U.S. Traditional
Subtraction
Algorithm
Objective To introduce U.S. traditional subtraction.
Project
P j t
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Assessment
Management
Common
Core State
Standards
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Doing the Project
Recommended Use After Lesson 113
Materials
Key Concepts and Skills
Math Journal 1 or 2, pp. 5P– 8P
• Identify places in whole numbers and the values of the digits in those places. My Reference Book, pp. 35A and 35B
[Number and Numeration Goal 2]
• Use subtraction facts to find differences of multidigit whole numbers. [Operations and Computation Goal 1]
$1, $10, $100 bills (Math Masters,
pp. 459– 461; optional)
base-10 blocks (optional)
• Subtract multidigit numbers. [Operations and Computation Goal 2]
• Write and solve subtraction number stories. [Operations and Computation Goal 4]
Key Activities
Children explore and practice U.S. traditional subtraction with multidigit whole numbers.
Key Vocabulary
U.S. traditional subtraction
Extending the Project
Ex
Children solve multidigit subtraction problems, first using the focus algorithm (trade-first
subtraction) and then using any algorithm they choose.
Materials
Online Additional Practice, pp. 8A−8D
My Reference Book, pp. 31–35, 35A,
and 35B
A6
Algorithm Project 2
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U.S. Traditional Subtraction
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Student Page
Date
1 Doing the Project
► Solving a Subtraction Problem
Time
PROJECT
U.S. Traditional Subtraction 1
2
Algorithm Project 2
INDEPENDENT
ACTIVITY
Write a number model to show your ballpark estimate.
Use any strategy to solve the problem.
1. Jakob has 93 red blocks and 58 blue blocks
in his toy box. How many more red blocks
than blue blocks are in the toy box?
(Math Journal 1 or 2, p. 5P; Math Masters, pp. 459–461)
Ballpark estimate:
Ask children to solve Problem 1 on journal page 5P. Tell them they
may use base-10 blocks, play money, paper and pencil, or any other
tools they wish, except calculators.
35
90 - 60 = 30
red blocks
Sample estimates shown.
Write a number model to show your ballpark estimate.
Use U.S. traditional subtraction to solve each problem.
2. Ballpark estimate:
3. Ballpark estimate:
100 - 50 = 50
80 - 40 = 40
► Discussing Solutions
WHOLE-CLASS
ACTIVITY
(Math Journal 1 or 2, p. 5P; Math Masters, pp. 459–461)
78
- 37
96
- 47
41
49
4. Ballpark estimate:
Discuss children’s solutions to Problem 1 on journal page 5P.
93 - 58 = 35 blocks Expect that children will use several different
methods, which may include modeling with base-10 blocks or other
manipulatives, applying various paper-and-pencil methods such as
counting up, and using trade-first subtraction. Some children may
also use U.S. traditional subtraction. Possible strategies:
5. Ballpark estimate:
190 - 80 = 110
250 - 170 = 80
193
- 76
252
- 169
117
83
Math Journal, p. 5P
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Modeling with base-10 blocks
Show 93 with 9 tens and 3 ones.
Trade 1 ten for 10 ones.
Subtract 58 by removing 5 tens and 8 ones.
35 (3 tens and 5 ones) remains.
Algorithm Project 2
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A7
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Counting up
58
+2
60
+30
90
+3
93
58 + 2 = 60
60 + 30 = 90
90 + 3 = 93
2 + 30 + 3 = 35
Using trade-first subtraction
-
8
13
9
5
3
8
3
5
Using U.S. traditional subtraction
-
8
13
9
5
3
8
3
5
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
After you have discussed children’s solutions, and even if one or
more children used U.S. traditional subtraction, demonstrate
it again as described below.
Example 1: 93 - 58
Step 1:
Start with the 1s.
Since 8 > 3, you need to regroup.
Trade 1 ten for 10 ones:
93 = 8 tens + 13 ones.
-
8
13
9
5
3
8
5
Subtract the 1s: 13 - 8 = 5.
A8
Algorithm Project 2
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Student Page
8
13
9
- 5
3
8
3
5
Step 2:
Go to the 10s. You don’t need to regroup.
Subtract the 10s: 8 - 5 = 3.
Date
Time
PROJECT
U.S. Traditional Subtraction 2
2
Algorithm Project 2
Write a number model to show your ballpark estimate.
Use U.S. traditional subtraction to solve each problem.
1. Rosa had 56 baseball cards.
There are 35 more red blocks than blue blocks
in the toy box.
She gave 17 cards to her
friend Andre. How many
cards does she have left?
Ballpark estimate:
39
Example 2: 342 - 168
Step 1:
Start with the 1s.
Since 8 > 2, you need to regroup.
