • Read the task aloud to students and make sure that all students have a clear understanding

of the task.

• Students may use manipulatives to complete the task.

• Allow students as much paper as they need to complete the task.

• Allow as much time as students need to complete the task.

• Students must complete the task individually, without collaboration.

• Collect all student work when the task is complete.


TASK SUMMARYStudents reason about the number of digits in a quotient. They divide using two different modeling methods. They use partial products to find a quotient. They explain why a given remainder is correct or incorrect.

REPRESENTATION In this task, teachers can…

• Help students break apart the individual tasks presented in the problems to list the steps in the correct order.

• Provide definitions for key words on the board or on a word wall.

ACTION and EXPRESSION In this task, teachers can…

• Provide options for students by providing grid paper and/or base-ten blocks as they work through the task.

• Encourage students to restate the problem in their own words.

ENGAGEMENT In this task, teachers can…

• Encourage abstract and quantitative thinking by posing pertinent questions if students hesitate during their work.

• Encourage perseverance by providing timely and specific feedback.

EXPECTED STUDENT OUTCOMES• Complete the task within the time allowed

• Reflect engagement in a productive struggle

• Find a quotient and/or a remainder to solve problems

SCORING Use the associated Rubric to evaluate each student’s work.


Performance Task Rubric

HELPING HANDS

A level 3 response • Demonstrates that the student has reasoned abstractly and quantitatively

• Shows application of the principles of division to solving word problems

• Shows significant comprehension of the meaning and application of division

• Offers a complete and correctly completed task, demonstrating full understanding

A level 2 response • Demonstrates that the student has reasoned abstractly and quantitatively

• Shows application of the principles of division to solving word problems

• Shows comprehension of the meaning and application of division

• Offers a full and mostly correct completed task

• May include a computational error within a correct procedure

A level 1 response • Shows that the student has made a good effort to reason abstractly or quantitatively

• Demonstrates an attempt to apply the principles of division to solve word problems

• Shows some comprehension of the meaning of division, but may lack an understanding of the application

• Demonstrates procedural uncertainty that leads to computational errors

• May show reliance on repeated subtraction to solve the problems

A level 0 response • Shows little evidence that the student has reasoned abstractly or quantitatively

• Reflects a lack of understanding of the principles of division

• Shows little evidence of adequately addresssing the components of the task


Chap

ter 4

Tes

tPa

ge 2

5

. The h

arb

orm

ast

er

decid

es

how

many

trip

s th

e f

err

y needs

to

make f

or

37

cars

. The f

err

y can c

arr

y 8

cars

at

a t

ime. W

hat

is

the b

est

way

to inte

rpre

t th

e r

em

ain

der

of

37

÷ 8

so t

hat

all

cars

can c

ross

the h

arb

or?

Incr

ease

th

e q

uo

tien

t by

1.

6

. K

ira m

akes

93

gre

eting c

ard

s fo

r a c

raft

fair

. She s

ells

the

card

s in

packs

of

5. H

ow

many

full

packs

of

gre

eting c

ard

s

does

Kir

a m

ake?

18 p

acks

7

. A

kennel is

movi

ng 1

60

dogs

to a

new

facili

ty. Each d

og

has

its

ow

n c

rate

. The f

acili

ty m

anager

rents

17

tru

cks.

Each

truck h

old

s 9

dogs

in t

heir

cra

tes.

Par

t A

Wri

te a

div

isio

n p

roble

m t

hat

can b

e u

sed t

o f

ind t

he n

um

ber

of

trucks

needed t

o c

arr

y th

e d

ogs

in t

heir

cra

tes.

Then s

olv

e.

160 ÷

9 =

17

r7

Par

t B

What

does

the r

em

ain

der

mean in t

he c

onte

xt o

f th

e p

roble

m?

A r

emai

nd

er o

f 7

mea

ns

that

7 d

og

s an

d t

hei

r cr

ates

d

o n

ot

fit in

th

e 17

tru

cks.

Par

t C

Ho

w c

an

you

use

you

r an

swer

to d

ete

rmin

e if

the f

acili

ty m

an

ag

er

ren

ted

en

ou

gh

tru

cks?

Exp

lain

.

Hav

ing

a r

emai

nd

er le

ts m

e kn

ow

th

at n

ot

all o

f th

e d

og

s an

d t

hei

r cr

ates

will

fit

in t

he

17 t

ruck

s. T

he

faci

lity

man

ger

did

no

t re

nt

eno

ug

h t

ruck

s.

