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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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Copyright © by Houghton Mifflin Harcourt Publishing Company
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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
GGGGaaGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGaaaaaaaaaaaaa eeeeemmeeeeeeeeeeeeemmmmmeeeeeeeeeeeeemmmmmmeeemmmmmmeeeeeeeeeeeeGameGame©
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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
4-7 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-8 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-9 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-10 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-11 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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?
2. When divided by 3, I am 700. When divided by 7, I am 300. What number am I?
3. When divided by 8, I am 70. When divided by 7, I am 80. What number am I?
4. When divided by 7, I am 400. When divided by 4, I am 700. What number am I?
5. When divided by 6, I am 200. When divided by 4, I am 300. What number am I?
6. When divided by 8, I am 30. When divided by 6, I am 40. What number am I?
Dividend Riddles
Solve each riddle.
Lesson 4.4Enrich
4-12 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-13 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-14 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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 =
4-15 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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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
4-16 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-17 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-18 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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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
4-19 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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#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
4-20 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-21 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-22 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-23 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-24 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-25 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-26 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-27 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-28 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
Chapter 4 TestPage 2
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 =
Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 4 Test4-30
Chapter 4 TestPage 3
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
Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 4 Test4-31
Chapter 4 TestPage 4
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?
Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 4 Test4-32
Chapter 4 TestPage 5
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
Chapter Resources© Houghton Mifflin Harcourt Publishing Company
Name
Chapter 4 Test4-33
Chapter 4 TestPage 6
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
Chapter Resources© Houghton Mifflin Harcourt Publishing Company
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.
4-36 Chapter 4 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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.
4-37 Chapter 4 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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.
4-38 Chapter 4 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
4-39 Chapter 4 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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
lin H
arco
urt P
ublis
hing
Com
pany
Nam
e
Chap
ter 4
Tes
t4-31
4-41 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company
Chap
ter 4
Tes
tPa
ge 6
19
. Eth
an n
eeds
to d
ivid
e these
base
-ten b
locks
into
3 e
qual gro
ups.
Dra
w o
r d
esc
rib
e t
he m
od
el to
sh
ow
how
man
y are
in
each
gro
up
.
Th
e m
od
el w
ill c
on
tain
3 t
ens
rod
s an
d 2
on
es c
ub
es O
R
20
. Ja
ke w
an
ts t
o d
istr
ibu
te 5
43
marb
les
eq
ually
am
on
g 7
of
his
frie
nd
s. In
wh
ich
pla
ce is
the f
irst
dig
it o
f th
e q
uotien
t? C
hoose
the w
ord
th
at
makes
the s
en
ten
ce t
rue.
Th
e f
irst
dig
it o
f th
e q
uotien
t is
in
th
e
on
es
ten
s
hu
nd
red
s
thou
san
ds
pla
ce.
21
. C
had
bou
gh
t 8
doze
n n
ote
pad
s fo
r h
is o
ffic
e. Th
e n
ote
pad
s
were
div
ided
eq
ually
in
to 6
boxe
s. H
ow
man
y n
ote
pad
s are
in
each
box?
16 n
ote
pad
s
22
. Th
ere
are
12
6 s
eats
in
a m
eetin
g r
oom
. Th
ere
are
9 s
eats
in
each
row
. Th
ere
are
90
peop
le s
eate
d, filli
ng
up
fu
ll ro
ws
of
seats
. H
ow
man
y ro
ws
are
em
pty
?
4 r
ow
s
Chap
ter R
esou
rces
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
Nam
e
4-34
Chap
ter 4
Tes
t
Chap
ter 4
Tes
tPa
ge 5
16
. W
hic
h m
od
el m
atc
hes
each
exp
ress
ion
? W
rite
th
e lett
er
in t
he
box
next
to t
he m
od
el.
180
900
B
120
4080
0
A
180
6012
00
D
120
600
C
17
. D
ieg
o b
ou
gh
t 4
88
fro
zen
yog
urt
bars
in
4 d
iffe
ren
t flavo
rs f
or
a p
art
y. H
e b
ou
gh
t th
e s
am
e n
um
ber
of
each
fla
vor. H
ow
man
y
of
each
fla
vor
did
he b
uy?
122
bars
of
each
fla
vor
18
. U
se p
art
ial q
uotien
ts. Fill
in
th
e b
lan
ks.
10
0 ×
7
100
7
× 7
+
7
107
7 q w
7
49
– 7
00
49 –
49
0
A
12
0 ÷
40
B
18
0 ÷
90
C
12
0 ÷
60
D
18
0 ÷
60
Chap
ter R
esou
rces
© H
ough
ton
Miff
lin H
arco
urt P
ublis
hing
Com
pany
Nam
e
Chap
ter 4
Tes
t4-33
4-42 Answer KeyChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 3 Response
4-43 Chapter 4 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 2 Response
4-44 Chapter 4 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 1 Response
4-45 Chapter 4 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
Sample Level 0 Response
4-46 Chapter 4 • Performance TaskChapter Resources© Houghton Mifflin Harcourt Publishing Company
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Chapter Resources Individual Record Form
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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