Objectives
To introduce and provide practice with the
partial-products algorithm for 2-digit multipliers.
1
materials
Teaching the Lesson
Key Activities
Students learn how to extend the partial-products algorithm to 2-digit multipliers.
They make rough estimates and then use the partial-products method.
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.
Math Journal 1, pp. 122 and 123
Study Link 5 5
Teaching Aid Masters (Math Masters, p. 403 or
431; p. 388 or 389; optional)
slate
See Advance Preparation
[Operations and Computation Goal 6]
• Apply the Distributive Property of Multiplication over Addition.
[Patterns, Functions, and Algebra Goal 4]
Ongoing Assessment: Recognizing Student Achievement
Use Mental Math and Reflexes. [Operations and Computation Goal 6]
Ongoing Assessment: Informing Instruction See page 345.
2
materials
Ongoing Learning & Practice
Students play Name That Number to practice representing numbers
in different ways.
Math Journal 1, p. 121
Student Reference Book, p. 254
Students practice and maintain skills through Math Boxes
and Study Link activities.
Study Link Master (Math Masters, p. 154)
Game Master (Math Masters, p. 489; optional)
per partnership: deck of number cards
3" by 5" index cards (optional); calculator (optional)
3
materials
Differentiation Options
READINESS
Students model
multiplication problems
with base-10 blocks.
ENRICHMENT
Students solve a
multistep number
story involving a
dart game.
ENRICHMENT
Students complete
Venn diagrams.
Teaching Masters (Math Masters, pp. 155 and 156)
Transparencies (Math Masters, pp. 432 and 433)
base-10 blocks
erasable marker; transparent tape
See Advance Preparation
Additional Information
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; cut them apart, and tape them together with transparent tape.
Technology
Assessment Management System
Mental Math and Reflexes
See the iTLG.
Lesson 5 6
343
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 52
4 26
9 74
3 50 150
4 30 120
10 74 740
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
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
WHOLE-CLASS
DISCUSSION
Go over the answers. Ask:
Multiplication Number Stories
Follow these steps for each problem.
17 18
184
a. Decide which two numbers need to be multiplied to give the exact answer.
●
How would you solve 4 29 in your head? Sample answer:
Multiply 4 30 and then subtract 4 from the product.
●
How would you solve 803 6 in your head? Sample answer:
Multiply 800 6 and 3 6 and then add the two products.
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.
1. 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 12
b.
numbers that give
the exact answer
10s
60 10 600
c.
number model for your estimate
100s
1,000s
10,000s
732
exact answer
100,000s 1,000,000s
Estimating Products
2. Eighteen newborn hummingbirds weigh about 1 ounce. About how many of them
does it take to make 1 pound? (1 pound 16 ounces)
a.
18 16
b.
numbers that give
the exact answer
10s
20 20 400
number model for your estimate
100s
1,000s
10,000s
c.
(Math Journal 1, pp. 122 and 123)
288
exact answer
100,000s 1,000,000s
122
Math Journal 1, p. 122
344
PARTNER
ACTIVITY
Unit 5 Big Numbers, Estimation, and Computation
Tell students that in this lesson they will apply the partialproducts algorithm to multiply a 2-digit number by a
2-digit number.
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
Time
LESSON
5 6
Multiplication Number Stories
continued
3. A test found that a lightbulb lasts an average of 63 days after being turned on.
About how many hours is that?
a.
63 24
b.
60 20 1,200
numbers that give
the exact answer
10s
c.
number model for your estimate
100s
1,000s
10,000s
1,512
exact answer
100,000s 1,000,000s
4. 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?
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.
a.
78 365
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.
123
Math Journal 1, p. 123
Extending the Partial-Products
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
345
Using the Partial-Products
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.
Lesson 9-8 introduces multiplication of decimals. This is a Grade 5 Goal.
2 Ongoing Learning & Practice
Student Page
Date
Playing Name That Number
Time
LESSON
5 6
(Student Reference Book, p. 254; Math Masters, p. 489)
Math Boxes
1. a. Measure the line segment to the nearest
5
About
1
4
inch.
Students play Name That Number to practice representing
numbers in different ways. See Lesson 2-2 for additional
information.
inches
b. Draw a line segment that is half as long as the one above.
1
c. How long is the line segment you drew?
About
2 2
inches
128
3. Multiply. Use the partial-products method.
2. Estimate the product. Write a number
model to show how you estimated.
2,236
a. 48 21
Math Boxes 5 6
52 43
4
º
5
2 0 0
1 5
8
3
2
0
0
0
6
2 2 3 6
Sample answers:
50 20 1,000
Number model:
b. 98 72
Number model:
100 70 7,000
4. Write each number using digits.
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.
18
5. If you remove 7 gallons per day from a
a. three hundred forty-two thousandths
0.342
65-gallon water tank, how many days will
it take to empty the tank?
About 10 days
b. six and twenty-five hundredths
6.25
27 28
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 121)
184
175
121
Math Journal 1, p. 121
346
PARTNER
ACTIVITY
Unit 5 Big Numbers, Estimation, and Computation
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.
Study Link Master
Study Link 5 6
INDEPENDENT
ACTIVITY
(Math Masters, p. 154)
Name
Date
STUDY LINK
56
Time
More Multiplication
Multiply using the partial-products algorithm. Show your work.
1.
Home Connection Students practice using the
partial-products algorithm with 2-digit multipliers.
3.
5.
4,074
42 º 50 2,100
3,266 46 º 71
582 º 7 2.
56 º 30 4.
486
18
1,680
27 º 18
17,000
6.
340 º 50 8.
37,632 768 º 49
Try This
7.
7,471
241 º 31
3 Differentiation Options
READINESS
Modeling Multiplication with
SMALL-GROUP
ACTIVITY
15–30 Min
Base-10 Blocks
(Math Masters, pp. 432 and 433)
Practice
9.
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.
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
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).
Start here.
Array model of 17 32
Lesson 5 6
347
Name
Date
LESSON
Time
A Dart Game
56
Ask students to cover the array using as few base-10 blocks
(flats, longs, and cubes) as possible.
Vanessa played a game of darts. She threw 9 darts.
Each dart hit the target. She scored 550 points.
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
2
4
Math Masters, page 155
Start here.
Base-10 block model of 17 32
Now match each part of the 17-by-32 array with a partial product.
Match the 3 flats with 10 30 300. These cover
300 squares.
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.
There are 7 rows with 2 cubes in each row. These cover
7 2 14 squares.
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.
Teaching Master
Name
Date
LESSON
56
ENRICHMENT
Time
Sorting Numbers
Study the Venn diagrams in Problems 1 and 2. Label each circle and add at least one
number to each section.
Sample
p answers:
Scoring a Dart Game
4,000
720
2,400
240
divisible by 80
300
180
4,200
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.
2,100
multiples of 30
Try This
2.
Sample answers:
Sample answers:
30 as a factor
990
1,230
360
ENRICHMENT
Solving Venn Diagram Puzzles
120
210
840
750
1,200
1,500
250
4,000
650
2,000
4,200
6,300
420
1,050
build arrays with
770
multiples of 70
50 rows
Math Masters, p. 156
348
PARTNER
ACTIVITY
5–15 Min
(Math Masters, p. 156)
560
490
280
350
7,000
3,500
5–15 Min
(Math Masters, p. 155)
1.
80
5,600
160
INDEPENDENT
ACTIVITY
Unit 5 Big Numbers, Estimation, and Computation
To apply students’ understanding of extended multiplication
and division facts, have them solve Venn diagram puzzles
based on factors.