8

. Solv

e.

4,5

00

÷ 9

=

500

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 4

Tes

t4-30

Chap

ter 4

Tes

tPa

ge 1

1

. K

elli

an

d h

er

fam

ily w

en

t to

th

e b

each

for

vacation

. Th

ey

dro

ve 2

93

mile

s in

7 h

ou

rs t

o g

et

there

. If

th

ey

dro

ve t

he

sam

e n

um

ber

of

mile

s each

hou

r, a

bou

t h

ow

man

y m

iles

did

th

ey

dri

ve e

ach

hou

r? S

ele

ct

the n

um

bers

th

e q

uotien

t

is b

etw

een

.

A

B

C

D

E

40

5

0

60

7

0

80

2

. B

etw

een

wh

ich

tw

o n

um

bers

is

the q

uotien

t of

88

÷ 5

?

Wri

te t

he n

um

bers

in

th

e b

oxe

s.

51

01

52

02

5

Th

e q

uotien

t is

betw

een

15

an

d

20.

3

. Look a

t th

e m

od

el.

Wh

at

div

isio

n d

oes

it s

how

?

20 ÷

3

6 r

2

4

. For

4a–4

d, ch

oose

Yes

or

No t

o t

ell

wh

eth

er

the d

ivis

ion

sen

ten

ce h

as

a r

em

ain

der.

4a.

32

÷ 4

Y

es

N

o

4b.

41

÷ 3

Y

es

N

o

4c.

65

÷ 4

Y

es

N

o

4d.

36

÷ 9

Y

es

N

o

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 4

Tes

t4-29

4-40 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company

Chap

ter 4

Tes

tPa

ge 4

14

. A

scie

nce s

how

bri

ng

s alo

ng

eve

ryth

ing

it

need

s fo

r a s

how

in b

ig t

rucks.

Par

t A

Th

e s

cie

nce s

how

sets

up

ch

air

s in

row

s w

ith

8 s

eats

in

each

row

. H

ow

man

y ro

ws

will

need

to b

e s

et

up

if

45

6 p

eop

le a

re

exp

ecte

d t

o a

tten

d t

he s

how

?

57 r

ow

s

Par

t B

Can

th

e r

ow

s b

e d

ivid

ed

in

to a

nu

mb

er

of

eq

ual se

ction

s?

Exp

lain

how

you

fou

nd

you

r an

swer.

Yes;

Po

ssib

le e

xpla

nat

ion

: I d

ivid

ed 4

56 b

y 8

to fi

nd

th

ere

will

nee

d to

be

57 r

ow

s. S

ince

57

can

be

div

ided

by

3 w

ith

no

rem

ain

der

, th

e ro

ws

can

be

arra

ng

ed in

to

3 eq

ual

sec

tio

ns.

Par

t C

Th

e liz

ard

s in

th

e s

how

eat

ab

ou

t 2

50

cri

ckets

per

week.

Ab

ou

t h

ow

man

y cri

ckets

do t

he liz

ard

s eat

each

day?

Exp

lain

.

Po

ssib

le a

nsw

er: a

bo

ut

40 c

rick

ets;

I m

ult

iplie

d 7

by

mu

ltip

les

of

10. 1

0 ×

7 =

70,

20

× 7

= 1

40, 3

0 ×

7 =

21

0, 4

0 ×

7 =

280

. 250

is c

lose

st to

280

, so

th

e b

est

esti

mat

e is

ab

ou

t 40

cri

cket

s p

er d

ay.

15

. S

ylvi

a p

lan

s to

pla

ce 6

17

sta

mp

s in

an

alb

um

. Each

pag

e o

f

the a

lbu

m h

old

s 5

sta

mp

s. S

he u

ses

div

isio

n t

o f

ind

ou

t h

ow

man

y fu

ll p

ag

es

she w

ill h

ave

. In

wh

at

pla

ce is

the f

irst

dig

it

of

the q

uotien

t?

hu

nd

red

s

Chap

ter R

esou

rces

© H

ough

ton

Miff

lin H

arco

urt P

ublis

hing

Com

pany

Nam

e

Chap

ter 4

Tes

t4-32

Chap

ter 4

Tes

tPa

ge 3

9

. W

hic

h q

uotien

ts a

re e

qu

al to

60

0?

Mark

all

that

ap

ply

.

