Sách Toán tiếng anh tham khảo hay_Progress in mathematics grade 5

For Progress in Mathematics Grades 3-6

www.progressinmathematics.com
AUDIO LEARNING

HEAR THE MATH!
VISUAL LEARNING

SEE THE MATH!
INTERACTIVE LEARNING

DO THE MATH!
SHARED LEARNING

SHARE THE MATH!

Sadlier-Oxford
A Division of William H.
Sadlier,
Inc.
Sadlier-Oxford
New York, NY 10005- SGT 1
1002

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Introduction

At www.progressinmathematics.com,
you will find a lot of technology resources that you can use at
home, and your teacher may make them available when you are
at school.

Technology Resources:
www.progressinmathematics.com

AUDIO GLOSSARY
From A to Z Find the meanings and hear the pronunciations
of math words and phrases.
ALTERNATIVE TEACHING MODELS
Tutorials Watch and listen to these animated math lessons.
VIRTUAL MANIPULATIVES
Manipulatives Practice and model math concepts with
virtual manipulatives.
PRACTICE
Problem of the Day Tackle a new problem every day!
Skills Update Review your skills with Lesson and
Practice pages.
Math Minutes Race against the clock with timed activities!
Practice Activities Practice makes perfect with these
fun activities!
Vocabulary Activities Review your math vocabulary while
playing Hangman or Word Scramble.
ENRICHMENT
Activities Challenge yourself with these interactive activities.
MATH ALIVE AT HOME
Take-Home Activities Share your

math experience at home!

SGT 2

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INTERACTIVE

AUDIO LEARNING

COMPATIBLE

AUDIO GLOSSARY
Click From A to Z.
If you are not sure what a certain word means or how
to pronounce it, use your online Audio Glossary. The
glossary is easy to use. Just choose your grade level
and the first letter of the term you want to review.
www.progressinmathematics.com

Grade home

Glossary home

# A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

1 Choose the first

letter of a term you
want to review.

2 Click on

3 Listen as

the glossary
pronounces
the word.

the term.

GRADE 3

SGT 3

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INTERACTIVE

VISUAL LEARNING

COMPATIBLE

ALTERNATIVE TEACHING MODELS

Click Tutorials.
If there is a skill or concept
that you need help with or do
not understand, review the
animated Alternative Teaching
Models (there are 2 for each
chapter). Each Alternative
Teaching Model gives a stepby-step explanation of one of
the skills or concepts in the
chapter.

www.progressinmathematics.com

Red Team
Blue Team
Green Team

www.progressinmathematics.com
Red Team
Blue Team

GRADE 3
SGT 4

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INTERACTIVE

VIRTUAL MANIPULATIVES
Click Manipulatives.
Virtual Manipulatives are
visual models that you
can actually move or
manipulate to show what
is happening. You can
use these tools to build
numbers, rotate shapes,
and even jump on a
number line.
Select your grade and the
chapter you are working
on. The manipulatives
that are listed will be
ones that you can use to
visualize the concepts of
the chapter.

COMPATIBLE

www.progressinmathematics.com

GRADE 6

www.progressinmathematics.com

GRADE 5

SGT 5

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INTERACTIVE

INTERACTIVE LEARNING

COMPATIBLE

PRACTICE
Click Practice Activities.
There is an interactive activity for
each chapter in your textbook.
The activity practices the most
important skills of the chapter.
Use the activity while you are
learning the skills, or come back
to it later to review.

www.progressinmathematics.com

www.progressinmathematics.com

www.progressinmathematics.com

GRADE 4

Click Math Minutes.
You can practice your basic facts
as well as compute with larger
numbers to see how accurately
you can compute if you are given
a time limit.
Click Vocabulary Activities.
In each chapter, you will be
learning new math terms that
you will need to know. A good
way to review these terms is to
play either the Hangman game
or Word Scramble in your online
vocabulary activities.

SGT 6

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www.progressinmathematics.com

GRADE 4

www.progressinmathematics.com

GRADE 5

7/25/08 12:12:53 PM

INTERACTIVE
COMPATIBLE

www.progressinmathematics.com

Click Problem of the Day.*
Sharpen your problemsolving skills every day.
Print and solve one
problem each day!
www.progressinmathematics.com

GRADE 6
Name

Date

Count by 2s, 5s, 10s

Click Skills Update.*
Print Skills Update lessons
and practice pages to review
previously taught math skills
and concepts.

Count by 2s.
14
16 ______,
18 20, ______,
22

24
26
28
1. 12, ______,
______,
______,
______,
______
17
19 ______,
21 23, ______,
25
27
29
31
2. 15, ______,
______,
______,
______,
______
Count by 5s.
20
30
35
40
45
50
55
3. 15, ______,
25, ______,

______,
______,
______,
______,
______
35
45
50
55
60
65
70
4. 30, ______,
40, ______,
______,
______,
______,
______,
______
Count by 10s.
20
30
40
50
60 ______,
70
80
90
5. 10, ______,
______,

______,
______,
______,
______,
______
30
40
50
60
70 ______,
80
90
100
6. 20, ______,
______,
______,
______,
______,
______,
______
Write the missing numbers.
16
18 20
7. 10, 12, 14, ______,
______,

28 30, ______
32
8. 22, 24, 26, ______,

GRADE 3

ENRICHMENT

www.progressinmathematics.com

Click Activities.
The Enrichment activities
online are topics that go
beyond what you are learning
in class.
Each activity starts with a page
that explains the concept and
then gives you time to practice
the concept.

