CHAPTE R
2
Multiply Whole Numbers
Planner
Skills Trace
The
BIG Idea
Vertical Alignment
In this chapter, students deepen their understanding of multiplication
multiplying up to a three-digit number by a two-digit number. Students develop
their understanding of number patterns by estimating products and using
multiplication properties. Students will apply this knowledge to real-world
problems.
Targeted Standards
Previous Grade
In the previous grade, students learned to:
• Multiply two- and three-digit numbers by one-digit
numbers.
• Multiply multiples of 10 and 100 using basic facts and
patterns.
GLE 0506.1.2 Apply and adapt a variety of appropriate strategies to problem
solving, including estimation, and reasonableness of the solution.
GLE 0506.2.5 Develop fluency in solving multi-step problems using whole
numbers, fractions, mixed numbers, and decimals.
This Grade
During this chapter, students learn to:
• Multiply up to a three-digit number by one- and two-digit
numbers.
• Multiply a whole number by a decimal and estimate
products by rounding and using compatible numbers.
After this chapter, students learn to:
• Identify common factors of a set of whole numbers.
Next Grade
Print and Online Professional Development
articles can be found in the Teacher Resource
Handbook. These articles on current issues
will allow you to implement new mathematical
strategies and enhance your classroom
performance.
In the next grade, students learn to:
• Use multiplication of multi-digit numbers to find the
areas of parallelograms.
• Use the properties of multiplication and number patterns
to estimate and find the product of decimals and whole
numbers.
Digital Videos The McGraw-Hill
Professional Development Video
Library provides short videos that support
McGraw-Hill’s Math Connects. For
support for this chapter, the following video
is available.
Rounding and Estimating Solutions
Other videos, program walkthroughs, online courses, and video
workshops are available at mhpdonline.com.
58A
Multiply Whole Numbers
Vertical Alignment and Backmapping
McGraw-Hill’s Math Connects program was conceived
and developed with the final results in mind: student success
in Algebra 1 and beyond. The authors developed this brand-new
series by backmapping from Algebra 1 concepts, and vertically
aligning the topics so that they build upon prior skills and
concepts and serve as a foundation for future topics.
Chapter at a Glance
Lesson
Multi-Part
Lesson
1
The Distributive Property
A
B
Multiplication Patterns
C
The Distributive Property
Multi-Part
Lesson
Pacing
2 Days
Days
Leveled Worksheets
Explore Worksheet
Visual Vocabulary Cards
Lesson Animations
Daily Transparencies
Problem of the Day
Self-Check Quiz
GLE 0506.2.5
Multiply by One-Digit Numbers
A
Estimate Products
GLE 0506.1.2
B
Multiply by One-Digit Numbers
GLE 0506.2.5
C
Problem-Solving Strategy:
GLE 0506.1.2
3 Days
3
Multiply by Two-Digit Numbers
A
Multiply by Two-Digit Numbers
GLE 0506.2.5
B
Multiplication Properties
GLE 0506.2.5
C
Problem-Solving Investigation:
GLE 0506.1.2
Choose the Best Strategy
Personal Tutor
Virtual Manipulatives
Math Song Animations
Hands-On Activity Tools and
Resources
Materials and Manipulatives
calculators, number lines, index cards, WorkMat 4: Place-Value Chart,
money, base-ten blocks,
money
blocks two-color counters,
counters rulers
Get ConnectED
Leveled Worksheets
Lesson Animations
Daily Transparencies
Problem of the Day
Self-Check Quiz
Personal Tutor
Draw a Picture
Multi-Part
Lesson
Materiials
Materials
l and
d Ma
Manipulatives
nipul
i latives
i
index cards, multiplication flash cards, colored pencils, grid paper
Get ConnectED
GLE 0506.2.5
Use Partial Products and the GLE 0506.2.5
Distributive Property
2
Resources
3 Days
Virtual Manipulatives
eGames
Graphic Novel Animations
Real World Problem Solvers
Hands-On Activity Tools and
Resources
Materials and Manipulatives
centimeter grid paper, scissors, index cards, two-color counters
Get ConnectED
Leveled Worksheets
Lesson Animations
Daily Transparencies
Problem of the Day
Self-Check Quiz
Personal Tutor
Virtual Manipulatives
Hands-On Activity Tools and
Resources
Multiply Whole Numbers
58B
CHAPTE R
2
Vocabulary and Language Connections
Planner
Math Vocabulary
Glossary
The following math vocabulary words are listed in the glossary of the Student Edition.
Get ConnectED
Find interactive definitions in 13 languages in the eGlossary and review
vocabulary eGames at connectED.mcgraw-hill.com.
Associative Property of Multiplication
Property that states that the way in which
factors are grouped does not change the
product.
Example: 8 × (9 × 5) = (8 × 9) × 5
Commutative Property of Multiplication
Property that states that the order in which
factors are multiplied does not change the
product.
Example: 8 × 9 = 9 × 8
Identity Property of Multiplication
Property that states that the product of
any factor and 1 equals the factor.
Example: 18 × 1 = 18
product The answer to a multiplication
problem.
Example: In the number sentence
4 × 6 = 24, the product is 24.
Distributive Property To multiply a sum by
a number, you can multiply each addend
by the same number and add the products.
Example:
8 × (9 + 5) = (8 × 9) + (8 × 5)
Transitive Property of Multiplication
Property that states that if one quantity
equals a second quantity and the second
quantity equals a third quantity, then the
first quantity equals the third.
Example: If 7 + 4 = 11 and 11 = 4 + 7,
then 7 + 4 = 4 + 7.
factor A number that is multiplied by
another number.
Example: In the number sentence
4 × 6 = 24, the factors are 4 and 6.
Zero Property of Multiplication Property
that states that any number multiplied by
zero has a product of zero.
Example: 47 × 0 = 0
Activity
Allow students to work in pairs. Provide students with a set of index
cards that name the various properties of multiplication, and a set of
number and symbol tiles. The first student chooses a property. The
second student creates a number sentence that exemplifies the property.
Student pairs can work together to check the answers.
The game can also be played in reverse. In this version, the first student
creates a number sentence. The second student matches the correct
property to the number sentence.
Visual Vocabulary Cards
Use Visual Vocabulary Cards to reinforce the vocabulary in
this chapter in English and Spanish. (The Define/Example/Ask
routine is printed on the back of each card.)
ISBN: 978-0-02-101742-3
MHID: 0-02-101742-5
Copyright © by The McGraw-Hill
Companies, Inc.
All rights reserved.
MM'12_VVC_G5_cov_
MM'12
VVC G5
101742-5.indd 1
12/3/09 2:48 PM
58C Multiply Whole Numbers
ELL
Support
Multi-Part
Lesson
1
Estimate Sums and Differences
Level
Activity
Modality
Word Meaning
Linguistic, Interpersonal
AL
Beginning
OL
Intermediate Scaffold
BL
Linguistic, Spatial
Advanced
Academic Vocabulary
Existential, Linguistic
Extend
Bilingual Peer Learning
On and Beyond Level
Multi-Part
Lesson
2
Activity
Modality
Word Meaning
Logical-Mathematical
AL
Beginning
OL
Intermediate Activate Prior Knowledge
Existential
BL
Advanced
Act It Out
Linguistic
Extend
Problem Solving
On and Beyond Level
Multi-Part
Lesson
3
Activity
Act It Out
Modality
Spatial
AL
Beginning
OL
Intermediate Word Meaning
Recognize and Act It Out
Advanced
Existential
Extend
On and Beyond Level
BL
Get ConnectED
Bilingual Peer Learning
The Best of Times
Greg Tang
Ten Times Better
Richard Michaelson
Pigs Will Be Pigs: Fun With Math
and Money
Amy Axelrod
Amanda Bean’s Amazing Dream
Cindy Neuschwander
Beanstalk: The Measure of a Giant
Ann McCallum
Multi-Part Lesson 3
Subtract Decimals
Level
Multi-Part Lesson 1
Multi-Part Lesson 2
Add Decimals
Level
Check with your school library or your local
public library for these titles. ✔ 0506.1.9
Logical-Mathematical
Find other English Language Learner strategies.
Sea Squares
Joy N. Hulme
My Full Moon Is Square
Elinor J. Pinczes
Real-World Problem
Solving Library ✔ 0506.1.9
Math and Social Studies: Early American Settlements
Use these leveled books to reinforce
rce
and extend problem-solving skills
and strategies.
K
1
2
3
4
5
*
*
Ma tem
ELL Resources
The Professional Development articles listed below can be found in print
and online in the Teacher Resource Handbook.
• “English Learners and Mathematics:
Best Practices for Effective Instruction”
by Kathryn Heinze (pp. TR32–TR33)
• “Engaging English Language Learners
in Your Classroom” by Gladis Kersaint
(pp. TR34–TR35)
• Multilingual eGlossary
• Visual Vocabulary Cards
• Language Alerts (pp. 67, 71, 87)
• ELL Guide (pp. 40–41)
átic as
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Ma tem
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AL Approaching Level
BL Beyond Level
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Reading and Language Arts Support
For activities to connect reading and language arts to this
chapter’s math concepts, see Reading and Language Arts
Support in the Grade 5 Math Connects Program Overview.
Leveled Reader Database
Get ConnectED
connectED.mcgraw-hill.com
Search by
• Content Area
• Guided Reading Level
• Lexile Score
• Benchmark Level
Multiply Whole Numbers
58D
CHAPTE R
2
Learning Stations
Planner
LOGICAL
pair
Apple Cart
Materials:
• Each person chooses an apple and weighs it in grams, using the
balance scale and gram weights.
• balance scale with gram
weights
• Then, using multiplication, determine how much weight an
apple cart would have to hold if you put enough of your apples
in it to feed the entire class (one apple per student).
• apples
• paper
• pencils
7
VISUAL
SPATIAL
individual
pair
Four-Square Art
Materials:
• Divide one sheet of grid paper into 4 equal sections. Color each section a
different color. Label each section 1–4.
8
• four colored hundredths
grids, cut into hundredths
• Choose a number between 5 and 10 and fill in that number of squares
with a black marker inside section one.
• markers
• Double the number of black squares from section one and fill in that
many for section 2.
• white paper
• scissors
• glue
• Triple the number of black squares filled in for section 3 and quadruple
the number for section 4.
individual
Sonnet Syllables
• In a Shakespearean sonnet, there are 14 lines. Each line has five groups
of two syllables each, called iambs. An iamb is a two-syllable group
where the strong syllable, or stressed syllable, is the second syllable. For
example, the word reflect has two syllables, and the second syllable is
where you hear the stress when you say the word.
• Try to write an unrhymed sonnet using five iambs per line.
• How many syllables does your poem have?
9
58E Multiply Whole Numbers
LOGICAL
Materials:
reFLECT
• paper
• pencils
group
Exercise Plan
LOGICAL
Materials:
Form groups of three and count your Calories.
• scissors
• Write the following exercises and Calorie counts on strips, one per strip:
Basketball: 210 Calories in 30 minutes
Jogging: 300 Calories in 30 minutes
Dancing: 150 Calories in 30 minutes
• basket
• paper
• pencils
• Each person picks a strip out of a basket. Decide how many times per
week you will exercise. How many Calories will each person burn in a
week? How many Calories will your group burn if you put your plans
10 into action?
individual
Music Library
LOGICAL
Materials:
Count up the CDs and find out how much they are worth.
• basket of 20 CD cases
with price stickers on
them
• Make a chart showing the price of each CD, next to the CD title.
• Group together similar prices and write a multiplication problem that
expresses the total value of the CDs.
• pencil
• paper
• Then solve the expression to figure out the total.
11
pair
What Can You Buy?
What if you had $100,000 to spend on computer equipment for your school?
• Make a spinner with six sections. Label the sections as follows: Monitor
$199, Computer $959, Scanner $99, Printer $129, Keyboard $29, and
Educational Software $69.
• Takes turns spinning to see what you will buy, and rolling the number
cube to see how many of that item you will buy. Use multiplication to
figure how much the item will cost.
LOGICAL
Materials:
Monitor
$199
Educational
Software
$69
Keyboard
$29
Computer
$959
Scanner
$99
• blank spinner
• number cube
• pencils
• paper
Printer
$129
• The last person to run out of his or her $100,000 amount wins.
12
Multiply Whole Numbers
58F
CHAPTER
2
CHAPTE R
2
Introduce the Chapter
E
Essential Question
Multiply Whole
Numbers
connectED.mcgraw-hill.com
How are number patterns and properties helpful in
solving multiplication problems? Sample answer:
Number patterns, such as those related to place value,
can be used to find patterns among products as well.
Estimation and properties, such as the Distributive
Property, can be used to find products mentally.
The
BIG Idea
Investigate
How can I multiply
whole numbers
accurately?
Animations
Vocabulary
Math Songs
Multilingual
eGlossary
E
WRITE MATH Ask students to write about
situations where they have seen multiplication in action.
Suggest that they give specific examples from in school
and out of school, such as in the lunchroom or in the
grocery store.
Learn
Personal Tutor
Virtual
Manipulatives
Dinah Zike’s
Foldables®
“Make this Foldable
to help you organize
information about
multiplying whole
numbers.”
ly
Multipmbers
Nu
Whole
erty
op
ive Pr
istribut
r
bers
itt Num
ne-Dig
rs
u be
t Num
i
it
o-Dig
Tw
by
ultiply
The D
ly by O
Multip
M
Audio
Foldables
Go to connectED.mcgraw-hill.com to provide
students with directions to create their own Foldables
graphic organizers for this chapter. Students may also use
their Foldables to study and review for chapter
assessments.
Practice
Self-Check Practice
eGames
Worksheets
When to Use It Multi-Part Lessons 1A, 1C, 2B, and 3A.
(Additional instructions for using the Foldable with these
lessons are found in the Mid-Chapter Check and Chapter
Study Guide and Review.)
Assessment
Review Vocabulary
ero
Whole Numbers número ent
4…
3,
2,
1,
The numbers 0,
Key Vocabulary
English
Distributive Property
factor
product
Español
Propiedad Distributiva
factor
producto
Key Vocabulary
Introduce the Key Vocabulary in the chapter using the
routine below.
Define: A product is the answer to a multiplication
problem.
Example: The product 3 × 5 is 15.
Ask: What are the parts of a multiplication sentence?
Student Glossary
Graphic Organizer
Notetaking
58
0058_0060_C02CO_103031.indd 58
Chapter Project
About How Much? Students create food-serving charts using nutrition guides.
• Students estimate how much of each food they eat for one day: breakfast, lunch,
dinner, and snacks. They keep a food diary to record their estimates. They give
estimated totals for each of the food groups for their one-day intake.
• Students use the Internet or nutritional resources to compare their food intake with
actual serving sizes.
• Challenge students to figure out how they might modify their daily food intake to be
closer to the recommended daily allowances for fifth-graders.
Refer to the Chapter Resource Masters for a rubric to assess students’ progress on this project.
58
Multiply Whole Numbers
2/26/10 12:13 P
When Will I Use This?
When Will I Use This?
Pizza Party!
Read the story. You may wish to use the blank Graphic
Novels provided in Hands-On Activity Tools and Resources
to help develop writing and speech skills.
• Have student pairs read the story. One student reads
Rico’s lines and the other student reads Desiree’s lines.
• How do you think Rico and Desiree could figure out
how much pizza they will need? Sample answer:
Estimate how many pieces of pizza each person will
eat, and find out how many pieces there are in
each pizza.
• What are some questions they should ask
themselves as they decide on the total number of
pizzas? Sample answers: How large are the pizzas?
How large are the slices?
• How many pizzas do you think will be needed for
Kim’s party? Check students’ work.
✔ 0506.1.9 Use age-appropriate books, stories, and videos to
convey ideas of mathematics.
For additional reading and language arts activities,
including support for reading a graphic novel, see Reading
and Language Arts Support in the Grade 5 Math Connects
Program Overview.
Visit connectED.mcgraw-hill.com to download
the animated version of “Pizza Party!”
Your Turn!
his
You will solve thi
errr.
problem in the chapte
Multiply Whole Numbers
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and have each student sign it. A Spanish versionn
is also included. Use the Spanish letter for
Spanish-speaking parents or guardians who
do not read English fluently.
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Print er PDF
Available in
English • Spanish
For more information about parent involvement,
read the article, “The Role of Parents and Guardians
in Young Children Learning Mathematics” by
Paul Giganti, Jr. See the Teacher Resource Handbook pp. TR44–TR45.
Your Turn!
In Lesson 2B, students will learn more about using the
Distributive Property to determine the total cost of pizza
the guests will eat.
Multiply Whole Numbers
59
Diagnostic Assessment
1 ASSESS
You have two options for checking Prerequisite Skills for this chapter.
Text Option
Are You Ready
“Are You Ready for the Chapter?”
SE
Student Edition
for the Chapter?
O
Online Option
Text Option
You have two options for checking
Prerequisite Skills for this chapter.
Take the Quick Check below.
Take the Online Readiness Quiz.
Multiply.
1. 6 × 3 18
2. 1 × 8 8
3. 5 × 4 20
4. 9 × 2 18
5. 7 × 8 56
6. 4 × 10 40
7. The cost of a coloring book is $2. Find the total
cost of 9 coloring books. $18
Write a multiplication problem for each. Then find
each product.
8. 8 groups of 6 pens 8 × 6; 48
9. 3 rows of 7 chairs 3 × 7; 21
10. 4 books at $2 each 4 × $2; $8
11. There are 4 model car kits in each box. How many
kits are in 5 boxes? 4 × 5; 20 kits
Add.
1,125
13.
14.
256
438
+ 32,060
+ 2,040
+ 1,470
−−−−−−
−−−−−−
−−−−−−
33,185
1,726
2,478
15. A Girl Scout troop sold 1,198 boxes of cookies last year.
This year they sold 204 more boxes than last year. Next
year the troop wants to sell 150 more boxes than this
year’s total. How many boxes of cookies does the troop
want to sell next year? 1,552 boxes
12.
Online Option
60
Multiply Whole Numbers
0058_0060_C02CO_101808.indd 60
60
Multiply Whole Numbers
Take the Online Readiness Quiz.
11/5/09 5:34 PM
3 REASSESS
2 DIAGNOSE AND PRESCRIBE
RtI (Response to Intervention)
Administer the Diagnostic Test.
Based on the results of the Diagnostic Assessment, use the charts below to address
individual needs before beginning the chapter.
Diagnostic Test
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Multiply.
1. 9 × 4
Name __________________
_________
3. 5 × 5
for the Chapter?
4. 6 × 8
Practice
2. 6 × 7
1.
3. 11 × 3
2.
3.
4. 7 × 8
4.
5. 4 × 6
(pp. 58E–58F)
8. 9 × 8
7.
8.
Companies, Inc.
9. 10 × 7
Self-check Quiz
10. 9 × 4
9.
11. 9 × 5
10.
12. 5 × 10
11.
12.
5.
4
6.
63
7.
28 in.
Write a multiplication
problem for each. Then
find each
product.
8. 5 people each have
8 toy cars
8. 5 × 8; 40 toy cars
9. 6 dolls at $6 each
9.
10. 2 boxes of 8 crayons
11. There are 7 students
sitting at each table in
the cafeteria.
How many students are
sitting at 8 tables?
Add.
Write a multiplication
problem for each. Then
find each
product.
12.
13. 3 groups of 5 students
4,238
+ 31,169
13.
173
+ 2,416
14.
914
+ 14,134
16. 5 bouquets with
12 roses
17. 2 beverages at $3
18. 4 CDs with 9 songs
19. 3 posters at $4
20. 6 cars with 4 tires
Grade 5 • Multiply Whole
Numbers
11. 7 × 8; 56 students
12.
14.
15. 7 cats with 4 paws
15. Sal’s Italian Café
sold 5,345 sandwiches
last month. This
month, they sold 173
more sandwiches than
last month.
Next month, they hope
to sell 250 more sandwich
es
than they sold this month.
How many sandwiches
does
Sal’s hope to sell next
month?
6 × $6; $36
10. 2 × 8; 16 crayons
35,407
13.
2,589
14.
15,048
15. 5,768 sandwiches
Inc.
3 × 5; 15
6 × 8; 48
15. 7 × 4; 28
16. 5 × 12; 60
17. 2 × $3; $6
18. 4 × 9; 36
19. 3 × $4; $12
20. 6 × 4; 24
13.
14. 6 tables with 8 chairs
48
6. 7 × 9
7. The length of a pencil
is 7 inches. Find the total
length of
4 pencils placed end
to end.
McGraw-Hill Companies,
Copyright © Macmillan/McGraw
-Hill, a division of The McGraw-Hill
Are You Ready? Practice
Get ConnectED
5.
6.
30
25
Copyright © Macmillan/McG
raw-Hill, a division of The
Learning Stations
6. 5 × 3
7. 6 × 9
20
42
33
56
24
15
54
72
70
36
45
50
36
2.
3.
4.
5. 1 × 4
1. 4 × 5
choose a resource:
1.
2. 3 × 10
Are You Ready
students miss three or four in Exercises 1–15,
TE
Date
Diagnostic Assessment
OL
Multiply.
Then
1:09:16 AM elhi1
Name
__ Date ________________
If
10/30/09
8
5
Grade 5 • Multiply Whole
Numbers
TIER
2
Strategic Intervention
approaching grade level
Print
AL
001_015_C02_101834.indd
Page 6
10/30/09
1:09:15 AM elhi1
PDF
/Volumes/121/GO00398/GO003
98_Math_Conne
_
ects_CRM_NA_G
cts_CRM_NA_G5
5%0/XXXXXXXXX
%0/XXXXXXXXXX
XXXX
XXX_SE/Appli...
Name __________________
___________
Date ________________
Are You Ready
If
Then
for the Chapter?
students miss five to nine in Exercises 1–15,
Review
Derek has three boxes
of markers. Each box
has nine markers.
Write a multiplication
problem that represents
the total number
of markers that Derek
has. Then find the total
number of markers.
There are three boxes
of markers. Each box
has nine markers.
3 × 9 Write the multiplicati
on expression.
You know that 3 × 9
is 27.
So, the total number
of markers is 27.
choose a resource:
Strategic Intervention Guide
Write a multiplication
expression for each.
Then find each product.
1. 6 trains with 7 cars
(pp. 44–55)
6 × 7; 42
8 × $3; $24
5 × 9; 45
6 × 9; 54
5. 4 × 8; 32
6. 8 × 10; 80
7. 4 × $9; $36
8. 6 × $11; $66
9. 4 × 12; 48
10. 3 × 7; 21
11. 5 × 8; 40
12. 7 × $9; $63
13. 5 × 10; 50
14. 3 × 4; 12
15. 2 × 12; 24
1.
2. 8 desserts for $3
2.
3. 5 crates with 9 apples
3.
Are You Ready? Review
4.
6. 8 packages of plastic
spoons with 10 spoons
7. 4 tickets for $9
8. 6 meals for $11
9. 4 boxes of crayons
with 12 crayons
10. 3 packages weighing
7 pounds
11. 5 miles at 8 minutes
per mile
12. 7 hours at $9 per
hour
Lesson Animations
Companies, Inc.
