project based learning (pbl) grade: 6...2011/08/21 · course name: project‐based learning (pbl)...
TRANSCRIPT
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CURRICULUMMANAGEMENTSYSTEM
MONROETOWNSHIPSCHOOLS
CourseName:PROJECT‐BASEDLEARNING(PBL)Grade:6
Foradoptionbyallregulareducationprograms BoardApproved:Month,2011asspecifiedandforadoptionoradaptationbyallSpecialEducationProgramsinaccordancewithBoardofEducationPolicy#2220.
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TABLEOFCONTENTSMonroeTownshipSchoolsAdministrationandBoardofEducationMembers Page….3
Acknowledgments Page…..4
DistrictVision,Mission,andGoals Pages….5
Introduction/Philosophy/EducationalGoals Page….6
CoreCurriculumContentStandards Page….7
ScopeandSequence Pages….8‐11
Goals/EssentialQuestions/Objectives/InstructionalTools/Activities Pages….12‐22
Benchmarks Page…..23
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MONROE TOWNSHIP SCHOOL DISTRICT
ADMINISTRATION
Dr.KennethR.Hamilton,Superintendent
Dr.JeffC.Gorman,AssistantSuperintendent
Ms.SharonM.Biggs,AdministrativeAssistanttotheDistrictSuperintendent
BOARDOFEDUCATIONMs.KathyKolupanowich,BoardPresidentMr.KenChiarella,BoardVicePresident
Ms.AmyAntelisMr.MarvinI.Braverman
Mr.LewKaufmanMr.MarkKleinMr.JohnLeary
Mr.LouisC.MastersMr.IraTessler
JamesburgRepresentativeMs.PatriceFaraone
STUDENTBOARDMEMBERSMr.JonathanKimMs.‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
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ACKNOWLEDGEMENTS
ThefollowingindividualsareacknowledgedfortheirassistanceinthepreparationofthisCurriculumManagementSystem:
WRITERS’NAMES
Laurie Pike & Maria Steffero
MATHEMATICSCURRICULUMINCHARGE(9‐12)
<Content Supervisor>
TECHNOLOGYSTAFF
Eliot Feldman Al Pulsinelli
Reggie Washington
SECRETARIALSTAFF
Debby Gialanella Gail Nemeth
Karen Rucando
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MONROETOWNSHIPSCHOOLS
VISION,MISSION,ANDGOALS
VisionStatement
TheMonroeTownshipBoardofEducationcommitsitselftoallchildrenbypreparingthemtoreachtheirfullpotentialandtofunctioninaglobalsocietythroughapreeminenteducation.
MissionStatement
TheMonroePublicSchoolsincollaborationwiththemembersofthecommunityshallensurethatallchildrenreceiveanexemplaryeducationbywell‐trainedcommittedstaffinasafeandorderlyenvironment.
Goals
Raiseachievementforallstudentspayingparticularattentiontodisparitiesbetweensubgroups.
Systematicallycollect,analyze,andevaluateavailabledatatoinformalldecisions.
Improvebusinessefficiencieswherepossibletoreduceoveralloperatingcosts.
Providesupportprogramsforstudentsacrossthecontinuumofacademicachievementwithanemphasisonthosewhoareinthemiddle.
Provideearlyinterventionsforallstudentswhoareatriskofnotreachingtheirfullpotential.
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PHILOSOPHY
MonroeTownshipSchoolsarecommittedtoprovidingallstudentswithaqualityeducationresultinginlife‐longlearnerswhocansucceedinaglobalsociety.Themathematicsprogram,gradesK‐12,ispredicatedonthatbeliefandisguidedbythefollowingsixprinciplesasstatedbytheNationalCouncilofTeachersofMathematics(NCTM)inthePrinciplesandStandardsforSchoolMathematics,2000.First,amathematicseducationrequiresequity.Allstudentswillbegivenworthwhileopportunitiesandstrongsupporttomeethighmathematicalexpectations.Second,acoherentmathematicscurriculumwilleffectivelyorganize,integrate,andarticulateimportantmathematicalideasacrossthegrades.Third,effectivemathematicsteachingrequiresthefollowing:a)knowingandunderstandingmathematics,studentsaslearners,andpedagogicalstrategiesb)havingachallengingandsupportiveclassroomenvironmentandc)continuallyreflectingonandrefininginstructionalpractice.Fourth,studentsmustlearnmathematicswithunderstanding.Astudent'spriorexperiencesandknowledgewillactivelybuildnewknowledge.Fifth,assessmentshouldsupportthelearningofimportantmathematicsandprovideusefulinformationtobothteachersandstudents.Lastly,technologyenhancesmathematicslearning,supportseffectivemathematicsteaching,andinfluenceswhatmathematicsistaught.
