This Is a Guide to How Calculations Are Recorded in Different Year Groups but There Will

Water Mill

Calculations

Policy

This is a guide to how calculations are recorded in different year groups but there will be children working at different levels within each year group.

Addition
Y1 / Y2 / Y3
+=signsand missing numbers
Childrenneedtounderstandtheconceptofequalitybeforeusing the ‘=’ sign. Calculations shouldbewritteneithersideoftheequalitysign so that thesignisnotjust interpretedas‘theanswer’.
2=1+1
2+3=4+1
3=3
2+2+2=4+2
Missingnumbersneedtobeplacedinallpossibleplaces.
3+4==3+4
3+=77=+4
+4=77=3+
+=77=+
Activities
Children shouldhaveaccess toawiderangeof countingequipment,everydayobjects,as wellashoops,sortingtrays,number tracks, numberednumberlines anddigitandsymbol cards.
Teacher modelling
Drawingjumps onnumberednumberlines tosupportunderstandingof the mentalmethod
Children
To createtheirownjumps usingrulers, fingers,pens,bodiesetc.

7 + 4 / +=signsand missing numbers
ContinueusingarangeofequationsasinYear1butwith appropriate,largernumbers.
Extend to
14+5=10+
and
32+ +=100 35=1++5
Counton in tensand ones
23+12=
/ +=signsand missing numbers
ContinueusingarangeofequationsasinYear1and2 butwithappropriate, largernumbers.
Pencil and paperprocedures
e.g.83+42=125
Horizontal expansion
80+3
+40+2
120+5=125
Moving to column recording
1.
300+60+7
+100+80+5
400+140+12=552
2.Verticalexpansion:
367
+185
12
140
400
552
3.Compact column:
367
+185
552
11
Addition
Y4 / Y5 / Y6
+=signsand missing numbers
ContinueusingarangeofequationsasinYear1and2but with appropriatenumbers.
Pencil and paperprocedures up to 4 digits
367+185=552
1.Building from Y3:
300+60+7
+100+80+5
400+140+12=552
2.Verticalexpansion:
367
+185
12
140
400
552
3.Compact column:
367
+185
552
11
Extend todecimalsinthecontextof money. / +=signsand missing numbers
ContinueusingarangeofequationsasinYear1and2 butwithappropriatenumbers.
Pencil and paperprocedures
Extend tonumbers withatleast fourdigits then more than 4
3587+675=4262
3587
+ 675
4262
111
Reverttoexpandedmethods if thechildrenexperience anydifficulty.
Extend toupto twoplaces of decimals (samenumberof decimals places)andaddingseveralnumbers(with different numbersofdigits).
72.8
+54.6
127.4 / +=signsand missing numbers
ContinueusingarangeofequationsasinYear1and2 butwithappropriatenumbers.
Pencil and paperprocedures
Extend tonumbers withanynumberofdigits and decimals with1,2and/or3decimalplaces.
13.86+9.481=23.341
13.86
+ 9.481
23.341
11 1
Reverttoexpandedmethods if thechildrenexperience anydifficulty.
Subtraction
Y1 / Y 2 / Y3
Understand subtractionas 'takeaway'

Calculatebycountingback;
I have11toycars. Thereare5cars toomanyto fit in thegarage.How manycarsfitinthegarage?
11-6=5

Use practical and informal written methods to support the subtractionofaone-digit numberfromaonedigit ortwo-digitnumber anda multipleof10froma two-digit number.
Use thevocabularyrelatedtoadditionandsubtractionand symbols to describeandrecordadditionandsubtractionnumber sentences Recordingby
-drawingjumpsonpreparedlines
-constructingownlines
-=signsand missing numbers
7-3==7-3
7-=44=-3
-3=44=7-
-=44=- / Finda smalldifferencebycountingup
42–39=3

Subtract9or11. Begin to add/subtract19or21
35–9=26

Useknown numberfactsand placevalueto subtract

Bridge through 10 where necessary
32-17

- = signs and missing numbers
Continue using a range of equations as in Year 1 but with appropriate numbers.
Extend to 14 + 5 = 20 - _ / Subtract mentally a ‘near multiple of 10’ to or from a two-digit number
Continue as in Year 2 but with appropriate numbers e.g. 78 – 49 is the same as 78 -50 + 1
Use known number facts and place value to subtract
Continue as in Year 2 but with appropriate numbers e.g. 97 – 15 = 72

