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PROJECT
Objective
To introduce the U.S. traditional long division
algorithm for single-digit divisors.
1
Doing the Project
Recommended Use: After Lesson 6-10
Key Activities
Students explore and practice the U.S. traditional long division algorithm for dividing
two- and three-digit whole numbers by single-digit whole numbers.
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.
materials
Math Journal, pp. 12–14
Student Reference Book,
pp. 24E–24G
$1 and $10 bills (Math Masters,
p. 428) (optional)
$100 bills (optional)
coins (optional)
base-10 blocks (optional)
index cards (optional)
See Advance Preparation
[Operations and Computation Goal 4]
Key Vocabulary
U.S. traditional long division method • dividend • divisor • quotient • remainder
2
Extending the Project
Students write and solve division number stories using the U.S. traditional
long division algorithm.
Additional Information
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 Third Grade Math Masters,
page 401. Alternatively, use index cards to create $100 bills.
975O
Project 11 Long Division, Part 1
materials
Student Reference Book,
pp. 24E–24G
Technology
See the iTLG and iSRB.
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Student Page
1 Doing the Project
Date
Time
PROJECT
LESSON
2110
▼
WHOLE-CLASS
DISCUSSION
Solving a Division Problem
Divisors
One-Digit
Lesson
Title
1. 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, p. 12)
$133
Be ready to explain how you found your answer.
Ask students to solve Problem 1 on journal page 12. Tell them
they may use play money, paper and pencil, or any other tools
they wish except calculators.
Discuss students’ solutions. $532 / 4 $133 Expect that students
will use several different methods, including the partial-quotients
algorithm, various informal paper-and-pencil methods, and
sharing or other actions with play money or other manipulatives.
Some students may also use the U.S. traditional long division
method, which is the focus of this project. For example:
2. 78 / 6 4.
188
13
564 / 3
3. 288 / 8 5.
109
36
763 / 7
Sharing play money
$100
$10
$1
$1
$1
$1
$1
$100
$10
$1
$1
$1
$1
$1
$1
$1
$100
$10
$100
$10
$10
$10
$100
$10
$10
$10
$10
$10
$10
$100
Math Journal, p. 12
$10
$100
$100
$100
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$1
$1
$1
$1
$1
$1
$1
$1
$1
$1
$1
$1
Sharing base-10 blocks
Project 11
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532
– 100
$25 for each class
432
– 100
$25 for each class
332
– 100
$25 for each class
232
– 100
$25 for each class
132
– 100
$25 for each class
32
– 32
Using an informal paper-and-pencil method (See margin.)
Using the partial-quotients algorithm
4 532
- 400
132
– 80
52
– 40
12
- 12
0
$8 for each class
0
$25 + $25 + $25 + $25 + $25 + $8 = $133
100
20
10
3
133
Using the U.S. traditional long division algorithm
133
4 532
- 4
13
– 12
12
– 12
▼
0
Introducing Long Division
WHOLE-CLASS
ACTIVITY
After discussing students’ solutions, regardless of whether one or
more students used the U.S. traditional long division algorithm,
demonstrate it again as described below. Illustrate each step in
the algorithm 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.
Money to
be Shared
Ms. A’s
Class
Ms. B’s
Class
Ms. C’s
Class
Mr. D’s
Class
Set up the problem. Think about sharing actual bills: 5 [$100]s,
3 [$10]s, and 2 [$1]s.
$100 $100 $100
$100 $100
$10
$10
$1
$1
Step 1:
$10
Long Division:
4 ..5
3
2
NOTE The long division algorithm is very
demanding. Encourage students who may be
overwhelmed to make a table of easy multiples
of the divisor. For example:
14
24
34
44
54
64
74
84
94
975Q
4
8
12
16
20
24
28
32
36
Project 11 Long Division, Part 1
$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.
The money is to be
shared by four classes.
We say 4 is the divisor.
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Step 2:
Money to
be Shared
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].
Ms. A’s
Class
Ms. B’s
Class
Ms. C’s
Class
Mr. D’s
Class
$100
$100
$100
$100
Ms. A’s
Class
Ms. B’s
Class
Ms. C’s
Class
Mr. D’s
Class
$100
$100
$100
$100
Ms. A’s
Class
Ms. B’s
Class
Ms. C’s
Class
Mr. D’s
Class
$100
$100
$100
$100
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$100
$10
$10
$1
$1
$10
Long Division:
1
4 ..5
3
2
4
Each class gets 1 [$100].
1 [$100] each for 4 classes 4 [$100]s.
1
1 [$100] is left.
Money to
be Shared
Step 3:
Trade the remaining [$100] for 10 [$10]s. That makes 13 [$10]s
in all.
Long Division:
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$1
1
4 ..5
3
2
$1
4
1
3
After trading the [$100] for 10 [$10]s, there
are 13 [$10]s in all.
Step 4:
Money to
be Shared
$10
Share the 13 [$10]s. Each class gets 3 [$10]s. That leaves 1 [$10]
still to be shared.
