U.S. Traditional
Multiplication
Algorithm
Project
Projjeect
Objective To introduce U.S. traditional multiplication.
www.everydaymathonline.com
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Family
Letters
Assessment
Management
Doing the Project
Recommended Use After Lesson 29
Common
Core State
Standards
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Mathematical Practices
SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP8
Content Standards
5.NBT.5
Key Concepts and Skills
• Identify places in whole numbers and the values of the digits in those places. [Number and Numeration Goal 1]
• Use multiplication facts to find products of multidigit whole numbers. Materials
Math Journal 1 or 2, pp. 17P–20P
Student Reference Book, pp. 24C and 24D
[Operations and Computation Goal 3]
• Multiply multidigit whole numbers. [Operations and Computation Goal 4]
• Solve multiplication number stories. [Operations and Computation Goal 4]
• Make reasonable estimates for multiplication problems. [Operations and Computation Goal 6]
Key Activities
Students explore and practice U.S. traditional multiplication with multidigit
whole numbers.
Key Vocabulary
U.S. traditional multiplication
Extending the Project
Ex
Students solve multidigit multiplication problems, first using the focus algorithm
(partial-products multiplication) and then using any algorithm they choose.
Materials
Online Additional Practice, pp. 20A−20D
Student Reference Book, pp. 19, 20, 24C,
and 24D
A22
Algorithm Project 5
U.S. Traditional Multiplication
Student Page
Date
1 Doing the Project
► Solving a Multiplication Problem
Time
PROJECT
5
U.S. Traditional Multiplication 1
Algorithm Project 5
Use any strategy to solve the problem.
INDEPENDENT
ACTIVITY
1.
(Math Journal 1 or 2, p. 17P)
A truck delivered 86 cases of juice to a
grocery store. Each case contains 24 bottles
of juice. How many bottles of juice did the
store get?
2,064 bottles
Sample estimates given.
Estimate and then use U.S. traditional multiplication to solve each problem.
Ask students to solve Problem 1 on journal page 17P. Tell them
they may use any methods they wish, except calculators.
► Discussing Solutions
WHOLE-CLASS
ACTIVITY
2.
12 ∗ 34
Estimate:
12 ∗ 34 =
4.
73 ∗ 288
Estimate:
350
3.
455 ∗ 600
408
Estimate:
455 ∗ 600 =
21,000
5.
49 ∗ 60
300,000
273,000
Estimate:
3,000
(Math Journal 1 or 2, p. 17P)
Discuss students’ solutions to Problem 1 on journal page 17P.
86 ∗ 24 = 2,064 bottles Expect that students will use several
different methods, including partial-products multiplication and
lattice multiplication. Some students may also use U.S. traditional
multiplication. Possible strategies:
Using partial-products multiplication
86
24
−−−−−
1600
120
320
24
−−−−−
2064
21,024
6.
92 ∗ 46
Estimate:
92 ∗ 46 =
= 73 ∗ 288
4,500
7.
4,232
2,940
180,000
Estimate:
49 ∗ 60 =
305 ∗ 592
180,560
= 305 ∗ 592
Math Journal, p. 17P
17P-20P_EMCS_S_MJ2_G5_P05_576434.indd 17
3/8/11 11:37 AM
∗
20 ∗ 80 →
20 ∗ 6 →
4 ∗ 80 →
4∗6→
Using lattice multiplication
8
1
2
0
1
3
6
6
2
NOTE Reinforce the use of estimation by
asking students to make an estimate prior to
solving each problem. The estimate is then
used to check the reasonableness of the
solution to the problem.
6
1
2
2
2
4
4
4
Using U.S. traditional multiplication
1
2
86
24
−−−−−−
344
+ 1720
−−−−−−
2064
∗
Algorithm Project 5
A23
► Introducing U.S. Traditional
WHOLE-CLASS
ACTIVITY
Multiplication
After you have discussed students’ solutions, and even if one or
more students used U.S. traditional multiplication,
demonstrate it again as described below.
Example 1: 24 ∗ 86
Step 1:
2
Multiply 86 by the 4 in 24,
as if the problem were 4 ∗ 86.
