U.S. Traditional
Long Division, Part 1
Algorithm
Objective To introduce U.S. traditional long division.
Project
Projject
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Common
Core State
Standards
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Doing the Project
Recommended Use After Lesson 610
Key Concepts and Skills
• Subtract multidigit numbers. [Operations and Computation Goal 2]
• Apply multiplication facts to long-division situations. [Operations and Computation Goal 3]
• Solve equal-sharing division problems and number stories. [Operations and Computation Goal 4]
Key Activities
Materials
Math Journal 1 or 2, pp. 25P–27P
Student Reference Book, pp. 24E–24H
$1 and $10 bills (Math Masters, p. 428;
optional)
$100 bills (optional)
coins (optional)
base-10 blocks (optional)
index cards (optional)
Students explore and practice U.S. traditional long division with two- and three-digit
whole numbers divided by single-digit whole numbers.
Key Vocabulary
U.S. traditional long division dividend divisor quotient remainder
Extending the Project
Ex
Students write and solve division number stories using U.S. traditional long division.
Materials
For additional practice, students solve division problems, first using the focus algorithm
(partial-quotients division) and then using any algorithm they choose.
Student Reference Book, pp. 22– 24 and
24E–24H
Online Additional Practice, pp. 27A–27C
Advance Preparation
If you intend to have students use coins and bills to model the division problems, you will need $100 bills. Make
several copies of Grade 3 Math Masters, page 401. Alternatively, use index cards to create $100 bills.
Algorithm Project 7
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Student Page
Date
Time
PROJECT
1 Doing the Project
Long Division with One-Digit Divisors
7
Algorithm Project 7
Use any strategy to solve the problem.
1.
$
WHOLE-CLASS
DISCUSSION
► Solving a Division Problem
The fourth-grade classes at Glendale School put on
puppet shows for their families and friends. Ticket sales
totaled $532, which the four classes are to share equally.
How much should each class get?
(Math Journal 1 or 2, p. 25P)
133
Be ready to explain how you found your answer.
Ask students to solve Problem 1 on journal page 25P. Tell them
they may use play money, paper and pencil, or any other tools
they wish except calculators.
Use U.S. traditional long division to solve each problem.
2.
13
78 / 6 =
188
4.
= 564 / 3
3.
5.
288 / 8 =
109
36
Discuss students’ solutions. $532 / 4 = $133 Expect that students
will use several different methods, including sharing or other
actions with play money or other manipulatives, various informal
paper-and-pencil methods, and partial-quotients division. Some
students may also use U.S. traditional long division. For example:
= 763 / 7
Sharing play money
Math Journal, p. 25P
25P-27P_EMCS_S_MJ1_G4_P07_576361.indd 25
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$532 / 4 = $133
Sharing base-10 blocks
$532 / 4 = $133
A32
Algorithm Project 7
U.S. Traditional Long Division, Part 1
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Using an informal paper-and-pencil method (See margin.)
532
- 100
Using partial-quotients division
4 532
- 400
100
432
- 100
332
- 100
20
232
- 100
132
- 80
52
- 40
10
12
- 12
3
0
133
132
- 100
32
- 32
0
$25 for each class
$25 for each class
$25 for each class
$25 for each class
$8 for each class
$25 + $25 + $25 + $25 + $25 + $8 = $133
Using U.S. traditional long division
133
4 532
-4
NOTE Long division is very demanding.
Encourage students who may be
overwhelmed to make a table of easy
multiples of the divisor. For example:
13
- 12
12
- 12
1∗4
2∗4
3∗4
4∗4
5∗4
6∗4
7∗4
8∗4
9∗4
0
► Introducing Long Division
$25 for each class
WHOLE-CLASS
ACTIVITY
After discussing students’ solutions, regardless of whether one or
more students used U.S. traditional long division, demonstrate
it again as described below. Illustrate each step with pictures and,
if possible, act out the problem using play money. Help students
make connections between the steps in the algorithm and the
actions of sharing the money.