AsstudentsbegintheirmathematicseducationinMonroeTownship,classroominstructionwillreflectthebestthinkingoftheday.Childrenwillengageinawidevarietyoflearningactivitiesdesignedtodeveloptheirabilitytoreasonandsolvecomplexproblems.Calculators,computers,manipulatives,technology,andtheInternetwillbeusedastoolstoenhancelearningandassistinproblemsolving.Groupwork,projects,literature,andinterdisciplinaryactivitieswillmakemathematicsmoremeaningfulandaidunderstanding.Classroominstructionwillbedesignedtomeetthelearningneedsofallchildrenandwillreflectavarietyoflearningstyles.
Inthischangingworldthosewhohaveagoodunderstandingofmathematicswillhavemanyopportunitiesanddoorsopentothemthroughouttheirlives.Mathematicsisnotfortheselectfewbutratherisforeveryone.MonroeTownshipSchoolsarecommittedtoprovidingallstudentswiththeopportunityandthesupportnecessarytolearnsignificantmathematicswithdepthandunderstanding.
EDUCATIONALGOALS
Havingevolvedfrommedicalandengineeringschoolmodels,“Project‐BasedLearning”isaninquiry‐based,hands‐oncurriculumthroughwhich“studentsdesignandconstructsimpleand/orcomplexinvestigationswhichrequirethemtogather,analyze,andinterpretdatatoreporttheirfindings”(NMSA2008).EndorsedandsupportedbytheNationalMiddleSchoolAssociation,Project‐BasedLearningfacilitatesstudentautonomy,engagesactivelearningwith21stCenturySkills,andconnectstotheappropriategrade‐levelCommonCoreStateStandardsinmathematicsencompassingTheNumberSystem,RatioandProportionalRelationships,Geometry,StatisticsandProbability,andExpressionsandEquations.
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NJDOE: CORE CURRICULUM CONTENT STANDARDS
A note about Common Core State Standards for Mathematics TheCommonCoreStateStandardsforMathematicswereadoptedbythestateofNewJerseyin2010.ThestandardsreferencedinthiscurriculumguiderefertothesenewstandardsandmaybefoundintheCurriculumfolderonthedistrictservers.AcompletecopyofthenewCommonCoreStateStandardsforMathematicsandtheendofyearalgebra1testcontentstandardsmayalsobefoundat:
i.e. http://www.corestandards.org/the-standards i.e. http://www.achieve.org/AlgebraITestOverview
SCOPEANDSEQUENCE:
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QuarterI – Project1:EXPLORINGTHEMOON!BigIdea:Modeling
Domains:Ratio&ProportionalRelationships,Geometry,Statistics,andExpressions&Equations
I. HISTORYOFNASA&LUNARSCIENCE
II. RATIOCONCEPTS&PROPORTIONALREASONING(6.RP.1,6.RP.2,6.RP.3)a. Solverealworldandmathematicalproblems
i. DistancetotheMoonii. DiameteroftheMooniii. ReapingRocks
b. Useratiolanguagetodescribearelationshipbetweentwoquantities;ratioa:bwithb≠0c. Understandunitrateanduseratelanguagetodescribearatiorelationship
III. DESCRIPTIVESTATISTICS(6.SP.3,6.SP.4,6.SP.5)
a. Relatethechoiceofmeasuretotheshapeofthedataandthecontexti. RegolithFormationii. ImpactCratersiii. MoonAnomalies
b. Displaynumericaldatainavarietyofwaysc. Summarizenumericaldata
i.Reportnumberofobservationsii.Describenatureofattributesiii.Measuresofcenter:mean,median,modeiv.Measuresofvariability:interquartilerangeand/ormeanabsolutedeviationv.Describeoverallpatternsorstrikingdeviation
**ForAcceleratedProgramStudents(8thGrade8.SP.1,8.SP,2,8.SP.3)d. Investigatepatternsofassociationinbivariatedata
i. Constructandinterpretscatterplotsforbivariatemeasurementdatatoinvestigatepatternsofassociationii. Knowthatstraightlinesarewidelyusedtomodelrelationshipsiii. Usetheequationofalinearmodeltosolveproblemsinthecontext,interpretingtheslopeandintercept.
