Objectives
To introduce multiplication of decimals by whole
numbers; and to reinforce the partial-products and lattice
methods for multiplication.
1
materials
Teaching the Lesson
Key Activities
Students use an estimation strategy for multiplying decimals. They solve a set of
decimal multiplication problems that offers review and practice of the partial-products
and lattice algorithms.
Key Concepts and Skills
•
•
•
•
•
•
Math Journal 2, pp. 268 and 269
Study Link 9 7
Teaching Aid Masters (Math
Masters, pp. 404 and 434)
slate
Identify place value in decimals through hundredths. [Number and Numeration Goal 1]
Multiply decimals by whole numbers. [Operations and Computation Goal 4]
Round decimals and estimate products. [Operations and Computation Goal 6]
Use repeated addition to model multiplication. [Operations and Computation Goal 7]
Use a formula to calculate the area of a rectangle. [Measurement and Reference Frames Goal 2]
Use conventional notation to write number sentences. [Patterns, Functions, and Algebra Goal 2]
Ongoing Assessment: Recognizing Student Achievement Use journal page 268.
[Operations and Computation Goal 6]
2
materials
Ongoing Learning & Practice
Students play Over and Up Squares to practice locating and plotting points on a
coordinate grid.
Students practice and maintain skills through Math Boxes and Study Link activities.
3
materials
Differentiation Options
READINESS
Students multiply whole
numbers and estimate
products.
READINESS
Students use bills and
coins to model multiplication
number stories involving
whole numbers and
decimals.
Math Journal 2, p. 267
Student Reference Book, p. 257
Study Link Master (Math Masters,
p. 296)
Game Master (Math Masters,
p. 494)
per partnership: 2 six-sided dice;
colored pencils
ENRICHMENT
Students estimate and
compare the product of
two decimal numbers
with the product of two
mixed numbers.
Teaching Masters (Math Masters,
pp. 114 and 297)
Teaching Aid Masters (Math
Masters, pp. 388 or 389 and 428)
coins
Technology
Assessment Management System
Journal page 268, Problem 4
See the iTLG.
762
Unit 9 Fractions, Decimals, and Percents
Getting Started
Mental Math and Reflexes
Pose multiplication problems. Have students estimate the product and write a number model to show how they estimated.
Discuss the strategies used. Suggestions:
Sample answers:
9 ⴱ 18
9 ⴱ 20 ⫽ 180
11 ⴱ 42 10 ⴱ 40 ⫽ 400
22 ⴱ 76 20 ⴱ 75 ⫽ 1,500
87 ⴱ 15 90 ⴱ 20 ⫽ 1,800
28 ⴱ 49
53 ⴱ 78
63 ⴱ 63
98 ⴱ 59
30 ⴱ 50 ⫽ 1,500
50 ⴱ 80 ⫽ 4,000
60 ⴱ 60 ⫽ 3,600
100 ⴱ 59 ⫽ 5,900
81 ⴱ 119
45 ⴱ 188
80 ⴱ 100 ⫽ 8,000
50 ⴱ 200 ⫽ 10,000
72 ⴱ 414
609 ⴱ 684
70 ⴱ 400 ⫽ 28,000
600 ⴱ 700 ⫽ 420,000
Math Message
Study Link 9 7 Follow-Up
Solve the problem at the top of journal page 268.
Have students share their answers and solution
strategies. Some students may note that when
working with populations rounded to the nearest
ten thousand, they only have to consider the first two digits.
䉬
1 Teaching the Lesson
䉴 Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
(Math Journal 2, p. 268)
Have students share their solution strategies.
䉯 Use repeated addition: 1.2 ⫹ 1.2 ⫹ . . . ⫹ 1.2 ⫽ 9.6.
䉯 Multiply 8 and 1 and then add up 0.2 eight times.
䉯 Others may approach it as a multiplication problem. Have
those students explain how they decided where to place the
decimal point. Ask: Why are 96 and 0.96 not reasonable
answers? Because 1.2 is less than 2, the answer must be less
than 16, so 96 is not a reasonable answer. Because 1.2 is
greater than 0.96, 0.96 is too small, so the answer must be 9.6.
Student Page
Date
Time
LESSON
9 8
䉬
Multiplying Decimals
Math Message
18 19
184
Toni has 8 blocks. Each block is 1.2 centimeters high.
If she stacks the blocks, what will be the height of the stack?
9.6
1. Devon measured the length of the room by pacing it off.
The length of his pace was 2.3 feet. He counted 14 paces.
How long is the room?
32.2
2. Spiral notebooks are on sale for $0.35 each.
How much will 25 spiral notebooks cost?
