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Objectives To review and provide practice with the partialproducts algorithm for 1-digit multipliers.
1
materials
Teaching the Lesson
Key Activities
Students review the partial-products algorithm. They practice this method for 1-digit
multipliers, using mental and paper-and-pencil procedures.
Key Concepts and Skills
•
•
•
•
Write numbers in expanded notation. [Number and Numeration Goal 4]
Add multidigit numbers. [Operations and Computation Goal 2]
Use basic facts to compute extended facts. [Operations and Computation Goal 3]
Use the partial-products algorithm to solve multiplication problems with 1-digit
multipliers. [Operations and Computation Goal 4]
• Estimate whether a product is in the tens, hundreds, thousands, or more.
Math Journal 1, pp.118 and 119
Study Link 5 4
Teaching Aid Master (Math Masters,
p. 403 or 431)
slate
[Operations and Computation Goal 6]
• Apply the Distributive Property of Multiplication over Addition.
[Patterns, Functions, and Algebra Goal 4]
Key Vocabulary partial-products method • partial product
Ongoing Assessment: Informing Instruction See page 339.
Ongoing Assessment: Recognizing Student Achievement Use journal page 118.
[Operations and Computation Goal 4]
2
materials
Ongoing Learning & Practice
Students use personal references for customary units of length to estimate
lengths of objects.
Students practice and maintain skills through Math Boxes and Study Link activities.
3
materials
Differentiation Options
READINESS
Students model 1-digit
times 2-digit multiplication
problems with base-10
blocks.
READINESS
Students explore patterns
in extended facts.
Math Journal 1, pp. 98, 117, and 120
Study Link Master (Math Masters, p. 151)
tape measure or ruler
ENRICHMENT
Students use
multiplication to solve an
old puzzle about houses,
cats, whiskers, and fleas.
Additional Information
Advance Preparation 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.
Teaching Masters
(Math Masters,
pp. 152 and 153)
Transparencies
(Math Masters,
pp. 432 and 433)
base-10 blocks;
erasable marker;
transparent tape
See Advance
Preparation
Technology
Assessment Management System
Journal page 118, Problems 1 and 2
See the iTLG.
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Getting Started
Mental Math and Reflexes
Pose extended multiplication facts
problems. Suggestions:
4 50 = 200
30 7 = 210
6 40 = 240
20 40 = 800
50 80 = 4,000
70 60 = 4,200
30 500 = 15,000
800 700 = 560,000
900 600 = 540,000
Math Message
Study Link 5 4 Follow-Up
Paul’s new baby sister sleeps about 16 hours
per day. About how many hours does she sleep
in one week?
Partners compare answers. Students should focus
on the number models they wrote for their estimates.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Have students share solution strategies.
Students may have tried either of these written strategies:
Use an algorithm to find the product of 7 and 16.
Use repeated addition: Add 16 seven times.
Or, they may have used one of these mental strategies:
Multiply 8 7. 56
Double the result. 56 56 112
Multiply 20 7. 140
Subtract 4 7 from the result. 140 – 28 112
If no one shares it, suggest the following strategy:
Multiply 10 7. 70
Multiply 6 7. 42
Add the results. 70 42 112
Tell the class that this last strategy makes use of the place value
of each digit. It is the strategy on which the partial-products
method, the multiplication method students will review in this
lesson, is based.
Finding Products Mentally
WHOLE-CLASS
ACTIVITY
Pose “easy” multiplication problems involving 1-digit times
2-digit numbers. Have students solve them mentally, write the
answers on their slates, and at a signal, display the answers.
Emphasize to students that they may write partial answers on
their slates, but not the original problem. Ask them to circle the
final answer.
338
Unit 5 Big Numbers, Estimation, and Computation
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Discuss solution strategies after each problem. Do not insist that
students use the last strategy mentioned in the Math Message
Follow-Up, but encourage its use. Keep this activity brief, especially
if students can solve the problems with ease. Suggestions:
●
3 54 = 162
●
8 37 = 296
●
24 4 = 96
●
6 83 = 498
●
7 62 = 434
●
15 9 = 135
Demonstrating the Partial-
WHOLE-CLASS
ACTIVITY
Products Algorithm for
1-Digit Multipliers
(Math Masters, p. 403 or 431)
Give each student a sheet of computation grid paper (Math
Masters, page 403 or 431). Write the following problem on the
board. If you think your class is not ready to start with a 3-digit
factor, start with a 1-digit times 2-digit problem instead.
NOTE Like the addition and subtraction
algorithms in Unit 2, the partial-products
algorithm is a “low-stress” algorithm. Even if
students have used a standard multiplication
algorithm or some other multiplication
method in the past, ask them to use the
partial-products algorithm to solve the
problems in this lesson.
