CalculationPolicy–2016-17
Subtraction
FoundationStage
Year1
Year2
Mathsforyoungchildrenshouldbemeaningful.
Wherepossible,conceptsshouldbetaughtinthe
contextofreallife.
Guidance/ModelsandImages
• Childrenbeginwithmostlypictorial
representations.
• Concreteapparatusisusedtorelate
subtractiontotakingawayandcountinghow
manyobjectsareleft.
• Concreteapparatusmodelsthesubtractionof
twoobjectsfromasetoffive.
• Constructnumbersentencesverballyorusing
cardstogowithpracticalactivities.
• Childrenareencouragedtoreadnumber
sentencesaloudindifferentways‘fivesubtract
oneleavesfour’‘fourisequaltofivesubtract
one’.
• Childrenmakearecordinpictures,wordsor
symbolsofsubtractionactivitiesalready
carriedout.
• Solvesimpleproblemsusingfingers.
MentalStrategies
• Childrenshouldexperienceregularcounting
backfromdifferentnumbersin1sandin
multiplesof2,5and10.
• Childrenshouldmemoriseandreasonwith
numberbondsfornumbersto20,experiencing
the=signindifferentpositions.
• Theyshouldseesubtractionastheinverse
operationofaddition.E.g.7+3=10isrelated
to10–3=7and10–7=3,understandingof
whichcouldbesupportedbyanimagelikethis.
• UsebundlesofstrawsandDienestomodel
partitioningteennumbersintotensandones.
• Childrenshouldbegintounderstand
subtractionasbothtakingawayandfinding
thedifferencebetween,andshouldfindsmall
differencesbycountingon.
• Missingnumberproblemse.g.7=□-9;20-□
=9;15–9=□;□-□=11;16–0=□
MentalStrategies
• Childrenshouldcountbackregularlyinsteps
of2,3,5and10.Countingbackintensfrom
anynumbershouldleadtosubtracting
multiplesof10.
• Numberlinesshouldcontinuetobean
importantimagetosupportthinking,for
exampletomodelhowtosubtract9by
adjusting.
• Childrenshouldpractisesubtractionto20to
becomeincreasinglyfluent.Theyshoulduse
thefactstheyknowtoderiveothers,e.gusing
10-7=3and7=10-3tocalculate100-70=
30and70=100-30.
• Numberlinesand100squarescanbeusedto
modelcalculationssuchas74–11,77–9or36
–14,wherepartitioningoradjustingareused.
Ontheexampleabove,1isinthebottomleft
cornersothat‘up’equatesto‘add’.
• Childrenshouldlearntochecktheir
Subtraction
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Numbertrackscanbeintroducedtocount
backandfindoneless
Whatis1lessthan9?1lessthan20?
Numberlinescanbeusedtoalongsidenumber
tracksandpracticalapparatustosolve
subtractioncalculationsandwordproblems.
Childrencountbackunderthenumberline.
Childrenwillneedopportunitiestolookatand
talkaboutdifferentmodelsandimagesasthey
movebetweenrepresentations.
Vocabulary
Gamesandsongscanbeausefulwaytobegin
usingvocabularyinvolvedinsubtractione.g.
Take(away),leave,howmanyareleft/leftover?
Howmanyhavegone?Oneless,twoless…ten
less…,howmanyfeweris…than…?Difference
between,isthesameas
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Useconcreteobjectsandpictorial
representations.Ifappropriate,progressfrom
usingnumberlineswitheverynumbershown
tonumberlineswithsignificantnumbers
shown.
Understandsubtractionastake-away:
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Understandsubtractionasfindingthe
difference:
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Theabovemodelwouldbeintroducedwith
concreteobjectswhichchildrencanmove
(includingcardswithpictures)before
progressingtopictorialrepresentation.
Theuseofotherimagesisalsovaluablefor
modellingsubtractione.g.Numicon,bundlesof straws,Dienesapparatus,multi-linkcubes,
beadstrings
calculations,includingbyaddingtocheck.
Theyshouldcontinuetoseesubtractionas
bothtakeawayandfindingthedifference,and
shouldfindasmalldifferencebycountingup.
TheyshoulduseDienestomodelpartitioning
intotensandonesandlearntopartition
numbersindifferentwayse.g.23=20+3=10
+13.
Missingnumberproblemse.g.52–8=□;□–
20=25;22=□–21;6+□+3=11
Itisvaluabletousearangeofrepresentations
(alsoseeY1)andtocontinuetousenumber
linestomodeltake-awayanddifference.E.g.
Thelinkbetweenthetwomaybesupportedby
animagelikethis,with47beingtakenaway
from72,leavingthedifference,whichis25.
Subtraction
Vocabulary
Subtraction,subtract,takeaway,distance
between,differencebetween,morethan,minus,
lessthan,equals=sameas,most,least,pattern,
odd,even,digit,
Generalisations
• Trueorfalse?Subtractionmakesnumbers
smaller
• Whenintroducedtotheequalssign,children
shouldseeitassignifyingequality.Theyshould
becomeusedtoseeingitindifferentpositions.
SomeKeyQuestions
• Howmanymoretomake…?Howmanymore
is…than…?Howmuchmoreis…?Howmany
areleft/leftover?Howmanyhavegone?One
less,twoless,tenless…Howmanyfeweris…
than…?Howmuchlessis…?
• Whatcanyouseehere?
• Isthistrueorfalse?
Towardswrittenmethods
• Recordingadditionandsubtractionin
expandedcolumnscansupportunderstanding
ofthequantityaspectofplacevalueand
prepareforefficientwrittenmethodswith
largernumbers.Thenumbersmaybe
representedwithDienesapparatus.E.g.75–
42
Vocabulary
Subtraction,subtract,takeaway,difference,
differencebetween,minus
Tens,ones,partition
Nearmultipleof10,tensboundary
Lessthan,oneless,twoless…tenless…one
hundredless
More,onemore,twomore...tenmore...one
hundredmore
Generalisation
• Noticingwhathappenswhenyoucountintens
(thedigitsintheonescolumnstaythesame)
• Odd–odd=even;odd–even=odd;etc
Subtraction
showthatadditionoftwonumberscanbe
doneinanyorder(commutative)and
subtractionofonenumberfromanother
cannot
• Recogniseandusetheinverserelationship
betweenadditionandsubtractionandusethis
tocheckcalculationsandmissingnumber
problems.Thisunderstandingcouldbe
supportedbyimagessuchasthis.
SomeKeyQuestions
• Howmanymoretomake…?Howmanymore
is…than…?Howmuchmoreis…?Howmany
areleft/leftover?Howmanyfeweris…than…?
Howmuchlessis…?
• Isthistrueorfalse?
• IfIknowthat7+2=9,whatelsedoIknow?
(e.g.2+7=9;9–7=2;9–2=7;90–20=70
etc).
• Whatdoyounotice?Whatpatternscanyou
see?
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