*Whiteboard projectable only.

001_008_3603_2_PE3-6.indd 7

GRADE 3

SGT 7

7/25/08 12:13:01 PM


SHARED LEARNING

MATH ALIVE AT HOME

Click Take-Home Activities.
Keep your family involved in
what you are learning. For
each chapter, there are two
letters to your family. Use the
first letter at the beginning
of the chapter, to review
previously learned skills with
a family activity, and read
about the new skills you will
learn. The second letter tells
your family about the skills you
learned in the chapter and has
another fun activity that you
and your family members can
do together.

www.progressinmathematics.com
Dear Family,

m quantities granted to users of Progress in Mathematics.

will learn about place value. Let’s do
Today our class began Chapter 1. We
to
review the skills I will need in order
the activity below together so I can
r. Then we can read some of the new
understand the math in this chapte
1.

vocabulary I will learn in Chapter
Love, ____________________

How Many Tens, How Many Ones?

tens

With your child, list the age of everyone in your family
on a sheet of paper. Ask your child to say how many
tens and how many ones there are in each age.
Draw a frame like the one at the right for each family
member. Tell your child to write in each frame the
number of tens and ones for each age. Then have
her/him write an addition with the number of tens and
the number of ones for each age, and find the sum.

+

ones

=

Chapter 1
expanded form
shows the place value of the digits
in a number
600 ϩ 40 ϩ 7

nearest ten
the number achieved after rounding

to the nearest ten
251

standard form
647

250

nearest hundred
the number achieved after rounding
to the nearest hundred

thousand

GRADE 3 - ENGLISH

Both letters are in English and
in Spanish.

Querida familia:

r
1. Aprendimos a leer, escribir, compara
Hoy nuestra clase terminó el capítulo
o
de miles. Este conocimiento es necesari
y ordenar números hasta los cientos
mos
r el valor posicional. Aprendi
para trabajar con números y para entende

nos
en 4, de 5 en 5 y de 10 en 10, lo que
a contar de 2 en 2, de 3 en 3, de 4
ar
de multiplicación. Aprendimos a redonde
servirá para aprender operaciones
o millar más cercano. Este
centena
decena,
la
hasta
dígitos
4
y
números de 3
También
.
números
con
ones
estimaci
conocimiento es necesario para hacer
cambio.
ayudará a la hora de dar o recibir
practicamos con dinero, lo cual nos
________
Con cariño, _____________________

Dear Family,

users of Progress in Mathematics.

Key Skills and Concepts
Students’ learning in Chapter 1 was guided by giving particular emphasis to the
following key skills and concepts:

• Identify the place value for each digit in

tics, para reproducir esta página para sus estudiantes.

1. We learned how to read, write,
Today our class completed Chapter
thousands. These skills are
compare, and order numbers to hundred
understand place value.
to
and
numbers
with
needed to work
with 2s, 3s, 4s, 5s, and 10s, which
We explored patterns of skip counting
facts. We practiced rounding 3- and
will help us to learn multiplication
, or thousand. This skill is
hundred
ten,
4-digit numbers to the nearest
Destrezas y conceptos claves
. We also worked with money,

necessary for estimating with numbers
Lo que aprendieron los estudiantes en el capítulo 1 se hizo poniendo énfasis
change.
count
and
make
us
which will help
en las siguientes destrezas y conceptos claves:
Love, ________________________
• Identificar el valor posicional de cada dígito de • Usar la forma desarrollada de representar
números hasta el 10,000.
números.
NS 2.3

U

l

it

i

i

i

t

d l

id

l

d

iñ

t

d

• Use expanded notation to represent numbers.

numbers to 10,000.
NS 2.3

GRADE 3 - SPANISH

GRADE 3 - ENGLISH
SGT 8

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8205-4_Proto_i

10/5/05

4:20 PM

Page i

Catherine D. LeTourneau
Alfred S. Posamentier
with

Elinor R. Ford

Madelaine Gallin

Frank Lucido

Lucy Lugones

Former Math Coordinator
Community School District #6
New York, NY

Associate Professor in
Bilingual/Multicultural Education
Texas A&M University
Corpus Christi, TX

Math Coordinator
St. Luke’s School
Whitestone, NY

Tim Mason

R. James Milgram

Rosalie Pedalino Porter

Title 1 Specialist
Palm Beach County School District
West Palm Beach, FL

Professor of Mathematics
Stanford University
Palo Alto, CA

Consultant Bilingual/ESL Programs
Amherst, MA



Sadlier-Oxford
A Division of William H. Sadlier, Inc.
www.sadlier-oxford.com


3605-6_PE5_ii_Copyright:8205-4_Proto_22-23PSintro copy

7/31/08

10:03 AM

Page ii

The publisher gratefully acknowledges Rose Anita McDonnell (1905–2003)
and her colleagues for the important role they played in the development of
Progress in Mathematics for more than sixty years.

The publisher wishes to thank the following teachers and administrators, who read
portions of the series prior to publication, for their valuable contributions.

Grades 3–6 Reviewers
Madonna Atwood

John Palladino

Debra Wright

Teacher
St. Louis, MO

Professor at Eastern Michigan University
Ypsilanti, MI

Principal
Winter Haven, FL

Judith A. Devine

Stephanie D. Garland

Educational Consultant
Springfield, PA

Educational Consultant
St. Louis, MO

Grade-Level Reviewers
Marie Bicsak

Sara Kobylarz

Br. Ralph Darmento, F.S.C.