869
6
Ask the class to estimate whether the answer will be in the tens,
hundreds, thousands, or more. thousands About how many
thousands? About 5 thousands, but less than 6 thousands. 869 is
close to, but less than, 1,000.
Next, have students find the exact product on their grid paper.
Ask a volunteer to demonstrate a solution method on the board.
If others used different methods, ask them to demonstrate them.
If no one used the partial-products method for multiplying,
demonstrate it on the board. (See margin.)
In this method, multiplication is usually done from left to right.
This ensures that the most important products—the largest
ones—are calculated first. But it is not incorrect for a student
to multiply from right to left.
Each part of the calculation, that is, each partial product, is
written on a separate line. Then the partial products are added.
This is usually very simple and has the benefit of providing
practice with column addition.
1,000s
100s
10s
1s
8
6
9
6
8
3
0
6
5
1
0
0
4
4
4
+
5,
2
Ò 6 [800s] or 6 800
Ò 6 [60s] or 6 60
Ò 6 [9s] or 6 9
Pose a few more multiplication problems until most students seem
to understand the partial-products method.
Ongoing Assessment: Informing Instruction
When students are explaining the steps in the partial-products algorithm, watch
for those who say “6 8”: the 8 in the problem to the right, for example, is in the
hundreds place and has a value of 800, not 8. Encourage students to think and
say “6 [800s]” or “6 800.” The notation 6 [800s], introduced in Third Grade
Everyday Mathematics, is read as “6 eight-hundreds.”
Lesson 5 5
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Student Page
Date
Time
LESSON
The Partial-Products Method
5 5
䉬
夹
夹
18
Using the Partial-Products
Algorithm with 1-Digit Multipliers
Multiply using the partial-products method. Show your work in the computation grid
on page 119.
246
1. 82 ⴱ 3 ⫽
4. 3 ⴱ 470 ⫽
318
2. 6 ⴱ 53 ⫽
1,410
5. 2 ⴱ 1,523 ⫽
3. 574 ⴱ 5 ⫽
3,046
6. 3,467 ⴱ 3 ⫽
2,870
(Math Journal 1, pp. 118 and 119)
10,401
Estimate whether your answer will be in the tens, hundreds, thousands, or more. Write
a number model to show how you estimated. Circle the correct box. Then calculate the
answer. Show your work on page 119.
Students complete journal page 118 independently. Partners
compare their answers.
7. China has the world’s longest school year at 251 days. How many school days
are in 7 years?
a. Number model:
10s
Sample answer: 10 ⴱ 250 ⫽ 2,500
100s
1,000s
b. Calculate the answer.
1,757
10,000s
Adjusting the Activity
100,000s 1,000,000s
days of school
Encourage students to write the number model for the partial products
if they are not using mental math to solve the extended facts. For example:
8. People living in the United States eat about 126 pounds of fresh fruit in one year.
About how many pounds of fresh fruit would a family of 6 eat in one year?
Sample answer: 6 ⴱ 130 ⫽ 780
a. Number model:
10s
INDEPENDENT
ACTIVITY
100s
1,000s
b. Calculate the answer. About
756
10,000s
4 [300s] or 4 300 1,200
100,000s 1,000,000s
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
pounds of fresh fruit
9. Explain how estimation can help you decide whether an answer to a multiplication
problem makes sense.
Sample answer: By estimating, I can quickly
get an answer that should be close to the exact
answer.
Ongoing Assessment:
Recognizing Student Achievement
118
Math Journal 1, p. 118
Journal
page 118
Problems 1 and 2
Use journal page 118, Problems 1 and 2 to assess students’ ability to use the
partial-products algorithm to multiply a 1-digit number by a 2-digit number.
Students are making adequate progress if they can correctly calculate and then
add the partial products. Some students may be able to solve Problems 3–6,
which involve the multiplication of a 1-digit number by a 3- or 4-digit number.
[Operations and Computation Goal 4]
2 Ongoing Learning & Practice
Estimating Lengths Using
Student Page
Date
LESSON
5 5
䉬
Personal References
Time
(Math Journal 1, pp. 98 and 120)
My Measurement Collection for Units of Length
Use your personal references on journal page 98 to estimate the length or height of an
object or distance in inches, feet, or yards. Describe the object or distance, and record
your estimate in the table below. Then measure the object or distance, and record the
actual measurement in the table.
Object or Distance
Estimated Length
INDEPENDENT
ACTIVITY
Students use their personal references for customary units of
length to help them estimate the lengths of various classroom
objects in inches, feet, and yards. Then they measure these
objects with rulers or tape measures to check the accuracy of
their estimates.
128 130
Actual Length
Answers vary.
Math Boxes 5 5
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 117)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 5-7. The skill in Problem 5
previews Unit 6 content.
