Table Of ContentSadlier-Oxford
A Division of William H.
Sadlier, Inc.
New York, NY 10005-
1002
AUDIO LEARNING
VISUAL LEARNING
HEAR THE MATH!
SEE THE MATH!
SHARED LEARNING
SHARE THE MATH!
INTERACTIVE LEARNING
DO THE MATH!
SGT 1
www.progressinmathematics.com
For Progress in Mathematics Grades 3-6
Sadlier-Oxford
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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!
Technology Resources:
www.progressinmathematics.com
Introduction At www.progressinmathematics.com,
you will fi nd a lot of technology resources that you can use at
home, and your teacher may make them available when you are
at school.
SGT 2
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# 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
Grade home
Glossary home
www.progressinmathematics.com
Choose the fi rst
letter of a term you
want to review.
1
Click on
the term.
2
Listen as
the glossary
pronounces
the word.
3
GRADE 3
AUDIO GLOSSARY
SGT 3
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 fi rst letter of the term you want to review.
INTERACTIVE
COMPATIBLE
AUDIO LEARNING
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Red Team
Blue Team
Green Team
Red Team
Blue Team
GRADE 3
www.progressinmathematics.com
SGT 4
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 step-
by-step explanation of one of
the skills or concepts in the
chapter.
www.progressinmathematics.com
INTERACTIVE
COMPATIBLE
VISUAL LEARNING
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www.progressinmathematics.com
www.progressinmathematics.com
GRADE 6
GRADE 5
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.
VIRTUAL MANIPULATIVES
SGT 5
INTERACTIVE
COMPATIBLE
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www.progressinmathematics.com
GRADE 5
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.
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
www.progressinmathematics.com
www.progressinmathematics.com
GRADE 4
GRADE 4
www.progressinmathematics.com
www.progressinmathematics.com
INTERACTIVE
COMPATIBLE
INTERACTIVE LEARNING
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GRADE 6
GRADE 3
*Whiteboard projectable only.
GRADE 3
ENRICHMENT
Click Skills Update.*
Print Skills Update lessons
and practice pages to review
previously taught math skills
and concepts.
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.
www.progressinmathematics.com
SGT 7
Name
Date
Count by 2s.
Count by 2s, 5s, 10s
14
16
18
22
24
26
28
17
19
21
25
27
29
31
20
30
35
40
45
50
55
35
45
50
55
60
65
70
20
30
40
50
60
70
80
90
30
40
50
60
70
80
90
100
16
18
28
32
1. 12, ______, ______, ______, 20, ______, ______, ______, ______
2. 15, ______, ______, ______, 23, ______, ______, ______, ______
Count by 5s.
3. 15, ______, 25, ______, ______, ______, ______, ______, ______
4. 30, ______, 40, ______, ______, ______, ______, ______, ______
Count by 10s.
5. 10, ______, ______, ______, ______, ______, ______, ______, ______
6. 20, ______, ______, ______, ______, ______, ______, ______, ______
Write the missing numbers.
7. 10, 12, 14, ______, ______, 20
8. 22, 24, 26, ______, 30, ______
www.progressinmathematics.com
www.progressinmathematics.com
Click Problem of the Day.*
Sharpen your problem-
solving skills every day.
Print and solve one
problem each day!
INTERACTIVE
COMPATIBLE
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Dear Family,
Today our class began Chapter 1. We will learn about place value. Let’s do
the activity below together so I can review the skills I will need in order to
understand the math in this chapter. Then we can read some of the new
vocabulary I will learn in Chapter 1.
Love, ____________________
How Many Tens, How Many Ones?
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.
expanded form
shows the place value of the digits
in a number
600 � 40 � 7
standard form
647
thousand
nearest ten
the number achieved after rounding
to the nearest ten
251
250
nearest hundred
the number achieved after rounding
to the nearest hundred
tens
ones
+
=
m quantities granted to users of Progress in Mathematics.
Chapter 1
www.progressinmathematics.com
GRADE 3 - ENGLISH
users of Progress in Mathematics.
Dear Family,
Today our class completed Chapter 1. We learned how to read, write,
compare, and order numbers to hundred thousands. These skills are
needed to work with numbers and to understand place value.