SCOPEANDSEQUENCE:
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QuarterI – Project1:EXPLORINGTHEMOON!IV. GEOMETRY:AREA,SURFACEAREA,ANDVOLUME(6.G.1,6.G.2,6.G.3,6.G.4)
a. Modelrealworldproblemswith2‐Dand3‐Dgeometryi. ApolloLandingSitesii. LavaFlowsiii. LavaLayeringiv. Biosphereconstructions
b. Drawpolygonsinthecoordinateplanec. Findsurfaceareaofthreedimensionalfigures
V. ARITHMETICTOALGEBRAICEXPRESSIONS(6.EE.1,6.EE.2)
a. Writeandevaluatenumericalexpressionsb. Write,read,andevaluateexpressionsusinglettersfornumbersc. *AcceleratedProgramStudents:analyzetherelationshipusinggraphsandtables(8.EE.1,8.EE.3,8.EE.4,8.EE.5)
i. Knowandapplythepropertiesofintegerexponentsii. Estimateverylargeorverysmallquantitieswithscientificnotationiii. Performoperationswithnumbersexpressedinscientificnotation,iv. Graphproportionalrelationships,interpretingtheunitrateastheslopeofthegraph.
SCOPEANDSEQUENCE:
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QuarterII–Project2:CHARITYEVENT!BigIdea:Representation
Domains:TheNumberSystem,Statistics,andProbabilityI. WHOLENUMBEROPERATIONS(6.NS.2,6.NS.4)
a. GreatestCommonFactor(GCF)&LeastCommonMultiple(LCM)
II. FRACTIONOPERATIONS(6.NS.1)*PizzaProblems*a. MultiplyandDivide
i. Interpretationii. Computationiii. Modelingiv. StoryProblems:PizzaProblem(s)
III. RATIONALNUMBERSREPRESENTATIONS&COMPARISONS(6.NS5,6.NS.6,6.NS.7,6.NS.8)
VI. RATIOCONCEPTS&REASONING(6.RP.1,6.RP.2,6.RP.3)‐*Event/BudgetPlanningProblems*
a. Useratiolanguagetodescribearelationshipbetweentwoquantities;ratioa:bwithb≠0b. Understandunitrateanduseratelanguagetodescribearatiorelationshipc. Solverealworldandmathematicalproblems
i.Maketablesofequivalentratios,findmissingvalues,andplotpairsonacoordinateplaneii.Solveunitrateproblems
iv. Findpercentofaquantityasarateperhundredv. Useratioreasoningtoconvertmeasurements
V. PROBABILITY(7.SP.5‐8)*CarnivalGames*
a. Eventchancebetween0and1(7.SP.5)b. TheoreticalandExperimentalprobability(7.SP.6)c. Compoundprobability(7.SP.7,7.SP.8)d. Developprobabilitymodelusingfrequencies(7.SP.7)e. Organizecompoundprobability(7.SP.8):AreaModels,Tables,Lists,TreeDiagrams,Simulationsf. Designandapplyasimulationtogeneratefrequenciesforcompoundevents.(7.SP.7,7.SP.8.c)
SCOPEANDSEQUENCE:
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EssentialQuestionsforMathematics Doesthismakesense? Whyismathematicsimportant?
EnduringUnderstandingsforMathematics Amathematicianissomeonewhoreasons,perseveres,argues,convinces,andcollaborates. Mathematicsisaspecializedlanguagethatallowsustocommunicateourintentionsclearlyandefficiently.