120
Math Journal 1, p. 120
340
Unit 5 Big Numbers, Estimation, and Computation
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Student Page
Writing/Reasoning Have students write a response to the
following: Donato said that there is more than one correct
answer for each of the estimates in Problem 2. Do you
agree or disagree? Explain. Sample answer: Yes. There can be more
than one correct answer because it depends on the place value to
which students round. For example, the following are both
reasonable estimates for Problem 2b: 600 + 1,800 + 2,400 = 4,800
and 600 + 2,000 + 2,000 = 4,600.
Date
Time
LESSON
Math Boxes
5 5
䉬
Immigration Statistics
1. In 2002, about 32,500,000 people living in the
United States had been born in other countries.
The circle graph shows where these people
were born.
Latin America
a. Where were most of these people born?
Other
Latin America
Europe
b. About what fraction of the people
were born in Asia?
Asia
1
ᎏᎏ
4
3. Complete.
2. Estimate the sum. Write a number model
to show how you estimated.
Rule:
a. 387 ⫹ 945 ⫹ 1,024
Multiply by 70.
in
Number model: Sample
answers:
400 ⫹ 1,000 ⫹ 1,000 ⫽ 2,400
Study Link 5 5
INDEPENDENT
ACTIVITY
280
80
5,600
b. 582 ⫹ 1,791 ⫹ 2,442
7
490
Number model:
90
6,300
300
21,000
600 ⫹ 2,000 ⫹ 2,000 ⫽ 4,600
(Math Masters, p. 151)
out
4
181
162–166
4. Write two hundred million, three thousand,
5. Look at the grid below.
eighty-eight using digits. Fill in the circle
next to the best answer.
a. In which column
Home Connection Students practice using the
partial-products algorithm to find products with
1-digit multipliers.
A
is the circle
located?
A. 2,030,088
B
C
2
B. 200,030,088
b. In which row is
C. 20,003,880
3
the circle located?
2
D. 200,003,088
4
Modeling Multiplication
144
117
3 Differentiation Options
READINESS
C
1
Math Journal 1, p. 117
SMALL-GROUP
ACTIVITY
15–30 Min
with Base -10 Blocks
(Math Masters, pp. 432 and 433)
To explore the partial-products algorithm using a concrete model,
have students model 1-digit times 2-digit multiplication problems
with base-10 blocks. Place taped transparencies of Math Masters,
pages 432 and 433 on a table. To model 4 28, use an erasable
marker to mark off a portion of the grid that is 4 squares high and
28 squares wide (4 by 28).
Study Link Master
Name
Date
STUDY LINK
Time
Multiplication
55
䉬
Multiply using the partial-product method. Show your work in the grid below.
18 184
392
11,916 ⫽ 1,324 ⴱ 9
56 º 7 ⫽
4.
Maya goes to school for 7 hours each day. If she does not miss any of the
181 school days, how many hours will Maya spend in school this year?
a.
10s
5.
3.
Estimate whether the answer will be in the tens, hundreds, thousands, or more. Write
a number model to show how you estimated. Circle the box that shows your estimate.
Number model:
b.
2.
8 º 275 ⫽
2,200
1.
7 ⴱ 200 ⫽ 1,400
100s
Exact answer:
1,000s
1,267
10,000s
100,000s 1,000,000s
hours
The average eye blinks once every 5 seconds. Is that more than or less than a hundred
thousand times per day? Explain your answer.
Sample answer:
Less; 60 / 5 ⫽ 12 blinks per minute; 12 º 60 ⫽ 720 blinks
per hour; 720 º 24 ⫽ 17,280 blinks per day
Start here.
Array model of 4 28
Practice
6.
8.
7,884
⫽ 495 ⫹ 7,389
7.
1,258
9.
3,007 ⫺ 1,749 ⫽
5,638 ⫹ 5,798 ⫽
4,689
11,436
⫽ 8,561 ⫺ 3,872
151
Math Masters, p. 151
Lesson 5 5
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Teaching Master
Name
LESSON
55
䉬
Date
Time
Ask students to cover the array using as few base-10 blocks
as possible.
Patterns in Extended Facts
Use base-10 blocks to help you solve the problems in the first 2 columns. Use the patterns
to help you solve the problems in the third column. Use a calculator to check your work.
1.
2
20
2 º 100 ⫽ 200
2º1⫽
2 º 10 ⫽
20
200
20 º 100 ⫽ 2,000
20 º 1 ⫽
20 º 10 ⫽
200
2,000
200 º 100 ⫽ 20,000
200 º 1 ⫽
200 º 10 ⫽
Use what you learned in Problem 1 to help you solve the problems in the table below.
Use a calculator to check your work.
2.
