OntarioeSecondarySchool CourseOutline–MDM4U:MathematicsofDataManagementPage1of10

OntarioeSecondarySchoolCourseOutline2018-2019

MinistryofEducationCourseTitle:MathematicsofDataManagement,UniversityPreparation

MinistryCourseCode:MDM4U

CourseType:UniversityPreparation

Grade:12

CreditValue:1.0

Prerequisite(s):Functions,Grade11,UniversityPreparation

Department:Mathematics

Coursedevelopedby:MuhammadHamzaQureshi

Date:August2018

Length:OneSemester

Hours:110

ThiscoursehasbeendevelopedbasedonthefollowingMinistrydocuments:1. TheOntarioCurriculum,Grades11and12Mathematics,Revised2007

OntarioeSecondarySchool CourseOutline–MDM4U:MathematicsofDataManagementPage2of10 COURSEDESCRIPTION/RATIONALEThiscoursebroadensstudents’understandingofmathematicsasitrelatestomanagingdata.Studentswillapplymethodsfororganizingandanalysinglargeamountsofinformation;solveproblemsinvolvingprobabilityandstatistics;andcarryoutaculminatinginvestigationthatintegratesstatisticalconceptsandskills.Studentswillalsorefinetheiruseofthemathematicalprocessesnecessaryforsuccessinseniormathematics.Studentsplanningtoenteruniversityprogramsinbusiness,thesocialsciences,andthehumanitieswillfindthiscourseofparticularinterest.

OVERALLCURRICULUMEXPECTATIONSUnit1Bytheendofthiscourse,studentswill:

1. Solveproblemsinvolvingtheprobabilityofaneventoracombinationofeventsfordiscretesamplespaces;

2. Solveproblemsinvolvingtheapplicationofpermutationsandcombinationstodeterminetheprobabilityofanevent.

Unit2Bytheendofthiscourse,studentswill:

1. Identifyabroadrangeofoptionsforpresentandfuturelearning,work,andcommunityinvolvement2. Demonstrateanunderstandingofdiscreteprobabilitydistributions,representthemnumerically,

graphically,andalgebraically,determineexpectedvalues,andsolverelatedproblemsfromavarietyofapplications;

3. Demonstrateanunderstandingofcontinuousprobabilitydistributions,makeconnectionstodiscreteprobabilitydistributions,determinestandarddeviations,describekeyfeaturesofthenormaldistribution,andsolverelatedproblemsfromavarietyofapplications.

Unit3Bytheendofthiscourse,studentswill:

1. Demonstrateanunderstandingoftheroleofdatainstatisticalstudiesandthevariabilityinherentindata,anddistinguishdifferenttypesofdata;

2. Describethecharacteristicsofagoodsample,somesamplingtechniques,andprinciplesofprimarydatacollection,andcollectandorganizedatatosolveaproblem.

Unit4Bytheendofthiscourse,studentswill:

1. Analyse,interpret,anddrawconclusionsfromone-variabledatausingnumericalandgraphicalsummaries;

2. Analyse,interpret,anddrawconclusionsfromtwo-variabledatausingnumerical,graphical,andalgebraicsummaries;

3. Demonstrateanunderstandingoftheapplicationsofdatamanagementusedbythemediaandtheadvertisingindustryandinvariousoccupations.

Unit5Bytheendofthiscourse,studentswill:

1. Designandcarryoutaculminatinginvestigation*thatrequirestheintegrationandapplicationoftheknowledgeandskillsrelatedtotheexpectationsofthiscourse;

2. Communicatethefindingsofaculminatinginvestigationandprovideconstructivecritiquesoftheinvestigationsofothers.

OntarioeSecondarySchool CourseOutline–MDM4U:MathematicsofDataManagementPage3of10

COURSECONTENTUnit Length

Unit1:CountingandProbability 28hoursUnit2:ProbabilityDistributions 24hoursUnit3:OrganizationofDataforAnalysis 16hoursUnit4:StatisticalAnalysis 30hoursUnit5:CulminatingDataManagementInvestigation 12hours Total 110Hours

UNITDESCRIPTIONSUnit1-CountingandProbability

§ Solvingprobabilityproblemsinvolvingdiscretesamplespaces§ Solvingproblemsusingcountingprinciples

Unit2-ProbabilityDistribution

§ Understandingprobabilitydistributionsfordiscreterandom§ Understandingprobabilitydistributionsforcontinuousrandomvariables

