114 Math Science 4-8

Preparation Manual

TExES | Texas Examinations of Educator Standards

114 Mathematics/Science 4–8

Copyright © 2011 by Texas Education Agency (TEA). All rights reserved. The Texas Education Agency logo and TEA are registered trademarks ofTexas Education Agency. Texas Examinations of Educator Standards, TExES and the TExES logo are trademarks of Texas Education Agency.

This publication has been produced for Texas Education Agency (TEA) by ETS. ETS is under contract to Texas Education Agency to administer theTexas Examinations of Educator Standards (TExES) program and the Examination for the Certification of Educators in Texas (ExCET) program. TheTExES and ExCET programs are administered under the authority of Texas Education Agency; regulations and standards governing the program aresubject to change at the discretion of Texas Education Agency. Texas Education Agency and ETS do not discriminate on the basis of race, color,national origin, sex, religion, age or disability in the administration of the testing program or the provision of related services.

Chapter 1: Introduction to the Mathematics/Science 4–8 Test and Suggestionsfor Using This Test Preparation Manual ........................................................1

OverviewUsing the Test FrameworkOrganization of the TExES Test Framework

• Sample Competency• Sample Descriptive Statements

Studying for the TExES Test

Chapter 2: Background Information on the TExES Testing Program................................7The TExES Tests for Texas Teachers

• Development of the New TExES TestsTaking the TExES Test and Receiving Scores

• Educator Standards

Chapter 3: Study Topics ...............................................................................................11Test Framework for Field 114: Mathematics/Science 4–8

• The Domains• Total Test Breakdown

The StandardsCompetencies

• Domain I — Number Concepts• Domain II — Patterns and Algebra• Domain III — Geometry and Measurement• Domain IV — Probability and Statistics• Domain V — Mathematical Processes and Perspectives• Domain VI — Mathematical Learning, Instruction and Assessment• Domain VII — Scientific Inquiry and Processes• Domain VIII — Physical Science• Domain IX — Life Science• Domain X — Earth and Space Science• Domain XI — Science Learning, Instruction and Assessment

Chapter 4: Succeeding on Multiple-Choice Questions.................................................39Approaches to Answering Multiple-Choice QuestionsQuestion Formats

• Single Questions• Questions with Stimulus Material• Clustered Questions

Chapter 5: Multiple-Choice Practice Questions...........................................................49Sample Multiple-Choice QuestionsAnswer Key

Chapter 6: Are You Ready? – Last-Minute Tips .............................................................97Preparing to Take the Test

Appendix A Study Plan Sheet.......................................................................................101

Appendix B Preparation Resources..............................................................................103

TA B L E O F CO N T E N T S

Chapter 1Introduction to the Mathematics/Science 4–8Test and Suggestions for Using This TestPreparation Manual

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OVERVIEW

The State Board for Educator Certification (SBEC) has approved Texas educator standards thatdelineate what the beginning educator should know and be able to do. These standards, whichare based on the state-required curriculum for students — the Texas Essential Knowledge and Skills(TEKS) — form the basis for the Texas Examinations of Educator Standards® (TExES®) program.This initiative, administered by Texas Education Agency (TEA), will affect all areas of Texaseducation — from the more than 170 approved Texas Educator Preparation Programs (EPPs) to themore than 7,000 Texas school campuses. This standards-based system reflects SBEC’s commitmentto help align Texas education from kindergarten through college. SBEC and TEA’s roles in thisK–16 initiative will ensure that newly certified Texas educators have the essential knowledge andskills to teach the TEKS to the state’s public school students.

This manual is designed to help examinees prepare for the TExES test in this field. Its purpose is tofamiliarize examinees with the competencies to be tested, test question formats and pertinent studyresources. EPP staff may also find this information useful as they help examinees prepare for careersas Texas educators.

KEY FEATURES OF THE MANUAL

• List of competencies that will be tested• Strategies for answering multiple-choice questions• Sample test questions and answer key

If you have any questions after reading this preparation manual or you would like additionalinformation about the TExES tests or the educator standards, please visit the TEA website atwww.tea.state.tx.us.

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TExES Preparation Manual — Mathematics/Science 4–82

INTRODUCTION TO THE MATHEMATICS/SCIENCE 4–8 TESTAND SUGGESTIONS FOR USING THIS TEST PREPARATION MANUAL

USING THE TEST FRAMEWORK

The Texas Examinations of Educator Standards (TExES) tests measure the content knowledgerequired of an entry-level educator in a particular field in Texas public schools. This manual isdesigned to guide your preparation by helping you become familiar with the material to be coveredon the test you are planning to take, identify areas where you feel you may be weak and increaseyour knowledge in those areas by helping you design a study plan.

When preparing for this test, you should focus on the competencies and descriptivestatements, which delineate the content that is eligible for testing. A portion of the contentis represented in the sample questions that are included in this manual. These test questionsrepresent only a sampling of questions. Thus, your test preparation should focus on thecompetencies and descriptive statements and not simply on the sample questions.

ORGANIZATION OF THE TEXES TEST FRAMEWORK

The test framework is based on the educator standards for this field.

The content covered by this test is organized into broad areas of content called domains. Eachdomain covers one or more of the educator standards for this field. Within each domain, the contentis further defined by a set of competencies. Each competency is composed of two major parts:

1. the competency statement, which broadly defines what an entry-level educator in this fieldin Texas public schools should know and be able to do, and

2. the descriptive statements, which describe in greater detail the knowledge and skills eligiblefor testing.

The educator standards being assessed within each domain are listed for reference at the beginningof the test framework, which begins on page 12. These are followed by a complete set of theframework’s competencies and descriptive statements.

TExES Preparation Manual — Mathematics/Science 4–8 3


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An example of a competency and its accompanying descriptive statements is provided below.

SAMPLE COMPETENCY

Mathematics/Science 4–8

competency 001THE TEACHER UNDERSTANDS THE STRUCTURE OF NUMBER SYSTEMS, THEDEVELOPMENT OF A SENSE OF QUANTITY AND THE RELATIONSHIP BETWEENQUANTITY AND SYMBOLIC REPRESENTATIONS.

SAMPLE DESCRIPTIVE STATEMENTS

The beginning teacher:

A. Analyzes the structure of numeration systems and the roles of place value and zero in thebase ten system.

B. Understands the relative magnitude of whole numbers, integers, rational numbers and realnumbers.

C. Demonstrates an understanding of a variety of models for representing numbers (e.g., fractionstrips, diagrams, patterns, shaded regions, number lines).

D. Demonstrates an understanding of equivalency among different representations of rationalnumbers.

E. Selects appropriate representations of real numbers (e.g., fractions, decimals, percents, roots,exponents, scientific notation) for particular situations.

F. Understands the characteristics of the set of whole numbers, integers, rational numbers, realnumbers and complex numbers (e.g., commutativity, order, closure, identity elements, inverseelements, density).

G. Demonstrates an understanding of how some situations that have no solution in one numbersystem (e.g., whole numbers, integers, rational numbers) have solutions in another numbersystem (e.g., real numbers, complex numbers).

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STUDYING FOR THE TEXES TESTThe following steps may be helpful in preparing for the TExES test.

1. Identify the information the test will cover by reading through the test competencies(see Chapter 3). Within each domain of this TExES test, each competency will receiveapproximately equal coverage.

2. Read each competency with its descriptive statements in order to get a more specific ideaof the knowledge you will be required to demonstrate on the test. You may wish to usethis review of the competencies to set priorities for your study time.

3. Review the “Preparation Resources” section of this manual (Appendix B) for possibleresources to consult. Also, compile key materials from your preparation course work thatare aligned with the competencies.

4. Study this manual for approaches to taking the TExES test.

5. When using resources, concentrate on the key skills and important abilities that arediscussed in the competencies and descriptive statements.

6. Use the study plan sheet (Appendix A) to help you plan your study.

NOTE: This preparation manual is the only TExES test study material endorsed by TexasEducation Agency (TEA) for this field. Other preparation materials may not accurately reflectthe content of the test or the policies and procedures of the TExES program.



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Chapter 2Background Information on the TExESTesting Program

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THE TEXES TESTS FOR TEXAS TEACHERS

As required by the Texas Education Code §21.048, successful performance on educator certificationexaminations is required for the issuance of a Texas educator certificate. Each TExES test is acriterion-referenced examination designed to measure the knowledge and skills delineated in thecorresponding TExES test framework. Each test framework is based on standards that weredeveloped by Texas educators and other education stakeholders.

Each TExES test is designed to measure the requisite knowledge and skills that an entry-leveleducator in this field in Texas public schools must possess. The tests include both individual(stand-alone) test questions and questions that are arranged in clustered sets based on real-worldsituations faced by educators.

DEVELOPMENT OF THE NEW TExES TESTS

Committees of Texas educators and members of the community guide the development of thenew TExES tests by participating in each stage of the test development process. These workingcommittees are composed of Texas educators from public and charter schools, university and EPPfaculty, education service center staff, representatives from professional educator organizations,content experts and members of the business community. The committees are balanced in terms ofposition, affiliation, years of experience, ethnicity, gender and geographical location. The committeemembership is rotated during the development process so that numerous Texas stakeholders may beactively involved. The steps in the process to develop the TExES tests are described below.

1. Develop Standards. Committees are established to recommend what the beginning educatorshould know and be able to do. Using the Texas Essential Knowledge and Skills (TEKS) asthe focal point, draft standards are prepared to define the knowledge and skills required of thebeginning educator.

2. Review Standards. Committees review and revise the draft standards. The revised draftstandards are then placed on the TEA website for public review and comment. Thesecomments are used to prepare a final draft of the standards that will be presented to the SBECBoard for discussion, the State Board of Education (SBOE) for review and comment and theSBEC Board for approval. Standards not based specifically on the TEKS, such as those forlibrarians and counselors, are proposed as rule by the SBEC Board; sent to the SBOE for its90-day review; and, if not rejected by the SBOE, adopted by the SBEC Board.

3. Develop Test Frameworks. Committees review and revise draft test frameworks that arebased on the standards. These frameworks outline the specific competencies to be measuredon the new TExES tests. Draft frameworks are not finalized until after the standards areapproved and the job analysis/content validation survey (see #4) is complete.

4. Conduct Job Analysis/Content Validation Surveys. A representative sample of Texaseducators who practice in or prepare individuals for each of the fields for which an educatorcertificate has been proposed are surveyed to determine the relative job importance of eachcompetency outlined in the test framework for that content area. Frameworks are revised asneeded following an analysis of the survey responses.

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BACKGROUND INFORMATION ON THE TEXES TESTING PROGRAM

5. Develop and Review New Test Questions. The test contractor develops draft questions thatare designed to measure the competencies described in the test framework. Committeesreview the newly developed test questions that have been written to reflect the competenciesin the new test framework. Committee members scrutinize the draft questions forappropriateness of content and difficulty; clarity; match to the competencies; and potentialethnic, gender and regional bias.

6. Conduct Pilot Test of New Test Questions. All of the newly developed test questions thathave been deemed acceptable by the question review committees are then administered to anappropriate sample of candidates for certification.

7. Review Pilot Test Data. Pilot test results are reviewed to ensure that the test questions arevalid, reliable and free from bias.

8. Administer TExES Tests. New TExES tests are constructed to reflect the competencies, andthe tests are administered to candidates for certification.

9. Set Passing Standard. A Standard Setting Committee convenes to review performance datafrom the initial administration of each new TExES test and to recommend a final passingstandard for that test. The SBEC Board considers this recommendation as it establishes apassing score on the test.



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TAKING THE TEXES TEST AND RECEIVING SCORES

Please refer to the current TExES Registration Bulletin or the ETS TExES website atwww.texes.ets.org for information on test dates, test centers, fees, registration procedures andprogram policies.

Your score report will be available to you in your testing account on the ETS TExES onlineregistration system by 5 p.m. Central time on the score reporting date indicated in theRegistration Bulletin. The report will indicate whether you have passed the test and will include:

• A total test scaled score. Scaled scores are reported to allow for the comparison ofscores on the same content-area test taken on different test administration dates.The total scaled score is not the percentage of questions answered correctly and isnot determined by averaging the number of questions answered correctly in eachdomain.

– For all TExES tests, the score scale is 100–300 with a scaled score of 240 as theminimum passing score. This score represents the minimum level of competencyrequired to be an entry-level educator in this field in Texas public schools.

• Your performance in the major content domains of the test and in the specificcontent competencies of the test.

– This information may be useful in identifying strengths and weaknesses in yourcontent preparation and can be used for further study or for preparing to retake thetest. However, it is important to use caution when interpreting scores reported bydomain and competency as these scores are typically based on a smaller number ofitems than the total score and therefore may not be as reliable as the total score.

• A link to information to help you understand the score scale and interpret yourresults.

A score report will not be available to you if you are absent or choose to cancel your score.

For more information about scores or to access scores online, go to www.texes.ets.org.

EDUCATOR STANDARDS

Complete, approved educator standards are posted on the TEA website at www.tea.state.tx.us.

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Chapter 3Study Topics

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TEST FRAMEWORK FOR FIELD 114: MATHEMATICS/SCIENCE 4–8

THE DOMAINS*

Domain IV8%

Domain II11%

Domain III11%

Domain I8%

Domain V5%

Domain VI8%

Domain VII11%

Domain VIII11%

Domain IX11%

Domain X11%

Domain XI6%

• Domain I: Number ConceptsStandard Assessed: Mathematics I

• Domain II: Patterns and AlgebraStandard Assessed: Mathematics II

• Domain III: Geometry and MeasurementStandard Assessed: Mathematics III

• Domain IV: Probability and StatisticsStandard Assessed: Mathematics IV

• Domain V: Mathematical Processes and PerspectivesStandards Assessed: Mathematics V–VI

• Domain VI: Mathematical Learning, Instruction and AssessmentStandards Assessed: Mathematics VII–VIII

• Domain VII: Scientific Inquiry and ProcessesStandards Assessed: Science I–III, VI–VII, XI

• Domain VIII: Physical ScienceStandard Assessed: Science VIII

• Domain IX: Life ScienceStandard Assessed: Science IX

• Domain X: Earth and Space ScienceStandard Assessed: Science X

• Domain XI: Science Learning, Instruction and AssessmentStandards Assessed: Science III–V

*Percentages do not add up to 100 due to rounding.

