U.S. Traditional
Multiplication
Algorithm
Project
Projject
Objective To introduce U.S. traditional multiplication.
www.everydaymathonline.com
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Family
Letters
Doing the Project
Recommended Use After Lesson 57
Assessment
Management
Common
Core State
Standards
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Mathematical Practices
SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP8
Content Standards
4.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]
• Write and solve multiplication number stories. [Operations and Computation Goal 4]
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. 18, 19, 24C,
and 24D
Algorithm Project 5
A21
Student Page
Date
Time
PROJECT
5
1 Doing the Project
U.S. Traditional Multiplication 1
Algorithm Project 5
► Solving a Multiplication Problem
Use any strategy to solve the problem.
1.
Mountain View Elementary School held a food drive.
Each student donated 4 cans of food. There are
676 students at the school. How many cans of food
did the students donate altogether?
2,704
(Math Journal 1 or 2, p. 17P)
cans
Ask students to solve Problem 1 on journal page 17P. Tell them
they may use any methods they wish, except calculators.
Use U.S. traditional multiplication to solve each problem.
2.
4.
826
2 ∗ 413 =
14,122
= 46 ∗ 307
INDEPENDENT
ACTIVITY
3.
265 ∗ 4 =
1,060
5.
278 ∗ 43 =
11,954
► Discussing Solutions
WHOLE-CLASS
ACTIVITY
(Math Journal 1 or 2, p. 17P)
6.
18 ∗ 72 =
1,296
7.
18,360
Discuss students’ solutions to Problem 1 on journal page 17P.
4 ∗ 676 = 2,704 cans 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:
= 459 ∗ 40
Math Journal, p. 17P
17P-20P_EMCS_S_MJ1_G4_P05_576361.indd 17
3/4/11 11:57 AM
Using partial-products multiplication
676
4
−−−−−
4 ∗ 600 → 2 4 0 0
4 ∗ 70 →
280
24
4∗6→ +
−−−−−−
2704
∗
Using lattice multiplication
6
2
2
7
4
7
1
2
8
0
6
2
4
4
Using U.S. traditional multiplication
3 2
676
∗
4
−−−−−
2704
A22
Algorithm Project 5
U.S. Traditional Multiplication
4
► 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: 4 ∗ 676
Step 1:
2
Multiply the ones.
4 ∗ 6 ones = 24 ones = 2 tens + 4 ones
Write 4 in the 1s place below the line.
Write 2 above the 7 in the 10s place.
Step 2:
676
∗
4
−−−−
4
3 2
Multiply the tens.
4 ∗ 7 tens = 28 tens
Remember the 2 tens from Step 1.
28 tens + 2 tens = 30 tens in all
30 tens = 3 hundreds + 0 tens
Write 0 in the 10s place below the line.
Write 3 above the 6 in the 100s place.
Step 3:
676
∗
4
−−−−
04
3 2
Multiply the hundreds.
4 ∗ 6 hundreds = 24 hundreds
Remember the 3 hundreds from Step 2.
24 hundreds + 3 hundreds = 27 hundreds
27 hundreds = 2 thousands + 7 hundreds
Write 7 in the 100s place below the line.
Write 2 in the 1,000s place below the line.
676
∗
4
−−−−−
2704
Student Page
Date
PROJECT
5
Time
U.S. Traditional Multiplication 2
Algorithm Project 5
4 ∗ 676 = 2,704
Use U.S. traditional multiplication to solve each problem.
The students donated 2,704 cans.
1.
19,200
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:
The Riveras’ cornfield has 75 rows. Each row
contains 256 corn plants. How many corn plants
do the Riveras have in all?
corn plants
2.
64 ∗ 6 =
384
3.
213 ∗ 30 =
6,390
4.
492 ∗ 8 =
3,936
5.
70 ∗ 572 =
40,040
6.
3 ∗ 359 =
1,077
7.
1 2
3 5
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”
since 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.
2,268
= 63 ∗ 36
Math Journal, p. 18P
17P-20P_EMCS_S_MJ1_G4_P05_576361.indd 18
3/4/11 11:57 AM
Algorithm Project 5
A23
Student Page
Date
Example 2: 487 ∗ 35
Time
PROJECT
U.S. Traditional Multiplication 3
5
Step 1:
Algorithm Project 5
1.
A machine can fill 258 bottles of juice per
minute. How many bottles can the machine
fill in 45 minutes?
11,610
2.