13. 5 packages of cookies
with 10 cookies
14. 3 cars with 4 passengers
15. 2 rows of parking
spaces with 12 spaces
-Hill, a division of The McGraw-Hill
Get ConnectED
Copyright © Macmillan/McGraw
4. 6 rows of 9 chairs
5. 4 pizzas with 8 slices
6
Grade 5 • Multiply Whole
Numbers
TIER
3
If
Then
Intensive Intervention
2 or more years below grade level
students miss ten or more in Exercises 1–15,
use Math Triumphs, an intensive math intervention
program from McGraw-Hill
Chapter 2 Multiplication
Chapter 4 Properties of Operations
Beyond Level
BL
001_015_C02_101834.indd
Page 7 11/20/09 5:58:12
PM u-s010
/Volumes/121/GO00398/GO00398_
Math_Connects_CRM_NA_G5%0/X
XXXXXXXXXXXX
XX_SE/Ap
_SE/Appli...
Name __________________
_________
__ Date ________________
If
Are You Ready
for the Chapter?
students miss two or less in Exercises 1–15,
Apply
Solve.
choose a resource:
2 miles
(p. 58)
Are You Ready? Apply
Get ConnectED
eGames: Robo Works
Companies, Inc.
Chapter Project
-Hill, a division of The McGraw-Hill
TE
Copyright © Macmillan/McGraw
Then
1. Felisa ran two miles
on Monday, three
miles on Tuesday, and
one mile on
Wednesday. If she wants
to run a total
of 8 miles by the end
of the next day,
how many miles will
she need to run
on Thursday?
3. During the first year
of a festival, there
were 1,205 attendees.
The second
year, there were 180
more attendees
than the first year. The
third year, there
were 500 more attendees
than the
second year. How many
people
attended the festival the
third year?
1,885 people
5. A bookstore sold 1,350
copies of a
book during the first month.
The
second month, the bookstore
sold 400
more copies than the
first month. The
third month, the bookstore
sold 175
more copies than the
second month.
How many copies of
the book did the
bookstore sell during
the third month?
2. Three friends went
to see a movie.
They each spent $9 on
the movie ticket
and $2 on a beverage.
If they had a
total of $40, how much
money
altogether did they have
left?
$7
4. Marcus scored 15
points during his first
basketball game. He scored
22 points
during his second basketball
game. If
he scored a total of 50
points during
his first three basketball
games, how
many points did he score
during his
third basketball game?
13 points
6. Mr. Fraser drove 240
miles on Friday.
On Saturday, he drove
180 miles. If he
needs to drive a total
of 600 miles by
Sunday, how many miles
does he
need to drive on Sunday?
180 miles
1,925 copies
7. Tony made 36 banana
muffins. He
gave 22 to his classmates
and three to
his sister. How many
did he have left?
11 muffins
Grade 5 • Multiply Whole
Numbers
8. Greg had 97 songs
on his MP3 player.
He deleted 14 songs
and downloaded
28. How many songs
does he have
now?
111 songs
7
Multiply Whole Numbers
60A
Multi-Part
Lesson
1
The Distributive Property
Planner
PART
A Multiplication Patterns
B
Use Partial Products
and the Distributive Property
C
The Distributive Property
E
PART
Focus on Math Background
In this multi-part lesson, students will use big
ideas and concepts of multiplication such as:
• Place value is multiplicative in nature.
Multiplication Patterns
Title / Objective
(pp. 61–63)
Use Partial Products
andd the
h Distributive
i
Property
Standards
Use basic facts and patterns to multiply
multiples of 10, 100, and 1,000
mentally.
Explore multiplication with regrouping
using models.
GLE 0506.2.5
GLE 0506.2.5
pproduct
roduct
Vocabulary
factor
Visual Vocabulary Card 24
multiplication flash cards
Materials/
Manipulatives
Resources
colored pencils, index cards
Get ConnecttED
✔ 0506.1.9
• The properties of multiplication can be used
to rewrite expressions so they can be
evaluated mentally. Students should learn
to recognize and use patterns when
multiplying.
Get ConnecttED
Leveled Worksheets
Explore Worksheet
VVisual Vocabulary Cards
Lesson Animations
Daily Transparencies
Math Song Animation: Multiplication
Rap
Problem of the Day
Self-Check Quiz
Personal Tutor
Math Song Animation: When You
Multiply
Hands-On Activity Tools and Resources
Blended Approach
IWB
All digital assets are Interactive
Whiteboard ready.
61a Multiply Whole Numbers
B
(pp. 64–65)
Essential Question
How can place value help you to solve
multiplication problems mentally? Using the
Distributive Property, you can separate twodigit numbers into numbers that can be easily
multiplied mentally. For example, the product
of 5 × 43 can be found by multiplying 5 × 40
and adding it to the product of 5 × 3. This can
be done easily mentally.
PART
A
Suggested Pacing
Multi-Part Lessons
1
PART
A
Days
1
2
B
C
1
(10 Days)
3
Assess
A
B
C
A
B
C
1
1
1
1
1
1
SGR PCT
1
1
The Distributive Property
PART
Notes
C
The Distributive Property
Title / Objective
(pp. 66–69)
Use the Distributive Property to multiply
mentally.
Standards
GLE 0506.2.5
Vocabulary
colored pencils
grid paper
Get ConnecttED
Leveled Worksheets
Materials/
Manipulatives
Resources
✔ 0506.1.9
Lesson Animations
Daily Transparencies
Problem of the Day
Self-Check Quiz
Personal Tutor
VVirtual Manipulatives
Hands-On Activity Tools and Resources
Blended Approach
The Distributive Property
61b
Differentiated Instruction
Approaching Level
On Level
AL
Option 1
Use with 1A
Hands-On Activity
Materials: two 5-10 number cubes, paper, pencil, stopwatch
• In groups of 2 to 4, have students take turns rolling two
number cubes. One student will be the scorekeeper. The roller
will say the fact family for the numbers rolled. One point is
awarded per correct fact given.
• The person with the greatest score at
the end of the game wins.
Option 2
Option 1
Use with 1C
• Give each student three index cards.
• On the front of the index cards, have students write problems
that exemplify the Distributive Property, like the ones shown
below.
(10 + 2) × 7 = (10 × 7) + (10 × 2 )
6 7
4 × (20 + 3) = (4 × 20) + (4 × 3)
10
9 6
10
• Timing the responses can add an extra
challenge to the game. Provide students
with a stopwatch and encourage them to
provide the fact family within 1 minute.
The time can also be adjusted according to
the needs of the students.
OL
Use after 1A
• Tell students to write the missing number that makes the
number sentence true on the back of each index card.
• Have students exchange cards with classmates in order to
solve the problems.
• Extend the activity by asking students to write a real-world
problem that could be represented by one of the cards.
Hands-On Activity
Materials: spinner marked 1–9, paper, pencil
Option 2
• Have students play in pairs. Players spin two times each,
writing down each digit they spin.
Hands-On Activity
Materials: paper and pencil
• Players use the numbers as factors, such as 2 and 5, and
multiply.
• Have students determine the greatest and least possible
products of a two-digit number and a one-digit number. 891
and 0
• Have students add one zero to one factor, such as changing
the 2 to become 20. Then, multiply again. Repeat this process
by adding two and then three zeroes to the same factor (so
that the 2 then becomes 200 and 2,000).
1
Other Options
TE
Learning Station Card 8
Get ConnectED
61c
Personal Tutor, Lesson Animations,
Virtual Manipulatives, Math Song
Animations: When You Multiply
Multiply Whole Numbers
2
3
4
5
6
7
8
9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
• Then students exchange papers and check each other’s work.
Each correct product earns a player 1 point.
• Have students play as time allows. The player that earns more
points at the end of the game wins.
Use with 1A
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
• What strategy did you use to find the products? Choose
the two-digit and one-digit numbers that have the greatest
and least values.
Other Options
TE
Learning Station Card 9
Get ConnectED
Personal Tutor, Lesson Animations,
Virtual Manipulatives, Math Song
Animations: When You Multiply
The Distributive Property
Beyond Level
English Language Learners
BL
Option 1
Use with 1A
Materials: spinner labeled 1, 2, and 3, two number cubes,
pencil, paper
• Ask students to work in pairs. One student rolls the number
cubes to generate the initial digits of two factors.
14 43
ELL
This strategy helps English Learners learn language associated
with multiplication.
Find Core Vocabulary and Common Use Verbs in the online
EL strategies to help students grasp the math skills; use
Language Alerts at point of use in the Teacher Edition.
Beginning
Word Meaning Introduce vocabulary words factor and
product.
• Create a set of index cards with factors on one card
(e.g., 5 × 9) and answers on a second card (e.g., 45).
• Have students play a matching game with a partner. Each
student turns over two cards. If a student matches a factor set
with the correct product, then the student keeps the cards.
• Once all matches have been made, have students practice
using the mathematical language. For example, 5 times
9 equals 45. The factors are 5 and 9. The product is 45.
AL
5
5
• The second student spins the spinner twice to determine the
number of zeros in each factor.
• Have both students write the equations generated and find
the products. Ask them to compare. After several equations
have been solved, have the partners write a statement about
where zeros occur in the factors and their bearing on the
product.
Intermediate
Scaffold Use new vocabulary to describe multiplication.
• Have pairs create a three-column chart and use factor, factor,
product as the column heads.
• Then have students roll number cubes and write the numbers
in the factor columns. Repeat five times.
• Have students trade charts with another pair. Have them solve
the problems using the numbers in the chart. For example, if
the factors are 8 and 5, their sentence will be 8 × 5 = 40.
• Model language students should use to express their work.
The factors are 8 and 5. The product is 40. 8 times 5 equals 40.
Have students repeat.
OL
Option 2
Use after 1A
Materials: sets of index cards numbered 1–9, two sets of index
cards labeled × 10; × 100; × 1,000
• Each student gets a set of 1–9 cards. Put the “10” multiple
cards face down on the table.
• Each student flips two number cards. One “10” card is flipped
for the group. Students should multiply the product of their
cards times the “10” card and write the total on a piece of
paper.
• Repeat 10 times. The player whose total score is closest to
100,000 wins.
2
7
5
×10
×100
9
×1000
Other Options
TE
Learning Station Cards 7, 9
Get ConnectED
Lesson Animations, Math Song
Animations: When You Multiply
BL Advanced
Academic Vocabulary Learn and use correct terminology for
describing properties of multiplication.
• Write 51 × 8 on the board. Have students solve. Then write
(50 × 8) + (1 × 8). Have students solve. Ask, Which
problem was easier?
• Tell students that they can separate a two-digit number into
tens and ones to make it easier to multiply. Say, Distributive
Property. Have students repeat. Write it on the board.
Extend
Have student pairs roll two 0-5 number cubes to create a twodigit factor and a 5-10 number cube to create a one-digit factor.
Have them use the Distributive Property to solve a problem with
those two factors.
The Distributive Property
61d
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Handboo
Notes
Teacher Tip:
As students begin to work with the
Distributive Property, remind them that when
they use this property, they are distributing
the factor to each number inside of the
parentheses. When papers are distributed to
each student, for example, each paper is
handed out to each student. Similarly, each
factor is handed out and multiplied by each
number within the parentheses.
For example, 8 × 72 can be written as
8 × (70 + 2). This means that we distribute
and multiply the factor 8 by 70 and by 2.
1
Multi-Part
Lesson
Multi-Part
Lesson
The Distributive Property
PART
A
Main Idea
I will use basic facts
and patterns to
multiply multiples of
10, 100, and 1,000
mentally.
Vocabulary
V
product
factor
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, and decimals.
Also addresses GLE 0506.1.5.
B
PART
C
PART
Multiplication Patterns
A
Many water parks now offer surfing
rides. About 900 gallons of water
flow through these rides each
second.
B
C
D
E
Multiplication
Patterns
Vocabulary
product
factor
When two or more numbers are multiplied, the result is called
a product . The numbers that are multiplied are factors of the
product.
27 is the product
of 3 and 9.
3 × 9 = 27
Resources
Materials: multiplication flash cards, Math Song
Animation: When You Multiply
Hands-On Activity Tools and Resources (p. 26)
3 and 9 are factors of 27.
Leveled Worksheets
You can multiply some numbers mentally by using basic facts and
patterns. Look at the pattern below.
← basic fact
9 = 27
90 = 270
THINK 3 × 9 tens = 27 tens or 270
900 = 2,700
THINK 3 × 9 hundreds = 27 hundreds or 2,700
9,000 = 27,000 THINK 3 × 9 thousands = 27 thousands
Get ConnectED
GLE 0506.2.5 Develop fluency in solving multi-step
problems using whole numbers, fractions, mixed numbers,
and decimals. Also addresses GLE 0506.1.5.
or 27,000
1 INTRODUCE
Use Patterns to Multiply Mentally
Activity Choice 1: Hands-On
Use a pattern to find 6 × 800 mentally.
Step 1
A
Use basic facts and patterns to multiply multiples of 10,
100, and 1,000 mentally.
Do you notice a pattern?
×
×
×
×
The Distributive Property
Objective
In 1 second: 1 × 900 = 900 gallons
In 2 seconds: 2 × 900 = 1,800 gallons
In 3 seconds: 3 × 900 = 2,700 gallons
3
3
3
3
1
Write the basic fact.
Step 2 Continue the pattern.
• Have each student fold a sheet of lined paper to make
3 columns. Label the first column “Basic Fact 4 × 9”
and write these equations down the column:
4 × 9 = 36; 4 × 90 = 360; 4 × 900 = 3,600
6 × 8 = 48
6 × 80 = 480
6 × 800 = 4,800
The product of 6 and 800 is 4,800.
Lesson 1A The Distributive Property 61
061_0063_C02L01_103031.indd 61
2/25/10 5:07 PM
Building Math Vocabulary
• What pattern do you see? When you multiply by a
multiple of 10, there is 1 zero in the product. When you
multiply by a multiple of 100, there are 2 zeros.
• What do you think would happen if you multiply by
a multiple of 1,000? The product might have 3 zeros.
Write the lesson vocabulary words and their definitions on
the board.
Ask students to write the words and their definitions in their
Math Journals. Have them write a sample multiplication equation
and label each part with the correct term.
Visual Vocabulary Cards
Use Visual Vocabulary Cards to reinforce
the vocabulary introduced in this lesson
in English and Spanish. (The Define/
Example/Ask routine is printed on the
back of each card.)
• Have students label the second column “Basic
Fact 7 × 8” and write the following down the column:
7 × 8 = 56; 7 × 80 = 560; 7 × 800 = 5,600
Activity Choice 2: Critical Thinking
Ask students to discuss situations where they have seen
multiplication at school or home. Ask them to apply the
following questions to each situation.
• How are multiplication patterns helpful in solving
real-world problems?
• How can place value and multiplication patterns be
applied to real-world problems involving money?
ISBN: 978-0-02-101742-3
MHID: 0-02-101742-5
Copyright © by The McGraw-Hill
Companies, Inc.
All rights reserved.
MM'12_VVC_G5_cov_1
MM'12
VVC G5
10
01742-5.indd 1
12/3/09 2:48 PM
• Why is it important to be able to estimate and multiply
mentally in real-world situations?
Lesson 1A The Distributive Property
61
2 TEACH
When multiplying factors that are multiples of 10, you can find
the product mentally by using basic facts and then counting
zeros in the factors.
Scaffolding Questions
Write the basic facts 6 × 5 = 30, 2 × 9 = 18, and
4 × 7 = 28 on the board.
• How are the products of these basic facts the
same? Sample answer: They are two-digit numbers.
Count Zeros to Multiply Mentally
Find 40 × 7,000 mentally.
Step 2 Count the number of
zeros in each factor.
40 × 7,000
280,000
So, the product is 280,000.
weight per box
total weight = 50 × 60
basic fact: 5 × 6 = 30
indicates multi-step problem
Find
i d each product mentally. See Examples 1-3
1. 2 × 300 600
2. 8 × 40 320
3. 100 × 13 1,300
4. 3 × 9,000 27,000
5. 70 × 60 4,200
6. 500 × 70 35,000
7. 10 × 120 1,200
8. 800 × 500 400,000
9. Paulita reads an average of 20 pages each day. She has 6 days to
read 115 pages. Will she finish her reading in 6 days? Explain.
Yes; she can read 20 × 6 or 120 pages in 6 days.
E TALK MATH Explain how many zeros are in the product 50 times 500. 3; There
is 1 zero in 50 and 2 zeros in 500; 1 + 2 = 3.
62 Multiply Whole Numbers
10.
0061_0063_C02L01_101808.indd 62
AL
Alternate Teaching Strategy
If
COMMON ERROR!
Exercise 8 Students may count the zeros in the
factors and conclude that there will be the same
number of zeros in the product. Encourage them to
write the product of the basic multiplication fact and
then count the zeros in the factors.
number of boxes
Since there are 2 zeros in the factors, write 2 zeros to the right
of 30. So, 50 × 60 = 3,000. The boxes weigh 3,000 pounds.
IWB INTERACTIVE WHITEBOARD READY
!
SKATEBOARDS A truck is loaded with 50 boxes of
skateboards. Each box weighs 60 pounds. What is the total
weight of the boxes?
If a basic fact ends with
a zero, there is an
extra zero in the
product. In Example 3,
the first zero in 3,000
is from 5 × 6 = 30.
Find 50 × 5,000 mentally. 5 × 5 = 25. There are
4 zeros in the factors, so the product is 250,000.
TALK MATH Use the Talk Math Exercise to assess
student comprehension before assigning the practice
exercises.
students have trouble multiplying with multiples of
10, 100, and 1,000 . . .
Then
1
2
AL
use one of these reteach options:
Reteach Worksheet
Personal Tutor Have students use Personal Tutor to
reteach the concept.
IWB
3 Use Flash Cards Have them work with a partner to review
basic multiplication facts using flash cards. Have the partner
ask follow-up questions such as, “What is 4 × 60?” or
“What is 40 × 60?” Students can write the problems and
answers below the basic fact.
62
Multiply Whole Numbers
4 zeros
{
Step 3 Write the zeros to the right
of the product from Step 1.
Use a pattern to find 4 × 600 mentally.
4 × 6 = 24, 4 × 60 = 240, 4 × 600 = 2,400
E
3 zeros
1 zero + 3 zeros = 4 zeros
• Why is the number of zeros different? Sample
answer: The product of the basic fact 6 × 5 includes
a zero.
As a class, have students complete the Check What You
Know Exercises as you observe their work.
1 zero
{
• Compare the product of 6 × 50 to the products of
2 × 90 and 4 × 70. How many zeros are in these
products? Sample answer: There are 2 zeros in the
product of 6 × 50 and one zero in the products of
2 × 90 and 4 × 70.
One bale of hay weighs 50 pounds. There are
20 bales in the barn. What is the total weight of
the hay? 2 × 5 = 10 There are 2 zeros in the
factors. So, 20 × 50 = 1,000 pounds.
4 × 7 = 28
Step 1 Write the basic fact.
12/11/09 11:51
EXTRA
%
#E
4) C
!# TI
2 AC
PR
0
Begins on page EP2.
Find
Fi
d each
h product
d t mentally.
t ll See Examples
l 1-3
11. 7 × 50 350
12. 80 × 2 160
13. 10 × 19 190
14. 60 × 80 4,800
15. 200 × 6 1,200
16. 9 × 500 4,500
17. 440 × 10 4,400
19. 22 × 1,000
22,000
23. 900 × 900
810,000
20. 3,000 × 20
60,000
24. 400 × 500
200,000
21. 8,000 × 30
240,000
25. 600 × 7,000
4,200,000
18. 70 × 200
14,000
22. 8 × 4,000
32,000
26. 5,000 × 300
1,500,000
27. A group of friends bought 7 concert
tickets for $30 each. How much did
they spend on the tickets?
$210
29. Each box contains 200 pencils. The
school store has 15 boxes of
pencils. How many pencils does the
school store have? 3,000 pencils
28. At a soccer tournament, there were 10
teams. If each team had 20 players, how
many soccer players were there?
200 soccer players
30. Measurement Some glaciers in Alaska
move forward 100 meters per day. At this
rate, how far would these glaciers move
in 6 weeks? 4,200 m
Differentiate practice using these leveled assignments for
the exercises in Practice and Problem Solving.
Level
Assignment
AL
Approaching Level
11–18, 27–28, 31–33, 40
OL
On Level
12–25, 28–33, 40
BL
Beyond Level
12–32 even, 33–40
Have students discuss and
complete the Higher Order Thinking problems. Encourage
students to begin by writing basic multiplication facts for a
product of 24.
E
WRITE MATH Have students complete the Write
Math Exercise in their Math Journals. You may choose to
use this exercise as an optional formative assessment.
To protect themselves from extreme hot or cold temperatures,
American Alligators dig burrows in the mud.
31. Suppose a group of alligators digs 10 burrows
that are each 65 feet long. What is the total length
of the burrows? 650 ft
4 ASSESS
32. Suppose there are 20 alligators, each
ch
with 50 feet of burrows. What is the
e
total length of all the burrows? 1,000
00 ft
Formative Assessment
Write the following on the board: 50 × 600.
• How many zeros could be in the product if the
factors have a total of 3 zeros? Explain. 3 or 4
depending on if the product of the basic fact has a
zero or not.
33. OPEN ENDED Write three different pairs of factors that each
have a product of 240. Sample answers: 10 × 24, 20 × 12, 3 × 80
CHALLENGE Find each missing factor.
34. 5 × = 4,000 800
35. 60 × = 1,200 20
36. 20,000 = × 500 40
37. 3 × = 2,100 700
38. 1,600 = 4 × 400
39. 28,000 = × 700 40
40.
3 PRACTICE
E WRITE MATH Explain how using basic facts can help you find
10 × 20 × 30 × 40 mentally. Then explain how you would find the product.
See Answer Appendix.
• How would you work this problem? Multiply the
basic facts, 5 × 6 = 30, count the zeros in the factors
50 and 600 and place them to the right of 30.
• What is the product? 30,000
Lesson 1A The Distributive Property 63
Are students continuing to struggle
with multiplication patterns?
061_0063_C02L01_101808.indd 63
Write 5,000 × 20 on the board.
W
Ask students how they would fifind the product. Encourage them
to explain each step as they solve the problem. Multiply 5 × 2 =
10. Count the zeros in the factors and place them to the right of
10. The product is 100,000.
12/11/09 11:52 AM
During Small Group Instruction
If Yes
AL
AL
AL
Daily Transparencies
Differentiated Instruction Options 1
and 2 (p. 61c)
Strategic Intervention Guide
(p. T44–T45, T54–T55)
If No
OL
BL
OL
BL
Differentiated Instruction Options 2 (p. 61c)
Differentiated Instruction Options 1
and 2 (p. 61d)
Skills Practice Worksheet
Enrich Worksheet
Lesson 1A The Distributive Property
63
1
Multi-Part
Lesson
PART
The Distributive Property
A
B
C
D
Multi-Part
Lesson
E
1
PART
The Distributive Property
A
PART
B
Use Partial Products and
the Distributive Property
Objective
Main Idea
I will explore
multiplication with
regrouping using
models.
