georgia high school mathematics

Georgia High School Mathematics

Program Components

Georgia High School MATHEMATICS

Coordinate Algebra • Analytic Geometry • Advanced Algebra

Program Overview

Guide

Georgia High School MATHEMATICS

Pearson Georgia High School Mathematics,fullyalignedtothe

Common Core Georgia Performance Standards,offers

ahybridinstructionalmodelthatconsistsofdigitaldelivery

ofcontentduringinstructionaltime,supplementedbya

write-instudentedition(worktext)inwhichstudentsrecord

theirunderstandingsoftheconceptspresentedastheywork

throughtheproblems.Thein-classinstructioncanbefurther

enhancedwiththerobustmathtoolsanddynamicactivities

thatarepartofthedigitalcourseware.

Thein-classlearningissupportedoutoftheclassroomwith

bothdigitalandprintresources.Studentshavefullaccessto

theanimatedcontentpresentedinclass.Theyalsocaneasily

accessmathtutorvideos.IntheStudentWorktext,students

willfindinstructionalsummariesofkeyconceptsineachlesson.

This guide will provide a comprehensive overview and

highlight the core components of the program.

Georgia High School Mathematics Program Overview

Teacher’sGuideLessonWalkthrough . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

DifferentiatedResources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

StudentTechnologyComponents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20

AssessStudentProgress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24

ExceptionalTeacherSupport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28

Common Core Georgia Performance Standards

CCGPSCorrelation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32

StandardsforMathematicalPracticeWalkthrough . . . . . . . . . . . . . . . . . . . . .46

PARCC—CommonCoreStateStandardsAssessment . . . . . . . . . . . . . . . . . . .62

Georgia High School Mathematics Table of Contents

CoordinateAlgebra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66

AnalyticGeometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68

AdvancedAlgebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70

Program Overview

Guide

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TheTeacher’sGuideisacomprehensivetoolthatteacherscanuseastheyplanforandteacheveryphaseofthe5-partlessonoftheprogram.Atthechapterlevel,teacherswillfindmathbackground,tipsforerrorprevention,andassignmentguidestohelptheminplanning.Atthelessonlevel,teacherswillfindresourcesforinstruction,practice,assessment,andremediation.Tohelpwithplanning,thereareteachingnotesandprobingquestionstotheleftofimagesofeachSolve It!andproblemthatteacherswillbepresentingfromthedigitalcourseware.

ThefollowingpagescontainawalkthroughoftheTeacher’sGuide.

Also includes information about the Student Worktext and Pearson SuccessNet®, the site

of the digital courseware, beginning on page 14.

Beginning of a Chapter

GetReady! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3

ChapterOpener. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

MathBackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

Lesson Walkthrough

5-StepLessonStructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

Step1:InteractiveLearning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

Step2:GuidedInstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

Step3:LessonCheck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9

Step4:Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Step5:AssessandRemediate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

End of a Chapter

ChapterReview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

PullItAllTogether. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

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Get Ready!OnthefirstpageofeachchapterarerecommendationsfortheGet Ready!diagnosticassessmentfoundintheStudentWorktext.Teacherscanusetheassessmenttodeterminewhetherstudentshavemasteredtheprerequisiteskillsforthechapter.

Theitemanalysischartidentifiesthecorrespondinglessonandremediationresourcesforeveryskillassessed.

IntherightcolumnisthereducedstudentpageshowingGet Ready!diagnosticassessmentthatisfoundintheStudentWorktext.Thisassessmentisalsoavailableonline.

Teachersfindanswersatpointofuseintheleftcolumn.

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TheCommon Core Georgia Performance

Standards addressedineachchapterarelisted

foreasyreference.

Key VocabularyforeachchapterislistedinEnglishandSpanish.Studentscanaccessfulldefinitions,inbothEnglishandSpanish,intheglossaryattheendoftheStudentWorktextandonlinewithfullaudiooption.

ThisprogramincorporatestheUnderstandingby

Designframework®*.EachlessonisstructuredaroundEssential Questionsthat

areconnectedtoBig Ideas.

PearsonSuccessNet®isthegateway

toallthedigitalcomponentsforthe

program.

Chapter OpenerTheChapterOpenerincludesanoverviewoftheBig IdeasandEssential Understandingsforthechaptertosupportteachersastheypreparetoteachachapterandplanforinstruction.AlsolistedareCommon Core Georgia Performance Standardsandapreviewofthelessonsinthechapter.

*UNDERSTANDINGBYDESIGN®ANDUbD™aretrademarksofASCD,andareusedunderlicense.

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Math BackgroundTheMath Backgroundpagesprovideillustratedexplanationsofthemainconceptspresentedinthechapter.TeacherswillalsofindexplanationsofopportunitiestodevelopproficiencywiththeStandards for Mathematical Practice.Thesepagesofferteachersjust-in-timeongoingprofessionaldevelopmenttoensurerigorousandaccuratemathinstruction.

TeachersareprovideddetailedexplanationoftheBig IdeasandEssential Understandingsofthechaptertofullydevelopconnections.

IncludedintheexplanationofkeyconceptsisadescriptionofCommon Errors studentsmake.

AlsoincludedareexamplesofopportunitiestodevelopproficiencywiththeStandards for Mathematical Practice.

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Fromapedagogicalperspective,thisprogramwillmaintainthesamefive-partlessonstructurethathasbeenshowntobeeffectivewithPearson Prentice Hall High School Mathematics:Interactive Learning, Guided Instruction, Lesson Check, Practice, and Assess and Remediate.Itwillalsointegratethefiveprinciplesoftheprogram:problemsolving,visuallearning,differentiatedinstruction,interactivelearning,anddigitalinstruction.Thefollowingpageswillprovideawalkthroughofthe5-steplessonstructure.

STEP 1 Interactive Learning

STEP 2 Guided Instruction

STEP 3 Lesson Check

STEP 4 Practice

STEP 5 Assess and Remediate

STUDENT WORKTEXT

TEACHER’S GUIDE

PEARSONSUCCESSNET.COM OR DIGITAL LESSON DVD

CORE COMPONENTS

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Interactive LearningEverylessonbeginswithproblem-basedinteractivelearning. ThroughtheSolve It!,atthebeginningofeverylesson,teacherscanactivatestudents’priorknowledgeandsetthecontextfortheEssential Understandingforthelesson.Studentsworkthroughthereal-worldproblembyfirstmakingsenseoftheproblem,andthenanalyzingthesituation,makingsolutionsplans,andpresentingandjustifyingtheiranswerstotheclass.

STEP 1

TheCommon Core Georgia Performance Standardsareshownatthebeginningofeverylesson.

Somelessonsinclude aDynamic Activity.Theseanimatedactivitiescanhelpstudentsunderstandimportantmathconcepts.

Eachpartofthe5-steplessonisclearlyidentified.

Teachersfindallnecessaryteachingnotestofacilitatethelessonintheleftcolumn.Thefacilitatingquestionsaresetoffinblueforeaseofnavigation.

TheimageoftheSolve It!fromthedigitalcoursewarefacilitatesplanningforteachers.ThisanimatedpartofthelessoncanbeprojectedwithanLCDprojectororonanInteractiveWhiteboard.

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TheGuided InstructionphaseofthelessonbeginswiththeEssential Understandinginwhichthefocusofstudyforthelessonisformalized. Aninterwovenstrandofreasoningconnectsthemaththatstudentslearn,fromthefirstlessontothelast,furthersupportingboththeCommon Core Georgia Performance Standards andtheStandards for Mathematical Practice.

STEP 2

TherightcolumnoftheTeacher’sGuide

showsallofthestudent-facingpieces:theproblemsfromthedigitalcoursewareandreducedpartsofthe

studentpages.Teachersseewhat

instructionalsupportstudentshavein

theirStudentWorktext.

Thesupportingquestions,intheleft

column,helpteachersguidestudentsto

deepunderstandingoftheconceptsandto

greaterfluencywiththemathematicalpractices.

TeachersalsofindimagesoftheanimatedproblemavailableintheInteractiveDigitalPathonPearsonSuccessNet®.Asteachersandstudentsworkthroughtheproblemsfromthedigitalcourseware,studentsrecordtheirunderstandingsintheStudentWorktext.

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Lesson CheckTheLesson Checkpresentstimelyopportunitiesforassessingstudents’understandingofthelessoncontent.Thequestionsin Do you know HOW?assessstudents’proceduralfluencywhilethequestionsinDo you UNDERSTAND?focusonstudents’conceptualunderstanding.

STEP 3

TeachershaveaccesstotheinstructionalsummariesfoundintheStudentWorktextandinthedigitalcourseware.

ThequestionintheCloseencouragesstudentstoexpressverballyorinwritingtheirunderstandingoftheconceptspresented.

MostoftheexercisesintheDo you UNDERSTAND?sectionfosterthedevelopmentofoneormoreMathematicalPractices.Exercises,suchasReasoning,CompareandContrast,andErrorAnalysis,focusonstructureandmeaningratherthanjustonthesolution.

StudentshaveadditionalspaceintheStudentWorktexttocompletetheLesson Check (seeexampleonpage16).Teacherscanreviewthesequestionsinclassorassignforindependentpractice.

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PracticeThePracticephaseaffordsstudentsopportunitiestosolidifytheirproceduralfluencyandconceptualunderstandingofthelessoncontent.TheexercisesfoundintheStudentWorktextareofthreedifferenttypes:practice,applicationandchallengeproblems.

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STEP 4

TheHomework Quick Checksavesteachers

timebysuggestingwhichproblemstocheckthenextdayforaquickreviewofkeyconcepts.

Theexercisesthatcorrespondtoa

specificStandard for Mathematical Practice aredocumentedinthe

Teacher’sGuide.

ExercisepagesfromtheStudentWorktextareincludedinreducedformat.TheexerciseswiththeCommonCorelogohelpstudentsbecomemoreproficientwiththeMathematicalPractices. TheApplicationexercisesrequirestudentstodevelopmathematicalmodelsforreal-worldproblemsituations.ApplicationexerciseswiththeSTEMlabelpresentreal-worldproblemsituationsrelatedtoscience,technology,orengineeringtopics.

Allanswersareprovidedat

pointofuse.

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Assess and RemediateThefinalphaseofthelessonisAssess and Remediate. EachlessonendswithaLesson Quizandopportunitiestoprovidedifferentiatedinstructionforstudentsbasedontheirquizresults.

STEP 5

TheLesson Quiz,alsoavailableasaPDF,assesseslessonskillsandconcepts.

Theprescriptionforremediationenablesteacherstomakedata-driveninstructionaldecisionsaboutassignmentsforintervention,on-level,andextensionbasedonastudent’sLesson Quizresults.

Inadditiontotheresourceslistedhere,additionalteacherandstudentresourcesareavailableonPearsonSuccessNet®.

TeachersalsohavetheoptionofassigningtestsandquizzesonlineviaSuccessTracker™.Eachonlineassessmentisautomaticallyscoredandtheappropriateinterventionisautomaticallyassignedtoeachstudentbasedonindividualstudentperformance.Thecompileddataappearsinthreedifferentreportsmakingiteasierforteacherstoanalyzewholeclassandindividualstudentperformance.

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Chapter ReviewEachchapterendswithaChapter ReviewwheretheBig IdeasaresummarizedandanswerstheEssential Questionsprovided.ItalsoincludesadditionalSummative Questionstoassessstudents’understandingoftheBig Ideas.

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Teachersareencouragedtoelicitfromstudentstheirunderstandingsoftheanswerstothe

Essential Questions.

Allanswersareprovidedatpointofuseintheleft

columnoftheTeacher’sGuide.

IntheStudentWorktext,theChapter Review

includesaQuick ReviewwhichconsistsofanExampleandsome

Exercisesforeachlessonofthechapter.

MathXL®forSchoolprovidesunlimitedpracticeandremediationwithstep-by-steptutorialsatthemid-chapterandendofchapter.Mostproblemsareshortanswerandrequirestudentstoactually“dothemath.”Eachproblemregeneratestoanewproblem,sostudentshaveunlimitedpracticeopportunities.

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Pull It All TogetherWiththePull It All Togetherperformancetasks,studentsdemonstratetheirreasoningandproblem-solvingskillsastheysolveproblemsthatinvolvekeymathconceptsandskillsasdefinedbytheCommon Core Georgia Performance Standards.Theperformancetasksaredesignedtoreflecttheperformancetasksthatstudentsarelikelytoencounter ontheNextGenerationAssessmentscurrentlyunderdevelopment.

TheCommon Core Georgia Performance Standards,includingtheStandards for Mathematical Practice,arelistedatpointofuse.

Teacherscanaskguidingquestionsasneededtosupportstudents’understandingofthetask.

TeacherswillfindarubricthatcanbeusedasaformativeassessmenttoolintheGeorgiaImplementationGuide.Teacherscanusetherubrictomonitorstudents’progresstowardsgreaterproficiency.

TeachersareprovidedwiththereducedstudentpageofthePull It All Together.Asstudentsprogressthroughthecourse,theperformancetasksbecomemorecomplexandofferlessscaffolding.

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Student WorktextTheStudentWorktextbecomesthestudents’personalrecordoftheirmathematicslearningoverthecourseoftheschoolyear. Italsoprovidesanartifactoflearningthattheycandrawfrominsubsequentcourses.Thisinteractiveformathelpsstudentsstayorganizedandprovidesaresourceforstudentstoreviewandpracticeindependently.

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ProbingquestionsintheThinkandPlanboxesmodelthethinkingembracedbytheStandards for Mathematical Practice,whicharepartoftheCommon Core Georgia Performance Standards.

ByscanningthelessonQRcodewithamobiledevice,studentscanaccesstutorialvideosthatrelatetothecontentinthelesson.ThesevideosarealsoavailableonPearsonSuccessNet.

ThereisamplespaceforstudentstocompletetheGot It?problemsthatfolloweachproblem.TeachersandstudentsworkthroughtheproblemfromtheInteractiveDigitalPath.

AftereachGot It?exercisearetwoadditionalexercisesthatstudentscancompletein-classorbeassignedforhomework.

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Pearson SuccessNet®

PearsonSuccessNetisthegatewayforstudentsandteacherstoallofthedigitalcomponentsforPearson Georgia High School Mathematics.Teacherscanenhanceinstructionwithinteractivelessoncontentandvideosthatmakereal-worldconnections.Theycanalsomodelthinkingandreasoningusinginteractivemathtools.Studentscancompletelessonsindependentlyusingtheonlinecontenttosupportin-classinstruction.

Interactive Digital PathTheInteractiveDigitalPath,availableonPearsonSuccessNet®,istheidealpresentationandstudytool.

Online Teacher Resources •Teacher’sGuide•EditableTeachingResources•ProgressMonitoringAssessments•GeorgiaImplementationGuide• InteractiveDigitalPath•AdditionalPresentationToolsandOnlineManipulatives

•SuccessTracker™AssessmentSystemwithautomaticgrading

•ClassandStudentReports•ClassroomManagementSystem•LessonPlannerwitheditablelessons•ContentSearchbyCommonCoreGeorgiaPerformanceStandard

Online Student Resources • InteractiveStudentWorktext•NotetakingandHighlightingtools•StudentWorksheets•HomeworkVideoTutorsinEnglishandSpanish

• InteractiveDigitalPath•OnlineGlossarywithaudioinEnglishandSpanish•MathXL®forSchool—stepbysteppracticewithimmediatefeedback

•MathToolsandOnlineManipulatives•VirtualNerd™TutorialVideos•MultilingualHandbook•Assessmentswithimmediatefeedbackandpersonalizedremediation

PEARSON SUCCESSNET ICONS

Showthestudent-producedvideodemonstratingrelevantandengagingapplicationsofthenewconceptsinthechapter.

FindonlinedefinitionsforthenewtermswithaudioexplanationsinbothEnglishandSpanish.

Starteachlessonwithanattention-gettingproblem.Viewtheproblemonlinewithhelpfulhints.

Increasestudents’depthofknowledgewithinteractiveonlineactivities.

ShowProblemsfromeachlessonsolvedstepbystep.Instantreplayallowsstudentstogoattheirownpacewhenstudyingonline.

PreparestudentsfortheMid-ChapterQuizandChapterTestwithonlinepracticeandreview.

ONGOING

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Differentiate InstructionStudentslearnindifferentwaysandatdifferentpaces.Unique,built-inresourcesdifferentiateinstructiontosupportalllevelsoflearnersinbecomingsuccessfulproblemsolvers.Differentiatinginstructionhelpsallstudentsdevelopconceptualunderstanding,fostersmathematicalreasoning,andrefinesproblem-solvingstrategies.Optionsareavailabletodifferentiateinstructionatthestartofeachchapterandthroughoutthelessons.

Check for UnderstandingFollowingeachproblem,theGot It?providesinstantassessmentofunderstanding.ImmediatePractice

followseachGot It?providingadditionalopportunitytocheckforstudentunderstandingthroughout

thedevelopmentofthelessonconcepts.WithintheLesson Check, Do you know HOW?andDo you

UNDERSTAND?assesshowwellstudentscanapplythelessonskills.

STRATEGIC

INTENSIVE

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Data-Driven DifferentiationLessonResourcesintheTeacher’sGuideprovideaLesson Quiztobeusedasatooltodifferentiateremediation.Resourcestomeetstudentneedsarelistedatpointofuse.

Intensive InterventionTheSuccessTracker™onlineassessment

systemprovidesinstantanalysisofstudentperformance.Itincludesbenchmark

assessmentscorrelatedtotheCommon Core Georgia Performance Standards.SuccessTrackerdiagnosesstudentsuccess,

prescribesautomaticremediation,andreportsonstudentandclassprogress.

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English Language Learner SupportThefollowingcomponentsaredesignedtosupportELLstudentsusingPearson Georgia High School Mathematics.

Additional Vocabulary Support Worksheets Availableforeverylesson,theseworksheetshelpstudentsdevelopandreinforcemathematicalvocabularyandkeyconcepts.

English/Spanish GlossaryOnlinewithaudio;allowsELLstudentstoreviewmathvocabularyintheirfirstlanguage.

Multilingual HandbookHasthefollowingtenlanguagesrepresentedasglossaries:English,Cambodian,Cantonese,Haitian,Korean,Spanish,Vietnamese,Hmong,Filipino,andMandarin.

Homework Video TutorsIncludedintheonlinestudentresources.AvailableinbothEnglishandSpanish.

