Table Of ContentIMPROVE
YOUR
Math
Problem Solving Made Simple
for Middle School Math
Francine D. Galko
NEW YORK
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Copyright © 2002 LearningExpress, LLC.
All rights reserved under International and Pan-American
Copyright Conventions. Published in the United States by
LearningExpress, LLC, New York.
Library of Congress Cataloging-in-Publication Data
Galko, Francine.
Improve your math : problem solving made easy for the middle school years / Francine
Galko.—1st ed.
p. cm.
ISBN 1-57685-406-X
1. Mathematics—Study and teaching (Middle school) I. Title
QA11.2 .G35 2002
513'.14—dc21
2001038994
Printed in the United States of America
9 8 7 6 5 4 3 2 1
First Edition
ISBN 1-57685-406-X
For more information or to place an order, contact
LearningExpress at:
900 Broadway
Suite 604
New York, NY 10003
Or visit us at:
www.learnatest.com
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Contents
INTRODUCTION vii
GETTING STARTED: Pretest 1
SECTION 1: Whole Numbers 15
(cid:2) Lesson 1: Order of Operations 17
(cid:2) Lesson 2: Finding Squares and Square Roots 23
Real World Problems 28
Answers and Explanations 30
SECTION 2: Fractions 33
(cid:2) Lesson 3: Converting Fractions 35
(cid:2) Lesson 4: Adding and Subtracting Fractions 44
(cid:2) Lesson 5: Multiplying and Dividing Fractions 50
(cid:2) Lesson 6: Working with Improper Fractions 56
and Mixed Numbers
Real World Problems 68
Answers and Explanations 70
SECTION 3: Decimals 87
(cid:2) Lesson 7: Adding and Subtracting Decimals 89
(cid:2) Lesson 8: Multiplying and Dividing Decimals 98
Real World Problems 107
Answers and Explanations 110
CONTENTS (cid:2) IMPROVE YOUR MATH v
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vi IMPROVE YOUR MATH (cid:2) CONTENTS
SECTION 4: Percentages 121
(cid:2) Lesson 9: Converting Percents, Decimals, and Fractions 123
(cid:2) Lesson 10: Solving Percent Problems 132
Real World Problems 141
Answers and Explanations 143
SECTION 5: Statistics 157
(cid:2) Lesson 11: Finding Mean, Median, and Mode 159
(cid:2) Lesson 12: Using Ratios and Proportions 165
(cid:2) Lesson 13: Understanding Probability 180
Real World Problems 186
Answers and Explanations 189
SECTION 6: Graphs, Tables, and Charts 199
(cid:2) Lesson 14: Interpreting Pie Charts, Line Graphs, and Bar Graphs 201
(cid:2) Lesson 15: Getting Information from Tables and Charts 212
Real World Problems 227
Answers and Explanations 235
SECTION 7: Introduction to Algebra 241
(cid:2) Lesson 16: Algebraic Expressions 243
(cid:2) Lesson 17: Solving Algebraic Equations 254
Real World Problems 260
Answers and Explanations 262
SECTION 8: Introduction to Geometry 275
(cid:2) Lesson 18: Points, Lines, Rays, Line Segments, and Angles 277
(cid:2) Lesson 19: Finding Perimeter, Circumference, Area, and Volume 294
(cid:2) Lesson 20: Congruence and Similarity 307
(cid:2) Lesson 21: The Pythagorean Theorem 320
Real World Problems 326
Answers and Explanations 329
CHECK YOUR UNDERSTANDING: Posttest 343
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Introduction
M
iddle schoolis an exciting time of your life. It’s full of changes and challenges. By eighth
grade, you are expected to be proficient in a number of areas—you’ll be required to take tests that mea-
sure your reading, writing, and math skills. So, take the time now to brush up your math skills before
you hit high school.
(cid:2) HOW THIS BOOK CAN HELP YOU
If you’re having trouble in math, this book can help you get on the right track. Even if you feel pretty
confident about your math skills, you can use this book to help you review what you’ve already learned
and practice with the same kinds of questions you’ll see on standardized and classroom math tests, so
you are sure to be prepared for the coming challenges of high school.
Many study guides tell you how to improve your math—this book doesn’t just tell you how to
solve math problems, it showsyou how. You’ll find page after page of strategies that work, and you are
never left stranded wondering how to get the right answer to a problem. You are shown all the steps
to take so that you can successfully solve every single problem, and see the strategies at work. This
book is like your own personal math tutor!