Materials
Explore multiplication with regrouping using models.
paper and pencil
B
C
Use Partial Products and
the Distributive Property
When you multiply a digit by the place value of another digit,
the result is a partial product.
Find 5 × 17.
One Way:
Resources
Materials: colored pencils, index cards, Math Song
Animation: Multiplication Rap
Area Model
10
Step 1
Explore Worksheet
Get ConnectED
Draw a model and
find the partial
products.
5
GLE 0506.2.5 Develop fluency in solving multi-step
problems using whole numbers, fractions, mixed numbers,
and decimals.
1 INTRODUCE
Step 2
Add the partial
products.
50
+ 35
85
Another Way:
5
5 × 10 = 50
+
7
5 × 7 = 35
Paper and Pencil
Step 1
Introduce the Concept
Multiply the ones and tens.
17
×5
5 × 7 ones = 35 ones
35
5 × 1 ten = 5 tens
50
Step 2 Add the partial products.
17
×5
35
+50
85
So, 5 × 17 = 85.
Have students draw an area model to represent 43.
• Have students represent the tens first by drawing a
rectangle to represent 40. Then have students represent
the ones by drawing a rectangle to represent 3.
+3
40
10
7
5 × 7 = 35
5 × 10 = 50
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, and decimals.
+
• Tell students to make sure that the sizes of the
rectangles represent the value of each place value.
64
Multiply Whole Numbers
• Have students shade and label each part of the model.
0064_0065_C02L01_103031.indd 64
• Next, draw the following models on the board.
30 +
6
30 +
30
+ 6
6
Building Math Vocabulary
• Which model would best represent 36? Explain.
Sample answer: the second model; The rectangles are
proportional to the values they represent.
64
Multiply Whole Numbers
Provide students with a stack of index cards labeled: 6, 4, 24, 5,
7, 35, and 3, 9, 27. Ask students to create three multiplication
number sentences using the cards. Then, ask them to make two
piles, one with the factors, and a second pile with the products.
Check their work by asking them to explain their responses.
2/26/10 12:28 P
2 TEACH
When you use partial products, you are also using a property
called the Distributive Property.
Activity 1 Have students look for similarities between the
area model strategy and the paper and pencil strategy.
Use the Distributive Property
Find
i d 7 × 56.
56
Step 1
Model 7 × 56.
Step 2
Think of 7 × 56
as
(7 × 50) + (7 × 6).
Step 3
7 × 56
= (7 × 50) + (7 × 6)
= 350 + 42
= 392
• Which step in the paper and pencil strategy is
asking for the same computation as Step 1 in the
area model strategy? Explain. Sample answer: Step 1;
This step of the paper and pencil strategy involves
finding partial products.
7
50
7
350
6
Activity 2 Tell students that the Distributive Property
strategy and the paper and pencil strategy are similar in
certain ways. Have students look for similarities between
the two strategies as you work through Activity 2.
7 ×6
7 × 50
50
7
+
+
6
About It
42
Assign the exercises in the Think About It section to
assess student comprehension of the concepts presented
in the Activities.
So, 7 × 56 = 392.
About It
1, 2. See margin.
1. How do area models show the partial products method?
3 PRACTICE
2. In Activity 2, why does the Distributive Property break 56 into
50 and 6?
Use Practice and Apply It Exercises to assess whether
students comprehend multiplication with regrouping using
models.
3. How would you use the Distributive Property to find 6 × 36?
6 × 36 = (6 × 30) + (6 × 6) = 180 + 36 = 216
and Apply It
For more practice of the concepts presented in this lesson,
see
Explore Worksheet.
Multiply. Use models if needed.
4. 4 × 16 64
5. 6 × 81 486
6. 7 × 29 203
7. Thirty-eight fish are in each aquarium. How many fish are
there in five aquariums? 190 fish
8.
E
4 ASSESS
WRITE MATH Explain why it is easier to think of
8 × 53 as (8 × 50) + (8 × 3) instead of as (8 × 49) + (8 × 4). Sample answer: When
using the Distributive Property, it is helpful to separate the 53 into factors that are easy to
multiply mentally. It is easier to find 8 × 50 than 8 × 49.
Lesson 1B The Distributive Property 65
064_0065_C02L01_103031.indd 65
2/25/10 5:07 PM
Additional Answers
1. Sample answer: The area models separate the factors into place values. Each
place value is multiplied by the other factor to find a part of the product.
2. Sample answer: It is easier to multiply 7 × 50 and 7 × 6 mentally than a
different pair of factors.
• Would you use grid paper to draw an area model
for 6 × 47? Explain. Sample answer: No; The area
model would be very long. It would be easier to draw
the area model freehand.
• What do you notice about the size of the rectangles
used to represent each place value of 56 in
Activity 2? Sample answer: The rectangle that
represents 50 is much larger than the rectangle that
represents 6.
From Concrete to Abstract Use Exercise 8 to determine
if students have made the transition from using models to
understand the concept of regrouping in multiplication to
understanding this concept at an abstract level.
Extending the Concept
BL
Explain how the area model strategy and the
Distributive Property are alike when finding 5 × 42.
Sample answer: Both strategies separate 42 into tens and
ones, the products of the tens and ones are found
separately, then they are added together.
Lesson 1B The Distributive Property
65
Multi-Part
Lesson
1
PART
PART
C
The Distributive Property
A
B
Multi-Part
Lesson
C
The Distributive
Property
1
The Distributive Property
PART
A
Main Idea
I will use the
Distributive Property
to multiply mentally.
Objective
Vocabulary
V
Use the Distributive Property to multiply mentally.
Distributive Property
Vocabulary
Distributive Property
Resources
Materials: colored pencils, grid paper
C
B
E
The Distributive Property
The table shows the costs for
activities at a fun center. How
much would it cost one person
to do both activities? $10
Activity
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, and decimals.
D
bumper boats
laser tag
Cost per
Person
$4
$6
How much would it cost 8 people to do both activities shown
above? There are two ways to find the answer.
Hands-On Activity Tools and Resources (p. 66)
One Way:
Leveled Worksheets
Multiply 8 by the cost for 1 person.
cost for 1 person
{
Get ConnectED
8 × (4 + 6) = 8 × 10 or $80
GLE 0506.2.5 Develop fluency in solving multi-step
problems using whole numbers, fractions, mixed numbers,
and decimals.
Another Way:
Find the cost of 8 bumper boat rides and
8 laser tag games. Then add.
cost of 8 boat rides cost of 8 games
Activity Choice 1: Hands-On
Using either method, the total cost for 8 people is $80. This
shows that 8 × (4 + 6) = (8 × 4) + (8 × 6). The Distributive
Property combines addition and multiplication.
• Have students shade a 3 × 10 rectangle on grid paper.
How many squares make up this rectangle? 30
• Then tell students to shade a 3 × 3 rectangle.
How many squares make up this rectangle? 9
Distributive Property
To multiply a sum by a number, multiply each addend by the
number. Then add.
• Next, have students shade a 3 × 13 rectangle.
How many squares make up this rectangle? 39
• Tell students that the Distributive Property shows how
the number of squares in one rectangle can be written
as the sum of the number of squares in two rectangles.
Activity Choice 2: Art
{
{
(8 × 4) + (8 × 6) = 32 + 48 or $80
1 INTRODUCE
3 × (5 + 2) = (3 × 5) + (3 × 2)
66
Multiply Whole Numbers
0066_0069_C02L01_103031.indd 66
• Give a piece of grid paper to each student. Tell students
to draw an area model of 4 × 17. Make sure students
just outline the area model and do not shade it.
• Write 4 × 17 = (4 × 10) + (4 × 7) on the board.
Shade the equation as shown.
• What section of the area model represents 4 × 10?
the section on the left side
• Have students shade the section on the left side of the
area model green.
• What section of the area model represents 4 × 7?
the section on the right side
• Have students shade the section on the right side of the
model blue.
66
Multiply Whole Numbers
Building Math Vocabulary
Write the vocabulary word and its definition on the board.
Have students write about a real-world situation in their Math
Journals in which multiplication of a two-digit number by a
one-digit number is needed. Have student volunteers share their
examples with the class.
2/25/10 5:06
2 TEACH
Use the Distributive Property
R
Rewrite 7 × (20 + 6) using the Distributive Property. Then
evaluate.
e
7 × (20 + 6) = (7 × 20) + (7 × 6) Distributive Property
= 140 + 42
THINK 7 × 20 = 140 and
7 × 6 = 42
= 182
Add 140 and 42 mentally.
M
Multiply Mentally
MONEY For a field trip, 42 students each paid $3 for
transportation. Use mental math and the Distributive
Property to find how much money was collected.
40
120
3
The numbers 120 and
6 are partial products.
3 × 42 = 3 × (40 + 2)
Distributive Property
Multiply.
= 126
Add.
• In what order will the operations on the right side
be performed? multiply, then add
• Explain the Distributive Property in your own
words. Sample answer: To multiply a sum by a
number, multiply each addend of the sum by the
number outside of the parentheses and then add the
products.
Write 42 as 40 + 2.
= 120 + 6
Write the following equation on the board:
9 × (3 + 5) = (9 × 3) + (9 × 5)
• In what order will the operations on the left side be
performed? add, then multiply
• What basic multiplication fact does this
represent? 9 × 8
2
6
= (3 × 40) + (3 × 2)
Scaffolding Questions
So, $126 was collected for the field trip.
Rewrite 7 × (60 + 4) using the Distributive
Property. Then evaluate. (7 × 60) + (7 × 4); 448
Rewrite each expression using the Distributive Property.
Property Then
evaluate. See Example 1
1. 5 × (10 + 8)
(5 × 10) + (5 × 8); 90
2. 2 × (20 + 1)
(2 × 20) + (2 × 1); 42
Suppose it costs students $4 to buy a movie
ticket and $5 to buy food. What is the cost for
25 students to attend the movie and buy food?
25 × ($4 + $5) = 25 × $9 = $225
3. 4 × (10 + 5)
(4 × 10) + (4 × 5); 60
Find each product mentally using the Distributive Property. Show the
steps that you used. See Examples 1, 2 4–9. See Answer Appendix for sample steps.
4. 6 × 13 78
5. 3 × 52 156
6. 5 × 26 130
7. 4 × 69 276
8. 2 × 49 98
9. 7 × 23 161
IWB INTERACTIVE WHITEBOARD READY
!
10. Measurement A horse is 17 hands tall. If 1 hand
equals 4 inches, how tall is the horse in inches? 68 in.
11.
E
TALK MATH Explain how to use the Distributive
Property to find a product mentally.
See Answer Appendix.
Lesson 1C The Distributive Property 67
066_0069_C02L01_101808.indd 67
COMMON ERROR!
Exercises 1–3, 12–17 Make sure that students write
the correct value for each tens place when using the
Distributive Property to solve these exercises. For
example, students should write 4 × 37 = (4 × 30)
+ (4 × 7) instead of 4 × 37 = (4 × 3) + (4 × 7).
10/27/09 10:26 AM
ELL
Extending Vocabulary The word distributive has as the base word
distribute. Help English Learners discuss how these words are connected.
Lesson 1C The Distributive Property
67
EXTRA
%
#E
4) C
!# TI
2 AC
0R
P
Begins on page EP2.
As a class, have students complete the Check What You
Know Exercises as you observe their work.
R
Rewrite
it each
h expression
i
using
i th
the Di
Distributive
t ib ti P
Property.
t
Then evaluate. See Example 1
E
12. 7 × (10 + 3)
(7 × 10) + (7 × 3); 91
15. 4 × (20 + 2)
(4 × 20) + (4 × 2); 88
TALK MATH Use the Talk Math Exercise to assess
student comprehension before assigning the practice
exercises.
Alternate Teaching Strategy
AL
If
students have trouble using the
Distributive Property to make
multiplication easier…
Then
1
2
13. 2 × (50 + 3)
(2 × 50) + (2 × 3); 106
16. 2 × (30 + 1)
(2 × 30) + (2 × 1); 62
Find each product mentally using the Distributive Property.
Show the steps that you used. See Examples 1, 2 18–22. See margin for sample steps.
18. 2 × 38 76
19. 4 × 61 244
22. 25 × 6 150
23. 52 × 3 156
23–28. See Answer Appendix.
26. Mr. Collins is buying 5 train tickets
for $36 each. What is the total cost
of the tickets? Show your steps. $180
use this reteach option:
AL
Reteach Worksheet
Virtual Manipulatives Use the virtual
grid paper to reteach the concept.
IWB
3 Use a Formula Have students write the
algebraic form of the Distributive Property,
a × (b + c) = (a × b) + (a × c), across the
top of their paper. Have them match the
numbers in each exercise with the letters and
then solve.
3 PRACTICE
Differentiate practice using these leveled assignments for
the exercises in Practice and Problem Solving.
Level
Assignment
AL
Approaching Level
13–29 odd, 30, 32–40
OL
On Level
12–30 even, 32–40
BL
Beyond Level
12–30 even, 31–40
14. 3 × (10 + 4)
(3 × 10) + (3 × 4); 42
17. 6 × (20 + 4)
(6 × 20) + (6 × 4); 144
28. In each bag, there are 3 blueberry
bagels and 3 raisin bagels. If you have
35 bags of bagels, how many bagels
do you have? Show your steps. 210
20. 3 × 14 42
21. 5 × 74 370
24. 2 × 31 62
25. 3 × 63 189
27. Measurement Melanie runs
23 miles each week. Use the
Distributive Property to find how
many miles she runs in 9 weeks.
Show your steps. 207 mi
29. Admission to a theme park is $28
and lunch costs $9. Use the Distributive
Property to find the cost of 4 tickets
and 4 lunches. Show your steps.
4 × ($28 + $9) = 4($37) or $148
30. FIND THE ERROR Dylan is using the Distributive Property
to simplify 6 × (9 + 4). Find his mistake and correct it.
See margin.
6×9+4
31. CHALLENGE The Distributive Property also combines subtraction
and multiplication. For example, 3 × (5 - 2) = (3 × 5) - (3 × 2).
Demonstrate how you could use the Distributive Property and
mental math to find 5 × 198. See margin.
32.
E WRITE MATH Use the Distributive Property to evaluate 8 × 62.
Check your work using pencil and paper. Which method is easier?
See margin.
68
Multiply Whole Numbers
0066_0069_C02L01_103031.indd 68
Have students discuss and
complete the Higher Order Thinking problems. Encourage
them to reread the Key Concept about the Distributive
Property and apply it when solving these problems.
E
WRITE MATH Have students complete the Write
Math Exercise in their Math Journals. You may choose to
use this exercise as an optional formative assessment.
Homework Practice Worksheet
Problem-Solving Practice Worksheet
3/9/10 10:13
Additional Answers
18. 2 × 38 = 2 × (30 + 8)
= (2 × 30) + (2 × 8)
= 60 + 16
= 76
19. 4 × 61 = 4 × (60 + 1)
= (4 × 60) + (4 × 1)
= 240 + 4
= 244
20. 3 × 14 = 3 × (10 + 4)
= (3 × 10) + (3 × 4)
= 30 + 12
= 42
21. 5 × 74 = 5 × (70 + 4)
= (5 × 70) + (5 × 4)
= 350 + 20
= 370
22. 25 × 6 = 6 × (20 + 5)
= (6 × 20) + (6 × 5)
= 120 + 30
= 150
30. Sample answer: Dylan multiplied 6 by the first addend, 9, but not the second
addend, 4. He should have simplified it to (6 × 9) + (6 × 4).
68
Multiply Whole Numbers
4 ASSESS
Test Practice
33. The table shows the number of hours
each week that Taran and Amelia
volunteer. Which expression can be
used to find the total number of
hours they volunteer in 4 weeks? B
Student
Amelia
Taran
35. When you multiply two multiples of
10, which is a true statement about
the product? D
Formative Assessment
Write the problem 9 × 32 on the board.
• How could you use the Distributive Property to
mentally find this product? Sample answer: think of
32 as 30 + 2; 9 × (30 + 2) = (9 × 30) + (9 × 2) =
270 + 18 = 288
A. It always has the same number
of zeros as the factors combined.
B. It always has one less zero than
the factors combined.
Number of Hours
2
1
• How did you decide which addends to use when
replacing 32? Sample answer: Use addends that are
easy to multiply mentally.
C. It never has the same number of
zeros as the factors combined.
A. 4 × 2 × 1
B. 4 × (2 + 1)
D. It always has the same number
of zeros or more zeros as the
factors combined.
C. 4 + 2 + 1
D. 4 × (2 - 1)
34. Mark wants to solve the equation
below.
7 × 28 = Which equation will help him solve
the problem? H
F. (7 + 20) × (7 + 8) = Are students continuing to struggle
with using the Distributive Property to
make multiplication easier?
36. Greg used an area model to
show 6 × 37.
7
During Small Group Instruction
6
(6 ×
)
+
(6 × 7)
If Yes
AL
Which factor will help Greg find
the product? H
G. (7 × 20) × (7 × 8) = F. 3
H. (7 × 20) + (7 × 8) = G. 6
I. (7 + 20) + (7 + 8) = H. 30
AL
If No
OL
OL
BL
Daily Transparencies
Strategic Intervention Guide
(pp. T48–T49)
Differentiated Instruction Option 1
Skills Practice Worksheet
Enrich Worksheet
(p. 61c)
I. 35
Write 3 × 17 on the
W
board. Have students use the D
Distributive Property to
findd the
h product.
d
Find each product mentally. (Lesson 1A)
37. 40 × 20 800
38. 7 × 3,000 21,000
39. 1,500 × 10 15,000
40. Mrs. Wheeler has 20 students in her class. Each
student paid $30 for activity fees. How much did
Mrs. Wheeler collect for activity fees? (Lesson 1A) $600
Lesson 1C The Distributive Property 69
066_0069_C02L01_103031.indd 69
Additional Answers
31. Sample answer:
5 × 198 = 5 × (200 - 2)
= (5 × 200) - (5 × 2)
= 1,000 - 10
= 990
2/25/10 5:06 PM
Write 198 as 200 - 2.
Distributive Property
Find 5 × 200 and 5 × 2 mentally.
Find 1,000 - 10 mentally.
Multi-Part Lesson 1 How do number patterns,
such as multiplying with multiples of 10, help you
to solve multiplication problems mentally? Sample
answer: If you know the product of the basic fact,
you can determine how many zeros to add to the
end of the product and solve the problem mentally.
32. Sample answer: Use the Distributive Property:
8 × 62 = 8 × (60 + 2)
= (8 × 60) + (8 × 2)
= 480 + 16
= 496
Use pencil and paper:
62
× 8
−−−
16
+ 480
−−−
496
Using the Distributive Property is easier, because you can solve the problem mentally.
Lesson 1C The Distributive Property
69
Multi-Part
Lesson
2
Multiply by One-Digit Numbers
Planner
PART
A Estimate Products
B
Multiply by One-Digit Numbers
C
Problem-Solving Strategy:
PART
E
Essential Question
How can number patterns be helpful in
estimating products? Sample answer: After
factors have been rounded to multiples of 10,
the same mental strategies can be applied as
when multiplying with zeroes.
Focus on Math Background
Estimate Products
Title / Objective
Draw a Picture
PART
A
Standards
B
Multiply by One-Digit
Numbers (pp. 74–77)
(pp. 70–73)
Estimate products by using rounding
and compatible numbers.
Multiply up to a three-digit number by
a one-digit number.
GLE 0506.1.2
GLE 0506.2.5
calculators, number lines, index cards
WorkMat 4: Place-Value Chart
money, base-ten blocks
Vocabulary
Materials/
Manipulatives
Resources
Get ConnecttED
✔ 0506.1.9
Students at this level should know their basic
multiplication facts and, therefore, be able to
multiply two single-digit numbers. They also
know how to multiply by multiples of powers
of ten. Putting those two ideas together
allows students to begin to multiply two-digit
numbers by one-digit numbers and then
advance to multiplying three-digit numbers
by one-digit numbers.
Get ConnecttED
Leveled Worksheets
Leveled Worksheets
Daily Transparencies
Lesson Animations
Problem of the Day
Daily Transparencies
Self-Check Quiz
Problem of the Day
Personal Tutor
Self-Check Quiz
VVirtual Manipulatives
Personal Tutor
eGames: Robo Works
VVirtual Manipulatives
Hands-On Activity Tools and Resources
eGames: Number Voyage
Graphic Novel Animation
Hands-On Activity Tools and Resources
Blended Approach
IWB
All digital assets are Interactive
Whiteboard ready.
70a Multiply Whole Numbers
Suggested Pacing
Multi-Part Lessons
1
PART
A
Days
1
2
B
C
1
(10 Days)
3
Assess
A
B
C
A
B
C
1
1
1
1
1
1
SGR PCT
1
1
Multiply by One-Digit Numbers
PART
Notes
C
Problem-Solving Strategy:
Draw a Picture
Title / Objective
(pp. 78–79)
Solve problems by drawing a picture.
Standards
GLE 0506.1.2
Vocabulary
two-color counters, rulers
Get ConnecttED
Leveled Worksheets
Materials/
Manipulatives
Resources
✔ 0506.1.9
Daily Transparencies
Problem of the Day
Personal Tutor
RWPS: Early American Settlements
Hands-On Activity Tools and Resources
Blended Approach
Mid-Chapter Check (p. 80)
Multiply by One-Digit Numbers
70b
Differentiated Instruction
Approaching Level
On Level
AL
Option 1
Use with 2A
OL
Option 1
Use with 2C
Materials: index cards, markers
Materials: index cards
• Give student pairs ten index cards and have them write each
of the following numbers on one card: 0, 10, 20, 30, 40, 50,
60, 70, 80, and 90.
• Have students draw a
picture on an index card
that could be used to find
a solution to a word problem.
• Write a two-digit by two-digit multiplication problem on the
board, such as 32 × 49.
• Have each pair find the two cards that would be the correct
estimates for the factors in this problem. Ask them to hold up
the cards. 30 and 50
• Have pairs work together to find the estimated product of the
multiplication problem. 1,500
• Repeat with other multiplication problems.
Option 2
• Ask students to label the length
of each line drawn and mark
the placement of objects.
Materials: multiplication table, pencil, paper
• Post a large multiplication table in the classroom for students’
reference.
is 8 ft.
110 ft.
• Students will then write a word problem that can be solved
using the drawing.
Option 2
Use after 2B
playground
6 ft between tables and edges
of playground
each table
5 ft between tables
Use after 2B
Hands-On Activity
Materials: paper and pencil
• Students struggling with multiplication of multi-digit numbers
by a one-digit number with regrouping may benefit from
using the lattice method.
• For 376 × 5, create the “kite” figure shown below.
• Have students work in pairs. They should alternate turns,
having one student create a multiplication problem, and the
other solving the problem.