ELL Teaching Strategies FoundafterEVERYlessonintheTeacher’sGuideandincludesFocusonLanguageandCommunication,ConnecttoPriorKnowledge,GraphicOrganizers,UsingRolePlaying,andAssessingUnderstanding

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TEACHING RESOURCES INTERVENTION ON-LEVEL ENRICHMENT ELL

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ThinkaboutaPlanWorksheet √ √ √ √

PracticeFormG √ √

PracticeFormK √ √

StandardizedTestPrepWorksheet √ √ √ √

Reteaching √ √

Enrichment √ √

AdditionalVocabularySupport(ELL) √ √

ExtendedConstructedResponse √ √ √ √

ChapterProjects √ √ √ √

FindtheErrors! √ √

Activities √ √ √ √

Games √ √

Puzzles √ √

MultilingualHandbook √

TeachingwithTITechnology √ √

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HomeworkVideoTutors √ √ √

MyMathVideos √ √ √ √

SolveIt √ √ √ √

VisualGlossary √ √ √ √

OnlineProblemswithaudio √ √ √ √

MathTools √ √ √ √

DynamicActivities √ √ √ √

MathXL®forSchool √ √ √ √

RESOURCES FOR DIFFERENTIATION

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Engage Today’s StudentsThestudentsoftodayaresurroundedwithtechnology.Pearson Georgia High School Mathematicsisaprogramthatembracesthetechnologythatengagesstudentsandenhancesstudentlearning.Varioustechnologydevicesareutilizedtoaccessstudentlearningaids(mobilephones,tablets,andcomputers),makingthisaprogramthatmeetsstudentswheretheyare...anytime,anywhere.

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QR codesEachlessonislinkedviaaQRcodetoVirtualNerd™Videosillustratingmath

concepts.Easilyaccessiblefromanysmartphone.

Math ToolsMath Toolshelpstudentsexploreandvisualizeconcepts.•OnlineGraphingUtility•InteractiveNumberLine•AlgebraTiles•2DGeometricConstructor•3DGeometricConstructor

Interactive Digital PathTheInteractiveDigitalPathistheidealpresentationandstudytool.Itcontainsinteractivelessonopeners,animatedproblemswithaudio,extrapractice,selfassessments,andaninteractiveglossary.StudentscanusetheDigitalLessonDVDtoaccesstheInteractiveDigitalPathwithoutInternetaccess.

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Homework Video Tutors (in English and Spanish) Teacherswalkstudentsthroughstep-by-stepexplanationsofeveryconceptandsamplehomeworkexercises.

MathXL® for SchoolMathXL®forSchoolincludes

interactivestep-by-steptutorialsforproblemssimilartohomeworkandchapterassessments.Eachproblem

regeneratestoanewproblem,sostudentshaveunlimited

practiceandhomeworkhelp.Mostproblemsareshortanswerproblemsthatrequirestudentsto

actually“dothemath.”

Student Mobile eTextThePearson Georgia High School MathematicseTextscanbeexperiencedonthegowiththedynamicfeaturesoftheiPad®andAndroid™devices.Pearson’seTextforSchoolsappallowsteachersandstudentstoviewtheirPearsoneTextonboththeiPad®andAndroid™device.

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Technology Componentsfor Students

TITLE COMPONENTS DESCRIPTION


PearsonSuccessNet.comservesastheportalintothedigitalworldofPearson Georgia High School Mathematics.ALL online components are easily accessible in this one location.Onlineaccessincludesawealthofassets,suchasthecompleteStudentWorktext,worksheets,interactiveonlineactivities,MyMathVideos,andonlineassessmentswithremediation.

MyMath VideoAvailableatPearsonSuccessNet

Student-Generated Chapter Opener Videos:

•Motivatestudentsthroughreal-worldconnections

•Videoillustrationsofcriticalmathematicsconceptsandreal-worldapplications

•YouTube®-stylevideorelevantandengagingtotoday’sstudentpopulation

Interactive Lessons for Every SectionAvailableatPearsonSuccessNetandontheDigitalLessonDVDforofflineaccess

Solve It!: InteractiveLessonOpeningProblem

Dynamic Activity:DigitalManipulativesforexploration,availableforselectedlessonswhereappropriate

Instruction: AllLessonproblemsaresteppedoutwithdetailedinstruction.Tochangetoadifferentproblem,clickontheproblemnumberintheblacktoolbar

Practice:LessonExercisepagesfromtheStudentTextareavailableforview

Assessment: Astudentself-checkquizwithanswersonthesecondscreen

Vocabulary: InteractiveGlossaryinEnglishandSpanishwithaudio

Math ToolsAvailableatPearsonSuccessNet

Math Toolshelpstudentsexploreandvisualizeconcepts.

•OnlineGraphingUtility

•InteractiveNumberLine

•AlgebraTiles

•2DGeometricConstructor

•3DGeometricConstructor

MathXL® for SchoolAvailableatPearsonSuccessNet

FO

R S C H OOL

MathXL ®

MathXL®forSchoolprovidesunlimitedpracticeandremediationwithtutoringandguidedassistanceforeverychapter.Mostproblemsareshortanswerproblemsthatrequirestudentstoactually“dothemath.”Therearethreeoptionsonceaproblemisstarted:

1)Workthroughtheproblemandreceiveinstantfeedback.

2)“HelpMeSolveThis”—interactivetutorialsupportsthedevelopmentofunderstanding.Oncethetutorialisfinishedanewproblemregeneratesforadditionalsupportorindependentpractice.

3)“ViewanExample”—asimilarproblemisdisplayedwithstep-by-stepinstruction

Log-onnowtopreviewtheonlinecomponents:GotoPearsonSuccessNet.com Username:GAHSMath Password:pearsonmath1 (Typeiscasesensitive)

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Student eTextAvailableonlineat

PearsonSuccessNet.com,iPad®orAndroid™

ThisStudentEditioneTextisavailableonlineandonbothiPadandAndroidtablets.ThiseTextprovidesstudentswithmanyofthesamefeaturesavailabletobrowser-basedeTextsubscribers—full-textsearch,highlights,notes,bookmarks,supportformultimediacontent,andaninteractiveglossary.

Online Multilingual HandbookAvailableatPearsonSuccessNet®

TheMultilingualHandbookcontainsatableofglossarytermsin10differentlanguagesandaglossarywithvisualrepresentationsforthefollowinglanguages:

•English

•Cambodian

•Cantonese

•HaitianCreole

•Korean

•Spanish

•Vietnamese

•Hmong

•Filipino

•Mandarin

Homework Video Tutor (in English and Spanish)AvailableatPearsonSuccessNet

HomeworkVideoTutorswalkstudentsthroughstep-by-stepexplanationsofeveryconceptandsamplehomeworkexercises.Studentsareprovidedopportunitiestoreceiveguidedpractice.HomeworkVideoTutorsaregreattouseasareteaching/remediationtoolorforstudentswhoareabsentfromclass.

Virtual Nerd™ VideosAvailableatPearsonSuccessNet

StudentscanscantheQRcodeintheirStudentWorktextorchooseVirtualNerd™VideosfromthetableofcontentswithintheInteractiveDigitalPathtoaccessVirtualNerdtutorialvideosthatdirectlyrelatetothecontentinthelesson.

SuccessTrackerAvailableatPearsonSuccessNet

PearsonSuccessTracker™onlineassessmentandremediationsystemprovidesinstantanalysisofstudentperformancewithassessmentsandreportscorrelatedtotheCommon Core Georgia Performance Standards.Studentsreceiveinstantresultsandremediationinmultiplemodalitiesincludingvideo,tutorials,audio,games,andworksheets.

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Assess Student ProgressPearson Georgia High School Mathematicsfeaturesaricharrayofdiagnostic,formative,andsummativeassessmenttoolssothatteacherscanassessandremediatestudents’progresseverystepoftheway.Theseassessments,availableinprintandonline,supportthetransitiontonewstate-wideassessmentsthatwillbealignedtotheCommon Core Georgia Performance Standards.

Embedded Program Assessment ASSESSMENT

Diagnostic

•Entry-LevelAssessment

•GetReady!

•GotIt?

•LessonCheck

•LessonQuiz

Formative

•PullitAllTogether

•ChapterTest

•End-of-CourseAssessment

Summative

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Additional Assessment Resources ASSESSMENT

SuccessTracker™diagnosesstudents’readinesstolearnnewskills,benchmarkstheirprogress,providesindividualizedremediationandenrichment,andreportsonmasteryoftheCommon Core Georgia Performance Standards.

Themostpowerfultestgeneratoravailable—withcomprehensivetestbankscorrelatedtotheCommon Core Georgia Performance Standards.

•QuickTestWizardhelpsyoubuildassessmentsinseconds.•Providessupportformodifyingtestsquicklyandeasily.• ImportimagesintoassessmentsusingtheMathArtGallery.•Testbanksareeditableandcanmodifyexistingpracticeworksheetsandchapterassessments.

Standards for Mathematical Practice Observational ProtocolEasilymonitorstudents’ongoingdevelopmentofthemathematicalpracticeswith rubricsdesignedtoassessproficiencyoftheStandards for Mathematical Practice.

Online Teaching Resources•EditableTestsandQuizzes•CommonCoreReadinessAssessments•ChapterProjects•PerformanceTasks

Assessment Resource BookAvailableinprintandonline,thisresourceprovidesallDiagnostic,Formative,andSummativeAssessmentsinonelocation.TheAssessmentResourceBookincludes:ScreeningTest,ChapterQuizesformsGandK,ChapterTestsformsGandK,EndofCourseTest,StandardsReports, andBenchmarkTestsalignedtotheCommon Core Georgia Performance Standards

Prepare your students for Common Core Assessments

with WEEKLY COMMON CORE STANDARDS PRACTICE

This rubric, which is based on the Standards for Mathematical Practice, can be used as a formative assessment tool to monitor students’ progress towards becoming proficient mathematical thinkers. Sense-Making Solution Plan Reasoning Execution Models Precision

4 The solution suggests a thorough understanding of the problem situation and the mathematics required to solve the problem.

The solution plan presented suggests a comprehensive understanding of the mathematical concepts required to solve the problem.

The explanations show logical and appropriate connections among concepts; they also show the thinking of a highly proficient problem-solver.

The solution shows clear, appropriate, and effective, execution of the solution plan. All steps are clearly and accurately presented.

The solution shows relevant and appropriate mathematical modeling of the problem situation.

The solution and explanation shows precise and appropriate mathematical terminology and notation.

3 The solution suggests an adequate understanding of the problem situation and the mathematics required to solve the problem.

The solution plan presented suggests an adequate understanding of the mathematical concepts required to solve the problem.

The explanations show some appropriate connections among concepts; they also show the thinking of a good problem-solver.

The solution shows clear, appropriate, and effective, execution of the solution plan. Most of the steps are accurately presented.

The solution shows appropriate mathematical modeling of the problem situation.

The solution and explanation show appropriate mathematical terminology and notation.

2 The solution suggests a limited understanding of the problem situation and the mathematics required to solve the problem.

The solution plan presented suggests a limited understanding of the mathematical concepts required to solve the problem.

The explanations show limited connections among concepts; they also show the thinking of an underdeveloped problem-solver.

The solution shows inconsistent execution of the solution plan. Only some steps are clearly and accurately presented.

The solution shows limited, but appropriate mathematical modeling of the problem situation.

The solution and explanation shows some imprecision or errors in use of mathematical terminology and notation.

1 The solution suggests a very limited understanding of the problem situation and the mathematics required to solve the problem.

The solution plan presented suggests a tentative understanding of the mathematical concepts required to solve the problem.

The explanations show minimal connections among concepts; they also show the thinking of a inefficient problem-solver.

The solution shows erratic execution of the solution plan. Many steps are not presented.

The solution shows limited and at time inappropriate mathematical modeling of the problem situation.

The solution and explanation shows many errors in the use of mathematical terminology and notation.

0 The solution suggests minimal understanding of the problem situation and the mathematics required to solve the problem.

The solution plan presented suggests no understanding of the mathematical concepts required to solve the problem.

The explanations show no connections among concepts; they also show the thinking of an ineffective problem-solver.

The solution shows ineffective execution of the solution plan. Few, if any, steps are presented.

The solution shows no mathematical modeling of the problem situation.

The solution and explanation shows an absence of mathematical terminology and notation.

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Performance TasksTheEndofChapterPull It All Togetheroffersarich,real-worldperformancetaskmodeledaftertheperformancetasksthatstudentswillencounterontheNextGenerationAssessmentsbeingdevelopedbyPARCC.Teachersupportincludesaholisticscoringrubrictouseinassessingstudents’workonthePerformanceTask.

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AssessmentPearson Georgia High School Mathematicsoffersawealthofformativeandsummativeassessments,allofwhicharealignedtotheCommon Core Georgia Performance StandardsandtheStandards for Mathematical Practice.

TEXTBOOKPEARSON

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ASSESSMENT RESOURCE

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Common Core Georgia Performance Standards Implementation GuideAllthesupportyouneedtomakethetransitiontoaCCGPSCurriculum!•OverviewofCommonCoreGeorgiaPerformanceStandards•OverviewofStandardsforMathematicalPractice•CommonCoreGeorgiaPerformanceStandardsCorrelations•StandardsforMathematicalPracticeObservationalProtocol•CommonCoreAssessmentResources•ParentLetter

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Online Teacher Resources (including editable worksheets and tests)AvailableatPearsonSuccessNet®

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✭=ModelingStandard

(+)indicatesadditionalmathematicsthatstudentsshouldlearninordertotakeadvancedcoursessuchascalculus,advancedstatistics,ordiscretemathematics.

Standards for Mathematical Content Coordinate Algebra

Analytic Geometry

Advanced Algebra

NUMBER AND QUANTITYThe Real Number System N.RNExtend the properties of exponents to rational exponentsMCC.N.RN.1 Explainhowthedefinitionofthemeaningofrational

exponentsfollowsfromextendingthepropertiesofintegerexponentstothosevalues,allowingforanotationforradicalsintermsofrationalexponents.

10-1,10-2,10-3,10-4

MCC.N.RN.2 Rewriteexpressionsinvolvingradicalsandrationalexponentsusingthepropertiesofexponents.

10-4

Use properties of rational and irrational numbersMCC.N.RN.3 Explainwhythesumorproductoftworationalnumbersis

rational;thatthesumofarationalnumberandanirrationalnumberisirrational;andthattheproductofanonzerorationalnumberandanirrationalnumberisirrational.

AL10-4

Quantities N.QReason quantitatively and use units to solve problemsMCC.N.Q.1 Useunitsasawaytounderstandproblemsandtoguidethe

solutionofmulti-stepproblems;chooseandinterpretunitsconsistentlyinformulas;chooseandinterpretthescaleandtheoriginingraphsanddatadisplays.

1-4,1-5,AL1-5a,1-6,2-4,6-1,6-3,6-4,9-1

MCC.N.Q.2 Defineappropriatequantitiesforthepurposeofdescriptivemodeling.

1-5,AL1-5a,2-5,3-5,4-4,6-2

MCC.N.Q.3 Choosealevelofaccuracyappropriatetolimitationsonmeasurementwhenreportingquantities.

AL1-5b,4-4

The Complex Number System N.CNPerform arithmetic operations with complex numbersMCC.N.CN.1 Knowthereisacomplexnumberi suchthati2 =−1,

andeverycomplexnumberhastheforma +bi witha andb real.

12-8

MCC.N.CN.2 Usetherelationi2=–1andthecommutative,associative,anddistributivepropertiestoadd,subtract,andmultiplycomplexnumbers.

12-8

MCC.N.CN.3 (+)Findtheconjugateofacomplexnumber;useconjugatestofindmoduliandquotientsofcomplexnumbers.

12-8

Correlation of the Common Core Georgia Performance Standards ThefollowingisanalignmentoftheCommon Core Georgia Performance StandardsforMathematicstoPearson’s Georgia High School Mathematicsprogram.

33✭=ModelingStandard



Analytic Geometry

Advanced Algebra

Represent complex numbers and their operations on the complex planeMCC.N.CN.4 (+)Representcomplexnumbersonthecomplexplanein

rectangularandpolarform(includingrealandimaginarynumbers),andexplainwhytherectangularandpolarformsofagivencomplexnumberrepresentthesamenumber.

Addressedin4thyearcourses

MCC.N.CN.5 (+)Representaddition,subtraction,multiplication,andconjugationofcomplexnumbersgeometricallyonthecomplexplane;usepropertiesofthisrepresentationforcomputation.


MCC.N.CN.6 (+)Calculatethedistancebetweennumbersinthecomplexplaneasthemodulusofthedifference,andthemidpointofasegmentastheaverageofthenumbersatitsendpoints.


Use complex numbers in polynomial identities and equationsMCC.N.CN.7 Solvequadraticequationswithrealcoefficientsthat

havecomplexsolutions..12-8

MCC.N.CN.8 (+)Extendpolynomialidentitiestothecomplexnumbers. 4-6,LL4-6,4-7

MCC.N.CN.9 (+)KnowtheFundamentalTheoremofAlgebra;showthatitistrueforquadraticpolynomials.

4-7

Vector and Matrix Quantities N.VMRepresent and model with vector quantitiesMCC.N.VM.1 (+)Recognizevectorquantitiesashavingbothmagnitude

anddirection.Representvectorquantitiesbydirectedlinesegments,anduseappropriatesymbolsforvectorsandtheirmagnitudes(e.g.,v,|v|,||v||,v).


MCC.N.VM.2 (+)Findthecomponentsofavectorbysubtractingthecoordinatesofaninitialpointfromthecoordinatesofaterminalpoint.


MCC.N.VM.3 (+)Solveproblemsinvolvingvelocityandotherquantitiesthatcanberepresentedbyvectors.


Perform operations on vectorsMCC.N.VM.4 (+)Addandsubtractvectors. Addressedin4thyearcourses

MCC.N.VM.4.a Addvectorsend-to-end,component-wise,andbytheparallelogramrule.Understandthatthemagnitudeofasumoftwovectorsistypicallynotthesumofthemagnitudes.


MCC.N.VM.4.b Giventwovectorsinmagnitudeanddirectionform,determinethemagnitudeanddirectionoftheirsum.


MCC.N.VM.4.c Understandvectorsubtractionv–wasv+(–w),where

–wistheadditiveinverseofw,withthesamemagnitude

aswandpointingintheoppositedirection.Representvectorsubtractiongraphicallybyconnectingthetipsintheappropriateorder,andperformvectorsubtractioncomponent-wise.