Math Coordinator
Mt. Clemens, MI

Grade 3 Teacher
Bronx, NY

Deputy Superintendent of Schools
Newark, NJ

Suzanne Ryan

Candace Govin

Sr. Adriana Cernoch

Grade 4 Teacher
Orono, MN

Grades 4–8 Math Teacher/Coordinator
Plantation, FL

Grade 6 Teacher
Dallas, TX

Brandy Roth

Elizabeth M. Johnson

Linda Hamby

Grade 3 Teacher
Kissimmee, FL

Grade 5 Teacher
Bettendorf, IA

Grade 5 Teacher
DesPeres, MO

Barbara Murphy

Sr. Martha Carmody, O.P.

Jacqueline A. Byrd

Grade 4 Teacher
Chesterfield, MO

Grade 4 Teacher
Springfield, IL

Grade 5 Teacher
Chesterfield, MO

Sr. Maristella Dunlavy, O.P.

Jeannine Frey

Mary E. Stokes

Principal
Springfield, IL

Grade 3 Teacher
Chesterfield, MO

Grade 5 Teacher
Oak Forest, IL

Copyright © 2009 by William H. Sadlier, Inc. All rights reserved.
This publication, or any part thereof, may not be reproduced in any form, or by any means, including electronic,
photographic, or mechanical, or by any sound recording system, or by any device for storage and retrieval of information,
without the written permission of the publisher. Address inquiries to Permissions Department, William H. Sadlier, Inc.,
9 Pine Street, New York, NY 10005-1002.
is a registered trademark of William H. Sadlier, Inc.
Printed in the United States of America
ISBN: 978-0-8215-3605-6

456789 RRDW 13 12 11 10


8205-4_iii

4/26/06

9:40 AM

Page iii

Progress in Mathematics, now in its sixth decade of user-proven success,
is a complete basal mathematics program. Written by experienced teacherauthors, it integrates a traditional course of study and today’s academic
Standards with the most up-to-date methods of teaching.
Progress in Mathematics is designed to meet the individual needs of all
learners. Teachers who use Progress come to understand that students
may progress as quickly as they can or as slowly as they must.
In Grade 5, the concepts of fractions and decimals will be further developed,
and your fifth grader will use all four operations with these number types.
There will also be an increased emphasis on algebraic thinking. Other topics
that are studied include: statistics, geometry, measurement, probability,
percents, and proportions. Special attention is given to critical thinking,
problem solving, mental math, and journalizing.
But overall success in achieving the goals of this program depends on
ongoing teacher-family-student interaction. It is important for you to
encourage your fifth grader to achieve success in mathematics and enjoy
it as well. You can help your student see math as useful and practical by
relating it to everyday situations. It is also helpful to provide a quiet space
and time for homework, and to reinforce the idea that by practicing math
concepts and skills in your home environment, your student can have fun

while learning mathematics.
Throughout the school year, you and your student can access
Math Alive At Home pages at www.sadlier-oxford.com. These
pages include the math vocabulary of each chapter plus
fun-filled activities that will help you relate the math your
student is learning in school to the real world.
We know that by using Progress in Mathematics
your fifth grader will not only learn to value math,
but become a confident problem solver and
learn to reason and communicate
mathematically as well.

iii


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Letter to the Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Skills Update
A handbook for reviewing essential
and previously taught skills
An Introduction to Skills Update . . . . . . . . xii
Numeration
I
Place Value to Thousands. . . . . . . . 1
II
Compare and Order
Whole Numbers
........2

III
Round Whole Numbers. . . . . . . . . . 3
Whole Number Operations
I
Add and Subtract
Whole Numbers . . . . . . . . . . . . . 4
II
Multiply One Digit . . . . . . . . . . . . . . 5
III
One-Digit Quotients . . . . . . . . . . . . 6
IV
Two-Digit Quotients . . . . . . . . . . . . . 7
Fractions
I
Fractions . . . . . . . . . . . . . . . . . . . . . 8
II
Equivalent Fractions
......9
III
Add and Subtract Fractions:
Like Denominators . . . . . . . . . . 10

Decimals
Tenths and Hundredths . . . . . . . . . 11
Geometry
I
Geometric Concepts . . . . . . . . . . . 12
II
Identify Polygons. . . . . . . . . . . . . . 13
Measurement

I
Customary Units of Length . . . . . . 14
II
Customary Units of Capacity
and Weight . . . . . . . . . . . . . . . . 15
III
Metric Units of Length . . . . . . . . . . 16
IV
Metric Units of Capacity
and Mass. . . . . . . . . . . . . . . . . . 17
Statistics
I
Make Pictographs . . . . . . . . . . . . . 18
II
Make Bar Graphs . . . . . . . . . . . . . 19
Probability
I
Equally/Not Equally Likely
Outcomes . . . . . . . . . . . . . . . . . 20
II
List Outcomes . . . . . . . . . . . . . . . . 21

Introduction to
Problem Solving
Problem-Solving Model . . . . . . . . . . . . . . 22
Problem-Solving Strategy:
Logical Reasoning . . . . . . . . . . . . . . . . 24
Problem-Solving Strategy:
Interpret the Remainder . . . . . . . . . . . . 25
Problem-Solving Strategy:

Use More Than One Step . . . . . . . . . . 26
Problem-Solving Strategy:
Make a Table . . . . . . . . . . . . . . . . . . . . 27
Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . . . . . . 28
iv

* Develops concept or skill with manipulatives.

Lesson promotes algebraic reasoning.