3
7
6
5
• Be certain that students understand how to use the chart to
determine factors and products.
×
1
2
3
4
5
1
1
2
3
4
5
2
2
4
6
8
10
3
3
6
9
12
15
4
4
8
12
16
20
5
5
10
15
20
25
• Then, multiply each digit in 376 by 5. Write the answers in the
kite as shown.
3
1
7
3
5
6
3
5
0
5
1
8
8
0
In the example above, students would write, “4 × 3 = 12.” The
factors are 4 and 3. The product is 12.
• Finally, add the numbers along each diagonal to find the
product of 376 and 5.
Other Options
Other Options
TE
Learning Station Card 9
Get ConnectED
Personal Tutor, Lesson Animations,
Virtual Manipulatives
70c Multiply Whole Numbers
TE
Learning Station Card 9
Get ConnectED
Personal Tutor, Lesson Animations,
Virtual Manipulatives
Multiply by One-Digit Numbers
Beyond Level
English Language Learners
BL
Option 1
Use with 2A
Materials: number cubes, pencil, paper
ELL
This strategy helps English Learners learn language for estimating
products.
• Have students generate two- and three-digit factors for several
multiplication problems by rolling a number cube. Have them
write the multiplication problems in a list.
Find Core Vocabulary and Common Use Verbs in the online
EL strategies to help students grasp the math skills; use
Language Alerts at point of use in the Teacher Edition.
• Tell students to write rounding directions beside each
problem. The directions should be one or two words telling
which place each factor should be rounded to.
Beginning
Word Meaning Introduce digits and rounding.
182
× 27
180
× 30
5,400
76
×5
80
×5
400
• Write zero to nine on the board. Point to one of the digits.
Say, This is a digit. Have students repeat. Write digit on the
board. Digits make numbers. Write 229 and ask, How many
digits in this number? Ask, Is 15 a digit? Say, No, only 0 to 9
can be digits.
tens
tens
greatest
factor
Option 2
• Write 214 on the board and ask, Which number is closer, 200
or 300? Tell students that increasing or decreasing a number
to the nearest 10 or 100 is rounding. Say, round, and have
students repeat. Have them use a spinner to create three-digit
numbers and then round those numbers.
Use after 2B
Materials: paper, pencils
• Give students this problem:
• Since the number 0 cannot be
used in the greatest place, the
answer is 18 three-digit numbers.
AL
How many different
three-digit numbers
can you make using
0, 1, 2, and 3?
102, 103, 120, 130, 123,
132, 201, 203, 210, 230,
213, 231, 301, 302, 310,
320, 321, 312
Intermediate
Activate Prior Knowledge Connect known idea of a “best
guess” to estimating.
OL
• Show students a box of paper clips and ask, How many paper
clips are there? This is an estimate. Say estimate, and write it
on the board.
• Write 196 × 9 on the board. Have students find the answer.
Have them estimate the answer. Ask students, what would
happen if you changed 196 to 200. Ask, What is the product?
• Tell students 196 × 9 is 1,764. Ask, Was 1,800 a good
estimate?
Other Options
TE
Learning Station Card 9
Get ConnectED
Lesson Animations
Advanced
Act It Out Use language for rounding and estimating.
BL
• Have partners practice language related to rounding and
estimating. Model language as necessary.
• Student 1: Estimate 232 times 8. Student 2: I estimate that
232 times 8 is 1,600.
Extend
Provide a selection of books. Without opening the books, have
students write the title of each book and a page estimate. Then
have them write the actual number of pages in each book and
round that number to the nearest 100.
Multiply by One-Digit Numbers
70d
Multi-Part
Lesson
2
PART
PART
A
Multiply by One-Digit Numbers
A
B
Multi-Part
Lesson
C
Estimate Products
2
PART
Multiply by One-Digit Numbers
A
Main Idea
I will estimate products
by using rounding and
compatible numbers.
Objective
Estimate products by using rounding and compatible
numbers.
Resources
Materials: calculators, number lines, index cards
B
C
Estimate Products
When a problem asks about how many, you can use
estimation, rounding, and compatible numbers.
Get ConnectED
GLE 0506.1.2
Apply and adapt a variety
of appropriate strategies to
problem solving, including
estimation, and reasonableness
of the solution.
Hands-On Activity Tools and Resources (p. 88)
Leveled Worksheets
ANIMALS About 13 harp seal
pups live in each square mile
of Greenland. About how many
pups live in a 92-square-mile
area?
Estimate the product of 92
and 13.
Get ConnectED
One Way:
THINK It is easier to compute 92 × 10 than 90 × 13.
GLE 0506.1.2 Apply and adapt a variety of
appropriate strategies to problem solving, including
estimation, and reasonableness of the solution.
92 → 92
×
13 → ×____
10 Round 13 to the nearest ten.
____
920
1 INTRODUCE
Round both factors.
92 → 90 Round 92 to the nearest ten.
×
13 → ×____
10 Round 13 to the nearest ten.
____
• Write the following factors and estimated products on
the board, one at a time: 6 × 87 ≈ 540;
9 × 41 ≈ 360; 58 × 75 ≈ 4,800; 24 × 43 ≈ 800;
84 × 26 ≈ 2,400.
900
Find 90 × 10 mentally.
Another Way:
• After writing each estimated product, have students
signal thumbs up for estimates that they think are
higher than the actual product, thumbs down for lower,
and no thumbs showing for undecided. Record the
results.
• Have students use a calculator to find the actual
products. Compare with the thumbs up and down on
the board.
Find 92 × 10 mentally.
Another Way:
Activity Choice 1: Hands-On
• How do you know if an estimate is higher or lower
than the actual product? If you round numbers up
and then multiply, the estimate will be higher. If you
round both numbers down, the estimate will be lower.
Round one factor.
Use compatible numbers.
92 → 100
×
13 → _____
× 13 100 and 13 are compatible numbers because
____
1,300
they are easy to multiply mentally.
So, 92 × 13 is about 900, 920, or 1,300. There are between
900 and 1,300 pups in a 92-square-mile area.
70
Multiply Whole Numbers
0070_0073_C02L02_103031.indd 70
Activity Choice 2: Story Telling
• Have students write a story that uses both estimated
products and exact products. For example, students could
write about estimating how much money a teacher spent
for a class set of school supplies. They should compare
the estimate with the actual amount spent.
• Allow students to share their stories with the class.
• Have listeners identify which numbers are estimates
and which are exact values. Encourage students to
“trick” listeners by using exact answers that might
appear to be estimates, such as 500 or 1,000.
70
Multiply Whole Numbers
Building Math Vocabulary
Write the vocabulary word product and its definition on the
board.
Ask students to make a list of where, and in what context they
have heard the word used. Encourage students to share
their lists.
2/25/10 5:08
2 TEACH
SCHOOL Mountain View Elementary
is sending 21 boxes of magazines
to a school in Paraguay. There
are 154 magazines in each box.
About how many magazines
are they sending?
Scaffolding Questions
Write the expression 44 × 37 on the board.
• If the estimated product is 1,200, how were the
numbers rounded? Explain. Both were rounded down
because 40 × 30 = 1,200.
Estimate the product of 21 and 154.
One Way:
Round each factor to its greatest place value.
154 → 200
× 21 → × 20
4,000
Another Way:
154 →
• What would be the estimated product if the
numbers were both rounded up? Explain.
2,000; 50 × 40 = 2,000
150
× 21 → × 20
3,000
• What could you do to get a more accurate estimate
for the product? What would be the estimated
product? Round each number to the nearest ten;
40 × 40 = 1,600
Round 154 to the nearest hundred.
Round 21 to the nearest ten.
Find 200 × 20 mentally.
• Tell students that they will be estimating products in
several different ways.
Round each factor to the nearest ten.
Round 154 to the nearest ten.
Round 21 to the nearest ten.
Find 150 × 20 mentally.
Estimate 67 × 32. Round each number to the
nearest ten. 70 × 30 = 2,100; so 67 × 32 is
about 2,100.
So, 154 × 21 is about 3,000 or 4,000. They are sending
about 3,000 or 4,000 magazines.
You can also use compatible numbers when a factor is close to
25 or 50.
Compatible Numbers
s
Multiplication problem
ten
writ
can be
horizontally and
vertically.
BIKING Tyson makes bike ramps. He can make 26 bike
ramps in a week. About how many can he make in eight
weeks?
Jessica makes beaded necklaces. She uses
53 beads for each necklace. About how many
beads will she use to make necklaces for 6 of
her friends? Sample answer: 6 × 50 = 300;
300 beads
8 × 26 → 8 × 25 Replace 26 with 25.
8 × 25 = 200
THINK Eight quarters are the same as
$2.00. So, 8 × 25 is 200.
So, Tyson can make about 200 bike ramps in eight weeks.
Lesson 2A Multiply by One-Digit Numbers
070_0073_C02L02_101808.indd 71
The students at DeSales Middle School collected
cans for recycling. In one week, each of the
24 classes collected 189 cans. About how many
cans did they collect that week? Sample answer:
24 × 200 = 4,800, and 20 × 200 = 4,000. They
collected between 4,000 and 4,800 cans.
71
IWB INTERACTIVE WHITEBOARD READY
10/27/09 11:18 AM
ELL
Spanish Cognates The word estimate is closely related to two Spanish
words: estimar, which is a verb, and estimación, which is a noun.
Lesson 2A Multiply by One-Digit Numbers
71
indicates multi-step problem
1–13. Sample answers are given.
As a class, have students complete the Check What You
Know Exercises as you observe their work.
Estimate by rounding or using compatible numbers.
numbers Show
your work. See Examples 1-3
4. 131
2.
3. 218
32
42
× 6
× 16
× 18
× 29
_____
_____
_____
_____
40 × 20 = 800
30 × 20 = 600
200 × 6 = 1,200
130 × 30 = 3,900
5. 61 × 68
6. 98 × 83
7. 392 × 46
8. 450 × 21
60 × 70 = 4,200
100 × 80 = 8,000
400 × 50 = 20,000
500 × 20 = 10,000
9. 4 × 24
10. 6 × 48
11. 12 × 27
4 × 25 = 100
6 × 50 = 300
12 × 25 = 300
TALK MATH Show two different
12. Measurement If a heart rate is 72
13. E
beats per minute, about how many
ways you could estimate 312 × 18.
times does it beat in an hour? Show
300 × 20 = 6,000; 310 × 20 = 6,200
how you estimated.
70 × 60 = 4,200 times
1.
E
TALK MATH Use the Talk Math Exercise to assess
student comprehension before assigning the practice
exercises.
AL
Alternate Teaching Strategy
If
students have trouble estimating
products by rounding …
EXTRA
Then
1
2
use one of these reteach options:
AL
Begins on page EP2.
Estimate by rounding or using compatible numbers. Show
your work. See Examples 1-3 14–35. Sample answers are given.
Reteach Worksheet
Virtual Manipulatives Use the virtual
base-ten blocks to reteach the concept.
IWB
3 Use Number Lines Have students use number
lines to help them round to the nearest ten or
hundred. Encourage students to rewrite the
multiplication problem after rounding the
factors. Then multiply, keeping track of the zeros
as they multiply multiples of tens and hundreds.
14.
6
× 33
_____
6 × 30 = 180
18.
42
× 89
_____
40 × 90 = 3,600
22. 88 × 31
90 × 30 = 2,700
15.
26. 79 × 56
80 × 60 = 4,800
27. 33 × 84
30 × 80 = 2,400
16.
106
× 52
_____
100 × 50 = 5,000
20. 508
× 27
_____
500 × 30 = 15,000
24. 17 × 939
20 × 900 = 18,000
7
× 68
_____
7 × 70 = 490
19.
76
× 78
_____
80 × 80 = 6,400
23. 64 × 91
60 × 90 = 5,400
30. 8 × 51
8 × 50 = 400
28. 729 × 42
700 × 40 = 28,000
31. 8 × 24
8 × 25 = 200
17. 127
×8
____
100 × 8 = 800
21.
19
× 238
______
20 × 200 = 4,000
25. 58 × 118
60 × 100 = 6,000
29. 609 × 44
600 × 40 = 24,000
32. 16 × 26
16 × 25 = 400
33. For a school assembly, students sit in chairs that are arranged in
53 rows. There are 12 chairs in each row. About how many students
can be seated? Show your work. 12 × 50 = 600
3 PRACTICE
Differentiate practice using these leveled assignments for
the exercises in Practice and Problem Solving.
Level
Assignment
AL
Approaching Level
14–32 even, 33, 35–37, 40,
42, 43
OL
On Level
14–40 even, 42, 43
BL
Beyond Level
14–38 even, 40–43
34. Measurement The table shows the number of
pounds of apples that were harvested each day.
Estimate how many pounds of apples were
harvested. Show your work.
2,100 lbs; (2 × 500) + 300 + (2 × 400)
35. In one week, a campground rented 18 cabins at
$225 each. About how much did they collect in
rent? Show how you estimated. 20 × $200 = $4,000
72
Multiply Whole Numbers
0070_0073_C02L02_101808.indd 72
Have students discuss and
complete the Higher Order Thinking problems. Encourage
students to work backward by choosing two multiples of
10 that are factors of 600 then choosing numbers that
would round to those multiples.
E
WRITE MATH Have students complete the Write
Math Exercise in their Math Journals. You may choose to
use this as an optional formative assessment.
72
%
#E
4) C
!# TI
2 AC
0R
P
Multiply Whole Numbers
!
COMMON ERROR!
Exercises 18, 19, 22, 23, 26, 27 Students may have trouble
choosing compatible numbers. Suggest students place the
numbers on a number line to find the closest multiple of 10.
11/5/09 5:51
4 ASSESS
Science Sound travels through
different materials at different speeds.
For example, the graph shows that in
1 second, sound travels 5,971 meters
through stone. However, it travels only
346 meters through air in 1 second.
36–39. Sample answers are given.
Formative Assessment
• What are ways to estimate the product of
436 × 24? round to greatest place value:
400 × 20 = 8,000; round to the tens place:
440 × 20 = 8,800
• Which is the more accurate estimation? Explain.
440 × 20; 440 is closer to 436 than 400
For Exercises 36–39, estimate to find
the distance that sound travels through
each material in each given time.
36. air, 20 seconds 350 × 20 = 7,000 m
Are students continuing to struggle
with estimating by rounding and the
clustering strategy?
37. aluminum, 12 seconds
5,000 × 10 = 50,000 m
38. water, 3 seconds 1,500 × 3 = 4,500 m
39. Estimate how much farther sound travels through stone
in 17 seconds than through aluminum in the same time.
During Small Group Instruction
(6,000 × 20) - (5,000
× 20) = 20,000 m
If Yes
AL
AL
If No
BL
OL
40. OPEN ENDED Use the digits 1, 3, 5, and 7 to create two whole
numbers whose product is estimated to be about 600. Sample answer: 35 × 17 = 595
BL
Daily Transparencies
Differentiated Instruction Option 1 (p. 70c)
Differentiated Instruction Option 1 (p. 70d)
Skills Practice Worksheet
Enrich Worksheet
41. CHALLENGE Without calculating, which of the following methods
gives a more accurate answer when estimating 42 × 13? Explain. See margin.
a. increase both factors
b. decrease both factors
42. FIND THE ERROR Rico is estimating 139 × 18.
Find his mistake and correct it.
Sample answer: Rico rounded
100 × 10 = 1,000
both factors down. The factor
18 should be rounded up to 20.
139 × 18 ≈ 140 × 20 = 2,800.
43.
070_0073_C02L02_101808.indd 73
E
W 276 × 14 on the board. Have
Write
students copy the problem on an index
card and show their work as they estimate. Sample
answer: 300 × 10 = 3,000
WRITE MATH Write a real-world problem in which an exact
answer is not needed. See margin.
Lesson 2A Multiply by One-Digit Numbers
73
11/6/09 12:48 PM
Additional Answers
41. Answer b. round both factors down; Sample
answer: 42 is closer to 40 than 50 and 13 is closer to
10 than 20.
43. Sample answer: There are 10 people in a group at a
restaurant and their dinners cost $12.95 each. To
estimate how much money is needed to pay the bill,
a good estimate would be 10 × 13 = $130.
Lesson 2A Multiply by One-Digit Numbers
73
Multi-Part
Lesson
2
PART
PART
B
Multiply by One-Digit Numbers
B
A
Multi-Part
Lesson
C
Multiply by
One-Digit Numbers
2
PART
Multiply by One-Digit Numbers
A
Main Idea
I will multiply up to a
three-digit number by a
one-digit number.
Objective
Get ConnectED
Multiply up to a three-digit number by a one-digit number.
Resources
Materials: WorkMat 4: Place-Value Chart
Manipulatives: money, base-ten blocks
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, and decimals.
Also addresses GLE 0506.1.7.
B
C
Multiply by One-Digit
Numbers
Grace and her three friends
each paid $38 for an admission
ticket to an amusement
park. The total paid can be
found by multiplying 4 and 38.
You have used an area model to multiply numbers like
4 and 38.
+
30
Hands-On Activity Tools and Resources
(pp. 67, 90–92, 120–121)
120
4
8
32
Leveled Worksheets
So, 4 × $38 = 120 + 32 or $152.
Get ConnectED
You can also use an area model to multiply expressions with
greater numbers.
GLE 0506.2.5 Develop fluency in solving multi-step
problems using whole numbers, fractions, mixed numbers,
and decimals. Also addresses GLE 0506.1.7.
Use an area model to find 5 × 317.
1 INTRODUCE
Step 1 Draw a model and find the partial products.
300
Activity Choice 1: Hands-On
5
• Use WorkMat 4: Place-Value Chart and label it “Dollar,”
“Dime,” and “Penny.” Place 1 dollar, 2 dimes, and
3 pennies on the workmat.
1,500
1,500
50
+
35
−−−−
1,585
• Tell students that you are going to double or multiply
by 2, the amount of money. Place coins on the chart as
you work the problem.
Multiply
Multiply
Multiply
Add the
74
35
Multiply Whole Numbers
• Encourage students to use a Math Journal to keep track
of various problem-solving exercises.
• Each problem should be worked on its own page.
Building Math Vocabulary
Write the vocabulary words factor and product and their
definitions on the board.
Ask students to draw a table with columns labeled “Factors” and
“Products.” Have them write several basic fact multiplication
expressions in the Factors column with the products written in
the Products column.
Multiply Whole Numbers
7
So, 5 × 317 = 1,585.
Activity Choice 2: Writing
74
50
+
the hundreds. 5 × 300
the tens. 5 × 10
the ones. 5 × 7
partial products.
0074_0077_C02L02_103031.indd 74
• Have students divide the pages into four sections: the
first section for writing key words, the second section
for completing mathematical operations, the third
section for drawing a picture, and the fourth section for
writing the solution and an explanation of the solution.
10
Step 2 Add the partial products.
• What is the value in dollars and cents? in just cents?
$1.23; 123 cents
• Write 2 × 123 = (2 × 100) + (2 × 20) + (2 × 3).
How many dollars, dimes, and pennies are there
now? What is the total value in cents? 2 dollars,
4 dimes, and 6 pennies; 246 cents
+
2/25/10 5:06
Two-Digit and
Three-Digit Numbers
SPELLING Karen was
preparing for a spelling
bee. She studied about
28 pages of the dictionary
every day. How many
pages did Karen study
in one week?
Scaffolding Questions
Write 5 × 136 on the board.
• Estimate the product. Sample answer: 5 × 140 = 700
• How could the Distributive Property be used to
solve this problem? 5 × 136 = (5 × 100) +
(5 × 30) + (5 × 6) = 500 + 150 + 30 = 680
• How many ones, tens, and hundreds does 5 × 136
have before regrouping? 30 ones, 15 tens, and
5 hundreds
Multiply 28 by 7, the number of days in one week.
Estimate 30
× 7 = 210
Step 1
Multiply the ones.
• Write the problem in vertical form. Write 30, 150, and
500 below the problem and add.
Step 2
Multiply the tens.
5
• How did you find the product 30? the product 150?
the product 500? 5 × 6 ones = 30; 5 × 3 tens =
150; 5 × 1 hundred = 500
5
28
×
7 7 × 8 = 56 ones
−−−
6
2 TEACH
28
×
7 7 × 2 tens = 14 tens
−−−
196 14 + 5 = 19 tens
Karen studied 196 pages. Compare to the estimate.
By estimating first, you
can determine if your
answer is reasonable.
RIDES A large Ferris wheel seats 260 people. How many
people can ride it in 9 rides?
Estimate 260 × 10 = 2,600
Step 1
Step 2
Step 3
Multiply the ones.
Regroup if necessary.
Multiply the tens.
Add any new tens.
Regroup if necessary.
Multiply the hundreds.
Add any new hundreds.
Regroup if necessary.
260
×
9
−−−
0
Use an area model to find 281 × 2.
400 + 160 + 2 = 562
Amelia charges $48 for each landscape
photograph. If she sells 6 photographs at a
local craft fair, how much money has she
earned? $288
9 × 0 = 0 ones
5
260
×
9
−−−
40
A theater can seat 450 people for each show. If
the theater fills for 8 shows, how many people
attend in all? 3,600 people
9 × 6 tens = 54 tens
5
260 9 × 2 hundreds =
× 9 18 hundreds
______
2,340 18 + 5 = 23 hundreds
IWB INTERACTIVE WHITEBOARD READY
So, 2,340 people can ride the Ferris wheel in 9 rides.
Lesson 2B Multiply by One-Digit Numbers
074_0077_C02L02_101808.indd 75
AL
75
12/11/09 12:22 PM
Alternate Teaching Strategy
If
students have trouble multiplying 3-digit numbers by
a 1-digit number . . .
Then
1
2
AL
As a class, have students complete the Check What You
Know Exercises as you observe their work.
E
TALK MATH Use the Talk Math Exercise to assess
student comprehension before assigning the practice
exercises.
use one of these reteach options:
Reteach Worksheet
Virtual Manipulatives Use the virtual base-ten blocks
to reteach the concept.
IWB
3 Use Base-Ten Blocks Use base-ten blocks to show three groups
of 345. Write the multiplication sentences modeled by the hundreds,
tens, and ones: 3 × 300, 3 × 40, 3 × 5. Find the sum of the products:
900 + 120 + 15 = 1,035. Have students repeat.
Lesson 2B Multiply by One-Digit Numbers
75
3 PRACTICE
Differentiate practice using these leveled assignments for
the exercises in Practice and Problem Solving.
Level
Assignment
AL
Approaching Level
11–16, 19–22, 27–28, 30,
33–36
OL
On Level
15–24, 28–31, 33–36
BL
Beyond Level
11–29 odd, 30–36
Multiply. Use an area model if needed.
Multiply
needed See Examples 1—3
1 3
1. 42 84
×
2
−−−
2. 61 305
×
5
−−−
3. 314 2,826
×
9
−−−
4. 18 144
×
8
−−−
5. 5 × 31 155
6. 208 × 3 624
7. 47 × 6 282
8. 7 × 624 4,368
9. One 747 airplane can carry 420 passengers. Will two of these planes
be able to carry 1,000 people? Explain. no; 420 × 2 = 840
10.