Withpractice, childrenwillneedtorecordless informationanddecidewhethertocountback or forward. Itisusefultoaskchildrenwhethercountingup orback is themoreefficient forcalculations such as 57 – 12, 86 – 77 or 43 – 28
Pencil and paper procedures
Partition subtraction
Moving towards

- = signs and missing numbers
Continue using a range of equations as in Year 1 and 2 but with appropriate numbers.
Subtraction
Y4 / Y5 / Y6
Find asmall differencebycountingback
e.g.5003–4996=7
This canbemodelledonanemptynumberline.Children shouldbe encouragedtouse knownnumberfacts toreduce thenumberof steps.
Subtractthenearestmultipleof10,then adjust.
ContinueasinYear2and3but withappropriatenumbers.
Useknown numberfactsand placevalueto subtract
92-25=67
Use column method recording up to 4 digits

-=signsand missing numbers
ContinueusingarangeofequationsasinYear1and2but with appropriatenumbers. / Find adifferencebycountingback
e.g.8006–2993=5013
This canbemodelledonanemptynumberline(see complementaryadditionbelow).
Subtractthenearestmultipleof10or100,thenadjust.
ContinueasinYear2,3and4but withappropriate numbers.
Useknown numberfactsand placevalueto subtract
6.1–2.4=3.7

-=signsand missing numbers
ContinueusingarangeofequationsasinYear1and2 butwithappropriatenumbers. / Find adifferencebycountingback
e.g.8000–2785=5215
To makethis methodmoreefficient, thenumberof steps shouldbereducedtoaminimum through childrenknowing:
 Complements to1, involvingdecimals totwo
decimalplaces (0.16+0.84)
 Complements to10, 100and100
Subtractthenearestmultipleof10,100or1000,then adjust
ContinueasinYear2,3,4and5but withappropriate numbers.
Useknown numberfactsand placevaluetosubtract
0.5–0.31 =0.19

Reduce thenumberof steps tomake thecalculation moreefficient.Extendto2placesofdecimals.
-=signsand missing numbers
ContinueusingarangeofequationsasinYear1and2 butwithappropriatenumbers.
Multiplication
Y1 / Y2 / Y 3
Multiplicationis relatedtodoubling and countinggroups ofthe samesize.

LookingatcolumnsLookingatrows
2+2+23+3
3groupsof22groupsof 3
Counting usingavariety ofpracticalresources
Countingin 2se.g.countingsocks,shoes,animal’s legs…
Countingin 5se.g.countingfingers,fingersingloves,toes…
Countingin10s e.g.fingers,toes…
Pictures/marks
Thereare3sweets inonebag.
Howmanysweets aretherein5bags?
/ x=signsand missing numbers
7x 2==2x 7
7x =1414=x 7
x 2=1414=2x 
x =1414=x 
Arraysandrepeatedaddition
4x 2or4+4
 2x 4or2+2+2+2
Doublingmultiplesof5up to50
15x 2=30
Partition
Childrenneedtobesecurewithpartitioningnumbersinto10sand1sandpartitioningindifferent ways:6=5+1 soe.g. Double6is thesameas doublefiveadddoubleone.

/ x=signsand missing numbers
ContinueusingarangeofequationsasinYear2but withappropriatenumbers.
Arraysand repeated addition
Continue tounderstandmultiplicationasrepeated additionandcontinuetousearrays(asinYear2).
Doubling multiplesof5up to 50
35x 2=70

Useknownfactsandplacevaluetocarryout simplemultiplications
Usethe samemethodas above(partitioning),e.g.

