Algorithm
U.S. Traditional
Multiplication: Decimals
Objective To introduce U.S. traditional multiplication
Project
Projject
ffor decimals.
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, 5.NBT.7
Key Concepts and Skills
• Identify places in whole numbers and decimals and the values of the digits
in those places.
[Number and Numeration Goal 1]
• Calculate products of decimals and whole numbers and of decimals and decimals.
[Operations and Computation Goal 3]
Materials
Math Journal 1 or 2, pp. 21P–24P
Student Reference Book, pp. 54C and 54D
play money (optional)
• Solve multiplication number stories with decimals.
[Operations and Computation Goal 3]
• Make reasonable estimates for multiplication with decimals.
[Operations and Computation Goal 6]
Key Activities
Students explore and practice U.S. traditional multiplication with decimals.
Extending the Project
Ex
Students solve decimal multiplication problems, first using the focus algorithm
(partial-products multiplication) and then using any algorithm they choose.
Materials
Online Additional Practice, pp. 24A−24D
Student Reference Book, pp. 37– 40, 54C,
and 54D
Algorithm Project 6
A27
Student Page
Date
Time
PROJECT
6
1 Doing the Project
U.S. Traditional Multiplication: Decimals 1
Algorithm Project 6
Use any strategy to solve the problem.
1.
► Solving a Decimal Multiplication
A small salad at Casey’s Diner costs $4.79.
What is the cost of 3 small salads?
$14.37
INDEPENDENT
ACTIVITY
Problem
Use U.S. traditional multiplication to solve each problem. Use estimation
or count decimal places to place the decimal point in your answers.
2.
40.06 ∗ 25 =
1,001.50
or 1,001.5
0.021
4.
= 0.7 ∗ 0.03
3.
5.
3.6 ∗ 6,072 =
0.09 ∗ 0.02 =
(Math Journal 1 or 2, p. 21P)
21,859.2
Ask students to solve Problem 1 on journal page 21P. Tell them
they may use play money, paper and pencil, or any other tools
they wish, except calculators.
0.0018
► Discussing Solutions
6.
175.34
= 79.7 ∗ 2.2
7.
3.91 ∗ 0.5 =
(Math Journal 1 or 2, p. 21P)
1.955
Math Journal, p. 21P
21P-24P_EMCS_S_MJ2_G5_P06_576434.indd 21
WHOLE-CLASS
ACTIVITY
3/8/11 11:38 AM
Discuss students’ solutions to Problem 1 on journal page 21P.
$4.79 ∗ 3 = $14.37 Expect that students will use several different
methods, which may include modeling with play money, using
repeated addition, using lattice multiplication, and using partialproducts multiplication. Some students may also use U.S.
traditional multiplication. Possible strategies:
Modeling with play money
$1
$1
$1
$1
$1
$1
$1
$1
$1
$1
$1
$1
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
D
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
P
Use play money to show the cost of 3 salads.
4 $1 + 4 $1 + 4 $1 = 12 $1
or 1 $10 and 2 $1
Combine the bills.
7 D + 7 D + 7 D = 21 D or 2 $1
and 1 D
Combine the dimes.
9 P + 9 P + 9 P = 27 P or 2 D and 7 P
Combine the pennies.
1 $10 + 2 $1 + 2 $1 + 1 D + 2 D + 7 P = $14.37
Combine the bills and coins.
A28
Algorithm Project 6
U.S. Traditional Multiplication: Decimals
Using repeated addition
$9.58
+ $4.79
−−−−−−
$13.00
$1.20
+ $0.17
−−−−−−
$14.37
$4.79
+ $4.79
−−−−−
$8.00
$1.40
+ $0.18
−−−−−
$9.58
$4.79 ∗ 3 = $14.37
Using lattice multiplication
4 · 7
1
1
2
2
9
1
2
7
7
4· 3
3
·
$4.79 ∗ 3 = $14.37
Using partial-products multiplication
$4.79 ∗ 3 = $14.37
$4 . 7 9
∗
3
−−−−−−−
12.00
3 [$4.00s] →
2.10
3 [$0.70s] →
0.27
3 [$0.09s] → +
−−−−−−−−
$1 4 . 3 7
Using U.S. traditional multiplication
2
2
$4 . 7 9
3
−−−−−−
$1 4 . 3 7
∗
$4.79 ∗ 3 = $14.37
► Introducing U.S. Traditional
WHOLE-CLASS
ACTIVITY
Multiplication for Decimals
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: $4.79 ∗ 3
Step 1:
Start with the pennies.
