Solution Manual for Mathematics in Action: An Introduction to Algebraic, Graphical, and Numerical Problem Solving, 6th Edition

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RESOURCEMANUALWITHTESTSMATHEMATICS INACTION:AN INTRODUCTION TOALGEBRAIC,GRAPHICAL,ANDNUMERICAL PROBLEM SOLVINGSIXTHEDITIONThe Consortium forFoundation Mathematics

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iiiCONTENTSFOREWORD............................................................................................................viSTUDENTOUTCOMES.......................................................................................................................... viiPERFORMANCEOBJECTIVES................................................................................................................ viiGENERALEDUCATIONCOMPETENCIES.............................................................................................. viiiSECTION1OVERVIEW.............................................................................................................1RESOURCES IN THIS GUIDE.....................................................................................................................1TEXTBOOKCONTENT ANDSTRUCTURE..................................................................................................1TEXTBOOKSUPPLEMENTS......................................................................................................................3PEDAGOGY..............................................................................................................................................5TECHNOLOGY.........................................................................................................................................6SUGGESTEDSYLLABI..............................................................................................................................6MATHEMATICALTOPICSCOVERED IN THETEXT………………………………………………… ........6ANNOTATEDLIST OFCORE AND RECOMMENDEDSUPPLEMENTALACTIVITIES…………………..........7SAMPLECOURSEOUTLINES……………………………………………………………………..........13ASSESSMENT.........................................................................................................................................19SECTION2CHAPTERNOTES..................................................................................................21CHAPTER1:NUMBERSENSE................................................................................................................22CLUSTER1INTRODUCTION TOPROBLEMSOLVING..........................................................................22CLUSTER2PROBLEMSOLVING WITHFRACTIONS&DECIMALS(RATIONALNUMBERS) .................23CLUSTER3COMPARISONS ANDPROPORTIONALREASONING...........................................................24CLUSTER4PROBLEM SOLVING WITHSIGNEDNUMBERS……………………………......................25CHAPTER2:VARIABLESENSE..............................................................................................................26CLUSTER1SYMBOLICRULES ANDEXPRESSIONS............................................................................26CLUSTER2SOLVINGEQUATIONS.....................................................................................................28CLUSTER3MOREPROBLEMSOLVINGUSINGALGEBRA……………………………… ..................29CHAPTER3:FUNCTIONSENSE ANDLINEARFUNCTIONS.......................................................... 30CLUSTER1FUNCTIONSENSE............................................................................................................30CLUSTER2INTRODUCTION TOLINEAR FUNCTIONS.........................................................................31CLUSTER3LINEAR REGRESSION,SYSTEMS,ANDINEQUALITIES……………………. ....................32CHAPTER4:ANINTRODUCTION TONONLINEARPROBLEMSOLVING..................................................34CLUSTER1MATHEMATICALMODELINGINVOLVINGPOLYNOMIALS...............................................34CLUSTER2PROBLEMSOLVING WITH QUADRATICEQUATIONS ANDFUNCTIONS.............................34CLUSTER3OTHERNONLINEAR FUNCTIONS........................................................................ 35SECTION3LEARNING INGROUPS..........................................................................................37QUESTIONS ANDANSWERS ABOUTLEARNING INGROUPS......................................................... 38What is collaborative learning? .........................................................................................................38What skills do students gain through active learning in a collaborative environment?.....................38What is our role as teachers in a collaborative learning environment? .............................................39What if you have not used collaborative learning strategies before? ................................................39How do we form groups? What size should they be?.......................................................................39How can we motivate students to learn in a collaborative setting? ...................................................40What can we do to ensure every student understands the major concepts?.......................................41A student claims, "This is not how I learned it." How do you respond? .........................................41How can time be used efficiently in a collaborative setting? ............................................................41What can be done when a group falls behind or gets ahead? ............................................................42