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STUDY TOPICS

TOTAL TEST BREAKDOWN

• Exam is offered as a computer-administered test

• 120 Multiple-Choice Questions (100 Scored Questions*)

*The number of scored questions will not vary; however, the number of questions that are not scoredmay vary in the actual test. Your final scaled score will be based only on scored questions.

THE STANDARDS

DOMAIN I — NUMBER CONCEPTS (approximately 8% of the test)

MATHEMATICS STANDARD INumber Concepts: The mathematics teacher understands and uses numbers, number systems

and their structure, operations and algorithms, quantitative reasoning and technologyappropriate to teach the statewide curriculum (Texas Essential Knowledge and Skills[TEKS]) in order to prepare students to use mathematics.

DOMAIN II — PATTERNS AND ALGEBRA (approximately 11% of the test)

MATHEMATICS STANDARD II:Patterns and Algebra: The mathematics teacher understands and uses patterns, relations,

functions, algebraic reasoning, analysis and technology appropriate to teach the statewidecurriculum (Texas Essential Knowledge and Skills [TEKS]) in order to prepare students touse mathematics.

DOMAIN III — GEOMETRY AND MEASUREMENT (approximately 11% of the test)

MATHEMATICS STANDARD III:Geometry and Measurement: The mathematics teacher understands and uses geometry, spatial

reasoning, measurement concepts and principles and technology appropriate to teach thestatewide curriculum (Texas Essential Knowledge and Skills [TEKS]) in order to preparestudents to use mathematics.

DOMAIN IV — PROBABILITY AND STATISTICS (approximately 8% of the test)

MATHEMATICS STANDARD IV:Probability and Statistics: The mathematics teacher understands and uses probability and

statistics, their applications and technology appropriate to teach the statewide curriculum(Texas Essential Knowledge and Skills [TEKS]) in order to prepare students to usemathematics.


STUDY TOPICS

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DOMAIN V — MATHEMATICAL PROCESSES AND PERSPECTIVES (approximately 5% ofthe test)

MATHEMATICS STANDARD V:Mathematical Processes: The mathematics teacher understands and uses mathematical

processes to reason mathematically, to solve mathematical problems, to make mathematicalconnections within and outside of mathematics and to communicate mathematically.

MATHEMATICS STANDARD VI:Mathematical Perspectives: The mathematics teacher understands the historical development

of mathematical ideas, the interrelationship between society and mathematics, the structureof mathematics and the evolving nature of mathematics and mathematical knowledge.

DOMAIN VI — MATHEMATICAL LEARNING, INSTRUCTION AND ASSESSMENT(approximately 8% of the test)

MATHEMATICS STANDARD VII:Mathematical Learning and Instruction: The mathematics teacher understands how children

learn and develop mathematical skills, procedures and concepts, knows typical errorsstudents make and uses this knowledge to plan, organize and implement instruction; to meetcurriculum goals; and to teach all students to understand and use mathematics.

MATHEMATICS STANDARD VIII:Mathematical Assessment: The mathematics teacher understands assessment and uses a

variety of formal and informal assessment techniques appropriate to the learner on anongoing basis to monitor and guide instruction and to evaluate and report student progress.

DOMAIN VII — SCIENTIFIC INQUIRY AND PROCESSES (approximately 11% of the test)

SCIENCE STANDARD I:The science teacher manages classroom, field and laboratory activities to ensure the safety of all

students and the ethical care and treatment of organisms and specimens.

SCIENCE STANDARD II:The science teacher understands the correct use of tools, materials, equipment and technologies.

SCIENCE STANDARD III:The science teacher understands the process of scientific inquiry and its role in science

instruction.

SCIENCE STANDARD VI:The science teacher understands the history and nature of science.

SCIENCE STANDARD VII:The science teacher understands how science affects the daily lives of students and how science

interacts with and influences personal and societal decisions.

SCIENCE STANDARD XI:The science teacher knows unifying concepts and processes that are common to all sciences.

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STUDY TOPICS

DOMAIN VIII — PHYSICAL SCIENCE (approximately 11% of the test)

SCIENCE STANDARD VIII:The science teacher knows and understands the science content appropriate to teach the

statewide curriculum (Texas Essential Knowledge and Skills [TEKS]) in physical science.

DOMAIN IX — LIFE SCIENCE (approximately 11% of the test)

SCIENCE STANDARD IX:The science teacher knows and understands the science content appropriate to teach the

statewide curriculum (Texas Essential Knowledge and Skills [TEKS]) in life science.

DOMAIN X — EARTH AND SPACE SCIENCE (approximately 11% of the test)

SCIENCE STANDARD X:The science teacher knows and understands the science content appropriate to teach the

statewide curriculum (Texas Essential Knowledge and Skills [TEKS]) in Earth and spacescience.

DOMAIN XI — SCIENCE LEARNING, INSTRUCTION AND ASSESSMENT(approximately 6% of the test)

SCIENCE STANDARD III:The science teacher understands the process of scientific inquiry and its role in science

instruction.

SCIENCE STANDARD IV:The science teacher has theoretical and practical knowledge about teaching science and about

how students learn science.

SCIENCE STANDARD V:The science teacher knows the varied and appropriate assessments and assessment practices to

monitor science learning.


STUDY TOPICS

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COMPETENCIES

DOMAIN I — NUMBER CONCEPTS

competency 001THE TEACHER UNDERSTANDS THE STRUCTURE OF NUMBER SYSTEMS, THEDEVELOPMENT OF A SENSE OF QUANTITY AND THE RELATIONSHIP BETWEENQUANTITY AND SYMBOLIC REPRESENTATIONS.


A. Analyzes the structure of numeration systems and the roles of place value and zeroin the base ten system.

B. Understands the relative magnitude of whole numbers, integers, rational numbersand real numbers.

C. Demonstrates an understanding of a variety of models for representing numbers(e.g., fraction strips, diagrams, patterns, shaded regions, number lines).

D. Demonstrates an understanding of equivalency among different representations ofrational numbers.

E. Selects appropriate representations of real numbers (e.g., fractions, decimals,percents, roots, exponents, scientific notation) for particular situations.

F. Understands the characteristics of the set of whole numbers, integers, rationalnumbers, real numbers and complex numbers (e.g., commutativity, order, closure,identity elements, inverse elements, density).

G. Demonstrates an understanding of how some situations that have no solution in onenumber system (e.g., whole numbers, integers, rational numbers) have solutions inanother number system (e.g., real numbers, complex numbers).

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STUDY TOPICS

competency 002THE TEACHER UNDERSTANDS NUMBER OPERATIONS AND COMPUTATIONALALGORITHMS.


A. Works proficiently with real and complex numbers and their operations.

B. Analyzes and describes relationships between number properties, operations andalgorithms for the four basic operations involving integers, rational numbers andreal numbers.

C. Uses a variety of concrete and visual representations to demonstrate the connectionsbetween operations and algorithms.

D. Justifies procedures used in algorithms for the four basic operations with integers,rational numbers and real numbers and analyzes error patterns that may occur intheir application.

E. Relates operations and algorithms involving numbers to algebraic procedures (e.g.,adding fractions to adding rational expressions, division of integers to division ofpolynomials).

F. Extends and generalizes the operations on rationals and integers to includeexponents, their properties and their applications to the real numbers.

competency 003THE TEACHER UNDERSTANDS IDEAS OF NUMBER THEORY AND USES NUMBERS TOMODEL AND SOLVE PROBLEMS WITHIN AND OUTSIDE OF MATHEMATICS.


A. Demonstrates an understanding of ideas from number theory (e.g., primefactorization, greatest common divisor) as they apply to whole numbers, integers andrational numbers and uses these ideas in problem situations.

B. Uses integers, rational numbers and real numbers to describe and quantifyphenomena such as money, length, area, volume and density.

C. Applies knowledge of place value and other number properties to develop techniquesof mental mathematics and computational estimation.

D. Applies knowledge of counting techniques such as permutations and combinations toquantify situations and solve problems.

E. Applies properties of the real numbers to solve a variety of theoretical and appliedproblems.


STUDY TOPICS

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DOMAIN II — PATTERNS AND ALGEBRA

competency 004THE TEACHER UNDERSTANDS AND USES MATHEMATICAL REASONING TO IDENTIFY,EXTEND AND ANALYZE PATTERNS AND UNDERSTANDS THE RELATIONSHIPS AMONGVARIABLES, EXPRESSIONS, EQUATIONS, INEQUALITIES, RELATIONS AND FUNCTIONS.


A. Uses inductive reasoning to identify, extend and create patterns using concretemodels, figures, numbers and algebraic expressions.

B. Formulates implicit and explicit rules to describe and construct sequences verbally,numerically, graphically and symbolically.

C. Makes, tests, validates and uses conjectures about patterns and relationships in datapresented in tables, sequences or graphs.

D. Gives appropriate justification of the manipulation of algebraic expressions.

E. Illustrates the concept of a function using concrete models, tables, graphs andsymbolic and verbal representations.

F. Uses transformations to illustrate properties of functions and relations and to solveproblems.

competency 005THE TEACHER UNDERSTANDS AND USES LINEAR FUNCTIONS TO MODEL AND SOLVEPROBLEMS.


A. Demonstrates an understanding of the concept of linear function using concretemodels, tables, graphs and symbolic and verbal representations.

B. Demonstrates an understanding of the connections among linear functions,proportions and direct variation.

C. Determines the linear function that best models a set of data.

D. Analyzes the relationship between a linear equation and its graph.

E. Uses linear functions, inequalities and systems to model problems.

F. Uses a variety of representations and methods (e.g., numerical methods, tables,graphs, algebraic techniques) to solve systems of linear equations and inequalities.

G. Demonstrates an understanding of the characteristics of linear models and theadvantages and disadvantages of using a linear model in a given situation.

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STUDY TOPICS

competency 006THE TEACHER UNDERSTANDS AND USES NONLINEAR FUNCTIONS AND RELATIONS TOMODEL AND SOLVE PROBLEMS.


A. Uses a variety of methods to investigate the roots (real and complex), vertex andsymmetry of a quadratic function or relation.

B. Demonstrates an understanding of the connections among geometric, graphic,numeric and symbolic representations of quadratic functions.

C. Analyzes data and represents and solves problems involving exponential growth anddecay.

D. Demonstrates an understanding of the connections among proportions, inversevariation and rational functions.

E. Understands the effects of transformations, such as f(x ± c) on the graph of anonlinear function f(x).

F. Applies properties, graphs and applications of nonlinear functions to analyze, modeland solve problems.

G. Uses a variety of representations and methods (e.g., numerical methods, tables,graphs, algebraic techniques) to solve systems of quadratic equations andinequalities.

H. Understands how to use properties, graphs and applications of non-linear relationsincluding polynomial, rational, radical, absolute value, exponential, logarithmic,trigonometric and piecewise functions and relations to analyze, model and solveproblems.

competency 007THE TEACHER USES AND UNDERSTANDS THE CONCEPTUAL FOUNDATIONS OFCALCULUS RELATED TO TOPICS IN MIDDLE SCHOOL MATHEMATICS.


A. Relates topics in middle school mathematics to the concept of limit in sequences andseries.

B. Relates the concept of average rate of change to the slope of the secant line andinstantaneous rate of change to the slope of the tangent line.

C. Relates topics in middle school mathematics to the area under a curve.

D. Demonstrates an understanding of the use of calculus concepts to answer questionsabout rates of change, areas, volumes and properties of functions and their graphs.


STUDY TOPICS

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DOMAIN III — GEOMETRY AND MEASUREMENT

competency 008THE TEACHER UNDERSTANDS MEASUREMENT AS A PROCESS.


A. Selects and uses appropriate units of measurement (e.g., temperature, money, mass,weight, area, capacity, density, percents, speed, acceleration) to quantify, compareand communicate information.

B. Develops, justifies and uses conversions within measurement systems.

C. Applies dimensional analysis to derive units and formulas in a variety of situations(e.g., rates of change of one variable with respect to another) and to find and evaluatesolutions to problems.

D. Describes the precision of measurement and the effects of error on measurement.

E. Applies the Pythagorean theorem, proportional reasoning and right triangletrigonometry to solve measurement problems.

competency 009THE TEACHER UNDERSTANDS THE GEOMETRIC RELATIONSHIPS AND AXIOMATICSTRUCTURE OF EUCLIDEAN GEOMETRY.


A. Understands concepts and properties of points, lines, planes, angles, lengths anddistances.

B. Analyzes and applies the properties of parallel and perpendicular lines.

C. Uses the properties of congruent triangles to explore geometric relationships andprove theorems.

D. Describes and justifies geometric constructions made using a compass and straightedge and other appropriate technologies.

E. Applies knowledge of the axiomatic structure of Euclidean geometry to justify andprove theorems.

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STUDY TOPICS

competency 010THE TEACHER ANALYZES THE PROPERTIES OF TWO- AND THREE-DIMENSIONALFIGURES.


A. Uses and understands the development of formulas to find lengths, perimeters, areasand volumes of basic geometric figures.

B. Applies relationships among similar figures, scale and proportion and analyzes howchanges in scale affect area and volume measurements.

C. Uses a variety of representations (e.g., numeric, verbal, graphic, symbolic) toanalyze and solve problems involving two- and three-dimensional figures such ascircles, triangles, polygons, cylinders, prisms and spheres.

D. Analyzes the relationship among three-dimensional figures and relatedtwo-dimensional representations (e.g., projections, cross-sections, nets) and usesthese representations to solve problems.

competency 011THE TEACHER UNDERSTANDS TRANSFORMATIONAL GEOMETRY AND RELATESALGEBRA TO GEOMETRY AND TRIGONOMETRY USING THE CARTESIAN COORDINATESYSTEM.


A. Describes and justifies geometric constructions made using a reflection device andother appropriate technologies.

B. Uses translations, reflections, glide-reflections and rotations to demonstratecongruence and to explore the symmetries of figures.

C. Uses dilations (expansions and contractions) to illustrate similar figures andproportionality.

D. Uses symmetry to describe tessellations and shows how they can be used to illustrategeometric concepts, properties and relationships.

E. Applies concepts and properties of slope, midpoint, parallelism and distance in thecoordinate plane to explore properties of geometric figures and solve problems.