86
∗ 24
−−−−
3 4 4 ← The partial product
4 ∗ 86 = 344
1
2
Step 2:
86
24
−−−−−
344
1 7 2 0 ← 20 ∗ 86 = 1,720
Multiply 86 by the 2 in 24,
as if the problem were 2 ∗ 86.
∗
The 2 in 24 stands for 2 tens,
so write the partial product
one place to the left.
Write a 0 in the 1s place to show
you are multiplying by tens.
Write the new carry above
the old carry.
1
2
Step 3:
Add the two partial products
to get the final answer.
24 ∗ 86 = 2,064
86
24
−−−−−−
344
+ 1720
−−−−−−
2 0 6 4 ← 24 ∗ 86 = 2,064
∗
The store purchased 2,064 bottles of juice.
NOTE U.S. traditional multiplication is so familiar that the details of its working
may appear more meaningful than they are. Consider the following example:
1 22
3 55
147
∗
38
−−−−−−
1176
+4410
−−−−−−−
5586
Many people, when asked why the “2” carried from “3 ∗ 7” is written in the
10s place, will explain that it stands for “2 tens.” But this “2” really means
“2 hundreds” because the “3” is really “3 tens.” U.S. traditional multiplication
is efficient—though not as efficient as a calculator—but it is not, despite its
familiarity, conceptually transparent.
A24
Algorithm Project 5
U.S. Traditional Multiplication
Student Page
Example 2: 237 ∗ 456
Date
Time
PROJECT
U.S. Traditional Multiplication 2
5
Step 1:
456
∗ 237
−−−−−−
3 1 9 2 ← The partial product
Multiply 456 by the 7 in 237,
as if the problem were 7 ∗ 456.
1 1
3 4
Step 2:
Multiply 456 by the 3 in 237,
as if the problem were 3 ∗ 456.
The 3 in 237 stands for 3 tens,
so write the partial product one
place to the left.
Algorithm Project 5
3 4
7 ∗ 456 = 3,192
456
237
−−−−−−
3192
1 3 6 8 0 ← 30 ∗ 456 = 13,680
Estimate and then use U.S. traditional multiplication to solve each problem.
1.
A rectangular wall is covered with small tiles.
The tiles are arranged in 136 rows and
84 columns. How many tiles are on the wall?
11,424 tiles
2.
46 ∗ 33
4.
649 ∗ 35
6.
316 ∗ 438
Estimate:
1 1
1 1
3 4
Step 3:
The 2 in 237 stands for
2 hundreds, so write the partial
product two places to the left.
Estimate:
316 ∗ 438 =
4,660
24,000
5.
82 ∗ 570
7.
277 ∗ 65
22,715
649 ∗ 35 =
Write the new carries above
the old carries.
Multiply 456 by the 2 in 237,
as if the problem were 2 ∗ 456.
1,518
46 ∗ 33 =
8,000
Sample estimates given.
3. 233 ∗ 20
Estimate: 4,000
1,500
Estimate:
∗
Write a 0 in the 1s place to show
you are multiplying by tens.
Estimate:
Estimate:
138,408
48,000
46,740
82 ∗ 570 =
120,000
= 233 ∗ 20
Estimate:
18,000
18,005
= 277 ∗ 65
Math Journal, p. 18P
17P-20P_EMCS_S_MJ2_G5_P05_576434.indd 18
3/8/11 11:37 AM
456
237
−−−−−−−
3192
13680
9 1 2 0 0 ← 200 ∗ 456 = 91,200
∗
Write 0s in the 10s and 1s places
to show you are multiplying by
hundreds.
Write the new carries above
the old carries.
Step 4:
Add the three partial products
to get the final answer.
237 ∗ 456 = 108,072
1 1
1 1
3 4
456
∗
237
−−−−−−−
3192
13680
+ 91200
−−−−−−−
1 0 8 0 7 2 ← 237 ∗ 456 = 108,072
You may want to work several more examples with the whole class.
Student Page
Date
Time
PROJECT
5
U.S. Traditional Multiplication 3
Algorithm Project 5
Use U.S. traditional multiplication to solve each problem.
1.
Raj delivers 47 newspapers each day. How
many newspapers will he deliver in the month
of August, which has 31 days?