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ivWhat homework should you assign? .................................................................................................42How is homework checked in a collaborative setting?......................................................................42What can be done when a group member does not actively participate or contribute?.....................43What can we do when a student is occasionally late to class?...........................................................43What can we do about absenteeism? ................................................................................................43What can be done when two group members have a conflict? .........................................................44How do we help students who lack the basic skills that are only reviewed in the course? ...............44How do we assess learning in groups? ..............................................................................................44SECTION4TECHNOLOGY........................................................................................45QUESTIONS ANDANSWERS ABOUTTECHNOLOGY................................................................................45How do scientific calculators assist students using this textbook? ..................................................45How do graphing calculators assist students using this textbook?...................................................46Which type of calculator should your students use? ........................................................................46Should students purchase their own calculators?.............................................................................46Will students be totally dependent on the calculators in using this text?.........................................43How should an instructor proceed when there are many different calculatormodels in the classroom? .........................................................................................................47Are procedures for using the graphing calculator included in this text?..........................................47What computer tutorial programs, graphing/computer algebra systems,or online resources are useful in connection with this textbook? ............................................47How can graphing assignments be assessed?...................................................................................48SAMPLEACTIVITIES USING THEGRAPHINGCALCULATOR ORCOMPUTERPROGRAMS........................48SECTION5WRITINGTOLEARN...............................................................................65HELPINGSTUDENTSKEEP ALEARNINGLOG........................................................................................65JOURNALASSIGNMENTS.......................................................................................................................66BRIEFESSAYASSIGNMENTS..................................................................................................................66ASSESSMENT OFWRITINGASSIGNMENTS.............................................................................................66CRITERIA FOREVALUATION OFASSIGNMENTS.....................................................................................67KEEPING AJOURNAL INMATH............................................................................................. 68SAMPLEJOURNALASSIGNMENTS......................................................................................... 72SECTION6BASICSKILLSPRACTICE.........................................................................89PRACTICING ANDASSESSINGBASICSKILLS.........................................................................................89Calculator Usage ...............................................................................................................................90Percents, Decimals, and Fractions .....................................................................................................92Order of Operations ...........................................................................................................................94Evaluating and Solving Linear Equations .........................................................................................96Solving Literal Equations ..................................................................................................................98Proportions ......................................................................................................................................100Functional Representations..............................................................................................................101Slopes, Intercepts, and Equations of Lines......................................................................................103Systems of Equations ......................................................................................................................105Properties of Exponents, Simplifying Algebraic Expressions .........................................................107Factoring Algebraic Expressions .....................................................................................................109Factoring Trinomials……………………………………………………………………................ 111

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vSECTION7ASSESSMENT.........................................................................................113INDIVIDUAL,GROUP ANDTAKEHOMEEXAMSBYCHAPTER....................................................113Chapter 1........................................................................................................................................114Chapter 2........................................................................................................................................136Chapter 3........................................................................................................................................153Chapter 4........................................................................................................................................195INDIVIDUAL ANDGROUPFINALEXAMS................................................................................213PORTFOLIOS ASASSESSMENTS............................................................................................229SECTION8ANSWERS TOBASICSKILLSPRACTICEWORKSHEETS.....................................231SECTION9ANSWERS TOASSESSMENTS(SECTIONS4AND7)..............................................235