3 ∗ 9 pennies = 27 pennies
27 pennies = 2 dimes + 7 pennies
Step 2:
Multiply the dimes.
3 ∗ 7 dimes = 21 dimes
Remember the 2 dimes from Step 1.
21 dimes + 2 dimes = 23 dimes in all
23 dimes = $2 + 3 dimes
2
4.79
∗
3
7
2
2
4.79
∗
3
37
Algorithm Project 6
A29
Student Page
Date
Step 3:
Time
PROJECT
Use U.S. traditional multiplication to solve each problem. Use estimation
or count decimal places to place the decimal point in your answers.
Find the area of the rectangle.
184.23 m2
8.9 m
20.7 m
2.
6.687
7.43 ∗ 0.9 =
3.
0.2494
0.86 ∗ 0.29 =
2
4.79
∗
3
14.37
Multiply the dollars.
3 ∗ $4 = $12
Remember the $2 from Step 2.
$12 + $2 = $14 in all
$14 = 1 [$10] + 4 [$1]s
Remember to include the decimal point.
Algorithm Project 6
1.
2
U.S. Traditional Multiplication: Decimals 2
6
$4.79 ∗ 3 = $14.37
Three small salads cost $14.37.
2,117
4.
= 7.3 ∗ 290
0.144
5. 0.9 ∗ 0.16 =
One way to use U.S. traditional multiplication with decimals is
to multiply the factors as though they were whole numbers and
then use estimation to place the decimal point.
2,291.4
6.
= 60.3 ∗ 38
7.
84.48
21.12 ∗ 4 =
Example 2: 6.07 ∗ 0.5
Step 1:
Math Journal, p. 22P
21P-24P_EMCS_S_MJ2_G5_P06_576434.indd 22
3/8/11 11:38 AM
3
Multiply as though both factors were whole numbers.
607
∗
5
3035
Step 2:
Estimate the product: 6.07 ∗ 0.5 ≈ 6 ∗ 0.5 = 3.
Step 3:
NOTE This second method for multiplying
Use the estimate to place the decimal point
in the answer. The estimate is 3, so place the
decimal point to make the answer close to
3: 3.035 is close to 3.
6.07 ∗ 0.5 = 3.035
decimals (used in Example 3) is useful when
there are many decimal places in the factors,
making it difficult to estimate the answer. For
example, 0.078 ∗ 0.029 = 0.002262.
Another way to use U.S. traditional multiplication with decimals
is to multiply as though both factors were whole numbers and
then find the total number of places to the right of the decimal
points of both factors to decide where to place the decimal point.
Student Page
Date
Time
PROJECT
U.S. Traditional Multiplication: Decimals 3
6
Example 3: 0.47 ∗ 0.82
Algorithm Project 6
Use U.S. traditional multiplication to solve each problem. Use estimation
or count decimal places to place the decimal point in your answers.
1.
Step 1:
A model train caboose is 7.75 inches long.
The actual caboose is 48 times as long as this.
How long is the actual caboose?
Multiply as though both factors were whole
numbers.
372.00 or 372 in.
2.
Write a number story for 40.06 ∗ 67.
Solve your number story.
2,684.02; Number stories vary.
1
1
3
∗
+ 1
1
4.
3
4
∗
2 . 7
5 . 6
1
9
6
3
8 . 0
6
2
3
5
0
8 3
. 1
2
4.8
5
5.
Count the total number of places to the right of the
decimal points of both factors. There are 2 places
to the right of the decimal point in 0.47. There are
2 places to the right of the decimal point in 0.82.