4
8
12
16
20
24
28
32
36
Step 1
Step 1:
Set up the problem. Think about sharing actual bills: 5 [$100]s,
3 [$10]s, and 2 [$1]s.
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4 532
$532 is to be shared. We say $532 is the dividend.
Think of $532 as 5 [$100]s, 3 [$10]s, and 2 [$1]s.
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The money is to be
shared by four classes.
We say 4 is the divisor.
Step 2:
Step 2
Share the [$100]s. There are 5 [$100]s, so each class gets 1 [$100].
That uses up 4 [$100]s and leaves 1 [$100].
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4 532
Each class gets 1 [$100].
-4
−−−
1 [$100] each for 4 classes = 4 [$100]s
1 [$100] is left.
1
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Algorithm Project 7
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Step 3:
Step 3
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4
−−−
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13
After trading the [$100] for 10 [$10]s, there are
13 [$10]s in all.
Step 4:
Step 4
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Trade the remaining [$100] for 10 [$10]s. That makes 13 [$10]s
in all.
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Share the 13 [$10]s. Each class gets 3 [$10]s. That leaves 1 [$10]
still to be shared.
13
4 532
Each class gets 3 [$10]s.
4
−−−
13
12
−−−−
1
Step 5:
Step 5
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3 [$10]s each for 4 classes = 12 [$10]s
1 [$10] is left.
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Trade the last [$10] to be shared for 10 [$1]s. That makes
12 [$1]s in all.
13
4 532
4
−−−
13
12
−−−−
12
Step 6:
Step 6
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A34
After trading the [$10] for 10 [$1]s, there are
12 [$1]s in all.
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Algorithm Project 7
Share the 12 [$1]s. Each class gets 3 [$1]s.
133
4 532
Each class gets 3 [$1]s.
4
−−−
13
12
−−−−
12
12
−−−−
0
3 [$1]s each for 4 classes = 12 [$1]s
0 [$1]s are left.
U.S. Traditional Long Division, Part 1
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Student Page
Step 7:
Date
PROJECT
Each class gets $133. We say $133 is the quotient. A number
model is a good way to show the answer. Since there is no
remainder, either
7
Time
Long Division with One-Digit Divisors
cont.
Algorithm Project 7
6.
350 / 4 →
87 R2
7.
802 / 9 →
89 R1
$532 / 4 → $133
or
$532 / 4 = $133
would be an acceptable number model for this problem.
U.S. traditional long division is complicated, so you may want to
work more examples with the whole class. For now, continue to use
sharing money as a context and continue drawing pictures and,
if possible, acting out the problems with play money. Later, the
algorithm can be generalized to non-money contexts.
124 R1
8.
← 869 / 7
9.
174 R4
← 874 / 5
Suggestions:
$84 / 7 $12
$807 / 4 $201 R$3
$785 / 5 $157
86 / 7 12 R2
$122 / 8 $15 R$2
468 / 5 93 R3
► Solving Long Division Problems
Math Journal, p. 26P
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PARTNER
ACTIVITY
with One-Digit Divisors
(Math Journal 1 or 2, pp. 25P–27P; Student Reference Book, pp. 24E–24H)
When students are ready, have them use U.S. traditional long
division to solve Problems 2–13 on journal pages 25P– 27P.
They may find the examples on Student Reference Book,
pages 24E–24H helpful. Students should note that Problems 6–9
involve remainders.
Student Page
Date
PROJECT
7
Long Division with One-Digit Divisors
cont.
Algorithm Project 7
2 Extending the Project
► Writing and Solving Division
Time
10.
11.
Eight people visited a marine theme
park. The total cost of the single-day
admission tickets was $424. What was
the cost per ticket?
$
A national park charges an entrance fee
of $3 per person. A school group visited
the site. The cost was $288. How many
people were in the school group?
53
96
people
PARTNER
ACTIVITY
Number Stories
(Student Reference Book, pp. 24E–24H)
Have students write division number stories for a partner to solve
using U.S. traditional long division. Again, students may find the
examples on Student Reference Book, pages 24E–24H helpful.
