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Maths andMe –Innovative DigitalResources Maths andMe providesaccess to an extensive rangeof over2,000 fun,innovative, easy-to-useandengagingFREE InteractiveDigital Resourcesincludingeditableplanningdocumentsandafull rangeof printables. All resourcesare central to theprogrammeandintegrated into lessons,providing richlearningopportunities forchildren, by encouragingactiveparticipationandpositiveengagement.
Designedspecifically for Maths andMe,withthekeypedagogical practicesinmind,the resourcespromotemathstalk,allow for formative assessment, include cognitivelychallengingtasks,mathematical modellingandlotsmore.
The extensive rangeofdigital resourcesinclude:
n Richmultimedia resourcesengagingvideosandanimations
n Interactiveclassroomactivities
n Virtual Manipulatives
n Editableplanningdocuments
n Printables
Explainervideoshelppupils to understandkeymaths conceptsandstrategies.
Classroomactivitiessuchas Concept Cartoons, Quick Imagesand Three Act Tasksengage learners,supportkeypedagogiessuchas mathstalkandplayfullearning,helpstudents developskillssuchas reasoningandallow for formativeassessment.
eeaccess to adedicated bappwithdigital sources forpupils to use at homeorinschoolondevices.
Engaginganimations feature the MathsandMe characters in relatablemaths-based real-lifescenarios.
Anextensive range of colourfulprintable resourcescanalso beaccessedviathe platform,including MathsLanguage Cards and Manipulative Printables.
Digital resourcesare accessedthroughan easy-to-use webplatform.
DigitalResources for4th Class,Unit4:Data ScantheQR codebelow to accessaselectionofour
NewDigital Resources for Maths andMe 3rdand4thClass:
FOR A DEMO OFTHE NEW DIGITALRESOURCES Pupil’sBook Contents Note: ThecontentsshownindicatewhatisincludedinthefullPupil’sBook.
Unit1:Place Value
Unit2:Locationand Transformation
Unit3:AdditionandSubtraction
Unit4:Data
Review1
Unit5:MultiplicationandDivision1
Unit6:Time
Unit7:MultiplicationandDivision2
Review2
Unit8:Fractions
Unit9:Measuring1(Length)
Unit 10:Money
Unit11:Shape
Review3
Unit12:Decimals
Unit13:Algebra
Review4
Unit 14:Measuring2(Area)
Unit15:MoreMultiplication
Unit 16:Measuring3 (Capacityand Weight)
Unit 17:Chance
Review5
Let’s TryMore
Glossary
The MathsandMe Pupil’s Pack includesa ProgressAssessmentBooklet andthe followinginsertsto supportlearning:mini-whiteboardwithopen-numberlineon reverse,spinners(forplayinggames), cut-outPlace ValueCountersandacut-outFraction Wall.
DataDisplays Look atthebargraphandanswerthequestions.
Title: Cartonsof milk sold Mon Tue Wed Thu Fri 0102030 40
Look atthebargraphandanswer thequestions.
Title: Heightsinmy family
1. Howmanycartonsof milk were soldonMonday?
2. Whatisthedifferencebetween thegreatestandtheleast numberof cartonssold?
3. Howmanycartonsweresoldin totalthatweek?
Thinkofastrategy forquestion3that doesn’tinvolve addition.
Inthis family,Sueisthetallest, Maxistheshortest,andJack is tallerthanAmy.
1. Work outwhereeachname belongsonthebargraph. (a) (b) (c) (d)
2. HowtallisAmy? cm
Look atthepiechartandanswerthequestions.
60peoplewereaskedif theypreferred dogsorcats.Estimatehowmany peoplechose…
3. neither dogs cats neither
1. dogs
2. cats
Trythis! 1. Chooseoneof thedatadisplaysaboveandcreatealist,chartortable forthe sameinformation.
2. Explainwhichyouthink isbetterandwhy.
LinePlots Look atthelineplotandcompletethesentencesbelow.
0123 4 5
1. Themode,ormostcommonnumberof siblings,was
2. Mostchildrenintheclasshad or siblings.
4. Themediannumberof siblingswas .
Let’stalk!
DoyouagreewithJay?Whyorwhynot?
Themedian isthemiddle valueinan orderedlist.
3. Very fewchildrenintheclasshadlessthan ormorethan siblings.
Ifweasksomeone howmanysiblings theyhave,theanswer iscertaintobe2or3.
Look atthelineplotandcompletethese.
Numberof raisinsinabox
Numberof siblingsof eachchildinourclass =1child 252627282930 31
1. Themode,ormostcommonnumberof raisins,was .
2. Mostboxeshad or raisins.
3. Thenumberof raisinsinaboxranged from to .
4. boxesof raisinswerecounted.
5. Themediannumberof raisinswas .
6. Trueor false:If weopenanotherboxof raisins,itishighlylikelythatitwill contain28or29raisins?
Thesewerethenumbersof booksreadbyagroupof childrenlastmonth:
1. Drawalineplottoshowthedata.
2. Writethreequestionsaboutthedata.
DataCards Let’stalk! Chooseonedatacardanddescribetheperson,usingtheinformationgiven.
Look atthedatacardsandanswerthequestions.
1. Whatisthemostcommonwayto traveltoschool?
2. Whatistherangeof values for thetimetakentotraveltoschool?
3. Whatistherangeof values for bedtime?
4. Whatisthemedianlengthof right foot?
Look atthedatacards.Trueor false?(3)
IthinkthatIcould usethemedian valuetoprovemy answers.
