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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 for3rd Class,Unit5:Multiplicationand Division1 Multiplesof2,10and 5SameButDifferent– Multiplesof2, 10and5
Multiplicationas Repeated Addition
Chooseoneormoreofthese, dependingontheneedsof yourclass:
Multiplesof2
Multiplesof10
Multiplesof5
Multiplication Sentences
Chooseoneormoreofthese, dependingontheneedsof yourclass:
Dot Multiples:Groupsof2
Dot Multiples:Groupsof5
Dot Multiples:Groupsof10
Write-Hide-ShowVideo 44 Turnaround FactsWhichOne Doesn’t Belong?
Images,with Write-Hide-ShowQuick Images Arrays
SameButDifferent–Turnaround Facts
Would You Rather?
Think-Pair-ShareSlideshow 55 Strategies for Multiplying by 2,10and5
Chooseoneormoreofthese, dependingontheneedsof yourclass:
Multiplying by2
Multiplying by 10
66 Divisionas Equal Sharing
77 Divisionas Repeated Subtraction
Respond,with Think-Pair-ShareSlideshow
Multiplying by5 Reason& Respond,with Write-Hide-ShowVideo
Chooseoneormoreofthese, dependingontheneedsof yourclass:
Multiplesof2
Multiplesof10
Multiplesof5 Choral Counting Slideshow Sharing€20 Equally Reason& Respond,with Write-Hide-ShowVideo
Chooseoneormoreofthese, dependingontheneedsof yourclass:
Multiplesof2
Multiplesof10
Multiplesof5
RepeatedSubtraction Reason& Respond,with Write-Hide-ShowVideo
88 Multiplicationand Divisionas Inverse Headline Stories
MultiplicationandDivisionas Inverse Concept Cartoon,with Think-Pair-Share; Buildit!Sketchit! Writeit! Concept Cartoon
99 Strategies forDividing by 2,10,and5
SameButDifferent–Number Sentences Reason& Respond,with Think-Pair-ShareSlideshow
ScantheQR codebelow to accessaselectionofour
NewDigital Resources for Maths andMe 3rdand4thClass:
FOR A DEMO OFTHE NEW DIGITALRESOURCES Pupil’sBook Contents Note: ThecontentsshownindicatewhatisincludedinthefullPupil’sBook.
Unit1:Numbersto1,000
Unit2:Locationand Transformation
Unit3:AdditionandSubtraction
Unit4:Data
Review1
Unit5:MultiplicationandDivision1
Unit6:Time
Unit7:Money
Review2
Unit8:MultiplicationandDivision2
Unit9:Fractions
Unit 10:Measuring1(Length)
Unit11:Decimals
Unit12:Shape
Review3
Unit13:MultiplicationandDivision3
Unit 14:Algebra
Unit15:Measuring2(Area)
Review4
Unit 16:MultiplicationandDivision4
Unit 17:Measuring3 (Capacityand Weight)
Unit18:Chance
Review5
Let’s TryMore
Glossary
The MathsandMe Pupil’s Pack includesa ProgressAssessmentBooklet andthe followinginsertsto supportlearning:mini-whiteboardwithopen-numberlineon reverse,spinners(forplayinggames),cutoutPlace ValueCountersandacut-outFraction Wall.
Multiplesof 2,10and5 Multiplesarenumbersthatgoupinjumpsofagivennumber.
Whatismissing? Countinmultiplestowork outthevalueof themoneyineach.
Let’stalk!
Discussasaclassoringroups:Arethesealways,sometimesornevertrue?
● Multiplesof 2areevennumbers.
● Multiplesof 5areoddnumbers.
● Multiplesof 5endina5.
● Multiplesof 2arealsomultiplesof 10.
Trythis!
Canyoufindan exampletoproveor disproveeachone?
Thelibrarywillbeopen fromMondaytoSaturdayeveryweek inNovember. Miaplanstogoonallthedatesthataremultiplesof 2, Daraplanstogoonallthedatesthataremultiplesof 5, andLexiplanstogoonallthedatesthataremultiplesof 10.
1. Whowillgotothelibrary… (a) themost? (b) theleast?
2. Onwhatdateswillallthreeof themgotothelibrary?
Let’stalk! Describetheimagesbelowindifferentways.
Thefirstonecouldbe10+ 10+10,orthreegroupsof 10,or3times10,or3tens. For ,thefirstone willbe:3×10=30
Writeandsolvethematchingmultiplicationsentence foreachof theimagesin above.
Writethesymbol forgreaterthan(>),lessthan(<) orequals(=)tomakethesetrue.
Trythis! Look attheimages.UseBuildit!Sketchit!Writeit! tomodelthese.
1. Miahas80crayons.Howmanypacksisthat?
2. Darahas35pens.Howmanypacksisthat?
3. Lexihas 4 packsof crayonsand3packsof pens. Howmanyitemsaltogether?
4. Jayhas 45crayonsandpensintotal. Whatpacksmighthehave?
123 10 crayons
Arrays Mathseyes Arraysareitems arrangedinrows andcolumns.
Writethematchingmultiplicationsentence foreacharray.
Modeltheseandwritethematchingnumbersentences.
1. 9rowsof carswith10ineachrow
2. 8rowsof childrenwith2ineachrow
3. 6rowsof pictureswith5ineachrow
4. 7rowsof counterswith2ineachrow
5. 9rowsof playingcardswith5ineachrow
Let’splay! Numberof players: 2
CapturetheArea Youwillneed: 1sheetof squaredpaper,amarker/pencil/crayonof adifferent colourperplayer,two0–9spinners,pencilandpaperclip
● Eachplayer,inturn,spinsthetwospinners,andthendrawsarectangle accordingtothenumbersspun,andwritesthetotalnumberof squareunits insideit.Forexample,if aplayerspinsa2anda9,theydrawarectanglethatis 9squaresby2squaresandwrite18insideit.
● If thereisnotenoughspaceonthepaper foraplayertodrawtheirrectangle, theplayermissesaturn.
● Playcontinuesuntiltimeisuporthereisnomorespaceleftonthepaper.
● Theplayerwiththegreatestnumberof squareunitsoverallwinsthegame.
Trythis! Headlinestory! 30playingcardswerearrangedasanarray.
Whatmaths questionscould youask?
Howcouldyou modelandsolve thequestions?
Strategies forMultiplying by 2,10and5 Usedoublingtosolvethese.
1. 2×3=double =
2. 2×8=double =
3. 2× 4 =double =
4. 2×9=double =
5. 2×6=double =
6. 2×7=double =
Movethedigitstosolvethese.
1. 10×8=
2. 10×3=
3. 10×9=
4. 10× 4 =
5. 10×1=
6. 10×6=
Use‘half the10times’tosolvethese.
1. 10×8= ,so5×8=
2. 10× 4 = ,so5× 4 =
3. 10×10= ,so5×10=
4. 10×6= ,so5×6=
5. 10×2= ,so5×2=
6. 10×5= ,so5×5=
D Solvethese.
To multiplyby 5,gethalfof 10timesthe number.
Trythis! Usemodelsorstrategiestosolvethese.
5. 10×16= 6. 5×20= 7. 10×19= 8. 5×14 = 3 When multiplying by2,think doubling.
2×5= 10 5+5= 10
To multiplyby 10,movethe digitsoneplace totheleft.
1. 2×15= 2. 5×12= 3. 10×13= 4. 2×25=
DivisionasSharingEqually Buildit!Sketchit!Writeit!Usematerialsandsketchesto representthese.Writethematchingdivisionsentence foreach.
Sharetheseequallyamong…
Modelandsolvethese.
