Progress in Mathematics Grade 4

522 Pages·2011·20.46 MB·English

Sadlier-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

001_008_3603_2_PE3-6.indd 4
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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

R. James Milgram
Professor of Mathematics
Stanford University
Palo Alto, CA

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

8204-6_G4_Titlepage 1/10/06 8:40 AM 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: 978-0-8215-3604-9

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

3604-9_PE4_ii_Copyright:8205-4_Proto_22-23PSintro copy 7/31/08 10:01 AM Page ii

456789 RRDW 13 12 11 10

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 4, multiplication and division will be further developed, and your
fourth grader will apply both operations throughout the grade-level, as he or
she studies the concepts of measurement, probability and statistics, fractions,
geometry, perimeter, area, volume, and decimals. There will also be an
increased emphasis on algebraic thinking. 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 fourth grader to achieve success in mathematics and to
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 fourth grader will not only learn to value math,
but become a confident problem solver and
learn to reason and communicate
mathematically as well.

8204-6_iii 1/7/06 4:11 AM Page iii

iv

Introduction to
Problem Solving

Problem-Solving Model . . . . . . . . . . . . . . 28

Problem-Solving Strategy:
Choose the Operation
. . . . . . . . 30

Problem-Solving Strategy:
Guess and Test
. . . . . . . . . . . . . 31

Problem-Solving Strategy:
Use More Than One Step
. . . . . 32

Problem-Solving Strategy:
Write a Number Sentence
. . . . . 33

Problem-Solving Applications . . . . . . . . . 34

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

Skills Update
A handbook for reviewing essential
and previously taught skills
Introduction to Skills Update . . . . . . . . . . xii
Numeration
I
Hundreds . . . . . . . . . . . . . . . . . . . . 1
II
Compare Whole Numbers
. . 2

Money
Recognize and Count Money. . . . . . . . . . . 3
Whole Number Operations
I
Addition and Subtraction Facts . . . . 4
II
Related Facts
. . . . . . . . . . . 5
III
Add and Subtract without
Regrouping . . . . . . . . . . . . . . . . . 6
IV
Meaning of Multiplication . . . . . . . . 7
V
Multiplication Facts . . . . . . . . . . . . . 8
VI
Multiply with 10, 11, and 12 . . . . . . 9
VII
Understand Division . . . . . . . . . . . 10
VIII
Division Facts . . . . . . . . . . . . . . . . 11
IX
Relate Multiplication and
Division
. . . . . . . . . . . . . 12

Fractions
Identify Fractions . . . . . . . . . . . . . . . . . . . 13
Measurement
I
Customary Units of Length . . . . . . 14
II
Cup, Pint, Quart, Gallon . . . . . . . . 15
III
Pound . . . . . . . . . . . . . . . . . . . . . . 16
IV
Centimeter and Meter . . . . . . . . . . 17
V
Liter . . . . . . . . . . . . . . . . . . . . . . . . 18
VI
Kilogram . . . . . . . . . . . . . . . . . . . . 19

Geometry
I
Perimeter. . . . . . . . . . . . . . . . . . . . 20
II
Congruent Figures . . . . . . . . . . . . 21
III
Lines of Symmetry . . . . . . . . . . . . 22
IV
Ordered Pairs on a Grid
. . 23
V
Area . . . . . . . . . . . . . . . . . . . . . . . 24

Statistics
I
Record and Organize Data . . . . . . 25
II
Graphing Sense . . . . . . . . . . . . . . 26

Probability
Probability Experiments . . . . . . . . . . . . . . 27

Lesson promotes algebraic reasoning.

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Chapter
Addition and
Subtraction Concepts