1. Therearemoreleft-handedboysthanleft-handedgirls.
2. Thechildrenwhotraveltoschoolbycarhavelongertravel timesthanthosewhotraveladifferentway.
3. The5thClasschildrenaretallerthanthe 4thClasschildren.
4. The 4thClasschildrenhaveashorterright footlengththan the5thClasschildren.
5. The6thClasschildrenaretallerandhavealongerright foot lengththantheotherchildren.
6. The6thClasschildrengotobedlaterthantheotherchildren.
Trythis! 1. Whatisthemedianheightof thechildrenin…
(a) 4thclass? cm
(b) 5thclass? cm
(c) 6thclass? cm
2. Whatisthemedianheightof the…
(a) girls? cm
(b) boys? cm
Teacher’sPlanningBook ExtractContents Unit4:Data The MathsandMe Teacher’sPack containsa Teacher’s PlanningBookanda Teacher’s ResourcesBook. Alongwiththeplans foreachunit,the Teacher’s PlanningBook alsocontainsacomprehensive introductorysection featuringthe followingsections:
● How MathsandMe alignstothenewPrimaryMathsCurriculum
● AGuideto MathsandMe
● SuggestionsonSupportingthe Teachingof MathsintheClassroom
● A YearlyOverview
The MathsandMe Teacher’s ResourcesBook includesalladditionalmaterialsoutsideofplanning.A rangeofphotocopiablematerials(PCMs)willbe available,includinggeneralPCMs. Foreachunitthe followingareprovided:
● Let’sStrengthenSuggestions for Teachers
● Let’sStrengthenPCMs
● Let’sDeepenPCMs
● GamesBank
Additionally,anAnswerBookletandvariousprintables(suchasmanipulativeprintables,Maths LanguageListsandEquipmentList)arealso available.
Strand(s)>StrandUnit(s) DataandChance>Data.
LearningOutcome ( s )T hroughappropriatelyplayfulandengaginglearningexperienceschildrenshouldbeabletoposequestionsofinterestandcollect,displayandcriticallyanalysedataina ra ngeofways fo ra ra nge ofpurposesandcommunicatethefindings.
CMLearningExperiencesAssessment IntuitiveAssessment: re spondingto emerging misconceptions
D C Re ason& Re spondL1–4
D C Think-Pair-ShareL1–4
D Notice& Wo nderL1–3
D C DataIn ve stigation Cy cle–Analysis andConclusionsL3
PlannedInteractions: re spondingtoinsights gleanedfrom children’s re sponses tolearning experiences
AssessmentEvents: informationgathered fromcompletionof theunitassessmentin theProgress AssessmentBooklet page12
Print re sources
Pupil’sBookpages34–37 PCMs1–3
Lesson Fo cusofLearning(withElements) 1 DataDisplays : Interpretsdifferentdatadisplays,includingbargraphsandsimplepiecharts (C );Makesdeductionsandinferences fromexistinginformationpr ov idedindatadisplays(A&PS)
2 LinePlots : Interpretslineplots(dotgraphs)to re presentdata (C );Exploresthemedianasthevalueinthemiddleofadataset(U&C); In ve stigatesthe ra nge(i.e.themeasureusedtocapturevariabilityorspreadofthedata)ofadataset(U&C)
3 DataCards: Comparesmultipledatasamplesin vo lvingothersandthemselves(A&PS);Identifiesanddisregardssurplusinformation (U&C);Justifieswhyasetofdataiscollected,sortedand re presentedinthewaychosen(R);Evaluatesthemethodsused by peersin re presentingdata(R)
4 DataIn ve stigation: Appliesanin ve stigativecycleofproblem-posing,planning,datagathering, re presentation,analysisand conclusion(A&PS);Exploresandestablisheshowtobesthandle, re cordand re presentdata fo ragivenpurpose,includingtheuseof appropriatescalesandlegends(U&C) (C)
5 Re viewand Re flect : Re viewsand re flectsonlearning(U&C) MathsandMe :4thClass–Shor
CM:CuntasMíosúil: pleasetickwhen yo u ha ve completedthe fo cusoflearning. LearningExperiences: C concreteactivity; D digitalactivity; P activitybasedonprintedmaterials, fo llo we d by lessonnumbers.
Ke y: Elements: (U&C)UnderstandingandConnecting; (C )Communicating;(R) Re asoning;(A&PS)ApplyingandProblem-Solving.
Additionalinformation forplanning ProgressionContinua
MathsLanguage
Equipment
InclusivePractices
Integration
See‘4thClass MathsandMe ProgressionContinuaOverview’ foradetailedbreakdownofhowallprogression continuaarecovered.
See‘4thClass MathsandMe LanguageOverview’,individuallessonplansandUnit4MathsLanguageCards.
See‘4thClass MathsandMe EquipmentOverview’andindividuallessonplans.
● SeeLet’sStrengthenandLet’sDeepensuggestionsthroughoutlessonplans.
● SeeUnit4Let’sStrengthenSuggestions for Teachers. (TheseaddresstheCommonMisconceptionsand Difficultieslistedonthenextpage.)
● SeeUnit4Let’sStrengthenPCM.
● SeeUnit4Let’sDeepenPCM.
Seeindividuallessonplans.
Background and rationale ● Peopleencounterdataeverysingledayanditisoftheutmostimportancethat we developtheskillsto interactwithdataandmakesenseofit.
● Thisunitisasingle-weekblockofcontentthatwill reviewthechildren’sunderstandingofvariousdata displays(particularlylineplotsandbargraphs,which were newin3rdClass)andextendtheir understanding by introducingsimplepiechartsanddatacards.
● Alsonewto4thClass,thechildrenwillbeaskedtoidentifythemedianvalue(middlevalueinanordered list)andthe rangeofvaluesinadataset.Previouslytheyexploredthedistributionofdata(i.e.howdatais spreadinadisplay)in3rdClass.Theywill revisemode(i.e.themostcommonoutcomeoccurringvalueina dataset)andtheproportionalityofthedata(e.g.inapiechart,thesizeofeachfractionisdirectly proportionaltoitsvalue),which were alsoexploredin3rdClass.
● At thisstage,itisimportantthatchildrenbegintoappreciatethedifferencebetweencategoricaldata(e.g. eyecolour,haircolour,gender,handedness,etc.)andnumericaldata(e.g.numberssuchasheight,age, timetakentotraveltoschool,distancefromschool,etc.).Whilecategoricaldatatendstobesimplerto organiseand represent,itisimportantthatchildren workwithnumericaldataalso,because youcan calculatethemedianinanumericaldataset,butnotinacategoricaldataset,sincethosevaluescannotbe ordered.