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Chapter

Chapter

Place Value, Addition,
and Subtraction

Multiplication

Chapter Opener . . . . . . . . . . . . . . . . . . . . 29

2-1

Factors and Products

2-2

Properties of
Multiplication

* 1-1

What Is a Billion? . . . . . . . . . . . . . 30

1-2

Place Value to Billions . . . . . . . . . . 32

1-3

Expanded Form . . . . . . . . . . . . . . 34

1-4

Thousandths . . . . . . . . . . . . . . . . . 36

1-5

Decimals Greater Than One . . . . . 38

1-6

Compare and
Order Numbers

Chapter Opener . . . . . . . . . . . . . . . . . . . . 65

. . . . 66
. . . . . . . . . 68

2-3

Mental Math: Special Factors . . . . 70

2-4

Patterns in Multiplication

2-5

Estimate Products. . . . . . . . . . . . . 74

2-6

Zeros in the Multiplicand . . . . . . . . 76

. . . . . . . 40

2-7

Multiply Two Digits. . . . . . . . . . . . . 78

1-7

Rounding Numbers . . . . . . . . . . . . 42

2-8

Multiply Three Digits . . . . . . . . . . . 80

1-8

Addition Properties/
Subtraction Rules

2-9

Zeros in the Multiplier . . . . . . . . . . 82

. . . . . 44

2-10

Multiplication with Money . . . . . . . 84

Estimate Sums and
Differences . . . . . . . . . . . . . . . . 46

2-11

Problem-Solving Strategy:

Addition: Three or More
Addends
. . . . . . . . . . . . 48

2-12

1-9
1-10

. . 72

Use More Than One Step . . . . . . . 86

Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . . 88

1-11

Subtraction with Zeros . . . . . . . . . 50

1-12

Larger Sums and Differences . . . . 52

Check Your Progress (Lessons 1–12) . . 90

1-13

Roman Numerals . . . . . . . . . . . . . 54

Problem-Solving Strategy:

Enrichment: Exponents

1-14

Guess and Test
1-15

. . . . . . . . . 56

Problem-Solving Applications:

End of Chapter
. . . . . . . . 91

Chapter 2 Test. . . . . . . . . . . . . . . . . . . . . 92
Cumulative Review. . . . . . . . . . . . . . . . . 93

Mixed Review . . . . . . . . . . . . . . . . 58
End of Chapter
Check Your Progress (Lessons 1–15) . . 60
Enrichment: Logic and Venn Diagrams . . 61
Chapter 1 Test. . . . . . . . . . . . . . . . . . . . . 62
Cumulative Review. . . . . . . . . . . . . . . . . 63

* Develops concept or skill with manipulatives.

Lesson promotes algebraic reasoning.

v


8205-4_iv-xi 10/3/05 12:58 AM Page vi

Chapter

Chapter

Division
Chapter Opener . . . . . . . . . . . . . . . . . . . . 95

Number Theory
and Fractions

3-1

Understanding Division . . . . . . . . . 96

Chapter Opener . . . . . . . . . . . . . . . . . . . 133

3-2

Division Patterns

3-3

Three-Digit Quotients . . . . . . . . . 100

* 4-1

Explore Prime and
Composite Numbers . . . . . . . . 134

3-4

Larger Quotients . . . . . . . . . . . . . 102

4-2

3-5

Zeros in the Quotient . . . . . . . . . 104

Factors, Primes, and
Composites . . . . . . . . . . . . . . . 136

3-6

Short Division . . . . . . . . . . . . . . . 106

4-3

Greatest Common Factor . . . . . . 138

* 3-7

Explore Divisibility . . . . . . . . . . . . 108

4-4

Fraction Sense . . . . . . . . . . . . . . 140

3-8

Divisibility and Mental Math . . . . 110

4-5

Fractions in Lowest Terms. . . . . . 142

3-9

Estimation: Compatible
Numbers . . . . . . . . . . . . . . . . . 112

4-6

Fractions in
Greater Terms

3-10

Teens as Divisors . . . . . . . . . . . . 114

4-7

Multiples: LCM and LCD . . . . . . . 146

3-11

Two-Digit Divisors . . . . . . . . . . . . 116

4-8

Mixed Numbers . . . . . . . . . . . . . . 148

3-12

Divide Larger Numbers . . . . . . . . 118

4-9

3-13

Divide Money . . . . . . . . . . . . . . . 120

Fractions Greater Than or
Equal to One . . . . . . . . . . . . . . 150

3-14

Order of Operations

4-10

3-15

Problem-Solving Strategy:

Compare and Order
Fractions
. . . . . . . . . . . 152

4-11

Problem-Solving Strategy:

. . . . . . . . 98

. . . . . 122

Make a Table/Find a
Pattern
. . . . . . . . . . . . . 124
3-16

Problem-Solving Applications:

Make an Organized List . . . . . . . 154
4-12

Check Your Progress (Lessons 1–16) . 128
Enrichment: Translate Algebraic
Expressions
. . . . . . . . . . . . . . 129
Chapter 3 Test. . . . . . . . . . . . . . . . . . . . 130

Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . 156

Mixed Review . . . . . . . . . . . . . . . 126
End of Chapter

. . . . . . . 144

End of Chapter
Check Your Progress (Lessons 1–12) . 158
Enrichment: Density of Fractions . . . . . . 159
Chapter 4 Test. . . . . . . . . . . . . . . . . . . . 160
Cumulative Review. . . . . . . . . . . . . . . . 161

Cumulative Review. . . . . . . . . . . . . . . . 131

vi

* Develops concept or skill with manipulatives.