F. Applies transformations in the coordinate plane.

G. Uses the unit circle in the coordinate plane to explore properties of trigonometricfunctions.


STUDY TOPICS

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DOMAIN IV — PROBABILITY AND STATISTICS

competency 012THE TEACHER UNDERSTANDS HOW TO USE GRAPHICAL AND NUMERICAL TECHNIQUESTO EXPLORE DATA, CHARACTERIZE PATTERNS AND DESCRIBE DEPARTURES FROMPATTERNS.


A. Organizes and displays data in a variety of formats (e.g., tables, frequencydistributions, stem-and-leaf plots, box-and-whisker plots, histograms, pie charts).

B. Applies concepts of center, spread, shape and skewness to describe a datadistribution.

C. Supports arguments, makes predictions and draws conclusions using summarystatistics and graphs to analyze and interpret one-variable data.

D. Demonstrates an understanding of measures of central tendency (e.g., mean, median,mode) and dispersion (e.g., range, interquartile range, variance, standard deviation).

E. Analyzes connections among concepts of center and spread, data clusters and gaps,data outliers and measures of central tendency and dispersion.

F. Calculates and interprets percentiles and quartiles.

competency 013THE TEACHER UNDERSTANDS THE THEORY OF PROBABILITY.


A. Explores concepts of probability through data collection, experiments andsimulations.

B. Uses the concepts and principles of probability to describe the outcome of simpleand compound events.

C. Generates, simulates and uses probability models to represent a situation.

D. Determines probabilities by constructing sample spaces to model situations.

E. Solves a variety of probability problems using combinations, permutations andgeometric probability (i.e., probability as the ratio of two areas).

F. Uses the binomial, geometric and normal distributions to solve problems.

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STUDY TOPICS

competency 014THE TEACHER UNDERSTANDS THE RELATIONSHIP AMONG PROBABILITY THEORY,SAMPLING AND STATISTICAL INFERENCE, AND HOW STATISTICAL INFERENCE ISUSED IN MAKING AND EVALUATING PREDICTIONS.


A. Applies knowledge of designing, conducting, analyzing and interpreting statisticalexperiments to investigate real-world problems.

B. Demonstrates an understanding of random samples, sample statistics and therelationship between sample size and confidence intervals.

C. Applies knowledge of the use of probability to make observations and drawconclusions from single variable data and to describe the level of confidence in theconclusion.

D. Makes inferences about a population using binomial, normal and geometricdistributions.

E. Demonstrates an understanding of the use of techniques such as scatter plots,regression lines, correlation coefficients and residual analysis to explore bivariatedata and to make and evaluate predictions.

DOMAIN V — MATHEMATICAL PROCESSES AND PERSPECTIVES

competency 015THE TEACHER UNDERSTANDS MATHEMATICAL REASONING AND PROBLEM SOLVING.


A. Demonstrates an understanding of proof, including indirect proof, in mathematics.

B. Applies correct mathematical reasoning to derive valid conclusions from a set ofpremises.

C. Demonstrates an understanding of the use of inductive reasoning to makeconjectures and deductive methods to evaluate the validity of conjectures.

D. Applies knowledge of the use of formal and informal reasoning to explore,investigate and justify mathematical ideas.

E. Recognizes that a mathematical problem can be solved in a variety of ways andselects an appropriate strategy for a given problem.

F. Evaluates the reasonableness of a solution to a given problem.

G. Applies content knowledge to develop a mathematical model of a real-worldsituation and analyzes and evaluates how well the model represents the situation.

H. Demonstrates an understanding of estimation and evaluates its appropriate uses.


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competency 016THE TEACHER UNDERSTANDS MATHEMATICAL CONNECTIONS WITHIN AND OUTSIDE OFMATHEMATICS AND HOW TO COMMUNICATE MATHEMATICAL IDEAS AND CONCEPTS.


A. Recognizes and uses multiple representations of a mathematical concept (e.g., apoint and its coordinates, the area of circle as a quadratic function in r, probabilityas the ratio of two areas).

B. Uses mathematics to model and solve problems in other disciplines, such as art,music, science, social science and business.

C. Expresses mathematical statements using developmentally appropriate language,standard English, mathematical language and symbolic mathematics.

D. Communicates mathematical ideas using a variety of representations (e.g., numeric,verbal, graphic, pictorial, symbolic, concrete).

E. Demonstrates an understanding of the use of visual media such as graphs, tables,diagrams and animations to communicate mathematical information.

F. Uses the language of mathematics as a precise means of expressing mathematicalideas.

G. Understands the structural properties common to the mathematical disciplines.

DOMAIN VI — MATHEMATICAL LEARNING, INSTRUCTION AND ASSESSMENT

competency 017THE TEACHER UNDERSTANDS HOW CHILDREN LEARN AND DEVELOP MATHEMATICALSKILLS, PROCEDURES AND CONCEPTS.


A. Applies theories and principles of learning mathematics to plan appropriateinstructional activities for all students.

B. Understands how students differ in their approaches to learning mathematics withregards to diversity.

C. Uses students’ prior mathematical knowledge to build conceptual links to newknowledge and plans instruction that builds on students’ strengths and addressesstudents’ needs.

D. Understands how learning may be assisted through the use of mathematicsmanipulatives and technological tools.

E. Understands how to motivate students and actively engage them in the learningprocess by using a variety of interesting, challenging and worthwhile mathematicaltasks in individual, small-group and large-group settings.

F. Understands how to provide instruction along a continuum from concrete to abstract.

G. Recognizes the implications of current trends and research in mathematics andmathematics education.

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STUDY TOPICS

competency 018THE TEACHER UNDERSTANDS HOW TO PLAN, ORGANIZE AND IMPLEMENTINSTRUCTION USING KNOWLEDGE OF STUDENTS, SUBJECT MATTER AND STATEWIDECURRICULUM (TEXAS ESSENTIAL KNOWLEDGE AND SKILLS [TEKS]) TO TEACH ALLSTUDENTS TO USE MATHEMATICS.


A. Demonstrates an understanding of a variety of instructional methods, tools and tasksthat promote students’ ability to do mathematics described in the TEKS.

B. Understands planning strategies for developing mathematical instruction as adiscipline of interconnected concepts and procedures.

C. Develops clear learning goals to plan, deliver, assess and reevaluate instruction basedon the TEKS.

D. Understands procedures for developing instruction that establishes transitionsbetween concrete, symbolic and abstract representations of mathematical knowledge.

E. Applies knowledge of a variety of instructional delivery methods, such as individual,structured small-group and large-group formats.

F. Understands how to create a learning environment that provides all students,including English-language learners, with opportunities to develop and improvemathematical skills and procedures.

G. Demonstrates an understanding of a variety of questioning strategies to encouragemathematical discourse and to help students analyze and evaluate their mathematicalthinking.

H. Understands how technological tools and manipulatives can be used appropriately toassist students in developing, comprehending and applying mathematical concepts.

I. Understands how to relate mathematics to students’ lives and a variety of careers andprofessions.


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competency 019THE TEACHER UNDERSTANDS ASSESSMENT AND USES A VARIETY OF FORMAL ANDINFORMAL ASSESSMENT TECHNIQUES TO MONITOR AND GUIDE MATHEMATICSINSTRUCTION AND TO EVALUATE STUDENT PROGRESS.


A. Demonstrates an understanding of the purpose, characteristics and uses of variousassessments in mathematics, including formative and summative assessments.

B. Understands how to select and develop assessments that are consistent with what istaught and how it is taught.

C. Demonstrates an understanding of how to develop a variety of assessments andscoring procedures consisting of worthwhile tasks that assess mathematicalunderstanding, common misconceptions and error patterns.

D. Understands how to evaluate a variety of assessment methods and materials forreliability, validity, absence of bias, clarity of language and appropriateness ofmathematical level.

E. Understands the relationship between assessment and instruction and knows how toevaluate assessment results to design, monitor and modify instruction to improvemathematical learning for all students, including English-language learners.

DOMAIN VII — SCIENTIFIC INQUIRY AND PROCESSES

competency 020THE TEACHER UNDERSTANDS HOW TO MANAGE LEARNING ACTIVITIES TO ENSURE THESAFETY OF ALL STUDENTS.


A. Understands safety regulations and guidelines for science facilities and scienceinstruction.

B. Knows procedures for and sources of information regarding the appropriatehandling, use, conservation, disposal, recycling, care and maintenance of chemicals,materials, specimens and equipment.

C. Knows procedures for the safe handling and ethical care and treatment of organismsand specimens.

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STUDY TOPICS

competency 021THE TEACHER UNDERSTANDS THE CORRECT USE OF TOOLS, MATERIALS, EQUIPMENTAND TECHNOLOGIES.


A. Selects and safely uses appropriate tools, technologies, materials and equipmentneeded for instructional activities.

B. Understands concepts of precision, accuracy and error with regard to reading andrecording numerical data from a scientific instrument.

C. Understands how to gather, organize, display and communicate data in a variety ofways (e.g., construct charts, tables, graphs, maps, satellite images, diagrams, writtenreports, oral presentations).

D. Understands the international system of measurement (i.e., metric system) andperforms unit conversions within measurement systems.

competency 022THE TEACHER UNDERSTANDS THE PROCESS OF SCIENTIFIC INQUIRY AND THE HISTORYAND NATURE OF SCIENCE.


A. Understands the characteristics of various types of scientific investigations (e.g.,descriptive studies, controlled experiments, comparative data analysis).

B. Understands how to design, conduct and communicate the results of a variety ofscientific investigations.

C. Understands the historical development of science and the contributions that diversecultures and individuals of both genders have made to scientific knowledge.

D. Understands the roles that logical reasoning, verifiable empirical evidence,prediction and peer review play in the process of generating and evaluating scientificknowledge.

E. Understands principles of scientific ethics.

F. Develops, analyzes and evaluates different explanations for a given scientific result.

G. Demonstrates an understanding of potential sources of error in inquiry-basedinvestigation and the use of multiple trials to increase reliability.

H. Demonstrates an understanding of how to communicate and defend the results of aninquiry-based investigation.


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competency 023THE TEACHER UNDERSTANDS HOW SCIENCE IMPACTS THE DAILY LIVES OF STUDENTSAND INTERACTS WITH AND INFLUENCES PERSONAL AND SOCIETAL DECISIONS.


A. Understands that decisions about the use of science are based on factors such asethical standards, economics and personal and societal needs.

B. Applies scientific principles and the theory of probability to analyze the advantagesof, disadvantages of or alternatives to a given decision or course of action.

C. Applies scientific principles and processes to analyze factors that influence personalchoices concerning fitness and health, including physiological and psychologicaleffects and risks associated with the use of substances and substance abuse.

D. Understands concepts, characteristics and issues related to changes in populationsand human population growth.

E. Understands the types and uses of natural resources (renewable, non-renewable) andthe effects of human consumption on the renewal and depletion of resources.

F. Understands the role science can play in helping resolve personal, societal andglobal challenges (e.g., recycling, evaluating product claims, alternative energysources).

competency 024THE TEACHER KNOWS AND UNDERSTANDS THE UNIFYING CONCEPTS AND PROCESSESTHAT ARE COMMON TO ALL SCIENCES.


A. Understands how the following concepts and processes provide a unifyingexplanatory framework across the science disciplines: systems, order andorganization; evidence, models and explanation; change, constancy andmeasurements; evolution and equilibrium; and form and function.

B. Demonstrates an understanding of how patterns in observations and data can be usedto make explanations and predictions.

C. Analyzes interactions and interrelationships between systems and subsystems.

D. Applies unifying concepts to explore similarities in a variety of natural phenomena.

E. Understands how properties and patterns of systems can be described in terms ofspace, time, energy and matter.

F. Understands how change and constancy occur in systems.

G. Understands the complementary nature of form and function in a given system.

H. Understands how models are used to represent the natural world and how to evaluatethe strengths and limitations of a variety of scientific models (e.g., physical,conceptual, mathematical).

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STUDY TOPICS

DOMAIN VIII — PHYSICAL SCIENCE

competency 025THE TEACHER UNDERSTANDS FORCES AND MOTION AND THEIR RELATIONSHIPS.


A. Demonstrates an understanding of properties of universal forces (e.g., gravitational,electrical, magnetic).

B. Understands how to measure, graph and describe changes in motion using conceptsof displacement, speed, velocity and acceleration.

C. Understands the vector nature of force.

D. Identifies the forces acting on a object and applies Newton’s laws to describe themotion of an object.

E. Analyzes the relationship between force and motion in a variety of situations (e.g.,simple machines, blood flow, geologic processes).

competency 026THE TEACHER UNDERSTANDS PHYSICAL PROPERTIES OF AND CHANGES IN MATTER.


A. Describes the physical properties of substances (e.g., density, boiling point, meltingpoint, solubility, thermal and electrical conductivity, luster, malleability).

B. Describes the physical properties and molecular structure of solids, liquids andgases.

C. Describes the relationship between the molecular structure of materials (e.g., metals,crystals, polymers) and their physical properties.

D. Relates the physical properties of an element to its placement in the periodic table,including metals, non-metals and metalloids.

E. Distinguishes between physical and chemical changes in matter.

F. Applies knowledge of physical properties of and changes in matter to processes andsituations that occur in life and earth/space science.


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competency 027THE TEACHER UNDERSTANDS CHEMICAL PROPERTIES OF AND CHANGES IN MATTER.


A. Describes the structure and components of the atom.

B. Distinguishes among elements, compounds, mixtures and solutions and describestheir properties.

C. Relates the chemical properties of an element to its placement in the periodic table.

D. Describes chemical bonds and chemical formulas.

E. Analyzes chemical reactions and their associated chemical equations.

F. Explains the importance of a variety of chemical reactions that occur in daily life(e.g., rusting, burning of fossil fuels, photosynthesis, cell respiration, chemicalbatteries, digestion of food).

G. Understands applications of chemical properties of matter in physical, life andearth/space science and technology (e.g., materials science, biochemistry,transportation, medicine, telecommunications).

competency 028THE TEACHER UNDERSTANDS ENERGY AND INTERACTIONS BETWEEN MATTER ANDENERGY.


A. Describes concepts of work, power, and potential and kinetic energy.

B. Understands the concept of heat energy and the difference between heat andtemperature.

C. Understands the principles of electricity and magnetism and their applications (e.g.,electric circuits, motors, audio speakers, nerve impulses, lightning).

