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PROJECT
Objective
To extend the U.S. traditional long division algorithm
for single-digit divisors to four- and five-digit dividends and
dividends in dollars-and-cents notation.
1
Doing the Project
Recommended Use: After Lesson 9-9 and after Project 11.
Key Activities
Students explore and practice the U.S. traditional long division algorithm for single-digit
divisors to four- and five-digit dividends and dividends in dollars-and-cents notation.
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]
materials
Math Journal, pp. 15–17
Student Reference Book,
pp. 24E–24H and 40D–40F
$1 and $10 bills (Math Masters,
p. 428; optional)
$100 bills (optional)
coins (optional)
base-10 blocks (optional)
index cards (optional)
See Advance Preparation
• Divide decimals by whole numbers.
[Operations and Computation Goal 4]
Key Vocabulary
long division • quotient • dividend
2
Extending the Project
Students write division number stories and use the U.S. traditional long division algorithm
to solve them.
Additional Information
Today there are no longer any bills larger than $100 in circulation, but it was not always so.
Beginning in the late 1920s and early 1930s the U.S. Treasury issued a small number of large
bills, including $500, $1,000, $5,000, $10,000, and $100,000 bills. By the mid-1940s, the
Treasury stopped making these bills, and in 1969 President Nixon removed them from
circulation because they were rarely used and attractive to counterfeiters.
Advance Preparation If you intend to have students use coins and bills to model the division
problems, you will need $100 and $1,000 bills. Make several copies of Third Grade Math
Masters, page 401 for the $100 bills or use index cards to create them. Use index cards to
create $1,000 bills.
975U
Project 12 Long Division, Part 2
materials
Student Reference Book,
pp. 24E–24H and 40D–40F
Technology
See the iTLG and iSRB.
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Student Page
1 Doing the Project
Date
PROJECT
▼
12
Solving a Division Problem
WHOLE-CLASS
DISCUSSION
Time
Larger Dividends
1. Four friends were playing a board game. Jen quit. The three other
players decided to divide Jen’s money equally. Jen had $4,353.
How much should each of the three other players get?
(Math Journal, p. 15)
$1,451
Be ready to explain how you got your answer.
Ask students to solve Problem 1 on journal page 15. Tell
them they may use paper and pencil or any tools they wish, except
calculators.
Have students discuss and share solutions. Expect a variety of
approaches, including the U.S. traditional long division
method, which was introduced in Project 11. Have students
explain why each of the steps in their procedures make sense.
For example:
2. $5,385 / 5 4.
1,225
$1,077
3. $7,896 / 6 8,575 / 7
5.
2,709
$1,316
8,127 / 3
Sharing play money or base-10 blocks
Using an informal paper-and-pencil method
4353
– 3000
1353
– 300
1053
– 300
753
– 300
453
– 300
153
– 150
3
– 3
0
$1000 for each player
$100 for each player
Math Journal, p. 15
$100 for each player
$100 for each player
$100 for each player
$50 for each player
$1 for each player
$1000 + $100 + $100 + $100 + $100 + $50 + $1 = $1451
Using the partial-quotients algorithm
3 4353
- 3000 1000
1353
– 1200
400
153
– 150
50
3
- 3
3
0 1451
Using the U.S. traditional long division algorithm
1451
3 4353
- 3
13
– 12
15
– 15
03
– 3
0
Project 12
975V
▼
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Extending Long Division to
Larger Dividends
WHOLE-CLASS
ACTIVITY
After you have discussed students’ solutions, regardless of
whether some students used the U.S. traditional long division
algorithm, demonstrate the problem again as described below.
Illustrate each step in the algorithm with pictures of play money.
Help students make connections between the steps in the
algorithm and the actions of sharing money.
Money to be Shared
Player A Player B Player C
$1,000 $1,000 $1,000 $1,000
$100
$100
$100
$10
$10
$10
$10
$10
$1
$1
Step 1:
Set up the problem. Think about sharing actual bills: 4 [$1,000]s,
3 [$100]s, 5 [$10]s, and 3 [$1]s. (See margin.)
Long Division:
$1
3 ..4
3
5
3
$4,353 is to be shared.
Three players will share Jen’s money.
Money to be Shared
$1,000
Player A Player B Player C
$1,000
$100
$100
$100
$10
$10
$10
$10
$10
$1
$1
$1,000
$1,000
Step 2:
Share the [$1,000]s. Each player gets 1 [$1,000]. There is
1 [$1,000] left. (See margin.)
Long Division:
$1
1
3 ..4
3
5
3
3
1
Money to be Shared
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$10
$10
$10
$10
$10
$1
$1
975W
$100
Player A Player B Player C
$1,000
$1,000
$100
$1
Project 12 Long Division, Part 2
$1,000
Each player gets 1 [$1,000].