CommonCoreMathematicalPractices1. Makesenseofproblemsandpersevereinsolvingthem.2. Reasonabstractlyandquantitatively.3. Constructviableargumentsandcritiquethereasoningofothers.4. Modelwithmathematics.5. Useappropriatetoolsstrategically.6. Attendtoprecision.7. Lookforandmakeuseofstructure.8. Lookforandexpressregularityinrepeatedreasoning.
BIGIDEAI:
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PROJECTI:EXPLORINGTHEMOON!Domain(s):RatioandProportionalRelationships,Geometry,Statistics,Expressions&Equations
CurriculumManagementSystemCOURSENAME:Project‐BasedLearning(PBL)
ESSENTIAL QUESTIONS Howdowe“model”withmathematics? Howdoweusetoolsappropriatelyandwithprecision? Whatproblemscanmoonexplorationhelpuswithnowandinthefuture?
SUGGESTEDDAYSFORINSTRUCTION:45(1QUARTER)
PROJECTCALENDAR(1Quarter=9weeks=45days)IntroductiontoPBL!Expectations&Procedures
Expectations&Procedures(continued)*AdministerPBLPre‐Assess.
HistoryofNASAandLunarScience–pre‐assessment
1. DistancetotheMoon–scalemodel
2. DiameteroftheMoon–scalemodel
Skills–RatioandProportion 3. ReapingRocks–describe,classify,andpredict
4. TheLunarDisk–describe,compare,andclassify
5. ApolloLandingSites–locatewithcoordinatesystem
6. RegolithFormation–modelcomparison
Skills–CoordinatePlane,MeasuresofCenter
7. LunarSurface– scalemodel
LunarSurface(cont.)–comparemodelswithclass
8. Differentiation 9. ImpactCraters – datacollection
ImpactCraters(cont.)–dataanalysisandsharingresults
Skills–Geometry(Circumference&Area)&Algebra(linearmodel)
10. LavaFlows– datacollection
LavaFlows– dataanalysisandsharingresults
11. LavaLayering
Mid‐QuarterPortfolioorganization&check
12. LunarLandingSite–teamduties&background
LunarLandingSite–spacecraftdesignandplanning
LunarLandingSite–spacecraftdesignandplanning
LunarLandingSite– classpresentations
Skills–similarityandscale,geometricareaformulas
13. LunarRovingVehicle 14. MoonAnomalies– team“dilemmas”
MoonAnomalies– team“dilemmas”(cont.)
MoonAnomalies– team“dilemmas”‐presentations
15. LunarLandUse–SocraticSeminar
LunarLanduse(cont.) LunarLandUse– (cont.) LunarLandUse– councilpresentations
LunarLandUse– councilpresentations
Skills–3‐Dgeometry 16. Settlementchoices(Air,Elect.,Comm.Food,etc.)
SettlementCommitteework SettlementCommitteeWork 17. LunarBiosphereMobiles
LunarBiosphereMobiles LunarBiosphereMobiles Presentations PortfolioReflectionsandPBLPost‐Assessment
FinalQuarterPortfolio
BIGIDEAI:
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KNOW UNDERSTAND DOStudentswillknowthat: Studentswillunderstandthat: Studentswillbeableto:
VOCABULARY:scale,diameter,ratio,proportion,geologist,mineral,rock,igneous,sedimentary,metamorphic,anorthosite,basalt,soil,breccia,latitude,longitude,coordinates,Descartes,regolith,weathering,erosion,crater,rille,mare,ray,terrain,differentiation,density,magma,impact,ejecta,angle,levee,pressure,stratigraphy,earthquake,moonquake,RichterScale,magnitude,biosphere
Modelinglinksclassroommathematicsandstatisticstoeverydaylife,work,anddecision‐making.Modelingistheprocessofchoosingandusingappropriatemathematicsandstatisticstoanalyzeempiricalsituations,tounderstandthembetter,andtoimprovedecisions.Quantitiesandtheirrelationshipsinphysical,economic,publicpolicy,social,andeverydaysituationscanbemodeledusingmathematicalandstatisticalmethods.Whenmakingmathematicalmodels,technologyisvaluableforvaryingassumptions,exploringconsequences,andcomparingpredictionswithdata.