MCC.N.VM.5 (+)Multiplyavectorbyascalar. Addressedin4thyearcourses

MCC.N.VM.5.a Representscalarmultiplicationgraphicallybyscalingvectorsandpossiblyreversingtheirdirection;performscalarmultiplicationcomponent-wise,e.g.,asc(vx,vy)=(cvx,cvy).


MCC.N.VM.5.b Computethemagnitudeofascalarmultiplecvusing||cv||=|c||v|.Computethedirectionofcvknowingthat

when|c| ≠0,thedirectionofcviseitheralongv(forc >

0)oragainstv(forc <0).


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Advanced Algebra

Perform operations on matrices and use matrices in applicationsMCC.N.VM.6 (+)Usematricestorepresentandmanipulatedata,e.g.,to

representpayoffsorincidencerelationshipsinanetwork.Addressedin4thyearcourses

MCC.N.VM.7 (+)Multiplymatricesbyscalarstoproducenewmatrices,e.g.,aswhenallofthepayoffsinagamearedoubled.


MCC.N.VM.8 (+)Add,subtract,andmultiplymatricesofappropriatedimensions.


MCC.N.VM.9 (+)Understandthat,unlikemultiplicationofnumbers,matrixmultiplicationforsquarematricesisnotacommutativeoperation,butstillsatisfiestheassociativeanddistributiveproperties.


MCC.N.VM.10 (+)Understandthatthezeroandidentitymatricesplayaroleinmatrixadditionandmultiplicationsimilartotheroleof0and1intherealnumbers.Thedeterminantofasquarematrixisnonzeroifandonlyifthematrixhasamultiplicativeinverse.


MCC.N.VM.11 (+)Multiplyavector(regardedasamatrixwithonecolumn)byamatrixofsuitabledimensionstoproduceanothervector.Workwithmatricesastransformationsofvectors.


MCC.N.VM.12 (+)Workwith2×2matricesastransformationsoftheplane,andinterprettheabsolutevalueofthedeterminantintermsofarea.


ALGEBRASeeing Structure in Expressions A.SSEInterpret the structure of expressionsMCC.A.SSE.1 Interpretexpressionsthatrepresentaquantityintermsof

itscontext.✭1-9,2-5,2-7,3-3,3-4,3-5,5-1,5-2,5-4,5-6

12-1,12-2,12-6,12-7,12-9

4-3

MCC.A.SSE.1.a Interpretpartsofanexpression,suchasterms,factors,andcoefficients.

1-1,2-5,2-7,3-3,3-4,5-4,5-6

11-5,11-6,11-7,11-8,12-1,12-2,12-5,12-6

3-3,3-4,4-1,4-3

MCC.A.SSE.1.b Interpretcomplicatedexpressionsbyviewingoneormoreoftheirpartsasasingleentity.

1-9,2-7,5-4 11-6,11-7,11-8,12-6

4-4,7-1,7-2,7-3

MCC.A.SSE.2 Usethestructureofanexpressiontoidentifywaystorewriteit.

11-7,11-8 3-3,3-5,4-4,6-1,6-2,6-3,6-4,7-4

Write expressions in equivalent forms to solve problemsMCC.A.SSE.3 Chooseandproduceanequivalentformofanexpression

torevealandexplainpropertiesofthequantityrepresentedbytheexpression.✭

12-5,12-6 7-3,7-4,7-5,7-6

MCC.A.SSE.3.a Factoraquadraticexpressiontorevealthezerosofthefunctionitdefines.

12-5

MCC.A.SSE.3.b Completethesquareinaquadraticexpressiontorevealthemaximumorminimumvalueofthefunctionitdefines.

12-6

MCC.A.SSE.3.c Usethepropertiesofexponentstotransformexpressionsforexponentialfunctions.

7-1

MCC.A.SSE.4 Derivetheformulaforthesumofafinitegeometricseries(whenthecommonratioisnot1),andusetheformulatosolveproblems.✭

AL9-5,9-5




Analytic Geometry

Advanced Algebra

Arithmetic with Polynomials and Rational Expressions A.APRPerform arithmetic operations on polynomialsMCC.A.APR.1 Understandthatpolynomialsformasystemanalogousto

theintegers;namely,theyareclosedundertheoperationsofaddition,subtraction,andmultiplication;add,subtract,andmultiplypolynomials.

11-1,11-2,11-3,11-4

6-2

Understand the relationship between zeros and factors of polynomialMCC.A.APR.2 KnowandapplytheRemainderTheorem:Forapolynomial

p(x)andanumbera,theremainderondivisionbyx –a isp(a),sop(a)=0ifandonlyif(x –a)isafactorofp(x).

MCC.A.APR.3 Identifyzerosofpolynomialswhensuitablefactorizationsareavailable,andusethezerostoconstructaroughgraphofthefunctiondefinedbythepolynomial.

3-4,4-3,4-7,AL4-7

Use polynomial identities to solve problemsMCC.A.APR.4 Provepolynomialidentitiesandusethemtodescribe

numericalrelationships.LL4-6

MCC.A.APR.5 (+)KnowandapplytheBinomialTheoremfortheexpansionof(x +y)n inpowersofx andy forapositiveintegern,wherex andy areanynumbers,withcoefficientsdeterminedforexamplebyPascal’sTriangle.

NOTE:TheBinomialTheoremcanbeprovedbymathematicalinductionorbyacombinatorialargument.

4-8,LL4-8

Rewrite rational expressionsMCC.A.APR.6 Rewritesimplerationalexpressionsindifferentforms;

writea(x)/b(x)intheformq(x)+ r(x)/b(x),wherea(x),b(x),q(x),andr(x)arepolynomialswiththedegreeofr(x)lessthanthedegreeofb(x),usinginspection,longdivision,or,forthemorecomplicatedexamples,acomputeralgebrasystem.

4-5,5-1

MCC.A.APR.7 (+)Understandthatrationalexpressionsformasystemanalogoustotherationalnumbers,closedunderaddition,subtraction,multiplication,anddivisionbyanonzerorationalexpression;add,subtract,multiply,anddividerationalexpressions.

5-2,5-3

Creating Equations A.CEDCreate equations that describe numbers or relationshipsMCC.A.CED.1 Createequationsandinequalitiesinonevariableanduse

themtosolveproblems.Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

1-2,1-3,1-4,1-6,1-7,1-8,1-9,5-5

12-4,12-5,12-6,12-7,LL12-10

2-1,2-2,3-4,3-5,3-6,5-7,TL5-7b,7-5,LL7-6

MCC.A.CED.2 Createequationsintwoormorevariablestorepresentrelationshipsbetweenquantities;graphequationsoncoordinateaxeswithlabelsandscales.

2-2,2-3,2-5,3-2,3-3,3-4,3-5,5-2,5-4

12-1,12-2 2-3,2-7,3-1,3-2,5-4,5-5,5-6,7-1,7-2

MCC.A.CED.3 Representconstraintsbyequationsorinequalities,andbysystemsofequationsand/orinequalities,andinterpretsolutionsasviableornon-viableoptionsinamodelingcontext.

3-5,4-1,4-2,4-3,4-4,4-5,4-6

2-6,2-7,2-8,3-7,AL5-7a

MCC.A.CED.4 Rearrangeformulastohighlightaquantityofinterest,usingthesamereasoningasinsolvingequations.

1-4 12-4,LL12-4 2-1,5-4,6-5

Reasoning with Equations and Inequalities A.REIUnderstand solving equations as a process of reasoning and explain the reasoningMCC.A.REI.1 Explaineachstepinsolvingasimpleequationasfollowing

fromtheequalityofnumbersassertedatthepreviousstep,startingfromtheassumptionthattheoriginalequationhasasolution.Constructaviableargumenttojustifyasolutionmethod.

1-2,1-3,1-4

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Advanced Algebra

MCC.A.REI.2 Solvesimplerationalandradicalequationsinonevariable,andgiveexamplesshowinghowextraneoussolutionsmayarise.

5-7,6-5

Solve equations and Inequalities in one variableMCC.A.REI.3 Solvelinearequationsandinequalitiesinonevariable,

includingequationswithcoefficientsrepresentedbyletters.

1-2,1-3,1-4,1-6,1-7,1-8,5-5

MCC.A.REI.4 Solvequadraticequationsinonevariable. 12-4,12-5,12-6,12-7

MCC.A.REI.4.a Usethemethodofcompletingthesquaretotransformanyquadraticequationinx intoanequationoftheform(x –p)2=q thathasthesamesolutions.Derivethequadraticformulafromthisform.

12-6,12-7

MCC.A.REI.4.b Solvequadraticequationsbyinspection(e.g.,forx2 = 49), takingsquareroots,completingthesquare,thequadraticformulaandfactoring,asappropriatetotheinitialformoftheequation.Recognizewhenthequadraticformulagivescomplexsolutionsandwritethemasa ±bi forrealnumbersa andb.

12-4,12-5,12-6,12-7,12-8

Solve systems of equationsMCC.A.REI.5 Provethat,givenasystemoftwoequationsintwo

variables,replacingoneequationbythesumofthatequationandamultipleoftheotherproducesasystemwiththesamesolutions.

4-3

MCC.A.REI.6 Solvesystemsoflinearequationsexactlyandapproximately(e.g.,withgraphs),focusingonpairsoflinearequationsintwovariables.

4-1,4-2,4-3,4-4

MCC.A.REI.7 Solveasimplesystemconsistingofalinearequationandaquadraticequationintwovariablesalgebraicallyandgraphically.

12-10 3-7

MCC.A.REI.8 (+)Representasystemoflinearequationsasasinglematrixequationinavectorvariable.


MCC.A.REI.9 (+)Findtheinverseofamatrixifitexistsanduseittosolvesystemsoflinearequations(usingtechnologyformatricesofdimension3×3orgreater).


Represent and solve equations and inequalities graphicallyMCC.A.REI.10 Understandthatthegraphofanequationintwovariables

isthesetofallitssolutionsplottedinthecoordinateplane,oftenformingacurve(whichcouldbeastraightline).

2-4

MCC.A.REI.11 Explainwhythex-coordinatesofthepointswherethegraphsoftheequationsy =f(x)andy =g(x)intersectarethesolutionsoftheequationf(x)=g(x);findthesolutionsapproximately,e.g.,usingtechnologytographthefunctions,maketablesofvalues,orfindsuccessiveapproximations.Includecaseswheref(x)and/org(x)arelinear,polynomial,rational,absolutevalue,exponential,andlogarithmicfunctions.✭

TL2-4,TL4-1,5-2,5-5

3-7,4-4,5-7,AL5-7a,7-5,LL7-6

MCC.A.REI.12 Graphthesolutionstoalinearinequalityintwovariablesasahalf-plane(excludingtheboundaryinthecaseofastrictinequality),andgraphthesolutionsettoasystemoflinearinequalitiesintwovariablesastheintersectionofthecorrespondinghalf-planes.

4-5,4-6




Analytic Geometry

Advanced Algebra

FUNCTIONSInterpreting Functions F.IFUnderstand the concept of a function and use function notationMCC.F.IF.1 Understandthatafunctionfromoneset(calledthe

domain)toanotherset(calledtherange)assignstoeachelementofthedomainexactlyoneelementoftherange.Iff isafunctionandx isanelementofitsdomain,thenf(x)denotestheoutputoff correspondingtotheinputx.Thegraphoff isthegraphoftheequationy =f(x).

2-6

MCC.F.IF.2 Usefunctionnotation,evaluatefunctionsforinputsintheirdomains,andinterpretstatementsthatusefunctionnotationintermsofacontext.

2-6

MCC.F.IF.3 Recognizethatsequencesarefunctions,sometimesdefinedrecursively,whosedomainisasubsetoftheintegers.

2-7,LL2-7,5-6

Interpret functions that arise in applications in terms of the contextMCC.F.IF.4 Forafunctionthatmodelsarelationshipbetweentwo

quantities,interpretkeyfeaturesofgraphsandtablesintermsofthequantities,andsketchgraphsshowingkeyfeaturesgivenaverbaldescriptionoftherelationship.Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.✭

2-1,2-2,2-3,3-3,3-4,3-5,5-2,5-4

12-1,12-2,12-3,12-9

2-3,3-1,3-2,4-1,4-9,5-4,5-5,5-6,6-8,8-1,8-4,8-5,8-6,8-8

MCC.F.IF.5 Relatethedomainofafunctiontoitsgraphand,whereapplicable,tothequantitativerelationshipitdescribes.

2-6,5-2 12-1,12-3 4-9,5-5,5-6,6-8

MCC.F.IF.6 Calculateandinterprettheaveragerateofchangeofafunction(presentedsymbolicallyorasatable)overaspecifiedinterval.Estimatetherateofchangefromagraph.✭

3-1,5-3 AL12-2 3-1,3-2,LL3-2,4-9

Analyze functions using different representationsMCC.F.IF.7 Graphfunctionsexpressedsymbolicallyandshowkey

featuresofthegraph,byhandinsimplecasesandusingtechnologyformorecomplicatedcases.

TL3-3,3-3,3-4,3-5,3-7,5-2,5-3,5-4

12-1,TL12-1,12-2

2-3,2-4,2-5,LL2-5,3-1,3-2,4-1,4-3,4-9,5-4,TL5-5,5-5,5-6,6-8,7-1,7-2,7-3,7-5,8-4,TL8-4,8-5,8-6,8-7,8-8

MCC.F.IF.7.a Graphlinearandquadraticfunctionsandshowintercepts,maxima,andminima.

3-3,3-4,3-5 12-1,12-2,12-4

2-3,3-1,3-2,3-4

MCC.F.IF.7.b Graphsquareroot,cuberoot,andpiecewise-definedfunctions,includingstepfunctionsandabsolutevaluefunctions.

2-5,LL2-5,6-8

MCC.F.IF.7.c Graphpolynomialfunctions,identifyingzeroswhensuitablefactorizationsareavailable,andshowingendbehavior.

4-1,4-3,4-10

MCC.F.IF.7.d (+)Graphrationalfunctions,identifyingzerosandasymptoteswhensuitablefactorizationsareavailable,andshowingendbehavior.

5-4,TL5-5,5-5,5-6,TL5-6

MCC.F.IF.7.e Graphexponentialandlogarithmicfunctions,showinginterceptsandendbehavior,andtrigonometricfunctions,showingperiod,midline,andamplitude.

5-2 7-1,7-2,7-3,TL7-5,8-4,8-5,8-6,8-7,8-8

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Analytic Geometry

Advanced Algebra

MCC.F.IF.8 Writeafunctiondefinedbyanexpressionindifferentbutequivalentformstorevealandexplaindifferentpropertiesofthefunction.

12-5,12-6 3-2,3-5,4-10,6-8,7-1,7-2,7-3,7-4,TL7-5

MCC.F.IF.8.a Usetheprocessoffactoringandcompletingthesquareinaquadraticfunctiontoshowzeros,extremevalues,andsymmetryofthegraph,andinterprettheseintermsofacontext.

12-5,12-6 3-3,3-4,3-5

MCC.F.IF.8.b Usethepropertiesofexponentstointerpretexpressionsforexponentialfunctions.

7-1,7-2

MCC.F.IF.9 Comparepropertiesoftwofunctionseachrepresentedinadifferentway(algebraically,graphically,numericallyintables,orbyverbaldescriptions).

3-5,5-2,5-3 12-2 3-2,4-10,5-6,6-8,7-3

Building Functions F.BFBuild a function that models a relationship between two quantitiesMCC.F.BF.1 Writeafunctionthatdescribesarelationshipbetween

twoquantities.✭2-7,3-3,3-4,3-5,5-4

12-2,12-9 3-1,3-2,4-3,5-5,5-6,6-6,7-2

MCC.F.BF.1.a Determineanexplicitexpression,arecursiveprocess,orstepsforcalculationfromacontext.

2-7,3-3,3-4,3-5,5-6

12-2 9-1,9-2,9-3,9-4

MCC.F.BF.1.b Combinestandardfunctiontypesusingarithmeticoperations.

5-7 12-9 5-6,6-6

MCC.F.BF.1.c (+)Composefunctions. 6-6

MCC.F.BF.2 Writearithmeticandgeometricsequencesbothrecursivelyandwithanexplicitformula,usethemtomodelsituations,andtranslatebetweenthetwoforms.✭

2-7,5-6

Build new functions from existing functionsMCC.F.BF.3 Identifytheeffectonthegraphofreplacingf(x)byf(x)

+k,k f(x),f(kx),andf(x +k)forspecificvaluesofk (bothpositiveandnegative);findthevalueofk giventhegraphs.Experimentwithcasesandillustrateanexplanationoftheeffectsonthegraphusingtechnology.Include recognizing even and odd functions from their graphs and algebraic expressions for them.

TL2-6,TL3-3,3-3,3-4,3-7,5-2,5-4

12-1,TL12-1,12-2

2-4,2-5,3-1,4-10,5-5,8-7

MCC.F.BF.4 Findinversefunctions. 6-7,6-8,7-3

MCC.F.BF.4.a Solveanequationoftheformf(x)=c forasimplefunctionf thathasaninverseandwriteanexpressionfortheinverse.

6-7,7-3

MCC.F.BF.4.b (+)Verifybycompositionthatonefunctionistheinverseofanother.

6-7

MCC.F.BF.4.c (+)Readvaluesofaninversefunctionfromagraphoratable,giventhatthefunctionhasaninverse.

6-7

MCC.F.BF.4.d (+)Produceaninvertiblefunctionfromanon-invertiblefunctionbyrestrictingthedomain.


MCC.F.BF.5 (+)Understandtheinverserelationshipbetweenexponentsandlogarithmsandusethisrelationshiptosolveproblemsinvolvinglogarithmsandexponents.

7-3,7-5

Linear and Exponential Models F.LEConstruct and compare linear and exponential models and solve problemsMCC.F.LE.1 Distinguishbetweensituationsthatcanbemodeled

withlinearfunctionsandwithexponentialfunctions.5-3

MCC.F.LE.1.a Provethatlinearfunctionsgrowbyequaldifferencesoverequalintervals,andthatexponentialfunctionsgrowbyequalfactorsoverequalintervals.

3-3,5-3

MCC.F.LE.1.b Recognizesituationsinwhichonequantitychangesataconstantrateperunitintervalrelativetoanother.

3-1




Analytic Geometry

Advanced Algebra

MCC.F.LE.1.c Recognizesituationsinwhichaquantitygrowsordecaysbyaconstantpercentrateperunitintervalrelativetoanother.

5-4

MCC.F.LE.2 Constructlinearandexponentialfunctions,includingarithmeticandgeometricsequences,givenagraph,adescriptionofarelationship,ortwoinput-outputpairs(includereadingthesefromatable).