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1SECTION1OVERVIEWRESOURCES IN THIS GUIDEWe hope that the content and format of thisInstructor’s Resource Manual with Testswill be of great help to you in teaching withMathematics in Action.This section of theManualis anannotated directory to the resources addressed at length in the other sections. What is available to you inthisGuideis described under the following headings.Textbook Content and StructureSupplements available with the textbookPedagogy: Learning in Groups and Writing to LearnTechnology: Scientific Calculators, Graphing Calculators, and Computer ProgramsSuggestions for Syllabi: Annotated List of the Major Mathematical Topics Covered in the TextSample Course OutlinesAssessment:Group Oral and Written Tests, Journals, Formal Writing Assignments,Traditional Testing, Basic Skills, PortfoliosMathematics in Actionis adaptable to the various needs of courses at the introductory foundation leveland we offer you an annotated list of the major mathematical topics covered in the text as the best guideto determining the content of your course.We also offer sample course syllabi, one for an elementaryalgebra course and one for an intermediate level algebra course. Please note that in planning your course,supplemental teaching and learning aids are available to you and your students. These supplements arelisted in this Overview Section for your convenience.We organized and formatted thisInstructor’s Resource Manual with Testsso, if you choose, you can usethe sample graphing calculator experiments, journal assignments, writing assignments, skills worksheets,tests, and exams as presented.TEXTBOOK CONTENT AND STRUCTUREThe text is divided into four chapters followed by appendices and a glossary.Chapter 1: Number SenseChapter 2: Variable SenseChapter 3: Function Sense and Linear FunctionsChapter 4: An Introduction to Nonlinear Problem SolvingEach chapter is subdivided into sections we call clusters.Each cluster focuses on a major mathematicaltopic within the context of a chapter.For example, Chapter 1 Cluster 3 focuses on comparisons andproportional reasoning and Chapter 4 Cluster 2 concentrates on problem solving using quadraticequations and functions.There are thirteen clusters in all; four in Chapter 1, three in Chapter 2, three in Chapter 3 and three inChapter 4. The clusters are listed here to give you a convenient overview.

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2OVERVIEWChapter 1Number SenseCluster 1Introduction to Problem SolvingCluster 2Problem Solving with Fractions and Decimals (Rational Numbers)Cluster 3Comparisons and Proportional ReasoningCluster 4Problem Solving with Signed NumbersChapter 2Variable SenseCluster 1Symbolic Rules and ExpressionsCluster 2Solving EquationsCluster 3More Problem Solving using AlgebraChapter 3Function Sense and Linear FunctionsCluster 1Function SenseCluster 2Introduction to Linear FunctionsCluster 3Linear Regression, Systems, and InequalitiesChapter 4An Introduction to Nonlinear Problem SolvingCluster 1Mathematical Modeling Involving PolynomialsCluster 2Problem Solving with Quadratic Equations and FunctionsCluster 3Other Nonlinear FunctionsEach cluster is further divided into sections namedActivities(with Exercises)What Have I Learned?How Can I Practice?Activitiesare the essence ofMathematics in Action.They are where mathematical concepts and skills areintroduced and developed in meaningful contextual problems and situations. We expect that students will seefor themselves the need to master arithmetic and algebra skills, and be able to answer their own frequentlyasked questions, “Why do I need to learn this?” and “When will I ever use this outside this class?”InActivities, students respond to a series of structured prompts and questions that direct them to recall andapply mathematical knowledge they already have, and that lead them to acquire the other concepts andskills they must have to be successful problem solvers.Basic arithmetic and algebra skills are presentedas they are needed in the contextual problems.Activitiesalso include exercises that may be assigned asadditional practice in class or for homework.A set ofActivitiesin a cluster is followed by a section entitledWhat Have I Learned?As the nameimplies, students stop here to think about what they have learned before continuing to the next cluster.They have the opportunity to analyze and synthesize the ideas they studied in the cluster, and to test theirknowledge by applying what they have learned to solve similar problems.You may want to use thesesections to assess your students’ progress. Journal and writing assignments are good assessment tools forthe questions inWhat Have I Learned?In addition, you will find suggestions for assessment in Sections

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OVERVIEW34, 5 and 7 of this guide.Students can also be encouraged to make these assignments part of theirportfolios where they will have easy access to what they have learned when they are preparing for exams.How Can I Practice?sections followWhat Have I Learned?sections to provide further opportunities forpractice.Our textbook also addresses the need for plentiful skills practice and preparation for gateway exams thatmay be required in various programs. Appendix C includes twoSkills Checksections specifically aimedto reinforce arithmetic skills.Each chapter concludes withChapter SummaryGateway ReviewTheChapter Summarylists important concepts and skills from the chapter, together with a briefdescription and example of the concept or skill.TheChapter Summaryprovides reinforcement of whathas been learned in the chapter and is helpful to students studying for exams.Following eachChapter SummaryareGateway Reviews,composed of exercises that test the fundamentalconcepts and skills in their respective chapters. Please note that some additional skills worksheets areprovided in Section 6 of thisGuide.You will also find several appendices inMathematics in Actionthatprovide just-in-time instruction on basic arithmetic and algebraic skills and the use of a graphingcalculator.Appendix A: FractionsAppendix B: DecimalsAppendix C: Skills ChecksAppendix D: Algebraic ExtensionsAppendix E: Getting Started with the TI-84 Plus Family of Graphing CalculatorsThe textbook also contains the following:Answers to selected problems and gateway questions (the Instructor’s Edition contains answersto every problem within the text itself)GlossaryIndexTEXTBOOK SUPPLEMENTSA number of supplemental instructional and learning aids are available for users ofMathematics in Actionand they are described here.Instructor SupplementsAnnotated Instructor’s EditionISBN 10 – 0-13-498931-7ISBN 13 – 978-0-13-498931-0Contains all the content found in the student edition, plus answers to all exercises directly beneath eachproblem and Learning Catalytics instructor annotations.