8
80
2 º 400 ⫽ 800
2º4⫽
2 º 40 ⫽
80
800
20 º 400 ⫽ 8,000
20 º 4 ⫽
20 º 40 ⫽
800
8,000
200 º 400 ⫽ 80,000
200 º 4 ⫽
200 º 40 ⫽
Explain how knowing 2 º 4 can help you find the answer to 20 º 40.
3.
Sample answer: I know 2 ⴱ 4 ⫽ 8, so 20 ⴱ 40
is just 8 with two zeros added on, or 800. I
added on two zeros because there is a total
of two zeros in the numerals 20 and 40.
Make up and solve some problems of your own that use this pattern.
4.
Answers vary.
Start here.
Base-10 block model of 4 28
Now match each part of the 4-by-28 array with a partial product.
There are 2 longs in each of 4 rows. These cover
4 20 80 squares.
Math Masters, p. 152
There are 8 cubes in each of 4 rows. These cover
4 8 32 squares.
The longs and cubes cover 80 32 112 squares in all.
Erase the transparencies. Use the transparencies and base-10
blocks to solve additional 1-digit times 2-digit problems.
READINESS
Exploring Patterns in
PARTNER
ACTIVITY
5–15 Min
Extended Facts
(Math Masters, p. 152)
To explore patterns in extended facts, have students use base-10
blocks to model the problems on Math Masters, page 152. Have
students describe the patterns they see in Problem 1.
Name
LESSON
55
䉬
Date
An Old Puzzle
An old puzzle begins like this: “A man has 6 houses. In each house, he keeps 6 cats.
Each cat has 6 whiskers. On each whisker sit 6 fleas.”
1.
ENRICHMENT
Time
Solving an Old Puzzle
Answer the last line of the puzzle: “Houses, cats, whiskers, fleas—how many are there in all?”
PARTNER
ACTIVITY
5–15 Min
(Math Masters, p. 153)
1,554
2.
Use number models or illustrations to explain how you solved the puzzle.
Sample answer: There are 6 houses,
6 ⴱ 6 ⫽ 36 cats, 36 ⴱ 6 ⫽ 216 whiskers,
216 ⴱ 6 ⫽ 1,296 fleas. The total is
6 ⫹ 36 ⫹ 216 ⫹ 1,296 ⫽ 1,554.
Math Masters, page 153
342
Unit 5 Big Numbers, Estimation, and Computation
To apply students’ multiplication skills, have them solve an old
puzzle involving numbers of houses, cats, whiskers, and fleas.
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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
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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 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
䉬
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 ⴱ 12
b.
numbers that give
the exact answer
10s
60 ⴱ 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 ⴱ 16
b.
numbers that give
the exact answer
10s
20 ⴱ 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.
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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
Time
LESSON
5 6
䉬
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 ⴱ 24
b.
60 ⴱ 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 ⴱ 365
b.
80 ⴱ 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
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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
䉬
(Student Reference Book, p. 254; Math Masters, p. 489)
Math Boxes
1
1. a. Measure the line segment to the nearest ᎏᎏ inch.
4
5
About
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 ᎏ2ᎏ
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 ⴱ 21
3
2
0
0
0
6
⫹
2 2 3 6
b. 98 ⴱ 72
Number model:
100 ⴱ 70 ⫽ 7,000
184
4. Write each number using digits.
Math Boxes 5 6
⫽ 52 ⴱ 43
4
º
5
2 0 0
1 5
8
Sample answers:
50 ⴱ 20 ⫽ 1,000
Number model:
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
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)
5. If you remove 7 gallons per day from a
a. three hundred forty-two thousandths
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.
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Study Link Master
Study Link 5 6
INDEPENDENT
ACTIVITY
(Math Masters, p. 154)
Name
Date
STUDY LINK
56
䉬
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.
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
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
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Time
A Dart Game
56
䉬
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
50
25
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
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
Sorting Numbers
56
䉬
Study the Venn diagrams in Problems 1 and 2. Label each circle and add at least one
number to each section.
Sample
p answers:
1.
80
5,600
160
4,000
720
2,400
240
divisible by 80
Scoring a Dart Game
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
Sample answers:
Sample answers:
30 as a factor
990
1,230
360
ENRICHMENT
Solving Venn Diagram Puzzles
120
1,500
210
840
250
4,000
650
2,000
4,200
6,300
560
490
280
350
7,000
build arrays with
770
multiples of 70
50 rows
Math Masters, p. 156
348
PARTNER
ACTIVITY
5–15 Min
(Math Masters, p. 156)
420
1,050
3,500
5–15 Min
(Math Masters, p. 155)
multiples of 30
750
1,200
INDEPENDENT
ACTIVITY
300
180
4,200
Try This
2.
ENRICHMENT
Time
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.