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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.