D. Applies knowledge of properties of light (e.g., reflection, refraction, dispersion) todescribe the function of optical systems and phenomena (e.g., camera, microscope,rainbow, eye).

E. Demonstrates an understanding of the properties, production and transmission ofsound.

F. Applies knowledge of properties and characteristics of waves (e.g., wavelength,frequency, interference) to describe a variety of waves (e.g., water, electromagnetic,sound).

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STUDY TOPICS

competency 029THE TEACHER UNDERSTANDS ENERGY TRANSFORMATIONS AND THE CONSERVATIONOF MATTER AND ENERGY.


A. Describes the processes that generate energy in the sun and other stars.

B. Applies the law of conservation of matter to analyze a variety of situations (e.g., thewater cycle, food chains, decomposition, balancing chemical equations).

C. Describes sources of electrical energy and processes of energy transformation forhuman uses (e.g., fossil fuels, solar panels, hydroelectric plants).

D. Understands exothermic and endothermic chemical reactions and their applications(e.g., hot and cold packs, energy content of food).

E. Applies knowledge of the transfer of energy in a variety of situations (e.g., theproduction of heat, light, sound and magnetic effects by electrical energy; theprocess of photosynthesis; weather processes; food webs; food/energy pyramids).

F. Applies the law of conservation of energy to analyze a variety of physicalphenomena (e.g., specific heat, nuclear reactions, efficiency of simple machines,collisions).

G. Understands applications of energy transformations and the conservation of matterand energy in life and earth/space science.

DOMAIN IX — LIFE SCIENCE

competency 030THE TEACHER UNDERSTANDS THE STRUCTURE AND FUNCTION OF LIVING THINGS.


A. Describes characteristics of organisms from the major taxonomic groups, includingdomains and kingdoms, and uses these characteristics to construct a dichotomouskey.

B. Analyzes how structure complements function in cells.

C. Analyzes how structure complements function in tissues, organs, organ systems andorganisms including both plants and animals.

D. Identifies human body systems and describes their functions (e.g., digestive,circulatory).

E. Describes how organisms, including producers, consumers and decomposers obtainand use energy and matter.

F. Applies chemical principles to describe the structure and function of the basicchemical components (e.g., proteins, carbohydrates, lipids, nucleic acids) of livingthings and distinguishes between organic and inorganic compounds.


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competency 031THE TEACHER UNDERSTANDS REPRODUCTION AND THE MECHANISMS OF HEREDITY.


A. Compares and contrasts sexual and asexual reproduction.

B. Understands the organization of hereditary material (e.g., DNA, genes,chromosomes).

C. Describes how an inherited trait can be determined by one or many genes and howmore than one trait can be influenced by a single gene.

D. Distinguishes between dominant and recessive traits and predicts the probableoutcomes of genetic combinations.

E. Evaluates the influence of environmental and genetic factors on the traits of anorganism.

F. Describes current applications of genetic research (e.g., related to cloning,reproduction, health, industry, agriculture).

competency 032THE TEACHER UNDERSTANDS ADAPTATIONS OF ORGANISMS AND THE THEORY OFEVOLUTION.


A. Describes similarities and differences among various types of organisms andmethods of classifying organisms (e.g., presence of a nucleus determines if a cell isprokaryotic and eukaryotic).

B. Describes traits in a population or species that enhance its survival and reproductivesuccess.

C. Describes how populations and species change through time.

D. Applies knowledge of the mechanisms and processes of biological evolution (e.g.,variation, mutation, environmental factors, natural selection).

E. Describes evidence that supports the theory of evolution of life on Earth.

competency 033THE TEACHER UNDERSTANDS REGULATORY MECHANISMS AND BEHAVIOR.


A. Describes how organisms respond to internal and external stimuli.

B. Applies knowledge of structures and physiological processes that maintain stableinternal conditions.

C. Demonstrates an understanding of feedback mechanisms that allow organisms tomaintain stable internal conditions.

D. Understands how evolutionary history affects behavior.

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competency 034THE TEACHER UNDERSTANDS THE RELATIONSHIPS BETWEEN ORGANISMS AND THEENVIRONMENT.


A. Understands the levels of organization within an ecosystem (organism, population,community) and identifies the abiotic and biotic components of an ecosystem.

B. Analyzes the interrelationships (food chains, food webs) among producers,consumers and decomposers in an ecosystem.

C. Identifies factors that influence the size and growth of populations in an ecosystem.

D. Analyzes adaptive characteristics that result in a population’s or species’ uniqueniche in an ecosystem.

E. Describes and analyzes energy flow through various types of ecosystems.

F. Knows how populations and species modify and affect ecosystems (e.g., succession),and how biodiversity affects the sustainability of ecosystems.

DOMAIN X — EARTH AND SPACE SCIENCE

competency 035THE TEACHER UNDERSTANDS THE STRUCTURE AND FUNCTION OF EARTH SYSTEMS.


A. Understands the layers and surface features (landforms) of Earth and usestopographic maps and satellite imaging to analyze constructive and destructiveprocesses that produce geologic change.

B. Understands the form and function of surface and subsurface water (e.g., watershed,aquifer).

C. Applies knowledge of the composition and structure of the atmosphere and itsproperties, including characteristics that allow life to exist.

D. Demonstrates an understanding of the interactions that occur among the biosphere,geosphere, hydrosphere and atmosphere.

E. Applies knowledge of how human activity and natural processes, both gradual andcatastrophic, can alter earth and ocean systems.

F. Identifies the sources of energy (e.g., solar, geothermal, wind, hydroelectric,biofuels) in earth systems and describes mechanisms of energy transfer (e.g.,conduction, convection, radiation).


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competency 036THE TEACHER UNDERSTANDS CYCLES IN EARTH SYSTEMS.


A. Understands the rock cycle and how rocks, minerals, fossil fuels and soils areformed.

B. Understands the water cycle and its relationship to weather processes; how the sunand the ocean interact in the water cycle.

C. Understands the nutrient (e.g., carbon, nitrogen) cycle and its relationship to earthsystems.

D. Applies knowledge of how human and natural processes affect earth systems.

E. Understands the dynamic interactions that occur among the various cycles in thebiosphere, geosphere, hydrosphere and atmosphere.

competency 037THE TEACHER UNDERSTANDS THE ROLE OF ENERGY IN WEATHER AND CLIMATE.


A. Understands the elements of weather (e.g., humidity, wind speed, pressure,temperature) and how they are measured.

B. Compares and contrasts weather and climate.

C. Analyzes weather charts and data to make weather predictions based on local andglobal patterns.

D. Applies knowledge of how transfers of energy among earth systems affect weatherand climate.

E. Analyzes how Earth’s position, orientation and surface features affect weather andclimate.

competency 038THE TEACHER UNDERSTANDS THE CHARACTERISTICS OF THE SOLAR SYSTEM AND THEUNIVERSE.


A. Understands the properties and characteristics of celestial objects.

B. Applies knowledge of the earth-moon-sun system and the interactions among them(e.g., seasons, lunar phases, eclipses).

C. Identifies properties of the components of the solar system, including systems thatallow life to exist.

D. Recognizes characteristics of stars, nebulae and galaxies and their distribution in theuniverse.

E. Demonstrates an understanding of scientific theories of the origin of the universe.

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STUDY TOPICS

competency 039THE TEACHER UNDERSTANDS THE HISTORY OF THE EARTH SYSTEM.


A. Understands the scope of the geologic time scale and its relationship to geologicprocesses.

B. Demonstrates an understanding of theories about the earth’s origin and geologichistory.

C. Demonstrates an understanding of how tectonic forces have shaped landforms overtime.

D. Understands the formation of fossils and the importance of the fossil record inexplaining the earth’s history.

DOMAIN XI — SCIENCE LEARNING, INSTRUCTION AND ASSESSMENT

competency 040THE TEACHER HAS THEORETICAL AND PRACTICAL KNOWLEDGE ABOUT TEACHINGSCIENCE AND ABOUT HOW STUDENTS LEARN SCIENCE.


A. Understands how the developmental characteristics, prior knowledge and experienceand attitudes of students influence science learning.

B. Selects and adapts science curricula, content, instructional materials and activities tomeet the interests, knowledge, understanding, abilities, experiences and needs of allstudents, including English-language learners.

C. Understands how to use situations from students’ daily lives to develop instructionalmaterials that investigate how science can be used to make informed decisions.

D. Understands common misconceptions in science and effective ways to address thesemisconceptions.

E. Understands the rationale for the use of active learning and inquiry processes forstudents.

F. Understands questioning strategies designed to elicit higher-level thinking and howto use them to move students from concrete to more abstract understanding.

G. Understands the importance of planning activities that are inclusive andaccommodate the needs of all students.

H. Understands how to sequence learning activities in a way that allows students tobuild upon their prior knowledge and challenges them to expand their understandingof science.


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competency 041THE TEACHER UNDERSTANDS THE PROCESS OF SCIENTIFIC INQUIRY AND ITS ROLE INSCIENCE INSTRUCTION.


A. Plans and implements instruction that provides opportunities for all students toengage in nonexperimental and experimental inquiry investigations.

B. Focuses inquiry-based instruction on questions and issues relevant to students anduses strategies to assist students with generating, refining and focusing scientificquestions and hypotheses.

C. Instructs students in the safe and proper use of a variety of grade-appropriate tools,equipment, resources, technology and techniques to access, gather, store, retrieve,organize and analyze data.

D. Knows how to guide and manage students in making systematic observations andmeasurements.

E. Knows how to promote the use of critical-thinking skills, logical reasoning andscientific problem solving to reach conclusions based on evidence.

F. Knows how to teach students to develop, analyze and evaluate different explanationsfor a given scientific result.

G. Knows how to teach students to demonstrate an understanding of potential sourcesof error in inquiry-based investigation.

H. Knows how to teach students to demonstrate an understanding of how tocommunicate and defend the results of an inquiry-based investigation.

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competency 042THE TEACHER KNOWS THE VARIED AND APPROPRIATE ASSESSMENTS AND ASSESSMENTPRACTICES TO MONITOR SCIENCE LEARNING IN LABORATORY, FIELD AND CLASSROOMSETTINGS.


A. Understands the relationships among science curriculum, assessment and instructionand bases instruction on information gathered through assessment of students’strengths and needs.

B. Understands the importance of monitoring and assessing students’ understanding ofscience concepts and skills on an ongoing basis.

C. Understands the importance of carefully selecting or designing formative andsummative assessments for the specific decisions they are intended to inform.

D. Selects or designs and administers a variety of appropriate assessment methods (e.g.,performance assessment, self-assessment, formal/informal, formative/summative) tomonitor student understanding and progress.

E. Uses formal and informal assessments of student performance and products (e.g.,projects, lab journals, rubrics, portfolios, student profiles, checklists) to evaluatestudent participation in and understanding of the inquiry process.

F. Understands the importance of sharing evaluation criteria and assessment resultswith students.


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Chapter 4Succeeding on Multiple-Choice Questions

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APPROACHES TO ANSWERING MULTIPLE-CHOICE QUESTIONS

The purpose of this section is to describe multiple-choice question formats that you will see onthe Mathematics/Science 4–8 test and to suggest possible ways to approach thinking about andanswering the multiple-choice questions. However, these approaches are not intended to replacefamiliar test-taking strategies with which you are already comfortable and that work for you.

The Mathematics/Science 4–8 test is designed to include a total of 120 multiple-choice questions,out of which 100 are scored. The number of scored questions will not vary; however, the number ofquestions that are not scored may vary in the actual test. Your final scaled score will be based onlyon scored questions. The questions that are not scored are being pilot tested in order to collectinformation about how these questions will perform under actual testing conditions. These questionsare not identified on the test.

All multiple-choice questions on this test are designed to assess your knowledge of the contentdescribed in the test framework. In most cases, you are expected to demonstrate more than just yourability to recall factual information. You may be asked to solve a multistep problem; analyze andinterpret mathematical information in a variety of formats; determine a mathematical function thatmodels a given situation; or supply information needed to prove a mathematical statement.

When you are ready to respond to a multiple-choice question, you must choose one of four answeroptions labeled A, B, C and D. Leave no questions unanswered. Nothing is subtracted from yourscore if you answer a question incorrectly. Questions for which you mark no answer are counted asincorrect. Your score will be determined by the number of questions for which you select the bestanswer.

Calculators. Scientific calculators will be provided at the test center. See the TExES RegistrationBulletin for the brand and model of the calculator that will be available.

Definitions and Formulas. A set of definitions and formulas will be provided as part of the test. Acopy of those definitions and formulas is provided in Chapter 5 of this preparation manual.

Periodic Table of the Elements. A Periodic Table of the Elements will be provided as part of thetest for use on science questions. A copy of this periodic table is provided in Chapter 5.

QUESTION FORMATS

You may see the following types of multiple-choice questions on the test.

— Single Questions

— Questions with Stimulus Materials

— Clustered Questions

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SUCCEEDING ON MULTIPLE-CHOICE QUESTIONS

On the following pages, you will find descriptions of these commonly used question formats, alongwith suggested approaches for responding to each type of question. In the actual testing situation,you may write on the scratch paper provided at the testing center. Your final response must beselected on the computer.

SINGLE QUESTIONS

In the single-question format, a problem is presented as a direct question or an incomplete statement,and four answer options appear below the question. The following question is an example of thistype. It tests knowledge of Mathematics/Science 4–8 Competency 010: The teacher analyzes theproperties of two- and three-dimensional figures.

EXAMPLE 1

1. The Great Pyramid at Giza is approximately 150 meters high and has a square baseapproximately 230 meters on a side. What is the approximate area of a horizontal crosssection of the pyramid taken 50 meters above its base?

A. 5,880 square meters

B. 11,760 square meters

C. 23,510 square meters

D. 35,270 square meters

SUGGESTED APPROACH

Read the question carefully and critically. Think about what it is asking and the situation it isdescribing. Eliminate any obviously wrong answers, select the correct answer choice and markyour answer.



4

The horizontal cross section will be a square in the plane parallel to the base of the pyramid and50 meters above it. In order to estimate the area of the cross section, you will need to know theapproximate length of one of its sides. This can be calculated using your knowledge of proportionsand the properties of similar geometric figures. In solving problems that involve geometry, drawinga diagram is often helpful.