● ApplyingtheDataInvestigation Cycle(PPDAC: Pose,Plan,Data,Analysis,Conclusion)isanessentialpart ofthelearninginthisunit,asthechildrenwillbeengaginginsomeorallofthestepsineverylesson.The childrenneedtodevelopstrategiestocollectand recordinformationusingfirst-handdata–information thattheycollectontheir own by counting,conductingsurveys/polls,conductingexperiments,and/or usingmeasuringdevices.First-handdatashould relatetothechildrenthemselves,andcanincludethe schooland/orcommunity.Ultimately,itishopedthatthechildrenwillposeanddeveloptheir own investigativequestions,collectand recorddatainanefficientandorganisedway, communicatetheir understanding by answeringandaskingquestions,andcometoaccurateandappropriateconclusions, basedonthedata.
● Asthereisa Reviewand Reflect weekimmediately followingthisunit,itis recommendedthatthechildren usesomeofthistimetoconductfurtherdatainvestigations.Itisalso recommendedthatthechildrenare providedwithmeaningfulopportunitiesthroughoutthe yeartocollect, representandinterpretdata,as partofmathsand/orothercurricularareas.
DataInvestigation Cycle(PPDAC) We typicallythinkofdataasbeingpresentedwithpremadegraphsandcharts,whichthenneedtobe read andinterpreted.Butin reallife, we allcollect,analyseanddrawconclusionsfromdataallthetime,without such representations.Babiesandchildrenareconstantlytakingininformation(data)aboutthe world aroundthem.Theirprocessingofthisdata(unconsciouslyandconsciously)isessentialtolanguageand cognitive development,decisionmaking,etc. Forexample,throughcollectingandprocessingdata, young childrenlearn:whichshapescanenterwhichholesinashapesorter;how rotatingpuzzlepiecesoften resultsinabetterfit;andhowblueand yellowpaintmixedtogethermakegreenpaint.As we getolder, we canusedatagainedthroughnewexperiencestolearnmoreaboutanyaspectofthe real world,andtohelp makeinformeddecisionsandtakeinformedaction.
Inthe real world,statisticianstypicallyusetheDataInvestigation Cycle.Thisconsistsofthefivestages involvedinprocessingdata:poseaproblem/question,plan,data,analysis,conclusion.Inexploringthestand unitofData,inallclasses,includingJuniorandSeniorInfants,itisexpectedthatthechildrenwillexperience all,orstagesof,theDataInvestigation Cycleasawaytousedatatosolve real-worldproblemsorquestions, thatare relevanttothechildren.
Investigativequestionsversussurveyquestions
Investigativequestionsarethebigquestionsthatshouldconsiderthewholesample/group,e.g. Whatare the favouriteice-creamflavoursofthechildreninourclass?
Investigativequestionsarealsooften reusedoradaptedtocreateatitle forthecompleteddatadisplay, e.g.Our favouriteice-creamflavours.
Surveyquestions(ifbeingused)usuallyevolvefromtheinvestigativequestionandare rephasedtobeasked ofanindividual respondent,e.g. Whatisyour favouriteice-creamflavour?
Poseaquestion Askaninvestigativequestionthatis interesting, relevant, worthinvestigating andisanswerable.Invitethechildrento posequestionsthattheyfindinteresting, whilealsoguidingthemtowardsselecting questionsthatwillbe feasibletoanswer.
● Whatdo we wanttofindout?
● Whatisthequestion we wanttoanswer?
● Isitaninterestingquestion?
● Isitananswerablequestion?
● Isit worthanswering?
● Howwill we findouttheanswer?
Posea Question
Plan Discussanddecidewhatdataneeds tobecollectedandhowitwillbe collected,e.g.whoandwhatistobe involved,whereandhowthisistobe done.
Thismayalsoinvolvedevelopinga surveyquestion(i.e.thequestionto beaskedofindividuals)inorderto collectthedataneededtoanswerthe investigativequestion.
Predictlikely/possibleanswer(s)based onwhatisalreadyknown.
Data Collectthedata forthechosen investigativequestion(s) by answering thesurveyquestion(s).Thedatais recordedaccordingtotheplan(e.g. usingafrequencytable,usingphysical cubes/images,tallymarks).
Analysis
Analysethedistributionand rangeof thedata.
Decidethebestwaytopresent/display thecollecteddata.
Readthedata, readbetweenthedata, readbeyondthedata.
Writeormakedescriptivestatements aboutthedata.
Conclusion
Sharethefindings.
Answertheoriginalinvestigative questionposed.
Evaluatethe reliabilityofthefindings. Comparethedatatotheinitial predictions.
Considerwhatfurtheractionsarenow requiredorwhatnewquestioncould nowbeposed;indoingso,startthe cycleagain.
● Howcan we findout?
● Whatshould we do?
● Whatdatado we needtocollect?(whatareour variables,i.e.whatare we measuring?)
● Whoshould we collectitfrom?(i.e.our population,who we ask/survey)
● Whowillcollectthedata?Where? Forhowlong?
● Howwill we recordandorganisethedata? (Whatsurveyquestion?Howwill we present thechoices/questions?Howwillthedatabe gathered/recorded?)
● Whatdo youthink we willfindout?
Collectthedataasplanned.
● Isthecollecteddataorganised?
● Isthecollecteddataclearandeasyto read?
Lookatthedatacarefully.
● Whatdo younotice?
● Whatarethegreatestandleastvalues?
● Howmight we displaythedata forothers?
● Whatgraph(andscale) wouldbemostsuitable?
● Whattitle?Labels?A key?
● Describetheshapeofthedata.Whatdoesittell us?(E.g.wheredoesmostofthedatalie/cluster? To theleft,rightorinthemiddle?Arethereany gaps?)
● Whatarethefindings?Whatdotheytellus?
● Havewe answeredtheoriginal(investigative) question?
● Whatisinterestingorsurprisingaboutthe findings?
● Arethereanypatterns?
● Howaccurateand reliablearethefindings?
● Whomightbeinterestedinthesefindings? Explainwhy.
● Howcouldthefindingsbesharedwithawider audience?
● Do we have anyunansweredornewquestions?
Forauthenticdatacollectionandanalysistotakeplace,theremustbeanauthenticproblemorquestion, onewhosesolution/answerisnotobviousorpredetermined.Thismeansthatthewaythedatacollection andanalysisprocessevolvesineachclassroomwillbeasindividualasthechildreninthat room. Forthe teacher, thisunpredictabilitybringsits ownchallenges,e.g.allowingthechildrenthefreedomtoinvestigate their ownquestionsandtotrytheirchosenmethods,evenif wewould rejectthequestions forbeing unanswerable,or rejectthemethodsasbeingineffectiveorinefficient.
