Algorithm
U.S. Traditional
Subtraction: Decimals
Project
Projjjectt
Objective To introduce U.S. traditional subtraction with decimals.
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Assessment
Management
Doing the Project
Common
Core State
Standards
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Mathematical Practices
Recommended Use After Lesson 4 5
SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP8
Key Concepts and Skills
• Identify places in whole numbers and decimals and the values of the digits
in those places. [Number and Numeration Goal 1]
• Use subtraction facts to find differences of decimals. [Operations and Computation Goal 1]
• Subtract decimals. [Operations and Computation Goal 2]
• Write and solve subtraction number stories with decimals. Materials
Math Journal 1 or 2, pp. 13P–16P
Student Reference Book, p. 40B
$1 and $10 bills (Math Masters, p. 428;
optional)
dimes and pennies (optional)
base-10 blocks (optional)
[Operations and Computation Goal 2]
Key Activities
Students explore and practice U.S. traditional subtraction with decimals.
Extending the Project
Ex
Students solve decimal subtraction problems, first using the focus algorithm
(trade-first subtraction) and then using any algorithm they choose.
Materials
Online Additional Practice, pp. 16A–16D
Student Reference Book, pp. 34–37 and 40B
Algorithm Project 4
A15
Student Page
Date
Time
PROJECT
4
1 Doing the Project
U.S. Traditional Subtraction: Decimals 1
Algorithm Project 4
► Solving a Decimal Subtraction
Use any strategy to solve the problem.
1.
Seth paid $6.72 for his lunch. Lily paid $3.79
for her lunch. How much more did Seth’s
lunch cost?
2.93
$
Problem
Use U.S. traditional subtraction to solve each problem.
2.
9.75 - 4.32 =
2.84
4.
5.43
= 8.2 - 5.36
3.
5.
5.06 - 2.49 =
(Math Journal 1 or 2, p.13P)
2.57
$34.27 - $16.38 = $
Ask students to solve Problem 1 on journal page 13P. Tell them
they may use base-10 blocks, play money, paper and pencil, or
any other tools they wish, except calculators.
17.89
► Discussing Solutions
6.
22.69
INDEPENDENT
ACTIVITY
= 50.08 - 27.39
7.
6.35 - 2.37 =
(Math Journal 1 or 2, p. 13P)
3.98
Math Journal, p. 13P
13P-16P_EMCS_S_MJ1_G4_P04_576361.indd 13
WHOLE-CLASS
ACTIVITY
3/4/11 11:56 AM
Discuss students’ solutions to Problem 1 on journal page 13P.
$6.72 - $3.79 = $2.93 Expect that students will use several
different methods, including modeling with base-10 blocks,
counting up, using partial-differences subtraction, and using
trade-first subtraction. Some students may also use U.S.
traditional subtraction. Possible strategies:
Modeling with base-10 blocks
Show 6.72 with blocks.
You want to take away 3.79. To do this, you need to first trade
1 flat for 10 longs and 1 long for 10 cubes.
Now remove 3 flats, 7 longs, and 9 cubes (3.79). Two flats, 9 longs,
and 3 cubes are left. These blocks show 2.93.
A16
Algorithm Project 4
U.S. Traditional Subtraction: Decimals
Using shorthand pictures of base-10 blocks (See margin.)
Counting up
3.79
+ 0.01
3.80
+ 0.20
4.00
+ 2.72
6.72
Draw a picture for 6.72.
0.01
0.20
+ 2.72
2.93
Trade 1 flat for 10 longs and
1 long for 10 cubes.
$6.72 - $3.79 = $2.93
Using partial-differences subtraction
Subtract the 1s.
Subtract the 0.1s.
Subtract the 0.01s.
Find the total.
6-3→
0.7 - 0.7 →
0.02 - 0.09 →
3 - 0.07 →
6. 7 2
- 3. 7 9
3. 0 0
0. 0 0
- 0. 0 7
2. 9 3
Remove 3 flats, 7 longs, and 9 cubes.
The drawing shows 2.93.
Using trade-first subtraction
1s 0.1s 0.01s
16
5
6
12
6. 7
- 3. 7
2
9
2. 9
3
Using U.S. traditional subtraction
1s 0.1s 0.01s
16
5
6
12
6. 7
- 3. 7
2
9
2. 9
3
NOTE Trade-first subtraction resembles U.S. traditional subtraction, except that
in trade-first subtraction, as the name implies, all the trading is done before any
subtractions are carried out, allowing the person to concentrate on one task at
a time.