Links to the Future
cm
$
ft
8.75
3. Find the area of each rectangle below. Include the correct unit.
Write a number model to show how you found the answer.
Use of mental arithmetic, paper-and-pencil algorithms, and calculators to solve
problems involving the multiplication of decimals is a Grade 5 Goal.
a. 1.5 cm
30 cm
Number model:
1.5 ⴱ 30 ⫽ 45
Area ⫽
45 cm2
6 ⴱ 15.4 ⫽ 92.4
Area ⫽
92.4 in2
b.
6 in.
15.4 in.
䉴 Estimating Products
Number model:
WHOLE-CLASS
ACTIVITY
of Decimals
is missing in the answer. Write a number model to show how you estimated the answer.
Then correctly place the decimal point in the answer. Sample answers for
a. 23 ⴱ 7.3 ⫽
1 6 7•9
Number model:
Tell students that in this lesson they will learn to find the product
of decimals by multiplying the numbers as if they were whole
numbers and then using estimation to place the decimal point in
the answer.
夹
4. For each problem below, the multiplication has been done correctly, but the decimal point
20 ⴱ 10 ⫽ 200
c. 5,203 ⴱ 12.6 ⫽
6 5 5 5 7•8
Number model:
5,200 ⴱ 10 ⫽ 52,000
268
number models:
5 6 6•6 2
b. 6.91 ⴱ 82 ⫽
Number model:
7 ⴱ 80 ⫽ 560
d. 0.38 ⴱ 51 ⫽
1 9•3 8
Number model:
1
0.4 ⴱ 50 ⫽ 20, or ᎏ2ᎏ of
50 ⫽ 25
Math Journal 2, p. 268
Lesson 9 8
䉬
763
To practice estimating products, write the following problems
on the board:
11 2.8
110 2.8
11 0.28
Ask students to estimate each product. Write some of their
responses next to the problems, and discuss their estimates.
For example, some students may round 11 2.8 to 11 3 and
estimate 33. Others may multiply 10 3 30 or 10 2 20.
The purpose of this estimate is to help them place the decimal
point, so any of these estimates is satisfactory. Ask:
●
Which problem is most likely to have the answer 30.8? 11 2.8
●
How do you know? The estimates made for this problem were
about 20 or 30. The estimates for the other problems were
much larger or smaller.
Write the number 308 next to the problem 110 2.8. Ask:
●
Where would you place the decimal point? After the 8
●
How do you know? Sample answer: The answer must be larger
than 110 1.
Write the number 308 next to the problem 11 0.28. Ask:
●
Where would you place the decimal point? Between the 3 and 0
●
How do you know? Sample answer: The answer is less than
11 1 11; so 308 and 30.8 are too large. The answer is much
larger than 1 0.28; so 0.308 is too small. That leaves 3.08
as the answer.
Now write the following problem on the board:
Calculators are on sale for $9.29 each. How much will 5 of
them cost?
Ask students to estimate the cost of 5 calculators.
5 $9 $45 and 5 $10 $50, so they will cost between 45 and
50 dollars.
929
5
4,500
100
+ 45
4,645
764
9
4
4
6
5
2
1
9
4
0 5
4 5
5
Unit 9 Fractions, Decimals, and Percents
Have volunteers come to the board and multiply 5 929
(9.29 without the decimal point). Ask some students to use the
partial-products method and others to use the lattice method.
(See margin.)
Finally, have students use their initial estimates of the total cost
to place the decimal. 5 929 4,645 and the estimate was about
$50. So place the decimal point after the 6; the total cost is $46.45.
Student Page
Date
Help students summarize the use of estimation to place the
decimal point in the answer when multiplying decimals.
Time
LESSON
9 8
䉬
Multiplying Decimals
Math Message
18 19
184
Toni has 8 blocks. Each block is 1.2 centimeters high.
If she stacks the blocks, what will be the height of the stack?
Example: 6 ⴱ 3.7 ⫽ ?
9.6
cm
1. Devon measured the length of the room by pacing it off.
1. Estimate the product.
The length of his pace was 2.3 feet. He counted 14 paces.
How long is the room?
6 ⴱ 3.7 is about 6 ⴱ 4, or 24.
32.2
2. Spiral notebooks are on sale for $0.35 each.
How much will 25 spiral notebooks cost?
2. Multiply the factors as though they were whole numbers.
ft
8.75
$
3. Find the area of each rectangle below. Include the correct unit.
Write a number model to show how you found the answer.
a. 1.5 cm
6 ⴱ 37 ⫽ 222
30 cm
Number model:
3. Use the estimate to place the decimal point in the answer.
1.5 ⴱ 30 45
Area 45 cm2
6 ⴱ 15.4 92.4
Area 92.4 in2
b.