With help from this book, you will be prepared for the higher-level mathematics you’ll encounter
in high school. So, now’s the time to improve your math skills because you will use them—both now
and in the future—in school, at work, and in your personal life. As you work through this book, you
will become more confident in math and you can pass standardized tests and classroom math tests more
easily.
INTRODUCTION (cid:2) IMPROVE YOUR MATH vii
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viii IMPROVE YOUR MATH (cid:2) INTRODUCTION
(cid:2) HOW THIS BOOK IS ORGANIZED
This book is organized into eight sections, or major areas of math, such as fractions, decimals, algebra,
and geometry. Each section is divided into short lessons that explain the main concepts you need to
know. Each lesson tells you what kinds of key words and problems to look for when you are solving
math problems, and gives you step-by-step strategies to solve each kind of problem you will encounter.
Sometimes math books assume you can follow explanations of difficult concepts even when they
move quickly or leave out steps. That’s notthe case with this book. In each lesson, you’ll find step-by-
step strategies for tackling the different kinds of math problems you are likely to find on standardized
tests and classroom math tests. Then, you’re given a chance to apply what you’ve learned with hun-
dreds of practice problems. Answers to the practice problems are provided at the end of each section,
so you can check your progress as you go along.
As you work through this book, you’ll notice that the lessons are sprinkled with all kinds of help-
ful tips and icons. Look for these icons and the tips they provide.
Shortcut When you see this icon, you’ll know that a quicker, easier way to
H O RTCUT
S solve a math problem follows. You’ll find this icon both in the lessons and in
the answer key, so you can practice the shortcuts and see how they work in real
problems.
Test Taking Tip This icon tells you about tips especially useful for taking
KINGTIP
A
T math tests. They cover additional strategies or well-organized information you
T I
S
E can use as a reference, long after you’ve worked through all the lessons in the
T
book.
Think About It This icon is used to signal another way of looking at a prob-
A B OUTIT
K lem or concept. You’ll get extra information and more in-depth discussions when
N
I
H
T you see this icon.
Real World Problems Each section ends with a set of Real World Problems. These aren’t the same
old practice problems you’ll find in other math books. These problems apply the skills you’ve learned
in each section to situations you encounter every day. As you work through these problems, you’ll see
that the skills you’re learning aren’t important only for math tests. They are also important skills to
know for questions that come up every day.
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INTRODUCTION (cid:2) IMPROVE YOUR MATH ix
A WORD ABOUT WORD PROBLEMS
If you’re looking specifically for help with word problems, you’ve come to the right
place! Every section of this book includes word problems and step-by-step strategies for
solving them. Not only do most of the lessons end with word problems, but every single
section ends with a set of word problems that you’ll encounter in the real world.
In addition to including lots of word problems for you to practice on, these Real World
Problem sections include test-taking tips for tackling all kinds of word problems. That’s
not all—the answer key will walk you through solving every word problem. You’ll feel like
you have your own personal tutor.
(cid:2) HOW TO USE THIS BOOK
You should get started by taking the Pretest. You’ll test your math skills and see where you might need
to focus your study.
Then, begin the lessons, study the example problems, and try your hand at the practice problems.
Check your answers as you go along, so if you miss a question, you can study a little more before mov-
ing on to the next lesson.
After you’ve completed all 21 lessons in the book, try your hand at the Posttest to see how much
you’ve learned. You’ll also be able see any areas where you may need a little more practice. You can go
back to the section that covers that skill for some more review and practice.
Good luck, and let’s get started!
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Getting
Started
(cid:2) PRETEST
Before you start Lesson 1, you might want to take this short Pretest. The Pretest is 25 multiple-
choice questions that cover the basic concepts and skills covered in this book. Of course, every skill,
shortcut, concept, and type of problem in the book cannot be covered in only 25 questions; however,
the Pretest can give you a general idea of which skills you know well and which skills you might need
to work on.
You can use the answer sheet on the next page to record your answers to the Pretest. Or, you can
simply circle your answers as you work through the Pretest. If this book doesn’t belong to you, write
the numbers 1-25 on a sheet of your own paper and record your answers there.
Take your time to work through the Pretest. Don’t feel rushed. It may take a few questions to get
your mind thinking about math. When you have completed the Pretest, check your answers against
the answer key at the end of the test.
GETTING STARTED (cid:2) IMPROVE YOUR MATH 1
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2 IMPROVE YOUR MATH (cid:2) GETTING STARTED Pretest
PRETEST ANSWER SHEET
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