Addition
Objectiveandstrategies
Concrete
Pictorial
Abstract
Addingthreesingledigit
thirddigit.
Regroupingtomake10
5+12=17
Countonfromthelargernumberandaddonthesmaller
number
Usingemptynumberlines
Onesorin1jumptofindtheanswer
Usinganumberlinetoaddon
thepartwholemodel.
ProgressioninMultiplication
Countingback
Objectives
and
strategies
ELG
Concrete
Pictorial
Abstract
Repeated groups of the same size
Informaljottings,mathematicalmarkmaking,,
problemsolvingprocess,useofblankpaper
Doubling
MentalCalculations
KnownFacts
Count repeated groups of the same size
Respond to/make up number stories
Instant recall
- Doubles of numbers to 5
- Use counting up in 3s, 5s and
10s (using fingers to keep track
of groups) to start to derive
multiplication facts, phrased as
‘what is 4 times 3’ or ;how many
in four groups of 3’
Instant recall
- Doubles of numbers to 10
- Begin to know times table
facts for 3x, 5x and 10x0
Drawpicturestoshowhowtodoubleanumber.
Partitionanumberthendoubleeachpart
beforerecombiningitbacktogether.
Childrenwillworkonpracticalproblemsolvingactivities
involvingdoubling.
Countinmultiplesofanumberaloud.
Writesentenceswithmultiplesofnumbers.
2,4,6,8,10
5,10,15,20,25,30
Countingin
multiples
Useanumberlineorpicturestocontinuesupportincounting
inmultiples.
Countinmultiplessupportedbyconcreteobjectsinequal
groups.
Repeated
addition
Arrays–
showing
commutative
multiplication
Childrenwilldeveloptheirunderstandingofmultiplication
andusejottingstosupportcalculation.
Createarraysusingcounters,cubestoshowmultiplication
sentences.
Drawarraysindifferentrotationstofindcommutative
multiplicationsentences.
Partitioning
Usingdienestopartitionandmultiply
Usearraytowritemultiplicationsentencesand
reinforcerepeatedaddition.
Linkarraystoareaofrectangles
Drawingdienestopartitionthenmultiply
5+5+5=15or3+3+3+3+3=15
5x3=153x5=15
38x5=(30X5)+(8X5)
=150+40
=190
GridMethod
Showthelinkwitharraystofirstintroducethegridmethod
- Multiply a number by doubling
and doubling again
- Multiply a 2 digit whole
number by 10
MoveontousingBase10tomovetowardsamorecompact
method.
Moveontoplacevaluecounterstoshowhowwearefinding
groupsofanumber.Wearefindinggroupsofanumber.We
aremultiplyingby4soweneed4rows.
Instant recall
- Double 15, 25, 35, 45
- Mental recall of 2, 3, 4, 5 and
10
- Begin to know times table
facts for 6x, 7x, 8x and 9x
Derived
- Times table facts for 6x, 7x,
8x and 9x
- Times tables & place value
calculations such as 70 x 3
Column
Method(1)
- Use place value to multiply a
whole number by 10 or 100
- Multiply two multiples of 10
together, e.g. 40 x 30
Partitioning
Multiply teens numbers
Instant recall
- Recall multiplication facts up
to 10 x 10
- Quickly derive
corresponding division facts
Derived
- Times tables & PV
calculations with decimals
such as 0.7 x 3
Column
Method(2)
Asbelow
- Multiply decimals and whole
number by 10, 100 and 1000
- Multiply a two digit number by
a single digit
Asbelow
Instant recall
- Times tables & place value
calculations such as 40 x 3
Derived
- Times tables & PV
calculations with decimals
such as 0.7 x 0.3
Using similar methods, they will be able to
multiply decimals with one decimal place by
a single digit number, approximating first.
They should know that the decimal points
line up under each other. A strategy that
can be used is to ask the children to
remove the decimal point, solve the
calculation and then replace the decimal
point.
ProgressioninDivision
Objectives
and
strategies
ELG
Concrete
Pictorial
Concrete resources to model operation
Abstract
Sharing
objectsinto
groups
Divisionas
grouping
Dividequantitiesintoequalgroups.
Usecubes,counters,objectsorplacevaluecounterstoaid
understanding.
MentalCalculations
KnownFacts
Informal jottings, mathematical mark making,,
problem solving, blank paper
Share9bunsbetween3people.
9÷3=3
Share objects into equal groups and count
how many in each group
Instant recall
- Halves of even numbers to
10
28÷7=4
Divide28into7groups.Howmanyareineach
group?
- Use counting up in 2s, 5s and
10s (using fingers to keep track
of groups) to start to derive
division facts phrased as ‘how
many groups of 3 in12?’
Instant recall
- Halves of even numbers to
20, incl recognising e.g. 14 ÷ 2
as finding a half
Useanumberlinetoshowjumpsingroups.Thenumberof
jumpsequalsthenumberofgroups.
Thinkofthebarasawhole.Splititintothenumberofgroups
youaredividingbyandworkouthowmanywouldbewithin
eachgroup.
Divisionwith
arrays
Divisionwith
aremainder
Linkdivisiontomultiplicationbycreatinganarrayand
thinkingaboutthenumbersentencesthatcanbecreated.
Eg15÷3=5
15÷5=3
5x3=15
3x5=15
Drawanarrayanduselinestosplitthearrayintogroupsto
makemultiplicationanddivisionsentences.
14÷3=
Divideobjectsbetweengroupsandseehowmuchisleftover
Jumpforwardinequaljumpsonanumberlinethenseehow
manymoreyouneedtojumptofindaremainder.
Findtheinverseofmultiplicationanddivision
sentencesbycreatingfourlinkingnumber
sentences.
7x4=28
4x7=28
28÷7=4
28÷4=7
Completewrittendivisionsandshowthe
remainderusingr.
- Use half and half again for ÷ 4
- Divide whole numbers by
10/100 (whole number answers)
- Calculate div facts with
remainders for 2, 3, 4, 5 and 10
times table
Instant recall
- Half of 30, 50, 70, 90
- Begin to know division facts
for 3, 4, 5 and 10 times table
– link to fractions
Drawdotsandgroupthemtodivideanamountandclearly
showaremainder.
Short
division
Useplacevaluecounterstodivideusingthebusstopmethod
alongside
42÷3=
Startwiththebiggestplacevalue,wearesharing40into
threegroups.Wecanput1tenineachgroupandwehave1
tenleftover.
Weexchangethistenfortenonesandthensharetheones
equallyamongthegroups.
Welookhowmuchin1groupsotheansweris14.
Pupilscancontinuetousedrawndiagramswithdotsorcircles
tohelpthemdividenumbersintoequalgroups.
Beginwithdivisionsthatdivideequallywithno
remainder.
Encouragethemtomovetowardscountinginmultiplesto
dividemoreefficiently.
Moveontodivisionswitharemainder.
Finallymoveintodecimalplacestodividethe
totalaccurately.
Jottings to support mental
chunking e.g. 2000 ÷ 250
2 x 250 = 500
4 x 250 = 1000
8 x 250 = 2000
- Dividing numbers by 10 or 100
- Mental chunking for ‘simple’
calculations, e.g. Yoghurts cost
45p each; how many can I buy
for £5?
- Multiply and divide decimals
and whole numbers by 10, 100
and 1000
- Multiply a two digit number by
a single digit
Instant recall
- Half of 1, 3, 5, 7, 9
Derived
- Quickly derive division facts
for tts up to 10 x 10,
- Division facts with
remainders for all tt
- Division facts & place value
calculations such as180 ÷ 3
Derived
- Division facts & place value
calculations such as 1.8 ÷ 3