revised addition policy

8/11/2019 Revised Addition Policy

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Francis Baily written

Calculations Policy

Updated July 2014

By the end of year 6, children will have a range of calculation methods, mental and written.Selection of the methods will depend upon the numbers involved.

Children should not to go onto the next stage if:1) They are not secure with a particular method or cannot apply their knowledge of

it2) They are not confident with that method.

Likewise, children can progress onto methods used in older year groups if they are securewith and can apply their knowledge of a particular method; children are not fixed to usinga particular method in their year group.

Children should be encouraged to approximate their answers before calculating.Children should be encouraged to check their answers after the calculation, using anappropriate strategy.Children should be encouraged to consider if a mental calculation would be appropriatebefore using written methods.


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Vocabulary introduced and used in the Foundation stage:COUNTINGnumberzero, one, two, three to twenty and beyondzero, ten, twenty one hundrednonehow many?count, count (up) tocount on (from, to)count back (from, to)count in ones, twos tensmore, less, many, fewodd, evenevery otherhow many times?pattern, pairguess how many, estimatenearly, close to, about the same asjust over, just undertoo many, too few, enough, not enough

COMPARING AND ORDERING NUMBERSthe same number as, as many asOf two objects/amounts:greater, more, larger, biggerless, fewer, smallerOf three or more objects/amounts:greatest, most, biggest, largestleast, fewest, smallestone more, ten moreone less, ten lesscompare

ordersizefirst, second, third tenthlast, last but onebefore, afternextbetweenabove, below

COMPARING AND ORDERING NUMBERSthe same number as, as many asOf two objects/amounts:

greater, more, larger, biggerless, fewer, smallerOf three or more objects/amounts:greatest, most, biggest, largestleast, fewest, smallestone more, ten moreone less, ten lesscompareordersizefirst, second, third tenthlast, last but one

before, afterbetweenabove, below

Adding and subtractingadd, more, andmake, sum, totalaltogetherscoredoubleone more, two more, ten more

how many more to make ?how many more is than?take (away), leavehow many are left/left over?how many have gone?one less, two less ten lesshow many fewer is than?difference betweenis the same as

Solving problemsREASONING ABOUT NUMBERS OR SHAPES

patternpuzzleanswerright, wrongwhat could we try next?how did you work it out?count, sortgroup, setmatchsame, differentlistPROBLEMS INVOLVING REAL LIFE

OR MONEYcomparedoublehalf, halvepaircount out, share outleft, left overmoneycoinpenny, pence, poundprice

costbuysellspend, spentpaychangedear, costs morecheap, costs less, cheapercosts the same ashow much? how many?total


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Vocabulary introduced and used in year 1:

Numbers and the number system

COUNTING, PROPERTIES OF NUMBERS

AND NUMBER SEQUENCES

numberzero, one, two, three to twenty andbeyond

zero, ten, twenty one hundrednonehow many?count, count (up) tocount on (from, to)count back (from, to)count in ones, twos tensmore, less, many, fewodd, evenevery otherhow many times?pattern, pair

PLACE VALUE AND ORDERING

units, onestensexchangedigitteens numberthe same number as, as many asequal to

Of two objects/amounts:greater, more, larger, biggerless, fewer, smallerOf three or more objects/amounts:greatest, most, biggest, largestleast, fewest, smallestone more, ten moreone less, ten lesscompareordersize

first, second, third tenth, eleventh twentiethlast, last but onebefore, afternextbetween, half-way betweenabove, below

ESTIMATING

guess how many, estimatenearly, roughly, close toabout the same as

just over, just undertoo many, too few, enough, not enough

Calculations

ADDITION AND SUBTRACTION

+, add, more, plusmake, sum, totalaltogetherscoredouble, near doubleone more, two more ten morehow many more to make?how many more is than?how much more is?-, subtract, take (away), minusleavehow many are left/left over?how many have gone?

one less, two less, ten lesshow many fewer is than?how much less is?difference betweenhalf, halve=, equals, sign, is thesame as

Solving problems

MAKING DECISIONS AND REASONINGpattern

puzzleanswerright, wrongwhat could we try next?how did you work it out?count out, share out, left, left overnumber sentencesign, operationMONEY

moneycoinpenny, pence, poundprice

costbuysellspend, spentpaychangedear, costs morecheap, costs less, cheapercosts the same ashow much? how many?total


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zero, one, two, three to twenty and beyondzero, ten, twenty one hundredzero, one hundred, two hundred one thousandnonehow many?count, count (up) tocount on (from, to)count back (from, to)count in ones, twos, threes, fours, fivescount in tensmore, less, many, few

tallyodd, evenevery otherhow many times?multiple ofsequencecontinuepredictpattern, pair, rule


units, onestens, hundredsdigitone-, two- or three-digit numberteens numberplace, place valuestands for, representsexchangethe same number as, as many asequal toOf two objects/amounts:greater, more, larger, biggerless, fewer, smallerOf three or more objects/amounts:greatest, most, biggest, largestleast, fewest, smallestone more, ten moreone less, ten lesscompareordersize

first, second, third tenth twentiethtwenty-first, twenty-secondlast, last but one

before, afternextbetween, half-way betweenabove, below

ESTIMATINGguess how many, estimatenearly, roughly, close toabout the same as

just over, just underexact, exactlytoo many, too few, enough, not enoughround, nearest, round to the nearest ten