Unit3-OrganizationofDataforAnalysis

§ Understandingdataconcepts§ CollectingandOrganizingdata

Unit4-StatisticalAnalysis

§ Analysingone-variabledata§ Analysingtwo-variabledata§ Evaluatingvalidity

Unit5-CulminatingDataManagementInvestigation

§ Designingandcarryingoutaculminatinginvestigation§ Presentingandcritiquingtheculminatinginvestigation

OntarioeSecondarySchool CourseOutline–MDM4U:MathematicsofDataManagementPage4of10

TEACHINGANDLEARNINGSTRATEGIESThestudentswillexperienceavarietyofactivities:

Teacherdemonstrations(researchskills,etc.)throughvideoconferencing,email,ortelephoneconversationswithsubjectteacher,orvideosprovidedofateacherorstudentdemonstratingtheconceptsandskillsbeingstudied.Thishelpsthestudentandteachercreateanatmosphereoftrustandrespecttoaidintheonlinelearningenvironment.

Videopresentationsandtechnologicalaids(research)withvideosembeddedtoenrichthecoursecontentandclarifyconceptsandskillsbeingstudied.Alsotheuseofonlinepre-approvedquizzesandgamestohelpastudentbecomemorefamiliarwiththeconceptsandskillsbeingstudied.

Diagnosticandreviewactivities(audioandvideotaping)canbestudent-leadorteacherleadtoworkasareviewforstudentsthroughaudioandvideomadetoshareamongeachothertohelpreinforcetheconceptsandskillsbeingstudied.

Brainstorming,chartsandgraphsareagreatwayforstudentstodemonstratetheirknowledgeofsubjectmatterthroughgraphicorganizers,pictures,andtexts.ThisiscommunicatedthroughassignmentsinMoodle.

SmallGroupActivities

Theteachersetsupsmallgroupactivitiestoprovideopportunitiesforactiveandorallearningaswellastobolsterpracticalcommunicationandteamworkskills.Theteacherplaysacriticalroleduringgroupactivitiesbymonitoringgroupprogressaswellasansweringquestionsthatariseandusingquestionstoassiststudentsintheirunderstanding.Inthisway,theteacheralsofacilitatesstudentunderstandingofeffectivelearning,communication,andteambuildingduringgroupactivities.

Thesmallgroupactivitiesincludethefollowing:

Practicalextensionandapplicationofknowledgeisusedasaneffectivelearningstrategyinthiscoursebecauseitallowsthestudentstoreadandlistentothetextsandstoriesandreflectbackwithconnectionstothemselves,othertextsandtheworld.Studentsareencouragedtosharetheirunderstandingsthroughworksubmittedeachday,phoneconversationsaboutcoursework,orvideoconferencing.

Oralpresentationsinanonlineenvironmentwehavetheequipmenttohavestudenteitherlivevideoconferenceoralpresentations,ormakevideosandsubmitthemfortheiroralpresentations.Theseoralpresentationscanbeviewedbyfellowstudents(whenappropriate)andtheteacher.Studentscanlearnfromoneanother,andfromtheirteacher.Suchactivitiesincludedramaticreadingsandperformances.

Chartsandgraphsareusedtopresenteffectivelearningopportunitiesofconceptsandskillstostudentswhowouldbenefitfromvisualobjectstolearn.Everystudentlearnsdifferently,anditisusedtohelpstudentsdiscoveranotherwaytopresenttheirinformationsuchasgraphicorganizers,lists,andpictures.

IndividualActivities

Theteachershouldprovideavarietyofindividualassignmentstoexpandandconsolidatethelearningthattakesplaceinthewhole-classandsmallgroupactivities.Individualactivitiesallowtheteachertoaccommodateinterestsandneedsandtoaccesstheprogressofindividualstudents.Theteacherplaysanimportantroleinsupportingtheseactivitiesthroughtheprovisionofongoingfeedbacktothestudents,bothorallyandinwriting.Teachersareencouragedtoincludeindividualactivitiessuchasthefollowinginthecourse:

OntarioeSecondarySchool CourseOutline–MDM4U:MathematicsofDataManagementPage5of10 Researchiscompletedinanonlineenvironmentbyteachingthestudentsfirstaboutplagiarismrulesandgivingexamplesofgoodsourcestouse.Thestudentsarenotonlylimitedtotheonlinesearchforinformation,buthaveresourcesavailablebylinksontheMoodlepageofinformationthathasbeenscannedanduploaded.

Individualassignmentsareworkedonatastudent’sownpace.Theteachercansupportthestudentintheseactivitieswithongoingfeedback.