We explored patterns of skip counting with 2s, 3s, 4s, 5s, and 10s, which
will help us to learn multiplication facts. We practiced rounding 3- and
4-digit numbers to the nearest ten, hundred, or thousand. This skill is
necessary for estimating with numbers. We also worked with money,
which will help us make and count change.
Love, ________________________
Key Skills and Concepts
Students’ learning in Chapter 1 was guided by giving particular emphasis to the
following key skills and concepts:
NS 2.3
• Identify the place value for each digit in
numbers to 10,000.
• Use expanded notation to represent numbers.
GRADE 3 - ENGLISH
tics, para reproducir esta página para sus estudiantes.
Querida familia:
Hoy nuestra clase terminó el capítulo 1. Aprendimos a leer, escribir, comparar
y ordenar números hasta los cientos de miles. Este conocimiento es necesario
para trabajar con números y para entender el valor posicional. Aprendimos
a contar de 2 en 2, de 3 en 3, de 4 en 4, de 5 en 5 y de 10 en 10, lo que nos
servirá para aprender operaciones de multiplicación. Aprendimos a redondear
números de 3 y 4 dígitos hasta la decena, centena o millar más cercano. Este
conocimiento es necesario para hacer estimaciones con números. También
practicamos con dinero, lo cual nos ayudará a la hora de dar o recibir cambio.
Con cariño, _____________________________
Destrezas y conceptos claves
U
l
it
i
i
i
t
d l
id
l
d
iñ
t
d
Lo que aprendieron los estudiantes en el capítulo 1 se hizo poniendo énfasis
en las siguientes destrezas y conceptos claves:
NS 2.3
• Identificar el valor posicional de cada dígito de
números hasta el 10,000.
• Usar la forma desarrollada de representar
números.
GRADE 3 - SPANISH
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
fi rst 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.
Both letters are in English and
in Spanish.
MATH ALIVE AT HOME
SGT 8
SHARED LEARNING
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Sadlier-Oxford
A Division of William H. Sadlier, Inc.
www.sadlier-oxford.com
Catherine D. LeTourneau
Alfred S. Posamentier
with
Elinor R. Ford
Frank Lucido
Associate Professor in
Bilingual/Multicultural Education
Texas A&M University
Corpus Christi, TX
Regina Panasuk
Professor of Mathematics Education
University of Massachusetts
Lowell, MA
Madelaine Gallin
Former Math Coordinator
Community School District #6
New York, NY
Tim Mason
Title 1 Specialist
Palm Beach County School District
West Palm Beach, FL
Lucy Lugones
Math Coordinator
St. Luke’s School
Whitestone, NY
Rosalie Pedalino Porter
Consultant Bilingual/ESL Programs
Amherst, MA
8206-2_PiM_Title 3/29/06 4:08 PM Page i
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: 978-0-8215-3606-3
3456789
13 12 11 10
The publisher wishes to thank the following teachers and administrators, who read
portions of the series prior to publication, for their valuable contributions.
Madonna Atwood
Teacher
St. Louis, MO
Debra Wright
Principal
Winter Haven, FL
John Palladino
Professor at Eastern Michigan University
Ypsilanti, MI
Marie Bicsak
Math Coordinator
Mt. Clemens, MI
Suzanne Ryan
Grade 4 Teacher
Orono, MN
Brandy Roth
Grade 3 Teacher
Kissimmee, FL
Barbara Murphy
Grade 4 Teacher
Chesterfield, MO
Sr. Maristella Dunlavy, O.P.
Principal
Springfield, IL
Sara Kobylarz
Grade 3 Teacher
Bronx, NY
Candace Govin
Grades 4– 8 Math Teacher/Coordinator
Plantation, FL
Elizabeth M. Johnson
Grade 5 Teacher
Bettendorf, IA
Sr. Martha Carmody, O.P.
Grade 4 Teacher
Springfield, IL
Jeannine Frey
Grade 3 Teacher
Chesterfield, MO
Br. Ralph Darmento, F.S.C.
Deputy Superintendent of Schools
Newark, NJ
Sr. Adriana Cernoch
Grade 6 Teacher
Dallas, TX
Linda Hamby
Grade 5 Teacher
DesPeres, MO
Jacqueline A. Byrd
Grade 5 Teacher
Chesterfield, MO
Mary E. Stokes
Grade 5 Teacher
Oak Forest, IL
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.
