Partial-Products
Multiplication (Part 2)
Objectives To introduce and provide practice with the
O
partial-products
algorithm for 2-digit multipliers.
p
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Write numbers in expanded notation. [Number and Numeration Goal 4]
• Use the partial-products algorithm to
solve multiplication problems with 2-digit
multipliers. [Operations and Computation Goal 4]
• Estimate whether a product is in the tens,
hundreds, thousands, or more. [Operations and Computation Goal 6]
• Apply the Distributive Property
of Multiplication over Addition. [Patterns, Functions, and Algebra Goal 4]
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Name That Number
Student Reference Book, p. 254
Math Masters, p. 489 (optional)
per partnership: deck of number
cards (the Everything Math Deck,
if available)
Students practice representing
numbers in different ways.
Math Boxes 5 6
Math Journal 1, p. 121
Students practice and maintain skills
through Math Box problems.
Study Link 5 6
Key Activities
Students learn how to extend the partialproducts algorithm to 2-digit multipliers.
They make rough estimates and then use
the partial-products method.
Math Masters, p. 154
Students practice and maintain skills
through Study Link activities.
Ongoing Assessment:
Recognizing Student Achievement
Use Mental Math and Reflexes. [Operations and Computation Goal 6]
Ongoing Assessment:
Informing Instruction See page 345.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Modeling Multiplication
with Base-10 Blocks
transparencies of Math Masters, pp. 432
and 433 base-10 blocks erasable
marker transparent tape
Students explore the partial-products
algorithm using a concrete model.
ENRICHMENT
Scoring a Dart Game
Math Masters, p. 155
Students solve a multistep number story
involving a dart game.
ENRICHMENT
Solving Venn Diagram Puzzles
Math Masters, p. 156
Students apply their understanding of
extended multiplication and division facts.
ENRICHMENT
Writing Multiplication Number Stories
Students write and solve multiplication
number stories.
Materials
Math Journal 1, pp. 122 and 123
Study Link 55
Math Masters, p. 403 or 431; p. 388 or 389
(optional)
slate
Advance Preparation
For Part 1, place copies of Math Masters, page 403 or 431 near the Math Message. For the optional Readiness
activity in Part 3, make transparencies of Math Masters, pages 432 and 433, and tape them together.
Teacher’s Reference Manual, Grades 4–6 pp. 39, 40, 126–132, 260, 261
Lesson 5 6
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Getting Started
Mental Math and Reflexes Write multiplication problems on the board. Have students write number models to show their estimates. Suggestions:
Sample answers are given.
3 ∗ 50 = 150
4 ∗ 30 = 120
10 ∗ 74 = 740
3 ∗ 52
4 ∗ 26
9 ∗ 74
8 ∗ 632
6 ∗ 569
3 ∗ 248
8 ∗ 600 = 4,800
6 ∗ 600 = 3,600
3 ∗ 250 = 750
2 ∗ 7,414
5 ∗ 8,299
7 ∗ 6,172
2 ∗ 7,500 = 15,000
5 ∗ 8,000 = 40,000
7 ∗ 6,000 = 42,000
Math Message
Study Link 5 5 Follow-Up
Solve the following problems on a computation grid:
Have students compare answers and share how
they decided whether an average person blinks
more than or fewer than 100,000 times per day.
4 ∗ 29 = 116
803 ∗ 6 = 4,818
3 ∗ 260 = 780
418 ∗ 7 = 2,926
NOTE For additional practice
using a standard procedure for
rounding whole numbers to the
nearest ten and hundred, see
www.everydaymathonline.com.
Ongoing Assessment:
Recognizing Student Achievement
Mental Math
and Reflexes
Use Mental Math and Reflexes to assess students’ ability to estimate
reasonable solutions to whole-number multiplication problems. Students are
making adequate progress if they can write appropriate number models for the
and
problems. Some students may be able to estimate products for
the
problems.
[Operations and Computation Goal 6]
1 Teaching the Lesson
Math Message Follow-Up
Student Page
Date
Time
LESSON
5 6
䉬
Multiplication Number Stories
WHOLE-CLASS
DISCUSSION
Go over the answers. Ask:
Follow these steps for each problem.
17 18
184
1.
a.