4 3
487
∗
35
−−−−−
2 4 3 5 ← The partial product
Multiply 487 by the 5 in 35,
as if the problem were 5 ∗ 487.
Use U.S. traditional multiplication to solve each problem.
bottles
5 ∗ 487 = 2,435
Write a number story for 725 ∗ 6.
Solve your number story.
2 2
4 3
Step 2:
4,350; Number stories vary.
Multiply 487 by the 3 in 35,
as if the problem were 3 ∗ 487.
The 3 in 35 stands for 3 tens,
so write the partial product
one place to the left.
Fill in the missing digits in the multiplication problems.
3.
1
5
4
2
3
4.
5
7
3
6
5
5
7
5
5
5
8 2
0
8
5
0
0
5
∗
6
2
4
3
9
∗
4
2
+ 1
2
5.
2
1
2
6
4
4
6
3
8
4
2 5
2 9
6
0
4
4
∗
+
487
35
−−−−−−
2435
1 4 6 1 0 ← 30 ∗ 487 = 14,610
∗
Write a 0 in the 1s place to show
you are multiplying by tens.
Write the new carries above
the old carries.
Math Journal, p. 19P
17P-20P_EMCS_S_MJ1_G4_P05_576361.indd 19
3/4/11 11:57 AM
2 2
4 3
Step 3:
Add the two partial products
to get the final answer.
35 ∗ 487 = 17,045
487
35
−−−−−−−−
2435
+ 14610
−−−−−−−−
1 7 0 4 5 ← 35 ∗ 487 = 17,045
∗
You may want to work several more examples with the
whole class.
Suggestions:
12 ∗ 43 = ? 516
509 ∗ 6 = ? 3,054
Student Page
Date
70 ∗ 384 = ? 26,880
Time
PROJECT
U.S. Traditional Multiplication 4
5
9 ∗ 500 = ? 4,500
Algorithm Project 5
830 ∗ 29 = ? 24,070
Use U.S. traditional multiplication to solve each problem.
1.
The zebra at the city zoo weighs 627 pounds. The
hippopotamus weighs 5 times as much as the zebra.
How much does the hippopotamus weigh?
3,135
2.
67 ∗ 30 = ? 2,010
pounds
► Practicing U.S. Traditional
Write a number story for 584 ∗ 23.
Solve your number story.
13,432; Number stories vary.
PARTNER
ACTIVITY
Multiplication
(Math Journal 1 or 2, pp. 17P–20P;
Student Reference Book, pp. 24C and 24D)
Fill in the missing digits in the multiplication problems.
3.
7
1
6
8
9
∗
6
4.
2
1
3
8
∗
1
5.
3
2
4
3
2
9
7
4
1
8
5
4
5
2
9
7
0
+ 1
1
8
8
0
0
1
2
3
2
5
5
1
∗
1
+
6
7
2
2
3
5
1
0
6 0
7 0
When students are ready, have them solve Problems 2–7 on
journal page 17P. They may find the examples on Student
Reference Book, pages 24C and 24D helpful.
Journal pages 18P–20P provide students with additional practice
using U.S. traditional multiplication. Use these journal pages as
necessary.
Math Journal, p. 20P
17P-20P_EMCS_S_MJ1_G4_P05_576361.indd 20
A24
Algorithm Project 5
3/4/11 11:57 AM
U.S. Traditional Multiplication
2 Extending the Project
Go to www.everydaymathonline.com
to access the additional practice
pages.
► Solving Multidigit Multiplication
INDEPENDENT
ACTIVITY
Problems
(Online Additional Practice, pp. 20A–20D; Student Reference Book, pp. 18,
19, 24C, and 24D)
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
18, 19, 24C, and 24D helpful.
Online Master
Name
PROJECT
5
Date
Time
Partial-Products Multiplication
Online
Additional
Practice
Algorithm Project 5
Use partial-products multiplication to solve each problem.
1.
Each student in Ms. Barker’s art class has
a box of 64 crayons. There are 27 students
in the class. How many crayons do the students
have altogether?
1,728
2.
Copyright © Wright Group/McGraw-Hill
4.
6.
309
103 ∗ 3 =
1,820
95 ∗ 40 =
crayons
= 28 ∗ 65
3,800
3.
63 ∗ 518 =
32,634
5.
47 ∗ 9 =
423
7.
16,148
= 44 ∗ 367
Online Additional Practice, p. 20A
EM3cuG4OP_20A-20D_P05.indd 20A
3/31/10 5:34 PM
Algorithm Project 5
A25