Objective
1
To introduce U.S. traditional subtraction.
Doing the Project
Recommended Use: After Lesson 2-8
Key Activities
Children explore and practice U.S. traditional subtraction with multidigit whole numbers.
Key Concepts and Skills
• Identify places in whole numbers and the values of the digits in those places.
materials
Math Journal, pp. 5P– 8P
Student Reference Book, p. 74B
$1, $10, $100 bills (Math Masters,
pp. 399 –402; optional)
base-10 blocks (optional)
[Number and Numeration Goal 1]
• Use subtraction facts to find differences of multidigit whole numbers.
[Operations and Computation Goal 1]
• Subtract multidigit numbers.
[Operations and Computation Goal 2]
• Write and solve subtraction number stories.
[Operations and Computation Goal 6]
Key Vocabulary
U.S. traditional subtraction
2
Extending the Project
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
Student Reference Book, pp. 60 – 63
and 74B
Algorithm Project 2
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Student Page
Date
Time
PROJECT
2
1 Doing the Project
U.S. Traditional Subtraction 1
Algorithm Project 2
Use any strategy to solve the problem.
► Solving a Subtraction Problem
1. In one year, the pet store sold
423 guppies and 256 goldfish.
How many more guppies were
sold?
167
(Math Journal, p. 5P)
guppies
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.
Use U.S. traditional subtraction to solve each problem.
2.
72
- 38
−−−
3.
251
- 89
−−−−
5. 682 - 388 =
573
- 441
−−−−
132
34
4.
► Discussing Solutions
294
162
WHOLE-CLASS
ACTIVITY
(Math Journal, p. 5P)
128
6.
INDEPENDENT
ACTIVITY
= 305 - 177
7.
288
= 824 - 536
Math Journal, p. 5P
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Discuss children’s solutions to Problem 1 on journal page 5P.
423 - 256 = 167 guppies 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:
Modeling with base-10 blocks
Show 423 with 4 hundreds, 2 tens, and 3 ones.
Trade 1 hundred for 10 tens.
Trade 1 ten for 10 ones.
Subtract 256 by removing 2 hundreds, 5 tens, and 6 ones.
167 (1 hundred, 6 tens, and 7 ones) remains.
A6
Algorithm Project 2
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U.S. Traditional Subtraction
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Counting up
+4
256
+40
+100
260
300
+20
400
+3
420
423
256 + 4 = 260
260 + 40 = 300
300 + 100 = 400
400 + 20 = 420
420 + 3 = 423
4 + 40 + 100 + 20 + 3 = 167
423 - 256 = 167
Using trade-first subtraction
11
3
1
13
4
- 2
2
5
3
6
1
6
7
Using U.S. traditional subtraction
11
3
1
13
4
- 2
2
5
3
6
1
6
7
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: 423 - 256
Step 1:
Start with the 1s.
Since 6 > 3, you need to regroup.
Trade 1 ten for 10 ones:
423 = 4 hundreds + 1 ten + 13 ones.
4
- 2
1
13
2
5
3
6
7
Subtract the 1s: 13 - 6 = 7.
Algorithm Project 2
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Student Page
Date
Step 2:
Time
PROJECT
U.S. Traditional Subtraction 2
2
Go to the 10s.
Algorithm Project 2
Since 5 > 1, you need to regroup.
Use U.S. traditional subtraction to solve each problem.
11
3
1
13
4
- 2
2
5
3
6
6
7
1. There were 307 children on the
Trade 1 hundred for 10 tens:
423 = 3 hundreds + 11 tens + 13 ones.
playground. When the school bell
rang, 129 went into the school.
How many children were still on
the playground?
178
2.
children
Subtract the 10s: 11 - 5 = 6.
3.
241
- 93
−−−−
312
- 65
−−−−
Step 3:
247
148
Go to the 100s. You don’t need to regroup.
4.
Subtract the 100s: 3 - 2 = 1.
198
5. 553 - 355 =
724
- 537
−−−−
187
423 - 256 = 167
11
3
1
13
4
- 2
2
5
3
6
1
6
7
167 more guppies than goldfish were sold.