6 in.
15.4 in.
22.2 is close to the estimate of 24.
Number model:
夹
4. For each problem below, the multiplication has been done correctly, but the decimal point
is missing in the answer. Write a number model to show how you estimated the answer.
Then correctly place the decimal point in the answer. Sample answers for
䉴 Multiplying Decimals
PARTNER
ACTIVITY
a. 23 ⴱ 7.3 number models:
5 6 6•6 2
1 6 7•9
b. 6.91 ⴱ 82 Number model:
Number model:
20 ⴱ 10 200
(Math Journal 2, pp. 268 and 269; Math Masters, pp. 404 and 434)
c. 5,203 ⴱ 12.6 7 ⴱ 80 560
6 5 5 5 7•8
d. 0.38 ⴱ 51 Number model:
Ask students to complete journal pages 268 and 269 and
compare answers.
1 9•3 8
Number model:
5,200 ⴱ 10 52,000
1
0.4 ⴱ 50 20, or 2 of
50 25
268
Math Journal 2, p. 268
Adjusting the Activity
Have students use lattice multiplication adapted for decimals. Show
them how to find the intersection of the decimal points along the horizontal and
vertical lines; then slide down the diagonal. Encourage students to still make
estimates in order to check their work.
2
2
6
0 11
6 8
0
0 2
8 8 4
8 4
6
0 11
6 8
0
0 2
8 8 4
8 4
3
4
Decimal multiplied by whole number
3
4
Student Page
Decimal multiplied by decimal
Date
LESSON
A U D I T O R Y
䉬
K I N E S T H E T I C
䉬
T A C T I L E
䉬
V I S U A L
9 8
䉬
Time
Multiplying Decimals
continued
Write a number model to estimate each product. Then multiply the factors as though they
were whole numbers. Use your estimate to help you place the decimal in the answer.
Sample answers for number models:
121.5
Number model: 3 ⴱ 50 150
7. 5.08 ⴱ 27 137.16
Number model: 5 ⴱ 30 150
5. 2.7 ⴱ 45 Ongoing Assessment:
Recognizing Student Achievement
Journal
page 268
Problem 4
夹
Use journal page 268, Problem 4 to assess students’ ability to estimate the
product of a whole number and a decimal. Students are making adequate
progress if they are able to correctly place the decimal points and write number
models for Problems 4a–4c. Some students may be able to solve Problem 4d,
which involves a decimal less than 1.
Try This
9. 22 ⴱ 0.32 45.6
8 ⴱ 6 48
42 ⴱ 0.97 40.74
Number model: 40 ⴱ 1 40
6. 8 ⴱ 5.7 Number model:
8.
Sample answers for number models:
7.04
10. 0.02 ⴱ 333 Number model:
20 ⴱ 0.3 6, or
of 21 7
6.66
Number model:
1
3
0.02 ⴱ 300 6, or
of 300 6
2
100
[Operations and Computation Goal 6]
Math Journal 2, p. 269
Lesson 9 8
䉬
765
Student Page
Date
Time
LESSON
2 Ongoing Learning & Practice
Math Boxes
9 8
1. a. If you threw a 6-sided die 48 times,
2. Name a percent value
about how many times would you
expect it to land on a number greater
than or equal to 4?
24
1
a. greater than and less than .
5
2
30%
Playing Over and Up Squares
times
3
3
b. less than and greater than .
4
5
b. If you threw a 6-sided die 54 times,
about how many times would you
expect it to land on a number greater
than 4?
18
Sample answers:
1
times
81
3. Homer’s is selling roller blades at 25% off
the regular price of $52.00. Martin’s is
1
selling them for off the regular price of
3
$60. Which store is offering the better buy?
Homer’s
70%
Sample answer:
Show how you solved the problem.
1
Homer’s: 25% 4, $52
(Student Reference Book, p. 257; Math Masters, p. 494)
61
62
4. If 1 centimeter on a map represents 300
kilometers, then 2.5 centimeters represents
kilometers. Choose the best answer.
600
350
Math Boxes 9 8
750
38 39
59
3.5C
Include the correct unit.
(Math Journal 2, p. 267)
How many degrees warmer?
5"
3.5C
11"
Area INDEPENDENT
ACTIVITY
145
6. a. Which is warmer, 7 C or 3.5C?
5. What is the area of the triangle?
Number model:
Students play Over and Up Squares to practice locating
and plotting points on a coordinate grid. See Lesson 6-9 for
additional information.
650
/ 4
$13, and $52 $13 $39.