There are 4 decimal places in all.
4
0 . 1
0 . 6
3
0
∗
0 .
9
0 . 5
0
9
5
Step 3:
Place the decimal point 4 places from
the right.
Math Journal, p. 23P
21P-24P_EMCS_S_MJ2_G5_P06_576434.indd 23
A30
Algorithm Project 6
47
82
−−−−−−
94
+ 3760
−−−−−−
3854
∗
Step 2:
Fill in the missing digits in the multiplication problems.
3.
5
1
3/8/11 11:38 AM
0.47 ∗ 0.82 = 0.3854
U.S. Traditional Multiplication: Decimals
. 3
8
5
4 .
Student Page
You may want to work several more examples with the whole class.
Date
Time
PROJECT
U.S. Traditional Multiplication: Decimals 4
6
Suggestions:
Algorithm Project 6
4.64 ∗ 24 = ? 111.36
Use U.S. traditional multiplication to solve each problem. Use estimation
or count decimal places to place the decimal point in your answers.
30.8 ∗ 52 = ? 1,601.6
1.
5.3 ∗ 953 = ? 5,050.9
A drugstore received a shipment of 504 bottles
of shampoo. Each bottle contains 8.4 ounces
of shampoo. How much shampoo is in all
the bottles combined?
4,233.6 ounces
0.8 ∗ 0.38 = ? 0.304
2.
Write a number story for 3.23 ∗ 22.
Solve your number story.
71.06; Number stories vary.
0.71 ∗ 0.04 = ? 0.0284
82.9 ∗ 8.1 = ? 671.49
Fill in the missing digits in the multiplication problems.
► Practicing U.S. Traditional
3.
PARTNER
ACTIVITY
4.
5
Multiplication for Decimals
8
0
∗
0
+
(Math Journal 1 or 2, pp. 21P–24P; Student Reference Book,
pp. 54C and 54D)
0
0 .
When students are ready, have them solve Problems 2–7 on journal
page 21P. They may find the examples on Student Reference Book,
pages 54C and 54D helpful.
5
4 6
3 0
0 .
6
5
4
7 . 5
0 . 0
0 . 7
0 .
4
3
0 . 0
∗
5.
2
2
0
0
0 2
3
0
∗
5
0 . 9
6.7
9
5
Math Journal, p. 24P
21P-24P_EMCS_S_MJ2_G5_P06_576434.indd 24
3/8/11 11:38 AM
Journal pages 22P–24P provide students with additional practice
using U.S. traditional multiplication. Use these journal pages as
necessary.
Go to www.everydaymathonline.com
to access the additional practice
pages.
2 Extending the Project
► Solving Decimal Multiplication
INDEPENDENT
ACTIVITY
Problems
(Online Additional Practice, pp. 24A–24D; Student Reference Book,
pp. 37–40, 54C, and 54D)
Online Master
Name
Date
PROJECT
6
Time
Partial-Products Multiplication: Decimals
Online
Additional
Practice
Algorithm Project 6
Online practice pages 24A–24D provide students with additional
practice solving decimal multiplication problems. Use these pages
as necessary.
Encourage students to use the focus algorithm (partial-products
multiplication) to solve the problems on practice page 24A. 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 37–40, 54C, and 54D helpful.
Use partial-products multiplication to solve each problem.
Use estimation to place the decimal point in your answers.
1.
A pack of 50 recordable DVDs sells for $26.08.
Max bought 4 packs. How much money did
he spend?
$104.32
2.
4.
6.
80.2 ∗ 55 =
3.
3.8 ∗ 9,504 =
36,115.2
= 0.3 ∗ 0.66
5.
0.04 ∗ 0.07 =
0.0028
= 59.6 ∗ 4.5
7.
8.83 ∗ 0.7 =
6.181
4,411.0
or 4,411
0.198
268.20
or 268.2
Online Additional Practice, p. 24A
EM3cuG5OP_24A-24D_P06.indd 24A
4/1/10 5:36 PM
Algorithm Project 6
A31