WhiletheDataInvestigation Cycleisdescribedsequentially,the realitymayoftenbe‘messier’,wherethe childrenmaymove forwardsandbackwardsthroughstagesandmaygoaroundthecyclemorethanonce. Furthermore,dependingonthescopeofthespecificquestionbeinginvestigated,theDataInvestigation Cyclemay ‘fit’inonelesson,orthestagesmaybespread overanumberoflessons.And,dependingon theneedsoftheclass,theteachermaychooseaparticularstagetobethe focusofaspecificlesson. For example,whilethe focusofanyunitondatashouldnotsolelybeonansweringquestionsonmanufactured graphsanddatasets,itmaysometimesbeappropriatetospendtimedevelopingthesedataandanalysis skills,aspartof(orinpreparation for)predesignedtasksandassessments.
Commonmisconceptions anddifficulties ● Thechildrenmanymiscountormisinterpretsymbols,talliesorscales.
● Theymaystrugglewithcomparing,i.e.identifyinghowmanymore/fewerchoseXthan Y, or preferredXto Y.
● Theymaynotappreciatetheimportanceofthe‘rules’governingthecreationofthedifferentgraph types(e.g.accuracyandconsistencyinorganisationandpresentation,consistentsizeandspacing, andtheinclusionofagraphtitle,labelsanda key/legend).
● Theymaystruggletodrawaccuratelyandneatlythevariousgraphtypes.
● Theymayincorrectlyassumethatonesymbol,block,interval,etc.,always representsoneitem. (Encouragethemtoalwayslookcarefullyatthe featuresthattellusaboutthevaluesinthegraph− scale, key, symbols,etc.)
● Theymayneedextrasupportwiththe keytopic-specificlanguage(i.e.bargraph,pictogram,line plot,piechart, key, mode,median, range).
TheUnit4Let’sStrengthenSuggestions for Teachersaddressthecommonmisconceptionsand difficultieslistedabove.
Mathematicalmodels and representations ● Blockgraphs
● Tallycharts
● Bargraphs
● Pictograms
● Lineplots
● Piecharts(informaluse)
● Datacards
● Representationsofvariousitems withinpictograms Teachingtip
Adatacardsmanipulativeprintableis availabletosupportthisunit.Clickonthe resourcesicononthe MathsandMe bookcoveron edcolearning.ie
Title: Cartonsof milk
Day1,Lesson1 DataDisplays Focusoflearning(withElements) ● Interpretsdifferentdatadisplays,includingsimplepiecharts (C)
● Makesdeductionsandinferencesfromexistinginformationprovidedindatadisplays(A&PS)
Digitalactivity:SameButDifferent:DataDisplays
MAM Routines: Reason& Respond,withThink-Pair-Share
Digitalactivity:Slow-RevealData(1) MAM Routines:Notice& Wonder,withThink-Pair-Share; Reason& Respond
Pupil’sBookpage34:DataDisplays
● data,pictogram,bargraph,tally,piechart,symbol(s),categories,label(s),title,interval,scale,mode, compare,survey,howmany, altogether,total,more/less/fewer…than…,most,greatest,least
Teachingtip Thislesson focusesspecificallyontheAnalysisand ConclusionstepsoftheDataInvestigation Cycle (PPDAC: Pose,Plan,Data,Analysis,Conclusion),in whichthechildrenareenabledtoanalyseand drawconclusionsfromdatathathasalreadybeen collectedanddisplayedinvariousways.
Teachingtip Throughouttheunit, remindthechildrento reflectonthedata,analyseitandexplainhowit mightbeused(e.g.topredicttrendsormostlikely responsesfromasimilargroupof respondents, andsoon).
Warm-up D Digitalactivity:SameButDifferent:Data Displays MAM Routines: Reason& Respond, withThink-Pair-Share
UsingThink-Pair-Share,playtheslideshowandask thechildrentosuggest reasons forwhytheimages arethesameordifferent.Ifnotsuggested,prompt themto refertothe featuresofthedisplays,suchas scale,interval,andthecorrespondenceused(i.e. to-oneormany-to-one),andtouselanguagesuchas more,less,etc.(seeUnit4MathsLanguageabove). Askthemalsotosuggest reasons forwhymany-toonecorrespondenceissometimesused ratherthan one-to-onecorrespondence.
Teachingtip Whilethechildrenhave not yetbeen formally introducedtopiecharts,theyshouldstillbeable toidentifysimilaritiesanddifferencesbetween thedatadisplayed,identifythe featuresofthe
variousdatadisplays,andusetheirknowledgeof proportionanddistributionofdataongraphsto estimatethevalues.
Teachingtip Thechildren were introducedtobargraphsin3rd Class.Abargraph(alsoknownasabarchart)isa graphthatuseshorizontalor verticalbarsto displaydata.Itneedstohave atitle,anda horizontalanda verticalaxis(bothlabelled–one withthecategories,andtheotherwiththe intervalscalenumberedattheintervallines rather thanatthespaces).Sinceatprimarylevel,the databeinggraphedisgenerallydiscretedata (dataobtained by countinginwholenumbers), therearealwaysspacesleftbetweenthebars.If thereisnodata foracategory(i.e.thevalueis0), aspacecanbeleftwhereabar wouldhave been placed,butthisisnotessential.
Mathslanguage
D Digitalactivity:Slow-RevealData(1)
Mainevent MAM Routines:Notice& WonderwithThinkPair-Share
Displaythefirstslideandask:
● Whatdo younotice?Whatdo you wonder?
● Whatdo youthinkismissing?(Dothey recognise thatthisisagraph,andcantheyidentifythe featuresofthegraphthatshouldhave been given?)
UseThink-Pair-Sharetocollect feedback.Whenthe feedbackhasallbeencollected,clickto revealthe nextslideandask:
● Whatnewinformationdo youhave?
● Howdoesthatchange yourthinking?
● Whatdo youthinkthismightbe about?
● Whatvalues/datacould youestimate? (Canthey justifywhytheychosethesevalues?)
Repeatasabove forthe restoftheslides.