► Introducing U.S. Traditional
WHOLE-CLASS
ACTIVITY
Subtraction for Decimals
After you have discussed students’ solutions, and even if one or
more students used U.S. traditional subtraction, demonstrate it
again as described on the next page.
Algorithm Project 4
A17
Example 1: $6.72 - $3.79
Step 1:
Start with the 0.01s.
Since 9 > 2, you need to regroup.
Trade 1 tenth for 10 hundredths:
6.72 = 6 ones + 6 tenths + 12 hundredths.
Subtract the 0.01s: 12 - 9 = 3.
6
12
6.7
- 3.7
2
9
3
16
Step 2:
Go to the 0.1s.
Since 7 > 6, you need to regroup.
Trade 1 one for 10 tenths:
6.72 = 5 ones + 16 tenths + 12 hundredths.
Subtract the 0.1s: 16 - 7 = 9.
6
12
6.7
- 3.7
5
2
9
9
3
16
Step 3:
Go to the 1s. You don’t need to regroup.
Subtract the 1s: 5 - 3 = 2.
Remember to include the decimal point
in the answer.
5
6
12
6.7
- 3.7
2
9
2.9
3
$6.72 - $3.79 = $2.93
Seth’s lunch cost $2.93 more than Lily’s lunch.
Example 2: 46.03 - 27.48
9
Step 1:
Start with the 0.01s.
Since 8 > 3, you need to regroup.
There are no tenths in 46.03, so trade 1 one
for 10 tenths and then trade 1 tenth for
10 hundredths: 46.03 = 4 tens + 5 ones +
9 tenths + 13 hundredths.
Subtract the 0.01s: 13 - 8 = 5.
5
4
- 2
Step 3:
Go to the 1s.
Since 7 > 5, you need to regroup.
Trade 1 ten for 10 ones: 46.03 = 3 tens +
15 ones + 9 tenths + 13 hundredths.
Subtract the ones: 15 - 7 = 8.
A18
Algorithm Project 4
U.S. Traditional Subtraction: Decimals
6.0
7.4
3
8
5
9
Step 2:
Go to the 0.1s.
You don’t need to regroup.
Subtract the 0.1s: 9 - 4 = 5.
10 13
5
4
- 2
3
4
- 2
10 13
6.0
7.4
3
8
5
5
15
9
5
10 13
6.0
7.4
3
8
8
5
5
Step 4:
Go to the 10s.
You don’t need to regroup.
Subtract the 10s: 3 - 2 = 1.
Remember to include the decimal point
in the answer.
3
Student Page
15
9
5
10 13
4
- 2
6.0
7.4
1
8.5
Date
3
8
Time
PROJECT
U.S. Traditional Subtraction: Decimals 2
4
Algorithm Project 4
Use U.S. traditional subtraction to solve each problem.
5
1.
Joanna had $73.48 in her bank account.
She wrote a check for $25.69. How much
money is in her bank account now?
47.79
$
46.03 - 27.48 = 18.55
3.29
3.
8.73 - 4.21 =
4.52
= 5.63 - 2.64
5.
31.5 - 7.82 =
23.68
7.
60.08 - 43.29 =
2.
6.04 - 2.75 =
4.
2.99
Example 3: 7.1 - 3.86
Step 1:
Write the problem in columns.
Be sure to line up the places correctly.
Since 3.86 has two decimal places, write
7.1 as 7.10.
7.1
- 3.8
Step 2:
Start with the 0.01s.
Since 6 > 0, you need to regroup.
Trade 1 tenth for 10 hundredths:
7.10 = 7 ones + 0 tenths + 10 hundredths.
Subtract the 0.01s: 10 - 6 = 4.
Step 3:
Go to the 0.1s.
Since 8 > 0, you need to regroup.
Trade 1 one for 10 tenths:
7.10 = 6 ones + 10 tenths + 10 hundredths.
Subtract the 0.1s: 10 - 8 = 2.
Step 4:
Go to the 1s. You don’t need to regroup.
Subtract the 1s: 6 - 3 = 3.
Remember to include the decimal point
in the answer.
0
6
6.
0
10
7.1
- 3.8
0
6
$
18.89
= $45.26 - $26.37
16.79
Math Journal, p. 14P
13P-16P_EMCS_S_MJ1_G4_P04_576361.indd 14
3/4/11 11:56 AM
4
10
6
0
10
7.1
- 3.8
0
6
2
4
Student Page
10
6
0
10
Date
Time
PROJECT
7.1
- 3.8
0
6
3.2
4
U.S. Traditional Subtraction: Decimals 3
4
Algorithm Project 4
Use U.S. traditional subtraction to solve each problem.