The figure shows a vertical cross section through the center of the square base of the pyramidperpendicular to a side of the base. The measurements given in the test question have beentransferred to the diagram. Notice that since CG + GF = 150, and it is given that GF = 50, thenCG = 100. You must find BD, the length of the sides of the square cross section. Also note that�CBD and �CAE are similar because they have two angles whose measures are equal; they share�C and the measure of �B is equal to the measure of �A since they are corresponding anglesformed by a transversal and two parallel lines. Because the two triangles are similar, their altitudes

and sides must be proportional and you can write: CGCF

BDAE

= . Now substitute the values for the

lengths of the line segments to get 100150 230

= BD. Solving this gives BD = 153.33. Since the horizontal

cross section is a square, its area is the square of the length of BD, or (153.33)2 = 23,511.11 square feet.Now look at the response options. The correct response is option C, rounded to the nearest tensquare meters.

Setting up the proportion incorrectly as 50150 230

= BD and using this value for the side of the cross

section leads to option A. Option B results from assuming that the cross section is an isosceles

right triangle instead of a square, and option D comes from assuming that the area of the cross

section is 100150

23

= of the area of the base of the pyramid.

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EXAMPLE 2

The following questions tests knowledge of Mathematics/Science 4–8 Competency 030: The teacherunderstands the structure and function of living things.

2. Use the diagram below to answer the question that follows.

On a class field trip, students encounter some brightly colored shelf-life structures attachedto the trunk of a dead tree. Which of the following is the best description of how thisorganism obtains matter and energy from the environment?

A. It obtains energy from the dead wood and absorbs carbon dioxide and water vaporfrom the air

B. It obtains energy from the sunlight, absorbs carbon from the dead wood and obtainswater vapor from the air

C. It obtains energy from sunlight and obtains carbon and water from the dead wood

D. It obtains energy, carbon and water from the dead wood

SUGGESTED APPROACH

Read the question carefully and critically. Think about what it is asking and the situation it isdescribing. Eliminate any obviously wrong answers, select the correct answer choice and markyour answer.

As you read this question, it should be clear from the diagram that the shelf-like structures arefungi. Think about the characteristics that distinguish fungi from other organisms. One importantdifference is how fungi obtain energy and nutrients. Unlike plants, fungi lack chlorophyll and donot photosynthesize, obtaining all their energy and nutrients from the absorption of organic matter.

Now look at the response options. The correct response is option D. All other options refer to somepart of the photosynthetic cycle and therefore do not pertain to fungi.



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QUESTIONS WITH STIMULUS MATERIAL

Some questions on this test are preceded by stimulus material that relates to the question. Sometypes of stimulus material included on the test are geometric diagrams, charts, data tables, graphs,equations, passages, samples of student work and descriptions of classroom situations. In such cases,you will generally be given information followed by an event to analyze, a problem to solve or adecision to make.

You can use several different approaches to respond to these types of questions. Some commonlyused strategies are listed below.

Strategy 1 Skim the stimulus material to understand its purpose, its arrangement and/or itscontent. Then read the question and refer again to the stimulus material to obtainthe specific information you need to answer the question.

Strategy 2 Read the question before considering the stimulus material. The theory behindthis strategy is that the content of the question will help you identify the purposeof the stimulus material and locate the information you need to answer thequestion.

Strategy 3 Use a combination of both strategies; apply the “read the stimulus first” strategywith shorter, more familiar stimuli and the “read the question first” strategy withlonger, more complex or less familiar stimuli. You can experiment with thesample questions in this manual and then use the strategy with which you aremost comfortable when you take the actual test.

Whether you read the stimulus before or after you read the question, you should read it carefully andcritically.

As you consider questions set in educational contexts, try to enter into the identified teacher’s frameof mind and use that teacher’s point of view to answer the questions that accompany the stimulus. Besure to consider the questions in terms of only the information provided in the stimulus — not interms of your own class experiences or individual students you may have known.

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EXAMPLE 1

First read the stimulus (a description of the concept being studied).

Use the diagram and the information below to answer the two questions that follow.

Students in a math class are investigating concepts related to motion in one dimension. Thevelocity-versus-time graph shows the velocity of a student walking in a straight line, collectedat one-second intervals over a period of nine seconds.

Now you are prepared to address the first of the two questions associated with this stimulus. The firstquestion measures Mathematics/Science 4–8 Competency 007: The teacher uses and understands theconceptual foundations of calculus related to topics in middle school mathematics.

Which of the following methods could be used to estimate the student’s acceleration betweent = 3 and t = 5 seconds?

A. Find the average of the velocities at t = 3 and t = 5 seconds

B. Find the equation of the curve that best fits the data and evaluate it at t = 4 seconds

C. Find the length of the line connecting the velocities between t = 3 and t = 5 seconds

D. Find the slope of the line connecting the velocities at t = 3 and t = 5 seconds

SUGGESTED APPROACH

You are asked to estimate the acceleration of the student between 3 and 5 seconds, that is, theaverage acceleration over this time period. Average acceleration is the rate of change of velocity with

respect to time, ΔΔvt

vt

= −−

2 1

12

vt

. Therefore, divide the difference in the velocities at 5 and 3 seconds

by the total time elapsed, here 5 – 3 = 2 seconds. You should recognize this expression as representingthe slope of a line connecting two points, or the difference in the y-coordinates divided by the differencein the x-coordinates. Therefore, option D is correct.



4

Option A finds the average velocity in the time interval, while option B finds an expression forvelocity as a function of time and interpolates how fast the student is moving at t = 4s. Option Cdetermines the length of the curve and has no physical significance.

Now you are ready to answer the next question. The second question also measures Mathematics/Science 4–8 Competency 007: The teacher uses and understands the conceptual foundations ofcalculus related to topics in middle school mathematics.

Which of the following methods could be used to estimate the total distance the student hastraveled between t = 0 and t = 5 seconds?

A. Find the median value of the velocities from t = 0 to t = 5 seconds, inclusive

B. Find the ratio of the velocities at t = 0 and t = 5 seconds

C. Find the area under the curve between t = 0 and t = 5 seconds

D. Find the average value of the velocity-over-time ratios for t = 0 and t = 5 seconds

SUGGESTED APPROACH

In order to calculate the distance traveled by the student during a particular time interval, multiplythe rate of travel by the length of time the student is moving; in other words, d = rt where drepresents distance, r represents rate (velocity), and t represents time. For example, during theinterval from t = 1 to t = 2 seconds, multiply the average velocity during the interval, approximately

0 25. ms ,by the length of the interval, 2 – 1 = 1 second. This can be represented geometrically by the area

of the rectangle of height = 0 25. ms , and base = 1s under the curve between t = 1s and t = 2s. To get

an estimate of the total distance traveled by the student, you need to sum the distance traveled duringeach of the one-second intervals from 0 through 5 seconds. This is approximately equal tothe area under the curve from t = 0 to t = 5 seconds. Therefore option C is correct.

Option A gives the median value for the velocity, which by itself cannot be used to estimate thedistance traveled by the student. The ratio of the velocities (option B) is not helpful in determiningthe total distance covered. Finding the average of the velocities at t = 0 and t = 5 (option D) is not byitself sufficient for calculating the distance traveled between those times.

4



EXAMPLE 2

First read the stimulus (a diagram of a stratigraphic section of rock).

Use the illustration below to answer the two questions that follow.

Now you are prepared to address the first of the two questions associated with this stimulus. The firstquestion measures Mathematics/Science 4–8 Competency 039: The teacher understands the historyof the earth system.

1. The igneous intrusion in the illustration has been dated to be 13 million years old, and thevolcanic ash layer has been dated to be 24 million years old. Which of the followingstatements about the ages of fossil X and fossil Y is most accurate?

A. Fossil X is younger than fossil Y, and both fossils are older than 24 million years old

B. Fossil X and fossil Y are both between 13 million and 24 million years old

C. Fossil X is older than fossil Y, and both fossils are younger than 13 million years old

D. Fossil X is younger than 13 million years old, and fossil Y is older than13 million years old



4

SUGGESTED APPROACH

First examine the figure in the stimulus, noting the positions of the rock layers and the fossils labeledX and Y. You should be able to create a combined stratigraphy for the entire section by matching upthe pattern of layers on either side of the igneous intrusion. Locate the fossils labeled X and Y andconsider their relationship in the combined stratigraphy. It is clear that the two fossils are found inthe same stratigraphic layer located above the 24-million-year-old volcanic ash. Since they are abovethe volcanic ash layer, they must be younger than 24 million years old. Since the igneous intrusioncut through the layer in which the fossils were located 13 million years ago, both fossils must be atleast that old. Options A, C and D all state that one fossil is older than the other. Therefore, thecorrect response is option B.

Now you are ready to answer the next question. The second question also measures Mathematics/Science 4–8 Competency 039: The teacher understands the history of the earth system.

2. The discontinuity represented by the line labeled W in the illustration is most likely to be

A. a thrust fault.

B. an igneous intrusion.

C. a transverse fault.

D. an erosion surface.

SUGGESTED APPROACH

The second question requires you to recognize the characteristics of an unconformity in astratigraphic section. Note that the unconformity in the diagram cuts across several stratigraphiclayers and the igneous intrusion and that these are missing above the unconformity. Options A, B andC all refer to faults or intrusions. Faults result in the displacement of layers relative to other layers,while intrusions are characterized by the insertion of igneous rock through or between layers. In thiscase, the relationship of the layers to one another and to the sandstone above the unconformityindicates that the unconformity is an erosion surface and that option D is the correct response.

CLUSTERED QUESTIONS

You may have one or more questions related to a single stimulus. When you have at least twoquestions related to a single stimulus, the group of questions is called a cluster.

4



Chapter 5Multiple-Choice Practice Questions

5

SAMPLE MULTIPLE-CHOICE QUESTIONS

This section presents some sample test questions for you to review as part of your preparation for thetest. To demonstrate how each competency may be assessed, each sample question is accompaniedby the competency that it measures. While studying, you may wish to read the competency beforeand after you consider each sample question. Please note that the competency statements will notappear on the actual test.

An answer key follows the sample questions. The answer key lists the question number and correctanswer for each sample test question. Please note that the answer key also lists the competencyassessed by each question and that the sample questions are not necessarily presented in competencyorder.

The sample questions are included to illustrate the formats and types of questions you will see on thetest; however, your performance on the sample questions should not be viewed as a predictor of yourperformance on the actual test.

5


MULTIPLE-CHOICE PRACTICE QUESTIONS



5

5



competency 0011. A fifth-grade class is using pattern blocks in the shape of congruent equilateral triangles to

devise and solve problems involving fractions. One group devises the problem illustratedbelow.

Given that the sum of Shapes A and B represents 58

, which of the following represents 114

?

A.

B.

C.

D.



5

competency 0012. Use the information below to answer the question that follows.

The Sahara Desert covers about 8.3 × 1013 square feet.

The average depth of the sand in the Sahara Desert is 200 feet.

A grain of sand has a volume of approximately 1.3 × 10–9 cubic feet.

Which of the following is the best estimate of the number of grains of sand in theSahara Desert?

A. 1022

B. 1023

C. 1024

D. 1025

competency 0023. Use the addition problem below to answer the question that follows.

12

29

88

+11

When given the addition problem above, a student quickly said “140.” When asked howshe solved the problem, the student replied, “I added 88 and 12 to get 100, and 29 and11 to get 40. Then I added these two numbers together.” Which of the following twoproperties of addition did the student use in solving this problem?

A. Associative and commutative

B. Associative and additive identity

C. Commutative and additive identity

D. Distributive and additive inverse

5



competency 0024. Use the diagram below to answer the question that follows.

Which of the following expressions is represented by the areas of the rectangles in thediagram above?

A. xy3 + xy2

B. x2 + 5xy + 6y2

C. 2x + y3 + y2

D. 2x + 5xy + 6y

competency 0035. Use the theorem below to answer the question that follows.

If the sum of a number’s digits is divisible by three, the number is divisible by three.

Which of the following ways of expressing a three digit number, n, with hundreds digit a,tens digit b and units digit c, best demonstrates why this theorem is true?

A. 3n = 3a(100) + 3b(10) + 3c = 300a + 30b + 3c

B. n = a(100) + b(10) + c

C. n = a(99 + 1) + b(9 + 1) + c = 99a + 9b + a + b + c

D. n = a(70 + 30) + b(7 + 3) + c = 70a + 7b + 30a + 3b + c



5

competency 0036. The density of gold is 19.3 grams per cubic centimeter. What is the mass of a cube made of

gold that measures 1.2 cm on a side?

A. 0.09 gram

B. 1.73 grams

C. 23.16 grams

D. 33.35 grams


In a store display, grapefruit are stacked 4 levels high in the shape of a pyramid with asquare base. Which of the following expressions can be used to determine how manygrapefruit can be stacked in a pyramid n layers high?

A. n! = (1)(2)(3)...(n)

B. n2 = 1 + 3 + 5 +...+ (2n – 1)

C. n nn

( )+ = + + + +12

1 2 3

D. n n nn

( )( )+ + = + + + +1 2 16

1 4 9 2

5



competency 0078. Use the graph below to answer the question that follows.

Which of the following equations could be solved to find the x-coordinate of point A on thegraph of the function y = f (x) shown in the xy-plane?

A. f (x) = 0

B. f (0) = x

C. f '(x) = 0

D. f "(x) = 0


The graph represents an equation of the form y = mx + b. Which of the followingstatements about m and b are true?

A. m > 0 and b > 0

B. m > 0 and b < 0

C. m < 0 and b > 0

D. m < 0 and b < 0



5


The graph in the xy-plane of which of the following lines passes through the point (6, 12)and has the same slope as the line shown?

A. y – 2x = 0

B. y + 3x = 30

C. y – 3x = –6

D. y + 3x = 42

competency 00611. The function f is given by the equation f (x) = x2 + 6x + 7 for all numbers x. Which of the

following statements is true?

A. The graph of y = f (x) in the xy-plane has a vertex at the point (–3, –2)

B. The graph of y = f (x) in the xy-plane crosses the x-axis at two points, (–7, 0) and (–6, 0)

C. The function f does not have any real roots

D. As x → ∞, f (x) → �∞

5



competency 00612. Use the function below to answer the question that follows.

f xx cx

( ) =− +4

92

When the rational function f given by the equation above is graphed in the xy-plane, whatvalue of c will produce exactly one vertical asymptote?