12.
13.
A family went on a six-day boat cruise.
They sailed a total of 432 miles. They
sailed the same distance each day. How
far did they travel each day?
72
Four friends have birthdays in the same
month. They decide to rent a hall to have
a birthday party and split the cost evenly.
The cost of renting the hall for one day is
$172. How much did each friend pay?
miles
$
43
Math Journal, p. 27P
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Algorithm Project 7
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Student Page
► Solving Division Problems
Whole Numbers
U.S. Traditional Long Division
INDEPENDENT
ACTIVITY
(Online Additional Practice, pp. 27A–27C; Student Reference Book,
pp. 22–24 and 24E–24H)
You can use U.S. traditional long division to divide.
$935 4
To begin, think about sharing $935 among 4 people: Aimee, Brad, Carla, and Duane.
Money to be Shared
Aimee
Brad
Carla
Duane
Aimee
Brad
Carla
Duane
$100
$100
$100
$100
$100
$100
$100
$100
Online practice pages 27A–27C provide students with additional
practice solving division problems. Use these pages as necessary.
$100 $100 $100 $100 $100
$100 $100 $100 $100
$10
$10
$10
$1
$1
$1
$1
$1
Encourage students to use the focus algorithm (partial-quotients
division) to solve the problems on practice page 27A. Invite them
to use any algorithm they wish to solve the problems on the
remaining pages. Students may find the examples on Student
Reference Book, pages 22–24 and 24E–24H helpful.
Step 1: Share the [$100]s.
Money to be Shared
$100
$10
$10
$10
$1
$1
$1
$1
$1
2
← Each person gets 2 [$100]s.
4 935
-8
← 2 [$100]s each for 4 people
1
← 1 [$100] is left.
Step 2: Trade the last [$100] for 10 [$10]s.
That makes 13 [$10]s in all.
Aimee
Brad
Carla
Duane
$10
$10
$10
$10
$10
$100
$100
$100
$100
$10
$10
$10
$10
$10
$100
$100
$100
$100
$10
$10
$10
$1
$1
$1
$1
$1
Money to be Shared
2
4 935
-8
13
← 13 [$10]s are to be shared.
Student Reference Book, p. 24E
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Go to www.everydaymathonline.com
to access the additional practice
pages.
Student Page
Online Master
Name
Whole Numbers
Date
PROJECT
Online
Additional
Practice
Partial-Quotients Division
7
continued
Time
Algorithm Project 7
Step 3: Share the [$10]s.
Money to be Shared
$10
$1
$1
$1
$1
$1
Aimee
Brad
Carla
Duane
$100
$100
$100
$100
$100
$100
$100
$100
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
Use partial-quotients division to solve each problem.
1.
Mrs. Johnson has a total of $872 that she
wants to divide equally among her 8 grandchildren.
How much should each grandchild get?
$
109
← Each person gets 3 [$10]s.
23
4
935
-8
13
-12
1
2.
78 / 6 =
13
3.
324 / 9 =
36
← 3 [$10]s each for 4 people
← 1 [$10] is left.
Step 4: Trade the last [$10] for 10 [$1]s.
That makes 15 [$1]s in all.
Brad
Carla
Duane
$1
$1
$1
$1
$100
$100
$100
$100
$1
$1
$1
$1
$1
$100
$100
$100
$100
$1
$1
$1
$1
$1
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
23
935
4
-8
13
-12
15
Copyright © Wright Group/McGraw-Hill
Aimee
$1
Money to be Shared
← 15 [$1]s are to be shared.
Student Reference Book, p. 24F
4.
146
A36
Algorithm Project 7
5.
126
= 882 / 7
Online Additional Practice, p. 27A
EM3cuG4OP_27A-27C_P07.indd 27A
024A-024J_EMCS_S_G4_SRB_576507.indd 24F
= 438 / 3
3/31/10 5:34 PM
3/1/11 8:46 AM
U.S. Traditional Long Division, Part 1
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