2-7,3-3,3-4,3-5,5-4,5-6

MCC.F.LE.3 Observeusinggraphsandtablesthataquantityincreasingexponentiallyeventuallyexceedsaquantityincreasinglinearly,quadratically,or(moregenerally)asapolynomialfunction.

5-3 AL12-2,12-9

MCC.F.LE.4 Forexponentialmodels,expressasalogarithmthesolutiontoabct =d wherea,c,andd arenumbersandthebaseb is2,10,ore;evaluatethelogarithmusingtechnology.

7-5,7-6

Interpret expressions for functions in terms of the situation they modelMCC.F.LE.5 Interprettheparametersinalinearorexponential

functionintermsofacontext.3-3,3-4,3-5,5-2,5-4,6-4

Trigonometric Functions F.TFExtend the domain of trigonometric functions using the unit circleMCC.F.TF.1 Understandradianmeasureofanangleasthelength

ofthearcontheunitcirclesubtendedbytheangle.8-3

MCC.F.TF.2 Explainhowtheunitcircleinthecoordinateplaneenablestheextensionoftrigonometricfunctionstoallrealnumbers,interpretedasradianmeasuresofanglestraversedcounterclockwisearoundtheunitcircle.

8-4,8-5,8-6,8-8

MCC.F.TF.3 (+)Usespecialtrianglestodeterminegeometricallythevaluesofsine,cosine,andtangentforπ/3,π/4andπ/6,andusetheunitcircletoexpressthevaluesofsine,cosine,andtangentforπ–x,π+x,and2π–x intermsoftheirvaluesforx,wherex isanyrealnumber.


MCC.F.TF.4 (+)Usetheunitcircletoexplainsymmetry(oddandeven)andperiodicityoftrigonometricfunctions.


Model periodic phenomena with trigonometric functionsMCC.F.TF.5 Choosetrigonometricfunctionstomodelperiodic

phenomenawithspecifiedamplitude,frequency,andmidline.

8-4,8-5,8-6,8-7,8-8

MCC.F.TF.6 (+)Understandthatrestrictingatrigonometricfunctiontoadomainonwhichitisalwaysincreasingoralwaysdecreasingallowsitsinversetobeconstructed.


MCC.F.TF.7 (+)Useinversefunctionstosolvetrigonometricequationsthatariseinmodelingcontexts;evaluatethesolutionsusingtechnology,andinterpretthemintermsofthecontext.✭


Prove and apply trigonometric identitiesMCC.F.TF.8 ProvethePythagoreanidentitysin2(q)+cos2(q)=1and

useittofindsin(q),cos(q),ortan(q),givensin(q),cos(q),ortan(q)andthequadrantoftheangle.

8-9

MCC.F.TF.9 (+)Provetheadditionandsubtractionformulasforsine,cosine,andtangentandusethemtosolveproblems.


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Analytic Geometry

Advanced Algebra

GEOMETRYCongruence G.COEXPERIMENT WITH TRANSFORMATIONS IN THE PLANEMCC.G.CO.1 Knowprecisedefinitionsofangle,circle,perpendicular

line,parallelline,andlinesegment,basedontheundefinednotionsofpoint,line,distancealongaline,anddistancearoundacirculararc.

7-2,7-3,7-4,7-5

MCC.G.CO.2 Representtransformationsintheplaneusing,e.g.,transparenciesandgeometrysoftware;describetransformationsasfunctionsthattakepointsintheplaneasinputsandgiveotherpointsasoutputs.Comparetransformationsthatpreservedistanceandangletothosethatdonot(e.g.,translationversushorizontalstretch).

AL8-1,8-1,8-2,8-3,TL8-4,8-4

MCC.G.CO.3 Givenarectangle,parallelogram,trapezoid,orregularpolygon,describetherotationsandreflectionsthatcarryitontoitself.

AL8-3

MCC.G.CO.4 Developdefinitionsofrotations,reflections,andtranslationsintermsofangles,circles,perpendicularlines,parallellines,andlinesegments.

8-1,8-2,8-3

MCC.G.CO.5 Givenageometricfigureandarotation,reflection,ortranslation,drawthetransformedfigureusing,e.g.,graphpaper,tracingpaper,orgeometrysoftware.Specifyasequenceoftransformationsthatwillcarryagivenfigureontoanother.

8-1,AL8-2,8-2,8-3,TL8-4,8-4

Understand congruence in terms of rigid motionsMCC.G.CO.6 Usegeometricdescriptionsofrigidmotionstotransform

figuresandtopredicttheeffectofagivenrigidmotiononagivenfigure;giventwofigures,usethedefinitionofcongruenceintermsofrigidmotionstodecideiftheyarecongruent.

LL3-8,3-8

MCC.G.CO.7 Usethedefinitionofcongruenceintermsofrigidmotionstoshowthattwotrianglesarecongruentifandonlyifcorrespondingpairsofsidesandcorrespondingpairsofanglesarecongruent..

3-8

MCC.G.CO.8 Explainhowthecriteriafortrianglecongruence(ASA,SAS,andSSS)followfromthedefinitionofcongruenceintermsofrigidmotions.

3-8

Prove geometric theoremsMCC.G.CO.9 Provetheoremsaboutlinesandangles.Theoremsinclude:

verticalanglesarecongruent;whenatransversalcrossesparallellines,alternateinterioranglesarecongruentandcorrespondinganglesarecongruent;pointsonaperpendicularbisectorofalinesegmentareexactlythoseequidistantfromthesegment’sendpoints.

1-7,2-2,2-3,2-4,4-2

MCC.G.CO.10 Provetheoremsabouttriangles.Theoremsinclude:measuresofinterioranglesofatrianglesumto180°;baseanglesofisoscelestrianglesarecongruent;thesegmentjoiningmidpointsoftwosidesofatriangleisparalleltothethirdsideandhalfthelength;themediansofatrianglemeetatapoint.

2-5,3-5,4-1,4-4,5-7,5-8

MCC.G.CO.11 Provetheoremsaboutparallelograms.Theoremsinclude:oppositesidesarecongruent,oppositeanglesarecongruent,thediagonalsofaparallelogrambisecteachotherandconversely,rectanglesareparallelogramswithcongruentdiagonals.

5-2,5-3,5-4,5-5,5-7,5-8




Analytic Geometry

Advanced Algebra

Make geometric constructionsMCC.G.CO.12 Makeformalgeometricconstructionswithavarietyof

toolsandmethods(compassandstraightedge,string,reflectivedevices,paperfolding,dynamicgeometricsoftware,etc.).Copyingasegment;copyinganangle;bisectingasegment;bisectinganangle;constructingperpendicularlines,includingtheperpendicularbisectorofalinesegment;andconstructingalineparalleltoagivenlinethroughapointnotontheline.

1-1,2-6,3-4,AL3-5,4-2,TL6-5

10-1

MCC.G.CO.13 Constructanequilateraltriangle,asquare,andaregularhexagoninscribedinacircle.

2-6,3-5,7-5 10-1

Similarity, Right Triangles, and Trigonometry G.SRTUnderstand similarity in terms of similarity transformationsMCC.G.SRT.1 Verifyexperimentallythepropertiesofdilationsgiven

byacenterandascalefactor.AL6-6,6-6

MCC.G.SRT.1.a Adilationtakesalinenotpassingthroughthecenterofthedilationtoaparallelline,andleavesalinepassingthroughthecenterunchanged.

AL6-6,6-6

MCC.G.SRT.1.b Thedilationofalinesegmentislongerorshorterintheratiogivenbythescalefactor.

AL6-6,6-6

MCC.G.SRT.2 Giventwofigures,usethedefinitionofsimilarityintermsofsimilaritytransformationstodecideiftheyaresimilar;explainusingsimilaritytransformationsthemeaningofsimilarityfortrianglesastheequalityofallcorrespondingpairsofanglesandtheproportionalityofallcorrespondingpairsofsides.

6-7

MCC.G.SRT.3 UsethepropertiesofsimilaritytransformationstoestablishtheAAcriterionfortwotrianglestobesimilar.

6-7

Prove theorems involving similarityMCC.G.SRT.4 Provetheoremsabouttriangles.Theoremsinclude:

alineparalleltoonesideofatriangledividestheothertwoproportionallyandconversely;thePythagoreanTheoremprovedusingtrianglesimilarity.

6-5,7-1

MCC.G.SRT.5 Usecongruenceandsimilaritycriteriafortrianglestosolveproblemsandtoproverelationshipsingeometricfigures.

3-2,3-3,3-4,3-5,3-6,3-7,4-1,4-2,4-4,5-1,5-2,5-3,5-4,5-5,5-6,6-2,6-3,6-4

Define trigonometric ratios and solve problems involving right trianglesMCC.G.SRT.6 Understandthatbysimilarity,sideratiosinrighttriangles

arepropertiesoftheanglesinthetriangle,leadingtodefinitionsoftrigonometricratiosforacuteangles.

TL7-3

MCC.G.SRT.7 Explainandusetherelationshipbetweenthesineandcosineofcomplementaryangles.

7-3

MCC.G.SRT.8 UsetrigonometricratiosandthePythagoreanTheoremtosolverighttrianglesinappliedproblems.

7-1,7-2,7-3,7-4

Apply trigonometry to general trianglesMCC.G.SRT.9 (+)DerivetheformulaA=½ab sin(C)fortheareaof

atrianglebydrawinganauxiliarylinefromavertexperpendiculartotheoppositeside.


MCC.G.SRT.10 (+)ProvetheLawsofSinesandCosinesandusethemtosolveproblems.


MCC.G.SRT.11 (+)UnderstandandapplytheLawofSinesandtheLawofCosinestofindunknownmeasurementsinrightandnon-righttriangles(e.g.,surveyingproblems,resultantforces).


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Advanced Algebra

CIRCLES G.CUnderstand and apply theorems about circlesMCC.G.C.1 Provethatallcirclesaresimilar. 8-1

MCC.G.C.2 Identifyanddescriberelationshipsamonginscribedangles,radii,andchords.Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

8-1,8-3,8-4,8-5,8-6

MCC.G.C.3 Constructtheinscribedandcircumscribedcirclesofatriangle,andprovepropertiesofanglesforaquadrilateralinscribedinacircle.

4-3,8-5

MCC.G.C.4 (+)Constructatangentlinefromapointoutsideagivencircletothecircle.

8-3,8-5

Find arc lengths and areas of sectors of circlesMCC.G.C.5 Deriveusingsimilaritythefactthatthelengthofthearc

interceptedbyanangleisproportionaltotheradius,anddefinetheradianmeasureoftheangleastheconstantofproportionality;derivetheformulafortheareaofasector.

8-1,8-2,AL8-2

Expressing Geometric Properties with Equations G.GPETranslate between the geometric description and the equation for a conic sectionMCC.G.GPE.1 Derivetheequationofacircleofgivencenterandradius

usingthePythagoreanTheorem;completethesquaretofindthecenterandradiusofacirclegivenbyanequation.

12-12

MCC.G.GPE.2 Derivetheequationofaparabolagivenafocusanddirectrix.

12-11

MCC.G.GPE.3 (+)Derivetheequationsofellipsesandhyperbolasgiventhefoci,usingthesumordifferenceofdistancesfromthefociisconstant.


Use coordinates to prove simple geometric theorems algebraicallyMCC.G.GPE.4 Usecoordinatestoprovesimplegeometric

theoremsalgebraically.9-4 12-11,12-12

MCC.G.GPE.5 Provetheslopecriteriaforparallelandperpendicularlinesandusethemtosolvegeometricproblems(e.g.,findtheequationofalineparallelorperpendiculartoagivenlinethatpassesthroughagivenpoint).

3-6,AL9-4 6-3,6-4

MCC.G.GPE.6 Findthepointonadirectedlinesegmentbetweentwogivenpointsthatpartitionsthesegmentinagivenratio.

LL9-1

MCC.G.GPE.7 Usecoordinatestocomputeperimetersofpolygonsandareasoftrianglesandrectangles,e.g.,usingthedistanceformula.✭

9-1,9-2

Geometric Measurement and Dimension G.GMDExplain volume formulas and use them to solve problemsMCC.G.GMD.1 Giveaninformalargumentfortheformulasforthe

circumferenceofacircle,areaofacircle,volumeofacylinder,pyramid,andcone.Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

8-1,AL9-1,9-3,AL9-4,9-4

MCC.G.GMD.2 (+)GiveaninformalargumentusingCavalieri’sprinciplefortheformulasforthevolumeofasphereandothersolidfigures.

9-3,9-4,9-5

MCC.G.GMD.3 Usevolumeformulasforcylinders,pyramids,cones,andspherestosolveproblems.✭

9-3,9-4,9-5

Visualize relationships between two-dimensional and three-dimensional objectsMCC.G.GMD.4 Identifytheshapesoftwo-dimensionalcross

sectionsofthree-dimensionalobjects,andidentifythree-dimensionalobjectsgeneratedbyrotationsoftwo-dimensionalobjects.

10-6,10-8




Analytic Geometry

Advanced Algebra

MODELING WITH GEOMETRY G.MGApply geometric concepts in modeling situationsMCC.G.MG.1 Usegeometricshapes,theirmeasures,andtheirproperties

todescribeobjects(e.g.,modelingatreetrunkorahumantorsoasacylinder).✭

9-1,9-2,9-3,9-4,9-5

10-3,10-4,10-5,10-7

MCC.G.MG.2 Applyconceptsofdensitybasedonareaandvolumeinmodelingsituations(e.g.,personspersquaremile,BTUspercubicfoot).✭

10-2,10-3,10-4,10-7

MCC.G.MG.3 Applygeometricmethodstosolvedesignproblems(e.g.,designinganobjectorstructuretosatisfyphysicalconstraintsorminimizecost;workingwithtypographicgridsystemsbasedonratios).✭

10-2,10-3,10-4,10-7

STATISTICS AND PROBABILITY✭

Interpreting Categorical and Quantitative Data S.IDSummarize, represent, and interpret data on a single count or measurement variableMCC.S.ID.1 Representdatawithplotsontherealnumberline

(dotplots,histograms,andboxplots).6-1,6-2,6-3

MCC.S.ID.2 Usestatisticsappropriatetotheshapeofthedatadistributiontocomparecenter(median,mean)andspread(interquartilerange,standarddeviation)oftwoormoredifferentdatasets.

6-2,AL6-2a,6-3

1-1,1-2,1-4

MCC.S.ID.3 Interpretdifferencesinshape,center,andspreadinthecontextofthedatasets,accountingforpossibleeffectsofextremedatapoints(outliers).

6-1,6-2

MCC.S.ID.4 Usethemeanandstandarddeviationofadatasettofitittoanormaldistributionandtoestimatepopulationpercentages.Recognizethattherearedatasetsforwhichsuchaprocedureisnotappropriate.Usecalculators,spreadsheets,andtablestoestimateareasunderthenormalcurve.

1-4

Summarize, represent, and interpret data on two categorical and quantitative variablesMCC.S.ID.5 Summarizecategoricaldatafortwocategoriesin

two-wayfrequencytables.Interpretrelativefrequenciesinthecontextofthedata(includingjoint,marginal,andconditionalrelativefrequencies).Recognizepossibleassociationsandtrendsinthedata.

6-5

MCC.S.ID.6 Representdataontwoquantitativevariablesonascatterplot,anddescribehowthevariablesarerelated.

6-4 12-3

MCC.S.ID.6.a Fitafunctiontothedata;usefunctionsfittedtodatatosolveproblemsinthecontextofthedata.Use given functions or choose a function suggested by the context. Emphasize linear and exponential models.

6-4 12-3,12-9

MCC.S.ID.6.b Informallyassessthefitofafunctionbyplottingandanalyzingresiduals.

AL6-4 LL12-9

MCC.S.ID.6.c Fitalinearfunctionforascatterplotthatsuggestsalinearassociation.

6-4

Interpret linear modelsMCC.S.ID.7 Interprettheslope(rateofchange)andtheintercept

(constantterm)ofalinearmodelinthecontextofthedata.6-4

MCC.S.ID.8 Compute(usingtechnology)andinterpretthecorrelationcoefficientofalinearfit.

6-4

MCC.S.ID.9 Distinguishbetweencorrelationandcausation. 6-4

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Advanced Algebra

Making Inferences and Justifying Conclusions S.ICUnderstand and evaluate random processes underlying statistical experimentsMCC.S.IC.1 Understandstatisticsasaprocessformakinginferencesto

bemadeaboutpopulationparametersbasedonarandomsamplefromthatpopulation.

1-3

MCC.S.IC.2 Decideifaspecifiedmodelisconsistentwithresultsfromagivendata-generatingprocess,e.g.,usingsimulation.

AL1-4a

Make inferences and justify conclusions from sample surveys, experiments, and observational studiesMCC.S.IC.3 Recognizethepurposesofanddifferencesamongsample

surveys,experiments,andobservationalstudies;explainhowrandomizationrelatestoeach.

1-3

MCC.S.IC.4 Usedatafromasamplesurveytoestimateapopulationmeanorproportion;developamarginoferrorthroughtheuseofsimulationmodelsforrandomsampling.

AL1-4b

MCC.S.IC.5 Usedatafromarandomizedexperimenttocomparetwotreatments;usesimulationstodecideifdifferencesbetweenparametersaresignificant.

AL1-4c

MCC.S.IC.6 Evaluatereportsbasedondata. 1-1,1-2,1-3

Conditional Probability and the Rules of Probability S.CPUnderstand independence and conditional probability and use them to interpret dataMCC.S.CP.1 Describeeventsassubsetsofasamplespace(theset

ofoutcomes)usingcharacteristics(orcategories)oftheoutcomes,orasunions,intersections,orcomplementsofotherevents(“or,”“and,”“not”).

13-1,13-3

MCC.S.CP.2 UnderstandthattwoeventsAandBareindependentiftheprobabilityofAandBoccurringtogetheristheproductoftheirprobabilities,andusethischaracterizationtodetermineiftheyareindependent.

13-3

MCC.S.CP.3 UnderstandtheconditionalprobabilityofAgivenBasP (AandB)/P(B),andinterpretindependenceofAandBassayingthattheconditionalprobabilityofAgivenBisthesameastheprobabilityofA,andtheconditionalprobabilityofBgivenAisthesameastheprobabilityofB.

13-5

MCC.S.CP.4 Constructandinterprettwo-wayfrequencytablesofdatawhentwocategoriesareassociatedwitheachobjectbeingclassified.Usethetwo-waytableasasamplespacetodecideifeventsareindependentandtoapproximateconditionalprobabilities.