1. 10÷5= 2. 20÷2= 3. 10÷10= 4. 30÷5= 5. 12÷2= 6. 35÷5= 7. 8÷2= 8. 50÷10=
k of astorytomatchsomeof thenumbersentencesin .
Trythis! Usemodelsanddivisionsentencestohelpyousolvethese.
1. 20sconesweredividedevenlyinto5bags.Howmanysconesweretherein eachbag?
2. Therewere18girlsand12boysinaclass.Theteacherdividedthem allinto10equalgroups.Howmanywerethereineachgroup?
Buildit!Sketchit!Writeit!Usematerialsandsketchesto representthese.Writethematchingdivisionsentence foreach.
Forhowmanydayswilltheapples last,if 2areeateneveryday?
If 5yoghurtsareeateneveryday, for howmanydayswilltheylast?
If Miaputs10starsoneverycardshe makes,howmanycardsisthat?
Howmanypairsof sockscanbe made fromthese?
Howmanysticksof 10canbemade from80cubes?
Forhowmanyweekswillthisbottle last,if 5washesaredoneeveryweek?
Drawingbarmodels
Thisbarmodelrepresentsquestion1in above. Drawbarmodelstomatchtwootherquestionsin
eupnewrepeatedsubtractionstories foreachbarmodelthatyou drewin
Writeamatchingmultiplicationanddivisionsentence foreachof these.
Writeamatchingmultiplicationanddivisionsentence foreachof thesebarmodels.
Arethesecorrect? 3 or 7.
D Let’stalk!
Whatstrategiesdidyouusetocheck theanswersin above?
Trythis! Drawabarmodelandwriteamatching numbersentencetoshoweachof these.
1. Miahas€18,whichshedividesequallybetween JayandDara.Howmuchdoeseachget?
Whatisthesameandwhat isdifferentaboutyourbar models?Explainwhy.
2. Lexihas€18in€2coins.Howmanycoinsdoesshehave?
Strategies forDividing by 2,10and5 Usehalvingtosolvethese.
1. 6÷2=half of =
2. 20÷2=half of =
3. 12÷2=half of =
4. 4 ÷2= 1 2 of =
5. 8÷2= 1 2 of =
6. 14 ÷2= 1 2 of =
Movethedigitstosolvethese.
1. 100÷10=
2. 80÷10=
3. 90÷10=
4. 70÷10=
5. 10÷10=
6. 30÷10=
To divideby 2,halvethe number.
50÷10= 5
TensOnes 50 5
Usetheinversetosolvethese.
1. ×5=15,so15÷5=
2. ×5=20,so20÷5=
3. ×5=35,so35÷5=
4. ×5=5,so5÷5=
5. ×5= 45,so 45÷5=
6. ×5=30,so30÷5=
D Solvethese.
To divideby 5,usethe inverse.
To divideby10, movethedigits oneplaceto theright.
5. 10÷5= 6. 18÷2= 7. 50÷10= 8. 25÷5= 6
45÷9= ?
I know5×9= 45, so 45÷5=9
1. 60÷10= 2. 40÷5= 3. 16÷2= 4. 40÷10=
Trythis!
Usemodelsorstrategiestosolvethese.
1. 24 ÷2= 2. 120÷10= 3. 60÷5= 4. 40÷2=
5. 150÷10= 6. 75÷5= 7. 50÷2= 8. 200÷10= 12÷2= 6
Teacher’sPlanningBoo 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. Unit5:MultiplicationandDivision1
Ed itableplanningdocument
ve mber: We eks1&2)
tTe rmPlan,Unit5:MultiplicationandDivision1(No
Strand(s)>Strandunit(s)Number>SetsandOperations; NumerationandCounting.Algebra> Pa tterns,Rulesand Re lationships;ExpressionsandEquations.
LearningOutcome ( s )T hroughappropriatelyplayfulandengaginglearningexperienceschildrenshouldbeabletounderstandandapplyflexiblythe fo uroperations;andunderstandthe re lationshipsbetween operations;identifyrulesthatdescribethestructureofapatternandusetheserulestomakepredictions; re presentthe re lationshipsbetweenquantities; re presentandexpressproblemswith knownandunknownvaluesindifferentwaystoincludetheuseofappropriateletter-symbolsor wo rds.
IntuitiveAssessment: re spondingto emerging misconceptions
PlannedInteractions: re spondingtoinsights gleanedfrom children’s re sponses tolearning experiences
AssessmentEvents: informationgathered fromcompletionof theunitassessmentin theProgress AssessmentBooklet page8
Lesson Fo cusofLearning(withElements)
D Re ason& Re spondL1–9
D Think-Pair-ShareL1,4–5,8–9
D Three-Act Ta skL1
D ChoralCountingL2,6–7
D C Wr ite-Hide-ShowL2–3,5–8
C D Buildit;Sketchit; Wr iteitL2–4,6–8
D QuickImagesL3
D ConceptCartoonL8
C Dividing by 2, 10 and5L9
Print re sources Pupil’sBookpages42–50 PCMs1,2,3
1 Multiplesof2, 10 and5: Practisescountinginmultiplesof2, 10 and5(U&C);Adoptsasystematicapproachintheidentificationof multiplesof2, 10 and5(U&C)
2 Multiplicationas Re peatedAddition: Exploresand re cognisesmultiplicationas re peatedaddition(U&C);Visualisesandcreates modelsofmultiplication,including re peatedaddition(U&C)
3 Arr ay s: Visualisesandcreatesmodelsofmultiplication,including re ctangulararr ay s(U&C)
4 Tu rnaround Fa cts: Exploresthecommutativepropertyofmultiplication(U&C)
5 Strategies fo rMultiplying by 2, 10 and5: Exploresandsuggestsstrategicapproachestothemultiplication fa ctsof2, 10 and5 (C ); Explorestheimplicationsofmultiplying by 10 (U&C)
6 DivisionasSharingEqually: Visualisesmodelsofdivisionasequalsharing(U&C)
7 Divisionas Re peatedSubtraction: Visualisesmodelsofdivisionas re peatedsubtraction(U&C)
8 MultiplicationandDivisionasIn ve rse: Beginstodevelopanunderstandingofmultiplicationanddivisionasbeingthein ve rseofeach other(U&C):Usesin ve rseoperationstoexplainandcheckanswers(R)
9 Strategies fo rDividing by 2, 10 and5: Exploresandsuggestsstrategicapproachestothedivision fa ctsof2, 10 ,and5 (C );Explores theimplicationsofdividing by 10 (U&C)
10 Re viewand Re flect: Re viewsand re flectsonlearning(U&C)
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‘3rdClass MathsandMe ProgressionContinuaOverview’ foradetailedbreakdownofhowallprogression continuaarecovered.
See‘3rdClass MathsandMe MathsLanguageOverview’,individuallessonplans,andUnit5MathsLanguage Cards.
See‘3rdClass MathsandMe MathsEquipmentOverview’andindividuallessonplans.
● SeeLet’sStrengthenandLet’sDeepensuggestionsthroughoutlessonplans.
● SeeUnit5Let’sStrengthenSuggestions for Teachers. (TheseaddresstheCommonMisconceptionsand Difficultieslistedonthenextpage.)
● SeeUnit5Let’sStrengthenPCM.
● SeeUnit5Let’sDeepenPCM.
Seeindividuallessonplans.
Background and rationale ● Thisunitisatwo-weekblockofcontent,designedto formallyintroducethechildrentotheconceptsof multiplicationanddivision.Inpreviousclasses,theexplorationofotherconcepts–suchasfractionsand sharingequally,doubles,developingstrategies,andcountingintwos,tensandfives–have already preparedthechildren formultiplicationanddivision.