Multiplication
Y4 / Y5 / Y6
x=signsand missing numbers
ContinueusingarangeofequationsasinYear2but withappropriatenumbers
Partition
Use thegridmethodof multiplication(as below)
Pencil and paperprocedures
Grid method
23x 7is approximately20x 10=200
x 20 3
714021= 161
Move towards Short multiplication method
/ x=signsand missing numbers
ContinueusingarangeofequationsasinYear2but withappropriatenumbers
Partition
Use thegridmethodof multiplication(as below)
Pencil and paperprocedures
Grid method
72x 38is approximately70x 40=2800

Extend tosimpledecimals withonedecimalplace.
Short Multiplication up to 4 digits by 1 digits
htu x u

Long Multiplication
72
X 38
2160 72 x 30
576 72 x 8
2736
1 / x=signsand missing numbers
ContinueusingarangeofequationsasinYear2but withappropriatenumbers
Partition
Use thegridmethodof multiplication(as below)
Pencil and paperprocedures
Grid method
372x 24is approximately400x 20=8000

Extend todecimals withuptotwodecimalplaces.
Short Multiplication
use larger numbers thtu x u
Long Multiplication
72
X 38
2160 72 x 30
576 72 x 8
2736
1
Division
Y 1 / Y2 / Y 3
Sharing
Requiressecurecountingskills
-see countingandunderstandingnumber strand Developsimportanceof one-to-onecorrespondence Seeappendixforadditionalinformationonx and÷and aspectsofnumber
Sharing–6sweets aresharedbetween2people.How manydo theyhaveeach?
 
    
Practicalactivities involvingsharing,distributingcards whenplayingagame, puttingobjectsontoplates, into cups, hoopsetc.
Grouping
Sortingobjects into2s/ 3s/4setc
Howmanypairsof socksarethere?

Thereare12crocus bulbs. Plant 3ineachpot. How manypotsarethere?
Johas 12Legowheels. How manycars canshe make? / ÷=signsand missing numbers
6÷2==6÷2
6÷=33=6÷ 
÷2=33=÷2
÷=33=÷
Grouping
Link to countingandunderstandingnumber strand Countup to100objectsbygroupingthem andcounting in tens, fivesor twos;…
Findonehalf, onequarterandthreequarters of shapes
and setsofobjects
62canbemodelledas: Thereare6 strawberries.
Howmanypeoplecanhave2each?How many2s make6?
62canbemodelledas:

In the contextof moneycount forwardsandbackwards using2p, 5pand10pcoins
Practicalgroupinge.g. inPE
12 children get into teams of 4 to play a game. How many teams are there?
/ ÷=signsand missing numbers
ContinueusingarangeofequationsasinYear2butwith appropriatenumbers.
Understand division assharing and grouping
18÷3canbemodelledas:
Sharing–18sharedbetween3(seeYear1diagram)
OR
Grouping-How many3’smake18?

Remainders
16÷3=5r1
Sharing-16sharedbetween3, how manyleftover?
Grouping–How many3’smake16,how manyleft over?
e.g.

Division
Y4 / Y5 / Y6
÷=signsand missing numbers
ContinueusingarangeofequationsasinYear2butwith appropriatenumbers.
Sharing and grouping
30÷6canbemodelledas:
grouping–groupsof 6placedonno.lineandthenumber
ofgroupscountede.g.

sharing–sharingamong6, thenumbergiventoeach person
Pencil and paperprocedures
Remainders
41÷4=10r1

Pencil and paperprocedures
72÷5lies between50 5=10and1005=20
 Partitionthedividendintomultiples of thedivisor:
e.g.
72

50 (10 groups)

22
- 20 (4 groups)
2
Answer: 14remainder2 / ÷=signsand missing numbers
ContinueusingarangeofequationsasinYear2but withappropriatenumbers.
Sharing and grouping
Continue tounderstanddivisionasbothsharingand grouping(repeatedsubtraction).
Remainders
Quotients expressedas fractionsordecimalfractions
61÷4=15¼or15.25
Pencil and paperprocedures
72÷5lies between50 5=10and1005=20
 Partitionthedividendintomultiples of thedivisor:
e.g. 72
50 (10 groups)
22
- 20 (4 groups)
2
Answer: 14remainder2
Move towards Bus shelter method then short division
style

/ ÷=signsand missing numbers
ContinueusingarangeofequationsasinYear2but withappropriatenumbers.
Sharing and grouping
Continue tounderstanddivisionasbothsharingand grouping(repeatedsubtraction).
Remainders
Quotients expressedas fractionsordecimalfractions 676÷8=84.5
Pencil and paperprocedures
977÷36is approximately100040=25
 Partitionthedividendintomultiples of thedivisor:
e.g.
OR
977
-720(20groups)
257
-180(5groups)
77
- 72(2groups)
5
Answer: 27 5/36