13-4,13-5

MCC.S.CP.5 Recognizeandexplaintheconceptsofconditionalprobabilityandindependenceineverydaylanguageandeverydaysituations.

13-3,13-5

Use the rules of probability to compute probabilities of compound events in a uniform probability modelMCC.S.CP.6 FindtheconditionalprobabilityofAgivenBasthefraction

ofB’soutcomesthatalsobelongtoA,andinterprettheanswerintermsofthemodel.

13-5

MCC.S.CP.7 ApplytheAdditionRule,P(AorB)=P(A)+P(B)–P (AandB),andinterprettheanswerintermsofthemodel.

13-3

MCC.S.CP.8 (+)ApplythegeneralMultiplicationRuleinauniformprobabilitymodel,P(AandB)=P(A)P(B|A)=P(B)P(A|B),andinterprettheanswerintermsofthemodel.


MCC.S.CP.9 (+)Usepermutationsandcombinationstocomputeprobabilitiesofcompoundeventsandsolveproblems.





Analytic Geometry

Advanced Algebra

Using Probability to Make Decisions S.MDCalculate expected values and use them to solve problemsMCC.S.MD.1 +)Definearandomvariableforaquantityofinterest

byassigninganumericalvaluetoeacheventinasamplespace;graphthecorrespondingprobabilitydistributionusingthesamegraphicaldisplaysasfordatadistributions.


MCC.S.MD.2 (+)Calculatetheexpectedvalueofarandomvariable;interpretitasthemeanoftheprobabilitydistribution.


MCC.S.MD.3 (+)Developaprobabilitydistributionforarandomvariabledefinedforasamplespaceinwhichtheoreticalprobabilitiescanbecalculated;findtheexpectedvalue.


MCC.S.MD.4 (+)Developaprobabilitydistributionforarandomvariabledefinedforasamplespaceinwhichprobabilitiesareassignedempirically;findtheexpectedvalue.


Use probability to evaluate outcomes of decisionsMCC.S.MD.5 (+)Weighthepossibleoutcomesofadecisionbyassigning

probabilitiestopayoffvaluesandfindingexpectedvalues.Addressedin4thyearcourses

MCC.S.MD.5.a Findtheexpectedpayoffforagameofchance. Addressedin4thyearcourses

MCC.S.MD.5.b Evaluateandcomparestrategiesonthebasisofexpectedvalues.


MCC.S.MD.6 (+)Useprobabilitiestomakefairdecisions(e.g.,drawingbylots,usingarandomnumbergenerator).


MCC.S.MD.7 (+)Analyzedecisionsandstrategiesusingprobabilityconcepts(e.g.,producttesting,medicaltesting,pullingahockeygoalieattheendofagame).


46

MAT

HEMAT

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PRA

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alkt

hrou

gh Standards for Mathematical PracticeTheStandards for Mathematical PracticeareanimportantpartoftheCommon Core Georgia Performance Standards.Theydescribevarietiesofproficiencythatteachersshouldfocusonhelpingtheirstudentsdevelop.ThesepracticesdrawfromtheNCTMProcessStandardsofproblemsolving,reasoningandproof,communication,representation,andconnectionsandthestrandsofmathematicalproficiencyspecifiedintheNationalResearchCouncil’sreportAddingItUp:adaptivereasoning,strategiccompetence,conceptualunderstanding,proceduralfluency,andproductivedisposition.

ThisisanoverviewofthefeaturesofPearson Georgia High School MathematicsthathelpstudentsdevelopproficiencyineachoftheStandards for Mathematical Practice.

TheMathematicalPracticesbeingdevelopedandassessedbyspecificlessonexercisesareclearlyidentifiedwithintheTeacher’sGuide.

47

1 Make Sense of Problems and Persevere in Solving Them.

2 Reason Abstractly and Quantitatively.

3 Construct Viable Arguments and Critique the Reasoning of Others.

4 Model with Mathematics.

5 Use Appropriate Tools Strategically.

6 Attend to Precision.

7 Look for and Make Use of Structure.

8 Look for and Express Regularity in Repeated Reasoning.

Lesson 7-3 More Multiplication Properties of Exponents 433

More Multiplication Properties of Exponents

7-3

Objectives To raise a power to a powerTo raise a product to a power

In the Solve It, the expression for the volume of the larger bubble involves a product raised to a power. In this lesson, you will use properties of exponents to simplify similar expressions.

Essential Understanding You can use properties of exponents to simplify a power raised to a power or a product raised to a power.

You can use repeated multiplication to simplify a power raised to a power.

(x 5)2 5 x 5 ? x 5 5 x 515 5 x 5?2 5 x 10

Notice that (x 5)2 5 x 5?2. Raising a power to a power is the same as raising the base to the product of the exponents.

Property Raising a Power to a Power

Words To raise a power to a power, multiply the exponents.

Algebra (a m)n 5 a mn, where a 2 0 and m and n are rational numbers

Examples (54)2 5 54?2 5 58 (m 3)5 5 m 3?5 5 m 15

(a32)3 5 a

32 ?3 5 a

92 (x

12)

35 5 x

12 ?

35 5 x

310

radius = in.radius = in.x x

Make a plan. What do you need to know before you can use the volume formula?

Dynamic ActivityMultiplying Exponential Expressions

AC T I V I T I

E S

DYNAMIC Dynamic Activity

The radius of a bubble made by the bubble machine on the right is 2.5 times as large as the radius of a bubble made by the bubble machine on the left. What is the volume of a bubble made by the machine on the right? Explain your reasoning. (Hint: 4

3V πr3 )

Content StandardN.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

MATHEMATICAL PRACTICES

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Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

TheSolve It!openerforeachlessonpresentsaproblemsituationforwhichstudentsworkcollaborativelyorindividually.TheSolve It!offersopportunitiesforstudentstomake sense of problemsandpersevereinsolvingthem.GuidingquestionsintheTeacher’sEditionhelpstudentspersevere to find entries into the problemsandtodevelop a workable solution plan.

Studentslooktounderstand the meaningoftheproblempresentedanddevelop and implement a solution plan.Therichvisualsupporthelpsstudentsmakesenseofproblemsituations.

Have you seen a problem like this one?Yes. Finding percent increase is like finding percent decrease. The difference is in calculating the amount of increase or decrease.

How are the speeds related?The air speed is a plane’s speed with no wind. Add wind speed and air speed to get the ground speed with a tailwind. Subtract wind speed from air speed to find the ground speed with a headwind.

Lesson 11-2 Multiplying and Dividing Rational Expressions 675

Multiply or divide.

51. t 2 1 5t 1 6t 2 3 ?

t 2 2 2t 2 3t 2 1 3t 1 2

52. c2 1 3c 1 2c2 2 4c 1 3

4c 1 2c 2 3

53. 7t 2 2 28t2t 2 2 5t 2 12

?6t 2 2 t 2 15

49t 3 54. 5x2 1 10x 2 155 2 6x 1 x2 4

2x2 1 7x 1 34x2 2 8x 2 5

55. x2 1 x 2 6x2 2 x 2 6

4x2 1 5x 1 6x2 1 4x 1 4

56. Qx2 2 25x2 2 4x

RQ x2 1 x 2 20x2 1 10x 1 25

R

Loan Payments The formula below gives the monthly payment m on a loan as a function of the amount borrowed A, the annual rate of interest r (expressed as a decimal), and the number of months n of the loan. Use this formula and a calculator for Exercises 57–60.

m 5AQ r12RQ1 1

r12R

n

Q1 1 r12R

n2 1

57. What is the monthly payment on a loan of $1500 at 8% annual interest paid over 18 months?

58. What is the monthly payment on a loan of $3000 at 6% annual interest paid over 24 months?

59. Think About a Plan Suppose a family wants to buy the house advertised at the right. They have $60,000 for a down payment. Their mortgage will have an annual interest rate of 6%. The loan is to be repaid over a 30-yr period. How much will it cost the family to repay this mortgage over the 30 yr?

• What information can you obtain from the formula above? • How can you use the information given by the formula to solve

the problem?

60. Auto Loans You want to purchase a car that costs $18,000. The car dealership offers two different 48-month financing plans. The first plan offers 0% interest for 4 yr. The second plan offers a $2000 discount, but you must finance the rest of the purchase price at an interest rate of 7.9% for 4 yr. For which financing plan will your total cost be less? How much less will it be?

61. Error Analysis In the work shown at the right, what error did the student make in dividing the rational expressions?

62. Open-Ended Write two rational expressions. Find their product.

63. Reasoning For what values of x is the expression 2x2 2 5x 2 12

6x 4 23x 2 12x2 2 16

undefined? Explain your reasoning.

ApplyB

÷ ÷= 3aa + 2

3aa + 2

(a + 2)2

a – 4(a + 2)2

a – 4

÷= 3a a + 2a – 4a – 4a + 2

•= 3a

= 3a(a – 4)a + 2

hsm11a1se_1104_t06130

$300,000518 Main St.

4 Bedroom2 Bath

Search Homes

Listing 2 of 35

Search Homes Home Finance Contact Us

LilyRealty

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TheKnow-Need-Planboxeshelpstudentsanalyze the givensintheproblemanddevelop a workable solution plan.

Lesson Check

Problem 5

Got It?

Lesson 9-1 Quadratic Graphs and Their Properties 549

Do you know HOW?Graph the parabola. Identify the vertex.

1. y 5 23x 2

2. y 5 4x 2

3. y 5 12 x 2 1 2

4. y 5 22x 2 2 1

Do you UNDERSTAND? 5. Vocabulary When is the vertex of a parabola the

minimum point? When is it the maximum point?

6. Compare and Contrast How are the graphs of y 5 21

2 x 2 and y 5 212 x 2 1 1 similar? How are

they different?

As an object falls, its speed continues to increase, so its height above the ground decreases at a faster and faster rate. Ignoring air resistance, you can model the object’s height with the function h 5 216t 2 1 c. The height h is in feet, the time t is in seconds, and the object’s initial height c is in feet.

Using the Falling Object Model

Nature An acorn drops from a tree branch 20 ft above the ground. The function h 5 216t 2 1 20 gives the height h of the acorn (in feet) after t seconds. What is the graph of this quadratic function? At about what time does the acorn hit the ground?

•Thefunctionfortheacorn’sheight

•Theinitialheightis20ft.

Thefunction’sgraphand the time the acorn hits the ground

Use a table of values to graph the function. Use the graph to estimate when the acorn hits the ground.

20

16

4

16

h 16t2 20t

0

0.5

1

1.5

Hei

ght

(ft)

, h

Time (s), t

10

20

0 210

Graph the function usingthe first three ordered pairs from the table. Do not plot(1.5, 16) because height cannot be negative.

hsm11a1se_0901_t05349.aiThe acorn hits the ground when its height above the ground is 0 ft. From the graph, you can see that the acorn hits the ground after slightly more than 1 s.

5. a. In Problem 5 above, suppose the acorn drops from a tree branch 70 ft above the ground. The function h 5 216t2 1 70 gives the height h of the acorn (in feet) after t seconds. What is the graph of this function? At about what time does the acorn hit the ground?

b. Reasoning What are a reasonable domain and range for the original function in Problem 5? Explain your reasoning.

Can you choose negative values for t?No. t represents time, so it cannot be negative.


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49

TheThink, Planboxesmodelthroughquestionsandanswersthethinking thatproficientproblemsolversuse.

Someremindstudentstolook for similar or analogous problem situationsthattheypreviouslysolved.Othersfocus onunderstandingtherelationshipsamongthevariablesorquantitiesintheproblem.

Throughouttheexercisesets,studentsarecalledontomakesenseoftheproblemstheyencounterandfindworkablesolutionplanstosolvethemwiththeThink About a Planexercises,studentsunderstand the meaningoftheproblemsituation,analyze the givensinaproblemsituation,anddevelop a solution plan.

As you work through the lessons, consider asking these questions to help your students develop proficiency with this standard:

•Whatistheproblemthatyouaresolvingfor?•Whatproblemhaveyourecentlysolvedthatmightbesimilartothisone?•Howwillyougoaboutsolvingtheproblem?(thatis,what’syourplan?)•Areyouprogressingtowardsasolution?Howdoyouknow?Shouldyoutryadifferentsolutionplan?•Didyoucheckyoursolutionbyusingadifferentmethod?

What does the solution represent in the real world?Check what the assigned variables represent. Here, (20, 40) represents 20 large snack packs and 40 small snack packs.

Does it make sensethat two differentprices can yield thesame profi t?Yes. You can generatea given profi t either byselling many CDs at alow price, or fewer CDsat a high price.

Why do you substitute 0 for y to find the x-intercept?The x-intercept is the x-coordinate of a point on the x-axis. Any point on the x-axis has a y-coordinate of 0.

Why does y = x − 2 represent the boundary line?For any value of x, the corresponding value of yis the boundary between values of y that are greater than x − 2 and values of y that are less than x − 2.

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Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

ReasoningisoneoftheguidingprinciplesofPearson Georgia High School Mathematics.TheThink, Planboxesguidestudentstorepresent problem situations symbolically.Someofferpromptstohelpstudentsrepresentasituationsymbolicallyandtomanipulate the symbolsinanequation.

Othersremindstudentstoidentify the referents of solutions.

Lesson Check

Problem 4

Got It?

442 Chapter 7 Exponents and Exponential Functions

Do you know HOW?Simplify each expression.

1. y 3

y 10 2. Q x

13

3 R3

3. Q mn

R23 4. Q

3x 2

5y 4 R24

5. A large cube is made up of many small cubes. The volume of the large cube is 7.506 3 105 mm3. The volume of each small cube is 2.78 3 104 mm3. How many small cubes make up the large cube?

Do you UNDERSTAND? 6. Vocabulary How is the property for raising a

quotient to a power similar to the property for raising a product to a power?

7. a. Reasoning Ross simplifies a 3

a 7 as shown at the right. Explain why Ross’s method works.

b. Open-Ended Write a quotient of powers and use Ross’s method to simplify it.

= =1 1a3a7 a7–3 a4

Simplifying an Exponential Expression

What is the simplified form of Q 2x 6

y 4 R23?

Q2x6

y4 R235 Q y4

2x6R3

Rewrite using the reciprocal of 2x 6

y 4 .

5(y 4)3

(2x 6)3 Raise the numerator and denominator to the third power.

5y 12

8x 18 Simplify.

4. What is the simplified form of Q a

5b R22?

How do you write an expression in simplified form?Use the properties of exponents to write each variable with a single positive exponent.

Practice and Problem-Solving Exercises

Copy and complete each equation.

8. 59

52 5 5j 9. 2

73

22 5 2j 10. 32

35 5 3j 11. 5253

5352 5 5j

Simplify each expression.

12. 38

36 13. 9

34

914 14. d 14

d 17

15. n 21

n 24 16. 5s 27

10s 29 17. x 11y 3

x 11y

18. c 23d 25

c 16d 21 19. 10m 6n 3

5m 2n 7 20. m 23n 2

m 21n 3

21. 32m 5t 6

35m 7t 25 22. x5y2

92z 3

xy2 4z 3 23. 12a21b6c 23

4a5b21c5

PracticeA See Problem 1.



0439_hsm12a1se_0704.indd 442 3/3/11 3:16:07 PM

Chapter 6 Pull It All Together 407

To solve these problems you will pull together many concepts and skills that you have studied about systems of equations and inequalities.

6

Solving Equations and InequalitiesThere are several ways to solve systems of equations and inequalities, including graphing and using equivalent forms of equations and inequalities within the system. The number of solutions depends on the type of system.

Performance Task 1Suppose two people begin walking in the same direction at different average speeds. Walker A starts at the 0.5-meter mark and walks at a speed of 1 m/s. Walker B starts at the 2-meter mark and walks at a speed of 0.5 m/s. When and where will Walker A pass Walker B?

Performance Task 2Solve. Show all your work and explain your steps.

The triangle on the left has a perimeter of 14. The triangle on the right has a perimeter of 21. What are the values of x and y?

ModelingYou can represent many real-world mathematical problems algebraically. When you need to find two unknowns, you may be able to write and solve a system of equations or inequalities.

Performance Task 3Solve the problem. Show all of your work and explain your steps.

A town is organizing a Fourth of July parade. There will be two sizes of floats in the parade, as shown below. A space of 10 ft will be left after each float.

a. Describe how the total length of the parade will be calculated. b. The parade must be at least 150 ft long, but less than 200 ft long. What

combinations of large and small floats are possible? c. Large floats cost $600 to operate. Small floats cost $300 to operate. The town has

a budget of $2500 to operate the floats. How does this change your answer to part (a)? What combinations of large and small floats are possible?

y y

x 3x

y54

y54

Pull It All Together

30 ft 15 ft10-ft space10-ft space

ASSESSMENT

0407_hsm12a1se_06pt.indd 407 2/21/11 1:53:15 PM

Got It?

556 Chapter 9 Quadratic Functions and Equations

2. In Problem 2, suppose a T-shirt is launched with an initial upward velocity of 64 ft/s and is caught 35 ft above the court. How long will it take the T-shirt to reach its maximum height? How far above court level will it be? What is the range of the function that models the height of the T-shirt over time?

Lesson CheckDo you know HOW?Graph each function.

1. y 5 x 2 2 4x 1 1

2. y 5 22x 2 2 8x 2 3

3. y 5 3x 2 1 6x 1 2

4. f (x) 5 2x 2 1 2x 2 5

Do you UNDERSTAND? 5. Reasoning How does each of the numbers a,

b, and c affect the graph of a quadratic function

y 5 ax 2 1 bx 1 c?

6. Writing Explain how you can use the y-intercept, vertex, and axis of symmetry to graph a quadratic function. Assume the vertex is not on the y-axis.


Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of each function.

7. y 5 2x 2 1 3 8. y 5 23x 2 1 12x 1 1 9. f (x) 5 2x 2 1 4x 2 1

10. y 5 x 2 2 8x 2 7 11. f (x) 5 3x 2 2 9x 1 2 12. y 5 24x 2 1 11

13. f (x) 5 25x 2 1 3x 1 2 14. y 5 24x 2 2 16x 2 3 15. f (x) 5 6x 2 1 6x 2 5

Match each function with its graph.

16. y 5 2x 2 2 6x 17. y 5 2x 2 1 6 18. y 5 x 2 2 6 19. y 5 x 2 1 6x

A. B.

C. D.


hsm11a1se_0902_t05230



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•Canyouwriteorrecallanexpressionorequationtomatchtheproblemsituation?•Whatdothenumbersorvariablesintheequationreferto?•What’stheconnectionamongthenumbersandvariablesintheequation?