● To enablethechildrentomakerichandmeaningfulconnectionsbetweenlearningexperiencesindifferent strandunits,thisunitcombineslearningexperiencesfromSetsandOperations, Patterns,Rulesand Relationships,ExpressionsandEquations,andNumerationandCounting(seepage18).
● Whilemostchildrenwillquicklybecomecomfortablewiththeanswerstothenumber factsoftwos,tens andfives(becausethese factsare familiartothem),itisstill veryimportantthatthechildrenaregiven ampletimeandexperiencestodevelopasolidunderstandingoftheconceptsofmultiplicationand divisionthemselves.
● Concrete–pictorial–abstractapproach:Thechildrenwillmove fromexperienceswith familiarobjectsthat theywillputintogroups,andobjectsthatarealreadygroupedintwos,tensandfives(e.g.numbershapes, dicedots,etc.)topictorialactivities(e.g.wherethechildrendraw representationsofthenumbers,using picturesoftheconcrete resources),andfinallytoabstractexercises,wherethe focusisprimarilyon numbersentencesandtheuseofthemultiplicationanddivisionsymbols.
● To reinforcecounting forwardsorbackwardsintwo,tensorfives,considerincorporatingaquick 1–2-minutecountingpractice(forwards,backwards,variousstartingpoints)aspartof yourdaily classroom routine,bothwithinandoutsideofmathslessons.Also,beawarethatachildwhoisquite proficientatcountingingroupsmaynotalways relatethistomultiplication.Therefore,ifthechildrenare countingalonganumberline, 100square,countingstick,etc.,itcanbehelpfultostopintermittentlyand ask,‘Howmanyfiveshavewe counted?Howmanygroupsoffivein35?’
● Whiletheultimateaimisthatthechildrenwillbeabletoefficiently recalltheirbasicnumber facts for multiplicationanddivision,the focusisnotonthe rotememorisationof‘tables’. Rather,theemphasiswill beonthechildrenhavingsufficientconcreteandpictorialexperiencessothattheycanbuildandvisualise models, recognisepatterns,deducetheconnectionsbetweengroupsof facts,andusetheirunderstanding ofwhattheyknowtosolvewhattheydon’tknow. Thechildrenshouldbealsobeencouragedtojustify theiranswers,notjusttogiveanswers.
Teachernote: Pleasenotethattheterm‘tables’todescribemultiplicationanddivisionnumber facts isnotusedineitherthe 1999or2023 PMC.Itoriginatesfromwhengroupsof facts were presentedin tables,andtheanswers were tobelearnedoff by rotememorisationwithlittleornoemphasison visualising,noticingpatterns,developingstrategies,makingconnectionsor recallingthrough understanding.
Commonmisconceptions anddifficulties ● Thechildrenmaynotcreateequalgroups.
● Theymayconfusethenumberofgroupswiththenumberineachgroup.
● Theymaystruggletomaketheconnectionbetween repeatedadditionandmultiplication.
● Theymaystruggleto recognisethedifferencesbetweensharingequallyand repeatedsubtraction.
● Theymaystruggleto recalltheirmultiplicationanddivision facts.
TheUnit5Let’sStrengthenSuggestions for Teachersaddressthecommonmisconceptionsand difficultieslistedabove.
Mathematicalmodels and representations ● Assortedcountableclassroom resources(e.g.bears,links,lollipopsticks,counters)
● Interlockingcubes
● 100squares
● Tenframesandcounters
● Tallymarks
● Numberlines
● Countingsticks
● Numbershapes
● Arrays
● Barmodels
Numbershapes ● Numbersentences(addition,subtraction, multiplicationanddivision)
Teachingtip 100dotarray
The followingmanipulativeprintablesare availabletosupporttheunit: 100Square, TenFrames,Number Line,NumberShapes, 100DotArray,BarModel.Clickonthe resourcesicononthe MathsandMebook coveron edcolearning.ie
Day1,Lesson1 Multiplesof2,10and5 Focusoflearning(withElements)
● Practisescountinginmultiplesof2, 10 and5(U&C)
● Adoptsasystematicapproachintheidentificationofmultiplesof2, 10 and5(U&C)
Learningexperiences
Digitalactivity:SameButDifferent–Multiples of2,5and10 MAM Routines:Reason& Respond,withThink-Pair-Share
Digitalactivity:Oranges MAM Routine: Three-ActTask
Equipment
● Anyavailableresourcesforrepresenting groups,suchasinterlockingcubes,links,pegs andpegboards,counters,numbershapes,play moneyindenominationsof2c,5c,10c,€2,€5 and€10,lollipop/matchsticks,paperclips, drinkingstraws,buttons,etc.
● Countingaids,suchas100squaresornumber lines
Mathslanguage ● multiple(s),count,twos,tens,fives,even,odd
Teachingtip In MathsandMe for1stand2ndClass,thechildren were enabledtocountgroupsof2, 10 and5.Thislesson revisesthisandemphasisesthesenumbersasbeingmultiples.
Warm-up D Digitalactivity:SameButDifferent–Multiples of2,10and5 MAM Routines:Reason& Respond,withThink-Pair-Share
UsingThink-Pair-Share,playtheslideshowandask thechildrentosuggestreasonsforwhytheimages arethesameordifferent.
Mainevent D Digitalactivity:Balloons MAM Routine:Three-ActTask
Act1:Notice&Wonder
Playthevideo,inwhichanumberofitems packagedin5sareopened.UsingThinkPair-Share,askthechildren:
● Whatdoyounotice?
● Whatdoyouwonder?
Recordthechildren’sresponsestobothquestionson theboard.Allowthechildrentheopportunityto respondto(agree/disagreewithorquery)others’ responses,butdonotconfirmorrejectanyofthe ideas.
● (Revealthefocusquestion.)Howmanyballoons doyouthinkarehere?
Act2:ProductiveStruggle
UsingThink-Pair-ShareandWrite-Hide-Show,click toplayorsay/ask:
● Makeanestimatethatistoohigh
● Makeanestimatethatistoolow
● Makeareasonableestimateforeach.
Thechildrenworkinpairsorsmallgroupstoanswer thefocusquestion.Ifnecessary,promptthemby asking:
● Doyouhaveenoughinformation?Whatelsedo youneedtoknow?
Oncethechildrenexplainthattheyneedtoknowthe numberofpacketsofeachthatwereopened,reveal thenextimageandask:
● Whatinformationdoyouhavenow?
● Togetananswer,whatneedstobedone?
● Whatstrategiescanyouuse?
UsingBuildit;Sketchit;Writeit,thechildrenshould choosetheirpreferredwaytomathematicallymodel theirstrategies/solution(s).
Act3:TheBigReveal
Thechildrenshareanddiscusstheirstrategies, solutionsandmodels.Clicktoplayorask:
● Whatanswerdidyouget?
● Whatstrategiesdidyouusetogettheanswer?
● Whatdoyouthinkwasthemostefficient strategy?
Playthevideotorevealtheactualtotal.Clicktoplay orask:
● Isthattheansweryouexpected?Whyorwhy not?
● What‘Iwonder’questionsdidyouanswer?
● Doyouhaveanynew‘Iwonder’questions?
Optionalconsolidation FurtherPractice Askthechildrentobuildmodelsof themultiplesof2,10and/or5usingtheirchoiceof theavailableclassroomresources(e.g.tenframes andcounters,lollipopssticks,interlockingcubes, playingcards,playmoneycoins,etc.).