SampleConceptualUnderstandingsSource:“ImpactCraters”Exploring the Moon -- A Teacher's Guide with Activities, NASA, p. 70
CalculatethedistancebetweenscalemodelsoftheEarthandmoonCalculatethediameteroftheMoonusingproportions
Makepredictionsabouttheoriginoflunarrocksbyfirstcollecting,describing,andclassifyingneighborhoodrocks
Carefullylookat,describe,andlearnabouttheoriginsofthesixlunarsamplescontainedinthedisk.
Scalemodelshelpusunderstandphysicalrelationshipsandmakepredictions;scalefactorisusedtodilatefigures
LearnaboutthelocationsandgeologyofthesixApollolandingsites
Ratioandproportionalreasoningcanbeusedtosolverealworldproblems
ComparetheprocessofregolithformationofEarthandontheMoon
Asetofdatahasadistributionthatcanbedescribedbyitscenter,spread,andoverallshape
MakeamodeloftheMoon’ssurfaceandtoconsiderthegeologicprocessesandrocksofeacharea
Numericaldatacanbeplottedinavarietyofways,includingnumberline,dotplots,histograms,andboxplots;*bivariatedatacanbeplottedandanalyzedusingscatterplots*accelerated
Seehowmineralsseparatefromeachotherinamagmaocean
BIGIDEAI:
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KNOW UNDERSTAND DOStudentswillknowthat: Studentswillunderstandthat: Studentswillbeableto:
Areaoftrianglesandpolygonscanbefoundbycomposingintorectanglesordecomposingintotrianglesandothershapes;Areasofcircles
Determinethefactorsaffectingtheappearanceofimpactcratersandejecta.
Theconstructionofashapeisdependentonthesideandanglemeasurements.
Understandsomeofthegeologicalprocessesandthestructuresthatformaslavaflowsacrossplanetarylandscapesbyusingmudasananalogforlava
Measurementsrequireattendancetoprecisionanduseofappropriatetools
Learnaboutthestratigraphyoflavaflowsproducedbymultipleeruptions
Avariablecanrepresentanunknownnumberoranynumberinaspecifiedset;variablesareusedtorepresentnumbersinexpressionswhensolvingareal‐worldormathematicalproblem
DesignaspacecraftfortraveltoandfromtheMoonandchooseaninterestinglunarlandingsite
Real‐worldormathematicalproblemscanbesolvedbywritingandsolvingequations
Investigateandtrytoexplainvariouslunaranomaliesusingstatisticalanalysis
Propertiesofintegerexponents.Scientificnotationisanabbreviatedformofexpressingverylargeorverysmallnumbers.*accelerated
DesignadevelopmentontheMoonthatissuitable,feasible,andbeneficial
Buildabiospherethatisabalanced,self‐enclosedlivingsystemabletorunefficientlyoveraperiodoftime
BIGIDEAI:
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21stCenturySkills
CreativityandInnovation CriticalThinkingandProblemSolving Communicationand CollaborationInformationLiteracy MediaLiteracy ICTLiteracyLifeandCareerSkills TechnologyBasedActivitieshttp://www.p21.org/index.php?option=com_content&task=view&id=254&Itemid=119http://www.iste.org/standards/nets‐for‐students.aspx
LearningActivities
ConceptActivities:Pleaseseeresourcesinhttp://www.nasa.gov/pdf/58199main_Exploring.The.Moon.pdfPerformanceAssessmentTaskSample Pleaseseeresourcesin http://www.nasa.gov/pdf/58199main_Exploring.The.Moon.pdf
AssessmentModels
NOTE:Theassessmentmodelsprovidedinthisdocumentaresuggestionsfortheteacher.Iftheteacherchoosestodevelophis/herownmodel,itmustbeofequalorbetterqualityandatthesameorhighercognitivelevels(asnotedinparentheses).
Dependingupontheneedsoftheclass,theassessmentquestionsmaybeansweredintheformofessays,quizzes,mobiles,PowerPoint,oralreports,booklets,orotherformatsofmeasurementusedbytheteacher.