IntheDo you UNDERSTAND?feature,foundattheendofeachlesson,studentsexplain their thinkingrelatedtotheconceptsstudiedinthelesson.

TheReasoningexercisesfocusstudents’attentiononthestructure or meaning of an operationratherthanthesolution.

InthePull It All Together,studentsdrawontheirreasoningskillstoputforthappropriatesymbolic representations of problemspresented.

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Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Pearson Georgia High School Mathematicshasastrongfocusoncriticalreasoning,argumentation,andcritiqueofarguments.Studentsareoftenaskedtoexplaintheirsolutionsandthethinkingthatledthemtothesesolutions.TheSolve It!activitiesalwaysaskstudentstojustify their solutions and their reasoning.


•Whatdoesyouranswermean?•Howdoyouknowthatyouransweriscorrect?• IfItoldyouIthinktheanswershouldbe[awronganswer],howwouldyouexplaintomewhyI’mwrong?

Can you solve this problem another way?Yes. You could actually solve the equation to find any solutions. However, you only need to know the number of solutions, so use the discriminant.

Does the locationof the circumcentermake sense?Yes, POS is aright triangle, so itscircumcenter should lieon its hypotenuse.

53

ManyoftheThink, Planboxesfocusonhelpingstudentsanalyze situations, justify conclusions, andreason inductively and deductively.

Throughouttheprogramareexercisesthataskstudentstoconstructargumentstodefendtheirsolutionsandtorespondtothesolutionsandargumentsofothers.IntheReasoningexercises,studentsareexpectedtoformulate argumentstosupporttheirsolutions.

TheError Analysisexercisesrequirestudentstocritique the solutionpresentedforaproblem.

Problem 1

Lesson 11-5 Solving Rational Equations 691

11-5

Objective To solve rational equations and proportions

Solving Rational Equations

Geb can run the distance between his house and Katy’s in 20 min. Katy can bicycle to Geb’s house in 10 min. Geb runs toward Katy’s house while Katy bicycles toward Geb’s house. How long will it be before they meet on the road? Justify your reasoning.

A rational equation is an equation that contains one or more rational expressions.

Essential Understanding You can solve a rational equation by first multiplying each side of the equation by the LCD. When each side of a rational equation is a single rational expression, you can solve the equation using the Cross Products Property.

Lesson Vocabulary

•rational equation

LessonVocabulary

Solving Equations With Rational Expressions

What is the solution of 512 2

12x 5

13x? Check the solution.

512 21

2x 51

3x The denominators are 12, 2x, and 3x. The LCD is 12x.

12x Q 512 2

12xR 5 12x Q 1

3xR Multiply each side by 12x.

121xQ 5112R 2 12x

6Q 112xR 5 12x

4Q 113xR Distributive Property

5x 2 6 5 4 Simplify.

5x 5 10 Add 6 to each side.

x 5 2 Divide each side by 5.

Check 512 2

12(2)

01

3(2) See if x 5 2 makes 5

12 212x 5

13x true.

16 516y

Have you seen an equation like this before?Yes. In Lesson 2-3, you solved equations that contained fractions. As you did there, you can clear the fractions from the equation by multiplying by a common denominator.

A diagram can help you understand this situation. Use a straight path.

Content StandardsA.CED.1 Create equations . . . in one variable and use them to solve problems. Include equations arising from . . . simple rational . . . functions.

Also A.REI.2


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Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts, and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Throughouttheprogram,studentsbuildmathematicalmodelsusingvisuals,suchasgraphs,tables,ordrawings;equations,expressions,orfunctions;andtools,includingtechnology.Studentsconstructmathematicalmodelsforthereal-lifesituationspresentedintheSolve It!activities.


•Whatformulaorrelationshipcanyouthinkofthatfitsthisproblemsituation?•Whatistheconnectionamongthenumbersintheproblem?• Isyouranswerreasonable?Howdoyouknow?•Whatdothenumbersinyoursolutionreferto?

480 in.480 in.

Problem 4

Got It?

Lesson 11-7 Areas and Volumes of Similar Solids 745

Using a Scale Factor to Find Capacity

Containers A bottle that is 10 in. high holds 34 oz of milk. The sandwich shop shown at the right is shaped like a milk bottle. To the nearest thousand ounces how much milk could the building hold?

The scale factor of the bottles is 1 i 48.

The ratio of their volumes, and hence the ratio of their capacities, is 13 i 483, or 1 i 110,592.

1110,592 5

34x

Let x 5 the capacity of the milk-bottle building.

x 5 34 ? 110,592 Use the Cross Products Property.

x 5 3,760,128 Simplify.

The milk-bottle building could hold about 3,760,000 oz.

4. A marble paperweight shaped like a pyramid weighs 0.15 lb. How much does a similarly shaped marble paperweight weigh if each dimension is three times as large?

Lesson CheckDo you know HOW? 1. Which two of the following cones are similar? What is

their scale factor?

2. The volumes of two similar containers are 115 in.3 and 67 in.3. The surface area of the smaller container is 108 in2. What is the surface area of the larger container?

Do you UNDERSTAND? 3. Vocabulary How are similar solids different from

similar polygons? Explain.

4. Error Analysis Two cubes have surface areas 49 cm2 and 64 cm2. Your classmate tried to find the scale factor of the larger cube to the smaller cube. Explain and correct your classmate’s error.

hsm11gmse_1107_t10073.ai

The scale factor of thelarger cube to the smallercube is 7 : 8.

20 m 25 m 30 mCone 1 Cone 2 Cone 3

45 m35 m30 m


How does capacity relate to volume?Since the capacities of similar objects are proportional to their volumes, the ratio of their capacities is equal to the ratio of their volumes.


STEM

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352 Chapter 5 Pull It All Together

To solve these problems you will pull together many concepts and skills that you have studied about linear functions.

5

FunctionsThere are several forms for the equation of a line. Each form communicates different information. For instance, from the point-slope form, you can determine a point and the slope of a line.

Performance Task 1During a hot-air balloon festival, data were gathered on the height y of a balloon after x minutes.

a. Is the rate of change constant? If so, what is the rate of change?

b. What are the units of the rate of change? What does the rate of change represent?

c. Write a linear equation in slope-intercept form to model this situation.

d. If the balloon continues to rise at the same rate, what will its height be after 8 minutes?

e. During what time interval is the height less than or equal to 500 meters?

ModelingYou can model the trend of real-world data in a scatter plot with an equation of a line. You can use the equation to estimate or to make predictions.

Performance Task 2At the beginning of a 20-month period, Stacie owns one clothing store. During that period, she opens a second clothing store in a different location. The table shows the total monthly sales of Stacie’s clothing stores for the 20-month period.

a. When do you think the second store was opened? Justify your answer and include a graph in your justification.

b. If Stacie’s stores continue increasing sales at the present rate, predict the amount of sales in the twenty-fourth month. Justify your conclusion.

Hot-Air Balloon Height

Time (min)

14

80

116

134

152

0

2.2

3.4

4

4.6

Height (m)

Month

Sales

Monthly Sales (thousands of dollars)

2

3

4

5

6

4

8

6

10

5

12

12

14

16

16

22

18

26

20

32

Pull It All Together ASSESSMENT

0352_hsm12a1se_05pt.indd 352 2/21/11 3:40:19 PM

55

Thevisuallyrichproblemsfacilitateunderstandingoftheproblemsituationssostudentscanconnecttomathematicalmodelsmoreeasily.

InthePull It All Togetheractivities,studentareoftenexpectedtoapply a mathematical modeltothesituationspresented.

576 Chapter 9 Quadratic Functions and Equations

Completing the Square9-5

Objective To solve quadratic equations by completing the square

Your school has a field with an area of 8400 yd2. The football coach is planning to section off the field to run a variety of practice drills. What is the value of x? Explain your reasoning.

In previous lessons, you solved quadratic equations by finding square roots and by factoring. These methods work in some cases, but not all.

Essential Understanding You can solve any quadratic equation by first writing it in the form m 2 5 n.

You can model this process using algebra tiles. The algebra tiles at the right represent the expression x 2 1 8x.

Here is the same expression rearranged to form part of a square. Notice that the x-tiles have been split evenly into two groups of four.

In general, you can change the expression x 2 1 bx into a perfect-square trinomial by

adding Qb2 R2

to x 2 1 bx. This process is called completing the square. The process is the same whether b is positive or negative.

Lesson Vocabulary

•completing the square

LessonVocabulary

x yd

x yd

x yd10 yd

10 yd10 yd

10 yd

You can complete the square by adding 42, or 16, 1-tiles. The completed square is x 2 1 8x 1 16, or (x 1 4)2.

Factoring is only one way to solve a quadratic equation. In this lesson, you’ll learn another way.

Content StandardsA.REI.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x 2 p)2 5 q . . .

Also N.Q.3, A.SSE.1.a, A.SSE.1.b, A.SSE.3.b, A.CED.1, A.REI.1, A.REI.4.b, F.IF.8.a


0576_hsm12a1se_0905.indd 576 3/3/11 8:53:36 AM

Problem 3

Problem 2

Got It?

Got It?

Got It?

How can you use a graph to fi nd the solutions?Find the zeros of the related quadratic function.

Lesson 4-5 Quadratic Equations 227

What should you look for in the calculator table?Look for x-values for which y 5 0.

1. What are the solutions of the quadratic equation x2 2 7x 5 212?

Solving a Quadratic Equation With Tables

What are the solutions of the quadratic equation 5x2 1 30x 1 14 5 2 2 2x?

5x2 1 30x 1 14 5 2 2 2x

5x2 1 32x 1 12 5 0 Rewrite in standard form.

Use your calculator’s TABLE feature to fi nd the zeros.

Th e solutions are x 5 26 and x 5 20.4.

2. What are the solutions of the quadratic equation 4x2 2 14x 1 7 5 4 2 x?

Solving a Quadratic Equation by Graphing

What are the solutions of the quadratic equation 2x2 1 7x 5 15?

2x2 1 7x 5 15

2x2 1 7x 2 15 5 0 Rewrite in standard form.

Th e solutions are x 5 25 and x 5 1.5.

3. What are the solutions of the quadratic equation x2 1 2x 2 24 5 0?

0–23–36–39–32–1512

X 6

X Y1–6–5–4–3–2–10

–10.4–7.95–5.4–2.7502.855.8

X .4

X Y1–.8–.7–.6–.5–.4–.3–.2

Plot1 Plot2 Plot3\Y1\Y2\Y3\Y4\Y5\Y6\Y7

= 5X2+32X+12= = = = = =

= 5X= 2+32X+12======

Enter theequation in standard formas Y1.

0–23–36

Y1

6925

6

Y1 = 0, x = –6is one zero.

7.95–5.4–2.7502.855.8

Y1 = 0, x = –.4is the second zero.

–10.4X Y1

–.8–.7 –7.95

x-intervalchanged to .1.

Second zero isbetween x = –1and x = 0.Notice changein sign fory-values.

Plot1 Plot2 Plot3\Y1\Y2\Y3\Y4\Y5\Y6\Y7

= 2X2+7X–15= = = = = =

ZeroX=–5 Y=0

ZeroX=1.5 Y=05 Y=0ZeroX=1.5

Use ZERO optionin CALC feature.

= 2X 2+7X–15======

Enter theequation instandard formas Y1.

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Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.


•Whattoolscouldyouusetosolvethisproblem?Howcaneachonehelpyou?•Whichtoolismoreusefulforthisproblem?Explainyourchoice.•Whyisthistoolbetterthan[anothertoolmentioned]?•Beforeyousolvetheproblem,canyouestimatethesolution?

InPearson Georgia High School Mathematics, studentsbecomefluentintheuseofawideassortmentoftools,rangingfromphysicaldevisestotechnologytools.Studentsareshownappropriateusesofvarioustoolsthroughouttheprogram.

Concept Byte Using Models to Multiply 497

Concept ByteUse With Lesson 8-3

A C T I V I T Y

Using Models to Multiply

You can use algebra tiles to model the multiplication of two binomials.

Find the product (x 1 4)(2x 1 3).

2x 2 1 3x 1 8x 1 12

2x 2 1 11x 1 12 Add coefficients of like terms.

The product is 2x 2 1 11x 1 12.

You can also model products that involve subtraction. Red tiles indicate negative variables and negative numbers.

Find the product (x 2 1)(2x 1 1).

2x 2 1 x 2 2x 2 1

2x 2 2 x 2 1 Add coefficients of like terms.

The product is 2x 2 2 x 2 1.

ExercisesUse algebra tiles to find each product.

1. (x 1 4)(x 1 2) 2. (x 1 2)(x 2 3) 3. (x 1 1)(3x 2 2) 4. (3x 1 2)(2x 1 1)

2x 3

x 4

2x 1

x 1

Content StandardPrepares for A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

0497_hsm12a1se_0803a.indd 497 2/17/11 11:37:38 AM

406 Concept Byte Graphing Linear Inequalities

Concept ByteUse With Lesson 6-6

T E C H N O L O G Y

Graphing Linear Inequalities

A graphing calculator can show the solutions of an inequality or a system of inequalities. To enter an inequality, press apps and scroll down to select INEQUAL. Move the cursor over the 5 symbol for one of the equations. Notice the inequality symbols at the bottom of the screen, above the keys labeled F2–F5. Change the 5 symbol to an inequality symbol by pressing alpha followed by one of F2–F5.

Graph the inequality y R 3x 2 7.

1. Move the cursor over the 5 symbol for Y1. Press alpha and F2 to select the , symbol.

2. Enter the given inequality as Y1.

3. Press graph to graph the inequality.

Graph the system. y R 22x 2 3 y L x 1 4

4. Move the cursor over the 5 symbol for Y1. Press alpha and F2 to select the , symbol. Enter the first inequality as Y1.

5. Then move the cursor over the 5 symbol for Y2, and press alpha and F5 to select the $ symbol. Enter the second inequality as Y2.

6. Press graph to graph the system of inequalities.

ExercisesUse a graphing calculator to graph each inequality. Sketch your graph.

7. y # x 8. y . 5x 2 9 9. y $ 21 10. y , 2x 1 8

Use a graphing calculator to graph each system of inequalities. Sketch your graph.

11. y $ 2x 1 3 12. y . x 13. y $ 21 14. y $ 2x 2 2

y # x 1 2 y $ 22x 1 5 y , 0.5x 2 2 y # 2x 2 4

X = Plot1 Plot2 Plot3\Y1\Y2\Y3\Y4\Y5\Y6

= 3X – 7= = == =

11

22

Content StandardA.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane . . . and graph the solution set to a system of linear inequalities . . .

0406_hsm12a1se_0606b.indd 406 2/21/11 1:52:19 PM

120 Chapter 2 Solving Equations

Choose a Method Choose paper and pencil, mental math, or a calculator to tell which measurement is greater.

31. 640 ft; 0.5 mi 32. 63 in.; 125 cm 33. 75 g; 5 oz

34. Think About a Plan A college student is considering a subscription to a social-networking Internet site that advertises its cost as “only 87 cents per day.” What is the cost of membership in dollars per year?

• How many conversion factors will you need to use to solve the problem? • How do you choose the appropriate conversion factors?

35. Recipes Recipe A makes 5 dinner rolls using 1 c of flour. Recipe B makes 24 rolls using 71

2 c of flour. Recipe C makes 45 rolls using 10 c of flour. Which recipe requires the most flour per roll?

36. Error Analysis Find the mistake in the conversion below. Explain the mistake and convert the units correctly.

37. Writing Suppose you want to convert kilometers to miles. Which unit should be in the numerator of the conversion factor? Which unit should be in the denominator? Explain how you know.

38. Reasoning Without performing the conversion, determine whether the number of new units will be greater or less than the number of original units.

a. 3 min 20 s converted to seconds b. 23 cm converted to inches c. kilometers per hour converted to miles per hour

39. Exchange Rates The table below shows some exchange rates on a particular day. If a sweater sells for $39.95 in U.S. dollars, what should its price be in rupees and pounds?

40. Estimation Five mi is approximately equal to 8 km. Use mental math to estimate the distance in kilometers to a town that is 30 mi away.

41. Reasoning A carpenter is building an entertainment center. She is calculating the size of the space to leave for the television. She wants to leave about a foot of space on either side of the television. Would measuring the size of the television exactly or estimating the size to the nearest inch be more appropriate? Explain.

9 yd = ? ft

= 27 ft3 yd1 ft9 yd

0116_hsm12a1se_0206.indd 120 2/10/11 10:57:21 AM

57

TheActivity Labsoftensuggesttoolstohelpstudentsdevelop fluency in the use of different tools.

TheTechnology Labsfocusonenhancingstudents’strategic competencewithtechnologytools.

TheChoose a Methodexercisesstrengthenstudents’abilitytoarticulatedifferencesamongtools,leadingthemtoexplaintheusefulness and appropriateness of different tools.

Problem 2

Got It?

A 5 P Q1 1 r

nRnt

462 Chapter 7 Exponents and Exponential Functions

Compound Interest

Finance Suppose that when your friend was born, your friend’s parents deposited $2000 in an account paying 4.5% interest compounded quarterly. What will the account balance be after 18 yr?

A 5 P(1 1 rn)nt Use the compound interest formula.

5 2000Q1 1 0.0454 R4?18

Substitute the values for P, r, n, and t.

5 2000(1.01125)72 Simplify.

The balance will be $4475.53 after 18 yr.

2. Suppose the account in Problem 2 pays interest compounded monthly. What will the account balance be after 18 yr?

• $2000 principal• 4.5% interest• interest compounded quarterly

Account balance in 18 yr Use the compound interest formula.

Key Concept Exponential Decay

DefinitionsExponential decay can be modeled by the function y 5 a ? b x, where a . 0 and 0 , b , 1. The base b is the decay factor, which equals 1 minus the percent rate of change expressed as a decimal.

Algebra

y a bx

initial amount (when x 0) T

c�e base is the decay factor.

d exponent

Is the formula an exponential growth function?Yes. You can rewrite the formula as A 5 P S A1 1 r

nBnTt . So it is an exponential function with initial amount P and growth factor A1 1 r

nBn.

Graph

y

(0, a)

xO

y a bx

0 b 1

You can use the following formula to find the balance of an account that earns compound interest.

A 5 the balance P 5 the principal (the initial deposit)

r 5 the annual interest rate (expressed as a decimal) n 5 the number of times interest is compounded per year t 5 the time in years

The function y 5 a ? b x can model exponential decay as well as exponential growth. In both cases, b represents the rate of change. The value of b tells if the equation models exponential growth or decay.

y a bx

initial amount (when x 0) T

c�e base is the decay factor.