Teachingtip As you revealeachnewpieceofinformation, encouragethechildrentonoticethe proportionalityofthegraph.Dothey realisethat thelengthofeachbarisdirectlyproportionalto itsvalue,i.e.longerbars representgreatervalues andvice versa?Giventhevalueofaspecificbaror interval,cantheyestimatethevalue represented by otherbarsbasedontheirlengthincomparison totheknownbar/value?
D Digitalactivity:Slow-RevealData(1)
MAM Routine: Reason& Respond
Whenthecompletebargraphhasbeen revealed, ask/say(someofthesequestionsmayalreadyhave beenanswered):
● Do you rememberwhatthistypeofgraphis called?
● Thisisabargraph.Whydo youthinkitiscalleda bargraph?
● Whereelsehaveyouusedbarsto represent valuesinmaths?(barmodels)
● Whatdo younoticeaboutthewidthofthebars andthespacingbetweenthem? (Theyarethe samethroughout.)
● Whatdoesthisbargraphtellus?(thenumberof differentcoloursontheflagsofcountries)
● Can you rememberthemaths word forthemost commonanswer?(mode)
● Whatisthemodeonthisgraph?Explainhow youknow.
● Lookattheshapeofthedata.Arethereany gaps?
● Wheredoesmostofthedatalie?Isthiscluster ofdatamoretotheleft,totherightorinthe middle?
● Whatistheleastnumberofdifferentcolourson theflagsofcountries?
● Tellmeasentenceabouttheinformationinthis bargraph,using‘more…than…’.
● Tellmeasentenceabouttheinformationinthis bargraph,using ‘fewer…than…’.
● Howdo youthinkthisdatamighthave been collected?
● Whatothertypeofdatadisplaymightbesuitable toshowthisinformation?
● Wouldalineplotbesuitable?Explainwhy. (It wouldnotbe veryefficient,sincesomeofthe numbersarequitebig.)
Let’sdeepen Challengethechildrentoidentifyorsuggest wheredatadisplayscouldbeusedin real-life situations.
P Pupil’sBookpage34: DataDisplays Teachingtip Whenaskingthechildrento readandinterpret dataortocomeupwiththeir ownquestionson thegivendata,itisimportanttostrikeabalance betweenthreedifferentcategoriesofquestions, involving:
1. Readingthedata–takinginformationdirectly fromthegraph(e.g.Howmany…?)
2. Readingbetweenthedata–usually by comparingquantities(e.g.Howmanymore… than…?)andusingoperationstoidentifythe mathematical relationshipsvisibleinthedata
3. Readingbeyondthedata–predictingor inferringfromthedata by connectingitwithone’s ownknowledge, ratherthanwhatisstatedeither explicitlyorimplicitlyonthegraph(e.g.likely trends/outcomes,consideringthesamplegroup, etc.).
Let’sstrengthen Thechildrenmightassumethatdatadisplays alwaysuse1:1correspondence.Encouragethem tolookfirst forcluesthatthesymbols represent morethanone(e.g.a key, halfsymbols,scale markings,etc.),andtoexplainwhatthistells them.ConsulttheUnit4Let’sStrengthen Suggestions for Teachers.
Optionalconsolidation andextension possibilities Integration Understandingofdatacanbe reinforced inothersubjects by askingthechildrentoapplythe DataInvestigation Cycletoaquestionarisingfrom enquiryinanycurriculararea,butespeciallyPE, SPHE,Geography, Science, Technologyand Engineering.Thisstrandunitalsoprovides opportunitiestodevelopandextendlearningin literacyanddigitalliteracy.
MathsEyes Findexamplesofdatadisplaysinprint oronlinemedia.Displaythemtotheclass.What informationdotheygive?Whatintervalscale(i.e. correspondence)wasused?Whatinferencescanbe made?Whatquestionscouldbeasked?
DataDisplay Setupadisplay fordatainthe classroom.Thiscouldincludeexamplesofvarious graphandcharttypessourcedinprintmediaand
online(seeabove),as wellasappropriatelabels(see theUnit4MathsLanguageCards).Thechildrencould contributesamplesoftheir own workfromthis lessonandlabelthem.
GamesBank Play‘ModeCards’.
Story Read TigerMath:LearningtoGraphfroma BabyTiger by AnnWhiteheadNagdaandCindy Bickel,whichdescribesthegrowthofanorphaned Siberiantigercub, by meansof wordsandgraphs.As wellasshowingthedwindlingpopulationoftigersin thewild,itservesasapowerfulexampleofa realworldneed fortrackingdata.
Reviewand Reflect Usethepromptquestionsin the Reviewand Reflectposter.
Day2,Lesson2 LinePlots ● Interpretslineplots(dotgraphs)to representdata (C)
● Exploresthemedianasthevalueinthemiddleofadataset(U&C)
● Investigatesthe range(i.e.themeasureusedtocapturevariabilityorspreadofthedata)ofadataset (U&C)
Digitalactivity:Slow-RevealData(2) MAM Routines:Notice& Wonder,withThink-Pair-Share; Reason& Respond
Concreteactivity:Let’sinvestigate!IdentifyingtheMedian MAM Routine: Reason& Respond,withThink-Pair-Share Pupil’sBookpage35: LinePlots
lineplot,dots,X,numberintervals,title,mode,median,
MWBs,orsmallpiecesof paper
Teachingtip Alineplot(alsoknownasadotplot/graph)consistsofanumberlinelongenoughtoencompassall numbersinadataset,showingamark(usuallyanXoralargedot) overthepositioncorrespondingto eachnumber.
Warm-up Teachingtip
Inthisunit,thechildrenarebeginningtosimply describethe rangeofthevaluesasgoingfromthe lowestvaluetothehighestvalue(e.g.0–10or 7–21)asopposedtothemorecorrectexpression of rangeasthenumericaldifferencebetweenthe largestandsmallestvaluesintheset(e.g. 10 [10 minus0]or 14 [21minus 7].
D Digitalactivity:Slow-RevealData(2)
MAM Routines:Notice& Wonder,withThinkPair-Share
Displaythefirstslideandask:
● Whatdo younotice?Whatdo you wonder?
● Whatdo youthinkismissing?(Dothey recognise thatthisisagraph,andcantheyidentifythe featuresofthegraphthatshouldhave been given?)