209
6.
= 467 - 258
116
7. 605 - 489 =
Example 2: 604 - 288
Step 1:
Math Journal, p. 6P
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Start with the 1s.
Since 8 > 4, you need to regroup.
9
5
6
- 2
10 14
0
8
4
8
6
There are no tens in 604, so trade 1 hundred
for 10 tens and then trade 1 ten for 10 ones:
604 = 5 hundreds + 9 tens + 14 ones.
Subtract the 1s: 14 - 8 = 6.
Step 2:
Go to the 10s. You don’t need to regroup.
Subtract the 10s: 9 - 8 = 1.
9
5
6
- 2
Student Page
Date
Time
PROJECT
Step 3:
U.S. Traditional Subtraction 3
2
Go to the 100s. You don’t need to regroup.
Algorithm Project 2
Use U.S. traditional subtraction to solve each problem.
Subtract the 100s: 5 - 2 = 3.
1. Marcus had 231 pictures on his computer.
He deleted 84 of them. How many
pictures were left on his computer?
147
604 - 288 = 316
pictures
10 14
0
8
4
8
1
6
9
5
10 14
6
- 2
0
8
4
8
3
1
6
2. Write a number story for 342 - 75.
Solve your number story.
You may want to work several more examples with the
whole class.
267; Number stories vary.
Suggestions:
Fill in the missing numbers in the subtraction problems.
3.
4.
13
-
5.
-
5
3
13
6
4
3
2
6
8
3
7
5
5
8
7
9
9
4 8
8
-
6.
9
6 10
11
7
0
1
3
7
7
3
2 4
46 - 18 = ? 28
17
4 7 17
529 - 313 = ? 216
131 - 56 = ? 75
944 - 576 = ? 368
14
-
2
4
18
3
5
8
1
6
9
1
8
9
730 - 237 = ? 493
302 - 124 = ? 178
Math Journal, p. 7P
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Algorithm Project 2
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U.S. Traditional Subtraction
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Student Page
► Practicing U.S. Traditional
PARTNER
ACTIVITY
Subtraction
Date
Time
PROJECT
U.S. Traditional Subtraction 4
2
Algorithm Project 2
Use U.S. traditional subtraction to solve each problem.
(Math Journal, pp. 5P– 8P; Student Reference Book, p. 74B)
1. Josh wrote a story with 364 words. Zoe
When children are ready, have them solve Problems 2–7 on journal
page 5P. They may find the example on Student Reference Book,
page 74B helpful.
Journal pages 6P– 8P provide children with additional practice
using U.S. traditional subtraction. Use these journal pages as
necessary.
wrote a story with 442 words. How
many more words are in Zoe’s story?
78
Solve your number story.
117; Number stories vary.
Fill in the missing numbers in the subtraction problems.
3.
11
4
9
0
1
4
5
6
4
4 5
5
2
8
4
3 6
8
► Solving Multidigit Subtraction
Problems
-
6.
11
-
9
8 10
5.
INDEPENDENT
ACTIVITY
4.
14
3 4 12
-
2 Extending the Project
words
2. Write a number story for 305 - 188.
11
7
1
12
5
1
12
8
2
2
6
2
2
4
2
9
5
6
9
3
9
3
-
5 3
Math Journal, p. 8P
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(Online Additional Practice, pp. 8A– 8D; Student Reference Book,
pp. 60 – 63 and 74B)
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.
Children may find the examples on Student Reference Book,
pages 60–63 and 74B helpful.
NOTE 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
Use trade-first subtraction to solve each problem.
1. Ravi had 144 marbles. He gave
59 marbles to his cousin. How
many marbles does he have left?
85
2.
marbles
682
- 401
−−−−
3.
281
4.
78
- 39
−−−
39
404
- 147
−−−−
5.
846
= 922 - 76
7.
178
= 236 - 58
257
6. 333 - 265 =
68
Online Additional Practice, p. 8A
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Algorithm Project 2
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