Pre‐Assessment/Diagnostic: Pleasedistributethe“PBLPre‐andPost‐AffectiveAssessment”bothbeforeandaftereachmajorproject. Teacherscanassigndiagnosticmeasures(KWL,pre‐test,donow)toassessstudentpriorknowledgeoflunarscience,ratioand
proportionalreasoning,mathematicalmodeling,scaledrawings,measuresofcentraltendencyandvariability,graphingonthecoordinateplane,2‐Dareaandperimetercalculations,and3‐Dvolumecalculations
Open‐Ended(Formative)Assessment: Groupandindividualworkisassigneddaily,fromvarioussources(Synthesis,Analysis,andEvaluation). IntroductoryandClosingActivitieswillbedoneeverydaytopre‐assessstudentknowledgeandassessunderstandingoftopics
(Synthesis,Analysis,andEvaluation).Summative Assessment: Assessment questions should be open‐ended and should follow the general format illustrated in the Essential Questions/Sample Conceptual
Understanding section. (Synthesis, Analysis, Evaluation) Studentswillbegivenquizzesthatprovideabriefreviewoftheconceptsandskillsinthepreviouslessons. Studentswillberesponsibleformaintainingandprovidingevidenceofunderstandingintheir“projectportfolios”
BIGIDEAI:
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Additional
Resources TeachermadePerformanceAssessmentTasks(PATs)
ReleasedPATsOnlineStateresourcesNASA“ExploringtheMoon”EducatorResourceshttp://www.nasa.gov/audience/foreducators/topnav/materials/listbytype/Exploring.the.Moon.html
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PROJECTII:CHARITYEVENT!Domain(s):TheNumberSystem,Probability,andStatistics
CurriculumManagementSystemCOURSENAME:Project‐BasedLearning(PBL)
ESSENTIAL QUESTIONS Howdowe“model”withmathematics? Howdoweusetoolsappropriatelyandwithprecision? Howcanmathematicsbeusedtopredictordrawconclusionswithintherealworld? Howdowejudgeifsomethingis“fair”?
SUGGESTEDDAYSFORINSTRUCTION:45(1QUARTER)
PROJECTCALENDAR(1Quarter=9weeks=45days)IntroductiontoPBL!Expectations&Procedures
Expectations&Procedures(continued)*AdministerPBLPre‐Assessment*
CharityEventProjectOverviewandPre‐assessment
1. EventProposalRequirementsProjectRoles
Skills– PrimeFactorization,GCF,LCM
2.GCFProblem–ConcessionProblemshttp://www.ixl.com/math/grade‐6/greatest‐common‐factor‐word‐problems
3.LCM–ConcessionProblemshttp://www.ixl.com/math/grade‐6/greatest‐common‐factor‐word‐problems
4.PizzaProblemFractions
PizzaProblemQuizLCM,GCF,PrimeFactorization
Skills‐ Convertingbetweenfractionsdecimalsandpercents
5.EventBudgetWorksheetQuiz–fraction,decimal,percent
Skills–ratio,rate,unitprice,proportionhttp://www.ixl.com/math/grade‐6/unit‐rates‐and‐equivalent‐rates
6.ConcessionMenu/Prices ConcessionMenu/pricesQuiz–Ratio,Proportion
7.Powerpoint
Skills–combinationhttp://www.ixl.com/math/grade‐6/combinations
Skill‐permutationhttp://www.ixl.com/math/grade‐6/permutations
8.EventMap UpdatePowerpoint 9.PlayCarnivalGame–experimentalandtheoreticalprobability
Mid‐QuarterPortfolioorganization&check
Skill‐simpleprobability,samplespace,experimental,theoretical,lineplot,fair,unfair,certain,impossible
10.DesignCarnivalgame–Supplies,rules,theoreticalprobabilities,chargetoplayandexpectedpayout
Createandtestcarnivalgame–Experimentalprobability
DesignCarnivalgame–Supplies,rules,theoreticalprobabilities,chargetoplayandexpectedpayout
Createandtestcarnivalgame–Experimentalprobability
DesignCarnivalgame– Supplies,rules,theoreticalprobabilities,chargetoplayandexpectedpayout
Createandtestcarnivalgame–Experimentalprobability
DesignCarnivalgame–Supplies,rules,theoreticalprobabilities,chargetoplay
Createandtestcarnivalgame–Experimentalprobability
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andexpectedpayout
DesignCarnivalgame–Supplies,rules,theoreticalprobabilities,chargetoplayandexpectedpayout
Createandtestcarnivalgame–Experimentalprobability
Quiz– ProbabilityPowerpoint
11.OverallEventProfitProjections
OverallEventProfitProjections
PortfolioReflectionsandSelf‐Assessment
PreparationforPanelPresentation PreparationforPanelPresentation
PreparationforPanelPresentation