Decide which two numbers need to be multiplied to give the exact answer.
Write the two numbers.
b.
Estimate whether the answer will be in the tens, hundreds, thousands, or more.
Write a number model for the estimate. Circle the box to show your estimate.
c.
On the grid below, find the exact answer by multiplying the two numbers.
Write the answer.
The average person in the United States drinks about 61 cups of soda per month.
About how many cups of soda is that per year?
a.
61 ⴱ 12
b.
numbers that give
the exact answer
10s
2.
60 ⴱ 10 ⫽ 600
c.
number model for your estimate
100s
1,000s
10,000s
18 ⴱ 16
b.
numbers that give
the exact answer
10s
number model for your estimate
100s
1,000s
10,000s
●
How would you solve 803 ∗ 6 in your head? Sample answer:
Multiply 800 ∗ 6 and 3 ∗ 6 and then add the two products.
732
100,000s 1,000,000s
20 ⴱ 20 ⫽ 400
How would you solve 4 ∗ 29 in your head? Sample answer:
Multiply 4 ∗ 30 and then subtract 4 from the product.
exact answer
Eighteen newborn hummingbirds weigh about 1 ounce. About how many of them
does it take to make 1 pound? (1 pound ⫽ 16 ounces)
a.
●
c.
Estimating Products
288
PARTNER
ACTIVITY
(Math Journal 1, pp. 122 and 123)
exact answer
100,000s 1,000,000s
Tell students that in this lesson they will apply the partialproducts algorithm to multiply a 2-digit number by a
2-digit number.
122
Math Journal 1, p. 122
344
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Student Page
For each problem on pages 122 and 123, students first decide
which two numbers need to be multiplied to give the exact answer
(Step a). In Step b, they make a rough estimate of that product
and write a number model that shows how they made that
estimate. They should not do Step c at this time. Do Problem 1
as a class:
Date
Multiplication Number Stories
56
3.
continued
A test found that a lightbulb lasts an average of 63 days after being turned on.
About how many hours is that?
63 ∗ 24
a.
b.
60 ∗ 20 = 1,200
numbers that give
the exact answer
10s
4.
Step a An average person drinks about 61 cups of soda in
1 month. In 1 year, a person will drink 12 times that amount.
To find the amount of soda a person drinks in one year, you would
multiply 12 ∗ 61. Write 12 ∗ 61, but do not calculate the exact
answer at this time.
Time
LESSON
c.
number model for your estimate
100s
1,000s
10,000s
1,512
exact answer
100,000s 1,000,000s
A full-grown oak tree loses about 78 gallons of water through its leaves per day.
About how many gallons of water is that per year?
78 ∗ 365
a.
b.
80 ∗ 400 = 32,000
numbers that give
the exact answer
10s
c.
number model for your estimate
100s
1,000s
10,000s
28,470
exact answer
100,000s 1,000,000s
Step b To estimate the answer, round 12 to 10 and write a
number model for the rough estimate: 10 ∗ 61 = 610. Or round
61 to 60 and write a number model for the rough estimate:
12 ∗ 60 = 720. Looking at the number models, you can tell that the
answer will be in the hundreds, so circle “100s.”
Have students work with a partner to complete Steps a and b for
the rest of the problems.
Math Journal 1, p. 123
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Extending the Partial-Products
1/14/11 9:08 AM
WHOLE-CLASS
ACTIVITY
Problem 1: 12 ∗ 61 = ?
Algorithm to 2-Digit Multipliers
100s
(Math Journal 1, pp. 122 and 123)
Demonstrate how to use the partial-products algorithm to find
the exact answer and check the estimate for Problem 1 on journal
page 122. (See margin.) Work from left to right. Point out that
each part of one factor is multiplied by each part of the other factor.
∗
6
1
Ongoing Assessment: Informing Instruction
As students say each step, watch for those who say, for example “1 times 6”
instead of “10 sixties” or “10 times 60.” Remind students to consider the value of
each digit.