$1
$1
Long Division:
1 3
4 ..5
3
2
Each class gets 3 [$10]s.
4
1
1
Student Page
3
2
1
Whole Numbers
3 [$10]s each for 4 classes = 12 [$10]s.
1 [$10] is left.
U.S. Traditional Long Division Method
You can use the U. S. traditional long division method
to divide.
$935 / 4 ?
To begin, think about sharing $935 among 4 people: Aimee, Brad, Carla, and Duane.
Aimee
Money to be Shared
Brad
Carla
Duane
Aimee
Brad
Carla
Duane
$100
$100
$100
$100
$100
$100
$100
$100
$100 $100 $100 $100 $100
$100 $100 $100 $100
$10
$10
$10
$1
$1
$1
$1
$1
Step 1: Share the [$100]s.
Money to be Shared
$100
$10
$10
$10
$1
$1
$1
$1
$1
Ò Each person gets 2 [$100]s.
2
49
3
5
8
1
Ò 2 [$100]s each for 4 people
Ò 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
49
3
5
8
13
Ò 13 [$10]s are to be shared.
24E
Student Resource Book, p. 24E
Project 11
975R
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Money to
be Shared
$1
$1
$1
$1
$1
$1
$1
$1
$1
$1
$1
$1
Ms. A’s
Class
Ms. B’s
Class
Ms. C’s
Class
Mr. D’s
Class
$100
$100
$100
$100
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
Step 5:
Trade the last [$10] to be shared for 10 [$1]s. That makes
12 [$1]s in all.
Long Division:
1 3
4 ..5
3
2
4
1
1
Money to
be Shared
Ms. A’s
Class
Ms. B’s
Class
Ms. C’s
Class
Mr. D’s
Class
$100
$100
$100
$100
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$1
$1
$1
$1
$1
$1
$1
$1
$1
$1
$1
$1
3
2
1
2
After trading the [$10] for 10 [$1]s, there
are 12 [$1]s in all.
Step 6:
Share the 12 [$1]s. Each class gets 3 [$1]s.
Long Division:
1 3 3
4 ..5
3
2
4
1
1
3
2
1
–1
2
2
0
Each class gets 3 [$1]s.
3 [$1]s each for 4 classes 12 [$1]s.
0 [$1]s are left.
Step 7:
Student Page
Whole Numbers
continued
$532 / 4 ∑ $133
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
Ò Each person gets 3 [$10]s.
23
49
3
5
8
13
12
1
Step 4: Trade the last [$10] for 10 [$1]s.
That makes 15 [$1]s in all.
Aimee
Brad
Carla
Duane
$1
$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
3
5
49
8
13
12
15
Ò 15 [$1]s are to be shared.
24F
Student Resource Book, p. 24F
975S
or
$532 / 4 $133
would be an acceptable number model for this problem.
Ò 3 [$10]s each for 4 people
Ò 1 [$10] is left.
Money to be Shared
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
California Project 11 Long Division, Part 1
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The U.S. traditional long division method 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.
Suggestions:
•
•
•
$84 / 7 ? $12
$785 / 5 ? $157
$122 / 8 ? $15.25
•
•
•
Student Page
Date
Time
PROJECT
LESSON
2110
One-Digit
Divisors
Lesson Title
6. 350 / 4 continued
87 R2
7. 802 / 9 89 R1
$807 / 4 ? $201.75
86 / 7 ? 12 R2
468 / 5 ? 93 R3
124 R1
▼
8.
Solving Long Division Problems
with One-Digit Divisors
869 / 7
9.
174 R4
874 / 5
PARTNER
ACTIVITY
(Math Journal, pp. 12–14; Student Reference Book, pp. 24E– 24G)
When students are ready, have them solve Problems 2–13 on
journal pages 12– 14. They may find the examples on Student
Reference Book, pages 24E–24G helpful. Students should note
that Problems 6–9 involve remainders.
Math Journal, p. 13
▼
2 Extending the Project
Writing and Solving Division
Number Stories
PARTNER
ACTIVITY
(Student Reference Book, pp. 24E – 24G)
Have students write division number stories for a partner to
solve using the U.S. traditional long division method. Again,
students may find the examples on Student Reference Book,
pages 24E–24G helpful.
Student Page
Date
Time
PROJECT
LESSON
2110
One-Digit
Divisors
Lesson
Title
10. Eight people visited a marine theme
park in San Diego. The total cost of the
single-day admission tickets was $424.
What was the cost per ticket?
$53
12. Six tourists took a ferry to visit Alcatraz in
continued
11. Muir Woods National Monument 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?
96
people
13. Four friends spent the day at an
the middle of San Francisco Bay. The
total cost of the trip was $99. What was
the price of each ticket?
amusement park in Los Angeles.
The total cost of the tickets was
$299.96. What was the price per ticket?
$16.50
$74.99
Math Journal, p. 14
Project 11
975T