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4OVERVIEWInstructor’s Resource Manual with TestsISBN 10 – 0-13-498933-3ISBN 13 – 978--0-13-498933-4This valuable teaching resource includes the following materials:Sample syllabi suggesting ways to structure the course around core and supplemental activities.Sample course outlines containing timelines for covering topics.Teaching notes for each chapter—ideal for using the text for the first time.Extra skills practice worksheets for difficult topics.Sample chapter tests and final exams.Information about incorporating technology in the classroom, such as graphing calculators.TestGen®ISBN 10 – 0-13-516330-7ISBN 13 – 978-0-13-516330-6TestGen®enables instructors to build, edit, print and administer tests using a computerized bank ofquestions developed to cover all the objectives of the text. TestGen is algorithmically based, allowinginstructors to create multiple but equivalent versions of the same question or test with the click of abutton. Instructors can also modify test bank questions or add new questions.Instructor’s Training VideosFrom author Ernie Danforth, the videos provide instructors with advice ranging from the Consortiumteaching philosophy to tips for implementing group-work.New! PowerPoint LecturesThese slides present key concepts and definitions from the text. These have been created to supportinstructors looking to implement this contextual approach in the classroom, and can also be used as astudent study aid.Student SupplementsWorksheets for Classroom or Lab PracticeISBN 10 – 0-13-516714-0ISBN 13 – 978-0-13-516714-4Provide extra practice to ensure that students have many opportunities to work problems related tothe concepts learned in every activity.Concept Connections, a feature unique to these worksheets, offer students an opportunity to showin words that they understand the mathematical concepts they have just practiced.Supplements for Instructors and StudentsMyLab Math® Online Course (access code required)MyLab Math from Pearson is the world’s leading online resource in mathematics, integrating interactivehomework, assessment, and media in a flexible, easy to use format. It provides engaging experiences that

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OVERVIEW5personalize, stimulate, and measure learning for each student.Moreover, it comes from an experiencedpartner with educational expertise and an eye on the future.MyLab Math is a complete online course that provides interactive, multimedia instruction correlated tothis textbook content. A MyLab course provides the full eText with a multimedia library to provideadditional support for students when they need it. For this revision, a new video series and PowerPointseries are available, in addition to MyLab's exercises with learning aids and feedback, a personalizedstudy plan, and more.Instructor’s Training Video available in MyLab Math® (access code required)The Instructor’s Training Video discusses effective ways to implement the teaching pedagogy of theMathematics in Actionseries, focusing on how to make collaborative learning, discovery learning, andalternative means of assessment work in the classroom. (Available in the Instructor Resources tab inMyLab Math®)PowerPoint Lectures are available in MyLab Math. These slides present key concepts and definitionsfrom the text. These have been created to support instructors looking to implement this contextualapproach in the classroom, and can also be used as a student study aid.To learn more about how MyLab Math combines proven learning applications with powerful assessment,visitwww.MyLabMath.comor contact your Pearson representative.PEDAGOGYThe pedagogical theme ofMathematics in Actionis active learning, facilitated by emphasis on:Writing to Learn MathematicsStrategies for Problem SolvingCollaborative Learning in GroupsWhole-Class Interactive DiscussionsUse of TechnologyWriting-to-learn strategies are built into the structure of the textbook, so students are consistently helpedto think by writing, a time-honored way to learn mathematics. Section 5 of thisGuidepresents additionalwriting-to-learn techniques to share with your students.Students need to recognize and assimilate thinking strategies for problem solving.In Section 2, wedescribe our insights on the purposes and goals of individual activities, problems, and exercise sets, andthe problem-solving strategies they elicit.In the classroom, we found, as many have, that the most active learning takes place in group settingswhere the teacher is a guide who helps students find their own correct understanding of concepts. Smallgroups promote attention to individual needs in learning, increase peer support for puzzling out solutions,andprovideexperienceinteamwork.Whole-classinteractivediscussionsallowaninstructortoefficiently explain key concepts and clear up common misunderstandings, give students the opportunity todevelop self-reliance in learning quantitative and algebraic skills for problem solving, and encourage thesharing and discussing of ideas in a large group setting. In Section 3, we share our experiences and offer