Lesson promotes algebraic reasoning.


8205-4_iv-xi 10/3/05 1:02 AM Page vii

Chapter

Chapter

Fractions: Addition and
Subtraction

Fractions: Multiplication
and Division

Chapter Opener . . . . . . . . . . . . . . . . . . . 163

Chapter Opener . . . . . . . . . . . . . . . . . . . 197

5-1

Rename Fraction Sums:
Like Denominators . . . . . . . . . 164

* 6-1

Multiply Fractions . . . . . . . . . . . . 198

6-2

Multiply Fractions
by Fractions. . . . . . . . . . . . . . . 200

6-3

Multiply Fractions
and Whole Numbers . . . . . . . . 202

5-2

Add Fractions:
Unlike Denominators. . . . . . . . 166

5-3

Add Three Fractions

5-4

Add Mixed Numbers . . . . . . . . . . 170

6-4

5-5

Rename Mixed Number
Sums . . . . . . . . . . . . . . . . . . . . 172

Multiply Fractions Using
the GCF. . . . . . . . . . . . . . . . . . 204

6-5

Rename Differences:
Like Denominators

Rename Mixed Numbers
as Fractions . . . . . . . . . . . . . . 206

6-6

Multiply Fractions
and Mixed Numbers

5-6
5-7
5-8

. . . . 168

. . . . 174

6-7

Multiply Mixed Numbers . . . . . . . 210

More Subtraction
of Fractions . . . . . . . . . . . . . . . 178

* 6-8

Division of Fractions . . . . . . . . . . 212

5-9

Subtract Mixed Numbers. . . . . . . 180

5-10

Subtraction with Renaming . . . . . 182

5-11

More Renaming in
Subtraction . . . . . . . . . . . . . . . 184

5-12

Estimate Sums and Differences
of Mixed Numbers . . . . . . . . . . 186

5-13

Problem-Solving Strategy:
Work Backward

5-14

. . . 208

Subtract Fractions: Unlike
Denominators . . . . . . . . . . . . . 176

. . . . . . . . 188

Problem-Solving Applications:

6-9

Reciprocals

6-10

Divide Whole Numbers
by Fractions . . . . . . . . . . . . . . 216

6-11

Divide Fractions by Fractions . . . 218

6-12

Divide Fractions
by Whole Numbers . . . . . . . . . 220

6-13

Divide Mixed Numbers
by Fractions . . . . . . . . . . . . . . 222

6-14

Divide Mixed Numbers . . . . . . . . 224

6-15

Estimate Products and Quotients
with Mixed Numbers . . . . . . . . 226

6-16

Problem-Solving Strategy:

Mixed Review . . . . . . . . . . . . . . . 190
End of Chapter
Check Your Progress (Lessons 1–14) . 192
Enrichment: Unit Fractions . . . . . . . . . . . 193

. . . . . . . . . . . 214

Use Simpler Numbers
6-17

. . . 228

Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . 230

Chapter 5 Test. . . . . . . . . . . . . . . . . . . . 194
Cumulative Review. . . . . . . . . . . . . . . . 195

End of Chapter
Check Your Progress (Lessons 1–17) . 232
Enrichment: Logic. . . . . . . . . . . . . . . . . . 233
Chapter 6 Test. . . . . . . . . . . . . . . . . . . . 234
Cumulative Review. . . . . . . . . . . . . . . . 235

* Develops concept or skill with manipulatives.

Lesson promotes algebraic reasoning.

vii


8205-4_iv-xi 10/3/05 1:02 AM Page viii

*

Chapter

Chapter

Probability and
Statistics

Decimals: Addition
and Subtraction

Chapter Opener . . . . . . . . . . . . . . . . . . . 237

Chapter Opener . . . . . . . . . . . . . . . . . . . 267

7-1

Probability . . . . . . . . . . . . . . . . . . 238

8-1

Decimal Sense . . . . . . . . . . . . . . 268

7-2

Tree Diagrams. . . . . . . . . . . . . . . 240

8-2

Decimals and Place Value . . . . . 270

7-3

Independent and
Dependent Events. . . . . . . . . . 242

8-3

Add Decimals . . . . . . . . . . . . . . . 272

8-4

Estimate Decimal Sums . . . . . . . 274

7-4

Collect and
Organize Data . . . . . . . . . . . . . 244

8-5

Add More Decimals . . . . . . . . . . 276

7-5

Range, Median, Mean,
and Mode . . . . . . . . . . . . . . . . 246

8-6

Subtract Decimals

8-7

Estimate Decimal Differences . . . 280

7-6

Graphing Sense . . . . . . . . . . . . . 248

8-8

7-7

Line Plots . . . . . . . . . . . . . . . . . . 250

Subtract More
Decimals

7-8

Histograms . . . . . . . . . . . . . . . . . 252

7-9

Make Line Graphs

7-10

Interpret Circle Graphs . . . . . . . . 256

7-11

Problem-Solving Strategy:

Mixed Review . . . . . . . . . . . . . . . 286

Use a Model/Diagram . . . . . . . . . 258

End of Chapter

7-12

8-9

Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . 260
End of Chapter

Check Your Progress (Lessons 1–12) . 262

8-10

. . . . . . . . . . . 282

Problem-Solving Strategy:
Use More Than
One Step

. . . . . . 254

. . . . . . 278

. . . . . . . . . . . 284

Problem-Solving Applications:

Check Your Progress (Lessons 1–10) . 288
Enrichment: Scientific Notation . . . . . . . 289
Chapter 8 Test. . . . . . . . . . . . . . . . . . . . 290
Cumulative Review. . . . . . . . . . . . . . . . 291

Enrichment: Double Line and
Double Bar Graphs. . . . . . . . . . . . . . . 263
Chapter 7 Test. . . . . . . . . . . . . . . . . . . . 264
Cumulative Review. . . . . . . . . . . . . . . . 265

viii

* Develops concept or skill with manipulatives.