E
TALK MATH Describe each step for finding 416 × 3. See Answer Appendix.
indicates multi-step problem
EXTRA
%
#E
4) C
!# TI
2 AC
0R
P
Begins on page EP2.
Have students discuss and
complete the Higher Order Thinking problems.
E
WRITE MATH Have students complete the Write
Math Exercise in their Math Journals. You may choose to
use this as an optional formative assessment.
!
COMMON ERROR!
Exercise 24 Students may have trouble remembering
when to add regrouped tens or hundreds. Show them
a problem using base-ten blocks so that they can see
that the regrouped tens or hundreds are not in the
groups being multiplied and are therefore added after
the multiplication takes place.
Multiply.
M
lti l Use
U an area model
d l if needed.
d d See Examples
l 1—3
21 63
×
3
−−−
12.
32 192
×
6
−−−
13.
52 468
×
9
−−−
14. 401 2,807
×
7
−−−
15. 143 1,287
×
9
−−−
16.
72 288
×
4
−−−
17.
64 320
×
5
−−−
18. 712 2,136
×
3
−−−
11.
19. 211 × 7 1,477
20. 82 × 5 410
21. 8 × 16 128
22. 67 × 8 536
23. 341 × 4 1,364
24. 5 × 182 910
25. 806 × 7 5,642
26. 6 × 97 582
15 ft
27. Measurement The world’s largest cactus is 5 times
as tall as the cactus shown. How tall is the world’s
largest cactus? 75 ft
28. Northeast Elementary School purchased 5 new
computer systems. Each system cost $1,468. What
was the total cost? $7,340
29. In the auditorium, there are 9 rows of seats with
18 seats in each row. There are also 6 rows of seats
with 24 seats in each row. How many seats are there
in the auditorium? 306
76
Multiply Whole Numbers
0074_0077_C02L02_101808.indd 76
Multi-Part Lesson 2 When is it acceptable to use estimates when multiplying
in real-world situations? When are exact answers needed? Sample answer: You
could use estimates when you are shopping for items while walking through
the store. This way, you can determine whether or not you might have enough
money to make your purchase. An exact answer will be needed when you are
paying the bill because you wouldn’t want to overpay or underpay.
76
Multiply Whole Numbers
12/11/09 12:27
Use the information to solve the problem.
Rewatch “Pizza Party.”
Pizza Party
We are going to
order 6 pizzas
for the party.
30. What is the total cost of the 6 pizzas, not including tax? $84
31. Measurement Malcolm ran the 440-yard dash and the
220-yard dash at a track meet. There are 3 feet in one yard.
How many total feet did Malcolm run? 1,980 ft
Checks for Understanding
✔ 0506.1.9 Use age-appropriate
books, stories, and videos to
convey ideas of mathematics.
32. CHALLENGE Explain why the product of a two-digit number
and a one-digit number can never be a four-digit number.
E
33. NUMBER SENSE Catalina multiplied 842 and 3 and got 3,526.
How can she check to see if her answer is reasonable? Sample answer: By rounding 842
to 800, the product should be around 800 × 3 or 2,400. So, her answer is unreasonable.
34.
E WRITE MATH Write a real-world problem that can be solved
by multiplying a three-digit number by 3. Sample answer: A plane ticket costs $350. A
group of three people is buying plane tickets. The total cost is $350 × 3 = $1,050.
TALK MATH Discuss how you could use an area
model and partial products to solve the problem presented
in the graphic novel.
4 ASSESS
Test Practice
Formative Assessment
35. A total of 189
people visited the
wildlife reserve this
week. Which best
represents the amount of money
collected from ticket sales? C
36.
SHORT RESPONSE Collin
bought 7 flats of flowers. Each flat
contains 24 flowers. How many
flowers did he buy? 168 flowers
Write 607 × 4 on the board.
• How would you solve this problem? Write it in
vertical form. Multiply 4 × 7 ones = 28. Write 8 ones
in the ones place, write 2 tens above the tens. Multiply
4 × 0 tens = 0 tens and add the 2 regrouped tens.
Write a 2 in the tens place. Multiply 4 × 6 hundreds =
24 hundreds. The product is 2,428.
A. less than $200
B. between $200 and $240
C. between $2,000 and $2,400
D. more than $2,400
32. Sample answer: The greatest two-digit number is 99 and the greatest one-digit number is 9.
The product of 99 and 9 is 891, which is a three-digit number.
Lesson 2B Multiply by One-Digit Numbers 77
074_0077_C02L02_103031.indd 77
Have students write a few
in previous lessons
sentences about how the concepts
con
helped them with today’s lesson.
2/25/10 5:07 PM
Are students continuing to struggle
with multiplying a three-digit number
by a one-digit number?
During Small Group Instruction
If Yes
AL
AL
AL
If No
OL
BL
OL
BL
Daily Transparencies
Strategic Intervention Guide (pp. T50–T51)
Differentiated Instruction Option 2 (p. 70c)
Differentiated Instruction Option 2 (p. 70c)
Differentiated Instruction Option 2 (p. 70d)
Skills Practice Worksheet
Enrich Worksheet
Lesson 2B Multiply by One-Digit Numbers
77
PART
PART
C
Multiply by
One-Digit Numbers
2
Multi-Part
Lesson
A
B
Multi-Part
Lesson
C
B
C
FFor the school carnival, there will be
game booths in the school parking
g
lot. Each game booth is 7 feet wide and
must be 5 feet from the next booth. The
booths at each end must be at least
10 feet from the end of the parking lot.
Solve problems by drawing a picture.
Resources
The parking lot is 82 feet long. Find the
greatest number of game booths that
can be placed.
Manipulatives: two-color counters, rulers
Understand
What facts do you know?
• The parking lot is 82 feet long.
• Information about the size and layout of the
th booths.
b th
Get ConnectED
What do you need to find?
• The greatest number of game booths the carnival can have.
Plan
Solve
1 INTRODUCE
Draw a picture to solve.
First, mark off 10 feet from each end. Then, mark 7 feet for
a game booth and 5 feet of space until you have no more
space remaining.
82 ft
Activity Choice 1: Review
• Write the following problem on the board: Ana, Marta,
Florinio, and Rowtag took a trip. Ana drove twice as far
as Marta. Marta drove 13 fewer miles than Florinio.
Florinio drove 3 times farther than Rowtag. Rowtag
drove 18 miles. How far did Ana drive? 82 miles
• What strategy could you use to solve the problem?
work backward
10 ft
7 ft
7 ft
5 ft
7 ft
5 ft
65 ft
7 ft
5 ft
10 ft
7 ft
5 ft
7 ft
10 ft
Since there is only 7 feet remaining, there is not enough space to
have a sixth booth. They can have 5 booths.
Check
• What information does the problem give to begin to
solve it? Rowtag drove 18 miles.
Activity Choice 2: RWPS Reader
Draw a Picture
Main Idea I will solve problems by drawing a picture.
Objective
GLE 0506.1.2 Apply and adapt a variety of
appropriate strategies to problem solving, including
estimation, and reasonableness of the solution. Also
addresses GLE 0506.1.4.
A
Problem-Solving Strategy:
Draw a Picture
Leveled Worksheets
Multiply by One-Digit Numbers
PART
Problem-Solving Strategy:
Hands-On Activity Tools and Resources (p. 83)
2
Look back. The space for 5 game booths is 5 × 7 or 35 feet. The
space needed at the ends is 10 + 10 or 20 feet. The space needed
between the booths is 5 × 4 or 20 feet. So, 35 + 20 + 20 =
75 feet and 75 < 82. So, the answer makes sense.
GLE 0506.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including estimation,
and reasonableness of the solution. Also addresses GLE 0506.1.4.
78
7
Multiply Whole Numbers
• Read Early American Settlements as a class.
• Have students solve the problems using the
four-step plan.
• Ask them to share which strategy they used.
• Encourage struggling students to work in pairs to solve
each problem.
2 TEACH
Have students read the problem on the student page.
Guide them through the problem-solving steps.
Understand
Using the questions, review what
students know and need to find.
Plan
78
Have them discuss their strategy.
Multiply Whole Numbers
0078_0079_C02PSS_103031.indd 78
!
COMMON ERROR!
Exercise 7 As students read the problem, have them note all the
data and then circle the data. Encourage students to use a bar
diagram and consider which step to complete first. They may
wish to mark through the data as it is used to complete
the problem.
2/25/10 5:07
indicates multi-step problem
Solve
Refer to the problem on the previous page.
1. Explain how drawing a picture
helped you solve the problem.
See Answer Appendix.
3. Determine the greatest number of
game booths that could be built if the
parking lot was 97 feet long.
6 game booths
2. Explain whether you think drawing a
picture is the best strategy to solve this
problem. See Answer Appendix.
4. Describe a real-world situation in
which you could use the draw a
picture strategy. See Answer Appendix.
EXTRA
%
#E
4) C
!# TI
2 AC
0R
P
Begins on page EP2.
5. A 1-mile long scenic route has
signposts placed every 40 yards. There
are signposts placed at the beginning
and end of the mile. How many
signposts are there? 45 signposts
8. Aaron is boxing up meals for a local
charity. Each box contains 8 meals. If
he has 24 boxes to fill, how many total
meals can he box? 192 meals
20
8
6. Measurement A table has the
dimensions shown below.
12 ft
4 ft
There are microphones on the table
placed every 2 feet along the edges.
There is also a microphone placed at
each corner. How many microphones
are on the table? 16 microphones
8 × 20
admission
lunch
? games
Check
Have students look back to make sure that the
answer fits the facts given.
Analyze the Strategy Use the Extend Exercises to
analyze and discuss the problem-solving strategy.
Using the Exercises
Exercise 5 Students need to convert 1 mile to yards. The
picture should show a signpost at the beginning point and
at the endpoint of the mile.
äFK
4 ASSESS
Formative Assessment
Give students the following problem:
10. Ernie has a piece of wood that is
43 inches long. How many 13-inch
pieces can he cut from the wood? Is
there any wood remaining?
3 pieces; 4 in.
E WRITE MATH How can words and
numbers be used with the draw a
picture strategy? See Answer Appendix.
Lesson 2C Multiply by One-Digit Numbers
078_0079_C02PSS_103031.indd 79
AL
• How can the distance between the edge of the
parking lot and the start of the third booth be
calculated? 10 + 5 + 7 + 5 + 7 = 34 ft
3 PRACTICE
8×4
9. Measurement The picture below
shows the length and width of a
bookmark. Find the number of
bookmarks this size that can be cut
from a piece of fabric whose length
is 24 inches and whose width is
36 inches. 36 bookmarks
11.
$50
• How much space is needed for the second booth?
Explain. 12 ft; 7 ft and 5 ft
+ 4
äFK
7. Aiden is going to the amusement park
and has $50 to spend. He must pay
$22 for admission and $12 for lunch.
Use the bar diagram to determine how
many $4 games he can play with the
remaining money. 4 games
Guide students to use the draw a picture strategy
to solve the problem.
• How many feet are needed for the end booth?
Explain. 22 ft; 10 ft + 7 ft + 5 ft
79
A playground is 120 yds long and 60 yds wide. If a light is
placed at each corner, and every 20 yds on the sides, how
many lights are there?
• How would you begin to solve the problem? Draw a
rectangle to represent the playground.
• How would you draw the lights? dots on each corner
and then every 20 yds
• How many lights are needed? 18 lights
2/25/10 5:07 PM
Alternate Teaching Strategy
If
students have trouble drawing pictures to solve problems . . .
Then
1
2
Are students continuing to struggle
with solving problems by drawing
a picture?
AL
use one of these reteach options:
Reteach Worksheet
Personal Tutor Have students use Personal Tutor to reteach
the concept.
During Small Group Instruction
If Yes
AL
Daily Transparencies
If No
OL
Differentiated Instruction Option 1 (p. 70c)
Skills Practice Worksheet
Enrich Worksheet
IWB
3 Use Two-Color Counters Have students use two-color counters and rulers
to model the information given. Encourage students to add to their model as
they read.
OL
BL
Lesson 2C Multiply by One-Digit Numbers
79
Mid-Chapter
Check
Mid-Chapter
Check
8–13. See Answer Appendix for sample steps.
Formative Assessment
Use the Mid-Chapter Check to assess students’ progress in
the first half of the chapter.
Find each product mentally. (Lesson 1A)
Customize and create multiple
versions of your Mid-Chapter Check and the test
answer keys.
1. 9 × 60 540
2. 200 × 40 8,000
3. 80 × 50 4,000
4. 1,000 × 17
17,000
F. 2,000
5. 300 × 100
30,000
6. 70 × 5,000
350,000
G. 20,000
7. Measurement The distance around
a skating rink is 420 feet. If Anthony
skates around the rink 10 times, how
far does he skate? (Lesson 1A) 4,200 ft
Dinah Zike’s
Foldables®
Find each product mentally using the
Distributive Property. Show the steps that
you used. (Lesson 1C)
Use these lesson suggestions to incorporate the Foldable
during the chapter.
8. 5 × 17 85
Lesson 1A Under the first tab of the Foldable, students
record information about multiplying whole numbers,
define terms, and provide examples about multiplication
patterns.
H. 200,000
I.
10. 6 × 25 150
11. 2 × 37 74
12. 4 × 43 172
13. 2 × 31 62
Class
1
2
3
4
Lesson 2B Under the third tab of the Foldable, students
demonstrate their ability to multiply multi-digit numbers
by a one-digit number.
21. 43 × 2 86
23.
25.
C. 100
D. 200
Estimate by rounding or compatible
numbers. Show your work. (Lesson 2A)
15. 39 × 8
Number of Cans
415
402
380
426
Multiply. (Lesson 2B)
A. 17
B. 33
2,000,000
20. The table shows the results of a canned
food drive. Estimate the total number
of cans collected in all four classes.
Show how you estimated. (Lesson 2A)
See Answer Appendix.
9. 3 × 71 213
14. MULTIPLE CHOICE A set of bleachers
has 8 rows of seats. Each row can seat
25 people. If the bleachers are full,
how many people are seated on the
bleachers? (Lesson 1C) D
Lesson 1C Under the second tab of the Foldable, students
demonstrate their understanding of the Distributive
Property.
19. MULTIPLE CHOICE Which is the best
estimate for the product of 502 and
423? (Lesson 2A) H
102 408
× 4
_____
22. 17 × 9 153
24.
513 3,078
× 6
_____
E WRITE MATH Zoe is cutting
9 pieces of wire like the one shown
below for her science fair project. How
much wire does she need? Estimate
and then solve. Compare your estimate
with the actual amount.
(Lessons 2A and 2B)
16. 17 × 62
17.
18. 285
114
× 56
× 48
_____
_____
15–18. See Answer Appendix.
80
25. See Answer Appendix.
Mid-Chapter Check
Data-Driven Decision Making
0080_C02MCC_101808.indd 80
Based on the results of the Mid-Chapter Check, use the following to review concepts that continue to present students with problems.
Exercises
1–7
Tennessee
Standards
GLE 0506.2.5
8–14
What’s the Mathematics?
Error Analysis
Resources for Review
Use basic facts and patterns to
multiply multiples of 10, 100,
and 1,000.
Does not put enough zeros in answer. Does
not know multiplication facts. Does not use
correct place value when multiplying.
Chapter Resource Masters
Use the distributive property to multiply.
Does not know multiplication facts. Does not
understand or know how to use “distributive
property.”
GLE 0506.2.5
15–20
GLE 0506.1.2
Estimate products by using rounding
and compatible numbers.
Does not round correctly. Does not
understand “estimate by rounding.” Rounds
one factor in multiplication problem, not two.
21–25
GLE 0506.2.5
Multiply up to a three-digit number by
a one-digit number.
Does not know multiplication facts. Does not
understand purpose of estimating to check
answers. Does not understand “actual.”
80
Multiply Whole Numbers
Get ConnectED
Lesson Animations • Personal Tutor
• Self-Check Quiz
10/27/09 1:19 P
Multi-Part
Lesson
3
Multiply by Two-Digit Numbers
Planner
PART
A Multiply by Two-Digit Numbers
B
Multiplication Properties
C
Problem-Solving Investigation:
PART
Title/Objective
Choose the Best Strategy
E
Essential Question
How are the Associative and Commutative
Properties helpful in solving multiplication
problems? Sample answer: According to both
properties, it isn’t important what order factors
are multiplied. This can be helpful in solving
problems mentally.
Focus on Math Background
Standards
PART
A
B
Multiply by Two-Digit Numbers
Multiplication Properties
(pp. 81–84)
(pp. 86–89)
Multiply up to a three-digit number by
a two-digit number.
Use the associative and commutative
properties to multiply mentally.
GLE 0506.2.5
GLE 0506.2.5
Associative Property
p y
Vocabulary
Commutative Property
p y
Identityy Property
p y
Transitive Property
p y
Zero Property
p y
centimeter grid paper, scissors
Materials/
Manipulatives
Resources
index cards
Get ConnecttED
✔ 0506.1.9
Multiplying three-digit numbers by two-digit
numbers is essentially an extension of
multiplying two-digit numbers by two-digit
numbers. When using the standard algorithm
to multiply multi-digit numbers by two-digit
numbers, one thing does remain constant—
there will always be two partial products:
Get ConnecttED
Leveled Worksheets
Leveled Worksheets
Lesson Animations
Daily Transparencies
Daily Transparencies
Problem of the Day
Problem of the Day
Self-Check Quiz
Self-Check Quiz
Personal Tutor
Personal Tutor
VVirtual Manipulatives
624
×
42
−−−
1248 ← 624 × 2
← 624 × 40
+
24,960
−−−−−
26,208
Hands-On Activity Tools and Resources
Blended Approach
Game Time (p
(p. 85
85))
IWB
All digital assets are Interactive
Whiteboard ready.
Suggested Pacing
Multi-Part Lessons
1
PART
A
Days
1
2
B
C
1
(10 Days)
3
Assess
A
B
C
A
B
C
1
1
1
1
1
1
SGR PCT
1
1
Multiply by Two-Digit Numbers
81a
PART
Title/Objective
C
Problem-Solving Investigation:
Choose the Best Strategy (pp. 90–91)
Choose the best strategy to solve a
problem.
Standards
GLE 0506.1.2
Vocabulary
Materials/
Manipulatives
Resources
✔ 0506.1.9
two-color counters
Get ConnecttED
Leveled Worksheets
Daily Transparencies
Problem of the Day
Personal Tutor
Hands-On Activity Tools and Resources
Blended Approach
Problem-Solving in Social Studies
Th
W i ht Measurements
M
t (p.
( 92)
The Wright
SStudy
d G
Guide
id and
dR
Review
i
((p. 94))
Practice Chapter Test (p. 99)
Test Practice (p. 100)
81b
Multiply Whole Numbers
Notes
Multiply by Two-Digit Numbers
Differentiated Instruction
Approaching Level
On Level
AL
Option 1
Use with 3B
OL
Option 1
Use with 3A
Materials: poster board
Materials: two number cubes, pencil, paper
• Have students create a poster illustrating examples of the
Associative, Commutative, and Identity Properties.
• Have students play in pairs.
Associative Property: (8 × 12) ×
97 = 8 × (12 × 97)
• One student rolls the number cubes and uses the numbers
rolled as factors. They will record the product at the top of the
page. The second student rolls and records.
• Students will then take turns rolling one number cube one
time per turn. After each roll, the student multiplies the
number rolled times the product of the previous rolls. The
student who reaches 1,000 first wins.
Commutative Property: 7 × 62 =
62 × 7
Identity Property: 192 × 1 = 192
Option 2
Option 2
Use after 3A
Materials: number cubes, pencil, paper
• Have students generate two- and three-digit factors for several
multiplication problems by rolling a number cube. Have them
write the multiplication problems in a list.
Materials: paper, pencil
• Challenge students to write a word problem that can be
solved using one of the problem-solving strategies listed in
Lesson 3C.
• Have students exchange problems with a partner and solve.
Sofia earns $6 on her first
day of selling plants. Every
day she earns twice as
much as she did the day
before. How much has she
earned at the end of one
week, assuming she sells
plants every day? Which
strategy would you use to
solve the problem?
$ 762; make a table or
guess and check.
5
10
6 7 96 43
10
• Tell students to write rounding directions beside each
problem. The directions should be one or two words telling to
which place each factor should be rounded.
Other Options
TE
Learning Station Card 10
Get ConnectED
Use after 3C
Personal Tutor, Lesson Animations
Other Options
TE
Learning Station Cards 10, 11, 12
Get ConnectED
Personal Tutor, Lesson Animations
Multiply by Two-Digit Numbers
81c
Beyond Level
English Language Learners
BL
Option 1
Use with 3C
Materials: paper, pencil, nametags
• Exercise 2 can be figured out by using
the act it out strategy.
Beginning
Act It Out Use counters to understand what happens when
multiplying by 1.
AL
• One student can be a narrator who
reads while the others participate in
a slow motion version of the race.
• Have students wear the nametag of the person whom they
are from the problem and make sure that students finish the
race in the order that corresponds to the correct answer.
Use after 3A
• Tell students that there is a special shortcut for multiplying
two-digit numbers ending in five times themselves. Challenge
them to discover the way it works. Give them the following
examples to try:
25
×
25
−−−
625
35
×
35
−−−
1,225
• What did you learn? In each case, multiply the fives,
5 × 5 = 25. Then increase the top tens position by 1 and
multiply i.e., 2 × 1 = 2 for the first example 3 × 2 = 6 for
the second example, and 4 × 3 = 12 for the third example.
• Does this method work for 45, 55, 65, 75, 85, and 95?
Yes, 45 × 45 = 2,025, 55 × 55 = 3,025, 65 × 65 = 4,225,
75 × 75 = 5,625, 85 × 85 = 7,225, 95 × 95 = 9,025.
• Does this special method work for problems like 25 × 35?
no Does it work for any other numbers? no
Other Options
TE
Learning Station Cards 11, 12
Get ConnectED
• Write 13. Have students arrange 1 set of 13 counters. Once
they have done so, ask How many do you have? Write
13 × 1 = 13 on the board. Repeat for 18, 22, and 26.
• Ask, If you multiply by 1, what is the answer? Say, Identity
Property. Have students repeat. Write Identity Property.
Intermediate
Word Meaning Discover the Commutative Property of
Multiplication.
OL
Materials: paper and pencil
15
×
15
−−−
225
This strategy helps English Learners learn the language of
properties of multiplication.
Find Core Vocabulary and Common Use Verbs in the online
EL strategies to help students grasp the math skills; use
Language Alerts at point of use in the Teacher Edition.
• Have students elaborate on the problem
by writing a script for the race.
Option 2
ELL
Lesson Animations
• Write 5 × 3 = ?. Say, Use your counters. Make 5 groups of 3.
Say, Count your counters. What is the answer?
• Write 3 × 5 = ?. Say, Use your counters. Make 3 groups of 5.