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6OVERVIEWsuggestions for using collaborative learning and interactive discussion with theActivitiesand othercomponents in the textbook.TECHNOLOGYCalculators and graphing programs are not only tools for doing mathematics and solving problems; theyhave fundamentally changed the way we teach and learn mathematics.We developed our textbookrecognizing this modern pedagogical truth and you will find suggestions and ideas for using technologywith the textbook in Section 4 of thisGuide.Technology is an integral part of the textbook and a number of technical tools are compatible with theactivities in the course.Scientific CalculatorsGraphing CalculatorsGraphing SoftwareTutorial Software for Skills PracticeScientific calculators are required and sufficient for the course, although graphing calculators are usefuland are occasionally referenced for visual representation of functions in Chapters 3 and 4.Tutorialsoftware can serve as an adjunct for practicing basic skills. You will find further discussion, suggestions,and examples regarding these tools in Section 4.SUGGESTIONS FOR SYLLABIMathematics in Action:An Introduction to Algebraic, Graphical, and Numerical Problem Solvingcan beused as the text in a variety of foundation level courses. Among the authors, we have adopted all or partof the book for courses in arithmetic, elementary algebra, intermediate algebra, and introduction tofunctions.The number of contact hours for each of these courses varies considerably from three to sixhours, with the latter often including a computer laboratory component.We compiled the following annotated list of the major mathematical topics covered in the textbook toserve as an effective guide for you to construct a syllabus that best suits your course.We have attemptedto identify those activities that provide the essence of each major topic.In addition to these coreactivities,wehavesuggestedotherhighlyrecommendedactivitiesthatexpandorreinforcethemathematical theme. We encourage you to use the many remaining activities for further exploration andpractice.MATHEMATICAL TOPICS COVERED IN THE TEXTBOOKBelow is a list of the major topics covered inMathematics in Action.We then present an annotated listthat indicates both the core activities and recommended supplemental activities that explore each of thesetopics.Arithmetic Operations using Whole Numbers, Fractions (Rational Numbers) and DecimalsNumerical Literacy through Proportional ReasoningArithmetic Operations using Signed Numbers

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OVERVIEW7Introduction to Variable Quantities; Numerical, Symbolic and Graphical Representations ofRelationships Between Input and Output VariablesSymbolic Representation of Variable QuantitiesConstructing, Evaluating, and Solving Single-Operation Algebraic ModelsConstructing, Evaluating, and Solving Two-Operation Algebraic (Linear) ModelsEquivalent Algebraic Expressions: Numerically, Graphically, and AlgebraicallySolving More Complex (Linear) EquationsFunction Definition and NotationRates of ChangeLinear Functions: Numerical, Graphical, and Algebraic FeaturesScatterplots and Linear Regression EquationsProblem Solving with Linear FunctionsSystems of Linear EquationsLinear InequalitiesPolynomials and Properties of ExponentsProblem Solving with Quadratic Equations and FunctionsA Brief Glimpse at Other Function FamiliesANNOTATED LIST OF CORE AND RECOMMENDED SUPPLEMENTALACTIVITIESArithmetic Operations using Whole Numbers, Fractions and Decimals (Rational Numbers)Recommended:Activity 1.1The BookstoreSteps in Problem SolvingDevelop communication skills and problem-solving skills; organize information.Recommended:Activity 1.2The ClassroomProblem-Solving StrategiesDevelop communication skills and problem-solving skills; organize information.Core:Activity 1.3Properties of ArithmeticProperties and Vocabulary for Arithmetic CalculationsUse the order of operations convention to evaluate arithmetic expressions containing positiveintegers; use the Distributive and Commutative Properties; exponential notation; use ScientificNotation for large numbers.Recommended:Appendix AFractionsTemplates and skill practice.Recommended:Appendix BDecimalsTemplates and skill practice.