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58

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Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

Studentsareexpectedtousemathematicaltermsandsymbolswithprecision.KeytermsarehighlightedineachlessonandkeyconceptsexplainedintheTake Notefeatures.


•Whatdothesymbolsthatyouusedmean?•Whatunitsofmeasureareyouusing(formeasurementproblems)?•Whatconceptsortheoremsdidyouusetosolvetheproblem? Howexactlydotheserelatetotheproblem?

What are the unitsof the answer?You are cubing theradius, which is inmeters (m), so youranswer should be incubic meters (m3).

Problem 4

Got It?

464 Chapter 7 Similarity

Finding a Distance

Robotics You are preparing for a robotics competition using the setup shown here. Points A, B, and C are located so that

AB 5 20 in., and AB ' BC . Point D

is located on AC so that BD ' AC and DC 5 9 in. You program the robot to move from A to D and to pick up the plastic bottle at D. How far does the robot travel from A to D?

x 1 920 5

20x Corollary 2

x2 1 9x 5 400 Cross Products Property

x2 1 9x 2 400 5 0 Subtract 400 from each side.

(x 2 16)(x 1 25) 5 0 Factor.

x 2 16 5 0 or (x 1 25) 5 0 Zero-Product Property

x 5 16 or x 5 225 Solve for x.

Only the positive solution makes sense in this situation. The robot travels 16 in.

4. From point D, the robot must turn right and move to point B to put the bottle in the recycling bin. How far does the robot travel from D to B?

Do you know HOW?Find the geometric mean of each pair of numbers.

1. 4 and 9 2. 4 and 12

Use the figure to complete each proportion.

3. ge 5

ej

4. jd 5

dj

5. jf 5f

j 6.

jj5jg

Do you UNDERSTAND? 7. Vocabulary Identify the following in nRST . a. the hypotenuse b. the segments of the hypotenuse c. the segment of the hypotenuse

adjacent to leg ST

8. Error Analysis A classmate wrote an incorrect proportion to find x. Explain and correct the error.

hsm11gmse_0704_t05268

d f

g he

jhsm11gmse_0704_t05269

S T

PR

hsm11gmse_0704_t05270

3 x8

3x

x8=

Lesson Check

You can’t solve this equation by taking the square root. What do you do?Write the quadratic equation in the standard form ax2 1 bx 1 c 5 0. Then solve by factoring or use the quadratic formula.

ADC

B

9 in.

20 in.

x

STEM



Lesson 6-7 Polygons in the Coordinate Plane 403

Lesson CheckDo you know HOW? 1. nTRI has vertices T(23, 4), R(3, 4), and I(0, 0). Is

nTRI scalene, isosceles, or equilateral?

2. Is QRST below a rectangle? Explain.

Do you UNDERSTAND? 3. Writing Describe how you would

determine whether the lengths of the medians from base angles D and F are congruent.

4. Error Analysis A student says that the quadrilateral with vertices D(1, 2), E(0, 7), F(5, 6), and G(7, 0) is a rhombus because its diagonals are perpendicular. What is the student’s error?


y

x

OQ

R

T

S

2

2

4


y

xO

D F

E

22

4


Determine whether kABC is scalene, isosceles, or equilateral. Explain.

5. 6. 7.

Determine whether the parallelogram is a rhombus, rectangle, square, or none. Explain.

8. P(21, 2), O(0, 0), S(4, 0), T(3, 2) 9. L(1, 2), M(3, 3), N(5, 2), P(3, 1)

10. R(22, 23), S(4, 0), T(3, 2), V(23, 21) 11. G(0, 0), H(6, 0), I(9, 1), J(3, 1)

12. W(23, 0), I(0, 3), N(3, 0), D(0, 23) 13. S(1, 3), P(4, 4), A(3, 1), T(0, 0)

What is the most precise classification of the quadrilateral formed by connecting in order the midpoints of each figure below?

14. parallelogram PART 15. rectangle EFGH 16. isosceles trapezoid JKLM



y

xO

C

B

A

2

2


y

xOC

B

A

2

2


y

xO

C

B

A

22 2

2

See Problem 2.

See Problem 3.

hsm11gmse_0607_t06582

y

xO

4

4 2

2 A

P

T

R

hsm11gmse_0607_t06583

y

xO

4

22

F

E

G

H

hsm11gmse_0607_t06584

y

x

O

2

2 2

J K

M L




59

TheThink, Planboxesremindstudentstouse appropriate units of measure and accurate labelswhenworkingthroughsolutions.

IntheDo you UNDERSTAND?feature,studentsrevisitthesekeytermsandprovide explicit definitionsorexplanationsoftheterms.

FortheWritingexercises,studentsareexpectedtoprovide clear, concise explanationsofterms,concepts,orprocesses.

Lesson 7-4 Division Properties of Exponents 439

In the Solve It, the expression for the volume of the dowel involves a quotient raised to a power.

Essential Understanding You can use properties of exponents to divide powers with the same base.

You can use repeated multiplication to simplify quotients of powers with the same base. Expand the numerator and the denominator. Then divide out the common factors.

4 4 4 4 4

4 4 4 4245

43

This example suggests the following property of exponents.

Property Dividing Powers With the Same Base

Words To divide powers with the same base, subtract the exponents.

Algebra a m

a n 5 a m2n, where a 2 0 and m and n are rational numbers

Examples 26

22 5 2622 5 24 x 4

x 7 5 x 427 5 x 23 5 1x 3

s34

s12

5 s342

12 5 s

342

24 5 s

14

Division Properties of Exponents

7-4

Objectives To divide powers with the same base To raise a quotient to a power

Dynamic ActivityDividing Exponential Expressions

AC T I V I T I

E S

DYNAMIC Dynamic Activity

x x x x

x x

A machine makes wooden dowels by removing material from a block of wood as shown in the diagram. What percent of the wood does the machine remove from the original piece of wood to form the dowel? Explain how you found your answer. (Hint: What is the volume of the dowel?)

Solve a simpler problem first. Use a value for x to understand all of the relationships in this problem.

Content StandardN.RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.


0439_hsm12a1se_0704.indd 439 3/3/11 3:16:01 PM

What values should you choose for x?Use the same values of x for graphing both functions so that you can see the relationship between corresponding y-coordinates.

Can you use thequadratic formula tosolve part (A)?Yes. You can use thequadratic formula witha = 3, b = 0, andc = −9. However, itis faster to use squareroots.

60

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Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square, and use that to realize that its value cannot be more than 5 for any real numbers x and y.

Throughouttheprogram,studentsareencouragedtodiscernpatternsandstructuresastheylooktoformulatesolutionplans.InmanyoftheSolve It! activities,studentsarepromptedtolookwithintheproblemsituationforsimplerproblemstosolve.

Theseblueboxesalsoremindstudentstothinkaboutthe structure of the equation.


•Whatdothedifferentpartsoftheexpressiontellyouaboutpossibleanswers?•Whatdoyounoticeabouttheanswerstotheseexercises?

Can you generalize these results?Yes. All points on a horizontal line have the same y-value, so the slope is always zero. Finding the slope of a vertical line always leads to division by zero. The slope is always undefined.

Have you seen a problem like this one?Yes. Finding percent increase is like finding percent decrease. The difference is in calculating the amount of increase or decrease.

61

8 Look for and Express Regularity in Repeated Reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Studentsareencouragedtothinkaboutsimilar problemstheysolvedpreviouslyortogeneralize resultstootherproblemsituations.

TheOnline ProblemsfoundintheInteractiveDigitalPath(PearsonSuccessNet.com)offerstudentsopportunitiestonotice regularityinthewayoperationsorfunctionsbehave.


•Whatpatternsdoyousee?Canyoumakeageneralization?•Whatrelationshipsdoyouseeintheproblem?

ThroughtheThink, Planboxes,studentsarepromptedtolook for repetition in calculationstodevisegeneralmethodsorshortcutsthatcanmaketheproblemsolvingprocessmoreefficient.

62

PARC

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Assessing the Common Core State StandardsTheadoptionandimplementationoftheCommonCoreStateStandardsforMathematicsisanimportantandcriticalsteptoimprovingstudents’mathachievementintheUnitedStates.Asecond,equallyimportantstepiscreatingassessmentsgroundedinthesestandardstomeasurestudents’progressagainstthesenewstandards.Thesecommonassessmentscanalsohelpensurethatallstudentshaveaccesstothesenewstandards.

TheRacetotheTopAssessmentProgram,fundedbytheAmericanRecoveryandReinvestmentActof2009(ARRA)awardedfundingtotwostateconsortiato develop next generation assessment and accountability systems.Thesevalidandreliableassessmentswillbeusedtomeasurestudents’progressagainsttheCommonCoreStateStandards,provideacommonmeasureofcollegeandcareerreadiness,andmakeuseofnewtechnologiesinassessmentandreportingsothatparentsandteachershavetimelyinformationaboutstudentperformance.

Thesenextgenerationassessmentsystems,whicharetobeoperationalby2014–2015,aretomeetthedualneedsofaccountabilityandinstructionalimprovement.Withthesecommonassessments,stateandlocalschoolofficialscangetanaccurateviewofhowtheirstudents’performancescomparetothoseofstudentsinotherdistrictsorstates.Theycanalsoreducechallengesassociatedwithstudentmobility.Studentsinover40stateswillbeexpectedtolearnthesamecontentandwilltakethesameor similarassessments.

ThesenewassessmentswillfocusonassessingthecriticalareasasdecidedbytheAssessmentConsortiabasedontheCommonCoreStateStandards.Theseassessmentswillalsoincludetaskstomeasurestudents’mathematicalproficiency asdescribedintheStandards for Mathematical Practice.

GeorgiaadoptedtheCommon Core Georgia Performance Standards for Mathematics inJuly2010andbecameagoverningmemberofthePartnership for Assessment of Readiness for College and Careers (PARCC)inthefallof2010.Asaresult,studentsinGeorgiawilltakethePARCCEnd-of-CourseAssessmentstartingin2014–2015.

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Partnership for Assessment of Readiness for College and CareersThePartnershipforAssessmentofReadinessforCollegeandCareersConsortiumismadeupof23statesandtheDistrictofColumbia.TheconsortiumisworkingwithAchieveInc.,anindependent,bipartisan,non-profiteducationreformorganization,andmorethan200collegesoruniversitiestodevelopitsnextgenerationassessmentsystem.

Asagoverningmemberoftheconsortium,Georgiaparticipatesindecisionsregardingthedesignoftheassessmentsystem,achievementlevels,andPARCC’sgovernancestructure.Schoolsthroughoutthestatewillpilotandfieldtestcomponentsoftheassessmentperiodduringthedevelopmentperiod.

The PARCC assessment system will be made up of a Performance-Based Assessment and an End-of-Year Comprehensive Assessment.

ThePerformance-Based Assessmentwillbeanextended,multi-sessionperformance-basedassessment.Itwillfocusonassessingstudents’proficiencywithapplyingmathcontentandskillslearnedthroughouttheschoolyear.

• Itwillbeadministeredinthethirdquarteroftheschoolyear.

• Studentswillsubmittheirresponsesoncomputersorotherdigitaldevices.

• Thescoringfortheseassessmentswillbeacombinationofcomputer-scored andhuman-scored.

TheEnd-of-Course Assessmentwillassessallofthestandardsforthecourse. Itwillmeasurestudents’conceptualunderstanding,proceduralfluency,and problemsolvingproficiency.

• Itwillbecomputer-based,butdeviseneutral.

• Itwillhave40to65items,witharangeofitemtypes(i.e.,selected-response, constructed-response,performancetasks)andcognitivedemand.

• Itwillbeentirelycomputer-scored.

A student’s score will be based on his or her score on the Performance-Based Assessment and the End-of-Year Comprehensive Assessment. This score will be used for the purposes of accountability.

PARCCwillalsomakeavailablealignedformativeassessmentsthatteacherscanuse intheclassroomthroughouttheschoolyear.

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SENSE-MAKING SOLUTION PLAN REASONING EXECUTION MODELS PRECISION

4 Thesolutionsuggestsathoroughunderstandingoftheproblemsituationandthemathematicsrequiredtosolvetheproblem.

Thesolutionplanpresentedsuggestsacomprehensiveunderstandingofthemathematicalconceptsrequiredtosolvetheproblem.

Theexplanationsshowlogicalandappropriateconnectionsamongconcepts;theyalsoshowthethinkingofahighlyproficientproblem-solver.

Thesolutionshowsclear,appropriate,andeffective,executionofthesolutionplan.Allstepsareclearlyandaccuratelypresented.

Thesolutionshowsrelevantandappropriatemathematicalmodelingoftheproblemsituation.

Thesolutionandexplanationshowspreciseandappropriatemathematicalterminologyandnotation.

3 Thesolutionsuggestsanadequateunderstandingoftheproblemsituationandthemathematicsrequiredtosolvetheproblem.

Thesolutionplanpresentedsuggestsanadequateunderstandingofthemathematicalconceptsrequiredtosolvetheproblem.

Theexplanationsshowsomeappropriateconnectionsamongconcepts;theyalsoshowthethinkingofagoodproblem-solver.

Thesolutionshowsclear,appropriate,andeffective,executionofthesolutionplan.Mostofthestepsareaccuratelypresented.

Thesolutionshowsappropriatemathematicalmodelingoftheproblemsituation.

Thesolutionandexplanationshowappropriatemathematicalterminologyandnotation.

2 Thesolutionsuggestsalimitedunderstandingoftheproblemsituationandthemathematicsrequiredtosolvetheproblem.

Thesolutionplanpresentedsuggestsalimitedunderstandingofthemathematicalconceptsrequiredtosolvetheproblem.

Theexplanationsshowlimitedconnectionsamongconcepts;theyalsoshowthethinkingofanunderdevelopedproblem-solver.

Thesolutionshowsinconsistentexecutionofthesolutionplan.Onlysomestepsareclearlyandaccuratelypresented.

Thesolutionshowslimited,butappropriatemathematicalmodelingoftheproblemsituation.

Thesolutionandexplanationshowssomeimprecisionorerrorsinuseofmathematicalterminologyandnotation.

1 Thesolutionsuggestsaverylimitedunderstandingoftheproblemsituationandthemathematicsrequiredtosolvetheproblem.

Thesolutionplanpresentedsuggestsatentativeunderstandingofthemathematicalconceptsrequiredtosolvetheproblem.

Theexplanationsshowminimalconnectionsamongconcepts;theyalsoshowthethinkingofaninefficientproblem-solver.

Thesolutionshowserraticexecutionofthesolutionplan.Manystepsarenotpresented.

Thesolutionshowslimitedand,attimes,inappropriatemathematicalmodelingoftheproblemsituation.

Thesolutionandexplanationshowmanyerrorsintheuseofmathematicalterminologyandnotation.

0 Thesolutionsuggestsminimalunderstandingoftheproblemsituationandthemathematicsrequiredtosolvetheproblem.

Thesolutionplanpresentedsuggestsnounderstandingofthemathematicalconceptsrequiredtosolvetheproblem.

Theexplanationsshownoconnectionsamongconcepts;theyalsoshowthethinkingofanineffectiveproblem-solver.

Thesolutionshowsineffectiveexecutionofthesolutionplan.Few,ifany,stepsarepresented.

Thesolutionshowsnomathematicalmodelingoftheproblemsituation.

Thesolutionandexplanationshowsanabsenceofmathematicalterminologyandnotation.

MAT

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Performance-Based Assessment General Rubric

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SENSE-MAKING SOLUTION PLAN REASONING EXECUTION MODELS PRECISION

4 Thesolutionsuggestsathoroughunderstandingoftheproblemsituationandthemathematicsrequiredtosolvetheproblem.

Thesolutionplanpresentedsuggestsacomprehensiveunderstandingofthemathematicalconceptsrequiredtosolvetheproblem.

Theexplanationsshowlogicalandappropriateconnectionsamongconcepts;theyalsoshowthethinkingofahighlyproficientproblem-solver.

Thesolutionshowsclear,appropriate,andeffective,executionofthesolutionplan.Allstepsareclearlyandaccuratelypresented.

Thesolutionshowsrelevantandappropriatemathematicalmodelingoftheproblemsituation.

Thesolutionandexplanationshowspreciseandappropriatemathematicalterminologyandnotation.

3 Thesolutionsuggestsanadequateunderstandingoftheproblemsituationandthemathematicsrequiredtosolvetheproblem.

Thesolutionplanpresentedsuggestsanadequateunderstandingofthemathematicalconceptsrequiredtosolvetheproblem.

Theexplanationsshowsomeappropriateconnectionsamongconcepts;theyalsoshowthethinkingofagoodproblem-solver.

Thesolutionshowsclear,appropriate,andeffective,executionofthesolutionplan.Mostofthestepsareaccuratelypresented.

Thesolutionshowsappropriatemathematicalmodelingoftheproblemsituation.

Thesolutionandexplanationshowappropriatemathematicalterminologyandnotation.

2 Thesolutionsuggestsalimitedunderstandingoftheproblemsituationandthemathematicsrequiredtosolvetheproblem.

Thesolutionplanpresentedsuggestsalimitedunderstandingofthemathematicalconceptsrequiredtosolvetheproblem.

Theexplanationsshowlimitedconnectionsamongconcepts;theyalsoshowthethinkingofanunderdevelopedproblem-solver.

Thesolutionshowsinconsistentexecutionofthesolutionplan.Onlysomestepsareclearlyandaccuratelypresented.

Thesolutionshowslimited,butappropriatemathematicalmodelingoftheproblemsituation.

Thesolutionandexplanationshowssomeimprecisionorerrorsinuseofmathematicalterminologyandnotation.

1 Thesolutionsuggestsaverylimitedunderstandingoftheproblemsituationandthemathematicsrequiredtosolvetheproblem.

Thesolutionplanpresentedsuggestsatentativeunderstandingofthemathematicalconceptsrequiredtosolvetheproblem.

Theexplanationsshowminimalconnectionsamongconcepts;theyalsoshowthethinkingofaninefficientproblem-solver.

Thesolutionshowserraticexecutionofthesolutionplan.Manystepsarenotpresented.

Thesolutionshowslimitedand,attimes,inappropriatemathematicalmodelingoftheproblemsituation.

Thesolutionandexplanationshowmanyerrorsintheuseofmathematicalterminologyandnotation.