GamesBank Playthe‘CountinginMultiples’version ofthegame‘21’.
SkipCountHopscotch Playhopscotchintheyard, butinsteadofthenumerals1–10,writethemultiples of2,5or10.
Story Read CountonPablo byBarbaradeRubertis, TheKing’sCommissioners byAileenFriedman, HandsDown:CountingbyFives byMichaelDahl,and/ or HowManySeedsinaPumpkin? byMargaret McNamara.
Teachingtip Thechildrencould recordintheirMathsJournals whattheybuilt,sketchedorwrote,usingimages and/or words.
Let’sstrengthen Encouragethechildrentouse availablecounting aids(e.g.the 100DotArray ontheinsideback coverofthePupil’sBookortheopennumberline ontheir MWBs).
P Pupil’sBookpage42: Multiplesof2,10and5
andextension possibilities Let’sStrengthen TaskAontheUnit5Let’s StrengthenPCMcouldbeusedtoconsolidatethis lesson.
EstimationStation Fillatransparentcontainerwith lessthan100smallitemsfromtheclassroom.Leave aboxnearby,wherethechildrencan‘post’their estimates.Aftertwoorthreedays,askagroupto counttheitemsingroups(notinones)andidentify whohadtheclosestestimate.Theycanthensetup thestationagainwithmore/lessitemsordifferent items.
ReviewandReflect Usethepromptquestionsin theReviewandReflectposter.
Day2,Lesson2 MultiplicationasRepeatedAddition ● Exploresand recognisesmultiplicationas repeatedaddition(U&C)
● Visualisesandcreatesmodelsofmultiplication,including repeatedaddition(U&C) Focusoflearning(withElements)
Learningexperiences
Digitalactivity:Multiplesof2/10/5
MAM Routine:ChoralCounting
Digitalactivity:MultiplicationSentences
MAM Routines:Reason&Respond,withWrite-Hide-Show
Concreteactivity:MakingandRecordingGroups
MAM Routine:Buildit;Sketchit;Writeit
Pupil’sBookpage43:MultiplicationasRepeatedAddition
Mathslanguage ● multiplicationsentence,repeatedaddition,groupsof,times
Warm-up Equipment
● Anyavailableresourcesfor representinggroups,asin Lesson1
● Countingaids,suchas100 squaresornumberlines
● PCMs1,2,3
D Digitalactivity:Multiplesof2/10/5
MAM Routine:ChoralCounting
Chooseoneofthefollowing,dependingontheneeds ofyourclass:
● Multiplesof2
● Multiplesof10
● Multiplesof5
Seeit,thensayit! Displaythefirstslide.Inunison, thechildrenshouldsaythenumberstheyseeonthe countingstick,forwardsandthenbackwards.Ask
● Whatpatternsdoyounotice?
● Whatisstayingthesame?
● Whatisdifferent?
Displayeachslideinturn.Oneachsubsequentslide, somenumber(s)havebeenremoved.Ontheseslides thechildrensayallthenumbersthattheyseeandthe missingnumbers.
Repeatasrequiredwithadifferentsetofmultiples.
Teachingtip Pleasenotethatthese resources were used previouslyin2ndClasstointroduceskipcounting in2s, 10sand5s,soitmaynotbenecessarytouse themall–andsequentially–ifthechildrenare alreadysecureintheirabilityto recallthe multiplesof2, 10 and/or5.
Let’sdeepen Splittheclassintwoormoregroups.Onegroup startsthecount,and,uponasignalfromthe teacher,theothergrouptakes over. Continue, movingfromonegroupbacktotheother.This encouragesthechildrentoconcentrateandlisten better.
Teachingtip If you wouldprefertoconductthisasaconcrete activitybutthereareinsufficientphysical resources availableintheclassroom,distributea copyofPCM1:DotMultiplesof2, 10 and5to eachpair.
Mainevent D Digitalactivity:MultiplicationSentences
MAM Routines:Reason&Respond,with Write-Hide-Show Playthevideoand,usingWrite-HideShow,promptthechildrentorespondon theirMWB,givingreasonsfortheir answersasappropriate.
C Concreteactivity:MakingandRecording Groups
MAM Routine:Buildit;Sketchit;Writeit
Teachingtip Ifthereareinsufficientphysical resources availableintheclassroom,distributeacopyof PCM1:DotMultiples2, 10 and5toeachpair.
Providethechildrenwithsuitableavailableclassroom resources(seeequipment).UsingPCM2:0–10 SpinnerandPCM3:2/10/5Spinner,spineachspinner once.Thenumbersspunindicatethegroupstobe represented(e.g.7groupsof5).
● Buildit!Canyouusetheclassroomresources(or PCM1:DotMultiplesof2,10and5)torepresent this?Showus.
● Sketchit!Canyourepresentthegroupsbuiltasa sketchonyourMWB?Showus.
● Writeit!Canyourepresentthegroupsusing numbersentences(additionand/or multiplication)orwords(e.g.3groupsof10)? Showus.
Ask:
● Canyouworkoutananswer?Whatstrategydid youuse?(e.g.repeatedaddition,countingin multiples,etc.)
● Whichisthemostefficientwaytoarriveatan answerinyouropinion?
Repeatasrequiredbyspinningnewcombinations.
Teachingtip Thechildrencould recordintheirMathsJournals whattheybuilt,sketchedorwrote,usingimages and/or words.
Let’sdeepen Asthechildrenbecomemoreconfidentand competent,challengethemtogivetheanswer withoutusing resources.
Let’sstrengthen Thechildrenmayuse‘countall’asthemeansto identifythetotalamount.Promptthechildrento usecountinginmultiplesinstead.Providethem withacopyofPCM1:DotMultiplesof2, 10 and 5,onwhichtheycouldwritethemultiplesasa support forcounting.
P Pupil’sBookpage43: Multiplicationas RepeatedAddition
Optionalconsolidation andextension possibilities NumberDisplay Setupadisplayformultiplication (anddivisioninthesecondweek)intheclassroom. Thiscouldincludeexamplesofvariousimagesof groupsinreallifefoundinprintmediaandonline,as wellasappropriatelabels(seetheUnit5Maths LanguageCards).Thechildrencouldcontribute samplesoftheirownworkfromthisandsubsequent lessons,andlabelthem.Theycouldalsosourcereal objectsorimagesfromhometoaddtothedisplay.
NumberLine Workinginpairs,askthechildren tousethetopopennumberlineonthebackof theirMWBstowriteasetofmultiplesinorder
(e.g.0,2,4,6…20).Oncewritten,thechildrenrecite themultiplestogetherforwardsandthenbackwards. Then,oneofthepairremoves(rubsout)oneofthe multiples.Thepairrecitesthemultiplesagain, includingthemissingnumber.Theyrepeatthisuntil allofthenumeralswrittenhavebeenremoved.They canalsorepeatthisusingadifferentsetofmultiples (e.g.0,5,10…50or0,10,20…100).
Let’sDeepen Challengethechildrentorecordand recitemultiplesbeyondthefamiliarranges(e.g.5s from50to100,2sfrom80to100,etc).
EstimationStation Remindchildrentosubmit estimates,counttheitemsand/orsetupanew station.
ReviewandReflect Usethepromptquestionsin theReviewandReflectposter.
Day3,Lesson3 Arrays Focusoflearning(withElements) ● Visualisesandcreatesmodelsofmultiplication,including rectangulararrays(U&C)
Learningexperiences Pupil’sBookpages44–45:Arrays D D C P
Digitalactivity:DotMultiples:Groupsof2/10/5
MAM Routines:QuickImages,withWrite-Hide-Show
Digitalactivity:Arrays
MAM Routines:Reason&Respond,withWrite-Hide-Show
Concreteactivity:MakingandRecordingArrays
MAM Routine:Buildit!Sketchit!Writeit!