Say, Count your counters. What is the answer?
• Write 5 × 3 = 3 × 5. Ask, Is order important when you
multiply? Say, This is the Commutative Property. Have
students repeat. Write Commutative Property on the board.
Advanced
Recognize and Act It Out Discover what happens when the
order of three or more factors is changed.
BL
• Roll three number cubes. Use each number as a factor in a
multiplication problem. For example, if you roll 2, 5, and 7,
then you write (2 × 5) × 7 = ?. Tell students to answer the
problem. Next, regroup the factors and rewrite the problem
as 2 × (5 × 7) = ? Tell students to answer the problem. Ask,
What is the same? Tell students that when multiplying numbers,
the order of the factors does not matter. Say, Associative
Property and write it on the board. Have students repeat.
• Students may repeat the activity using the number cubes.
Extend
Have Beyond Level students act as “teachers” and create
problems to test Approaching and On Level students’
understanding of the properties of multiplication.
81d
Multiply Whole Numbers
3
Multi-Part
Lesson
PART
Multi-Part
Lesson
Multiply by Two-Digit Numbers
A
Main Idea
I will multiply up to a
three-digit number by a
two-digit number.
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, and decimals.
B
3
A
PART
C
PART
Multiply by Two-Digit
Numbers
A
B
C
Multiply by
Two-Digit Numbers
Objective
You have already learned how to multiply by one-digit
numbers using an area model. You can also use an area
model to multiply two-digit numbers.
Multiply up to a three-digit number by a two-digit number.
Resources
Use an Area Model to
Find Products
Materials: centimeter grid paper, scissors
Use an area model to find 27 × 35.
Hands-On Activity Tools and Resources (p. 66)
35
Step 1 Draw a rectangle.
Multiply by
Two-Digit Numbers
Leveled Worksheets
Get ConnectED
27
30
Step 2 Separate the
tens and ones.
GLE 0506.2.5 Develop fluency in solving multi-step
problems using whole numbers, fractions, mixed numbers,
and decimals.
5
20
1 INTRODUCE
7
Step 3
Find each
partial product.
Then add.
20
20 × 30
= 600
20 × 5
= 100
7 × 30
= 210
7×5
= +
35
−−−−
= 945
7
Activity Choice 1: Hands-On
30
5
20 × 30 = 600
20 × 5 = 100
7 × 30 = 210
7 × 5 = 35
• Direct students to draw
a 15 × 13 rectangle
on graph paper.
• First, break up the
15 to 10 and 5.
Next, break up the
13 to 10 and 3.
So, 27 × 35 = 945.
Lesson 3A Multiply by Two-Digit Numbers
• Students can use what they know about partial
products and decomposing numbers to multiply 2 digit
numbers.
13
10
5
10
5
10
10 × 10 = 100
10 × 5 =
50
3
3 × 10 = 30
3×5=
15
10
3
81
• Find each product.
Then add. 195
081_0084_C02L03_103031.indd 81
15
2/26/10 12:30 PM
Activity Choice 2: Learning Station:
Health, Card 10
• Direct students to the Health Learning Station Card 10
for opportunities to explore and extend the lesson.
Building Math Vocabulary
Write the vocabulary words sum and product and their
definitions on the board.
Have students review the meaning of the words. Encourage
students to work in pairs. Have one student use the words to
write questions such as, “What is the sum of 45 plus 16?” The
second student’s role is to answer the question.
• Students can also research additional activities to
determine the number of Calories burned in a given
amount of time.
• Challenge above-level students by having them
research Calories consumed in one meal and
comparing this to the number of Calories burned.
Lesson 3A Multiply by Two-Digit Numbers
81
Multiply Two-Digit
Numbers
2 TEACH
COYOTES Coyotes
can run up to
44 feet per second
on land! At this
rate, how many
feet could a coyote
run in 12 seconds?
Scaffolding Questions
Write 16 × 14 in vertical form on the board using a
rectangle model.
• What is the first step in multiplying? Multiply the
ones; 4 × 6 = 24. Write 24 below the line.
Multiply 44 and 12. Estimate
timate 44 × 10 = 440
• What is the second multiplication? Ones times tens;
4 × 10 = 40. Write 40 below 24.
Step 1
Multiply the ones.
44
× 12
_____
88 44 × 2 = 88
• What is the next step? 10 × 6 = 60
• Tell students that in 14, the 1 is in the tens place and is
therefore a ten. Write 60 below 40.
• How do we complete the problem? multiply
10 × 10 = 100, and add all four products:
24 + 40 + 60 + 100 = 224
Step 2
Multiply the tens.
44
×
12
−−−−
88
440 44 × 10 = 440
Step 3
Add.
44
×
12
−−−−
88
+
440
−−−−
528
So, a coyote could run 528 feet in 12 seconds.
Multiply Three-Digit Numbers
Find 165 × 31. Estimate 200 × 30 = 6,000
Use an area model to find 52 × 31.
1,500 + 50 + 60 + 2 = 1,612
Step 1
Multiply the ones.
Step 2
Multiply the tens.
Step 3
Add.
165
165
×
31
×
31
−−−−
−−−−
165 165 × 1 = 165 165
4950 165 × 30 = 4,950
The fastest human runner was clocked at
11 feet per second. How far will the runner run
in 55 seconds? 605 feet
So, 165 × 31 = 5,115.
Find 438 × 46. 20,148
165
×
31
−−−−
165
+
4950
−−−−−
5115
Compare to the estimate.
IWB INTERACTIVE WHITEBOARD READY
Multiply. See Examples 1—3
Multiply
1 3
1.
As a class, have students complete the Check What You
Know Exercises as you observe their work.
E
TALK MATH Use the Talk Math Exercise to assess
student comprehension before assigning the practice
exercises.
AL
Alternate Teaching Strategy
If
students have trouble multiplying by
two-digit numbers . . .
Then
1
2
AL
use one of these reteach options:
Reteach Worksheet
Virtual Manipulatives Use the virtual
grid paper to reteach the concept.
IWB
3 Use Grid Paper Have students work with a grid
paper model for several problems. As they write
the partial products, they will see the four steps
needed to multiply two 2-digit numbers.
82
Multiply Whole Numbers
32 416
×
13
−−−−
5. 21 × 42 882
2.
26 1,170
×
45
−−−−
6. 69 × 14 966
9. A cow can eat 25 pounds of hay a day.
At that rate, how many pounds of hay
can a cow eat in 31 days? 775 lb
82
3. 104 1,248
×
12
−−−−
4. 102 5,712
×
56
−−−−
7. 83 × 367 30,461
8. 534 × 67 35,778
10.
E
TALK MATH Describe how addition
is used when you multiply by two-digit
numbers. See Answer Appendix.
Multiply Whole Numbers
0081_0084_C02L03_101808.indd 82
12/11/09 12:30
indicates multi-step problem
EXTRA
%
#E
4) C
!# TI
2 AC
0R
P
Begins on page EP2.
Multiply.
M
lti l See Examples
l 1—3
11.
24 504
×
21
−−−−
12.
39 1,326
×
34
−−−−
13.
13 702
×
54
−−−−
14.
51 4,182
×
82
−−−−
15.
141 3,525
× 25
_____
16.
229 7,099
× 31
−−−−
17.
470 26,320
× 56
−−−−
18.
321 20,544
× 64
−−−−
Differentiate practice using these leveled assignments for
the exercises in Practice and Problem Solving.
Level
19. 19 × 15 285
20. 43 × 65 2,795
21. 72 × 36 2,592
22. 23 × 84 1,932
23. 48 × 101 4,848
24. 441 × 20 8,820
25. 281 × 52 14,612
26. 347 × 89 30,883
27. Measurement A delivery truck
travels 278 miles each day. How far
does it travel in 25 days? 6,950 mi
29. Marshall’s mother buys 2 boxes of
granola bars each week. Each box
contains 8 granola bars. If she
continues buying 2 boxes each
week, how many granola bars will
she buy in a year? 832 granola bars
31. Each day, a person loses about 75
strands of hair. About how many
strands of hair will a person lose
in one year? 27,375 strands
33. Measurement Alicia lives in
Nashville. Last year her family drove
to Atlanta each month to visit her
grandmother. Find the total distance
they drove for the year. 5,976 mi
081_0084_C02L03_101808.indd 83
Destination City
From Nashville
One-Way
Distance (mi)
Atlanta
249
Raleigh
540
3 PRACTICE
28. Leon earns $14 an hour. How much
does he earn in 4 weeks if he works
12 hours each week? $672
30. Ms. Jenkins was arranging chairs for a
school awards assembly. Each row
contained 15 chairs. If there were 21
rows, how many chairs had to be
arranged? 315 chairs
32. Mr. Walsh has 26 students in his class.
Each student must pay $35 for a trip to
the museum. How much does
Mr. Walsh collect altogether? $910
34. The table below shows Katrina’s
prices for dog walking. If she walks
5 medium-sized dogs and 8 large-sized
dogs for 12 weeks, how much will she
earn? $2,064
Assignment
AL
Approaching Level
11–15, 19–23, 27, 29–31,
36–46
OL
On Level
15–26, 28, 29–33, 36–46
BL
Beyond Level
11–31 odd, 33–34, 36–46
Have students discuss and
complete the Higher Order Thinking problems. Ask
students to explain using place-value terminology.
E
WRITE MATH Have students complete the Write
Math Exercise in their Math Journals. You may choose to
use this exercise as an optional formative assessment.
!
COMMON ERROR!
Exercises 11–26 Students may have trouble
remembering to place the zero in the ones place
when multiplying by tens. Encourage them to
automatically write a zero in the ones place of the
tens product before they begin multiplying by tens.
Dog Type Cost Per
er Week ($)
Small
10
Medium
12
Large
14
Lesson 3A Multiply by Two-Digit Numbers
83
12/11/09 12:30 PM
Lesson 3A Multiply by Two-Digit Numbers
83
4 ASSESS
Formative Assessment
Write 47 × 32 on the board.
• What are the first steps in multiplying 47 × 32?
Multiply 2 × 7 ones and 2 × 4 tens.
35. CHALLENGE Find 235 × 124. Use the same strategy for multiplying
by a three-digit number that you used for multiplying by a two-digit
number except include multiplying by the hundreds place. 29,140
36.
• Why is there a zero in the ones place when 47 is
multiplied by 3? The 3 is in the tens place, so it is
really 30 × 47.
• What is the product of 47 × 32? 1,504
Are students continuing to struggle
with multiplying 2-digit by 3-digit
number?
Test Practice
37. Each day there are 7 tours at the
glass factory. Twenty-eight people
can go on a tour. How many people
can tour the glass factory each day? C
A. 156
B. 180
C. 196
During Small Group Instruction
If Yes
AL
AL
E WRITE MATH Choose four different numbers from 1 through 9
to create a multiplication problem that gives you the greatest
product. Explain how you know it is the greatest. See Answer Appendix.
D. 200
Daily Transparencies
Strategic Intervention Guide
38. The table shows the average number
of meals a restaurant makes each
day. About how many dinners does
the restaurant make in a two-week
period? G
Number of Lunches
225
Number of Dinners
425
F. 9,100
H. 2,975
G. 5,950
I. 850
(pp. T46–T47, T52–T53)
If No
AL
Differentiated Instruction Option 2
(p. 81c)
OL
Differentiated Instruction Option 1
Differentiated Instruction Option 2
Skills Practice Worksheet
Enrich Worksheet
(p. 81c)
BL
OL
BL
(p. 81d)
39. Measurement Leslie is making jewelry. She has a piece
of wire that is 81 inches long. She uses a piece that is 3 inches
long to make a pair of earrings. Find the number of 6-inch
pieces she can cut from the remaining piece to make bracelets.
Use the draw a picture strategy. (Lesson 2C) 13
Multiply. (Lesson 2B)
Write 372 × 45 on the
W
step-by-step, how they
board. Ask students to write, st
would
372 × 45 = 16,740
ld findd the
h product.
d
40.
27 108
×4
−−−
41.
48 288
×6
−−−
43.
78 390
×
5
−−−
44. 208 624
×
3
−−−
42.
62 310
×5
____
45. 327 1,962
×
6
−−−
46. Mr. Batista was buying supplies for a picnic. He bought
6 packages of cups with 36 in each package. Use the
Distributive Property to find the number of cups he
bought. Show the steps you used. (Lesson 1C) See Answer Appendix.
Review and assess mastery of skills and concepts from the
previous lessons in the chapter.
84
Multiply Whole Numbers
0081_0084_C02L03_103031.indd 84
84
Multiply Whole Numbers
2/25/10 5:08
What’s
the Difference?
Multiplying Two Numbers
What’s the
Difference?
You will need: 0–9 spinner, paper
Multiplying Two Numbers
Materials: spinner with digits 0 through 9, paper, pencils
Get Ready!
Players: 2 players
Introduce the game to your students to play as a class, in
small groups, or at a learning station to review concepts
introduced in this chapter.
Get Set!
Make a spinner as shown.
0 1
Each player needs a sheet of
paper and a pencil.
2
9
8
Go!
Each player spins the
spinner four times to make
a multiplication problem
with two two-digit factors or
a one-digit and a three-digit
factor.
3
4
7
Instructions
6 5
• Students play in pairs. Each student needs a sheet of
paper and a pencil. They make a spinner as shown on
the student page.
• Each player spins the spinner four times to make a
multiplication problem with two 2-digit factors or a
1-digit and 3-digit factor.
Each player then spins four
times to make a different
multiplication problem with
two two-digit factors or a
one-digit and a three-digit
factor.
• Each player then spins four times to make a different
multiplication problem with two 2-digit factors or a
1-digit and a 3-digit factor.
• Each player finds the product of each of his or her
problems. Then the players find the difference between
the two products.
Each player finds the
product of each of his or her
problems. Then the players
find the difference between
the two products.
• The player with the greatest difference wins the round.
• Play five rounds.
The player with the greater
difference wins the round.
Extend the Game
Play 5 rounds.
BL
• Have students play for ten rounds rather than five.
Greater
Grea
Gr
What’s
eate
te
er the
Number
Numb
Numb
Nu
mber
Difference?
er Game
Gam
ame
e 85
85
085_C02GT_101808.indd 85
• For another game focusing on the same mathematical
concept, see
Game Time.
12/11/09 12:32 PM
Differentiated Practice
Use these leveled suggestions to differentiate the game for all learners.
Level
Assignment
AL
Approaching Level
Students spin three times to get one twodigit number and one one-digit number.
OL
On Level
Have students play the game with the rules
as written.
Game Time What’s the Difference?
85
Multi-Part
Lesson
3
PART
PART
B
Multiply by Two-Digit Numbers
B
A
Multi-Part
Lesson
C
Multiplication
Properties
Objective
PART
Materials: index cards
Multiply by Two-Digit Numbers
A
Main Idea
I will use the associative
and commutative
properties to multiply
mentally.
Use the associative and commutative Properties to multiply
mentally.
Resources
3
B
C
Multiplication Properties
Gabriela has five $2 bills and
nd
Noriko has two $5 bills. They
hey
each have the same amount.
unt.
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, and decimals.
Leveled Worksheets
5 × $2 = $10
2 × $5 = $10
The order in which you multiply numbers does not matter. This
and other properties of multiplication are listed below.
Get ConnectED
Multiplication Properties
Associative Property The way in which factors are
grouped does not change the product.
GLE 0506.2.5 Develop fluency in solving multi-step
problems using whole numbers, fractions, mixed numbers,
and decimals.
Example (9 × 2) × 5 = 9 × (2 × 5)
Commutative Property The order in which factors are
multiplied does not change the product.
1 INTRODUCE
Example 4 × 8 = 8 × 4
Activity Choice 1: Hands-On
Identity Property The product of any factor and 1 equals
the factor.
• What are all of the ways to make a product of 24?
1 × 24, 2 × 12, 3 × 8, 4 × 6, 6 × 2 × 2, 4 × 2 × 3,
2×2×2×3
Example 16 × 1 = 16
• Write the following on the board:
2 × 6 × 2 = 4 × 2 × 3.
Identify Multiplication Properties
• Is this equation true or false? Explain. True; both
sides equal 24.
Identify the multiplication property used to rewrite the
problem below.
• Write the following on the board:
2 × 6 × 2 × 20 = 20 × 4 × 2 × 3.
7 × 11 = 11 × 7
The order of the factors changed.
This is the Commutative Property.
• Is this a true equation? Explain.
Yes; both sides equal 20 × 24.
• Ask students to multiply mentally to find the product of
each side of the equation. Encourage them to move
factors around and group them in ways that will make
the multiplication easier. What is the product? 480
86
Multiply Whole Numbers
0086_0089_C02L03_103031.indd 86
Activity Choice 2: Math Game
• Give pairs of students one set of index cards with
problems that demonstrate the Commutative,
Associative, and Identity Properties of Multiplication.
• Give students a second set of cards with “Commutative,”
“Associative,” and “Identity” written on them.
• Allow pairs to shuffle the sets separately and match
them with the correct property.
• After checking their work with another student pair, the
answers and explanations can be recorded in each
student’s Math Journal to extend the activity.
86
Multiply Whole Numbers
Building Math Vocabulary
Write the multiplication properties and their definitions on
the board. Review the Associate Property, Commutative Property,
and the Identity Property in relation to addition. Ask students to
write what they think each of the properties mean in relation to
multiplication. Have students write an example of each.
2/25/10 5:07
Use Properties to
Multiply Mentally
2 TEACH
SPORTS A coach had 2 groups of 16 players in each group.
Each player had to score 5 goals. Use properties of
multiplication to find the total number of goals scored.
Since you can easily multiply 2 and 5, change the order and
group the numbers together.
It is easier to multiply
mentally if you can
find products that are
2 × 16 × 5 = 2 × 5 × 16
= 10 × 16
Find 2 × 5 mentally.
= 160
Find 10 × 16 mentally.
RUNNING Brenda ran 45 minutes a day, 5 days a week for
20 weeks. Use properties of multiplication to find the total
number of minutes she ran.
45 × 5 × 20 = 45 × (5 × 20)
Write 5 × 6 × 7 on the board.
• What is the product? 210
• If the factors are put in a different order, will the
product the change? Explain. No; 5 × 6 = 30, and
30 × 7 = 210. 7 × 5 = 35, and 35 × 6 = 210.
Commutative Property
= (2 × 5) × 16 Associative Property
multiples of 10.
Scaffolding Questions
Write on the board: (5 × 6) × 7 = 5 × (6 × 7)
• Is this equation true? Explain. Yes; 5 × 6 = 30, and
30 × 7 = 210. 6 × 7 = 42, and 5 × 42 = 210.
• Explain the Associative and Commutative Properties of
Multiplication.
p
Associative Property
= 45 × 100
Find 5 × 20 mentally.
= 4,500
Find 45 × 100 mentally.
Identify the multiplication property used to
rewrite (6 × 7) × 3 = 6 × (7 × 3).
Associative Property
indicates multi-step problem
Use properties of multiplication to find
8 × 15 × 5 mentally.
8 × 15 × 5 = 8 × 5 × 15; Commutative Property
= (8 × 5) × 15; Associative Property
= 40 × 15
= 600
Identify the multiplication property used to rewrite each
problem. See Example 1
1. 6 × 100 × 7 = 6 × 7 × 100 Commutative 2. (8 × 2) × 3 = 8 × (2 × 3) Associative
Use properties of multiplication to find each product mentally.
Show your steps and identify the properties that you used.
See Examples 2, 3 3–8. See Answer Appendix.
3. 5 × 2 × 34
4. 2 × 51 × 50
5. (8 × 4) × 5
6. 4 × (25 × 6)
7. 9 × 500 × 2
8. 200 × 14 × 5
Use properties of multiplication to find
67 × 25 × 4 mentally.
67 × 25 × 4 = 67 × (25 × 4); Associative Property
= 67 × 100
= 6,700
9. For a party, Shandra and James each bought 5 packages
of hot dog buns, with 12 buns in each package. How many
hot dog buns did they buy altogether? 120 hot dog buns
10.
E
IWB INTERACTIVE WHITEBOARD READY
TALK MATH Explain how you could use mental math
and multiplication properties to find 50 × 35 × 2.
See Answer Appendix.
Lesson 3B Multiply by Two-Digit Numbers 87
086_0089_C02L03_101808.indd 87
11/5/09 7:15 PM
ELL
Using Synonyms A synonym for identity is sameness. Write sameness,
and underline same. Help them use this synonym to connect the idea of
the identity property. Write 27 × 1 = ? Have students give the answer.
They should be able to note that the answer is the same as one of the
original factors.
As a class, have students complete the Check What You
Know Exercises as you observe their work.
E
TALK MATH Use the Talk Math Exercise to assess
student comprehension before assigning the practice
exercises.
AL
Alternate Teaching Strategy
If
students have trouble using the
multiplication properties . . .
Then
1
AL
use one of these reteach options:
Reteach Worksheet
2 Use Factor Cards Write the factors for several
problems on index cards. Have students group
the cards to find factors that yield multiples of
10. Have students rewrite the problems based
on how the factors are grouped.
Lesson 3B Multiply by Two-Digit Numbers
87
3 PRACTICE
EXTRA
%
#E
4) C
!# TI
2 AC
PR
0
Begins on page EP2.
Differentiate practice using these leveled assignments for
the exercises in Practice and Problem Solving.
Identify
d
if the
h multiplication
l i li i
property used
d to rewrite
i each
h
problem. See Example 1
11. 15 × 2 = 2 × 15 Commutative
Associative
12. 3 × (9 × 10) = (3 × 9) × 10
13. 71 × 1 = 71 Identity
14. 4 × 13 × 5 = 4 × 5 × 13 Commutative
Level
Assignment
AL
Approaching Level
11–20, 28–29, 32, 34, 36–41
OL
On Level
11–14, 18–30, 32, 34, 36–41
Use properties of multiplication to find each product mentally.
Show your steps and identify the properties that you used.
See Examples 2, 3 15–26. See margin.
BL
Beyond Level
12–30 even, 31–41
15. 16 × 2 × 5
16. 25 × 4 × 27
17. 20 × (5 × 15)
18. 40 × (11 × 5)
19. 5 × 17 × 2
20. 200 × 5 × 9
21. 50 × (20 × 13)
22. (16 × 25) × 4
23. 50 × 38 × 2
24. 200 × 5 × 44
25. 20 × 56 × 50
26. 4 × 23 × 250
Have students discuss and
complete the Higher Order Thinking problems.
Algebra Find the number that makes each sentence true.
WRITE MATH Have students complete the Write
Math Exercise in their Math Journals. You may choose to
use this as an optional formative assessment.
16. 25 × 4 × 27
= (25 × 4) × 27
= 100 × 27
= 2,700
Associative Property
Find 25 × 4 mentally.
Find 100 × 27 mentally.
17. 20 × (5 × 15)
= (20 × 5) × 15
= 100 × 15
= 1,500
Associative Property
Find 20 × 5 mentally.
Find 100 × 15 mentally.