UseThink-Pair-Sharetocollect feedback.Whenthe feedbackhasallbeencollected,clickto revealthe nextslideandask:
● Whatnewinformationdo youhave?
● Howdoesthatchange yourthinking?
● Whatdo youthinkthismightbeabout?
● Whatvalues/datacould youestimate?
Repeatasabove forthe restoftheslides.
Mainevent D Interactiveslideshow:Slow-RevealData(2)
MAM Routine: Reason& Respond
Whenthecompletelineplothasbeen revealed,ask/ say(someofthesequestionsmayalreadyhave been answered):
● Do you rememberwhatthistypeofgraphis called?
● Thisisalineplot.Whyisitcalledalineplot? (The valuesareplottedalonganopennumberline.)
● Howisthislineplotthesameordifferentfrom otherlineplots youmayhave seen?(Otherline plotssometimesuseXsinsteadofdots.)
● Whatdoesthislineplottellus?(thenumbersof daysofabsence forthechildrenin4thClass)
● Tellmesomethingthat younoticeaboutthis data.
● Can you rememberthemaths word forthemost commonanswer?(mode)
● Whatisthemodeonthislineplot?Explainhow youknow?(1;mostcommonanswer)
● Whatdoesthistellus?(Mostchildrenhadonly1 absence.)
● (Nextslide) Lookattheshapeofthedata.Are thereanygaps?
● (Nextslide) Wheredoesmostofthedatalie?Is thisclusterofdatamoretotheleft,totheright orinthemiddle?
● Whatdoesthistellus?(Mostofthechildrenin theclassmissed4orlessdaysofschool;onlya smallnumberofchildrenhad6ormore absences.)
● (Nextslide) Anoutlierisavalue farawayfrom mostofthe restinasetofdata.Arethereany outliersonthisgraph? (Yes, 10.)
● Whatdoesthistellusaboutthedata?(Inthe class,only1personmissedmorethan8days.)
● (Nextslide) The rangeofdatainthisdataset goesfromwhatnumbertowhatnumber? (The data rangegoesfrom0to 10,i.e.fromthelowest valuetothehighestvalue.)
● Tellmeasentenceabouttheinformationinthis lineplot,using‘more…than…’/ ‘fewer…than…’/ ‘twice’/‘half’.
● Whatothertypeofdatadisplaymightbesuitable toshowthisinformation?Whattypeofdata displaydo youthinkismostsuitable?Explainwhy.
● Howdo youthinkthisdatamighthave been collected?
● Ifanothergroupofpeople were surveyedanda lineplotcreated, wouldthatlineplotlookexactly likethisone?Explainwhy.
● If we createdasimilarlineplot forourclass,do youthinkit wouldlooksimilarordifferent?
C Concreteactivity:Let’sinvestigate!Identifying theMedian MAM Routine: Reason& Respond, withThink-Pair-Share
Teachingtip Themedian(atypeof average,ormeasureof centre)isthemiddlevalueofanorderedset(least togreatestusually)ofdatavalues.
Withthecompletelineplotstillondisplay, andusing Think-Pair-Sharetocollect feedback,say/ask:
● Whenexaminingdata,anotherwaytomakea statementabouttheinformationistoidentifythe median.Themedianisthemiddlevalueinadata setthathasbeenordered.
● Estimatewhat youthinkisthemedianinthisdata set.Explainwhy.
● Howmight we identifythemedianormiddlevalue?
Teachingtip Inthisdataset,becausethereisanoddnumberof values,thereisaclearandobviousmiddlevalue/ number,whichisalsothemedian.Iftherewasan evennumberofvalues,thenthere wouldbetwo middlenumbers,which wouldthenbeusedto calculatethemedianorvalueinthemiddleof bothnumbers.(Strictlyspeaking,thisisthe averageofthetwonumbers. Average/meanwill beintroducedin5thClass.)
Allowthechildrentimetoexploreandinvestigate their ownstrategies. Possiblestrategiesinclude:
● Writingoutallthenumbersinanorderedlineon their MWBsoronsmallpiecesofpaper,and orderingthesetofindthemedian(whichis3)
● Countinginwards,dot by dot,frombothendsof thelineplotuntilmeetingatthemiddledot
● Countingthetotalnumberof responses/dots(29) andusingthisnumberto workoutthemiddle response/dot(which wouldbethe15th)andthen countingfromeitherendtolocatethepositionof the15thdot(inthecolumn for3absences).
Afterwards,ask/say:
● Arethemodeandmedianthesamevalueornot? Explainwhy.
● Willthemodeandmedianalwaysbedifferentor cantheybethesame?
● Modeandmedianareoftencalled‘measuresof centre’.Whydo youthinkthisisso?
● Howmightknowingthemodeormedianbe useful?
● Basedonthisdata,if we investigatedthe numbersofabsencesinanother4thClass,what would youexpecttobethemostlikelyanswer(s)? Explainwhy.
● If we conductedthisdatainvestigationinour class,what would youexpecttobethemost likelyanswer(s)?Explainwhy. (Thismaydiffer fromtheiranswertothepreviousquestion,based onwhattheyknowabouttheir ownclassandhow manyabsencestherearetypically.)
P Pupil’sBookpage35: LinePlots
Optionalconsolidation andextension possibilities GamesBank Play‘MedianCards’or‘RangeCards’. Let’sCreate Askthechildrentocomeupwiththeir ownquestion/problem, forwhichtheycould represent thedataasalineplot. Forexample,theycouldaskthe question,‘Howmanyabsencesdidthechildreninour classhave last year?’Firstly,thechildrencould estimatetheir ownnumberofabsences forthe previousschool year,thencollectthedata(e.g.the teacherfindsthedatainthe rollbook)anddisplayitas alineplot(e.g.usethe11intervalopennumberlineon their MWBsto record),ortheteachercoulddisplaythe opennumberlineprintableontheboardandeach
childinturncouldbeaskedtocomeuptotheboardto recordthelocationoftheirXordot. Roundstickers, ontowhichthechildrenhave writtentheirnumberof absences,couldalsobeusedandaddedtoachartor numberline.Oncedone,askthechildrentoidentify themode,medianand range.