1 [$1,000] each for 3 players 3 [$1,000]s.
1 [$1,000] is left.
Step 3:
Trade the 1 [$1,000] for 10 [$100]s. (See margin.)
1
3 ..4
3
5
3
3
1 3
10 [$100]s from the 1 [$1,000] 3 [$100]s 13 [$100]s.
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Step 4:
Share the 13 [$100]s. Each player gets 4 [$100]s; 1 [$100] is left.
(See margin.)
1 4
3 ..4
3
5
3
3
1 3
1 2
1
Each player gets 4 [$100]s.
Money to be Shared
$100
$10
$10
$10
$10
$1
$1
$10
$1
Player A Player B Player C
$1,000
$1,000
$1,000
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
4 [$100]s each for 3 players 12 [$100]s.
1 [$100] is left.
Step 5:
Trade the 1 [$100] for 10 [$10]s. (See margin.)
1 4
3 ..4
3
5
3
3
1 3
1 2
1 5
Money to be Shared
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$1
$1
$10
$10
$10
Player A Player B Player C
$1,000
$1,000
$1,000
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$1
10 [$10]s from the 1 [$100] 5 [$10]s
15 [$10]s.
Step 6:
Share the 15 [$10]s. Each player gets 5 [$10]s. (See margin.)
1 4 5
3 ..4
3
5
3
3
1 3
1 2
1 5
1 5
0
Each player gets 5 [$10]s.
Money to be Shared
$1
$1
$1
5 [$10]s each for 3 players 15 [$10]s.
0 [$10]s are left.
Player A Player B Player C
$1,000
$1,000
$1,000
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
Step 7:
Share the 3 [$1]s. Each player gets 1 [$1]. (See margin.)
1 4 5 1
3 ..4
3
5
3
3
1 3
1 2
1 5
1 5
0 3
3
0
Each player gets 1 [$1]s.
3 [$1]s are to be shared.
1 [$1] each for 3 players 3 [$1]s.
0 [$1]s are left to be shared.
Money to be Shared
Player A Player B Player C
$1,000
$1,000
$1,000
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$100
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$10
$1
$1
$1
$4,353 / 3 $1,451. Each of the continuing players gets $1,451.
Project 12
975X
▼
EM3TLG2_G4_975U-Z_NEW.qxd 6/20/08 1:34 PM Page 582
Date
(Math Journal, pp. 15 and 16;
Student Reference Book, pp. 24E–24H)
Time
PROJECT
12
Larger Dividends
PARTNER
ACTIVITY
Solving Long Division Problems
Student Page
continued
Fill in the missing numbers.
7.
173 9
5 8 6 9 5
–5
3 6
–3 5
19
–1 5
0
6 3
–0
3
–3
54 2
25 2
2
0
25
–24
1 2
–1 2
0
45
– 4 5
0
8. The total cost for one year (2006-2007) at University of California, Los Angeles (UCLA) is
about $23,394 for a California resident living in a residence hall. Books and supplies account
for about $1,544 of the total cost.
a. How many hours of babysitting at $4 per
b. How many hours of babysitting at $6
hour would it take to earn $1,544?
386
per hour would it take to earn $23,394?
3,899
hours
hours
Have partners use the U.S. traditional long division algorithm
to solve the problems on journal pages 15 and 16. Students
may find the examples on Student Reference Book, pages
24E–24H helpful.
▼
6.
Extending Long Division to
Dollars-and-Cents Notation
WHOLE-CLASS
DISCUSSION
(Math Journal, p. 17; Student Reference Book, pp. 40D–40F)
Have students solve Problems 1 and 2 on journal page 17. As a
class, discuss how Dennis solved the problem. Be sure to include
the following points:
The long division algorithm for dollars and cents looks almost
exactly the same as for whole numbers.
The money in Dennis’s method would include dimes and
pennies, not just bills as in whole-number long division
with money.
Math Journal, p. 16
There are decimal points separating dollars from cents in
Dennis’s quotient and dividend. In whole-number long
division there were no decimal points.
With Dennis’s method, we know exactly where the decimal
point belongs. If we use partial quotients division to solve the
problem, we use estimation to place the decimal point. For
example, to solve $9.45 / 7 by partial quotients:
•
Estimate the answer. $9.45 / 7 would be more than
$1 but less than $2.
•
Divide as though the dividend were a whole number.
945 / 7 135
•
Use the estimate to place the decimal point in the quotient.
Since the answer must be between $1 and $2, the decimal
point must go between the 1 and the 3; $1.35.
Student Page
Date
Time
PROJECT
12
Dividing Dollars and Cents
1.3 5
7 9.4 5
–7
1. Dennis solved $9.45 / 7 like this.
a. Study Dennis’s work.