Place value, estimation, ordering and counting
Reception / Year 1 / Year 2
Counting
• Say and use the number names in order In familiar contexts such as number rhymes, songs, stories, counting games and activities (first to five, then ten, then twenty and beyond).
• Recite the number names in order, continuing the count forwards or backwards from a given number.
• Count reliably up to 10 everyday objects (first to 5, then 10, then beyond), giving just one number name to each object.
Recognise small numbers without counting.
• Begin to recognise ‘none’ and ‘zero’ in stories, rhymes and when counting.
• Count reliably in other contexts, such as clapping sounds or hopping movements.
• Count in tens.
• Count in twos.
• Estimate a number in the range that can be counted reliably, then check by counting.
Comparing and ordering numbers
• Use language such as more or less, greater or smaller, to compare two numbers and say which is more or less, and say a number which lies between two given numbers.
• Order a given set of numbers: for example, the set of numbers 1 to 6 given in random order.
• Order a given set of selected numbers:
for example, the set 2, 5, 1, 8, 4.
• Begin to understand and use ordinal numbers in different contexts. / Counting, properties of numbers and number sequences
• Know the number names and recite them in order to at least 100, from and back to zero.
• Count reliably at least 20 objects.
• Describe and extend number sequences:
count on and back in ones from any small number, and in tens from and back to zero;
count on in twos from zero, then one, and begin to recognize odd or even numbers to about 100 as ‘every other number’;
count in steps of 5 from zero to100
Place value and ordering
Read and write numerals from 0 to at least 20.
• Begin to know what each digit in a two-digit number represents. Partition a ‘teens’ number and begin to partition larger two-digit numbers into a multiple of 10 and ones (TU).
• Understand and use the vocabulary of comparing and ordering numbers, including ordinal numbers to at least 20.
Use the = sign to represent equality.
Compare two familiar numbers, say which is more or less, and give a number which lies between them.
• Within the range 0 to 30, say the number that is 1 or 10 more or less than any given number.
• Order numbers to at least 20, and position them on anumber track.
Estimating
• Understand and use the vocabulary of estimation.
Give a sensible estimate of a number of objects that can bechecked by counting (e.g. up to about 30 objects). / Counting, properties of numbers and number sequences
• Say the number names in order to at least 100, from and back to zero.
• Count reliably up to 100 objects by grouping them: for example, in tens, then in fives or twos.
• Describe and extend simple number sequences:count on or back in ones or tens, starting from any two digit number;
count in hundreds from and back to zero;count on in twos from and back to zero or any small number,and recognise odd and even numbers to at least 30;count on in steps of 3, 4 or 5 to at least 30, from and back tozero, then from and back to any given small number.
• Begin to recognise two-digit multiples of 2, 5 or 10.
Place value and ordering
• Read and write whole numbers to at least 100 in figuresand words.
• Know what each digit in a two-digit number represents,including 0 as a place holder, and partition two-digitnumbers into a multiple of ten and ones (TU).
• Use and begin to read the vocabulary of comparing andordering numbers, including ordinal numbers to 100. Use < > = signs
Use the = sign to represent equality.
Compare two given two-digit numbers, say which is more orless, and give a number which lies between them.
• Say the number that is 1 or 10 more or less than any giventwo-digit number.
• Order whole numbers to at least 100, and position them ona number line and 100 square.
Estimating and rounding
• Use and begin to read the vocabulary of estimation andapproximation; give a sensible estimate of at least 50 objects.
• Round numbers less than 100 to the nearest 10.
Place value, estimation, ordering and counting
Year 3 / Year 4
Counting, properties of numbers and number sequences
• Count larger collections by grouping them: for example, intens, then other numbers.
• Describe and extend number sequences:
count on or back in tens or hundreds, starting from anytwo- or three-digit number.
count on or back in twos starting from any two-digit number,and recognise odd and even numbers to at least 100;
count on in steps of 4 or 8, 50 and 100
• Recognise two-digit and three-digit multiples of 4, 8and three-digit multiples of 50 and 100.
Place value and ordering
• Read and write whole numbers to at least 1000 in figuresand words.
• Know what each digit represents, and partition three-digitnumbers into a multiple of 100, a multiple of ten and ones(HTU).