Martin’s: $60 / 3 $20,
and $60 $20 $40.
1
2
PARTNER
ACTIVITY
(11 5) 27.5
27.5 in2
b. Which is colder, 18C or 9.6C?
18C
How many degrees colder?
136
8.4C
60
139
267
Math Journal 2, p. 267
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 9-6. The skill in Problem 6
previews Unit 10 content.
Writing/Reasoning Have students write a response to the
following: Explain how you solved Problem 2b. Sample answer:
3
3
is equivalent to 75%. is equivalent to 60%. I named a percent
4
5
value between 60% and 75%.
Study Link 9 8
INDEPENDENT
ACTIVITY
(Math Masters, p. 296)
Home Connection Students estimate products of
decimals and whole numbers. They multiply decimals
and whole numbers.
Study Link Master
Name
Date
STUDY LINK
9 8
Time
Multiplying Decimals
For each problem below, the multiplication has been done correctly, but the decimal point
is missing in the answer. Correctly place the decimal point in the answer.
2 5•8
4 8 9•6
1.
6 º 4.3 3.
0.96 º 47 5.
8,457 º 9.8 7.
Explain how you decided where to place the decimal point in Problem 4.
4 5 •1 2
8 2 8 7 8 •6
2.
72 º 6.8 4.
5.12 º 22 6.
0.04 º 140 1 1 2 •6 4
5•6
Sample
answer:
I rounded the numbers to 5 and 20 and then
multiplied to get 100. So, the product should
be close to 100, and 112.64 is.
Try This
Multiply. Show your work.
8.
5.9 º 36 212.4
9.
0.46 º 84 38.64
Practice
11.
13.
16
137
96 6
12.
411 / 3
14.
Math Masters, p. 296
766
Unit 9 Fractions, Decimals, and Percents
10.
382.13 7.21 º 53
16 R3, or 1634
3
9冄9
苶苶0苶
3 100 R3, or 100 9
4冄6
苶苶
7
Teaching Master
Name
3 Differentiation Options
Multiplying Whole Numbers
Time
Multiplying Whole Numbers
98
Write a number model to estimate each product. Then multiply
with a paper-and-pencil algorithm. Show your work.
1.
READINESS
Date
LESSON
INDEPENDENT
ACTIVITY
476
7 º 68 Number model:
2.
18 19
3,204
534 º 6 Number model:
Sample answer:
7 º 70 490
Sample answer:
500 º 6 3,000
5–15 Min
and Estimating Products
(Math Masters, p. 297)
3.
To provide experience with whole-number multiplication and
estimating products, have students complete Math Masters,
page 297.
3,886
58 º 67
9,075
Number model:
33 º 275 Number model:
Sample answer:
60 º 70 4,200
Sample answer:
30 º 300 9,000
4.
Try This
5.
READINESS
Solving Number Stories
PARTNER
ACTIVITY
Margo’s favorite socks are on sale for $2.89 per pair.
She has $25. Can she buy 6 pairs?
yes
Explain how to solve this problem without using a paper-and-pencil algorithm.
Sample answer: Round $2.89 to $3.00, then multiply by 6,
5–15 Min
which gives $18. She has $25, so she has more than enough
money.
(Math Masters, pp. 114 and 428)
To explore multiplication of whole numbers by decimals using a
money context, have students use the items on Math Masters,
page 114 and dollars and cents to model, write, and solve
multiplication number stories. For example:
Math Masters, p. 297
Max bought 5 packs of light bulbs.
Teaching Master
About how much money did he spend?
5 $1.09 $5.45
Name
Date
LESSON
4 4
light bulbs
4-pack
ENRICHMENT
Comparing Products
PARTNER
ACTIVITY
Time
Items to Purchase
VCR tape
$3.25
tissues
$0.73
batteries
toothpaste
$1.39
$1.09
5–15 Min
(Math Masters, p. 388 or 389)
To apply students’ understanding of decimal multiplication
and decimal/fraction equivalencies, have students estimate and
compare the product of two mixed numbers and the product
of two decimals. Ask students to record their responses to the
following in a Math Log or on an Exit Slip:
Think about these two multiplication problems:
1
1
52 23
2.36 5.206
Without using a paper-and-pencil algorithm or a calculator, which
1
1
product do you think is greater? Explain. Sample answer: 52 23;
1
1
52 5.5 and 5.5 5.206. 23 2.33
苶, which is only a bit less than
2.36. So the first product is greater.
transparent tape
$0.84
4-pack
$3.59
ballpoint pen
$0.39
tennis balls
can of 3
paperback book
$2.99
$2.59
Math Masters, p. 114
Lesson 9 8
767