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TExES Mathematics Grades 4-8 (115)
The Most Complete Subject Review
Everything you need to know for the TExES Mathematics Grades 4-8 (115) exam, prepared by leading specialists in teacher education. Comprehensive review chapters cover all the subjects and skills tested on the exam. Examples in each chapter reinforce knowledge as you study.
The Best Practice Exams Available
2 practice exams based on the official TExES 115 Mathematics Grades 4-8 test – balanced to include every topic and type of question you can expect on the actual TExES Mathematics exam.
Total Explanations of Questions & Answers
Each practice exam comes with detailed feedback on every question. We don’t just say which answers are right – but explain why the others are wrong, so you’ll be prepared on test day!
Proven Test Prep Methods
REA’s focused TExES Mathematics content and practical advice have helped millions succeed on their exams. With our step-by-step study plan, you can score high on the TExES and get certified to teach in Texas!
Federal Guidelines for NCLB Compliance
You can expect that candidates with NCLB-compliant credentials will enjoy preferential status in hiring. In Texas, this means you need to pass the TExES assessments. Maximize your exam performance and master the TExES with the unrivaled certification expertise that only REA can offer.
Get the World’s Most Advanced TExES Software
REA’s TExES Mathematics Grades 4-8 TestWare combines a realistic test environment with the most powerful scoring analysis and diagnostic tools available. With every practice test you take, you’ll gain knowledge and confidence for the real exam. Automatic scoring and instant reports help you zero in on the topics and types of questions that give you trouble now, so you’ll succeed on the TExES!
About the Author
She received her undergraduate degree from Mississippi College in 1976 with a major in mathematics. Masters work was completed in 1980 at Southeastern Louisiana University in Hammond, Louisiana with an emphasis in mathematics education. In 1992 she received her Ph.D. from the University of Southern Mississippi in Hattiesburg, Mississippi in Curriculum & Instruction with a focus in mathematics.
Her professional interests include mathematics education, teacher education, teacher efficacy, teaching and learning of mathematics, professional development, and assessment. She is interested in effective teaching of mathematics and its effects on student learning.
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About This Book and TestWare®
REA’s TExES Mathematics 48 (115) test prep is a comprehensive guide designed to
assist you in preparing to take this TExES test, the purpose of which is to ensure that you
have the prerequisite content and professional knowledge necessary for an entry-level
position in Texas public schools. To help you to succeed in this important step toward
your teaching career, this book features:
An accurate and complete overview of the competencies for the test
The information you need to know about how the exam works
A targeted review of each section of the exam
Tips and strategies for successfully completing standardized tests
Diagnostic tools to identify areas of strength and weakness
Two full-length practice tests that replicate the question format and level of difficulty. The practice tests are provided in two formats: in printed form in this book and on the enclosed TestWare® CD-ROM.
Detailed explanations for each answer on the practice tests. Designed specifically
to clarify the material, the explanations not only provide the correct answers, but
also explain why the other answer choices are incorrect.
When creating this test prep, the authors and editors considered the most recent test
administrations and professional standards. They also researched information from the
Texas Education Agency, professional journals, textbooks, and educators. The result is
the best TExES test preparation materials based on the latest information available.
We strongly recommend that you begin you preparation with the TestWare® tests,
which provide timed conditions and instantaneous, accurate scoring. To get the most out
of your studying time, follow the Study Schedule that appears on page 9 of this book. It
details how you can best budget your time.
About the TExES Mathematics 48 Test
The purpose of the TExES Mathematics 48 test is to assess the knowledge and skills
of prospective Texas teachers in the areas of mathematics. The Mathematics 4-8 test will
contain 80 scorable multiple-choice items and approximately 10 nonscorable items. Your
final scaled score will be based only on scorable items. The nonscorable multiple-choice
items are included for the purpose of pilot-testing of proposed new questions. These pilot
questions do not count toward your score. However, they are not identified on the test
There will be four answer choices for each multiple-choice question. Answers will be
marked on a separate answer sheet. Examinees are provided with both a definitions/formula page and a scientific calculator.
Who Administers the Test?
The Texas Education Agency has contracted with Educational Testing Service (ETS)
to assist in the development and administration of the TExES.
For additional information you can contact:
ETS-Texas Educator Certification Program
PO Box 6051
Princeton, NJ 08541-6051
Telephone: 1-800-205-2626 (U.S., U.S. Territories, and Canada)
1-609-771-7393 (all other locations)
Hours: Monday-Friday 8:00 a.m.-5:00 p.m. Central time
Fax: 1-973-735-0156 or 1-866-484-5860
The TExES tests are administered six times during the testing year. Each test date has
morning and afternoon test sessions. Each session is five hours long.
Do I Pay a Registration Fee?
To take the TExES, you must pay a registration fee. For information about the fees,
log on to http://www.texes.ets.org/texes/AboutTheTest/.
