Algorithm
U.S. Traditional
Subtraction
Project
P j t
Objective To introduce U.S. traditional subtraction.
www.everydaymathonline.com
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Family
Letters
Doing the Project
Recommended Use After Lesson 28
Assessment
Management
Common
Core State
Standards
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Mathematical Practices
SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP7
Content Standards
3.OA.8, 3.NBT.2
Key Concepts and Skills
• Identify places in whole numbers and the values of the digits in those places. [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]
Materials
Math Journal 1 or 2, pp. 5P– 8P
Student Reference Book, p. 74B
$1, $10, $100 bills (Math Masters,
pp. 399 –402; optional)
base-10 blocks (optional)
• Write and solve subtraction number stories. [Operations and Computation Goal 6]
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
Student Reference Book, pp. 60–63 and 74B
Algorithm Project 2
A5
Student Page
Date
Time
PROJECT
1 Doing the Project
U.S. Traditional Subtraction 1
2
Algorithm Project 2
Make a ballpark estimate. Write a number model
to show your estimate. Use any strategy
to solve the problem.
Sample answer:
1.
Ballpark estimate:
► Solving a Subtraction Problem
400 - 250 = 150
In one year, the pet store sold
423 guppies and 256 goldfish.
How many more guppies were sold?
167
guppies
(Math Journal, p. 5P)
Sample estimates shown.
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.
Ballpark estimate:
3.
Ballpark estimate:
600 - 450 = 150
70 - 40 = 30
573
- 441
−−−−
72
- 38
−−−
132
4.
► Discussing Solutions
34
Ballpark estimate:
INDEPENDENT
ACTIVITY
5.
250 - 100 = 150
(Math Journal, p. 5P)
Ballpark estimate:
700 - 400 = 300
682 - 388 =
251
- 89
−−−−
294
162
Math Journal, p. 5P
EM3cuMJ2_G3_05P-08P_P02.indd 5
WHOLE-CLASS
ACTIVITY
4/28/10 4:28 PM
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
U.S. Traditional Subtraction
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
A7
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.
Make a ballpark estimate. Write a number model
to show your estimate. Use U.S. traditional subtraction
to solve each problem.
Sample answer:
1.
There were 307 children on the playground.
When the school bell rang, 129 went into the school.
How many children were still on the playground?
178
children
Sample estimates shown.
2.
3.
Ballpark estimate:
300 - 50 = 250
Subtract the 100s: 3 - 2 = 1.
247
148
4.
Go to the 100s. You don’t need to regroup.
312
- 65
−−−−
241
- 93
−−−−
5.
Ballpark estimate:
423 - 256 = 167
Ballpark estimate:
550 - 350 = 200
700 - 500 = 200
4
- 2
2
5
3
6
6
7
11
3
1
13
4
- 2
2
5
3
6
1
6
7
5
10 14
167 more guppies than goldfish were sold.
198
553 - 355 =
724
- 537
−−−−
13
Subtract the 10s: 11 - 5 = 6.
Step 3:
Ballpark estimate:
250 - 100 = 150
1
Trade 1 hundred for 10 tens:
423 = 3 hundreds + 11 tens + 13 ones.
300 - 100 = 200
Ballpark estimate:
11
3
187
Example 2: 604 - 288
Step 1:
Math Journal, p. 6P
EM3cuMJ2_G3_05P-08P_P02.indd 6
4/28/10 4:28 PM
Start with the 1s.
Since 8 > 4, you need to regroup.
9
6
- 2
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
Algorithm Project 2
Go to the 100s. You don’t need to regroup.
Make a ballpark estimate. Write a number model
to show your estimate. Use U.S. traditional subtraction
to solve each problem.
Sample answer:
Subtract the 100s: 5 - 2 = 3.
1.
Ballpark estimate:
250 - 100 = 150
604 - 288 = 316
Marcus had 231 pictures on his computer.
He deleted 84 of them. How many pictures
were left on his computer?
147
2.
pictures
Ballpark estimate:
350 - 100 = 250
Write a number story for 342 - 75.
Solve your number story.
Sample estimate
shown.
46 - 18 = ? 28
529 - 313 = ? 216
Fill in the missing numbers in the subtraction problems.
3.
4.
13
-
5
3
13
6
4
3
2
6
8
3
7
5
-
131 - 56 = ? 75
9
6 10
11
7
0
1
3
7
7
3
2 4
944 - 576 = ? 368
730 - 237 = ? 493
302 - 124 = ? 178
Math Journal, p. 7P
EM3cuMJ2_G3_05P-08P_P02.indd 7
A8
4/28/10 4:28 PM
Algorithm Project 2
U.S. Traditional Subtraction
0
8
4
8
1
6
9
5
10 14
6
- 2
0
8
4
8
3
1
6
You may want to work several more examples with the
whole class.
Suggestions:
267; Number stories vary.
10 14
Student Page
► Practicing U.S. Traditional
PARTNER
ACTIVITY
Subtraction
Date
Time
PROJECT
U.S. Traditional Subtraction 4
2
Algorithm Project 2
Make a ballpark estimate. Write a number model
to show your estimate. Use U.S. traditional subtraction
to solve each problem.
Sample answer:
(Math Journal, pp. 5P– 8P; Student Reference Book, p. 74B)
When children are ready, have them solve Problems 2–5 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.
1.
450 - 350 = 100
Ballpark estimate:
Josh wrote a story with 364 words. Zoe
wrote a story with 442 words. How
many more words are in Zoe’s story?
78
2.
words
300 - 200 = 100
Ballpark estimate:
Sample estimate
shown.
Write a number story for 305 - 188.
Solve your number story.
117; Number stories vary.
Fill in the missing numbers in the subtraction problems.
3.
2 Extending the Project
► Solving Multidigit Subtraction
4.
9
8 10
11
9
0
1
4
5
6
4
4 5
-
11
-
5
1
12
6
2
2
5
6
9
5 3
INDEPENDENT
ACTIVITY
Problems
Math Journal, p. 8P
EM3cuMJ2_G3_05P-08P_P02.indd 8
4/28/10 4:28 PM
(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.
Go to www.everydaymathonline.com
to access the additional practice
pages.
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.
Online Master
Name
Date
PROJECT
Time
Online
Additional
Practice
Trade-First Subtraction
2
Algorithm Project 2
Make a ballpark estimate. Write a number model to show your estimate.
Use trade-first subtraction to solve each problem.
1. Ballpark estimate:
Sample answer: 140 - 60 = 80
Ravi had 144 marbles. He gave
59 marbles to his cousin. How
many marbles does he have left?
85
marbles
Sample estimates shown.
2. Ballpark estimate:
80 - 40 = 40
78
- 39
−−−
39
4. Ballpark estimate:
400 - 150 = 250
404
- 147
−−−−−
3. Ballpark estimate:
240 - 60 = 180
236
- 58
−−−−
178
5. Ballpark estimate:
920 - 80 = 840
846
= 922 - 76
257
Online Additional Practice, p. 8A
EM3cuG3OP_08A-08D_P02.indd 8A
4/26/10 1:44 PM
Algorithm Project 2
A9