Oralpresentationsarefacilitatedthroughtheuseofvideoconferencingandvideorecording.

Practicalextensionandapplicationofknowledgehelpsstudentsdeveloptheirownvoice,andgivesthemtheabilitytomakepersonalconnections,andconnectionstotheworldthroughouttheircourse.Studentsaregivenavarietyorreadingandviewingtextstogivethemmanychancestoapplytheirnewconcepts,skills,andknowledge.

OngoingprojectworkissomethingthatisvaluedintheearningofanEnglishcredit.Theongoingprojectcanbesubmittedtotheteacherforongoingfeedbackinbothwrittenandoralwork.

Readingstudentsareabletoreadavarietyoftextsonline.Thestudentsmayprintoutthereadingmaterialtouseittohighlight,takenotes,andhavewiththemwhenacomputerisnotavailable.

Writtenassignmentsareusedtoallowstudentstodeveloptheirskillsinwriting,comprehension,andcommunication.Withtheonlineformatstudentssubmittheirwork,andhaveachancetogetfeedbackfromtheteacher,andsubmittheirbestwork.Thiscanbedemonstratedwithreadingresponses,personalwriting,reportwriting,essaywriting,scriptwriting,businessandtechnicalwriting,andindividualresearchassignments.

ASSESSMENT,EVALUATION,ANDREPORTINGAssessment:Theprocessofgatheringinformationthataccuratelyreflectshowwellastudentisachievingtheidentifiedcurriculumexpectations.Teachersprovidestudentswithdescriptivefeedbackthatguidestheireffortstowardsimprovedperformance.Evaluation:AssessmentofLearningfocusesonEvaluation,whichistheprocessofmakingajudgementaboutthequalityofstudentworkonthebasisofestablishedcriteriaoveralimited,reasonableperiodoftime.Reporting:InvolvescommunicatingstudentachievementofthecurriculumexpectationsandLearningSkillsandWorkHabitsintheformofmarksandcommentsasdeterminedbytheteacher’suseofprofessionaljudgement.

STRATEGIESFORASSESSMENTAssessmentpracticescannurturestudents’senseofprogressandcompetencyandinformationinstruction.Manydiagnostictools,e.g.checklistsandinventories,areusedatregularintervalsthroughouttheunitstoencouragestudents’understandingoftheircurrentstatusaslearnersandtoprovidefrequentandtimelyreviewsoftheirprogress.Assessmentofstudentacquisitionoflisteningandtalking,readingandviewingandwritingskillsalsooccursregularlythroughunobtrusiveteacherobservationandconferencing.

Unitsconcludewithperformancetasks,e.g.,interviewsandfromessaysthatbuildtowardsandpreparestudentsfortheend-of-courseculminatingtaskinUnitFive.Teachersareencouragedtosharegoalswithstudentsearlyinthecourseandtoconnectunitlearningexperiencesfrequentlyandexplicitlywithbigideas,overallexpectations,andperformancetasks,i.e.checkbricks;teacher-adaptedgenericrubrics

OntarioeSecondarySchool CourseOutline–MDM4U:MathematicsofDataManagementPage6of10 availableinmanysources,includingtheOntarioSecondarySchoolLiteracyCourse(OSSLC)Profile,sothattheyaremoretask-specific.Theteachermightask:“Whatdoesthecriterialooklikeforthisparticulartask?”Or“Whatdoeslimitedeffectivenesslooklike?”Theteachercouldinvolvestudentsinthediscussion,modification,orcreationofrubrics,andteachstudentstouserubricsasalearningtoolthatcansupportthewritingprocessandpractice.

ASSESSMENTACTIVITIESq Homeworkassignmentsq Individualconferencemeetingsq DiscussionForumsq Diagnostictestsandwritingtasksq Free-writingjournals/blogsq Outliningandplanningsheetsq CompletedTemplates&GraphicOrganizersq EditingChecklistsq Reflectionsq Oralpresentations&ActiveListeningq Tests&Examq EssayWritingq Evaluations

EVALUATIONThefinalgradewillbedeterminedasfollows:

q Seventypercentofthegradewillbebasedonevaluationconductedthroughoutthecourse.Thisportionofthegradeshouldreflectthestudent’smostconsistentlevelofachievementthroughoutthecourse,althoughspecialconsiderationwillbegiventomorerecentevidenceofachievement.

q Thirtypercentofthegradewillbebasedonafinalevaluationadministeredatortowardstheendofthecourse.Thisevaluationwillbebasedonevidencefromoneoracombinationofthefollowing:anexamination,aperformance,anessay,and/oranothermethodofevaluationsuitabletothecoursecontent.Thefinalevaluationallowsthestudentanopportunitytodemonstratecomprehensiveachievementoftheoverallexpectationsforthecourse.