10s
1s
6
1
1
2
0
1
2
0
0
0
2
2
+
7
3
Ò 10 [60s] or 10 ∗ 60
Ò 10 [1s] or 10 ∗ 1
Ò 2 [60s] or 2 ∗ 60
Ò 2 [1s] or 2 ∗ 1
Do several more problems with the class. Suggestions:
●
18 ∗ 52 = 936
●
29 ∗ 73 = 2,117
●
26 ∗ 34 = 884
●
28 ∗ 434 = 12,152
Adjusting the Activity
Organize the multiplication problems as follows:
12 ∗ 61 = (10 + 2) ∗ (60 + 1)
60
1
10
600
10
2
120
2
Students then add the partial products in the table to find the total:
600 + 10 + 120 + 2 = 732.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
Lesson 5 6
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Using the Partial-Products
Algorithm Project The focus of this
lesson is partial products. To teach U.S.
traditional multiplication, see Algorithm
Project 5 on page A21.
PARTNER
ACTIVITY
Algorithm
(Math Journal 1, pp. 122 and 123)
Students complete the remaining problems on journal pages 122
and 123 in the same way. They check their estimates and
complete Step c by finding the exact answer using the partialproducts algorithm.
Adjusting the Activity
Ask students to respond to the following question in a Math Log
or on an Exit Slip (Math Masters, page 388 or 389): Explain how the
partial-products algorithm is similar to finding a team’s score in a game of
Multiplication Wrestling.
Look for students to note that every part of one factor is multiplied by every part
of the other factor.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
Links to the Future
Do not expect all students to master the
partial-products algorithm for two 2-digit
multipliers at this time. This algorithm will
be practiced and reinforced throughout
Fourth Grade Everyday Mathematics.
2 Ongoing Learning & Practice
Fluently multiplying whole numbers using
the standard algorithm is expected in
Grade 5.
Playing Name That Number
Lesson 9-8 introduces multiplication of
decimals. This is a Grade 5 Goal.
PARTNER
ACTIVITY
(Student Reference Book, p. 254; Math Masters, p. 489)
Students play Name That Number to practice representing
numbers in different ways. See Lesson 2-2 for additional
information.
Math Boxes 5 6
Student Page
Date
Time
LESSON
5 6
䉬
1. a.
(Math Journal 1, p. 121)
Math Boxes
1
4
Measure the line segment to the nearest ᎏᎏ inch.
5
About
Mixed Practice Math Boxes in this lesson are linked
with Math Boxes in Lessons 5-8 and 5-10. The skill in
Problem 5 previews Unit 6 content.
inches
b.
Draw a line segment that is half as long as the one above.
c.
How long is the line segment you drew?
1
2.
Estimate the product. Write a number
model to show how you estimated.
a.
About
3.
98 ⴱ 72
Number model:
100 ⴱ 70 ⫽ 7,000
184
Write each number using digits.
5.
a.
three hundred forty-two thousandths
b.
six and twenty-five hundredths
inches
0.342
128
Writing/Reasoning Have students write a response to the
following: Devon wrote 342,000 for Problem 4a. Explain the error
he might have made. Sample answer: He wrote 342 thousands,
not 342 thousandths.
Multiply. Use the partial-products method.
⫽ 52 ⴱ 43
4 3
º
5 2
2 0 0 0
1 5 0
8 0
6
⫹
2 2 3 6
Sample answers:
50 ⴱ 20 ⫽ 1,000
4.
2 ᎏ2ᎏ
2,236
48 ⴱ 21
Number model:
b.
INDEPENDENT
ACTIVITY
Study Link 5 6
18
(Math Masters, p. 154)
If you remove 7 gallons per day from a
65-gallon water tank, how many days will
it take to empty the tank?
Home Connection Students practice using the
partial-products algorithm with 2-digit multipliers.
About 10 days
6.25
27 28
INDEPENDENT
ACTIVITY
175
121
Math Journal 1, p. 121
346
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Study Link Master
Name
3 Differentiation Options
56
䉬
Modeling Multiplication
Time
More Multiplication
Multiply using the partial-products algorithm. Show your work.
1.
READINESS
Date
STUDY LINK
SMALL-GROUP
ACTIVITY
3.
5.
4,074
42 º 50 ⫽ 2,100
3,266 ⫽ 46 º 71
582 º 7 ⫽
2.
4.
56 º 30 ⫽
18
1,680
486
⫽ 27 º 18
17,000
6.
340 º 50 ⫽
8.