1.
Riley bought two card games at the store. The total
cost (before tax) was $9.25. One game cost $3.89.
How much did the other game cost?
$
7.1 - 3.86 = 3.24
2.
5.36
Write a number story for $38.42 - $19.76.
Solve your number story.
$18.66; Number stories vary.
You may want to work several more examples with the whole class.
Suggestions:
$8.49 - $6.35 = ? $2.14
Fill in the missing numbers in the subtraction problems.
3.
5.61 - 3.74 = ? 1.87
-
7.06 - 4.98 = ? 2.08
3.9 - 2.62 = ? 1.28
7 . 0
6
3 . 8
9
3
5.
$28.74 - $19.86 = ? $8.88
40.07 - 26.39 = ? 13.68
4.
9
6 10 16
-
-
7
. 1
9 9
10
10 17
6
0 . 0
1
. 2
8
7
9
6 .
1
3
. 6
8
9
3
6.
3
-
14 13
4
3
10
5 . 4
0
1
8 . 8
5
2
6.5
5
4
7
11
5 . 6
1 .
5
4 3
15
5
4
Math Journal, p. 15P
13P-16P_EMCS_S_MJ1_G4_P04_576361.indd 15
3/4/11 11:56 AM
Algorithm Project 4
A19
Student Page
Date
► Practicing U.S. Traditional
Time
PROJECT
U.S. Traditional Subtraction: Decimals 4
4
Subtraction for Decimals
Algorithm Project 4
Use U.S. traditional subtraction to solve each problem.
1.
(Math Journal 1 or 2, pp. 13P–16P; Student Reference Book, p. 40B)
Quinn has two pieces of ribbon. The yellow ribbon is
12.42 meters long. The pink ribbon is 16.75 meters
long. How much shorter is the yellow ribbon?
4.33
When students are ready, have them solve Problems 2–7 on
journal page 13P. They may find the example on Student
Reference Book, page 40B helpful.
meters
Write a number story for 7.63 - 1.84.
Solve your number story.
2.
5.79; Number stories vary.
Journal pages 14P–16P provide students with additional practice
using U.S. traditional subtraction. Use these journal pages as
necessary.
Fill in the missing numbers in the subtraction problems.
3.
-
10
3
6 . 4
0
2
7 . 9
5
8.4
5
5.
7
9
4
9 9
10 10 16
0 . 0
3 3
6
. 1
7
8
9
6 .
2 Extending the Project
9
8 10 14
1
. 3
2 .
4
-
11
8 . 3
5
3
6.
12
2
7
-
4.
15 13
5
3
2
PARTNER
ACTIVITY
9 . 0
-
2 . 7
6
. 2
4
► Solving Decimal Subtraction
7
7
Math Journal, p. 16P
13P-16P_EMCS_S_MJ1_G4_P04_576361.indd 16
3/4/11 11:57 AM
INDEPENDENT
ACTIVITY
Problems
(Online Additional Practice, pp. 16A–16D; Student Reference Book,
pp. 34 –37 and 40B)
Go to www.everydaymathonline.com
to access the additional practice
pages.
Date
PROJECT
4
Encourage students to use the focus algorithm (trade-first
subtraction) to solve the problems on practice page 16A. 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 34–37 and 40B helpful.
Online Master
Name
Online practice pages 16A–16D provide students with additional
practice solving decimal subtraction problems. Use these pages
as necessary.
Time
Online
Additional
Practice
Trade-First Subtraction: Decimals
Algorithm Project 4
Use trade-first subtraction to solve each problem.
1.
Matthew was building a house for his dog. He
had a board that was 2.45 meters long. He cut
off 1.75 meters. How long is the board now?
Copyright © Wright Group/McGraw-Hill
0.7
meters
2.
8.72 - 4.61 =
4.
3.75
6.
23.77
4.11
3.15
3.
9.02 - 5.87 =
= 7.6 - 3.85
5.
$82.43 - $56.77 = $
= 70.05 - 46.28
7.
6.54 - 3.59 =
25.66
2.95
Online Additional Practice, p. 16A
EM3cuG4OP_16A-16D_P04.indd 16A
A20
Algorithm Project 4
3/31/10 5:34 PM
U.S. Traditional Subtraction: Decimals