0 Thesolutionsuggestsminimalunderstandingoftheproblemsituationandthemathematicsrequiredtosolvetheproblem.

Thesolutionplanpresentedsuggestsnounderstandingofthemathematicalconceptsrequiredtosolvetheproblem.

Theexplanationsshownoconnectionsamongconcepts;theyalsoshowthethinkingofanineffectiveproblem-solver.

Thesolutionshowsineffectiveexecutionofthesolutionplan.Few,ifany,stepsarepresented.

Thesolutionshowsnomathematicalmodelingoftheproblemsituation.

Thesolutionandexplanationshowsanabsenceofmathematicalterminologyandnotation.

Thisrubric,whichisbasedontheStandards for Mathematical Practice,canbeusedasaformativeassessmenttooltomonitorstudents’progresstowardsbecomingproficientmathematicalthinkers.

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Chapter 1 Solving Equations and InequalitiesLesson1-1:TheDistributivePropertyLesson1-2:SolvingMulti-StepEquationsLesson1-3:SolvingEquationswithVariables onBothSidesLesson1-4:LiteralEquationsandFormulasLesson1-5:Ratios,Rates,andConversionsACTIVITYLAB1-5a:UnitAnalysisACTIVITYLAB1-5b:AccuracyandMeasurementLesson1-6:SolvingProportionsLesson1-7:SolvingMulti-StepInequalitiesLesson1-8:CompoundInequalitiesLesson1-9:AbsoluteValueEquationsandInequalities

Chapter 2 An Introduction to Functions Lesson2-1:UsingGraphstoRelateTwoQuantitiesLesson2-2:PatternsandLinearFunctionsLesson2-3:PatternsandNonlinearFunctionsLesson2-4:GraphingaFunctionRuleTECHNOLOGYLAB2-4:GraphingFunctions andSolvingLesson2-5:WritingaFunctionRuleLesson2-6:FormalizingRelationsandFunctionsTECHNOLOGYLAB2-6:EvenandOddFunctionsLesson2-7:ArithmeticSequencesLESSONLAB2-7:TheFibonacciSequence

Chapter 3 Linear FunctionsLesson3-1:RateofChangeandSlopeLesson3-2:DirectVariationTECHNOLOGYLAB3-3:Investigatingy=mx+bLesson3-3:Slope-InterceptFormLesson3-4:Point-SlopeFormLesson3-5:StandardFormLesson3-6:SlopesofParallelandPerpendicularLinesLesson3-7:GraphingAbsoluteValueFunctions

Chapter 4 Systems of Equations and InequalitiesLesson4-1:SolvingSystemsbyGraphingTECHNOLOGYLAB4-1:SolvingSystems UsingTablesandGraphsLesson4-2:SolvingSystemsUsingSubstitutionLesson4-3:SolvingSystemsUsingEliminationLesson4-4:ApplicationsofLinearSystemsLesson4-5:LinearInequalitiesLesson4-6:SystemsofLinearInequalities

Chapter 5 Exponential and Radical FunctionsLesson5-1:ZeroandNegativeExponentsLesson5-2:ExponentialFunctionsLesson5-3:ComparingLinearand ExponentialFunctionsLesson5-4:ExponentialGrowthandDecayLESSONLAB5-4:UsingPropertiesofExponents toTransformFunctionsLesson5-5:SolvingExponentialEquationsLesson5-6:GeometricSequencesLesson5-7:CombiningFunctionsLesson5-8:SimplifyingRadicalsLesson5-9:RadicalandPiecewiseFunctions

Coordinate AlgebraTable of Contents

67

Chapter 6 Data AnalysisLesson6-1:FrequencyandHistogramsLesson6-2:MeasuresofCentralTendency andDispersionACTIVITYLAB6-2a:MeanAbsoluteDeviationLESSONLAB6-2b:StandardDeviationLesson6-3:Box-and-WhiskerPlotsLesson6-4:ScatterPlotsandTrendLinesACTIVITYLAB6-4:UsingResidualsLesson6-5:Two-WayFrequencyTables

Chapter 7 Tools of Geometry Lesson7-1:NetsandDrawingsfor VisualizingGeometryLesson7-2:Points,Lines,andPlanesLesson7-3:MeasuringSegmentsLesson7-4:MeasuringAnglesLesson7-5:ExploringAnglePairsLesson7-6:MidpointandDistance intheCoordinatePlaneLESSONLAB7-6:Quadrilateralsand OtherPolygons

Chapter 8 Transformations ACTIVITYLAB8-1:TracingPaperTransformationsLesson8-1:TranslationsACTIVITYLAB8-2:PaperFoldingandReflectionsLesson8-2:ReflectionsLesson8-3:RotationsACTIVITYLAB8-3:SymmetryTECHNOLOGYLAB8-4:ExploringMultipleTransformationsLesson8-4:CompositionsofIsometries

Chapter 9 Connecting Algebra and GeometryLesson9-1:PerimeterandAreaintheCoordinatePlaneLESSONLAB9-1:PartitioningaSegmentLesson9-2:AreasofParallelogramsandTrianglesLesson9-3:AreasofTrapezoids,Rhombuses,andKitesACTIVITYLAB9-4:ProvingSlopeCriteriaforParallelandPerpendicularLinesLesson9-4:PolygonsintheCoordinatePlane

Aligned to the Common Core

Georgia Performance

Standards and Curriculum

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Chapter 1 Reasoning and ProofLesson1-1:BasicConstructionsLesson1-2:PatternsandInductiveReasoningLesson1-3:ConditionalStatementsLesson1-4:BiconditionalsandDefinitionsLesson1-5:DeductiveReasoningLesson1-6:ReasoninginAlgebraandGeometryLesson1-7:ProvingAnglesCongruent

Chapter 2 Proving Theorems About Lines and Angles Lesson2-1:LinesandAnglesLesson2-2:PropertiesofParallelLinesLesson2-3:ProvingLinesParallelLesson2-4:ParallelandPerpendicularLinesLesson2-5:ParallelLinesandTrianglesLesson2-6:ConstructingParalleland PerpendicularLines

Chapter 3 Congruent Triangles Lesson3-1:CongruentFiguresLesson3-2:TriangleCongruencebySSSandSASLesson3-3:TriangleCongruencebyASAandAASLesson3-4:UsingCorrespondingParts ofCongruentTriangles ACTIVITYLAB3-5:Paper-FoldingConjecturesLesson3-5:IsoscelesandEquilateralTrianglesLesson3-6:CongruenceinRightTrianglesLesson3-7:CongruenceinOverlappingTrianglesLESSONLAB3-8:ReviewofTransformationsLesson3-8:CongruenceTransformations

Chapter 4 Proving Theorems About Triangles Lesson4-1:MidsegmentsofTrianglesLesson4-2:PerpendicularandAngleBisectorsLesson4-3:BisectorsinTrianglesLesson4-4:MediansandAltitudesLesson4-5:IndirectProofLesson4-6:InequalitiesinOneTriangleLesson4-7:InequalitiesinTwoTriangles

Chapter 5 Proving Theorems About Quadrilaterals Lesson5-1:ThePolygonAngle-SumTheoremsLesson5-2:PropertiesofParallelogramsLesson5-3:ProvingThataQuadrilateral IsaParallelogramLesson5-4:PropertiesofRhombuses,Rectangles,andSquaresLesson5-5:ConditionsforRhombuses, Rectangles,andSquaresLesson5-6:TrapezoidsandKitesLesson5-7:ApplyingCoordinateGeometryLesson5-8:ProofsUsingCoordinateGeometry

Chapter 6 Similarity Lesson6-1:RatiosandProportionsLesson6-2:SimilarPolygonsLesson6-3:ProvingTrianglesSimilarLesson6-4:SimilarityinRightTrianglesTECHNOLOGYLAB6-5:ExploringProportions inTrianglesACTIVITYLAB6-6:ExploringDilations Lesson6-5:ProportionsinTrianglesLesson6-6:DilationsLesson6-7:SimilarityTransformations

Analytic GeometryTable of Contents

69

Chapter 7 Right Triangles and Trigonometry Lesson7-1:ThePythagoreanTheoremandItsConverseLesson7-2:SpecialRightTrianglesTECHNOLOGYLAB7-3:ExploringTrigonometricRatiosLesson7-3:TrigonometryLesson7-4:AnglesofElevationandDepressionLesson7-5:AreasofRegularPolygons

Chapter 8 Circles Lesson8-1:CirclesandArcsLesson8-2:AreasofCirclesandSectorsACTIVITYLAB8-2:CirclesandRadiansLesson8-3:TangentLinesLesson8-4:ChordsandArcsLesson8-5:InscribedAnglesLesson8-6:AngleMeasuresandSegmentLengths

Chapter 9 Surface Area and Volume ACTIVITYLAB9-1: ExploringtheCircumference andAreaofaCircleLesson9-1:SurfaceAreasofPrismsandCylindersLesson9-2:SurfaceAreasofPyramidsandConesLesson9-3:VolumesofPrismsandCylindersACTIVITYLAB9-4:FindingVolumeLesson9-4:VolumesofPyramidsandConesLesson9-5:SurfaceAreasandVolumesofSpheres

Chapter 10 Properties of Exponents with Rational Exponents Lesson10-1:MultiplyingPowerswiththeSameBaseLesson10-2:MoreMultiplicationPropertiesofExponentsLesson10-3:DivisionPropertiesofExponentsLesson10-4:RationalExponentsandRadicalsACTIVITYLAB10-4:OperationswithRational andIrrationalNumbers

Chapter 11 Polynomials and Factoring Lesson11-1: AddingandSubtractingPolynomialsLesson11-2:MultiplyingandFactoringLesson11-3:MultiplyingBinomialsLesson11-4:MultiplyingSpecialCasesLesson11-5:Factoringx2+bx+cLesson11-6:Factoringax2+bx+cLesson11-7: FactoringSpecialCasesLesson11-8:FactoringbyGrouping

Chapter 12 Quadratic Functions Lesson12-1:QuadraticGraphsandTheirPropertiesTECHNOLOGYLAB12-1:FamiliesofQuadraticFunctionsLesson12-2:QuadraticFunctionsACTIVITYLAB12-2:RatesofIncreaseLesson12-3:ModelingwithQuadraticFunctionsLesson12-4:SolvingQuadraticEquationsLESSONLAB12-4:FormulaswithQuadraticExpressionsLesson12-5:FactoringtoSolveQuadraticEquationsLesson12-6:CompletingtheSquareLesson12-7:TheQuadraticFormulaandtheDiscriminantLesson12-8:ComplexNumbersLesson12-9:Linear,Quadratic,andExponentialModelsLESSONLAB12-9:AnalyzingResidualPlotsLesson12-10:SystemsofLinearandQuadraticEquationsLESSONLAB12-10:QuadraticInequalitiesLesson12-11:ANewLookatParabolasLesson12-12:CirclesintheCoordinatePlane

Chapter 13 Probability Lesson13-1:ExperimentalandTheoreticalProbabilityLesson13-2:ProbabilityDistributionsandFrequencyTablesLesson13-3:CompoundProbabilityLesson13-4:ProbabilityModelsLesson13-5:ConditionalProbabilityFormulas


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Chapter 1 Drawing Conclusions from Data Lesson1-1:AnalyzingDataLESSONLAB1-2:AnIntroduction toSummationNotationLesson1-2:StandardDeviationLesson1-3:SamplesandSurveysACTIVITYLAB1-4a:ProbabilityDistributionsLesson1-4:NormalDistributionsACTIVITYLAB1-4b:MarginofErrorACTIVITYLAB1-4c:DrawingConclusionsfromSamples

Chapter 2 Linear Equations, Inequalities, and Functions Lesson2-1:SolvingEquationsLesson2-2:SolvingInequalitiesLesson2-3:LinearFunctionsand Slope-InterceptFormLesson2-4:FamiliesofFunctionsLesson2-5:AbsoluteValueFunctionsandGraphsLESSONLAB2-5:PiecewiseFunctionsLesson2-6:Two-VariableInequalitiesLesson2-7:SolvingSystemsofEquationsLesson2-8:SystemsofInequalities

Chapter 3 Quadratic Functions and Equations Lesson3-1:QuadraticFunctionsandTransformationsLesson3-2:StandardFormofaQuadraticFunctionLESSONLAB3-2:IdentifyingQuadraticDataLesson3-3:FactoringQuadraticExpressionsLesson3-4:QuadraticEquationsLesson3-5:CompletingtheSquareLesson3-6:TheQuadraticFormula Lesson3-7:QuadraticSystemsLesson3-8:ANewLookatParabolasLesson3-9:CirclesintheCoordinatePlane

Chapter 4 Polynomials and Polynomial Functions Lesson4-1: PolynomialFunctionsTECHNOLOGYLAB4-1:EvenandOddFunctionsLesson4-2:Adding,Subtracting,and MultiplyingPolynomialsLesson4-3:Polynomials,LinearFactors,andZerosLesson4-4:SolvingPolynomialEquationsLesson4-5:DividingPolynomialsLesson4-6:TheoremsAboutRootsof PolynomialEquationsLESSONLAB4-6:UsingPolynomialIdentitiesLesson4-7: TheFundamentalTheoremofAlgebraLesson4-8:TheBinomialTheoremLESSONLAB4-8:MathematicalInductionLesson4-9:PolynomialModelsintheRealWorld Lesson4-10:TransformingPolynomialFunctions

Chapter 5 Rational Expressions and Functions Lesson5-1: SimplifyingRationalExpressionsLesson5-2:MultiplyingandDividingRationalExpressionsLesson5-3:AddingandSubtractingRationalExpressionsLesson5-4:InverseVariationTECHNOLOGYLAB5-5:GraphingRationalFunctionsLesson5-5:TheReciprocalFunctionFamilyLesson5-6:RationalFunctionsandTheirGraphsTECHNOLOGYLAB5-6:ObliqueAsymptotesLesson5-7: SolvingRationalEquationsACTIVITYLAB5-7a:SystemswithRationalEquationsTECHNOLOGYLAB5-7b:RationalInequalities

Advanced AlgebraTable of Contents

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Chapter 6 Radical Expressions and Functions Lesson6-1: RootsandRadicalExpressionsLesson6-2:MultiplyingandDividing RadicalExpressionsLesson6-3:BinomialRadicalExpressionsLesson6-4:RationalExponentsLesson6-5:SolvingSquareRootand OtherRadicalEquationsLesson6-6:FunctionOperationsLesson6-7: InverseRelationsandFunctionsLesson6-8:GraphingRadicalFunctions

Chapter 7 Exponential and Logarithmic Functions Lesson7-1: ExploringExponentialModelsLesson7-2: PropertiesofExponentialFunctionsLesson7-3: LogarithmicFunctionsasInversesLesson7-4:PropertiesofLogarithmsLesson7-5: ExponentialandLogarithmicEquationsTECHNOLOGYLAB7-5:UsingLogarithmsforExponentialModelsLesson7-6:NaturalLogarithmsLESSONLAB7-6:ExponentialandLogarithmicInequalities

Chapter 8 Trigonometric Functions Lesson8-1:ExploringPeriodicDataLesson8-2:AnglesandtheUnitCircleLesson8-3:RadianMeasureLesson8-4:TheSineFunctionTECHNOLOGYLAB8-4:GraphingTrigonometricFunctionsLesson8-5:TheCosineFunctionLesson8-6:TheTangentFunctionLesson8-7:TranslatingSineandCosineFunctionsLesson8-8:ReciprocalTrigonometricFunctionsLesson8-9:TrigonometricIdentities

Chapter 9 Sequences and Series Lesson9-1: MathematicalPatternsLesson9-2: ArithmeticSequencesLesson9-3: GeometricSequencesLesson9-4: ArithmeticSeriesACTIVITYLAB9-5:GeometryandInfiniteSeriesLesson9-5: GeometricSeries

Chapter 10 Applying Geometric Concepts Lesson10-1:ApplyingConstructionsLesson10-2:SolvingDensityandDesignProblemsLesson10-3:PerimetersandAreasofSimilarFiguresLesson10-4:TrigonometryandAreaLesson10-5:GeometricProbabilityLesson10-6:SpaceFiguresandCrossSectionsLesson10-7:AreasandVolumesofSimilarSolidsLesson10-8:Locus:ASetofPoints


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Georgia High School Mathematics

Program Components

Georgia Student Worktext• Write-InStudentEditionpromotespersonalizedengagement

• StandardsforMathematicalPracticeinfusedthroughouteachlesson

• UnderstandingbyDesign®*Framework• Leveledpracticeandproblem-solvingexercises

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Georgia Teacher’s Guide• 5-StepLessonStructure:InteractiveLearning,GuidedInstruction,LessonCheck,Practice,AssessandRemediate

• MathBackground,withcorrelationstotheCommonCoreGeorgiaPerformanceStandardsprovidedatthechapterandlessonlevel

• Scaffoldingquestionsthroughouteverylessonengagestudentsinhigher-orderthinking

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Georgia Implementation Guide• OverviewofCommonCoreGeorgiaPerformanceStandards

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• StandardsCorrelations• NextGenerationAssessmentResources• StandardsforMathematicalPracticeObservationalTool

• ParentLetter• PerformanceTaskRubric• AuthorMonographs• DepthofKnowledgeResources

Editable Teaching Resources • ProblemSolving(editable)• LeveledPracticeFormGandK(editable)• Reteaching(editable)• ELL/VocabularySupport(editable)• Activities,Games,andPuzzles• StandardizedTestPrep• Enrichment(editable)• LessonQuiz• FindtheErrors• TeachingwithTITechnology• PerformanceTasks• ChapterProject• AnswerKeys

Assessment Resource Book• Availableinprintandonline• Diagnostic,Formative,andSummative• ScreeningTest• ChapterQuizformGandK• WeeklyCommonCorePractice• CommonCoreExtended ConstructedResponse

• ChapterTestformGandK• EndofCourseTest• BenchmarkTestsalignedto theCommonCoreGeorgia PerformanceStandards

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Digital Courseware on Pearson SuccessNet® Includes:

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• VocabularywithaudioinEnglishandSpanish

• SelfCheckQuizzes•MathTools—OnlineGraphingUtility,InteractiveNumberLine,AlgebraTiles,2DGeometricConstructor,3DGeometricConstructor

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Virtual Nerd™—step-by-step tutorials for every lesson

Homework Video Tutors in English and Spanish

Online Lesson Planner • Pre-madeplansalignedtotheCommonCoreGeorgiaPerformanceStandardsforeverylesson

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• DiagnosticTests,BenchmarkTests,ChapterTests,LessonQuizzes

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