1,457 newspapers
2.
Write a number story for 327 ∗ 283.
Solve your number story.
92,541; Number stories vary.
Suggestions:
320 ∗ 21 = ? 6,720
48 ∗ 73 = ? 3,504
675 ∗ 50 = ? 33,750
59 ∗ 302 = ? 17,818
700 ∗ 36 = ? 25,200
Fill in the missing digits in the multiplication problems.
3.
4.
1
∗
+ 1
1 ,
5.
4
4
2
3
3
5
6
2
7
3
9
2
1
2
0
5
1
2
∗
0
8
6
4
1
2
3
2
+1
8
4
8
0
1
9
, 7
1
2
1
∗
+
4
2
2
4
, 5
8
5
5
3
5
5
5
0
0
5
284 ∗ 77 = ? 21,868
Math Journal, p. 19P
17P-20P_EMCS_S_MJ2_G5_P05_576434.indd 19
3/8/11 11:37 AM
Algorithm Project 5
A25
Student Page
Date
Time
PROJECT
► Practicing U.S. Traditional
U.S. Traditional Multiplication 4
5
Multiplication
Algorithm Project 5
Use U.S. traditional multiplication to solve each problem.
1.
PARTNER
ACTIVITY
(Math Journal 1 or 2, pp. 17P–20P; Student Reference Book,
pp. 24C and 24D)
Jackie’s Web site had 697 visitors in its first
month. In the second month, the site had
74 times as many visitors. How many people
visited Jackie’s Web site in the second month?
51,578 people
2.
When students are ready, have them estimate and then solve
Problems 2–7 on journal page 17P. They may find the examples
on Student Reference Book, pages 24C and 24D helpful.
Write a number story for 48 ∗ 575.
Solve your number story.
27,600; Number stories vary.
Journal pages 18P–20P provide students with additional practice
using U.S. traditional multiplication. Use these journal pages as
necessary.
Fill in the missing digits in the multiplication problems.
3.
4.
1
1
2
6
∗
+ 1
2
4
5
3
1
2
0
7
2
0
1 ,
8
4
0
2
4
3
2
2
3
8
3
9
1
4
1
8
2
9
7
∗
4
7
5
5
2 Extending the Project
0
+ 1
1
8
8
0
0
1
2
3 , 2
5
5
Math Journal, p. 20P
17P-20P_EMCS_S_MJ2_G5_P05_576434.indd 20
3/8/11 11:37 AM
► Solving Multidigit Multiplication
INDEPENDENT
ACTIVITY
Problems
(Online Additional Practice, pp. 20A–20D; Student Reference Book,
pp. 19, 20, 24C, and 24D)
Go to www.everydaymathonline.com
to access the additional practice
pages.
Online practice pages 20A–20D provide students with additional
practice solving multidigit multiplication problems. Use these
pages as necessary.
Encourage students to use the focus algorithm (partial-products
multiplication) to solve the problems on practice page 20A. 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 19, 20, 24C, and 24D helpful.
Online Master
Name
Date
PROJECT
Time
Online
Additional
Practice
Partial-Products Multiplication
5
Algorithm Project 5
Estimate and then use partial-products multiplication to solve each problem.
1.
Last week, a theater showed a popular movie
35 times. Each time, all 218 seats in the theater
were full. How many people saw the movie at
that theater last week?
8,000
Estimate:
7,630 people
2.
300 ∗ 21
4.
23 ∗ 84
6.
60 ∗ 504
Estimate:
300 ∗ 21 =
Estimate:
23 ∗ 84 =
Estimate:
60 ∗ 504 =
6,000
Sample estimates given.
3. 75 ∗ 363
Estimate: 28,000
6,300
1,600
5.
38 ∗ 59
27,225
1,932
30,000
7.
182 ∗ 797
Estimate:
38 ∗ 59 =
30,240
Estimate:
= 75 ∗ 363
2,400
2,242
160,000
145,054 = 182 ∗ 797
Online Additional Practice, p. 20A
EM3cuG5OP_20A-20D_P05.indd 20A
A26
4/1/10 5:36 PM
Algorithm Project 5
U.S. Traditional Multiplication