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  • Sixth Grade Mathematics

    Curriculum Essentials Document

    Boulder Valley School District Department of Curriculum and Instruction

    May 2009

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  • SixthGradeMathematicsCurriculumEssentialsMay2009 2

    BoulderValleySchoolDistrictSixthGradeMathematicsCurriculumEssentialsDocument

    DistrictAHelayneJones,[email protected]:303.245.5815fax:303.545.6477

    DistrictBVicePresidentLesleySmith,[email protected]:303.245.5814

    DistrictCLaurieAlbright,[email protected]:303.245.5817

    [email protected]:303.245.5813

    [email protected]:303.245.5816

    [email protected]:303.245.5818fax:303.438.8572

    [email protected]:303.245.5819

    BVSDSuperintendentChristopherKing,[email protected]:303.447.5114fax:303.447.5134

    BoulderValleySchoolDistrictBoardofEducation

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  • SixthGradeMathematicsCurriculumEssentialsMay2009 3

    BoulderValleySchoolDistrictSixthGradeMathematicsCurriculumEssentialsDocument

    TableofContents

    GeneralIntroduction

    WhatisaCurriculumEssentialsDocument?..................................................Page5CurriculumFramework:MacroandMicro.....................................................Page6NewCenturyGraduate..............................................................................Pages78WhatareEnduringUnderstandingsandEssentialQuestions?.......................Page9TeachingforUnderstanding..........................................................................Page10WhatDoesitMeantoUnderstand?.............................................................Page11InstructionalFramework...............................................................................Page14CharacteristicsofaStandardsbasedCurriculum..................................Pages1516MiddleSchoolMathematicsEssentialLearnings...Pages1718DesignTemplates...................................................................................Pages1929CurriculumGlossary.................................................................................Page3032

    SixthGradeMathematicsCurriculumEssentials

    MathematicsBackground..............................................................................Page2MathematicsProcessStandards.....................................................................Page3MathematicsContentStandards....................................................................Page4MathematicsEnduringUnderstandingsandEssentialQuestions...................Page5SixthGradeMathematicsEssentialLearnings................................................Page6SixthGradeMathematicsCourseOverview...................................................Page7SixthGradeMathematicsCurriculumEssentials....................................Pages811SuggestedTimelines.....Page12MathematicsScopeandSequence......Pages1316MathematicsGlossaryofTerms........Pages1721

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  • SixthGradeMathematicsCurriculumEssentialsMay2009 4

    BoulderValleySchoolDistrictSixthGradeMathematicsCurriculumEssentialsDocument

    General Introduction

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  • SixthGradeMathematicsCurriculumEssentialsMay2009 5

    BoulderValleySchoolDistrictSixthGradeMathematicsCurriculumEssentialsDocument

    Becausewearefacedwithmorecontentthanwecanreasonablyaddress,weareobligatedtomakechoicesandframepriorities.Ausefulframeworkforestablishingprioritiesisgraphicallydepictedusing4nestedovals. The innermostoval,NewCenturyGraduate, represents thegoalsofschoolingthathavebeenidentifiedbytheBoulderValleySchoolDistrictcommunity.Movingtothenextoval,ContentStandards,levelsofperformanceforeachprogramofstudyareclearlyarticulated. Thethirdoval,EssentialLearnings,representstheviablecurriculum.Acurriculumisviablewhenthenumberoflearningscanbeaccomplishedinthetimeprovided(usuallyasemester,trimester,oryear).Thus,anEssentialsDocumentidentifiestheprioritiesforlearningthatarenecessaryforsuccessfullearningataparticulargradelevelorcourseandbeyond.Italsoidentifiestheessentialknowledge,skills,concepts,topics,andprocessesthatsupporttheattainmentoftheessentiallearning.Finally,thelargestovalrepresentsthefieldofallpossiblecontentthatmightbeexaminedduringagradelevelorcourse.Thisincludesextendedlearningopportunitiesforstudentswhohaveachievedtheessentiallearningsorattendingtobackgroundknowledgeandskillsthatstudentsmayneedtorevieworlearntoensureachievementofgradelevelorcourseessentiallearnings.

    WhatisaCurriculumEssentialsDocument?HowDoesitRelatetoaGuaranteedandViableCurriculum?

  • SixthGradeMathematicsCurriculumEssentialsMay2009 6

    BoulderValleySchoolDistrictSixthGradeMathematicsCurriculumEssentialsDocument

    The New Century Graduate identifies the knowledge, skills and personal characteristics that our community hasidentifiedasthegoalsofschooling.Programsofstudyandcurricularcontentareidentifiedandaddressedasameans

    Schoo

    lDistrict

    CurriculumFramework:MacroandMicroLevels

    AdaptedfromGrantWigginsandJayMcTighe(2007).SchoolingbyDesign.Alexandria,VA:AssociationforSupervisionandCurriculum

  • SixthGradeMathematicsCurriculumEssentialsMay2009 7

    BoulderValleySchoolDistrictSixthGradeMathematicsCurriculumEssentialsDocument

    New Century Graduate KnowledgeandSkills

    LifeCompetencies

    Leadsabalancedlife:exhibitsphysicalfitness,knowsgoodnutritionrules,stayssafeanddrugfree,knowshowtohavefunandrelax,managesangerandstress,exhibitsselfsufficiencyandselfconfidence,andfinishestasks.