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8OVERVIEWCore:Activity 1.4Top ChefOperations with Fractions and Mixed NumbersAdd and subtract fractions; multiply and divide fractions.Core:Project 1.5Course Grades and Your GPAProblem Solving Using Fractions and DecimalsSolve problems with fractions and decimals.Numerical Literacy through Proportional ReasoningCore:Activity 1.6Everything is RelativeRatios as Fractions, Decimals, and PercentsRelative versus actual measures; express ratios as fractions, percents, and decimals; ratios ascomparison.Core:Activity 1.7The Opioid EpidemicProportional ReasoningProportional reasoning using ratios.Core:Activity 1.8WhoReally Did Better?Actual and Relative Change, Percent Increase and DecreaseInvestigate relative (percent) versus actual change – percent increase or percent decrease.Core:Activity 1.9Going Shopping?Growth and Decay FactorsDefine and explore growth and decay factors.Core:Activity 1.10Take an Additional 20% OffConsecutive Growth and Decay FactorsApply growth or decay factors consecutively.Core:Activity 1.11Fuel EconomyRates and Unit AnalysisSolve problems involving unit-of-measure conversions by Unit (Dimensional) Analysis.Arithmetic Operations using Signed NumbersRecommended:Activity 1.12Celsius ThermometersAddition and Subtraction of IntegersAdd, subtract, and compare signed numbers; compute absolute values.Recommended:Activity 1.13Shedding the Extra PoundsMultiplication and Division of IntegersMultiply and divide signed numbers.Core:Activity 1.14Order of Operations RevisitedNegative Exponents and Scientific NotationEvaluate arithmetic expressions containing positive and negative numbers using the order ofoperations convention; evaluate expressions with negative exponents; Scientific Notation for verysmall numbers.

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OVERVIEW9Introduction to Variable Quantities; Numerical, Graphical and Symbolic Representations ofRelationships Between Input and Output VariablesCore:Activity 2.1Symbolizing ArithmeticFormulas and Algebraic ExpressionsGeneralize from an arithmetic calculation to a symbolic representation by utilizing variables.Core:Activity 2.2Blood Alcohol LevelsRepresent a Two-Variable Relationship Algebraically, Numerically, andGraphicallyIdentify input and output in situations involving two variables; interpret relationships numericallyand graphically.Recommended:Activity 2.3College ExpensesSymbolic RulesIdentify input and output variables from a graph; write verbal rules and translate into symbolicrules.Symbolic Representation of Variable QuantitiesCore:Activity 2.4Are they the Same?Equivalent Expressions and Grouping SymbolsIdentify equivalent algebraic expressions by examining their outputs and comparing the graphs.Constructing, Evaluating and Solving Single-Operation Algebraic ModelsCore:Activity 2.5Let’s Go ShoppingSolve an Equation Containing One OperationConstruct, evaluate and solve equations of the formaxbandxab.Constructing, Evaluating, and Solving Two-Operation (Linear) Algebraic ModelsCore:Activity 2.6Leasing a CopierSolve an Equation Containing Two or More OperationsConstruct, evaluate and solve equations of the form ax + b = c, a ≠ 0.Core:Activity 2.7The Algebra of WeatherSolve a Formula for a Specified VariableSolve a formula (literal equation) for a specified variable.Core:Activity 2.8Four Out of Five Dentists Prefer CrestProportionsConstruct and solve proportion equations using equivalent fractions and cross multiplication.Equivalent Algebraic Expressions: Numerically, Graphically and AlgebraicallyCore:Activity 2.9Do It Two WaysDistributive Property, Greatest Common Factor, and Combining Like TermsUse the distributive property to transform one algebraic expression into an equivalent one.Expand and factor expressions; combine like terms.