(GrowingSuccess:Assessment,EvaluationandReportinginOntarioSchools.OntarioMinistryofEducationPublication,2010p.41)

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Weightings

CourseWork 70Knowledge/Understanding 17.5Thinking/Inquiry 17.5Communication 17.5Application

17.5

Final 30FinalExam 30

TERMWORKEVALUATIONS(70%):EvaluationItem Description Category

Reflectiveresearchprojects

Research-basedprojectsforunits1through4withafocusonapplicationofknowledgetoreal-worldsituationsandfinancialliteracy.Suchas“AMarkedImprovement”,“Fill’erup”and“PieAnyone?”

K,T,C,A

Problemsets Problemsetssupplementlessonsandareusedtoassesswhetherornotstudentsaremeetingcriteriaforsuccess

K,T,C,A

Simulation/interview Liveinterviewsareusedtoevaluatestudentsthroughobservationandconversation.Someoftheseareapartofotherresearchprojects.

K,T,C,A

UnitTest(s) Unittestsarebasedoncurriculumexpectationsandcovertheentiretyofeachunit

K,T,C,A

FINALEVALUATIONS(30%):EvaluationItem Description Category

CulminatingProject Unit5ofthiscourse(describedabove)isaculminatingproject.

K,T,C,A

FinalExam Afinal,writtenexamination,coveringallcurriculumexpectationsforthecourse.

K,T,C,A

AFL/AAL/AOLTrackingsheet:Unit1:CountingandProbability–28hours AAL AFL AOL

OntarioeSecondarySchool CourseOutline–MDM4U:MathematicsofDataManagementPage8of10 Lesson1.2NotesandProblemsSetsAssignment

Lesson1.1ProbabilityandOddsForum

CountingStoriesProject

Lesson1.5Pascal’sTriangleForum

Lesson1.1NotesandProblemsSetsAssignment

Unit1CulminatingAssignment

Lesson1.6NotesandProblemsSetsAssignment

Lesson1.3NotesandProblemsSetsAssignment

CombinationsQuiz Lesson1.4NotesandProblems

SetsAssignment

Lesson1.5NotesandProblemsSetsAssignment

Lesson1.6MutuallyExclusivevsIndependentEventsForum

LiveInterviewassignment Unit2:ProbabilityDistributions–24hoursAAL AFL AOLLesson2.2NotesandProblemsSetsAssignment

Lesson2.1NotesandProblemsSetsAssignment

Fill’erupProject

Lesson2.4NotesandProblemsSetsAssignment

Lesson2.3NotesandProblemsSetsAssignment

Lesson2.5NotesandProblemsSetsAssignment

Lesson2.4UniformProbabilityDistributionsForum

Lesson2.6GeometricDistributionsForum

Lesson2.6NotesandProblemsSetsAssignment

Lesson2.7NotesandProblemsSetsAssignment

Unit3:OrganizationofDataforAnalysis–16hoursAAL AFL AOLLesson3.2SamplingTechniques Lesson3.1NotesandProblems

SetsAssignmentSamplingBiasProject

Lesson3.3NotesandProblemsSetsAssignment

Lesson3.2NotesandProblemsSetsAssignment

Lesson3.4NotesandProblemsSetsAssignment

Lesson3.4HistogramForum

Lesson3.5NotesandProblemsSetsAssignment

Lesson3.6NotesandProblemsSetsAssignment

Unit4:StatisticalAnalysis–40hoursAAL AFL AOLLesson4.2NotesandProblemsSetsAssignment

Lesson4.1NotesandProblemsSetsAssignment

Lesson4.3NotesandProblemsSetsAssignment

Lesson4.3Measuresofspread,StandardDeviation,andVarianceForum

Unit4projects–“MarkedImprovement”and“PieAnyone?”