3
- 1
3
12
4
6
2
8
2. Ballpark estimate:
3. Ballpark estimate:
90 - 70 = 20
50 - 30 = 20
89
- 71
46
- 28
18
18
4. Ballpark estimate:
5. Ballpark estimate:
150 - 50 = 100
Subtract the 1s: 12 - 8 = 4.
Step 2:
Since 6 > 3, you need to regroup.
Sample estimates shown.
4
Trade 1 ten for 10 ones:
342 = 3 hundreds + 3 tens + 12 ones.
Go to the 10s.
60 - 20 = 40
baseball cards
550 - 260 = 290
154
- 45
548
- 259
109
289
13
2
3
12
3
- 1
4
6
2
8
7
4
Trade 1 hundred for 10 tens:
342 = 2 hundreds + 13 tens + 12 ones.
Math Journal, p. 6P
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Subtract the 10s: 13 - 6 = 7.
Step 3:
Go to the 100s. You don’t need to regroup.
Subtract the 100s: 2 - 1 = 1.
342 - 168 = 174
2
13 12
3
- 1
4
6
2
8
1
7
4
Student Page
You may want to work several more examples with the whole class.
Date
Suggestions:
Time
PROJECT
U.S. Traditional Subtraction 3
2
81 - 56 = ? 25
Algorithm Project 2
? = 49 - 17 32
Write a number model to show your ballpark estimate.
Use U.S. traditional subtraction to solve the problem.
1. There are 84 children who ride a
78 - 49 = ? 29
bus to school. 65 of them are boys.
How many girls ride a bus to school?
134 - 78 = ? 56
Ballpark estimate:
19
403 - 238 = ? 165
2. Write a number story for 79 - 68.
Solve your number story.
526 - 329 = ? 197
► Practicing U.S. Traditional
Sample answer: 85 - 65 = 20
girls
11; Number stories vary.
PARTNER
ACTIVITY
Subtraction
Fill in the missing numbers in the subtraction problems.
3.
(Math Journal 1 or 2, pp. 5P– 8P; My Reference Book, pp. 35A and 35B)
-
When children are ready, have them solve Problems 2–5 on journal
page 5P. They may find the examples on My Reference Book, pages
35A and 35B helpful.
4.
4 14
5
4
2
5
2
9
8 11
1
-
1
9
1
4
6
4
5
Math Journal, p. 7P
Journal pages 6P– 8P provide children with additional practice using
U.S. traditional subtraction. Use these journal pages as necessary.
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Algorithm Project 2
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Student Page
Date
Time
PROJECT
2 Extending the Project
U.S. Traditional Subtraction 4
2
Algorithm Project 2
Write a number model to show your ballpark estimate.
Use U.S. traditional subtraction to solve the problem.
► Solving Multidigit Subtraction
1. Jenna’s book has 46 pages. Shen’s book
has 97 pages. How many more pages are
in Shen’s book?
Ballpark estimate:
51
INDEPENDENT
ACTIVITY
Problems
Sample answer: 100 - 50 = 50
(Online Additional Practice, pp. 8A– 8D; My Reference Book, pp. 34, 35,
35A, and 35B)
pages
2. Write a number story for 37 - 18.
Solve your number story.
19; Number stories vary.
Online practice pages 8A– 8D provide children with additional
practice solving multidigit subtraction problems. Use these pages
as necessary.
Encourage children to use the focus algorithm (trade-first
subtraction) to solve the problems on practice page 8A. Invite
them to use any algorithm they wish to solve the problems on the
remaining pages.
Fill in the missing numbers in the subtraction problems.
3.
4.
8 10
-
9
0
6
4
2
6
6 13
-
3
7
3
1
3
6
2 3
7
Children may find the examples on My Reference Book, pages 34,
35, 35A, and 35B helpful.
Math Journal, p. 8P
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Go to www.everydaymathonline.com
to access the additional practice
pages.
Online Master
Name
Date
PROJECT
Time
Online
Additional
Practice
Trade-First Subtraction
2
Algorithm Project 2
Write a number model to show your ballpark estimate.
Use trade-first subtraction to solve each problem.
1. Meera had 87 rocks in
her collection. She gave
68 rocks to her sister.
How many rocks did she
have left?
Ballpark estimate:
19
90 - 70 = 20
rocks
Sample estimates shown.
2. Ballpark estimate:
3. Ballpark estimate:
80 - 40 = 40
60 - 40 = 20
76
- 39
−−−
63
- 41
−−−
22
37
4. Ballpark estimate:
160 - 70 = 90
156
- 68
−−−−
88
5. Ballpark estimate:
380 - 200 = 180
379
- 197
−−−−
182
Online Additional Practice, p. 8A
EM3cuG2OP_08A-08D_P02.indd 8A
A10
Algorithm Project 2
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U.S. Traditional Subtraction
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