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10OVERVIEWRecommended:Activity 2.10DecodingSimplifying Algebraic ExpressionsRecognize an algebraic expression as a code of instruction; simplify algebraic expressions.Solving More Complex (Linear) EquationsCore:Activity 2.11Comparing Energy CostsMathematical Models, General Strategy for Solving Linear EquationsModel and solve equations of the formaxbcxd.Recommended:Project Activity 2.12Summer Job OpportunitiesProblem Solving Using Linear EquationsUse critical thinking skills to make decisions based on solutions of systems of two linearequations.Function Definition and NotationCore:Activity 3.1Summer OlympicsFunctions, Numerical and Graphical Representation of FunctionsIntroduction to functions; function notation; graphical and numerical representations; expansionof rectangular coordinate system to include all 4 quadrants in the planeCore:Project 3.3Comparing Symbolically Defined Functions and their GraphsDefine functions by symbolic rules.Core:Activity 3.4Course GradeRepresenting Functions SymbolicallyDetermine symbolic rule that defines a function as well as practical domain and range of afunction.Rates of ChangeCore:Activity 3.2How Fast Did You Lose?Average Rate of ChangeAverage rate of change—definition, contextual interpretationsLinear Functions: Numerical, Graphical, and Algebraic FeaturesCore:Activity 3.5The Snowy Tree CricketSlope and Intercepts of a LineDefine linear functions by their constant rate of change and graph consisting of a single line;identify slope as the constant rate of change.Core:Activity 3.6Software SalesSlope-Intercept Equation of a LineWrite equation of line in slope intercept form; graph linear function using y-intercept and slope;use intercepts to graph linear equation.Recommended:Activity 3.7Predicting PopulationProblem Solving Using Slope-Intercept Equation of a LineThe slope-intercept form of a linear function; relative error in measurement using a linear model

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OVERVIEW11Core:Activity 3.8College TuitionPoint-Slope Equation of a LineDetermine equation for linear function when given two points. Identify lines having negative,zero or undefined slopes; equations of horizontal and vertical lines.Scatterplots and Regression LinesRecommended:Activity 3.9Education PaysLine of Best Fit and Regression EquationsConstruct scatterplots from sets of data; use a scatterplot to estimate a line of best fit; generatelinear regression models using technology.Recommended:Lab Activity 3.10Body PartsProblem Solving Using Regression EquationsCollect sets of data by measurement; use a scatterplot to estimate a line of best fit; generate linearregression models using technology.Systems of Linear EquationsCore:Activity 3.11Smartphone Plan OptionsSystems of Linear Equations in Two VariablesSolve a system of two linear equations numerically, graphically and symbolically by thesubstitution method; interpret the solution.Recommended:Appendix D Addition Method for Solving a System of Two Linear EquationsCore:Activity 3.12Healthy LifestyleSolving a System of Linear Equations in Two Variables Using theAddition MethodSolve a system of two linear equations algebraically by the substitution method and by theaddition method.Recommended:Project Activity 3.13Modeling a BusinessProblem Solving Using Systems of Linear Equations inTwo VariablesSolve a system of two linear equations by any method; determine and interpret the break-evenpoint; interpret break-even points in contextual situations.Linear InequalitiesRecommended:Activity 3.14How Long Can You Live?Linear InequalitiesSolve linear inequalities in one variable algebraically and graphically.Polynomials and Properties of ExponentsCore:Activity 4.1Fatal CrashesPolynomialsIdentify, classify and simplify polynomials; add and subtract polynomials; evaluate and interpretpolynomial models.Core:Activity 4.2Volume of a Storage BoxProperties of Exponents

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