PreparationforPanelPresentation
PreparationforPanelPresentation
Presentations Presentations FinalGroupEvaluation*PBLPostAssessment
FinalQuarterPortfolio
KNOW UNDERSTAND DOStudentswillknowthat: Studentswillunderstandthat: Studentswillbeableto:
VOCABULARY: LCM, GCF, prime factorization, ratio, rate, unit rate, proportion, unit price, combination, permutation, experimental probability, theoretical probability, sample space, certain event, possible event, expected value, line plot
Modelinglinksclassroommathematicsandprobabilitytoeverydaylife,work,anddecision‐making.Modelingistheprocessofchoosingandusingappropriatemathematicstoanalyzeempiricalsituations,tounderstandthembetter,andtoimprovedecisions.MathematicsisaspecializedlanguagethatwecanusetocommunicateourideasclearlyandefficientlyNumberscanbeexpressedinavarietyofwayswithequalvalues.Probabilityofachanceeventisbetween0and1thatexpressesthelikelihoodoftheeventoccurring.Thereareavarietyofwaystocalculateprobability,boththeoreticalandexperimental.
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). The student will use greatest
common factor to solve real world-world problems
The student will use least common multiple to solve real world-world problems.
Apply prime factorization to solve real world problems.
- The student will define greatest common factor.
The student will convert an improper fraction to a mixed number.
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KNOW UNDERSTAND DOStudentswillknowthat: Studentswillunderstandthat: Studentswillbeableto:
- The student will define least common multiple. - The student will define prime factorization. - The student will know that a number can be expressed in different forms.
Aratioisamultiplicativecomparisonoftwoquantities,oritisajoiningoftwoquantitiesinacomposedunit.Inaproportion,theratiooftwoquantitiesremainsconstantasthecorrespondingvaluesofthequantitieschange.SAMPLE CONCEPTUAL UNDERSTANDING Within their carnival game, there will be many
opportunities for students to determine experimental probability. They will use the results to set the price to play and determine the long-term payout for their game!
See What Do You Expect? Investigations 3 & 4 Suppose Nishi has a 60% free-throw percentage and is in a one-and-one free-throw situation 100 times during the season. a. How many times can she expect to score 0 points?
1 point? 2 points? b. What total number of points do you expect Nishi
to score in 100 situations at the free-throw line? c. What would Nishi’s average number of points
(expected value) per situation be?
The student will convert between fractions, decimals, and percents.
Thestudentwillunderstandtheconceptofratioandbeabletouseratiolanguagetodescribeaquantitativerelationship.Thestudentwillbeabletounderstand,interpret,andapplytheconceptofunitrate.Ratioandproportionalreasoningcanhelpsolvereal‐worldandmathematicalproblems.A ratio is a comparison of two amounts and that a proportion expresses equivalent ratios
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape
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KNOW UNDERSTAND DOStudentswillknowthat: Studentswillunderstandthat: Studentswillbeableto:
diagrams, double number line diagrams, or equations.
Probabilityofachanceeventisanumberbetween0and1thatexpressesthelikelihoodoftheeventoccurring.Probabilityallowsustomakepredictions.Methodsofcounting(likecombinationandpermutation)helpdeterminesamplespace.
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
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KNOW UNDERSTAND DOStudentswillknowthat: Studentswillunderstandthat: Studentswillbeableto:
Use methods of counting to determine sample space (*use combination and permutations)
Using thoughts, ideas, and conceptual understanding efficiently, accurately and in a compelling manner will enhance the oral or written presentation through the use of technology
Present a proposal for the charity event including technology and answer panel questions.