2 4
–2 1
3 5
–3 5
0
b. Explain to your partner how he
solved the problem.
Solve these division problems using Dennis’s method.
2. $8.92 / 4 4.
1.97
$2.23
15.76 / 8
3. $7.56 / 6 5.
2.13
$1.26
19.17 / 9
Math Journal, p. 17
975Y
Project 12 Long Division, Part 2
Pose additional problems such as the following. Review
Student Reference Book, pages 40D–40F as necessary.
•
•
•
•
$1.72 / 4 $0.43
$7.05 / 5 $1.41
$9.27 / 3 $3.09
$9.42 / 6 $1.57
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Student Page
2 Extending the Project
Decimals and Percents
▼
U.S. Traditional Long Division Method: Decimals
PARTNER
ACTIVITY
Writing and Solving Division
Number Stories
You can use the U.S. traditional long division method to divide money
in dollars and cents notation.
Share $7.95 among 3 people: Aidan, Maya, and Zeynep.
Aidan
Money to be Shared
(Student Reference Book, pp. 24E –24H and 40D–40F)
Have students write division number stories that include
single-digit divisors, four- and five-digit dividends, and dividends
in dollars-and-cents notation. Partners use the U.S. traditional
long division algorithm to solve them. Students may find the
examples on Student Reference Book, pages 24E–24H and
40D–40F helpful.
$1
$1
$1
$1
$1
$1
$1
10¢
10¢
1¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
1¢
1¢
1¢
Maya
Zeynep
1¢
Step 1: Share the [$1]s.
Aidan
Money to be Shared
$1
$1
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
1¢
1¢
1¢
1¢
Maya
$1
$1
Zeynep
$1
$1
$1
10¢
1¢
Ò Each person gets 2 [$1]s.
2
.9
5
37
Ò 2 [$1]s each for 3 people
6
1
Ò 1 [$1] is left.
Step 2: Trade the one [$1] for ten [10¢]s.
Aidan
Money to be Shared
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
10¢
1¢
1¢
1¢
1¢
$1
Maya
$1
$1
Zeynep
$1
$1
$1
1¢
2
37
.9
5
6
1 9 Ò 10 [10¢]s 9 [10¢]s
40D
Student Reference Book, p. 40D
Student Page
Student Page
Decimals and Percents
Decimals and Percents
continued
continued
Step 3: Share the [10¢]s.
Aidan
Money to be Shared
10¢
1¢
Step 5: Share the [1¢]s.
$1
1¢
1¢
1¢
2.6
.9
5
37
6
19
1 8
1
1¢
$1
Maya
$1
$1
Zeynep
$1
Money to be Shared
$1
Maya
$1
Zeynep
$1
$1
$1
10¢ 10¢ 10¢
10¢ 10¢ 10¢
10¢ 10¢ 10¢
10¢ 10¢ 10¢
10¢ 10¢ 10¢
10¢ 10¢ 10¢
10¢ 10¢ 10¢
10¢ 10¢ 10¢
10¢ 10¢ 10¢
10¢ 10¢ 10¢
1¢ 1¢ 1¢
1¢ 1¢ 1¢
1¢ 1¢ 1¢
1¢ 1¢
1¢ 1¢
1¢ 1¢
2.65
.9
5
37
6
19
1 8
15
15
0
Ò 6 [10¢]s each for 3 people
Ò 1 [10¢] is left.
Step 4: Trade the one [10¢] for ten [1¢]s.
Aidan
Maya
1¢
1¢
1¢
1¢
1¢
1¢
1¢
1¢
1¢
10¢ 10¢ 10¢
10¢ 10¢ 10¢
10¢ 10¢ 10¢
1¢
1¢
1¢
1¢
1¢
10¢ 10¢ 10¢
10¢ 10¢ 10¢
10¢ 10¢ 10¢
$1
$1
$1
$1
Ò Each person gets 5 [1¢]s.
Ò 5 [1¢]s each for 3 people
Ò 0 [1¢]s are left.
Zeynep
1¢
2.6
.9
5
37
6
19
1 8
15
$1
10¢ 10¢ 10¢
Ò Each person gets 6 [10¢]s. Write a decimal point
above the line to show amounts less than $1.
Money to be Shared
Aidan
$1
10¢ 10¢ 10¢
$1
$1
Each person gets $2.65.
$7.95 / 3 $2.65
Divide.
1. $6.25 / 5 ?
Ò 10 [1¢]s 5 [1¢]s
3. 84
.8
0
4. $38.96 / 4 ?
Check your answers on page 347.
40E
Student Reference Book, p. 40E
2. 56
.7
5
40F
Student Reference Book, p. 40F
Project 12
975Z