A. 0

B. 4

C. 6

D. 9


Which of the following statements describes how the value of y depends on the value of xin the triangles shown above?

A. y is directly proportional to x

B. y is directly proportional to the square of x

C. y is inversely proportional to x

D. y is inversely proportional to the square of x



5

competency 00814. The shape of a city park is a square with sides that are each 1.5 miles long. What is the area

of the park in acres? (1 square mile = 640 acres)

A. 720

B. 1280

C. 1440

D. 1920

competency 00815. Using a protractor, a student measures the interior angles in a triangle and finds the sum of

the angles to be 176°. What is the percent error of this measurement?

A. 0.04%

B. 2.22%

C. 2.27%

D. 4.00%


In this diagram, m�LAT = m�RAE. Which property is most likely to be used in provingthat m�LAR = m�TAE?

A. The multiplication property of equality

B. The addition property of equality

C. The distributive property

D. The properties of complementary angles

5



competency 00917. Use the figure below to answer the question that follows.

In triangle ABC shown, EF is parallel to AC, and ED is parallel to BC. Which of thefollowing statements gives sufficient additional information to conclude that trianglesAED, EBF, DFC and FED are congruent?

A. BF is equal to FC

B. AED is a right angle

C. ABC is a right triangle

D. ABC is an isosceles triangle

competency 01018. Use the diagrams below to answer the question that follows.

The diagrams show three regular polygons and their central angles. Which of the followinggives the measure of the central angle of a regular polygon, q (n), as a function of thenumber of sides n, where n is greater than 2 ?

A. q ( )nn

= 360

B. q ( )nn

= −360 360

C. q ( )n n= −360

D. q ( )n n= −360 2



5


An overhead light source projects parallelogram ABCD to A'B'C'D'. Given that the projectionis a dilation, which of the following expressions represents the perimeter of the smallerfigure, ABCD, in terms of x ?

A. 2 6x−

B. 33

+ x

C. 3 18x−

D. 6 23

+ x

5



competency 01120. Which of the following is the reflection of the point 3

545

,⎛⎝⎜

⎞⎠⎟

through the line y = – x in thexy-plane?

A. 35

45

,−⎛⎝⎜

⎞⎠⎟

B. −⎛⎝⎜

⎞⎠⎟

35

45

,

C. 45

35

,⎛⎝⎜

⎞⎠⎟

D. − −⎛⎝⎜

⎞⎠⎟

45

35

,


The function f xe x( ) =

+ −200

0 25 6 0 1. . is used to model the number of fish in a certain

aquarium, where x is the number of days after the aquarium has been stocked with 32 fish.The graph of y = f (x) is shown in the xy-plane above. Which of the following statementsis true about the number of fish in the aquarium?

A. It approaches 0 as x increases

B. It approaches 200 as x increases

C. It approaches 800 as x increases

D. It increases without bound as x increases



5

competency 01222. The amount of money, after taxes, spent by a family on various expenses during one month

is given in the table below.

Type of Expense Amount Spent in One Month

Rent $750

Food $575

Utilities $120

Car loan, gas and repairs $450

Medical expenses $65

Entertainment $120

Credit card payment $350

Miscellaneous expenses $95

Total expenses $2525

If the family constructs a pie chart using these figures, what is the approximate measureof the central angle of the sector used to represent the percentage of total expenses spenton food?

A. 23°

B. 63°

C. 77°

D. 82°

5



competency 01323. Two teams meet in a playoff series at the end of the regular season. Team A won 55 of 81

games played in its home stadium during the regular season, while Team B won 48 of 81games played in its home stadium. The first two games of the series will be played inTeam A’s home stadium, the next two games in Team B’s home stadium. In the absenceof any other information, which expression is equal to the probability that Team A willwin the first four games in a row?

A. 5555555581 81 81 81

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

B. 485581

5581 81

4881

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

C. 5581

5581

3381

3381

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

D. 5581

5581

2681

2681

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

competency 01324. Use the table below to answer the question that follows.

Number of Pieces of Beef withSpecified Grade

Cuts of BeefHigh FatContent

Low FatContent Total

Flank Steaks 74 386 460

Rump Roasts 258 142 400

Total 332 528 860

A United States Department of Agriculture (USDA) inspector graded cuts of beef at a meatpacking plant. If a piece of beef is selected at random, which of the following is the bestestimate of the probability that it will be a flank steak with high fat content?

A. 0.086

B. 0.161

C. 0.223

D. 0.386



5

competency 01425. A scatterplot was drawn to represent the relationship between two variables. If the

correlation coefficient of the two variables was 0.95, which of the following could be thescatterplot?

A.

B.

C.

D.

competency 01326. One number is to be randomly selected from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

What is the probability of selecting a number that is odd or is a multiple of 3 ?

A. 13

B. 12

C. 23

D. 56

5



competency 01527. Use the table below to answer the question that follows.

n n2 Remainder when n2

is divided by 4

8 64 0

9 81 1

10 100 0

11 121 1

A student constructed the table shown and conjectured that the square of an integer hasremainder 0 or 1 when divided by 4. Which of the following would be the best approachfor a teacher to suggest to the student to prove or disprove this conjecture?

A. Look for a counterexample using prime numbers as values for n

B. Construct a proof by induction on the set of positive integers

C. Examine the cases of n = 2k and n = 2k + 1, where k is an integer, and compute n2 ineach case

D. Examine the cases of n = 3k, n = 3k + 1 and n = 3k + 2, where k is an integer, and computen2 in each case

competency 01528. Use the identity below to answer the question that follows.

1 + 3 + 5 + ... + (2n – 1) = n2 for all integers n ≥ 1

Which of the following would be the best technique to use to prove the identity shown?

A. Binomial expansion

B. Mathematical induction

C. Prime factorization

D. Proof by contradiction



5

competency 01629. A shopper sees some gloves on sale for 20% off their original price of $28. The next week

the gloves have been reduced another 15% off the sale price. If there is a 6% sales tax,how much would the shopper now pay for the gloves?

A. $16.52

B. $17.11

C. $19.29

D. $20.18

competency 01530. Use the conjecture in the box below to answer the question that follows.

If the integer n can be factored as n = ab forpositive integers a and b and if p is a factor of n,then p is a factor of a or p is a factor of b.

A student makes the conjecture shown. Which of the following is a counterexample that ateacher could use to show the student that the conjecture is false?

A. n = 24 = (8)(3) and p = 2

B. n = 35 = (5)(7) and p = 7

C. n = 42 = (6)(7) and p = 13

D. n = 48 = (16)(3) and p = 12

competency 01731. Which of the following activities would best foster sixth-grade students’ development of

the mathematical concept of function?

A. Each student uses 30 one-inch squares to make a variety of different shapes with the samearea; the class then makes a table showing characteristics of each figure, and studentsdiscuss which shape has the smallest perimeter

B. Students measure various properties (e.g., mass, length) of a number of three-dimensionalobjects; they then discuss the number of quantitative descriptions that can be assigned toeach object

C. Students measure the perimeters of six squares of different sizes and fill in a table with theheadings “Length of side” and “Perimeter”; they then attempt to predict values for largerand smaller squares given the data they have obtained

D. Students measure the perimeter and determine the area of each of a number of regulargeometric figures; they then enter the data in a table and discuss any patterns they observe

5



competency 01732. A seventh-grade mathematics teacher notices that several students are having difficulty

remembering definitions for math terms discussed in class. Which of the followingindependent exercises would be most useful to ensure that all the students in the classunderstand and remember mathematical vocabulary?

A. Ask students to keep personal lists of definitions of mathematical terms they don’tunderstand and periodically discuss the lists with the students

B. Provide all students with a list of definitions that is copied from the main text for allmathematical terms used in the class

C. Ask students who are familiar with the mathematical vocabulary used in the class toinformally tutor those students who are having difficulty

D. Provide extra time at the end of each class for students to ask questions about themathematical vocabulary used during that day’s lesson

competency 01833. Which of the following best illustrates an application of Piaget’s theory of intellectual

development in a lesson on the number π for sixth-grade students at the concreteoperational stage?

A. A teacher has students measure the circumference and diameter of a variety of circularobjects; the students then compare the ratios of circumference to diameter

B. A teacher presents a lecture on the development and use of the number π duringBabylonian and Egyptian times; the teacher concludes by discussing Archimedes’smethod for calculating π

C. A teacher defines π as the ratio of the circumference to the diameter of a circle and solvesseveral different problems; students are then asked to solve a series of similar problemswith different numbers

D. A teacher has students work in groups of two to solve a series of problems involving π ;the teacher tells students that a prize will be given to members of the first three groups thatsuccessfully solve all of the problems

competency 01834. A teacher is planning a unit on proportional relationships. Which of the following topics

could the teacher include in the unit?

A. Properties of similar triangles

B. Solving quadratic equations

C. Finding formulas for the perimeters of figures

D. Solving problems with the Pythagorean theorem



5

competency 01835. Two groups of students are using a dynamic geometry software program to investigate the

properties of quadrilaterals. The first group has concluded that the diagonals of aquadrilateral always bisect each other. The second group of students is not convinced.Which of the following should the teacher encourage the students to do to resolve theapparent contradiction?

A. Assume that the diagonals of a quadrilateral don’t bisect each other and derive acontradiction

B. Find an example of a quadrilateral with diagonals that do not bisect each other

C. Formally prove that if the diagonals of a quadrilateral bisect each other, the quadrilateral isa parallelogram

D. Use informal reasoning to show that the diagonals of a quadrilateral create two triangleswith an adjacent side

competency 01936. Students in a mathematics class have completed an activity in which they found the areas

of rectangles by dividing the rectangles into smaller squares and adding up the areas ofthe smaller squares. Which of the following would be the best method for the teacher touse to assess the students’ ability to apply this method of calculating area?

A. Calculate the area of an equilateral triangle by dividing it into smaller equilateral triangles

B. Calculate the area of a circle by dividing it into smaller circles

C. Calculate the area of a regular pentagon by dividing it into smaller squares

D. Calculate the volume of a cylinder by dividing it into smaller cylinders

competency 01937. A fifth-grade teacher is beginning a new unit on geometry. The teacher would like to

identify which aspects of the new topic are most difficult for students to understand inorder to be able to adjust her lesson plans as the unit progresses. Which of the followingassessment methods would be most appropriate for achieving this goal?

A. Periodic surprise quizzes

B. Regular peer reviews of other students’ work

C. Performance assessments at the beginning and end of the unit

D. Informal observations and interviews during each class

5



competency 02038. A student will be using an alcohol lamp to heat a test tube containing a liquid. Using a test

tube holder, it would be safest for the student to position the test tube

A. directly above the flame, shaking it gently and keeping it loosely corked at all times duringheating.

B. in an upright position, while moving it slowly in a circular motion around the flame.

C. at about a 45° angle with its mouth pointed away from people, while moving it slowly backand forth through the flame.

D. in a vertical position, keeping the bottom of the tube in the blue part of the flame at alltimes.



5

competency 02139. Laboratory instructions for measuring the mass of a dry chemical on a balance, as shown

below, are as follows.

Instructions:

(1) Remove any mass from the balance.

(2) Move the riders to zero.

(3) If the pointer does not read zero, rotate the adjustment knob until it does.

(4) .

(5) .

(6) .

Which of the following should be steps 4, 5 and 6 in these instructions?

A. (4) Place the dry chemical on the balance(5) Add counterweights until the pointer reads zero(6) Read the mass of the chemical from the measurement bar

B. (4) Measure the mass of a watch glass(5) Place the dry chemical on the watch glass and measure the combined mass(6) Subtract the mass of the watch glass from the combined mass to find the mass

of the chemical

C. (4) Place the dry chemical on the balance(5) Rotate the adjustment knob until the pointer reads zero(6) Read the mass of the chemical from the measurement bar

D. (4) Place a watch glass on the balance(5) Move the riders to balance the beam(6) Place the dry chemical on the watch glass and re-adjust the riders until the beam

is again balanced

5



competency 02140. The table below lists measurement tasks included in laboratory activities conducted by

students in a middle school science class. Which line of the table matches a measurementactivity with the correct measurement tools?

A. Line 1

B. Line 2

C. Line 3

D. Line 4



5


At the beginning of the year, students in a middle school science class are given thefollowing form, outlining a problem analysis procedure.

After students have become familiar with the problem analysis procedure, they work insmall groups to use the procedure to explore information in several research papers onglobal warming. Each paper presents a different perspective on the problem, its causes, itseffects and possible solutions. Groups then share and discuss what they have discoveredand are surprised to find that the papers present so many different perspectives. Thisactivity is best for helping students recognize that

A. science has few absolute answers to the world’s problems.

B. making new scientific discoveries requires interaction among many different scientificdisciplines.

C. new scientific theories must be tested before they are accepted.

D. scientists cannot draw conclusions about a phenomenon until they have observed it manytimes.

5



competency 02442. Use the statements below to answer the question that follows.

Which of the following unifying concepts in science is illustrated by the statements givenabove?

A. How complex systems can change and evolve in unpredictable patterns

B. How changes in one system can lead to changes in other systems

C. How negative feedback acts to maintain stability in a system over time

D. How changes in the input of matter and energy of a system affect the output of matter andenergy in the system



5

Use the passage below to answer the two questions that follow.

More than half of the world’s population cooks and heats with biomass fuels: wood, dung or cropwastes. Such fuels are inexpensive and available in remote rural locations, but they produce smokecontaining large amounts of soot and cancer-causing agents. Research in the United States andZimbabwe suggests that people could improve their health and their cooking efficiency by usingroots and gourds as fuels instead of other types of biomass. The roots and gourds, which are native toand grow well in arid climates, ignite more easily than other biomass fuels and give off virtually nosmoke. This cleaner burning is a result of more thorough and efficient combustion. More efficientburning means people burn fewer roots and gourds than they do other fuels.

competency 02243. Scientists could best test the hypothesis

of improved health by

A. comparing a population that uses rootsand gourds with a similar populationthat uses other biomass fuels.

B. developing a computer simulation tocompare the burning processes of rootsand gourds with those of other biomassfuels.

C. analyzing the chemical structure ofroots and gourds to determine whatfeatures cause them to burn morecleanly.

D. analyzing the efficiency of roots andgourds as a fuel by comparing theirmasses before and after burning.

competency 03544. Based on current theories about the

effects of human activities on theenvironment, and assuming theresearch results described in thepassage are correct, it is most likelythat a worldwide switch fromtraditional biomass fuels to the rootsand gourds in the study would

A. slow global warming due to reducedemission of greenhouse gases.

B. rebuild the ozone layer by reducinghydrocarbon emissions.

C. increase water pollution due toincreased fertilization of farm land.

D. worsen acid rain problems byincreasing reliance on biomass fuels.

5



competency 02645. Use the passage below to answer the question that follows.