Mathslanguage ● array(s),row(s),column(s)
Warm-up D Digitalactivity:DotMultiples:Groupsof2/10/5
MAM Routine:QuickImageswithWrite-HideShow
Chooseoneofthefollowing,dependingontheneeds ofyourclass:
● DotMultiples:Groupsof2
● DotMultiples:Groupsof10
● GroupMultiples:Groupsof5
Brieflyrevealandthenhidetheimage(s).Askthe childrentowritethematchingmultiplication sentenceandanswerontheirMWBs.Next,askthem toshowtheiranswers,andrecordtheseonthe board.Becarefulnottoconfirmthecorrectanswer. Ask:
Equipment ● Anyavailableresourcesfor representinggroups,asin Lesson1
● A4sheetsofpaper
● Countingaids,suchas100 squaresornumberlines
● PCMs2,3,4
D Digitalactivity:Arrays MAM Routines:Reason& Respond,withWrite-Hide-Show
● Arethereanyanswersthatareunreasonable/not likelybecausetheydon’tmakesense?Which ones?Whydoyouthinkthis?
● Whichanswerdoyouagreewith?Explainthe strategyyouusedtogetyouranswer.
● Didanybodyuseadifferentstrategy?
Whentherearenonewstrategiestodiscuss,reveal theimageagainandconfirmtheanswer,usinga varietyofpossiblestrategies.
Teachingtip Therearetenslidesinthisactivity,butitisnot necessaryoradvisabletouseallofthese.Choose aselectionthatbestsuitstheabilityof yourclass.
Playtheresourceand,usingWrite-Hide-Show, promptthechildrentorespondon theirMWBs,givingreasonsfortheir answersasappropriate.
C Concreteactivity:MakingandRecordingArrays MAM Routine:Buildit!Sketchit!Writeit! ProvidepairsofchildrenwithanA4sheetofpaper cutlengthwaystooverlapthe100DotArrayonthe insidecoveroftheirPupil’sBook.UsingPCM2:0–10 SpinnerandPCM3:2/10/5Spinner,spineachspinner once.Thenumbersspunindicatethearraytobe represented(e.g.3rowsof10).Askthechildrento:
● Buildit!Usethe100-dotarrayontheinsidecover ofyourPupil’sBooktorepresentthisarray.
● Sketchit!Canyourepresentthearrayasasketch onyourMWB?Showus.(Ifnotsuggested, demonstratehowtheycoulddrawarectangular shapewiththeamountineachrowwrittenalong thetopandtheamountofrowswrittendown alongtheleft-handside.
● Writeit!Canyourepresentthearrayusing numbersentences(additionand/or multiplication)orwords(e.g.3rowsof10)? Showus.
Ask:
● Canyouworkoutananswer?Whatstrategydid youuse?(e.g.repeatedaddition,countingin multiples,other,etc.)
● Whichisthemostefficientwaytoarriveatan answerinyouropinion?
Repeatasrequiredbyspinningnewcombinations.
Teachingtip ThechildrencouldalsousePCM4: 100-dotArray placedinsidea reusabledry-erasepocket,if available.This wouldallowthemtoringthearrays andwritethematchingnumbersentencesdirectly onthepocket.
Teachingtip Thechildrencould recordintheirMathsJournals whattheybuilt,sketchedorwrote,usingimages and/or words.
Let’sstrengthen Thechildrenmayuse‘countall’asthemeansto identifythetotalamount.Promptthechildrento usecountinginmultiplesinstead.Providethem withacopyofPCM1:DotMultiples2, 10 and5, onwhichtheycouldwritethemultiplesasa support forcounting.
Let’sdeepen Challengethechildrentoproposestrategies for thevariouscalculationsthat reducetheneedto countmultiples,etc.
Let’sstrengthen
Thechildrenmayfindwritingtheaddition sentencestimeconsumingordifficult.Allow themtheopportunityto verbalisethematching additionsentence forthemultiplication sentencestheyhave written.
Optionalconsolidation andextension possibilities GamesBank Play‘CapturetheArea’,usingPCM2: 0–10SpinnerandPCM3:2/10/5Spinner,sothatthe totalofallareasisamultipleof2,5or10.
MathsEyes Canthechildrenfindsimilararrayswith rowsof2,10and5intheclassroomorschool?Can theyuseclassroomresourcestomakearrays?A partnercouldbeaskedtowriteamatchingnumber sentenceandsolveit.Imagescouldalsobetakenof thefoundormadearrays,andthesecouldbeadded totheclassdisplayand/orusedtocreateadigital display,quickimagesfile,etc.
Let’sDeepen TaskAontheUnit5Let’sDeepen PCMcouldbeexploredatanystageafterthislesson. ReviewandReflect Usethepromptquestionsin theReviewandReflectposter.
Day4,Lesson4 TurnaroundFacts Focusoflearning(withElements) ● Exploresthecommutativepropertyofmultiplication(U&C)
Learningexperiences Digitalactivity:WhichOneDoesn’tBelong?
MAM Routines:Reason&Respond,withThink-Pair-Share
Digitalactivity:SameButDifferent–TurnaroundFacts
MAM Routines:Reason&Respond,withThink-Pair-Share
Concreteactivity:ModelingCommutativeArrangements
MAM Routine:Buildit!Sketchit!Writeit!
● turnaroundfacts(commutative)
Mathslanguage Warm-up D Digitalactivity:WhichOneDoesn’tBelong?
MAM Routines:Reason&Respond,withThinkPair-Share
Equipment ● Anyavailableresourcesfor representinggroups,asin Lesson1
● A4sheetsofpaper
● Countingaids,suchas100 squaresornumberlines
● PCMs2,3
Playtheslideshowand,usingThink-Pair-Share,ask thechildrentoproposereasonsforwhyeachofthe imagesdoesnotbelong.
Mainevent D Slideshow:SameButDifferent–Turnaround Facts MAM Routines:Reason&Respond,with Think-Pair-Share
Playtheslideshowand,usingThink-Pair-Share,ask thechildrentoproposereasonsforwhytheimages arethesameordifferent. Afterwardsgobackthoughtheslides, andask(ifnotansweredalready):
● OnyourMWBs,writethematchingadditionand multiplicationsentencesforeachimage.
● Whatdoyounoticeabouttheanswersforthe imagesoneachslide?
● Haveyouseenthisbeforeinaddition?Whatdo wecallit?(Turnaroundfacts.Refertothe CalculationStrategyWallCardforTurnaround Factsifitisondisplay.)
● Explainwhatwemeanbyturnaroundfacts?(If theorderofthenumbersisswapped,theanswer isthesame,i.e.samevalue,different appearance.)
● Theproperwaytodescribethisinmathsistosay thatadditioniscommutativemeaningthateven iftheorderofthenumbersbeingaddedis
swappedtheanswerremainsthesame.Is multiplicationcommutative?Explainwhy.
● Issubtractioncommutative?Explainwhy.
C Concreteactivity:ModelingCommutative Arrangements
MAM Routine:Buildit!Sketchit!Writeit! ProvidepairsofchildrenwithanA4sheetofpaper cutlengthwaystooverlapthe100-dotarrayonthe insidecoveroftheirPupil’sBook.UsingPCM2:0–10 SpinnerandPCM3:2/10/5Spinner,spineachspinner once.Thenumbersspunindicatethearraytobe represented(e.g.4rowsof2).Askthechildrento:
● Buildit!Usethe100-dotarrayontheinsidecover ofyourPupil’sBooktorepresentthisarray.Then, rotatethearrayaquarterturntoshowthe turnaroundfact.