Lesson4.5PercentilesandQuartilesForum

Lesson4.4NotesandProblemsSetsAssignment

Lesson4.5NotesandProblems Lesson4.6NotesandProblems

OntarioeSecondarySchool CourseOutline–MDM4U:MathematicsofDataManagementPage9of10 SetsAssignment SetsAssignmentFinalsAOLCulminatingProjectFinalExam

CONSIDERATIONFORPROGRAMPLANNING

Studentslearnbestwhentheyareengagedinavarietyofwaysoflearning.Guidanceandcareereducationcourseslendthemselvestoawiderangeofapproachesinthattheyrequirestudentstoresearch,thinkcritically,workcooperatively,discussrelevantissues,andlearnthroughpracticeinavarietyofsettings.Helpingstudentsbecomeself-directed,lifelonglearnersisafundamentalaimoftheguidanceandcareereducationcurriculum.Whenstudentsareengagedinactiveandexperientiallearningstrategies,theytendtoretainknowledgeforlongerperiodsanddevelopmeaningfulskills.Activeandexperientiallearningstrategiesalsoenablestudentstoapplytheirknowledgeandskillstoreal-lifeissuesandsituations. ANTIDISCRIMINATIONEDUCATIONINGUIDANCEANDCAREEREDUCATIONClassroom teachers are the key educators of students who have special education needs. They have aresponsibility to help all students learn, and they work collaboratively with special education teachers,where appropriate, to achieve this goal. Special Education Transformation: The Report of the Co-ChairswiththeRecommendationsoftheWorkingTableonSpecialEducation,2006endorsesasetofbeliefsthatshouldguideprogramplanningforstudentswithspecialeducationneedsinalldisciplines.Thosebeliefsareas follows: All students can succeed. Universal design and differentiated instruction are effective andinterconnectedmeansofmeetingthe learningorproductivityneedsofanygroupofstudents.Successfulinstructionalpracticesarefoundedonevidence-basedresearch,temperedbyexperience.PROGRAMCONSIDERATIONSFORENGLISHLANGUAGELEARNERSOntarioschoolshavesomeofthemostmultilingualstudentpopulationsintheworld.Thefirstlanguageofapproximately20percentof thestudents inOntario’sEnglish languageschools isa languageother thanEnglish. Ontario’s linguistic heritage includes several Aboriginal languages; many African, Asian, andEuropean languages; and some varieties of English, such as Jamaican Creole. Many English languagelearnerswereborninCanadaandraisedinfamiliesandcommunitiesinwhichlanguagesotherthanEnglishwere spoken, or inwhich the variety of English spokendiffered significantly from the English ofOntarioclassrooms.OtherEnglishlanguagelearnersarriveinOntarioasnewcomersfromothercountries;theymayhaveexperienceofhighlysophisticatededucationalsystems,ortheymayhavecomefromregionswhereaccess to formal schooling was limited.When they start school in Ontario,many of these students areenteringanewlinguisticandculturalenvironment.THEROLEOFTECHNOLOGYINTHEENGLISHPROGRAMInformationandcommunicationstechnologies (ICT)providearangeof tools thatcansignificantlyextendand enrich teachers’ instructional strategies and support students’ language learning. ICT tools include

OntarioeSecondarySchool CourseOutline–MDM4U:MathematicsofDataManagementPage10of10 multimediaresources,databases,Internetwebsites,digitalcameras,andword-processingprograms.Toolssuchasthesecanhelpstudentstocollect,organize,andsortthedatatheygatherandtowrite,edit,andpresent reports on their findings. Information and communications technologies can also be used toconnectstudentstootherschools,athomeandabroad,andtobringtheglobalcommunityintothelocalclassroom.Whenever appropriate, therefore, students should be encouraged to use ICT to support andcommunicatetheirlearning.ACCOMMODATIONSAccommodationswillbebasedonmeetingwithparent,teachers,administrationandexternaleducationalassessmentreport.Thefollowingthreetypesofaccommodationsmaybeprovided:

q Instructionalaccommodations:suchaschangesinteachingstrategies,includingstylesofpresentation,methodsoforganization,oruseoftechnologyandmultimedia.

q Environmentalaccommodations:suchaspreferentialseatingorspeciallighting.q Assessmentaccommodations:suchasallowingadditionaltimetocompletetestsorassignmentsor

permittingoralresponsestotestquestions.

Otherexamplesofmodificationsandaids,whichmaybeusedinthiscourse,are:

q Providestep-by-stepinstructions.q Helpstudentscreateorganizersforplanningwritingtasks.q Recordkeywordsontheboardoroverheadwhenstudentsareexpectedtomaketheirownnotes.q Allowstudentstoreportverballytoascribe(teacher/student)whocanhelpinnotetaking.q Permitstudentsarangeofoptionsforreadingandwritingtasks.q Whereanactivityrequiresreading,provideitinadvance.q Provideopportunitiesforenrichment.