• Read and begin to write the vocabulary of comparing andordering numbers, including ordinal numbers to at least 100.
Compare two given three-digit numbers, say which is more orless, and give a number which lies between them.
• Say the number that is 1, 10 or 100 more or less than anygiven two- or three-digit number.
• Order whole numbers to at least 1000, and position themon a number line.
Estimating and rounding
• Read and begin to write the vocabulary of estimationand approximation.
Give a sensible estimate of up to about 100 objects.
• Round any two-digit number to the nearest 10 and any threedigitnumber to the nearest 100. / Place value, ordering and rounding (whole numbers)
• Read and write whole numbers to at least 10 000 in figures and words, and know what each digit represents.
Partition numbers into thousands, hundreds, tens and ones.
• Add/subtract 1, 10, 100 or 1000 to/from any integer, and count on or back in tens, hundreds or thousands from any whole number up to 10000.
• Multiply or divide any integer up to 1000 by 10 (whole-number answers), and understand the effect. Begin to multiply by 100.
• Read and write the vocabulary of comparing and ordering numbers.
Use symbols correctly, including less than (<), greater than (>), equals (=).
Give one or more numbers lying between two given numbers and order a set of whole numbers less than 10000.
• Read and write the vocabulary of estimation and approximation. Make and justify estimates up to about 250, and estimate a proportion.
Round any positive integer less than 1000 to the nearest 10 or 100.
• Recognise negative numbers in context (e.g. on a number line, on a temperature scale).
Read Roman numerals to 100
Properties of numbers and number sequences
• Recognise and extend number sequences formed by counting from any number in steps of constant size, extending beyond zero when counting back: for example, count on in steps of 25 to 500, and then back to, say, –100.
• Recognise odd and even numbers up to 1000, and some of their properties, including the outcome of sums or differences of pairs of odd/even numbers.
• Recognise multiples of 6, 7, 9, 25 and 1000
Place value, estimation, ordering and counting
Year 5 / Year 6
Place value, ordering and rounding
• Read and write whole numbers in figures and words, and know what each digit represents. (decimals) up to 1 000 000
• Multiply and divide any positive integer up to 10000 by 10 or 100 and understand the effect (e.g. 9900 ÷ 10, 737 ÷ 10, 2060 ÷ 100).
• Use the vocabulary of comparing and ordering numbers, including symbols such as <, >, =. Give one or more numbers lying between two given numbers. Order a set of integers less than 1 million. (decimals)
• Use the vocabulary of estimation and approximation.
Make and justify estimates of large numbers, and estimate simple proportions such as one third, seven tenths.
Round any integer up to 10000 to the nearest 10, 100 or 1 000, 10 000,
100 000(rounding decimals)
• Order a given set of positive and negative integers (e.g. on a number line, on a temperature scale). Calculate a temperature rise or fall across 0 °C.
Read Roman numerals up to 1000
Properties of numbers and number sequences
• Recognise and extend number sequences formed bycounting from any number in steps of constant size,extending beyond zero when counting back. For example:
count on in steps of 25 to 1000, and then back;
count on or back in steps of 0.1, 0.2, 0.3…
• Make general statements about odd or even numbers,including the outcome of sums and differences.
• Recognise multiples of 6, 7, 8, 9, up to the 10th multiple.
Know and apply tests of divisibility by 2, 4, 5, 10 or 100.
• Know squares of numbers to at least 10 10.
• Find all the pairs of factors of any number up to 100. / Place value, ordering and rounding
• Multiply and divide decimals mentally by 10 or 100, andintegers by 1000, and explain the effect.
• Use the vocabulary of estimation and approximation.
Numbers up to 100 000
Consolidate rounding an integer to the nearest 10, 100 or1000.
• Find the difference between a positive and a negative integer,or two negative integers, in a context such as temperature orthe number line, and order a set of positive and negativeintegers.
Properties of numbers and number sequences
• Recognise and extend number sequences, such as thesequence of square numbers, or the sequence of triangularnumbers 1, 3, 6, 10, 15…
Count on in steps of 0.1, 0.2, 0.25, 0.5…, and then back.
• Make general statements about odd or even numbers,including the outcome of products.
• Recognise multiples up to 10 10. Know and apply simpletests of divisibility. Find simple common multiples.
• Recognise squares of numbers to at least 12 12.
• Recognise prime numbers to at least 20.Factorise numbers to 100 into prime factors.

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