How Is the TExES Mathematics 48 Test Scored?
Test results are reported as scaled scores in a range from 100 to 300. Your total scaled
score shows how you performed on the test as a whole and whether you passed the test.
Your report will include Domain and Competency performance on each domain and each
The scale score allows comparison among any version of the same test. The raw
scores cannot be compared from one version of a test to another. You receive one point
for each correct response and no points for each incorrect response. Most tests will also
include nonscorable questions. Therefore the total number of questions reported on your
score report is usually less than the total number of questions that you saw on the test.
The nonscorable questions will not be used in the calculation of your score.
A total test scaled score that is reported on a scale of 100-300. The minimum passing
score is a scaled score of 240. This score represents the minimum level of competency
required to be an entry-level educator in this fi eld in Texas public schools.
To gauge how well you do on the practice tests in this book and TestWare®, calculate
your percentage right; a score of a 75% correct will assure that you will pass the TExES
When Will I Receive My Score Report, and What Will It Look Like?
Approximately four weeks after the test, you will receive a score report in the mail.
The report will say if you have passed the test and will include your performance in the
major content domains of the test and in the specific content competencies of the test.
Be aware that this information may be less reliable because it may be based on fewer test
Unofficial test scores will be posted on the Internet on the score report mailing date of
each test administration. You can find information about receiving your unofficial scores,
your score scale, and other score report topics on the SBEC Website at www.sbec.state.tx.us.
Can I Retake the Test?
If you wish to retake the paper-based test, you may do so at any subsequent
paper-based test administration. You must wait 60 days to retake the test online.
Please consult the TExES website at http://texes.ets.org/texes/ for information about test
registration. The TExES website also includes information regarding test retakes and
When Should I Start Studying?
It is never too early to start studying for the TExES Mathematics 4-8 test. The earlier
you begin, the more time you will have to sharpen your skills. Do not procrastinate!
Cramming is not an effective way to study because it does not allow you the time you
need to think about the content, review the domains, and take the practice tests.
What Do the Review Sections Cover?
The targeted review in this book is designed to help you sharpen the mathematical
skills you need to approach the TExES Mathematics 4-8 Test, as well as provide strategies
for attacking the questions.
Each competency area included in the TExES Mathematics 4-8 test is examined in a
separate chapter. The skills required for all domains are extensively discussed to optimize
your understanding of what the examination covers.
Your schooling has taught you most of the information you need to answer the questions
on the test. The review sections in this book are designed to help you fit the information
you have acquired into the domains and competencies specified on the TExES.
Going over your class notes and textbooks together with the reviews provided here will
give you an excellent springboard for passing the examination.
Studying for the TExES Mathematics 48 Test
Choose the time and place for studying that works best for you. Some people set aside
a certain number of hours every morning to study, while others prefer to study at night
before going to sleep. Other people study off and on during the day for instance, while
waiting for a bus or during a lunch break. Only you can determine when and where your
study time will be most effective.
Be consistent and use your time efficiently. Work out a study routine and stick to it.
When you take the practice tests, simulate the conditions of the actual test as closely
as possible. Turn off your television and radio, and sit down at a table in a quiet room,
free from distraction. On completing a practice test, score it and thoroughly review the
explanations to the questions you answered incorrectly; however, do not review too much
at any one time. Concentrate on one problem area at a time by reviewing the question
and explanation, and by studying the review in this guide until you are confident that
you have mastered the material. Keep track of your scores so you can gauge your progress
and discover general weaknesses in particular sections. Give extra attention to the
reviews that cover your areas of difficulty, so you can build your skills in those areas.
Many have found the use of study or note cards very helpful for this review.
But you can condense or expand the time-line to suit your personal schedule. It is
vital that you adhere to a structured plan and set aside ample time each day to study. The
more time you devote to studying, the more prepared and confident you will be on the day
of the test. Don’t wait until the last minute to begin your studying!
Although you may not be familiar with tests like the TExES, this book will acquaint
you with this type of exam and help alleviate your test-taking anxieties. By following the
seven suggestions listed here, you can become more relaxed about taking the TExES, as
well as other tests.
Tip 1. Become comfortable with the format of the TExES. When you are practicing,
stay calm and pace yourself. After simulating the test only once, you will boost your
chances of doing well, and you will be able to sit down for the actual TExES with much
Tip 2. Read all the possible answers. Just because you think you have found the correct
response, do not automatically assume that it is the best answer. Read through each
choice to be sure that you are not making a mistake by jumping to conclusions.
Tip 3. Use the process of elimination. Go through each answer to a question and
eliminate as many of the answer choices as possible. If you can eliminate two answer
choices, you have given yourself a better chance of getting the item correct, because only
two choices are left from which to make your guess. Do not leave an answer blank; it is
better to guess than not to answer a question on the TExES test because you will not be
penalized for incorrect answers.