Grades 3–6 Reviewers
Grade-Level Reviewers
Judith A. Devine
Educational Consultant
Springfield, PA
Stephanie D. Garland
Educational Consultant
St. Louis, MO
3606-3_PE6_ii_Copyright:8205-4_Proto_22-23PSintro copy 7/31/08 10:05 AM Page ii
RRDW
iii
Progress in Mathematics, now in its sixth decade of user-proven success,
is a complete basal mathematics program. Written by experienced teacher-
authors, 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 6, the concepts of integers and rational numbers will be further
developed as well as ratios, percents, and coordinate geometry. There will
be an increased emphasis on algebraic thinking. Other topics that are
studied include: data and statistics, probability, geometry, measurement,
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 sixth 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 sixth grader will not only learn to value math,
but become a confident problem solver and
learn to reason and communicate
mathematically as well.
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iv
Letter to the Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Lesson promotes algebraic reasoning.
Skills Update
A handbook for reviewing essential
and previously taught skills
Introduction to Skills Update . . . . . . . . . . xii
Numeration
I
Whole Numbers: Place Value,
Compare, and Order
. . . . 1
II
Round Whole Numbers. . . . . . . . . . 2
III
Factors, Multiples, and Divisibility . . 3
IV
Decimals to Hundredths . . . . . . . . . 4
Operations
I
Add Whole Numbers and
Decimals . . . . . . . . . . . . . . . . . . . 5
II
Subtract Whole Numbers
and Decimals . . . . . . . . . . . . . . . 6
III
Inverse Operations . . . . . . . . . . . . . 7
IV
Properties of Addition and
Multiplication . . . . . . . . . . . . . . . . 8
V
Multiply 1- and 2-Digit
Whole Numbers . . . . . . . . . . . . . 9
VI
Trial Quotients. . . . . . . . . . . . . . . . 10
VII
Divide Whole Numbers . . . . . . . . . 11
Fractions
I
Add and Subtract Fractions:
Like Denominators . . . . . . . . . . 12
Statistics and Graphs
I
Make Pictographs . . . . . . . . . . . . . 13
II
Make Bar Graphs . . . . . . . . . . . . . 14
Probability
I
Equally/Not Equally Likely
Outcomes . . . . . . . . . . . . . . . . . 15
II
List Outcomes . . . . . . . . . . . . . . . . 16
Geometry
I
Geometric Figures . . . . . . . . . . . . 17
II
Lines: Intersecting and Parallel . . . 18
III
Polygons . . . . . . . . . . . . . . . . . . . . 19
Measurement
I
Metric Units of Length. . . . . . . . . . 20
II
Metric Units of Capacity
and Mass. . . . . . . . . . . . . . . . . . 21
III
Customary Units of Length . . . . . . 22
IV
Customary Units of Capacity
and Weight . . . . . . . . . . . . . . . . 23
V
Read an Inch Ruler . . . . . . . . . . . . 24
VI
Perimeter and Area
of Rectangles . . . . . . . . . . . . . . 25
Introduction to
Problem Solving
Problem-Solving Model . . . . . . . . . . . . . . 26
Problem-Solving Strategy:
Guess and Test . . . . . . . . . . . . . . . . . . 28
Problem-Solving Strategy:
Use More Than One Step . . . . . . . . . . 29
Problem-Solving Strategy:
Use a Graph. . . . . . . . . . . . . . . . . . . . . 30
Problem-Solving Strategy:
Write an Equation
. . . . . . . . . . . 31
Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . . . . . . 32
8206-2_iv-xi 3/25/06 1:03 PM Page iv
Chapter
Multiplication: Whole
Numbers and Decimals
Chapter Opener . . . . . . . . . . . . . . . . . . . . 65
2-1
Multiplication Patterns
. . . . 66
2-2
Estimate Products. . . . . . . . . . . . . 68
2-3
Multiply Whole Numbers
. . 70
2-4
Multiply with Decimals . . . . . . . . . 72
2-5
Exponents
. . . . . . . . . . . . . 74
2-6
Scientific Notation . . . . . . . . . . . . . 76
2-7
Problem-Solving Strategy:
Use Simpler Numbers. . . . . . . . . . 78
2-8
Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . . 80
End of Chapter
Check Your Progress (Lessons 1–8) . . . 82
Enrichment: Square Roots . . . . . . . . . . . . 83
Chapter 2 Test. . . . . . . . . . . . . . . . . . . . . 84
Cumulative Review. . . . . . . . . . . . . . . . . 85
v
Lesson promotes algebraic reasoning.