21stCenturySkills
CreativityandInnovation CriticalThinkingandProblemSolving CommunicationandCollaborationInformationLiteracy MediaLiteracy ICTLiteracyLifeandCareerSkills TechnologyBasedActivitieshttp://www.p21.org/index.php?option=com_content&task=view&id=254&Itemid=119http://www.iste.org/standards/nets‐for‐students.aspx
LearningActivities
Technology:seebelowforuseofpresentationsoftwarePerformanceAssessmentTaskSample Throughout the project, students will use advanced features and utilities of presentation software (e.g.,
design templates, design layouts (fonts/ colors/ backgrounds) animation and graphics, inserting pictures, objects, movies, sound, charts, hyperlinks, and graphs) to create an original product with their carnival game.
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AssessmentModels
NOTE:Theassessmentmodelsprovidedinthisdocumentaresuggestionsfortheteacher.Iftheteacherchoosestodevelophis/herownmodel,itmustbeofequalorbetterqualityandatthesameorhighercognitivelevels(asnotedinparentheses).
Dependingupontheneedsoftheclass,theassessmentquestionsmaybeansweredintheformofessays,quizzes,mobiles,PowerPoint,oralreports,booklets,orotherformatsofmeasurementusedbytheteacher.
Pre‐Assessment/Diagnostic: Pleasedistributethe“PBLPre‐andPost‐AffectiveAssessment”bothbeforeandaftereachmajorproject. Teacherscanassigndiagnosticmeasures(KWL,pre‐test,donow)toassessstudentpriorknowledgeofGCF,LCM,fractions,decimals,
percents,andprobability.Open‐Ended(Formative)Assessment: Groupandindividualworkisassigneddaily,fromvarioussources(Synthesis,Analysis,andEvaluation). IntroductoryandClosingActivitieswillbedoneeverydaytopre‐assessstudentknowledgeandassessunderstandingoftopics
(Synthesis,Analysis,andEvaluation).Summative Assessment: Assessment questions should be open‐ended and should follow the general format illustrated in the Essential Questions/Sample Conceptual
Understanding section. (Synthesis, Analysis, Evaluation) Studentswillbegivenquizzesthatprovideabriefreviewoftheconceptsandskillsinthepreviouslessons. Studentswillberesponsibleformaintainingandprovidingevidenceofunderstandingintheir“projectportfolios”
Additional
Resources
TeachermadePerformanceAssessmentTasks(PATs)ReleasedPATs
HowLikelyIsIt? WhatDoYouExpect?(ParticularlyInvestigations3&4)
OnlineResource;SeetheBuckInstituteforEducationhttp://www.bie.org/“StepRightUpforaGoodCause”http://wveis.k12.wv.us/teach21/public/project/Guide.cfm?upid=3314&tsele1=2&tsele2=106
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COURSENAME:PROJECT‐BASEDLEARNING(PBL)MATHEMATICS
1. Modelinglinksclassroommathematicsandstatisticstoeverydaylife,work,anddecision‐making.
2. Modelingistheprocessofchoosingandusingappropriatemathematicsandstatisticstoanalyzeempiricalsituations,tounderstandthembetter,andtoimprovedecisions.
3. Quantitiesandtheirrelationshipsinphysical,economic,publicpolicy,social,andeverydaysituationscanbemodeledusingmathematicalandstatisticalmethods.
4. Whenmakingmathematicalmodels,technologyisvaluableforvaryingassumptions,exploringconsequences,andcomparingpredictionswithdata.
5. Mathematicsisaspecializedlanguagethatwecanusetocommunicateourideasclearlyandefficiently
6. Numberscanbeexpressedinavarietyofwayswithequalvalues.
7. Probabilityofachanceeventisbetween0and1thatexpressesthelikelihoodoftheeventoccurring.
8. Thereareavarietyofwaystocalculateprobability,boththeoreticalandexperimental.
9. Aratioisamultiplicativecomparisonoftwoquantities,oritisajoiningoftwoquantitiesinacomposedunit.
10. Inaproportion,theratiooftwoquantitiesremainsconstantasthecorrespondingvaluesofthequantitieschange.