Chapter Opener . . . . . . . . . . . . . . . . . . . . 67

2-1
Addition Properties
. . . . . . 68

2-2
Addition Strategies . . . . . . . . . . . . 70

2-3
Subtraction Concepts
. . . . 72

2-4
Expressions and
Variables
. . . . . . . . . . . . 74

2-5
Addition and Subtraction
Sentences
. . . . . . . . . . . 76

2-6
Mental Math
. . . . . . . . . . . . 78

2-7
Estimate Sums and
Differences . . . . . . . . . . . . . . . . 80

2-8
Add and Subtract Money. . . . . . . . 82

2-9
Check Addition and
Subtraction
. . . . . . . . . . . 84

2-10
Problem-Solving Strategy:
Logical Reasoning . . . . . . . . . . . . 86

2-11
Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . . 88

End of Chapter

Check Your Progress (Lessons 1–11) . . 90

Enrichment: The Abacus . . . . . . . . . . . . . 91

Chapter 2 Test. . . . . . . . . . . . . . . . . . . . . 92

Cumulative Review. . . . . . . . . . . . . . . . . 93

v

Chapter
Place Value

Chapter Opener . . . . . . . . . . . . . . . . . . . . 35

1-1
Thousands . . . . . . . . . . . . . . . . . . 36

1-2
What Is One Million?. . . . . . . . . . . 38

1-3
Millions . . . . . . . . . . . . . . . . . . . . . 40

1-4
Place Value . . . . . . . . . . . . . . . . . . 42

1-5
Estimation . . . . . . . . . . . . . . . . . . . 44

1-6
Compare and Order
Whole Numbers
. . . . . . . 46

1-7
Number Sense: Use a
Number Line
. . . . . . . . . 48

1-8
Make Change . . . . . . . . . . . . . . . . 50

1-9
Compare and Order
Money
. . . . . . . . . . . . . . 52

1-10
Rounding. . . . . . . . . . . . . . . . . . . . 54

1-11
Work with Money. . . . . . . . . . . . . . 56

1-12
Problem-Solving Strategy:
Make a Table or List . . . . . . . . . . . 58

1-13
Problem-Solving Applications:

Mixed Review . . . . . . . . . . . . . . 60

End of Chapter

Check Your Progress (Lessons 1–13) . . 62

Enrichment: Billions . . . . . . . . . . . . . . . . . 63

Chapter 1 Test. . . . . . . . . . . . . . . . . . . . . 64

Cumulative Review. . . . . . . . . . . . . . . . . 65

*

*

*Develops concept or skill with manipulatives.
Lesson promotes algebraic reasoning.

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vi

Chapter
Addition and
Subtraction

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

3-1
Front-End Estimation . . . . . . . . . . 96

3-2
Add with Regrouping. . . . . . . . . . . 98

3-3
Four-Digit Addition . . . . . . . . . . . 100

3-4
Add Larger Numbers. . . . . . . . . . 102

3-5
Three or More Addends
. 104

3-6
Subtract with Regrouping . . . . . . 106

3-7
Subtraction: Regroup Twice. . . . . 108

3-8
Subtract Larger Numbers . . . . . . 110

3-9
Zeros in Subtraction . . . . . . . . . . 112

3-10
Addition and Subtraction
Practice
. . . . . . . . . . . . 114

3-11
Problem-Solving Strategy:
Choose the Operation. . . . . . . . . 116

3-12
Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . 118

End of Chapter

Check Your Progress (Lessons 1–12) . 120

Enrichment: Roman Numerals . . . . . . . . 121

Chapter 3 Test. . . . . . . . . . . . . . . . . . . . 122

Cumulative Review. . . . . . . . . . . . . . . . 123

Chapter
Multiply by One
and Two Digits

Chapter Opener . . . . . . . . . . . . . . . . . . . 125

4-1
Multiplication Properties
. 126

4-2
Multiplication Models . . . . . . . . . 128

4-3
Special Factors
. . . . . . . . 130

4-4
Multiply by One-Digit
Numbers . . . . . . . . . . . . . . . . . 132

4-5
Products: Front-End
Estimation . . . . . . . . . . . . . . . . 134

4-6
Multiply with Regrouping. . . . . . . 136

4-7
Multiply Three-Digit Numbers . . . 138

4-8
Multiply Money . . . . . . . . . . . . . . 140

4-9
Multiply Four-Digit Numbers . . . . 142

4-10
Patterns in Multiplication
. 144

4-11
Products: Rounding to
Estimate . . . . . . . . . . . . . . . . . 146

4-12
Multiply by Two-Digit
Numbers . . . . . . . . . . . . . . . . . 148

4-13
More Multiplying by
Two-Digit Numbers . . . . . . . . . 150

4-14
Multiply with Three-Digit
Numbers . . . . . . . . . . . . . . . . . 152

4-15
Problem-Solving Strategy:
Work Backward. . . . . . . . . . . . . . 154

4-16
Problem-Solving Applications:
Mixed Review . . . . . . . . . . . . . . . 156

End of Chapter

Check Your Progress (Lessons 1–16) . 158

Enrichment: Clustering. . . . . . . . . . . . . . 159

Chapter 4 Test. . . . . . . . . . . . . . . . . . . . 160

Cumulative Review. . . . . . . . . . . . . . . . 161

*Develops concept or skill with manipulatives.
Lesson promotes algebraic reasoning.

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