Lesson promotes algebraic reasoning.


8205-4_iv-xi 10/3/05 1:03 AM Page ix

Chapter

Chapter

Decimals: Multiplication
and Division

Geometry

Chapter Opener . . . . . . . . . . . . . . . . . . . 293

10-1

Measure and Draw Angles . . . . . 324

10-2

Identify Angles . . . . . . . . . . . . . . 326

* 10-3

Polygons . . . . . . . . . . . . . . . . . . 328

10-4

Congruent and
Similar Figures . . . . . . . . . . . . 330

10-5

Triangles . . . . . . . . . . . . . . . . . . . 332

Multiply Decimals
by Decimals. . . . . . . . . . . . . . . 300

10-6

Quadrilaterals . . . . . . . . . . . . . . . 334

10-7

Perimeter. . . . . . . . . . . . . . . . . . . 336

9-5

Zeros in the Product . . . . . . . . . . 302

10-8

Circles . . . . . . . . . . . . . . . . . . . . . 338

9-6

Divide by 10, 100,
and 1000
. . . . . . . . . . . 304

10-9

Circumference

9-7

Divide Decimals by

Whole Numbers . . . . . . . . . . . 306

9-8

Zeros in Division . . . . . . . . . . . . . 308

9-9

Estimate Decimal Quotients . . . . 310

9-10

Estimate with Money . . . . . . . . . . 312

9-11

Problem-Solving Strategy:

* 9-1

Multiply by 10, 100,
and 1000
. . . . . . . . . . . 294

9-2

Estimate Decimal Products. . . . . 296

9-3

Multiply Decimals by
Whole Numbers . . . . . . . . . . . 298

9-4

*

Write a Number
Sentence
9-12

. . . . . . . . . . . 314

Chapter Opener . . . . . . . . . . . . . . . . . . . 323

. . . . . . . . . 340

10-10 Lines of Symmetry . . . . . . . . . . . 342

* 10-11

Transformations. . . . . . . . . . . . . . 344

10-12 Tessellations . . . . . . . . . . . . . . . . 346
10-13 Problem-Solving Strategy:
Use a Diagram/Model

. . . 348

10-14 Problem-Solving Applications:

Mixed Review . . . . . . . . . . . . . . . 350
End of Chapter

Problem-Solving Applications:

Check Your Progress (Lessons 1–14) . 352

Mixed Review . . . . . . . . . . . . . . . 316

Enrichment: Triangular and
Square Numbers
. . . . . . . . . . 353

End of Chapter
Check Your Progress (Lessons 1–12) . 318

Chapter 10 Test. . . . . . . . . . . . . . . . . . . 354

Enrichment: Fractions to Decimals. . . . . 319

Cumulative Review. . . . . . . . . . . . . . . . 355

Chapter 9 Test. . . . . . . . . . . . . . . . . . . . 320
Cumulative Review. . . . . . . . . . . . . . . . 321

* Develops concept or skill with manipulatives.

Lesson promotes algebraic reasoning.

ix

8205-4_iv-xi

4/26/06

10:27 AM

Page x

Chapter

Chapter

Measurement Topics

Metric Measurement,
Area, and Volume

Chapter Opener . . . . . . . . . . . . . . . . . . . 357

* 11-1

Relate Customary Units
of Length . . . . . . . . . . . . . . . . . 358

11-2

Relate Customary Units
of Capacity . . . . . . . . . . . . . . . 360

12-1

Metric Measurement . . . . . . . . . . 382

* 12-2

* 11-3

Relate Customary Units
of Weight . . . . . . . . . . . . . . . . . 362

Relate Metric Units
of Length . . . . . . . . . . . . . . . . . 384

12-3

Relate Metric Units
of Capacity . . . . . . . . . . . . . . . 386

. . . . . . . . . . 364

Chapter Opener . . . . . . . . . . . . . . . . . . . 381

11-4

Temperature

11-5

Units of Time . . . . . . . . . . . . . . . . 366

* 12-4

Relate Metric Units
of Mass . . . . . . . . . . . . . . . . . . 388

11-6

Time Zones . . . . . . . . . . . . . . . . . 368

12-5

Square Measure . . . . . . . . . . . . . 390

11-7

Compute with
Customary Units . . . . . . . . . . . 370

12-6

Areas of Rectangles
and Squares

11-8

Problem-Solving Strategy:

12-7

Areas of Parallelograms
and Triangles
. . . . . . . . 394

12-8

Solid Figures . . . . . . . . . . . . . . . . 396

12-9

Surface Area

Use More Than One Step . . . . . . 372
11-9

Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . 374
End of Chapter

. . . . . . . . . . 398

12-10 Cubic Measure . . . . . . . . . . . . . . 400

Check Your Progress (Lessons 1–9) . . 376
Enrichment: Pascal’s Triangle

. . . . . . . . 392

. . . 377

Chapter 11 Test. . . . . . . . . . . . . . . . . . . 378
Cumulative Review. . . . . . . . . . . . . . . . 379

12-11 Volume

* 12-12

. . . . . . . . . . . . . . . 402

Estimate Volume . . . . . . . . . . . . . 404

12-13 Problem-Solving Strategy:
Draw a Picture
. . . . . . . . . 406
12-14 Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . 408
End of Chapter
Check Your Progress (Lessons 1–14) . 410
Enrichment: Views of Solid Figures . . . . 411
Chapter 12 Test. . . . . . . . . . . . . . . . . . . 412
Cumulative Review. . . . . . . . . . . . . . . . 413

x

* Develops concept or skill with manipulatives.