● Sketchit!Representthearrayasasketchonyour MWBs.Then,rotatethesketchtoshowthe turnaroundfact.
● Writeit!Representtheoriginalarrayusing numbersentences(additionand/or multiplication)and/orwords(e.g.3rowsof10). Then,writetheturnaroundfact.
Say/ask:
● Workouttheanswer.
● Whatstrategydidyouuse? Whichversionofthefactwaseasiertoanswer and/orrepresent?
Repeatasrequiredbyspinningnewcombinations.
Teachingtip Thechildrencould recordintheirMathsJournals whattheybuilt,sketchedorwrote,usingimages and/or words.
Let’sdeepen Challengethechildrentoarrange20counters/ cubesinvarious rectangulararraysandtowrite thematchingmultiplicationsentences.Areanyof thesealsopairsofturnaround facts?Whichones? Whataboutusing40counters/cubes?
Optionalconsolidation andextension possibilities StrategyWall AddtheTurnaroundFactsCalculation StrategyWallCard(Multiplication)totheclass StrategyWall,ifnotalreadyadded.Refertothisas relevantthroughoutthisandsubsequentunits.The childrencouldalsoaddtheirownsketchesofthis strategybothtotheStrategyWallandtheirMaths Journals.
GamesBank Play‘CapturetheArea’,asinthe previouslesson,butthistimeencouragethechildren torotatetherectanglesbeingdrawnifdoingsowill
allowmoreshapestobeaddedandthereforeextend thegameforlonger.
NumberDisplay Ifevidentintheclassdisplay, examplesofturnaroundfactscanbelabelledassuch. EstimationStation Remindchildrentosubmit estimates,counttheitemsand/orsetupanew station.
ReviewandReflect Usethepromptquestionsin theReviewandReflectposter.
Day5,Lesson5 StrategiesforMultiplyingby2,10and5 ● Exploresandsuggestsstrategicapproachestothemultiplication factsof2, 10 and5(U&C)
● Explorestheimplicationsofmultiplying by 10 (U&C)
Digitalactivity:WouldYouRather?
MAM Routines:Reason&Respond,withThink-Pair-Share
Digitalactivity:Multiplyingby2/10/5
MAM Routines:Reason&Respond,withWrite-Hide-Show
P
Pupil’sBookpage46:StrategiesforMultiplyingby2,10and5
● Countingaids,suchas100 squaresornumberlines Equipment ● strategies/strategy,samevalue,differentappearance,double,half,movingdigits,necessaryzero
D Digitalactivity:WouldYouRather?
MAM Routines:Reason&Respond,with Think-Pair-Share
● Anyavailableresourcesfor representinggroups,asin Lesson1
Playtheslideshowand,usingThink-Pair-Share,ask thechildrentoproposereasonsforwhytheywould preferoneoptionovertheother.
Mainevent D Digitalactivity:Multiplyingby2/10/5
MAM Routines:Reason&Respond,with Write-Hide-Show
Askthechildrentojustifytheiranswerstothe followingquestions,givingreasonsfortheiranswers:
● Whatstrategycouldbeusedwhenmultiplying by2?
● Whatstrategycouldbeusedwhenmultiplying by10?
● Whatstrategycouldbeusedwhenmultiplying by5?
● Whatdoyouthinkmightbeshownonthe CalculationStrategyWallCardforeachofthese?
Playeachofthevideosinturn:
● Multiplyingby2
● Multiplyingby10
● Multiplyingby5
UsingWrite-Hide-Show,promptthechildrento respondontheirMWBs,givingreasonsfortheir answersasappropriate.
Afterwards,dependingontheneedsof theclass,thechildrencouldbeaskedto useBuildit;Sketchit;Writeittoexplore anddemonstratethestrategiesoutlinedinthe videos,usingfurtherexamples.Formultiplyingby5, encouragethechildrentousethe100-dotarrayon theinsidecoveroftheirPupil’sBooktorevealan
arrayfor10timesthenumber,andthenuseapencil tovisuallydividethearrayinhalftorepresent5times thenumber.
Teachingtip Formultiplying by 10,usethe vocabularyof‘moving digits’andthenaddinga‘necessary zero’.Itisnot correcttosaythatinordertomakenumbersten timesbigger, we adda zero,becausethisdoesnot workwithdecimals(e.g.5.3× 10 ≠5.30).
P Pupil’sBookpage46: StrategiesforMultiplying by2,10and5
Teachingtip ActivityCisdesignedspecificallytoencourage thechildrentoapplytheirunderstandingofthe calculationstrategiestomentallycalculate answersbeyondthetraditionallimits. For example,if5timesanumberishalfof 10 times thenumber,then5×18=90(halfof180).
Optionalconsolidation andextension possibilities GamesBank Play‘TimesSnap’withthe2s,5s,and 10sinonepile(seetheLet’sStrengthenoption).
Let’sPlay Play‘CapturetheArea’onpage45ofthe Pupil’sBook.
CalculationStrategies AddtheCalculation StrategyWallCardsforMultiplyingby2,10and5to theclassStrategyWall,ifnotalreadyadded.Referto theseasrelevantthroughoutthisandsubsequent units.Thechildrencouldalsoaddtheirownsketches ofthesestrategiesbothtotheStrategyWalland theirMathsJournals.
Story Readastorybasedondoubling,suchas Twoof Everything byLilyToyHongor Minnie’sDiner:a MultiplyingMenu byDayleAnnDodds.
Let’sStrengthen TasksBandContheUnit5Let’s StrengthenPCMcouldbeusedtoconsolidatethis lesson.
ReviewandReflect Usethepromptquestionsin theReviewandReflectposter.
Day6,Lesson6 DivisionasSharingEqually Focusoflearning(withElements) ● Visualisesmodelsofdivisionasequalsharing(U&C)
Digitalactivity:Multiplesof2/10/5
MAM Routines:ChoralCounting,withWrite-Hide-Show
Digitalactivity:Sharing€20Equally
MAM Routines:Reason&Respond,withWrite-Hide-Show
Concreteactivity:DivisionasSharingEqually MAM Routine:Buildit!Sketchit!Writeit! P Pupil’sBookpage47:DivisionasSharingEqually
● division,divide,fairshare,between,equally,equal
D Digitalactivity:Multiplesof2/10/5
MAM Routines:ChoralCounting,with Write-Hide-Show
Warm-up UsethesameresourceaswasusedintheWarm-up ofLesson2fromoneoftheoptionsbelow:
● Multiples of2
● Multiples of10
● Multiples of5
D Digitalactivity:Sharing€20Equally MAM Routines:Reason&Respond,with Write-Hide-Show
Provideeachpairwith20items(e.g. interlockingcubes,counters,etc.).Ask thechildrentoexplorewaysinwhichthe amountcouldbedividedfairlyintogroups.After sufficienttime,playtheresourceand,usingWriteHide-Show,promptthechildrentorespondontheir MWB,givingreasonsfortheiranswersas appropriate.
C Concreteactivity:DivisionasSharingEqually MAM Routine:Buildit!Sketchit!Writeit!
Providepairsofchildrenwithanassortmentof classroomresources.Usingtheresourcesandtheir
● Anyavailableresourcesfor representinggroups,asin Lesson1
● Countingaids,suchas100 squaresornumberlines Equipment
Pauseforawhileonthefinalslideineachgroup(i.e. theblankslide)and,pointingtoarandompositionon thecountingstick,askthechildren,usingWriteHide-Showtoidentifythemultiplethatwasthere.