Otherpossiblequestionstoposethatcouldeasilybe representedaslineplotsinclude:numberofpets; numberoflettersinfirstname;numberof raisinsina box;numberofhoursofsleepeachnight;numberof hoursspent reading/exercisinglast week;numberof books readlastmonth;numberofchildrenina
classroom,heightsofchildrentothenearest 10cm/5cm; weightsofschoolbagstothenearest kg; numberofskips/push-upsin30seconds;numberof secondstakentorun 100m.
Reviewand Reflect Usethepromptquestionsin the Reviewand Reflectposter.
Day3,Lesson3 DataCards Focusoflearning(withElements) ● Comparesmultipledatasamplesinvolvingothersandthemselves(A&PS)
● Identifiesanddisregardssurplusinformation(U&C)
● Justifieswhyasetofdataiscollected,sortedand representedinthewaychosen(R)
● Evaluatesthemethodsused by peersin representingdata(R)
Learningexperiences Digitalactivity:DataCards MAM Routines:Notice& Wonder,with Think-Pair-Share; Reason& Respond
Digitalactivity:DataInvestigation Cycle–AnalysisandConclusions Pupil’sBookpages36–37:DataCards
● datacards,variables
Warm-up D Digitalactivity:DataCards MAM Routines: Notice& Wonder,withThink-Pair-Share
UsingThink-Pair-Share,displaytheposter,which showseightdatacardsandclicktoplayorask:
● Whatdo younotice?
● Whatdo you wonder?
D Digitalactivity:DataCards
MAM Routine: Reason& Respond
● DataCards manipulative printable
Recordthechildren’s responsestobothquestionson theboard.Allowthechildrentheopportunityto respondto(agree/disagreewithorquery)others’ responses,butdonotconfirmor rejectanyofthe ideas.Noteany‘wonderings’thatcouldbecomethe basis forasubsequentmathsinvestigation.
Mainevent Displaytheposteragain,andaskorclicktoplaythe followingquestions:
● Thesearedatacards.Whatinformationdothey giveus?
● Inwhatwaysarethedatacardssimilar?
● Inwhatwaysaretheydifferent?
● Whatunitsofmeasurementareused?Explain whytheseareused.
● Howdo youthinkthisdatawascollected? (perhapsasurvey)
● Characteristicsthatcanhave differentvaluesare calledvariables.Whatvariablesare represented here?
● Foreachvariable,suggestwhatthesurvey questionmighthave been.
● Foreachvariable,whatarethepossible outcomes?
● Whomightbeinterestedinthisdata?
● Pickoneofthesecards.Describein wordswhat youknowaboutthe person.
Mathslanguage
D C Digitalactivity:DataInvestigation Cycle –AnalysisandConclusions
Teachingtip Inthisactivity,thechildrenwillengageinthe AnalysisandConclusionstepsoftheData Investigation Cycletoanalyseanddraw conclusionsfromthepre-collectedinformationin thedatacards. FormoreontheDataInvestigation Cycle,pleaseseepages4–5.
Teachingtip ThechildrencouldalsousePCM2:BlankData Cardstocreatesimilarcardsoftheir owntouse foranalysisandconclusion.
Let’sstrengthen Thedatacardscontainbothcategoricaldata(e.g. eyecolour,haircolour,gender,handedness,etc.) andnumericaldata(e.g.height,lengthof foot, timetakentotraveltoschool).Categoricaldata tendstobesimplertoorganiseand represent, andthereforesomechildrenshouldbe encouragedto focusononeofthesevariables and/orto workwithexamplesofcategoricaldata first,beforeproceedingto workwithexamplesof numericaldata.
Let’sdeepen ProvideeachchildwithacopyoftheDataCards manipulativeprintable.Displaytheslideshowofthe DataInvestigation Cycleand readthroughthesteps. Afterwards,ask/say:
● To createthesedatacards,whatstepsoftheData Investigation Cycle were used?(1. Posea question/problem,2.Plan,3.CollectData)
● Describewhat youthinkwasdoneateachof thesesteps.
● Whatstepscouldhappennext?(4.Analysis,5. Conclusion)
● Howmightthisbedone?(Identifya focus variable, representtheinformationinasuitable datadisplay, analysethedisplayandsharethe findings,etc.)
● Whatdatadisplaysdo youthinkmightbemost suitable?Explainwhy.
Arrangethechildrenintogroups,andallowthem plentyoftimetoanalyseanddrawconclusionsfrom theirchosenvariable.Eachgroupmustbecarefulto focusontheirchosenvariableanddisregardsurplus informationthatisnot relevanttothem.
Teachingtip AcopyofPCM1:DataInvestigation Cycle (PPDAC)AssessmentRubriccouldbedistributed toeachgrouptohelpguidethechildren.Itcould thenbeusedafterwardstoassess.
Thechildrencouldbechallengedtoconsiderhow theymight representandorganisethedatafrom oneofthenumericalvariables.Ofthese, foot lengthwillhave thenarrowest rangeofnumbers, andsomightbethebestonetostartwith.The childrencouldthenbeaskedtoidentifythe range andmedianofthe focusnumericaldata.
Thechildrencouldalsobechallengedtoconsider howtwovariablesinteract, forexample, by organisingthedatacardsaccordingto foot length,andthenagainaccordingtogender.What doesthattellus?
Afterwards,whenthevariousgroupsaresharing theirfindings,askthemtoexplainandjustifythe methodsthattheychose. Peersshouldalsobeasked toevaluatethemethodschosen.
● Howdid youdoit?
● Whydid youchoosetodoitthisway?
● Wouldadifferentdatadisplayhave beenmore suitable?
Optionalconsolidation andextension possibilities Story Read SortingFur, Feather, Tails,andScales by MarcieAboff,whichusesanimalsontheAfrican savannahtoexplorehowsortingcanhelpusto organiseandunderstandinformation.It featuressets, Venndiagramsandbargraphs.
Reviewand Reflect Usethepromptquestionsin the Reviewand Reflectposter.
Day4,Lesson4 DataInvestigation ● Appliesaninvestigativecycleofproblem-posing,planning,datagathering, representation,analysisand conclusion(A&PS)
● Exploresandestablisheshowtobesthandle, recordand representdata foragivenpurpose,including theuseofappropriatescalesandlegends(U&C) (C)
Learningexperiences Digitalactivity:WhichOneDoesn’tBelong?–Data
MAM Routines: Reason& Respond,withThink-Pair-Share
Digitalactivity:DataInvestigation Cycle
MAM Routines: Reason& Respond,withThink-Pair-Share
Mathslanguage Warm-up ● To beused by theteacher:posethequestion,plan,data,analysis,conclusion
D Digitalactivity:WhichOneDoesn’tBelong?