Lesson promotes algebraic reasoning.

8205-4_iv-xi 10/3/05 1:04 AM Page xi

Chapter

Chapter

Ratio, Proportion,
and Percent

More Concepts in

Chapter Opener . . . . . . . . . . . . . . . . . . . 415

14-1

Algebraic Expressions
and Equations . . . . . . . . . . . . 440

14-2

Properties of Equality . . . . . . . . . 442

14-3

Addition and Subtraction
Equations . . . . . . . . . . . . . . . . 444

Chapter Opener . . . . . . . . . . . . . . . . . . . 439

13-1

Ratios as Fractions

. . . . . 416

13-2

Proportions

13-3

Scale and Maps

13-4

Relate Fractions
to Percents . . . . . . . . . . . . . . . 422

14-4

Multiplication and Division
Equations . . . . . . . . . . . . . . . . 446

13-5

Relate Percents
to Decimals . . . . . . . . . . . . . . . 424

14-5

Equations with Fractions . . . . . . . 448

13-6

Find the Percent
of a Number

14-6

Introduction to Integers . . . . . . . . 450

. . . . . . . . . 426

14-7

Compare and Order Integers . . . 452

13-7

Use Percent . . . . . . . . . . . . . . . . 428

14-8

Add Integers with Like Signs . . . 454

13-8

Problem-Solving Strategy:

14-9

Add Integers with Unlike Signs . . 456

*14-10

Subtract Integers . . . . . . . . . . . . 458

. . . . . . . . . . . 418
. . . . . . . . 420

Combine Strategies
13-9

. . . . 430

Problem-Solving Applications:

14-11 Multiply Integers . . . . . . . . . . . . . 460

Mixed Review . . . . . . . . . . . . . . . 432

14-12 Divide Integers . . . . . . . . . . . . . . 462

End of Chapter

14-13 The Coordinate Plane . . . . . . . . 464

Check Your Progress (Lessons 1–9) . . 434

14-14 Function Tables . . . . . . . . . . . . . . 466

Enrichment: Percent Patterns

14-15 Functions and Coordinate
Graphs . . . . . . . . . . . . . . . . . . 468

. . . 435

Chapter 13 Test. . . . . . . . . . . . . . . . . . . 436
Cumulative Review. . . . . . . . . . . . . . . . 437

14-16 Problem-Solving Strategy:
Write an Equation . . . . . . . . . . . . 470
14-17 Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . 472
End of Chapter
Check Your Progress (Lessons 1–17) . 474
Enrichment: Rational Numbers . . . . . . . 475
Chapter 14 Test. . . . . . . . . . . . . . . . . . . 476

End-of-Book Materials
Still More Practice . . . . . . . . . . . . . . . . . 477
Brain Builders. . . . . . . . . . . . . . . . . . . . . 489
Mental Math . . . . . . . . . . . . . . . . . . . . . . 493
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . 502
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . 507
Symbols and Tables . . . . . . . . . . . . . . . . 515

* Develops concept or skill with manipulatives.

Lesson promotes algebraic reasoning.

xi


8205-4_xii 9/30/05 5:33 AM Page xii

A Review of Mathematical
Skills from Grade 4
Progress in Mathematics includes a
“handbook” of essential skills, Skills Update,
at the beginning of the text. These one-page
lessons review skills you learned in previous
years. It is important for you to know this
content so that you can succeed in math
this year.
If you need to review a concept in Skills
Update, your teacher can work with you,
using manipulatives, which will help
you understand the concept better.
The Skills Update handbook can be used
throughout the year to review skills you
may already know. Since many lessons
in your textbook refer to pages in the Skills Update, you can use a particular
lesson at the beginning of class as a warm-up activity. Or your class may
choose to do the Skills Update lessons at the beginning of the year so that
you and your teacher can assess your understanding of these previously
learned skills.
You may even want to practice specific skills at home.
If you need more practice than what is provided on

the Skills Update page, you can use the practice
pages available online at www.sadlier-oxford.com.
These practice pages have an abundance of
exercises for each one-page lesson.

xii


8205-4_1-21 9/30/05 5:40 AM Page 1

Place Value to Thousands
Each period has
three digits.

You can show 158,706 in a place-value chart.
The value of each digit in a number depends
on its place in the number.

Thousands
Period

In 158,706 the value of:

5 is 5 ten thousands or 50,000.

hu
nd
ten reds
s
on

es
hu
nd
ten reds
s
on
es

1 is 1 hundred thousand or 100,000.

Ones
Period

8 is 8 thousands or 8000.