Teachingtip Aphysicalcountingstickcouldalsobeusedif available.
Mainevent Pupil’sBook,askthemtorepresentthevarious scenarios.
Teachingtip Thechildrencouldalsobeaskedtosuggesttheir own ‘sharing’or‘dividing’storiesandscenariosto model.This wouldbeagreatwaytoassessifthey have fullygraspedtheconcept.
● Buildit!Canyouusetheclassroomresourcesto representthisstory?Showus.
● Sketchit!Canyourepresentthestoryasasketch onyourMWB?Showus.
● Writeit!Canyourepresentthestoryusing divisionsentences?Showus.
Mathslanguage
Ask:
● Canyouworkoutananswer?Whatstrategydid youuse?
Teachingtip
IntheirMathsJournals,thechildrencould record whattheysketchedandwrote.
Let’sdeepen
Whentheybecomemoreconfident,challengethe childrentocalculatetheanswer by mentally visualisingtheamount ratherthanbuildingor sketchingit.
P Pupil’sBookpage47: DivisionasSharing Equally
Optionalconsolidation andextension possibilities Let’sDeepen TaskBontheUnit5let’sDeepenPCM couldbeexploredatanystageafterthislesson. NumberDisplay Examplesofdivisionassharing equally,andassociatedlabels,couldbeaddedtothe classdisplay.
GamesBank Play‘TimesSnap’withthe2s,5s,and 10sinonepile(seetheLet’sStrengthenoption). ReviewandReflect Usethepromptquestionsin theReviewandReflectposter.
Day 7, Lesson7 DivisionasRepeatedSubtraction Digitalactivity:Multiplesof2/10/5 MAM Routine:ChoralCounting
Digitalactivity:RepeatedSubtraction
MAM Routines:Reason&Respond,withWrite-Hide-Show
Concreteactivity:DivisionasSharingEqually
MAM Routine:Buildit!Sketchit!Writeit!
Pupil’sBookpage48:DivisionasDivisionasRepeatedSubtraction
MAM Routine:ChoralCounting
UsethesameresourceaswasusedintheWarm-up ofLesson2fromoneoftheoptionsbelow: ● Multiples of2
Anyavailable resourcesfor representinggroups, asinLesson1
Countingaids,such as100squaresor numberlines
Multiples of10
Multiples of5 Puttheemphasisonthechildrensayingthemultiples
Mainevent D Digitalactivity:RepeatedSubtraction MAM Routines:Reason&Respond,with Write-Hide-Show Playtheresourceand,usingWrite-Hide-Show, promptthechildrentorespondontheirMWBs, givingreasonsfortheiranswersasappropriate.
C Concreteactivity:RepeatedSubtraction MAM Routine:Buildit!Sketchit!Writeit! Providepairsofchildrenwithanassortmentof classroomresources.Usingthematerialsandtheir Pupil’sBook,askthemtorepresentthevarious scenarios.
Teachingtip Thechildrencouldalsobeaskedtosuggesttheir own ‘sharing’or‘dividing’storiesandscenariosto model.This wouldbeagreatwaytoassessifthey have fullygraspedtheconcept.
● Buildit!Canyouusetheclassroomresourcesto representthisstory?Showus.
● Sketchit!Canyourepresentthestoryasasketch onyourMWBs?Showus.
● Writeit!Canyourepresentthestoryusing divisionsentences?Showus.
Ask:
● Canyouworkoutananswer?What strategydidyouuse?
Teachingtip IntheirMathsJournals,thechildrencould record whattheysketchedandwrote.
Let’sdeepen Whentheybecomemoreconfident,challengethe childrentocalculatetheanswer by mentally visualisingtheamount ratherthanbuildingor sketchingit.
P Pupil’sBookpage48: DivisionasRepeated Subtraction
Optionalconsolidation andextension possibilities NumberDisplay Examplesofdivisionasrepeated subtraction,andassociatedlabels,couldbeaddedto theclassdisplay.
GamesBank Play‘TimesSnap’withthe2s,5s,and 10sinonepile(seetheLet’sStrengthenoption).
Let’sDeepen TasksCandDontheUnit5Let’s DeepenPCMcouldbeexploredatanystageafter thislesson.
Story Read OneHundredHungryAnts byElinorJ. Pinczes,andcreatemultiplicationanddivision sentencestomatchthearrangements. ReviewandReflect Usethepromptquestionsin theReviewandReflectposter.
Learningexperiences Digitalactivity:HeadlineStories MAM Routines:Reason& Respond,withThink-Pair-Share;Buildit!Sketchit!Writeit!
Digitalactivity:MultiplicationandDivisionasInverse MAM Routines:ConceptCartoon,withThink-Pair-Share;Build it!Sketchit!Writeit!
Concreteactivity:MultiplicationandDivisionasInverse MAM Routine:Write-Hide-Show
Pupil’sBookpage49:MultiplicationandDivisionasInverse
D Digitalactivity:HeadlineStories
Warm-up MAM Routines:Reason&Respond,withThinkPair-Share;Buildit!Sketchit!Writeit!
ChooseoneoftheHeadlinestodisplaytotheclass. Displaytheinformation(presentedinwordsand/or images)totheclass.
● Firstly,usingThink-Pair-Share,askthechildrento createandsharewiththeclass,mathsquestions inspiredbytheinformation.
D Digitalactivity:MultiplicationandDivisionas
Inverse MAM Routines:ConceptCartoon,with Think-Pair-Share;Buildit!Sketchit!Writeit!
DisplaytheimageandfacilitateThink-Pair-Share. Afterwards,ifnotansweredalready,ask:
● Whatdoyouthink?Explainwhy.
● Whodoyounotagreewith?Whydoyouthink theythinkthat?
● Howcanwefindoutwhosethinkingiscorrect?
UsingBuildit;Sketchit;Writeitandconcreteresources, sketchesand/ornumbersentences,encouragethe childrentoprovewhysomeoftheproposednumber sentencesworkandwhysomedonot.
C Concreteactivity:MultiplicationandDivisionas
Inverse MAM Routine:Write-Hide-Show
Teachingtip Visual representationsofarrayshave morescope herethanvisual representationofgroups(e.g.an array canbeviewedasY rowsofZ,orZcolumnsof Y, whereasagroupisYgroupsofZonly,unlessitis rearranged).
● Anyavailableresourcesfor representinggroups,asin Lesson1
● Countingaids,suchas100 squaresornumberlines
● Secondly,usingBuildit;Sketchit;Writeit,allow thechildrentimetomodelandsolvesomeofthe questionsposed–eithertheirownorthoseof others.
Ifnotsuggested,askthechildrentosuggestsuitable numbersentencesthatcouldbewrittenbasedonthe information.
Forthisactivity,returntothearrayimagesonpages 44–45ofthePupil’sBook.Foreachimagechosen, askthechildren:
● OnyourMWBs,writethisasamultiplication sentence.(Ifnotsuggested,promptthechildren torealisethatthereismorethan onepossiblewaytowritea matchingmultiplicationsentence, e.g.4×5=20;5×4=20.)
● OnyourMWBs,writethisasadivisionsentence. (Ifnotsuggested,promptthechildrentorealise thatthereismorethanonepossiblewaytowrite amatchingdivisionsentence,e.g.20÷5=4; 20÷4=5.)
● Eoghansaid:‘Thisisafactfamily.’Doyouagree? Explainwhy.
● Whatareturnaroundfacts?(swappingtheorder ofthenumbers,whilestillgettingthesame answer)
● Whichnumbersentencesareexamplesof turnaroundfacts?Whicharenot?