A

1,2

00

÷ 2

C

2

,40

0 ÷

4

E

42

0 ÷

7

B

18

0 ÷

3

D

3,0

00

÷ 5

F

6

,00

0 ÷

3

10

. Liz

est

imate

d 2

28

÷ 7

to b

e b

etw

een

30

an

d 4

0. W

hic

h b

asi

c

facts

did

sh

e u

se t

o h

elp

her

est

imate

? M

ark

all

that

ap

ply

.

A 2

0 ÷

5

B 2

1 ÷

7

C 2

8 ÷

7

D 3

0 ÷

5

11

. A

man

da a

nd

her

fou

r si

sters

div

ided

1,0

21

stickers

eq

ually

.

Ab

ou

t h

ow

man

y st

ickers

did

each

gir

l re

ceiv

e?

Po

ssib

le a

nsw

er: a

bo

ut

200

stic

kers

12

. For

nu

mb

ers

12

a–1

2d

, ch

oose

Yes

or

No t

o s

how

how

to u

se

the D

istr

ibu

tive

Pro

pert

y to

bre

ak a

part

th

e d

ivid

en

d t

o f

ind

the q

uotien

t 1

28

÷ 4

.

12a.

(1

00

÷ 4

) +

(2

8 ÷

4)

Y

es

N

o

12b.

(1

03

÷ 4

) +

(2

5 ÷

4)

Y

es

N

o

12c.

(6

4 ÷

4) +

(6

4 ÷

4)

Y

es

N

o

12d.

(1

2 ÷

4) +

(2

8 ÷

4)

Y

es

N

o

13

. Th

ere

are

48

peop

le w

aitin

g f

or

a f

ish

ing

tou

r. E

ach

boat

hold

s 1

2 p

eop

le. R

od

ney

use

d t

he w

ork

belo

w t

o f

ind

th

e

nu

mb

er

of

boats

need

ed

. Exp

lain

how

Rod

ney’

s w

ork

can

be

use

d t

o f

ind

th

e n

um

ber

of

boats

need

ed

.

12

q w

48

−1

2

_

3

6

−1

2

_

2

4

−1

2

_

1

2

−1

2

_

0

P

oss

ible

an

swer

: I c

an c

ou

nt

the

nu

mb

er

of

tim

es R

od

ney

su

btr

acte

d 1

2. S

ince

he

su

btr

acte

d 1

2 fo

ur

tim

es, 4

bo

ats

are

nee

ded

.

Chap

ter R

esou

rces

© H

ough

ton

Miff

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Chap

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t4-31


Chap

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19

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Chap

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Tes

t4-33


Sample Level 3 Response


4-47© Houghton Mifflin Harcourt Publishing Company

Chapter Resources Individual Record Form

Student’s Name Date

Chapter 4 Test

Item Lesson Standard Content Focus Intervene with

Personal Math Trainer

1, 2, 14 4.1 4.NBT.B.6 Use multiples to estimate quotients with up to 4-digit dividends and 1-digit divisors. R—4.1 4.NBT.6

3 4.2 4.NBT.B.6 Use models to divide whole numbers that result in remainders. R—4.2 4.NBT.6

5, 6, 7 4.3 4.OA.A.3Interpret the remainder when solving word problems involving division of two whole numbers.

R—4.3 4.OA.3

8, 9 4.4 4.NBT.B.6Use basic facts and place value to divide tens, hundreds, and thousands by 1-digit divisors.

R—4.4 4.NBT.6

10, 11 4.5 4.NBT.B.6 Estimate quotients of two whole numbers using compatible numbers. R—4.5 4.NBT.6

12 4.6 4.NBT.B.6 Use the Distributive Property to find quotients. R—4.6 4.NBT.6

13, 16 4.7 4.NBT.B.6 Divide using repeated subtraction. R—4.7 4.NBT.6

18 4.8 4.NBT.B.6 Divide using partial quotients. R—4.8 4.NBT.6

19 4.9 4.NBT.B.6 Use base-ten blocks to model division with regrouping. R—4.9 4.NBT.6

15, 20 4.10 4.NBT.B.6 Use place value to decide where to place the first digit in a quotient. R—4.10 4.NBT.6

4, 14, 17 4.11 4.NBT.B.6 Divide by 1-digit numbers. R—4.11 4.NBT.6

21, 22 4.12 4.OA.A.2 Solve multistep word problems involving division. R—4.12 4.OA.2

Key: R—Reteach

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