Scientists long thought that the element carbon existed in only two pure forms, graphiteand diamond. Graphite, the soft, black substance used in pencils, is formed of looselylinked chains of carbon atoms. Diamonds are very hard crystals of closely packed carbonatoms. Recently, however, scientists discovered a new form of pure carbon they dubbedbuckminsterfullerenes, or buckyballs. Buckyballs are hollow, spherical cages of carbonatoms that have very different properties than either graphite or diamond.

This passage best illustrates the relationship between the

A. number of isotopes of an element and the ways in which that element can be used.

B. length of the atomic bonds in a substance and the strength of those bonds.

C. the arrangement of atoms in different forms of a pure element and the properties of thoseforms.

D. abundance of an element in nature and the number of compounds that can be formed bythat element.



5

competency 02746. Which of the following lines correctly matches a type of chemical bond with a description

of some of its characteristics?

A. Line 1

B. Line 2

C. Line 3

D. Line 4

competency 02747. Which of the following equations is balanced?

A. CaBr2 + Na2CO3 → 2 CaCO3 + NaBr

B. CaBr2 + Na2CO3 → CaCO3 + 2 NaBr

C. CaBr2 + Na2CO3 → 2 CaCO3 + 2 NaBr

D. CaBr2 + Na2CO3 → CaCO3 + NaBr

5



competency 02848. A boulder at the top of a cliff has 300 units of energy. A person pushes the boulder over the

edge. Which of the following diagrams correctly shows how much total kinetic andpotential energy the boulder has

• at the top of the cliff just before it goes over the edge,

• halfway to the bottom, and

• just before hitting the ground?

A.

B.

C.

D.



5

competency 02849. Which of the following shows a correct method for using shielded copper wire to construct

an electromagnet?

A.

B.

C.

D.

5



competency 02950. A student fills a beaker with ice and

places it on a hot plate. As the icemelts, the temperature (degreesCelsius) of the ice water mixture isrecorded at fifteen-second intervals.The temperature is then graphed withrespect to time. Which of thefollowing graphs is most likely toresult from this experiment?

A.

B.

C.

D.

competency 02951. A bottle of juice is submerged in a lake.

The temperature of the lake water is afew degrees warmer than that of thebottle of juice. According to thesecond law of thermodynamics, whichof the following statements is true?

A. Heat will flow from the bottle of juiceto the lake until the two are at the sametemperature

B. Heat will flow from the bottle of juiceto the lake until the bottle is coolerthan the lake

C. Heat will flow from the lake to thebottle of juice until the two are at thesame temperature

D. Heat will flow from the lake to thebottle of juice until the bottle iswarmer than the lake



5

competency 03052. A teacher wants to prepare a model to illustrate the operation of the human nervous system.

Which of the following models is most accurate?

A.

B.

C.

D.

5



Use the information below to answer the two questions that follow.

Students in a science class cross-pollinate potato plant A with potato plant B. The resulting seeds arecollected and planted as plot I. The class also cuts several eyes from potatoes harvested from potatoplant A and plants them as plot II.

competency 03153. Which of the following statements best

describes the type of reproductionused to produce offspring in plot Iand plot II?

A. Potato plants in plot I are produced bysexual reproduction, and potato plantsin plot II are produced by asexualreproduction

B. Potato plants in plot I are produced byasexual reproduction, and potato plantsin plot II are produced by sexualreproduction

C. The potato plants in both plot I andplot II are produced by asexualreproduction

D. The potato plants in both plot I andplot II are produced by sexualreproduction

competency 03154. Which of the following statements

about the genetic makeup of thepotato plants grown by the class ismost accurate?

A. All potato plants grown from seeds(plot I) will be genetically identical toeach other but different from bothpotato plant A and potato plant B

B. All potato plants grown from seeds(plot I) will have half as manychromosomes as do the potato plantsgrown from potato pieces (plot II)

C. All potato plants grown from potatopieces (plot II) will be geneticallyidentical to potato plant A

D. All potato plants grown from potatopieces (plot II) will have half as manychromosomes as do the potato plantsgrown from seeds (plot I)



5

competency 03255. Use the illustrations below to answer the question that follows.

Compared to incomplete metamorphosis, complete metamorphosis in an insect speciesmost likely contributes to the survival and reproductive success of the species in which ofthe following ways?

A. In species with complete metamorphosis, immature members of the species can avoidpredators more easily

B. In species with complete metamorphosis, growth and development occurs more rapidlyand the individual reaches sexual maturity at an earlier age

C. In species with complete metamorphosis, immature members of the species can disperseover a wider area after hatching

D. In species with complete metamorphosis, immature and adult life stages can utilizedifferent parts of the larger environment

competency 03256. Which of the following is the most accurate method for classifying two organisms

according to their degree of relationship?

A. Compare similarities and differences in the DNA of both organisms

B. Identify traits shared by both organisms during early embryonic development

C. Compare similarities and differences in the behavior of both organisms

D. Count the number of adaptive morphological traits shared by both organisms

5



competency 03357. When a person is confronted with a dangerous situation, the adrenal medulla secretes

epinephrine (adrenaline), which triggers a “fight or flight” response. Which line in thetable below most accurately summarizes some of the physiological changes characteristicof this response?

A. Line 1

B. Line 2

C. Line 3

D. Line 4



5

competency 03358. A middle school science teacher presents the following model to students.

As you probably know, escalators are moving stairs. Imagine a person walking up anescalator that is going down. If the person walks up at the same speed as the escalator ismoving down, she will remain in one spot. If she walks faster than the escalator, she movesup. If she walks slower, the escalator carries her down.

This model would be most appropriate for helping students discover which of thefollowing science concepts?

A. Newton’s law relating gravity to mass and distance

B. The process of erosion due to flowing water

C. The process of maintaining homeostasis in the human body

D. The energy changes that occur during photosynthesis

competency 03459. When an agricultural field is abandoned, it usually undergoes ecological succession

involving a sequence of changes in vegetation. In most of North America, species of pinetrees tend to be characteristic of early stages of succession, while hardwoods such as oak,beech and maple are more often found in later stages. Which of the following bestexplains this pattern of succession?

A. Pines are better adapted to the nutrient levels characteristic of abandoned fields.Hardwoods eventually replace the pines when nutrient levels return to more normal levels.

B. Pine seeds and seedlings germinate and grow more rapidly in open, sunny areas. The shadefrom the mature pine trees eventually favors the establishment and growth of the hardwoodspecies.

C. Pine needles are better able to resist the many plant pests initially present in a fieldecosystem. Hardwoods are eventually able to grow as the insect population decreases.

D. Pine seeds are more abundant than seeds of hardwoods in abandoned fields. The slowinflux of hardwood seeds eventually allows these species to overtake the pines.

5



competency 03460. Which of the following changes in an

ecosystem would most likely lead toan increase in the population of agiven plant species?

A. An increase in herbivory of thatspecies

B. An increase in intraspecificcompetition for space

C. A decrease in the population of aspecies occupying a similar niche

D. A decrease in the population of amajor insect pollinator

competency 03561. Which of the following is the most

significant cause of the spread ofdeserts in arid regions of the Earth?

A. Construction of large hydroelectricprojects to generate electricity

B. Diversion of underground watersources to supply cities and towns

C. Use of surface water to provideintensive irrigation for agriculture

D. Removal of native vegetation due toovergrazing and farming

competency 03662. Use the information below to answer

the question that follows.

Students in a science class areexperimenting with a tablet thatreleases carbon dioxide when placed inwater. The students place a tablet in100 mL of water and measure howlong it takes until the tablet stopsproducing gas bubbles. The studentsrepeat the experiment using a wholetablet broken into halves, a wholetablet broken into quarters and a wholetablet crushed into powder.

Which of the following questions ismost closely related to thisexperiment?

A. What kind of chemical reactionsproduce the gases released fromvolcanoes?

B. How does increasing the surface areaof rock by mechanical weatheringaffect the rate of chemical weathering?

C. How much carbon dioxide gas can bedissolved in 100 mL of ocean water atroom temperature?

D. How much carbon dioxide is stored ina given mass of sedimentary rock?



5

competency 03663. As part of its plan for reducing

greenhouse gases in the atmosphere,the U.S. government has called forthe planting of millions offast-growing trees. The primary goalof this program is to reduceatmospheric carbon dioxide. Basedon current understanding of theEarth’s oxygen-carbon dioxide cycle,which of the following is the bestanalysis of the likely long-termeffectiveness of this program?

A. The trees will remove carbon from thesoil during growth, which willpermanently increase the soil’s abilityto absorb atmospheric carbon dioxide

B. The trees will remove carbon dioxidefrom the air during photosynthesis, butsome of that carbon dioxide will laterbe returned to the atmosphere after thetrees die and decompose

C. The trees will remove some carbondioxide from the air duringphotosynthesis, but will release morecarbon dioxide during transpiration

D. The trees will remove both carbondioxide and oxygen from the air, so theratio of these two gases will remainconstant

competency 03764. Under which of the following

conditions are thunderstorms mostlikely to form?

A. Two fronts meet and prevent eachother from moving

B. Heavy, moist air overtakes light, dryair, causing the lighter air to sinkrapidly toward the ground

C. Warm air meets a stationary front andcauses it to begin rapidly advancing

D. A fast-moving cold front enters an areain which there is a warm, humid airmass5




Based on the information in the map, which of the following weather conditions is mostlikely to exist at the locations specified?

A. Denver, Colorado, is having showers and light winds out of the southeast

B. Kansas City, Kansas, is having periods of rain with a breeze out of the southwest

C. Columbia, South Carolina, is having heavy rain and very strong winds

D. Fort Worth, Texas, is having an overcast and hot day, with strong winds out of thenorthwest



5

competency 03866. Which of the following observations

best supports the big bang theory ofthe origin of the universe?

A. Galaxies may be clumped or clusteredin a region of space

B. New stars are being formedcontinuously from cosmic dust clouds

C. Microwave background radiation isfairly evenly distributed across space

D. Large black holes have been found atthe centers of some galaxies

competency 04067. Use the passage below to answer the

question that follows.

In a unit on the solar system, a scienceteacher uses a beach ball to representthe Sun while the students brainstormeveryday objects that are the rightrelative sizes to represent the planets.Next, the class determines how manymeters are required in their model torepresent accurately the relativedistance between each planet and theSun, based on actual distances in thesolar system. Finally, the class sets upits model in the area around the schoolby measuring distances and placingthe beach ball and the objectsrepresenting the planets around theschool grounds in the correct relativepositions.

The activities described in the passageare effective for communicatinginformation about the solar systemprimarily because they providestudents with

A. an opportunity to re-create the processby which Kepler derived the laws ofplanetary motion.

B. a conceptual model of the effects thatthe movement of other planets has onthe motion of the Earth.

C. a framework for understandingprocesses involved in the formationand evolution of the solar system.

D. a concrete way of visualizing abstractideas about the relationships amongthe planets in the solar system.

5



competency 04068. A science teacher wants to build

students’ ability to use scientificreasoning and procedures inclassifying living things. Of thefollowing, the best activity forachieving this goal is to

A. discuss mechanisms of evolution andhow the evolutionary process leads toadaptation of species to theirenvironments.

B. dissect preserved specimens of twoclosely related insect species anddiscuss morphological differencesbetween them.

C. compare the similarities anddifferences of living and fossilspecimens of related insect species.

D. examine a wide variety of living thingsand organize them into groupsaccording to criteria established by theclass.

competency 04169. Students in a science class are doing a

research project on a small pond neartheir school. The students know froman archive of the local newspaper thatthe pond once supported a healthyfish population. There are currentlyno fish in the pond. Which of thefollowing activities could the teacheruse to help students understand theconcept of developing a scientifichypothesis?

A. Have students brainstorm possiblereasons for why the pond no longersupports a fish population

B. Ask students to develop a list ofpossible sources of chemical pollutionthat could have killed the fish in thepond

C. Have students search the newspaperarchives for stories dealing with thedeclining fish population to see if atrend emerges

D. Ask students to use the Internet to finda method for measuring the oxygencontent of the water in the pond



5

Use the information below to answer the four questions that follow.

A group of fifth-grade students wishes to test the hypothesis that adding mass to a cart rolled down aramp will increase the distance the cart will travel along the floor. To do this, they design and carryout the following experiment using a toy cart with a mass of 200 grams, a small ramp and a supply of25 gram masses.

A. Make a line across the ramp near the top.

B. Line up the front wheels of the cart with the line.

C. Let go of the cart without pushing it.

D. When the cart stops, measure the distance from the bottom of the ramp to the placewhere the front wheels stopped. Write down this distance.

E. Add a 25 gram mass to the cart.

F. Repeat until a total of 200 grams has been added to the cart.

To see more clearly the relationship between the amount of mass added to the cart and the distancethe cart travels, the students graph their results. Their graph is shown below.

5



competency 02270. The students are concerned about

the measurement they obtained when75 grams were added to the cartbecause it did not seem to fit into thepattern created by the other results.They would like to repeat theinvestigation to determine whetherthis distance is correct. To improvetheir investigative design and toobtain more reliable results, thestudents should

A. measure the total distance the carttraveled from the top of the ramp towhere it stopped.

B. have two students measureindependently the distance the carttraveled.

C. change the height on the ramp at whichthe cart is released.

D. release the cart several times with eachmass and use the average distancetraveled at each mass.

competency 02571. The results of this experiment best

illustrate which of the followingphysical principles?

A. An object with more mass has agreater force of friction acting on itthan one with less mass

B. A moving object with more mass hasgreater momentum than one with lessmass

C. An object with less mass requires lessforce to start it moving than one withmore mass

D. An object with less mass exerts lessdownward force on a level surface thanan object with more mass

competency 04172. The teacher wants to help her students

understand the role of variables inscientific experiments. Which of thefollowing would be the mosteffective way to introduce this topicin the context of this experiment?