37,632 ⫽ 768 º 49
Try This
15–30 Min
7.
7,471
⫽ 241 º 31
with Base-10 Blocks
(Math Masters, pp. 432 and 433)
To explore the partial-products algorithm using a concrete model,
have students use base-10 blocks to model multiplication problems
involving two 2-digit numbers.
Place taped transparencies of Math Masters, pages 432 and 433
on a table. To model 17 * 32, use an erasable marker to mark off
a portion of the grid that is 17 squares high and 32 squares wide
(17 by 32).
Practice
9.
11.
5,722
⫽ 283 ⫹ 5,439
5,583 ⫺ 4,667 ⫽
916
10.
12.
6,473 ⫹ 4,278 ⫽
2,769
10,751
⫽ 9,141 ⫺ 6,372
Math Masters, p. 154
Start here.
Array model of 17 ∗ 32
Ask students to cover the array using as few base-10 blocks
(flats, longs, and cubes) as possible.
Start here.
Base-10 block model of 17 ∗ 32
Lesson 5 6
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Name
Date
LESSON
56
Time
A Dart Game
Now match each part of the 17-by-32 array with a partial product.
Vanessa played a game of darts. She threw 9 darts.
Each dart hit the target. She scored 550 points.
Match the 3 flats with 10 ∗ 30 = 300. These cover 300 squares.
200
100
Where might each of her 9 darts have hit? Use the
table to show all possible solutions.
200
100
1
1
1
1
2
2
3
4
50
25
50
25
6
3
2
4
6
7
4
1
Match the 2 vertical longs with 10 ∗ 2 = 20. These cover
20 squares.
There are 7 rows with 3 longs in each row. These cover
7 ∗ 30 = 210 squares.
2
4
There are 7 rows with 2 cubes in each row. These cover
7 ∗ 2 = 14 squares.
Math Masters, page 155
There are 544 (300 + 20 + 210 + 14) cubes in all.
Erase the transparencies. Use the transparencies and base-10
blocks to model and solve other 2-digit-times-2-digit problems.
ENRICHMENT
Scoring a Dart Game
INDEPENDENT
ACTIVITY
5–15 Min
(Math Masters, p. 155)
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To apply students’ multidigit multiplication skills, have them use
various strategies to solve a multistep number story involving a
dart game with more than one possible answer. Ask students to
explain how they know they found all the solutions.
ENRICHMENT
Solving Venn Diagram Puzzles
PARTNER
ACTIVITY
5–15 Min
(Math Masters, p. 156)
To apply students’ understanding of extended multiplication
and division facts, have them solve Venn diagram puzzles
based on factors.
Teaching Master
Name
Date
LESSON
Sorting Numbers
56
ENRICHMENT
Time
Study the Venn diagrams in Problems 1 and 2. Label each circle and add at least one
number to each section.
Writing Multiplication
Sample
p answers:
1.
80
5,600
160
4,000
720
2,400
240
divisible by 80
To apply students’ understanding of multiplication algorithms,
have them write and solve multistep multiplication number
stories. Then have them record a number model using a letter for
the unknown. Some students may be interested in writing and
solving problems that involve distances, intervals of time, liquid
volumes, masses of objects, or money. Stories may look similar to
the following:
2,100
multiples of 30
Sample answers:
Sample answers:
30 as a factor
990
1,230
360
120
1,500
250
4,000
650
2,000
Simon is filling the ketchup bottles at his restaurant. Each bottle holds 16 ounces of ketchup. There are 12 tables in each room
and 3 rooms in the restaurant. How many ounces of ketchup
will he need to fill one bottle for each table? Answer: 576 oz;
Number model with unknown: (12 ∗ 3) ∗ 16 = n; Number model
with answer: (12 ∗ 3) ∗ 16 = 576
210
840
750
1,200
4,200
6,300
420
1,050
560
490
280
350
7,000
3,500
build arrays with
5–15 Min
Number Stories
300
180
4,200
Try This
2.
PARTNER
ACTIVITY
770
multiples of 70
50 rows
Provide opportunities for students to revise and share their
writing. Then have partners solve each other’s problems.
Math Masters, p. 156
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Unit 5 Big Numbers, Estimation, and Computation
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