Chapter
Number Sense, Addition,
and Subtraction
Chapter Opener . . . . . . . . . . . . . . . . . . . . 33
1-1
Place Value . . . . . . . . . . . . . . . . . . 34
1-2
Expanded Form . . . . . . . . . . . . . . 36
1-3
Place Value and Exponents . . . . . 38
1-4
Compare and Order
Decimals
. . . . . . . . . . . . 40
1-5
Round Whole Numbers
and Decimals . . . . . . . . . . . . . . 42
1-6
Estimate Decimal Sums
and Differences . . . . . . . . . . . . 44
1-7
Addition of Whole Numbers
and Decimals . . . . . . . . . . . . . . 46
1-8
Subtraction of Whole Numbers
and Decimals . . . . . . . . . . . . . . 48
1-9
Addition and Subtraction
of Decimals . . . . . . . . . . . . . . . . 50
1-10
Addition and Subtraction
Expressions
. . . . . . . . . . 52
1-11
Evaluate Addition and Subtraction
Expressions
. . . . . . . . . . 54
1-12
Problem-Solving Strategy:
Write an Equation . . . . . . . . . . . . . 56
1-13
Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . . 58
End of Chapter
Check Your Progress (Lessons 1–13) . . 60
Enrichment: Roman Numerals . . . . . . . . . 61
Chapter 1 Test. . . . . . . . . . . . . . . . . . . . . 62
Cumulative Review. . . . . . . . . . . . . . . . . 63
8206-2_iv-xi 3/25/06 1:07 PM Page v
vi
Chapter
Division: Whole
Numbers and Decimals
Chapter Opener . . . . . . . . . . . . . . . . . . . . 87
3-1
Short Division . . . . . . . . . . . . . . . . 88
3-2
Estimate Quotients . . . . . . . . . . . . 90
3-3
Divide Whole Numbers . . . . . . . . . 92
3-4
Divide Decimals by 10, 100,
and 1000
. . . . . . . . . . . . 94
3-5
Divide Decimals by Whole
Numbers . . . . . . . . . . . . . . . . . . 96
3-6
Patterns with Tenths, Hundredths,
and Thousandths
. . . . . . 98
3-7
Estimate Decimal Quotients . . . . 100
3-8
Decimal Divisors . . . . . . . . . . . . 102
3-9
Zeros in Division
. . . . . . . . . . . . 104
3-10
Multiplication and Division
Expressions
. . . . . . . . . 106
3-11
Evaluate Multiplication and Division
Expressions
. . . . . . . . . 108
3-12
Round Quotients . . . . . . . . . . . . 110
3-13
Problem-Solving Strategy:
Interpret the Remainder . . . . . . . 112
3-14
Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . 114
End of Chapter
Check Your Progress (Lessons 1–14) . 116
Enrichment: Logic: Open and Closed
Statements . . . . . . . . . . . . . . . . . . . . 117
Chapter 3 Test. . . . . . . . . . . . . . . . . . . . 118
Cumulative Review. . . . . . . . . . . . . . . . 119
Chapter
Expressions and
Equations
Chapter Opener . . . . . . . . . . . . . . . . . . . 121
4-1
Order of Operations
. . . . . 122
4-2
Translate Expressions
. . . 124
4-3
Evaluate Algebraic
Expressions
. . . . . . . . . 126
4-4
Equations and
Inequalities
. . . . . . . . . 128
4-5
Addition Equations
. . . . . 130
4-6
Subtraction Equations
. . . 132
4-7
Multiplication and Division
Equations
. . . . . . . . . . . 134
4-8
Use Formulas
. . . . . . . . . 136
4-9
Explore Order of Operations
with a Calculator
. . . . . 138
4-10
Problem-Solving Strategy:
Use More Than One
Step
. . . . . . . . . . . . . . . 140
4-11
Problem-Solving Applications:
Mixed Review
. . . . . . . . . 142
End of Chapter
Check Your Progress (Lessons 1–11) . 144
Enrichment: Patterns:
Sequences
. . . . . . . . . . . . . . . 145
Chapter 4 Test. . . . . . . . . . . . . . . . . . . . 146
Cumulative Review. . . . . . . . . . . . . . . . 147
Lesson promotes algebraic reasoning.
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