A. Ask the students to describe asprecisely as they can how themovement of the cart changed as moremass was added to it

B. Ask the students to identify whatfactors stayed the same during theexperiment, what factors changed andwhat results the changes produced

C. Ask the students to predict what theirresults would have been if they hadchanged the slope of the ramp insteadof the mass of the cart with each trial

D. Ask the students to suggest otherexperimental designs that could beused to demonstrate the same principlethat was discovered in this experiment

competency 04273. An appropriate way to assess the

students’ ability to draw conclusionsbased on these experimental datawould be to have the students

A. predict the distance the cart wouldtravel if 250 grams were added.

B. determine how much farther the carttraveled with 200 grams than with100 grams.

C. use a graphing calculator to determinethe linear regression line that best fitsthe data.

D. describe what the graph would looklike if the divisions on the vertical axiswere spaced farther apart.



5

competency 04274. Use the student expectation below from the Texas Essential Knowledge and Skills

(TEKS) to answer the question that follows.

The student is expected to collect data and make measurements with precision.

Which of the following types of assessment would be most effective for measuringstudents’ achievement of the above objective?

A. A written response, in which studentsexplain significant figures and analyzehow measurement errors arepropagated through calculations

B. A portfolio, in which samples ofstudents’ more recent experimentaldesigns are compared to previousdesigns in order to evaluate studentimprovement

C. A performance assessment, in whichstudents input data into a spreadsheet,analyze the data using spreadsheetfunctions and display the data inappropriate graphic formats

D. A performance assessment, in whichstudents use tools to measure theattributes of various objects atmeasurement stations locatedthroughout the classroom

5



ANSWER KEY

QuestionNumber

CorrectAnswer Competency

1 B 0012 D 0013 A 0024 B 0025 C 0036 D 0037 D 0048 A 0079 B 00510 B 00511 A 00612 C 00613 C 00614 C 00815 B 00816 B 00917 A 00918 A 01019 D 01120 D 01121 C 01222 D 01223 C 01324 A 01325 B 01426 C 013

QuestionNumber


27 C 01528 B 01529 D 01630 D 01531 C 01732 A 01733 A 01834 A 01835 B 01836 A 01937 D 01938 C 02039 B 02140 C 02141 A 02342 B 02443 A 02244 A 03545 C 02646 C 02747 B 02748 C 02849 B 02850 B 02951 C 02952 B 030



5

QuestionNumber


53 A 03154 C 03155 D 03256 A 03257 D 03358 C 03359 B 03460 C 03461 D 03562 B 03663 B 036

QuestionNumber


64 D 03765 B 03766 C 03867 D 04068 D 04069 A 04170 D 02271 B 02572 B 04173 A 04274 D 042

5



6

Chapter 6Are You Ready? – Last-Minute Tips

6

PREPARING TO TAKE THE TEST

CHECKLIST

Complete this checklist to determine if you are ready to take your test.

Do you know the testing requirements for your teaching field?

Have you followed the test registration procedures?

Have you reviewed the test center identification document requirements in the RegistrationBulletin or on the ETS TExES website at www.texes.ets.org?

Do you know the test frameworks that will be covered in each of the tests you plan to take?

Have you used the study plan sheet at the end of this manual to identify what content youalready know well and what content you will need to focus on in your studying?

Have you reviewed any textbooks, class notes and course readings that relate to theframeworks covered?

Do you know how long the test will take and the number of questions it contains? Have youconsidered how you will pace your work?

Are you familiar with the test directions and the types of questions for your test?

Are you familiar with the recommended test-taking strategies and tips?

Have you practiced by working through the sample test questions at a pace similar to that ofan actual test?

If constructed-response questions are part of your test, do you understand the scoring criteriafor these questions?

If you are repeating a test, have you analyzed your previous score report to determine areaswhere additional study and test preparation could be useful?


ARE YOU READY? – LAST-MINUTE TIPS

6

THE DAY OF THE TEST

You should have ended your review a day or two before the actual test date. Many clichés you mayhave heard about the day of the test are true. You should:

• Be well rested.

• Take the appropriate identification document(s) with you to the test center (identificationrequirements are listed in the Registration Bulletin and on the ETS TExES website atwww.texes.ets.org).

• Take 3 or 4 well-sharpened soft-lead (No. 2 or HD) pencils with good erasers.

• Eat before you take the test.

• Be prepared to stand in line to check in or to wait while other test takers are beingchecked in.

• Stay calm. You can’t control the testing situation, but you can control yourself. Testadministrators are well trained and make every effort to provide uniform testingconditions, but don’t let it bother you if a test doesn’t start exactly on time. You will havethe necessary amount of time once it does start. Using the Reducing Test Anxiety bookletin the days before you test may be helpful in mentally and emotionally preparing yourselfto test. It is available free at www.texes.ets.org.

You can think of preparing for this test as training for an athletic event. Once you have trained,prepared and rested, give it everything you’ve got. Good luck.


ARE YOU READY? – LAST-MINUTE TIPS

Appendix AStudy Plan Sheet

A

STUDY PLAN

Content coveredon test

How well do Iknow the content?

Dates planned forstudy of content

Datecompleted

Where can I findthe materials

I need?

What material do Ihave for studying

this content?

What material do Ineed for studying

this content?

A


STUDY PLAN SHEET

Appendix BPreparation Resources

B

PREPARATION RESOURCES

The resources listed below may help you prepare for the TExES test in this field. These preparationresources have been identified by content experts in the field to provide up-to-date information thatrelates to the field in general. You may wish to use current issues or editions to obtain information onspecific topics for study and review.

MATHEMATICS

Journals

Mathematics Teacher, National Council of Teachers of Mathematics.

Mathematics Teaching in the Middle School, National Council of Teachers of Mathematics.

Ball, D. L. (1992). Magical Hopes: Manipulatives and the Reform of Math Education. AmericanEducator; v16 n2, 14–18, 46–47.

Brahier, D. J. (1999). Teaching Secondary and Middle School Mathematics. Needham Heights,Mass.: Allyn & Bacon.

Burns, M. (2000). About Teaching Mathematics: A K–8 Resource, Second edition. Sausalito, Calif.:Math Solutions Publications.

Coxford, A., Usiskin, Z., & Hirschhorn, D. (1998). The University of Chicago School ofMathematics Project: Geometry. Glenview, Ill.: Scott, Foresman and Company.

Crouse, R. J., & Sloyer, C. W. (1987). Mathematical Questions from the Classroom — Parts I and II.Providence, R.I.: Janson Publications.

Danielson, C. (1997). A Collection of Performance Tasks and Rubrics: Middle School Mathematics.Larchmont, N.Y.: Eye On Education, Inc.

Demana, F., Waits, B. K., Clemens, S. R., & Foley, G. D. (1997). Precalculus: A GraphingApproach, Fourth Edition. Menlo Park, Calif.: Addison-Wesley.

Foerster, P. A. (1998). Calculus Concepts and Applications. Berkeley, Calif.: Key Curriculum Press.

Gottlieb, R. J. (2001). Calculus: An Integrated Approach to Functions and Their Rates of Change,Preliminary Edition. Boston, Mass.: Addison Wesley Longman.

Harshbarger, R. J., & Reynolds, J. J. (1992). Mathematical Applications for the Management, Life,and Social Sciences, Fourth Edition. Lexington, Mass.: D. C. Heath and Company.

Hungerford, T. W. (2001). Contemporary College Algebra and Trigonometry: A Graphing Approach.Philadelphia, Pa.: Harcourt College Publishers.

Ma, L. (1999). Knowing and Teaching Elementary Mathematics: Teachers’ Understanding ofFundamental Mathematics in China and the United States. Mahwah, N.J.: Lawrence Erlbaum.

Morrow, L. J., & Kenney, M. J. (Eds.). (1998). The Teaching and Learning of Algorithms in SchoolMathematics. Reston, Va.: The National Council of Teachers of Mathematics, Inc.

National Council of Teachers of Mathematics. (1995). Assessment Standards for SchoolMathematics. Reston, Va.: The National Council of Teachers of Mathematics, Inc.

B



National Council of Teachers of Mathematics. (2000). Principles and Standards for SchoolMathematics. Reston, Va.: The National Council of Teachers of Mathematics, Inc.

Newmark, J. (1997). Statistics and Probability in Modern Life, Sixth Edition. Philadelphia, Pa.:Saunders College Publishing.

Ostebee, A., & Zorn, P. (1997). Calculus from Graphical, Numerical, and Symbolic Points of View.Philadelphia, Pa.: Harcourt College Publishers.

Serra, M. (1997). Discovering Geometry: An Inductive Approach, Second Edition. Emeryville,Calif.: Key Curriculum Press.

Swanson, T., Andersen, J., & Keeley, R. (2000). Precalculus: A Study of Functions and TheirApplication. Fort Worth, Texas: Harcourt College Publishers.

Swokowski, E. W., Olinick, M., & Pence, D. D. (1994). Calculus of a Single Variable, SecondEdition. Stamford, Conn.: Brooks/Cole.

Texas Education Agency (1997). Texas Essential Knowledge and Skills (TEKS).

Triola, M. F. (2001). Elementary Statistics, Eighth Edition. Boston, Mass.: Addison WesleyLongman, Inc.

Wallace, E. C., & West, S. F. (1998). Roads to Geometry, Second Edition. Upper Saddle River, N.J.:Prentice-Hall, Inc.

Williams, G. (2000). Applied College Algebra: A Graphing Approach. Philadelphia, Pa.: HarcourtCollege Publishers.

Wu, H. (1999). Basic Skills Versus Conceptual Understanding: A Bogus Dichotomy in MathematicsEducation. American Educator; v 23 n3, 14–19, 50–52.

Online Resources

Internet4Classrooms — www.internet4classrooms.com

Pearson Prentice Hall — www.phschool.com

Pearson Welcome K–12 AP Teacher! — www.pearsonhighered.com/educator/K-12_AP_teacher.page



B

SCIENCE

Journals

Science and Children, National Science Teachers Association.

Science Scope, National Science Teachers Association.

The Science Teacher, National Science Teachers Association.

Texas Science Teacher, Science Teachers Association of Texas.

Other Resources

Arons, A. B. (1997). Teaching Introductory Physics. Wiley.

Campbell, N. A., Reece, J. B., et al. (2007). Biology, Eighth Edition. Benjamin/Cummings.

Center for Science, Mathematics, and Engineering Education, National Research Council. (2000).Inquiry and the National Science Education Standards: A Guide for Teaching and Learning.Washington, District of Columbia: National Academy Press.

Chang, R. (2010). Chemistry, Tenth Edition. McGraw-Hill.

Chiappetta, E. L., Koballa, T. R., and Collette, A. T. (2009). Science Instruction in the Middle andSecondary Schools, Seventh Edition. Allyn & Bacon.

Crotts, D. (1995). Critical Thinking Skills: Science. Frank Schaffer Publications, Inc.

Cunningham, W. P., and Cunningham, M. A. (2009). Environmental Science: A Global Concern,Eleventh Edition. McGraw-Hill.

Halliday, D., Resnick, R., and Walker, J. (2010). Fundamentals of Physics, Ninth Edition. Wiley.

Hamblin, W. K., and Christiansen, E. H. (2003). Earth’s Dynamic Systems, Tenth Edition.Prentice-Hall.

Hewitt, P., Suchocki, J., and Hewitt, L. A. (2007). Conceptual Physical Science, Fourth Edition.Addison-Wesley.

Joyce, B. R., Weil, M., and Calhoun, E. (2003). Models of Teaching, Seventh Edition. Allyn &Bacon.

Levin, H. L. (2010). The Earth Through Time, Ninth Edition. Wiley.

National Research Council. (1996). National Science Education Standards. Washington, District ofColumbia: National Academy Press.

Ostlund, K. L. (1992). Science Process Skills: Assessing Hands-On Student Performance. MenloPark, Calif.: Addison-Wesley Publishing Company, Inc.

Project 2061 (American Association for the Advancement of Science) (1993). Benchmarks forScience Literacy. New York, N.Y.: Oxford University Press.

Rakow, S. J. (Ed.). (1998). NSTA Pathways to the Science Standards: Guidelines for Moving theVision into Practice, Middle School Edition. Arlington, Va.: National Science TeachersAssociation.

Ramig, J., Bailer, J., and Ramsey, J. (1995). Teaching Science Process Skills. Torrence, Calif.: FrankSchaffer Publications, Inc.B



Rezba, R., et al. (2008). Learning and Assessing Science Process Skills, Fifth Edition. Kendall/HuntPublishing Company.

Santa, C. M., and Alverman, D. E. (Eds.). (1991). Science Learning: Processes and Applications.Newark, Del.: International Reading Association, Inc.

Serway, R. A., Vuille, C., and Faughn, J. S. (2009). College Physics, Eighth Edition. Brooks Cole.

Starr, C., Taggart, R., and Evers, C. (2009). Biology: The Unity and Diversity of Life, TwelfthEdition. Brooks Cole.

Tarbuck, E. J., Lutgens, F. K., and Tasa, D. (2007). Earth: An Introduction to Physical Geology,Ninth Edition. Prentice-Hall.

Texas Education Agency. (2010). Texas Essential Knowledge and Skills (TEKS).

Texas Education Agency. (2010). Texas Safety Standards: Kindergarten through Grade 12, FourthEdition.

Thompson, G., and Turk, J. (2009). Earth Science and the Environment, Fourth Edition. BrooksCole.

Whitten, K. W., Davis, R. E., Peck, L., and Stanley, G. G. (2006). General Chemistry, EighthEdition. Brooks Cole.

Wright, R. T. (2008). Environmental Science: Toward a Sustainable Future, Ninth Edition.Prentice-Hall.

Zumdahl, S. S., and Zumdahl, S. A. (2007). Chemistry, Seventh Edition. Houghton Mifflin.

Online Resources

American Association for the Advancement of Science — www.aaas.org

American Association of Physics Teachers — www.aapt.org

American Astronomical Society — www.aas.org

American Chemical Society — www.acs.org

American Institute of Biological Sciences — www.aibs.org

American Physical Society — www.aps.org

National Association of Biology Teachers — www.nabt.org

National Association of Geoscience Teachers — www.nagt.org

National Science Teachers Association — www.nsta.org

The Geological Society of America — www.geosociety.org



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