18. 40 × (11 × 5)
= 11 × (5 × 40)
= 11 × 200
= 2,200
Associative Property
Find 5 × 40 mentally.
Find 11 × 200 mentally.
19. 5 × 17 × 2
= 5 × 2 × 17
= (5 × 2) × 17
= 10 × 17
= 170
Commutative Property
Associative Property
Find 5 × 2 mentally.
Find 10 × 17 mentally.
20. 200 × 5 × 9
= (200 × 5) × 9
= 1,000 × 9
= 9,000
Associative Property
Find 200 × 5 mentally.
Find 1,000 × 9 mentally.
21. 50 × (20 × 13)
= (50 × 20) × 13 Associative Property
= 1,000 × 13
Find 50 × 20 mentally.
= 13,000
Find 100 × 13 mentally.
22. (16 × 25) × 4
= 16 × (25 × 4)
= 16 × 100
= 1,600
88
Associative Property
Find 25 × 4 mentally.
Find 16 × 100 mentally.
Multiply Whole Numbers
28. 40 × (2 × 11) = (40 × ) × 11 2
29. (28 × 7) × 5 = 7 × (28 × ) 5
30. 12 × 9 × 4 = 4 × × 12 9
31. Elijan and 4 of his friends are each paid $20 per afternoon for
stuffing envelopes. If they work 8 afternoons, what is the total
amount of their earnings? $800
"EST
32. Each package of juice contains 6 cans. Each
carton of juice contains 8 packages of juice.
If you have fifty cartons, how many cans of
juice do you have? 2,400
"EST
"EST
"EST
ST
"E
Additional Answers
15. 16 × 2 × 5
= 16 × (2 × 5)
Associative Property
= 16 × 10
Find 2 × 5 mentally.
= 160
Find 16 × 10 mentally.
27. 4 × 3 × 8 = 4 × × 3 8
"E
ST
E
"EST
"EST
"EST
"
"E
"
EST
"E
"
EST
"E
"
EST
33. Replace the in 87 × × 5 with a number
greater than 10 so that the problem is easy
to solve mentally. Explain. 33–36. See Answer Appendix
34. OPEN ENDED Write a multiplication sentence to show how the
Associative Property can help you solve a problem mentally. Explain.
35. CHALLENGE Show the steps and the properties of multiplication
that you could use to find 4 × 96 × 25 × 50 × 2 mentally.
36.
E WRITE MATH Without calculating, is the statement
(7 × 5) × 4 = 5 × (7 × 4) true or false? Explain your reasoning.
88
Multiply Whole Numbers
0086_0089_C02L03_101808.indd 88
11/5/09 7:16
23. 50 × 38 × 2 = 50 × 2 × 38
= (50 × 2) × 38
= 100 × 38
= 3,800
Commutative Property
Associative Property
Find 50 × 2 mentally.
Find 100 × 38 mentally.
24. 200 × 5 × 44 = (200 × 5) × 44
= 1,000 × 44
= 44,000
Associative Property
Find 200 × 5 mentally.
Find 1,000 × 44 mentally.
25. 20 × 56 × 50 = 20 × 50 × 56
= (20 × 50) × 56
= 1,000 × 56
= 56,000
Commutative Property
Associative Property
Find 20 × 50 mentally.
Find 1,000 × 56 mentally.
26. 4 × 23 × 250 = 4 × 250 × 23
= (4 × 250) × 23
= 1,000 × 23
= 23,000
Commutative Property
Associative Property
Find 4 × 250 mentally.
Find 1,000 × 23 mentally.
4 ASSESS
Test Practice
37. A school has 13 classrooms with
28 desks in each room. All the
desks in the school are being used
by students. How many students
are using the desks? D
Formative Assessment
38. The Stallions basketball team has
sold out their last 8 home games.
Their gym has 50 rows. Each row
has 20 seats. How many people
have attended the 8 games? G
A. 41
C. 244
F. 80,000
H. 800
B. 182
D. 364
G. 8,000
I. 80
Write 6 × 7 × 50 on the board.
• How can the Commutative Property be used to
make this problem easier to solve? Explain.
Change the order of the factors to 6 × 50 × 7 because
6 × 50 = 300, which is a multiple of 10.
• How would you use the Associative Property in this
problem? Group the 6 × 50 using parentheses.
• What is the product? 2,100
Properties
Transitive Property
In the balance on the left, the prism and the two cylinders have the
same mass. On the right, the same two cylinders have the same mass
as the pyramid. We can reason that the prism and the pyramid have the
same mass.
Are students continuing to struggle
with using the Associative and
Commutative Properties to multiply
mentally?
During Small Group Instruction
If Yes
The Transitive Property states if a = b and b = c, then a = c.
AL
AL
Zero Property
The Zero Property states that the product of any number and
zero is zero.
4×0=0
3×9×0=0
If No
OL
BL
Daily Transparencies
Differentiated Instruction Option 1
(p. 81c)
Skills Practice Worksheet
Enrich Worksheet
39. Using the balances shown below, what statement can be made
using the Transitive Property? The two prisms have the same mass as the pyramid.
Have students write how
two-digit numbers
yesterday’s concepts on multiplying
mult
helped them with what they learned today.
40. If 6 + 4 = 10 and 10 = 4 + 6, what conclusion can you make
using the Transitive Property? 6 + 4 = 4 + 6
E WRITE MATH Explain whether it would be easier to use the
Associative Property or the Zero Property to find the product of
40 × 50 × 0. Sample answer: It would be easier to use the Zero Property. Since zero is one
of the factors, it does not matter what the product of the other factors is.
Lesson 3B Multiply by Two-Digit Numbers 89
41.
086_0089_C02L03_103031.indd 89
2/25/10 5:07 PM
!
COMMON ERROR!
Exercises 19 and 23 Students may have trouble with
identifying the factors of multiples of 10 when they do not occur
next to each other. Have students rewrite the problem with the
factors in a different order to group together those that multiply
to make a multiple of 10.
Tell students that the Transitive and Zero Properties can
also be used when multiplying numbers.
• Use the equations 2 × 3 = 6 and 1 × 6 = 6 to explain
the Transitive Property.
• What is product of 2 × 3 and 1 × 6? 6
• Use an equal sign to show that 2 × 3 is equal to
1 × 6. 2 × 3 = 1 × 6
• Work the Example as a class.
• Assign the exercises.
• Have students complete the Write Math Exercise in
their Math Journals.
Lesson 3B Multiply by Two-Digit Numbers
89
Multi-Part
Lesson
3
PART
PART
C
Multiply by Two-Digit Numbers
A
B
Multi-Part
Lesson
C
3
PART
Multiply by Two-Digit Numbers
A
B
C
Problem-Solving Investigation
Problem-Solving
Investigation
Main Idea I will choose the best strategy to solve a problem.
Objective
Choose the best strategy to solve a problem.
MAI: I noticed that there were more dogs
than cats in the veterinarian’s waiting
room. The vet said that for about every
3 dogs he sees, he sees 2 cats. If 20
animals were brought in, I wonder how
many would be dogs?
Resources
Manipulatives: two-color counters
Hands-On Activity Tools and Resources (p. 83)
Leveled Worksheets
YOUR MISSION: Find about how many dogs
the vet will see if 20 animals come
into the office.
Get ConnectED
Understand
GLE 0506.1.2 Apply and adapt a variety of
appropriate strategies to problem solving, including
estimation, and reasonableness of the solution.
Plan
Solve
1 INTRODUCE
Activity Choice 1: Review
You know that for every 3 dogs, there are 2 cats. You
need to find the number of dogs.
To solve this problem, you can use red and yellow counters
to act out how many dogs and cats the vet will see.
Use red counters to represent the dogs and yellow
counters to represent the cats. Place 3 red counters and
2 yellow counters in a group. Make groups of 5 counters
until you have 20 counters.
• Present students with the following problem:
Montego and Cristobal are brothers whose ages add
up to 30 years. Montego is 8 years younger than
Cristobal. How old is each brother? Cristobal: 19,
Montego: 11
Add the number of red counters to find about how many
dogs the vet will see.
3 + 3 + 3 + 3 = 12
So, about 12 of the animals will be dogs.
Check
• What problem-solving strategy could you use?
guess and check
• Guide the class to work together to use the guess and
check strategy to solve the problem.
Work backward. Start with 12 red counters and 8 yellow
counters. Remove groups of 3 red and 2 yellow counters
until none remain.
GLE 0506.1.2 Apply and adapt a variety of appropriate strategies to problem solving,
including estimation, and reasonableness of the solution.
2 TEACH
Have students read the problem on the student page.
Guide them through the problem-solving steps.
90
Multiply Whole Numbers
0090_0091_C02PSI_103031.indd 90
Understand
Using the questions, review what
students know and need to find.
Plan Have them discuss their strategy.
Solve Guide students to use the act it out strategy.
• What does one red counter represent? one dog
• What does one yellow counter represent? one cat
• Why do you put three red counters and two
yellow counters in every group? because the vet
sees two cats for every three dogs
Check
Have students look back at the problem to make
sure that the answer fits the facts given.
90
Multiply Whole Numbers
!
COMMON ERROR!
Exercise 7 Some students may only look at the first two entries
of the table and think the pattern is “add 1, add 2, and so on.”
Have students reread the problem and ask them what the word
“doubles” means.
2/25/10 5:08
indicates multi-step problem
EXTRA
%
#E
4) C
!# TI
2 AC
0R
P
Begins on page EP2.
• Four-step plan.
• Act it out.
1. Zach purchases two books. The total
cost is $32. One book costs $8 more
than the other. How much does each
book cost? $12 and $20
Minutes
0
10
20
30
60
3. Measurement A recipe for banana
nut muffins calls for 1 cup of bananas
and 2 cups of flour. Eboni wants to
make more muffins than the recipe
yields. In Eboni’s batter, there are
6 cups of flour. If she is using the
recipe as a guide, how many cups of
bananas will she need? 3 c
1
2
Number of Cells
1
2
4
8
10.
090_0091_C02PSI_103031.indd 91
Personal Tutor Have students use
Personal Tutor to reteach the concept.
IWB
Using the Exercises
Exercise 2 Have groups of four students work together to
act out this problem.
Exercise 8 Encourage students to make a table to solve
this problem.
Exercise 9 Students might also choose to draw a picture
or act it out to solve this problem.
4 ASSESS
Formative Assessment
E WRITE MATH What strategy did
you use to solve Exercise 9? Explain
why your strategy makes sense.
See Answer Appendix.
Lesson 3C Multiply by Two-Digit Numbers
Reteach Worksheet
3 PRACTICE
9. Austin is having a birthday party
with 7 people. He asks the guests
to introduce themselves and shake
hands with each of the other
guests. How many handshakes
will there be? 21 handshakes
5. Mr. Clark buys about 15.8 gallons of
gas each week for his car. Each gallon
costs $2.79. Estimate how much will he
spend in 5 weeks? Sample answer:
about $240
AL
use one of these reteach options:
3 Use Cooperative Groups Ask small groups of
students to work together to choose strategies
and solve the Mixed Problem Solving Exercises.
For each Exercise, have a different group explain
the strategy they used and why they chose it.
8. Erica is saving money to buy a new
hamster cage. In the first week, she
saved $24.80. Each week after the
first, she saves $6.50. How much
money will Erica have saved in six
weeks? $57.30
4. A gel pen at a craft store costs
$1.05. Lucinda wants to buy three
gel pens. She has $5 to spend.
Estimate the amount of change she
will receive. about $2
students have trouble choosing the best
strategy to solve a problem . . .
Then
7. Algebra A certain type of bacterial
cell doubles every 10 minutes. Use
the table to determine how many
cells there will be after 60 minutes.
64 cells
2. Four friends ran a race. Benny finished
after Diego and before Alana. Marcia
finished after Benny but before Alana.
Who won the race? Diego
Alternate Teaching Strategy
If
6. Cameron has $40 in his bank
account and his brother, Caden,
has $35. Caden saves $5 per week
and Cameron saves $4 per week.
In how many weeks will they both
have the same amount in their
accounts? 5 weeks
Use any strategy to solve each problem.
AL
91
• Why is it helpful to use manipulatives, such as
counters, to solve some problems? Sample answer:
You can use counters to represent data in the problem.
Then you can use the act it out strategy.
2/25/10 5:08 PM
Are students continuing to struggle
with choosing a strategy to solve
a problem?
Multi-Part Lesson 3 Compare the Identity Property of Addition to the Identity
Property of Multiplication. Explain how they are similar and how they are
different. Sample answer: The Identity Property of Addition states that if 0 is
added to a number, the sum is the same as the given number. The Identity
Property of Multiplication states that if 1 is multiplied by a number, the product
is the same as the given number. In either case, the given number is
unchanged by adding zero or by multiplying by one.
During Small Group Instruction
If Yes
AL
Daily Transparencies
If No
OL
Differentiated Instruction Option 2
Differentiated Instruction Option 1
Skills Practice Worksheet
Enrich Worksheet
BL
OL
BL
(p. 81c)
(p. 81c)
Lesson 3C Multiply by Two-Digit Numbers
91
Objective
Interpret information and data from social studies to solve
problems.
Resources
Leveled Worksheets
Get ConnectED
GLE 0506.2.5 Develop fluency in solving multi-step
problems using whole numbers, fractions, mixed numbers,
and decimals. GLE 0506.1.7 Recognize the historical
development of mathematics, mathematics in context, and
the connections between mathematics and the real world.
✔ 0506.1.9 Use age-appropriate books, stories, and videos to
convey ideas of mathematics.
Activate Prior Knowledge
Before you turn students’ attention to the pages, ask them
to discuss the Wright Brothers.
• For what accomplishment were the Wright Brothers
famous? They were the first people to fly.
• What was the name of their flyer? the Kitty Hawk
Use the Student Page
Ask students to read the information on the student page
and answer these questions:
• Was the temperature on the day of the Wright
Brothers’ first flight greater or less than 0 degrees
Celsius? greater
• What was the difference between the distance of
the first flight and the second flight? 55 feet
Th W
The
Wright
i ht b
brothers
th
were
self-trained engineers from Ohio
who designed, built, and piloted
the first engine-powered airplane.
On December 17, 1903, the Wright
brothers completed the world’s first
successful controlled flight. They
later named the flyer the Kitty
Hawk, after the location in North
Carolina near where they made this
historic flight.
The temperature at Kitty Hawk
on this day was 34°F, but because
of the wind chill factor, the
temperature felt like 8°F. These
might not have been the most
comfortable weather conditions,
but the winds definitely helped
the Wright Brothers’ flyer to stay
in the air!
92
On
the
O that
th t cold
ld December
D
b day,
d
th
Wright brothers made four flights
in their flyer. On the first flight,
which was piloted by Orville Wright,
the flyer traveled 120 feet in
12 seconds. On the fourth flight,
Wilbur flew 852 feet in 59 seconds.
Wright Brothers’
1903 Flight Data
Flight
Distance (ft)
1
120
2
175
3
200
4
852
Multiply Whole Numbers
0092_0093_C02CC_101808.indd 92
Fast Facts
• Orville Wright was once quoted for saying, “The airplane stays up
because it doesn’t have the time to fall.”
• Orville and Wilbur Wright owned a bicycle business in Dayton,
Ohio called the Wright Cycle Company.
• Orville and Wilbur had three other siblings: Reuchlin, Lorin, and
Katharine.
• Three axes of motion (pitch, roll, and yaw) are essential to
controlling an airplane.
92
Multiply Whole Numbers
10/27/09 2:44 P
Assign the exercises. Encourage students to choose a
problem-solving strategy before beginning each exercise.
Exercise 2 Remind students that there are 60 seconds in
one minute.
Exercise 4 Remind students that they can also use an
area model to solve the problem.
Before their
experiments with
airplanes, the
Wright brothers were
successful bicycle
manufacturers.
E
WRITE MATH Have students create a word
problem that uses the information found in the text and in
the chart.
Orville and Wilbur Wright
Extend the Activity
Have students estimate the actual temperature and the
temperature with wind chill in degrees Celsius, and plot
the two temperatures on a number line to show the
difference between the two.
Use the information and the table to solve each problem.
092_0093_C02CC_101808.indd 93
1
How much farther was the fourth
flight than the first flight? 732 ft
2
During the first flight, Orville flew
about 10 feet per second. If he
were to keep that speed, how
many feet would he have flown
in 25 seconds? 250 ft
3
If Orville kept his speed during the
first flight for one minute, about
how many feet would he have
flown? 600 ft
4
During the fourth flight, Wilbur flew
about 14 feet per second. If he kept
a constant speed, about how many
feet did he fly in 15 seconds? 210 ft
5
The flyer weighed about 605 pounds.
If one pound is equal to 16 ounces,
about how many ounces did the flyer
weigh? 9,680 oz
6
S
Suppose
Orville Wright’s weight was
178 pounds at the time of the flight.
What was the combined weight of
the flyer and Orville Wright? 783 lb
Problem Solving in Social Studies
BL
93
10/27/09 2:45 PM
Problem Solving in Social Studies
93
Chapter Study
Guide and Review
Chapter Study
Guide and Review
The
BIG Idea
Be sure the following
Big Ideas are written
in your Foldable.
As a class, revisit this chapter’s Big Idea.
How can I multiply whole numbers accurately?
product
Who Multip
le N ly
umb
The
ers
D
Mult
iply
Mult
iply
istrib
utiv
e Pro
pert
ne-D
y
igit
Num
wo-D
bers
igit
Num
bers
by O
by T
Key Concepts with
Lesson 3A Under the last tab of the Foldable, students
demonstrate their ability to multiply multi-digit numbers
by a two-digit number.
Key Concepts
Multiplying Mentally (Lesson 1)
• You can multiply multiples of 10 mentally
by using basic facts and then counting
zeros in the factors.
2 zeros
•
• To multiply a sum by a number, multiply
each addend by the number. Then add.
5 × (10 + 2) = (5 × 10) + (5 × 2)
Multiplying Whole Numbers
Vocabulary Test
Vocabulary Check
3 zeros
Distributive Property (Lesson 1)
• Visual Vocabulary Card (24)
• eGlossary
1 zero
300 × 60 = 18,000
Key Vocabulary
Review chapter vocabulary using one of the following
options.
Distributive Property
factor
Sample answer: Using number patterns, partial products,
and multiplication properties can help you to multiply
whole numbers accurately.
Use this lesson suggestion to incorporate the Foldable
during the chapter. Students can then use their Foldables
to review for the test.
Vocabulary
(Lessons 2 and 3)
• The steps for multiplying by one- and
two-digit numbers are similar.
14
×
___3
_
42
If students have difficulty answering the exercises, remind
them they can use the Key Vocabulary terms listed on the
student page. You may wish to also direct them to the
lesson in which each term is taught.
94
14
× 23
_____
42
280
____
322
14 × 3 = 42
14 × 20 = 280
Vocabulary Check
State whether each sentence is true
or false. If false, replace the
underlined word or number to
make a true sentence.
1. In the sentence 8 × 2 = 16,
the numbers 8 and 2 are factors
of 16. true
2. The result when two numbers
are multiplied is called a
difference false; product
3. According to the Distributive
Property, 2 × (3 + 1) =
(2 × 3) + (2 × 1). true
4. To estimate 38 × 186, you could
find 40 × 200. true
5. When you multiply 80 and 70, the
result has 4 zeros. false; 2
6. The sentence 2 × 85 = 85 × 2
is an example of the Associative
Property. false; Commutative
Property
7. The Identity Property states that
a number multiplied by 1 equals
the number. true
Multiply Whole Numbers
0094_0099_C02SGR_103031.indd 94
Chapter Project
About How Much? In pairs, small groups, or as a class have students discuss the
results of their completed chapter project. Assess their work using the Project Rubric
found in the
Chapter Resource Masters.
94
Multiply Whole Numbers
3/9/10 10:16
Multi-Part Lesson Review
Lesson 1
Multi-Part Lesson Review
The Distributive Property
Multiplication Patterns
Find each product mentally.
8. 50 × 3 150
EXAMPLE 1
Find 20 × 70 mentally.
9. 26 × 10 260
The basic fact is 2 × 7 = 14. Now count
the zeros in the factors.
10. 80 × 90 7,200 11. 300 × 4 1,200
12. 420 × 100
42,000
1 zero
13. 500 × 600
300,000
The Distributive Property
The product will have 1 + 1 or 2 zeros.
Write 2 zeros to the right of 14.
15. 4 × (20 + 6)
• Use the multi-part lesson titles above each set of
exercises to review that topic in the Student Edition.
20 × 70 = 1,400
(Lessons 1B and 1C)
Rewrite each expression using the
Distributive Property. Then evaluate.
Intervention If the given examples are not sufficient to
review the topics covered by the questions, remind
students to:
1 zero
20 × 70
14. A bank cash machine has 600
$20 bills. What is the total value
of the $20 bills in the machine?
$12,000
•
15–22. See margin.
Rewrite 2 × (40 + 1) using the
Distributive Property. Then evaluate.
Find 2 × 40
and 2 × 1.
Add.
= 80 + 2
18. 2 × (80 + 1)
= 82
Find each product mentally using the
Distributive Property. Show the steps
that you used.
19. 3 × 17
20. 2 × 28
21. 8 × 31
22. 3 × 65
23. Mia fills 45 pages of her photo album
with photos that she took. If she puts
4 photos on each page, how many
photos are in the album? 180
Review Personal Tutors
Additional Answers
15. (4 × 20) + (4 × 6) = 104
= (2 × 40) + (2 × 1) Distributive Property
17. 7 × (10 + 2)
Get ConnectED
Reflecting on the Chapter
EXAMPLE 2
2 × (40 + 1)
16. 3 × (60 + 1)
094_0099_C02SGR_101808.indd 95
Have students complete the Multi-Part Lesson Review.
Then you can use ExamView® Assessment Suite to
customize another review worksheet that practices all the
objectives of this chapter or only the objectives on which
your students need more help.
(Lesson 1A)
16. (3 × 60) + (3 × 1) = 183
17. (7 × 10) + (7 × 2) = 84
18. (2 × 80) + (2 × 1) = 162
19. 3 × 17 = 3 × (10 + 7)
EXAMPLE 3
Find 3 × 24 mentally.
= (3 × 10) + (3 × 7)
3 × 24
= 30 + 21
= 3 × (20 + 4)
= (3 × 20) + (3 × 4)
= 60 + 12
= 72
= 51
Write 24 as 20 + 4.
20. 2 × 28 = 2 × (20 + 8)
Distributive
Property
= (2 × 20) + (2 × 8)
= 40 + 16
THINK: 3 × 20 = 60
and 3 × 4 = 12
Add 60 and 12.
= 56
21. 8 × 31 = 8 × (30 + 1)
Chapter Study Guide and Review
95
= (8 × 30) + (8 × 1)
= 240 + 8
12/11/09 12:44 PM
= 248
22. 3 × 65 = 3 × (60 + 5)
= (3 × 60) + (3 × 5)
= 180 + 15
= 195
Chapter Study Guide and Review
95
Chapter Study
Guide and Review
Additional Answers
24. 40 × 20 = 800
25. 10 × 70 = 700
26. 800 × 9 = 7,200
27. 500 × 30 = 15,000
Chapter Study Guide and Review
Lesson 2
Multiply by One-Digit Numbers
Estimate Products
24–29. See margin.