Tip 4. Place a question mark in your answer booklet next to the answers you guessed,
and then recheck them later if you have time.
Tip 5. Work quickly and steadily. You will have a total of five hours to complete the
test. Taking the practice tests in this book will help you learn to budget your time.
Tip 6. Learn the directions and format of the test. This will not only save time but
also will help you avoid anxiety (and the mistakes caused by being anxious).
Tip 7. When taking the multiple-choice portion of the test, be sure that the answer
oval you fill in corresponds to the number of the question in the test booklet. The multiple-
choice test is graded by machine, and marking one wrong answer can throw off your
answer key and your score. Be extremely careful.
Before the Test
On the morning of the test, be sure to dress comfortably so you are not distracted
by being too hot or too cold while taking the test. Plan to arrive at the test center early.
This will allow you to collect your thoughts and relax before the test and will also spare
you the anguish that comes with rushing. You should check your TExES Registration
Bulletin to find out what time to arrive at the center.
What to Bring
Before you leave for the test center, make sure that you have your admission ticket.
Your admission ticket lists your test selection, test site, test date, and reporting time. See
the test selection at www.texes.ets.org/faq. You must also bring personal identification
that includes one piece of current, government-issued identification, in the name in which
you registered, bearing a recent photograph and signature and one additional piece of
identification (with or without a photograph). If the name on your identification differs
from the name in which you are registered, you must bring official verification of the
change (e.g., marriage certificate, court order). Be sure to check the TExES website for
any updates or changes in the identification policy.
You must bring several sharpened No. 2 pencils with erasers, because none will be
provided at the test center. No mechanical pencils or mechanical erasers may be used.
If you like, you can wear a watch to the test center. However, you cannot wear one that
makes noise, because it might disturb the other test takers. Dictionaries, textbooks, notebooks,
cell phones, beepers, PDAs, scratch paper, listening and recording devices, briefcases,
or packages are not permitted. Drinking, smoking, and eating during the test are
prohibited. Remember that cell phones are not allowed in the test center.
Using or having a cell phone in your possession in the test center may be grounds for
As part of the identity verification process, your thumbprint, or your photograph or
videotape may be taken at the test site. A refusal to participate would lead to dismissal
with no refund of test fees. This is in addition to the requirement that you must present
acceptable and valid identification. It is important that you visit the testing website
for the latest updates and security requirements and updates at http://texes.ets.org/texes/
Late Arrival Policy
You must report to the test site by the time stipulated. If you are late for a test session
you will not be admitted.
During the Test
Any time that you take for restroom breaks is considered part of the available testing
time, and additional testing time will not be granted. Procedures will be followed to maintain
test security. Once you enter the test center, follow all the rules and instructions given
by the test supervisor. If you do not, you risk being dismissed from the test and having
your score canceled.
Once the test begins, mark only one answer per question, completely erase unwanted
answers and marks, and fill in answers darkly and neatly.
When you finish your test, hand in your materials and you will be dismissed. Then, go
home and relax you deserve it!
Table of Contents
CHAPTER 1 INTRODUCTION
About This Book and TestWare®
About the TExES 4-8 (115) Mathematics Test
Studying for the TExES 4-8 (115) Mathematics Test
The Day of the Test
CHAPTER 2 NUMBER CONCEPTS
Order of Operations
Chapter 2 Quiz
CHAPTER 3 PATTERNS AND ALGEBRA
Inductive Reasoning Applied to Patterns
Variables, Algebraic Expressions and Properties
Operations with Polynomials
Cartesian Coordinate System
Relations and Functions
Solving Systems of Linear Equations
Applications of Equations, Relations, and Functions
Graphing Inequities on the Number Line
Graphing Linear Inequalities
Graphing Quadratic Inequalities
Foundations of Calculus
Chapter 3 Quiz
CHAPTER 4 GEOMETRY AND MEASUREMENT
Interior and Exterior Angle Sum Relationships in Polygons
Basic Trigonometric Functions
The Unit Circle
Three-Dimensional Geometric Shapes
Chapter 4 Quiz
CHAPTER 5 PROBABILITY AND STATISTICS
Measures of Central Tendency and Dispersion
Chapter 5 Quiz
CHAPTER 6 MATHEMATICAL PROCESSES AND PERSPECTIVES
Role of Problem Solving in Mathematics
Role of Communication in Mathematics
Role of Connections in Mathematics
Role of Reasoning in Mathematics
Chapter 6 Quiz
CHAPTER 7 MATHEMATICAL LEARNING, INSTRUCTION, AND ASSESSMENT
Teaching and Learning Mathematics
Relationship of Content and Pedagogical Knowledge
Assessing Mathematical Understanding
Chapter 7 Quiz
PRACTICE TEST 1
Questions by Domain
PRACTICE TEST 2
Questions by Domain
INSTALLING REA’s TestWare®