–Data MAM Routines: Reason& Respond,with Think-Pair-Share
D Digitalactivity:DataInvestigation Cycle
DisplayeachslideinturnandusingThink-Pair-Share tocollect feedback,askthechildrentosuggest reasonswhyeachofthegraphsdoesnotbelong.
Mainevent MAM Routines: Reason& Respond,withThinkPair-Share
Teachingtip Thepurposeofthislessonis forthechildrento applytheDataInvestigation Cycletoaquestionor problemoftheir ownchoosing.Alternatively, a question/problemcouldbechosenfromPCM3: DataInvestigationSampleInvestigativeQuestions.
Displaytheslideshowandasktheaccompanying questionstostructurethestepsofDataInvestigation Cycle.Allowthechildrenplentyoftimeto work
throughthesteps.DistributeacopyofPCM1:Data Investigation Cycle(PPDAC)Assessment Rubrictoeachgrouptohelpguidethem. Thiscouldalsobeusedafterwardsto assess.
Teachingtip Whenconstructinggraphs,many-to-one correspondenceshouldbethe focus(i.e.symbols standing for/intervalsof2,4,5, 10,25,50,etc.).
Thesymbols/intervalsshouldbeconsistentandbe chosenbasedonthedatabeinggraphed(e.g.size and rangeofvalues).Encouragethechildrento describeandjustifytheirdecisions.
Let’sstrengthen Childrenmaystruggletodrawaccuratelyand neatlythevariousgraphtypes.Demonstrateand teachthechildrenhowtousesoftwaresuchas GoogleSheetsorMicrosoftExceltomakegraphs. Therearelotsofvideos availableonlinetoshow this.
Teachingtip Thechildrenshouldbeabletoconstructdata displays,butmoreimportantlytheyneedtobe abletointerpretthedisplaysandtousethe informationtoanswerquestionsandsolve problems.Themajorityoftimespent workingon datadisplaysshouldbeontheinterpretation ratherthanontheconstruction.
Itmighttakemorethanonelessontocomplete theinvestigation. Part ormostofDay5couldbe used forthis.
Optionalconsolidation andextension possibilities MathsJournals IntheirMathsJournals,thechildren coulduseimagesand/or wordsto recordhowthey conductedtheinvestigation,as wellastheirfindings. Theycoulddesigntheir ownquestionsbasedonthe findings,andthenswapwithanothergroup/child.
Story Read BirdCount by SusanEdwardsRichmond, anaward-winningbook,inwhich we readabouta verymeaningfulapplicationoftheDataInvestigative Cycle by a younggirlwhoisparticipatinginanannual
censusofbirdsinhercommunity by collectingdata usinghandwrittentallies.Thechildrencouldbeasked tosuggestanappropriatewaytoanalysethedata andpresentthefindings.
DataDisplay Thechildrencouldcontributesamples oftheir own workfromthislessonandlabelthem.
Reviewand Reflect Usethepromptquestionsin the Reviewand Reflectposter.
Day5,Lesson5 Reviewand Reflect Warm-up Carryoutawarm-upactivityof yourchoosingfromoneofthelessonsinthisunit.
Mainevent Choosefromthismenuofactivityideas,orchoose your ownwaytobeststructurethislastlessontosuit your needsandtheneedsof yourclass.
Let’stalk! Reviewand Reflect Poster:UseThink-Pair-Share alongsidethepromptquestionsto reviewtheunit. Thechildrencould recordwhattheyknowintheir MathsJournals(e.g.usingaconceptmap).
Individualchildrencouldpresentexamplesoftheir owndrawings/work/constructionstotheclass,and talkaboutwhattheyhave learned.
Let’sinvestigate! Askthechildrentoconductanothersurvey,eitheras aclass,ingroups/pairsorindividually.
Let’sstrengthen Thechildrenmaybenefitfromextrasupports toplanand record,suchasPCM4:BarGraph Template.
Let’sdeepen Challengethechildrentoconducttheirsurvey individuallyorinpairs,andtodisplaytheir datawithoutthesupportofPCM4:BarGraph Template.Askthemtoconsiderthe‘rules’ for drawingbargraphsastheycompletethetask. Couldtheyuseadigitaldeviceoronlinetoolsto help?
Mathslanguage Mathsstrategiesandmodels UsetheUnit4MathsLanguageCardsto revise key terms. Forexample:Iftheimageandtextarecut apart,canthechildrenmatchthem?
Ask:Whatarethe‘rules’ fordrawingbargraphs/ lineplots?(Usesymbolsofthesamesizeandequal spacing.Uselabels,atitleanda key/legend.)
ProgressAssessmentBooklet CompleteQuestions20–25onpage12. Alternatively,thesecanbelefttodoaspartofa bigger reviewduringthenext review week.
Let’sstrengthen Identifychildrenwhomightbenefitfromextra practicewithsomeofthe keyconceptsorskillsin thisunit.UsetheUnit4Let’sStrengthenPCM. ConsulttheUnit4Let’sStrengthenSuggestions for Teachers.
Askthechildrentogiveexamplesofthestrategies theyusedinthisunit(e.g.comparingtoidentifyhow manymore/fewer, readingtheintervalscale,the DataInvestigation Cycleanditsimportance).
Askthechildrentogiveexamplesofthemodelsthey usedinthisunitandtolistthe required featuresof thevarioustypesofgraphs. Forthevarioustasksand investigations,howdidthey recordandpresenttheir findings?Whatdidtheybuild,sketchorwrite?
Mathseyes Askthechildrentocollect representationsofvarious examplesofdatadisplaysandchartsinprintmedia (newspapers,magazines,etc.)and/oronlinesources. Thesemayincludeexamplesthechildrenhave not encountered formally yet(e.g.piecharts).Askthe childrentosuggesthowtheyaresimilar/differentto thoselookedatduringthisunit.Createadisplayof theseintheclassroom.
Let’sdeepen UsetheUnit4Let’sDeepenPCM.