    Understandsmoneymanagement,budgeting,balancingacheckbook,debtmanagement,andrecordkeeping.

    Demonstratestimemanagementskillsandabroadbaseofknowledgeinpracticalskillssuchascooking,sewing,driving,andmapreading.

    Knowshowtosearchforajobandknowswheretogotofindanswers.

    Communication:SpeakingandWritingWritesandspeaksthoughtfullyandarticulatelytoinform,toexpressonesthinkingandcreativity,andto

    communicatetodiverseaudiences.

    Usescorrectgrammar,spelling,andmechanics;organizesforeffectiveness

    Usestechnologyforeffectivecommunication.

    Multicultural/GlobalPerspectiveUnderstandsglobalcustoms,economics,literature,history,politics,religions,geography,anddemographics.

    Understandsthecontributionsofdifferentculturestooursociety

    DemonstratesproficiencyinalanguageotherthanEnglish.

    Literacy:ReadingReadscritically,fluently,andwithcomprehension.

    Readsforinformationresearch,pleasureandknowledgeofliterature.

    MathematicsDemonstratesbasicmathcomputationalskillsandunderstandhigherlevelmathematicalconceptsandreasoning.

    Understandsconservationandresourcemanagement.

    HistoryPossessesknowledgeofAmericanandWorldHistoriesandtheirinfluenceuponthepresentandthefuture.

    Employsliteratureasatoolforlearningabouthistoryacrosscultures.

    ScienceDemonstratesbasicsciencesknowledgeandunderstandshighlevelscientificsystemsincluding

    environmentalsystems.

    Knowshowtoapplythescientificmethodtorealsituations.

    ArtsExperiencesandappreciatesmusic,visualarts,danceandtheater.

  • SixthGradeMathematicsCurriculumEssentialsMay2009 8

    BoulderValleySchoolDistrictSixthGradeMathematicsCurriculumEssentialsDocument

    New Century Graduate PersonalCharacteristics

    RespectforOthers(ValuesOthers)Understandsandvaluesdifferencesincluding:cultural,religious,

    ethnic,gender,age,andability.

    InitiativeandCourageExhibitsselfmotivation,selfdiscipline,persistence,independence,confidence,curiosity,and

    willingnesstotakerisks,withoutbeingafraidtofail.

    CitizenshipUnderstandshisorherroleandresponsibilitiesandcontributestothecommunity,nation,andworld.

    ResponsibilityTakesresponsibilityforownthoughtsandactions,acceptingthe

    consequences.

    EthicalBehaviorExhibitspersonalintegritythroughhonesty,fairness,sincerity,andasenseofjustice.

    FlexibilityandOpenMindednessDemonstratesflexibility,openmindedness,adaptability,resiliency,andopennesstochange.

    SelfrespectPossessesselfrespectandconfidence,whilerecognizingonesownlimitations.

  • SixthGradeMathematicsCurriculumEssentialsMay2009 9

    BoulderValleySchoolDistrictSixthGradeMathematicsCurriculumEssentialsDocument

    EnduringUnderstandingsarethebigideascentraltoacontentareathathavelastingvaluebeyondtheclassroomandaretransferabletonewsituations.Enduringunderstandingsdescribewhat,specifically,studentsshouldunderstandaboutthetopic.Suchunderstandingsaregenerallyabstractinnatureandareoftennotobvious,thusrequiringuncoveringofatopicthroughsustainedinquiry.Anunderstandingcanbeoverarchingortopical.Overarchingunderstandingsarebroad(asthenameimplies)andofferapossiblebridgetootherunitsandcourses.Overarchingunderstandingsatidentifiedatthedistrictlevel.Topicalunderstandingsareunitspecific,identifiedbyteachersabouttheunderstandingstheunitwillcultivateaboutspecifictopics.EssentialQuestionsprovokedeepthought,livelydiscussion,sustainedinquiry,andnewunderstandingsculminatinginmeaningfulperformances.Theyrequirestudentstoconsideralternatives,weighevidence,supporttheirideas,andjustifyanswers.Essentialquestionsdonotyieldasinglestraightforwardanswer,butproducedifferentplausibleresponses,aboutwhichthoughtfulandknowledgeablepeoplemaydisagree.Essentialquestionssparkmeaningfulconnectionswithpriorlearningsandpersonalexperiencesandcreateopportunitiesfortransfertoothersituationsandsubjects.Anessentialquestionscanbeeitheroverarchingortopicalinscope.Overarchingessentialquestionsaregeneralinnature,causinggenuineandrelevantinquiryintothebigideasandcorecontent.Theycutacrossunitsand/orcourses.Topicalessentialquestionsfocusonaspecifictopicandmeanttobeansweredifonlyprovisionallybyunitsend.

    WhatareEnduringUnderstandingsandEssentialQuestions?