Mathslanguage
Mainevent
● Alinasaid:‘Divisionistheinverseof multiplication.’Doyouagree?Explainwhy.
● Whatotheroperationsaresimilartothis? (Additioniscommutative,butsubtractionisnot. Subtractionistheinverseofaddition.)
● Howcanweuseinverseoperationstohelpusin ourmaths?(Wecanusethisunderstandingto solveand/orcheckcalculations.)
Repeatasabovewithotherimagesasrequired.
Teachingtip Thechildrencould recordintheirMathsJournals theirunderstandingofturnaround factsand inverseoperations.
Let’sdeepen Challengethechildrentoidentifyotherwaysto representtheimagesasmultiplicationand divisionnumbersentences(e.g.20=4×5; 20=5×4;5=20÷4;5=20÷4),andalsoto refer tothe relationshipsascommutativeandinverse.
P Pupil’sBookpage49: Multiplicationand DivisionasInverse
Optionalconsolidation andextension possibilities StrategyWall AddtheCalculationStrategyWall CardforDivisionastheinverseofMultiplicationto theclassStrategyWall,ifnotalreadyadded.Referto itasrelevantthroughoutthisandsubsequentunits. Thechildrencouldalsoaddtheirownsketchesofthis strategybothtotheStrategyWallandtheirMaths Journals.
GamesBank Play‘TimesSnap’withthe2s,5s,and 10sinonepile(seetheLet’sStrengthenoption).
NumberDisplay Examplesofmultiplicationand divisionastheinverse,andassociatedlabels,could beaddedtotheclassdisplay.
ReviewandReflect Usethepromptquestionsin theReviewandReflectposter.
Warm-up D Slideshow:SameButDifferent–Number Sentences MAM Routines:Reason&Respond, withThink-Pair-Share
Playanumberofslidesfromtheslideshowand,using Think-Pair-Share,askthechildrentoproposereasons forwhytheimagesarethesameordifferent.
Mainevent C Concreteactivity:Dividingby2,10and5 Inpairs,askthechildrentowriteoutthefactsfor dividingbyeither2,10or5.Afterwards,askthe childrentogivefeedbackontheirfacts.Forexample, forthechildrenwhowroteoutthedividingby2facts, ask:
● Whatfactsdidyouwriteout?(Record theseontheboard.)
● Whatpatternsdoyounotice?What stayedthesame?Whatwasdifferent?
● Whatdoyounoticeabouttheanswers?
● Inwhatwayaretheanswersrelatedtothe numberbeingdivided(i.e.thenumberinfrontof thedivisionsymbol)?(Eachanswerishalfofthe numberbeingdivided.)
● Whatstrategycouldbeusedwhenmultiplyinga numberby2?(Doublethenumber.)
● Whatstrategycouldbeusedwhendividinga numberby2?(Sincedivisionistheinverseof multiplication,wedotheopposite,i.e.halvethe number.)
● Whatdoyouthinkmightbeshownonthe CalculationStrategyWallCardforthisdivision strategy?
Teachingtip Ifnecessary, replaythedigital resource ‘Multiplying by 2/10/5’fromLesson5.
Repeatthesequestionswiththechildrenwhowrote outthedividingby10factsandthedividingby5
facts.Fordividingby10,itisimportantthatthey recognisethatsincedivisionistheinverseof multiplication,wedotheopposite(i.e.thedigitthat wasinthetensplacehasmovedoneplacetothe rightandisnowintheonesplace,havingreplaced thezero,whichisnotneeded).
Fordividingby5,thechildrenmaysuggestthat dividingby10anddoublingtheresultgivesthesame answerasdividingby5.However,thiswillbetoo complexformost.Therefore,atthisstage,themost suitablestrategyforthedivisionoffactsof5isto relatethemtotheirinverse(i.e.for45÷5,askhow many5sequal45).
Teachingtip Fordividing by 10,usethe vocabularyof‘moving digits’.Itisnotcorrecttosaythatinordertomake numberstentimessmaller, we remove a zero, becausethisdoesnot workwithallnumbers(e.g. wholenumbersthatarenotamultipleof 10,and decimals,suchas54÷ 10 =5.4).
P Pupil’sBookpage50: StrategiesforDividing by2,10and5
Optionalconsolidation andextension possibilities StrategyWall AddtheCalculationStrategyWall CardsforDividingby2,10and5totheclassStrategy Zone,ifnotalreadyadded.Refertotheseasrelevant throughoutthisandsubsequentunits.Thechildren couldalsoaddtheirownsketchesofthesestrategies bothtotheStrategyWallandtheirMathsJournals.
Let’sStrengthen TaskDontheUnit5Let’s StrengthenPCMcouldbeusedtoconsolidatethis lesson.
Story Read IfyouwereanOddNumber byMarcie Abofftolearnwhichnumbersarenotdivisibleby2. ReviewandReflect Usethepromptquestionsin theReviewandReflectposter.
Day10,Lesson10 ReviewandReflect Focusoflearning(withElements) ● Reviewsandreflectsonlearning(U&C)
Warm-up Carryoutawarm-upactivityofyourchoosingfromoneofthelessonsinthisunit.
Mainevent Usethismenuofactivityideastochoosehowbesttostructurethislastlessonoftheunittosuityourneeds andtheneedsofyourclass.
Let’stalk! Reviewand Reflect Poster:UseThink-Pair-Share alongsidethepromptquestionsto reviewtheunit. Thechildrencould recordwhattheyknowintheir MathsJournals(e.g.usingaconceptmap).
Individualchildrencouldpresentexamplesoftheir owndrawings/work/constructionstotheclass,and talkaboutwhattheyhave learned.
Mathslanguage Askthechildrentoexplaintheseterms(perhaps usingexamplesordrawingson MWBs):multiple(s), even,odd,multiplication, repeatedaddition,same valuedifferentappearance,double,half,division, (fair)share, repeatedsubtraction, fact family.
UsetheUnit5MathsLanguageCardsto revise key terms. Forexample:Iftheimageandtextarecut apart,canthechildrenmatchthem?
ProgressAssessmentBooklet CompleteQuestions25–30onpage8.Alternatively, thesecanbelefttodoaspartofabigger review duringthenext review week.
Let’splay! ChoosefromavarietyofgamesintheGamesBank:
● ‘21’
● ‘CapturetheArea’
● ‘TimesSnap’
Mathsstrategiesandmodels Askthechildrentogiveexamplesofthestrategies theyusedinthisunit(e.g.howtomultiply/divide by 2 by doubling/halving;howtomove thedigitsto multiply/divide by 10,how5timesishalf 10 times, howtouseturnaround factsandtheinversetosolve andcheckcalculations).
Askthechildrentogiveexamplesofthemodelsthey usedinthisunit,especiallygroups,arrays,number linesandbarmodels.
Whichstrategiesandmodelsdidtheyprefer?Why?
Mathseyes ● Goforawalkaroundtheschooland/orlocal area.Wherecanyouseeexamplesofequal groupsorarrays?
● Takephotosofreal-lifeexamplesofequal groupsorarraysathome.Thesecouldbesentin digitallytobeaddedtotheclassdisplayand/or compiledintoadigitalslideshow.
Let’sstrengthen
Identifychildrenwhomightbenefitfromextra practicewithsomeofthe keyconceptsorskills inthisunit.UsetheUnit5Let’sStrengthenPCM. ConsulttheUnit5Let’sStrengthenSuggestions for Teachers.
Let’sdeepen
UsetheUnit5Let’sDeepenPCM.