EXAMPLE 4
Estimate by rounding or compatible
numbers. Show your work.
24.
42
× 16
_____
25.
791
× 9
_____
27.
28. 80 × 800 = 64,000
29. 300 × 300 = 90,000
(Lesson 2A)
26.
28. 81 × 815
Estimate 21 × 38.
Round each factor to the nearest ten.
13
× 65
_____
21 →
× 38 →
_____
20 21 is rounded to 20.
× 40 38 is rounded to 40.
−−−
800
So, 21 × 38 is about 800.
521
× 27
_____
29. 312 × 259
EXAMPLE 5
30. Measurement A steamboat
tour guide makes the 148-mile
trip between Birmingham, Alabama,
and Chattanooga, Tennessee, four
times. Estimate the total number of
miles she travels. Show your work.
Sample answer: 150 × 4 = 600 mi
Multiply by One-Digit Numbers
43
×2
−−−
86
Round each factor to its greatest
place value.
46 →
× 107 →
______
50 46 is rounded to 50.
× 100 107 is rounded to 100.
−−−−
5,000
So, 46 × 107 is about 5,000.
(Lesson 2B)
EXAMPLE 6
Multiply.
31.
Estimate 46 × 107.
32.
67
×4
−−−
268
33. 112
×5
−−−
560
34. 6 × 32 35. 5 × 142 36. 381 × 3
1,143
192
710
37. A group uses 8 rafts on a white
water rafting trip. Each raft carries
14 people. How many people go
rafting? 112 people
Find 7 × 54.
Estimate 7 × 50 = 350
2
Step 1 Multiply the
ones. Regroup.
54
×7
8
Step 2 Multiply the
tens. Add the
new tens.
54
×7
378
2
So, 7 × 54 = 378. Since 378 is close to
the estimate, the answer is reasonable.
96
Multiply Whole Numbers
0094_0099_C02SGR_103031.indd 96
96
Multiply Whole Numbers
2/25/10 5:06
Problem-Solving Strategy: Draw a Picture
EXAMPLE 7
Solve by drawing a picture.
38. Rudy’s bedroom wall is 13 feet wide.
He wants to place two equal-size
picture frames side by side along the
wall so that the distance between each
frame and each edge of the wall is
4 feet. If each picture frame is 2 feet
wide, how many feet of space will be
between the two frames? 1 ft
39. A camp is putting a rope fence in
a lake to mark the end of the
swimming area. The rope is 60 yards
long. A buoy is placed at the beginning
of the rope. Another buoy is placed
every 10 yards. A buoy is placed at
the end of the rope. How many buoys
are there? 7 buoys
Lesson 3
(Lesson 2C)
Tony’s garden is a square 12 feet long.
He wants to plant shrubs 4 feet apart
around the garden. There will be a
shrub in each corner. How many shrubs
will he need?
Make a
drawing of
the garden
and the
shrubs.
4 ft
4 ft
4 ft
4 ft
4 ft
Tony will need 12 shrubs.
Multiply by Two-Digit Numbers
Multiply by Two-Digit Numbers
(Lesson 3A)
Multiply.
EXAMPLE 8
41.
42. 108
12
71
× 55
× 23
× 14
−−−−
−−−−
−−−
5,940
1,633
168
43. 52 × 130 6,76044. 42 × 312 13,104
Find 26 × 34.
40.
45. 19 × 63 1,197 46. 761 × 85 64,685
47. Measurement A giant salamander
weighs about 45 pounds. If 1 pound
equals 16 ounces, how many ounces
does a giant salamander weigh?
720 oz
094_0099_C02SGR_101808.indd 97
4 ft
Step 1
Multiply the
ones.
Step 2
Multiply the
tens.
2
1
26
× 34
−−−
104
26
× 34
−−−
104
780
Step 3
Add.
26
× 34
−−−
104
+ 780
−−−−
884
So, 26 × 34 = 884.
Chapter Study Guide and Review
97
12/11/09 2:19 PM
Chapter Study Guide and Review
97
Chapter Study
Guide and Review
Chapter Study Guide and Review
Multiplication Properties
(Lesson 3B)
Use properties of multiplication to find
each product mentally. Show your steps
and identify the properties that you
used. 48–49. See margin.
48. 4 × 28 × 25
49. (19 × 20) × 5
50. 10 × 4 × 7 28051. 15 × (4 × 5) 300
52. 100 × 32 × 3 53. 25 × (4 ×17)
9,600
1,700
54. Algebra What is the value of in
the equation below? 4
EXAMPLE 9
Use properties of multiplication to find
(14 × 2) × 5 mentally.
(14 × 2) × 5
= 14 × (2 × 5)
Associative Property
= 14 × 10
Find 2 × 5 mentally.
= 140
Find 14 × 10 mentally.
(35 × 4) × 5 = 35 × ( × 5)
Problem-Solving Investigation: Choose the Best Strategy
EXAMPLE 10
Solve each problem.
Algebra For a science experiment,
55. Find five consecutive odd numbers
that have a sum of 65.
9, 11, 13, 15, 17
56. Marina bought 3 sweaters and 2 pairs
of pants that coordinate. If she wears
only her new clothes, how many days
will pass before she must repeat an
outfit? 6 days
57. There are four rabbits. Fluffy is larger
than Max but smaller than Cotton.
Max is larger than Pepper. Which
rabbit is the smallest? Pepper
98
(Lesson 3C)
Miss Washington added 6 drops of
salt water to a solution on Day 1. She
added 11 drops on Day 2 and 16 drops
on Day 3. If the pattern continues, how
many drops of salt water will she add
on Day 5?
Day
1
2
3
4
5
Drops
6
11
16
21
26
+5
+5
2/25/10 5:06
Additional Answers
48. 4 × 28 × 25 = 4 × 25 × 28
Commutative Property
= (4 × 25) × 28
Associative Property
= 100 × 28
Find 4 × 25 mentally.
= 2,800
Find 100 × 28 mentally.
49. (19 × 20) × 5 = 19 × (20 × 5)
Multiply Whole Numbers
+5
Multiply Whole Numbers
0094_0099_C02SGR_103031.indd 98
98
+5
So, on Day 5, she will add 26 drops of
salt water.
Associative Property
= 19 × 100
Find 20 × 5 mentally.
= 1,900
Find 19 × 100 mentally.
Practice
Chapter Test
Find each product mentally. 2. 420,000
1. 400 × 5 2,000
2. 60 × 7,000
Find each product mentally using the
Distributive Property. Show your work.
3–6. See Answer Appendix.
4. 3 × 27
3. 4 × 35
7. The sports center is buying new
equipment. Use the table to find the
cost of 7 kickballs and 5 basketballs. $153
Ball
Basketball
Kickball
Soccer ball
Cost
$11
$14
$19
92
× 31
_____
9.
B. 320
D. 240
Multiply.
11.
46 690
× 15
_____
12.
108 2,268
× 21
_____
Chapter Tests
Type
Level
Form
62 cm
AL
Multiple Choice
1A
16. MULTIPLE CHOICE Identify the
multiplication property that is shown
in the sentence below. G
(14 × 2) × 50 = 14 × (2 × 50)
AL
Multiple Choice
1B
OL
Multiple Choice/Free
Response
2A
OL
Multiple Choice/Free
Response
2B
BL
Free Response
3A
BL
Free Response
3B
H. Distributive
I. Identity
17. A technician installed speakers around
a square auditorium. She places 10
speakers on each side and one at each
corner. How many speakers did she
install? Use the draw a picture strategy.
44
10. MULTIPLE CHOICE Each hour, about
88 people visit a particular tourist
attraction in Florida. At this rate,
about how many people will visit the
attraction in four hours? A
C. 270
Use these alternate leveled chapter tests to differentiate
assessment for the specific needs of your students.
34 cm
G. Associative
410
× 77
_____
A. 360
Summative Assessment
15. Measurement The area of a
rectangle is the product of its length and
width. What is the area of the rectangle
below in square centimeters? 2,108 sq cm
F. Commutative
8–9. See Answer Appendix.
Estimate. Show your work.
8.
19. Waban likes mysteries, Josie
likes science fiction, and Jacylyn
likes biographies.
6. 2 × 49
5. 5 × 63
Practice
Chapter Test
Additional Chapter Resource Masters
18. Identify the multiplication property that
is shown in the sentence below.
4 × 1 = 4 Identity
19. Waban, Josie, and Jacylyn like
mysteries, biographies, and science
fiction, but not necessarily in that order.
Josie does not like mysteries or
biographies. Jacylyn does not like
mysteries or science fiction. Which type
of book does each like to read?
20.
E
AL
OL
BL
at a table. If two tables are put
together, 6 people can be seated. How
13.
14. 179 2,148
53 1,590
many tables are needed to make a long
× 30
× 12
_____
_____
table that will seat 12 people? Explain.
20. 5 tables; Sample answer: Since one table seats 4 people and two tables seat 6 people, adding a
table will seat two more people than before. Continuing the pattern, three tables seat 8 people, four
Practice Chapter Test 99
tables seat 10 people, and 5 tables seat 12 people.
Data-Driven Decision Making
Vocabulary Test
OL
Extended Response Test
OL
Oral Assessment
= approaching grade level
= on grade level
= beyond grade level
Customize and create multiple
versions of your Chapter Test and the test answer keys.
WRITE MATH Four people can sit
094_0099_C02SGR_101808.indd 99
OL
11/5/09 7:29 PM
Based on the results of the Chapter Test, use the following to review concepts that continue to present students with problems.
Exercises
1–7
Tennessee
Standards
GLE 0506.2.5
What’s the Math?
Error Analysis
Use basic facts and patterns to
multiply. Use the distributive property
to mentally multiply.
Does not know basic multiplication facts.
Does not understand distributive property.
Resources for Review
Chapter Resource Masters
Get ConnectED
8–14
16, 18
GLE 0506.2.5
Estimate by rounding, then multiply.
Know associative property in
multiplication.
Does not know “estimate by rounding,”
“associative property.”
15
GLE 0506.2.5
Find the area of a rectangle.
Does not understand “product.” Computes
inaccurately.
17, 19, 20
GLE 0506.1.2
Use problem-solving strategies to
solve problems.
Does not read accurately. Does not know all
needed components to solve a problem.
Lesson Animations • Personal Tutor
• Self-Check Quiz
Practice Chapter Test
99
Test Practice
Test Practice
1 INTRODUCE
As a class, discuss the example on the page. As students
make estimates, it is often helpful to ask them to consider
a variety of methods. Students may choose to round one
factor, to round both factors, or to use compatible
numbers. In the example provided, only one factor was
rounded. This method provides the best estimate because
the result is closest to the exact answer.
A souvenir shop has 51 boxes of seashells
in stock. Each box contains 9 shells. Which
number is the best estimate for the total
number of shells?
A. 380
C. 420
B. 400
D. 450
You can use the Associative
Property of Multiplication to
change the way the factors
are grouped.
Read the Test Item
You need to estimate the total number of shells.
2 TEACH
Before beginning the practice test, give students an
opportunity to solve the Additional Example.
Solve the Test Item
You know the souvenir shop has 51 boxes of
seashells with 9 shells in each box. To estimate the
total number of shells, round 51 to 50 and multiply.
So, the total number of seashells is about 50 × 9 or
450 shells. The answer is D.
Mrs. Ross earns $78 a week tutoring students.
Which number is the best estimate of her yearly
earnings if she works every week in the year? B
A. $40,000
B. $4,000
C. $3,500
D. $400
IWB INTERACTIVE WHITEBOARD READY
Read each question. Then fill in the correct answer on the
answer sheet provided by your teacher or on a sheet of paper.
1. Kenny has 250 stickers in his collection.
He has 40 stickers more than Placido
and 25 stickers less than Paloma. How
many stickers does Paloma have? C
A. 210
B. 225
2.
GRIDDED RESPONSE How much
larger is the area of Colorado than
Utah, in square miles? 19,309
State
Area (sq mi)
Colorado
104,185
Utah
84,876
C. 275
D. 290
100 Multiply Whole Numbers
0100_0101_C02STP_103031.indd 100
3 ASSESS
Formative Assessment
• Use these pages as practice and cumulative review. The
questions are written in the same style as those found
on standardized tests.
• You can use these pages to benchmark student
progress, or as an alternative homework assignment.
100
Multiply Whole Numbers
3/9/10 10:19
3. A car rental company has 7 luxury cars
and 22 sedans on its lot. Each vehicle
has 4 wheels. How many wheels are
there altogether at the car rental
company lot? H
F. 84
Answer Sheet Practice
6. During the first week of school, Mrs.
Mease asked each of her students to
bring in three boxes of tissues. If
there are 12 boys and 15 girls in
Mrs. Mease’s classroom, how many
boxes of tissues will there be? G
Have students simulate taking a standardized test by
recording their answers on a practice recording sheets.
Student Recording Sheet
057_080_C02_101834.indd Page 79
10/30/09
1:20:52 AM elhi1
G. 108
Name _____________________________ Date ________________
G. 81
H. 116
Student Recording Sheet
H. 84
I. 122
Use this recording sheet with the Test Practice pages located at the end
of the chapter in the Student Edition.
Read each question. Then fill in the correct answer.
I. 92
1.
A
B
C
D
Price ($)
1
2
3
4
5
1.00
1.80
2.60
3.40
?
7.
SHORT RESPONSE Show how to
use the Distributive Property to find
4 × (9 + 6).
(4 × 9) + (4 × 6) = 36 + 24 or 60
8. Mrs. O’Brien has 28 calculators in her
classroom. If each calculator takes
4 batteries, how many batteries are
needed altogether? A
A. $3.80
B. $4.00
A. 112
C. $4.10
B. 116
D. $4.20
C. 118
SHORT RESPONSE There are 9
tables in the school cafeteria. Each
table can seat 12 people. If every table
is full, how many people are seated in
the cafeteria at the same time? Draw a
diagram to solve. See margin.
9.
A
B
C
D
9.
3.
F
G
H
I
4.
A
B
C
D
F
G
H
I
5.
6.
79
Additional Practice
GRIDDED RESPONSE A car
wash company charges $9 per car. If
86 cars were washed in one day, how
much money, in dollars, would the
company collect? 774
NEED EXTRA HELP?
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Grade 5 • Multiply Whole Numbers
D. 124
5.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. The price of a stock over the past
4 weeks is shown in the table. If the
pattern continues, what will the price
be after 5 weeks? D
7.
8.
2.
Week
/Volumes/121/GO00398/GO00398_Math_Connects_CRM_NA_G5%0/XXXXXXXXXXXXX_SE/Appli...
F. 71
•
Standardized Test Practice
•
Get ConnectED
•
Find additional test practice.
Create practice worksheets or
tests that align to your state’s
standards.
GLE 1.2 GLE 1.2 GLE 2.5 GLE 1.2 GLE 1.2 GLE 2.5 GLE 2.5 GLE 2.5 GLE 2.5
Test Practice 101
100_0101_C02STP_103031.indd 101
2/25/10 5:08 PM
Additional Answer
5. 432
12
12
12
12
12
12
12
12
12
Test Practice
101
Chapter Answer Appendix
Multi-Part Lesson
1
PART A
PAGE 63
40. Sample answer: You can write the basic fact and find its product.
Then add 4 zeros since there are 4 zeros in the factors. The basic
fact for 10 × 20 × 30 × 40 is 1 × 2 × 3 × 4. Add 4 zeros to
24. The product is 240,000.
PART C
PAGES 67–68
4. 6 × 13 = 6 × (10 + 3)
= (6 × 10) + (6 × 3)
= 60 + 18
= 78
5. 3 × 52 = 3 × (50 + 2)
= (3 × 50) + (3 × 2)
= 150 + 6
= 156
6. 5 × 26 = 5 × (20 + 6)
= (5 × 20) + (5 × 6)
= 100 + 30
= 130
7. 4 × 69 = 4 × (60 + 9)
= (4 × 60) + (4 × 9)
= 240 + 36
= 276
8. 2 × 49 = 2 × (40 + 9)
= (2 × 40) + (2 × 9)
= 80 + 18
= 98
9. 7 × 23 = 7 × (20 + 3)
= (7 × 20) + (7 × 3)
= 140 + 21
= 161
11. Sample answer: You can think of one of the factors as the sum
of two numbers, each of which can be easily multiplied by the
other factor. Then use the Distributive Property to multiply each
part by the other factor and then add.
23. 52 × 3 = 3 × (50 + 2)
= (3 × 50) + (3 × 2)
= 150 + 6
= 156
24. 2 × 31 = 2 × (30 + 1)
= (2 × 30) + (2 × 1)
= 60 + 2
= 62
25. 3 × 63 = 3 × (60 + 3)
= (3 × 60) + (3 × 3)
= 180 + 9
= 189
101a Multiply Whole Numbers
26. Sample answer: 5 × 36 = 5 × (30 + 6)
= (5 × 30) + (5 × 6)
= 150 + 30
= 180
27. Sample answer: 9 × 23 = 9 × (20 + 3)
= (9 × 20) + (9 × 3)
= 180 + 27
= 207
28. 210; 6 × 35 = 6 × (30 + 5)
= (6 × 30) + (6 × 5)
= 180 + 30
= 210
Multi-Part Lesson
2
PART B
PAGE 76
10. Multiply the ones: 6 × 3 = 18. Write 8 in the ones place and
regroup by writing 1 above the tens place. Multiply the tens:
1 × 3 = 3. Then add the 1 from regrouping: 3 + 1 = 4. Write
4 in the tens place. Multiply the hundreds: 4 × 3 = 12. Write
12 in the hundreds place. The product is 1,248.
PART C
PAGE 79
1. Sample answer: By drawing a picture, you could see exactly
where to place each booth and how much space was used.
2. Sample answer: By drawing a picture, you can see exactly how
many booths can be put in the given dimensions. The other
strategies do not allow you to visually understand the problem.
4. Sample answer: finding the distance around a garden given the
dimensions
11. Sample answer: They allow you to see the problem situation
which helps you understand the problem better.
Mid-Chapter Check
8. 5 × 17 = 5 × (10 + 7)
= (5 × 10) + (5 × 7)
= 50 + 35
= 85
9. 3 × 71 = 3 × (70 + 1)
= (3 × 70) + (3 × 1)
= 210 + 3
= 213
10. 6 × 25 = 6 × (20 + 5)
= (6 × 20) + (6 × 5)
= 120 + 30
= 150
11. 2 × 37 = 2 × (30 + 7)
= (2 × 30) + (2 × 7)
= 60 + 14
= 74
PAGE 80
Commutative Property
Associative Property
Find 200 × 5 mentally.
Find 1,000 × 14 mentally.
13. 2 × 31 = 2 × (30 + 1)
= (2 × 30) + (2 × 1)
= 60 + 2
= 62
10. Sample answer: Use the Commutative Property to rewrite the
expression as 50 × 2 × 35. Then use the Associative Property to
group 50 and 2: (50 × 2) × 35. Then use mental math to find
the value. (50 × 2) × 35 = 100 × 35 = 3,500
15. Sample answer: 40 × 8 = 320
33. Sample answer: 20; If 20 is a factor, then you could use the
Associative Property to write 87 × (20 × 5) = 87 × 100 =
8,700.
16. Sample answer: 20 × 60 = 1,200
17. Sample answer: 100 × 50 = 5,000
34. Sample answer: (7 × 4) × 5 = 7 × (4 × 5); it is easier to
multiply 7 and 20 mentally than it is to multiply 28 and
5 mentally.
18. Sample answer: 300 × 60 = 18,000
20. Sample answer: 1,600; 400 + 400 + 400 + 400
25. Sample answer: 250; 216; The estimate is close to the
actual amount.
Multi-Part Lesson
3
PAGES 82– 84
PART A
10. Sample answer: Each digit in a 2-digit number is multiplied by
the other factor. Then the two products are added to find the
final product.
36. Sample answer: 9 × 8 × 7 × 6 = 3,024. It is the greatest
product because the four greatest numbers from 1 through
9 were factors.
35. Sample answer:
4 × 96 × 25 × 50 × 2
= 96 × 4 × 25 × 50 × 2
Commutative Property
= 96 × (4 × 25) × (50 × 2) Associative Property
= 96 × 100 × 100
Find 4 × 25 and 50 × 2 mentally.
= 96 × (100 × 100)
Associative Property
= 96 × 10,000
Find 100 × 100 mentally.
= 960,000
Find 96 × 10,000 mentally.
36. Sample answer: true; The order in which factors are multiplied
or grouped does not change the product.
PART C
PAGE 91
10. Act it out; You can find the total number of handshakes by
having 7 people shake hands with each other.
46. 216 cups; 6 × (30 + 6) = (6 × 30) + (6 × 6)
= 180 + 36
= 216
Practice Chapter Test
PART B
PAGE 99
PAGES 87–88
3. 5 × 2 × 34 = (5 × 2) × 34
= 10 × 34
= 340
Associative Property
Find 5 × 2 mentally.
Find 10 × 34 mentally.
3. Sample answer: 4 × 35 = 4 × (30 + 5)
= (4 × 30) + (4 × 5)
= 120 + 20
= 140
4. 2 × 51 × 50 = 2 × 50 × 51
= (2 × 50) × 51
= 100 × 51
= 5,100
Commutative Property
Associative Property
Find 2 × 50 mentally.
Find 100 × 51 mentally.
4. Sample answer: 3 × 27 = 3 × (20 + 7)
= (3 × 20) + (3 × 7)
= 60 + 21
= 81
5. (8 × 4) × 5 = 8 × (4 × 5)
= 8 × 20
= 160
Associative Property
Find 4 × 5 mentally.
Find 8 × 20 mentally.
6. 4 × (25 × 6) = (4 × 25) × 6
= 100 × 6
= 600
Associative Property
Find 4 × 25 mentally.
Find 100 × 6 mentally.
7. 9 × 500 × 2 = 9 × (500 × 2)
= 9 × 1,000
= 9,000
Associative Property
Find 500 × 2 mentally.
Find 9 × 1,000 mentally.
5. Sample answer: 5 × 63 = 5 × (60 + 3)
= (5 × 60) + (5 × 3)
= 300 + 15
= 315
6. Sample answer: 2 × 49 = 2 × (50 - 1)
= (2 × 50) - (2 × 1)
= 100 - 2
= 98
8. Sample answer: 90 × 30 = 2,700
9. Sample answer: 400 × 80 =32,000
Chapter Answer Appendix
101b
Chapter Answer Appendix
8. 200 × 14 × 5 = 200 × 5 × 14
= (200 × 5) × 14
= 1,000 × 14
= 14,000
12. 4 × 43 = 4 × (40 + 3)
= (4 × 40) + (4 × 3)
= 160 + 12
= 172
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Tennessee Math Connects, Grade 5