1 5 8, 7 0 6

7 is 7 hundreds or 700.
0 is 0 tens or 0.
6 is 6 ones or 6.
Standard Form: 158,706

Word Name:

Remember:
Four-digit numbers may be written with or
without a comma. In numbers larger than
9999, use a comma to separate the periods.

one hundred fifty-eight thousand,

seven hundred six

Write the place of the underlined digit. Then write its value.
1. 224
_2

2. 63_,666

3. _
199,999

4. 88_
0,888

Place a comma where needed in each. Then write the period name
for the underlined digit.
5. 3 4 2 5 _9

6. _
16432

7. 2 0 _0 0 6 0

8. _8 0 5 0 2 7

Write the number in standard form.
9. forty-five thousand, seven hundred sixty-two
11. nine hundred thousand, seven

10. five thousand, six

12. ten thousand, nineteen

Write the word name for each number.
13. 7046

14. 37,008

15. 231,075

Numeration I

16. 923,780
1


8205-4_1-21 9/30/05 5:41 AM Page 2

Compare and Order Whole Numbers
Remember:
Ͻ means “is less than.”
Ͼ means “is greater than.”
ϭ means “is equal to.”

Compare 363,420 and 381,787.
363,420
381,787

To compare whole numbers:
Align the digits by place value.
Start at the left and find the first

place where the digits are different.

363,420
381,787

3

Compare the value of these digits
to find which number is greater.

363,420
381,787

8Ͼ6

So 381,787 Ͼ 363,420.

3

You could also say 363,420 Ͻ 381,787.

Order from greatest to least: 69,520; 19,478; 160,434; 63,215
To order whole numbers:
Align the digits by place value.
Compare the digits in each place, starting with the greatest place.
69,520
19,478
160,434
63,215
There are no hundred

thousands in the other
numbers. 160,434 is
the greatest.

69,520
19,478
160,434
63,215
6 ϭ 6 and 1 Ͻ 6
19,478 is the least.

69,520
19,478
160,434
63,215
3Ͻ9
63,215 Ͻ 69,520

In order from greatest to least the numbers are:
160,434; 69,520; 63,215; 19,478
The order from least to greatest: 19,478; 63,215; 69,520; 160,434
Compare. Write ,, 5, or ..
1. 1563 ? 1519

2. 67,234 ? 67,234

3. 479,059 ? 479,065

Write in order from least to greatest.

2

4. 9458; 9124; 948; 972

5. 3951; 3068; 369; 3547

6. 99,407; 91,568; 90,999; 93,697

7. 216,418; 215,783; 213,614; 221,986

Numeration II


8205-4_1-21 9/30/05 5:42 AM Page 3

Round Whole Numbers
To round a number to a given place:
Find the place you are rounding to.
Look at the digit to its right.
If the digit is less than 5, round down.
If the digit is 5 or more, round up.
Round 13,528 to the nearest ten.
13,528
13,530

5
8
Round up
to 13,530.
Round 13,528 to the

nearest thousand.

Round 13,528 to the
nearest hundred.
13,528
13,500

5
2
Round down
to 13,500.

13,528
14,000

5 5
Round up
to 14,000.

Round to the nearest ten.
1. 27

2. 25

3. 51

7. 469

8. 875

9. 2587

4. 86

5. 174

6. 397

10. 4351

11. 9289

12. 3542

Round to the nearest hundred.
13. 158

14. 426

15. 375

16. 896

17. 719

18. 950

19. 1047

20. 3888

21. 5942

22. 6891

23. 3098

24. 8762

25. 37,405

26. 62,345

27. 88,088

28. 65,097

29. 58,706

30. 66,636

Round to the nearest thousand.
31. 9155

32. 7983

33. 4550

34. 6237

35. 8396

36. 33,888

37. 15,942

38. 93,192

39. 87,983

40. 46,237

41. 326,150

42. 145,706

43. 357,029

44. 563,498

45. 807,476

46. 821,593

47. 450,513

48. 435,127

49. 205,120

50. 761,604

Numeration III

3


8205-4_1-21 9/30/05 5:42 AM Page 4

Add and Subtract Whole Numbers
To add or subtract whole numbers:
Estimate.
Align the numbers. Add or subtract, starting
with the ones. Regroup when necessary.
Add: 3458 ϩ 2596 ϭ ? .
Round to estimate: 3000 ϩ 3000 ϭ 6000.
Add the ones.
Regroup.
1

Add the tens.
Regroup.

Add the hundreds.
Regroup.

1 1

3 4 5 8
ϩ2 5 9 6

4
14 ones
1 ten 4 ones

Add the
thousands.

1 1 1

1 1 1

3 4 5 8
ϩ2 5 9 6
5 4

3 4 5 8
ϩ2 5 9 6
0 5 4

15 tens
1 hundred 5 tens

10 hundreds
1 thousand 0 hundreds

3 4 5 8
ϩ2 5 9 6
6 0 5 4
Think
6054 is close

to the estimate
of 6000.

Subtract: 2842 Ϫ 1645 ϭ ? .
Round to estimate: 3000 Ϫ 2000 ϭ 1000.
More ones needed.
Regroup. Subtract.

More tens needed.
Regroup. Subtract.

3 12

13
7 3 12

2 8 4 2
1 6 4 5
7

2 8 4 2
1 6 4 5
9 7

4 tens 2 ones
3 tens 12 ones

Subtract.
13
7 3 12

2 8 4 2
1 6 4 5
1 1 9 7
Think
1197 is close to
the estimate of 1000.

8 hundreds 3 tens
7 hundreds 13 tens

Estimate by rounding. Then add or subtract. (Watch for 1 or 2.)

4

1. 215 ϩ 687

2. 4306 ϩ 3849

3. 6287 ϩ 318

4. 659 Ϫ 286

5. 7583 Ϫ 2948

6. 3717 Ϫ 839

Whole Number Operations I