FRACTIONS

part, equal parts

fractionone wholeone half, two halvesone quarter, two three four quarters

Calculations


+, add, addition, more, plusmake, sum, total

altogetherscoredouble, near doubleone more, two more... ten more... one hundred morehow many more to make?how many more is than?how much more is?-, subtract, subtraction, take (away), minusleave, how many are left/left over?one less, two less ten less one hundred lesshow many fewer is than?how much less is?difference betweenhalf, halve=, equals, sign, is the same astens boundary


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MULTIPLICATION AND DIVISION

lots of, groups of, times, multiply, multiplied bymultiple ofonce, twice, three times ten timestimes as (big, long, wide and so on)repeated addition

arrayrow, columndouble, halveshare, share equallyone each, two each, three eachgroup in pairs, threes tensequal groups of, divide, divided by, divided intoleft, left over

Solving problems

MAKING DECISIONS AND REASONING

pattern, puzzlecalculate, calculationmental calculation

jottinganswer

right, correct, wrongwhat could we try next?how did you work it out?number sentencesign, operation, symbol

MONEY

moneycoinpenny, pence, pound ()price, costbuy, bought, sell, soldspend, spentpaychangedear, costs morecheap, costs less, cheaperhow much? how many?total


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numberzero, one, two, three to twenty and beyondzero, ten, twenty one hundredzero, one hundred, two hundred one thousandnonehow many?count, count (up) tocount on (from, to)count back (from, to)count in ones, twos, threes, fours, fives

count in tens, hundredsmore, less, many, fewtallyodd, evenevery otherhow many times?multiple ofsequencecontinuepredictpattern, pair, rule

relationship


units, onestens, hundredsdigitone-, two- or three-digit numberteens numberplace, place valuestands for, representsexchangethe same number as, as many asequal toOf two objects/amounts:greater, more, larger, biggerless, fewer, smallerOf three or more objects/amounts:greatest, most, biggest, largestleast, fewest, smallestone more, ten more, one hundred moreone less, ten less, one hundred less

compareordersize

first, second, third tenth twentiethtwenty-first, twenty-secondlast, last but onebefore, after

nextbetween, half-way betweenabove, belowESTIMATING

guess how many, estimatenearly, roughly, close toapproximate, approximatelyabout the same as

just over, just underexact, exactlytoo many, too few, enough, not enough

round (up or down)nearest, round to the nearest ten

FRACTIONS

part, equal partsfractionone wholeone half, two halvesone quarter, two three four quartersone third, two thirds, three thirds

one tenth

Calculations


+, add, addition, more, plusmake, sum, totalaltogetherscoredouble, near doubleone more, two more... ten more... one hundred morehow many more to make?how many more is than?how much more is?-, subtract, subtraction, take (away), minusleave, how many are left/left over?one less, two less ten less one hundred lesshow many fewer is than?how much less is?difference betweenhalf, halve

=, equals, sign, is the same astens boundary, hundreds boundary


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lots of, groups of, times, multiply, multiplication, multiplied bymultiple of, productonce, twice, three times ten timestimes as (big, long, wide and so on)repeated additionarray

row, columndouble, halveshare, share equallyone each, two each, three eachgroup in pairs, threes tensequal groups of, divide, division, divided by, divided intoleft, left over, remainder

Solving problems


pattern, puzzlecalculate, calculationmental calculationmethod

jottinganswerright, correct, wrongwhat could we try next?how did you work it out?

number sentencesign, operation, symbol, equation

MONEY

moneycoin, notepenny, pence, pound ()price, costbuy, bought, sell, soldspend, spentpay

changedear, costs more, more/most expensivecheap, costs less, cheaper, less/least expensivehow much? how many?total, amountvalue, worth


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PLACE VALUE, ORDERING AND ROUNDING

units, onestens, hundreds, thousandsten thousand, hundred thousand, milliondigit, one-, two-, three- or four-digit numbernumeralteens numberplace, place valuestands for, representsexchangethe same number as, as many asequal toOf two objects/amounts:

>, greater than, more than, larger than, biggerthan


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lots of, groups oftimes, multiply, multiplication, multiplied bymultiple of, productonce, twice, three times ten timestimes as (big, long, wide and so on)repeated additionarray

row, columndouble, halveshare, share equallyone each, two each, three eachgroup in pairs, threes tensequal groups ofdivide, division, divided by, divided intoremainderfactor, quotient, divisible byinverse

Solving problems


pattern, puzzlecalculate, calculationmental calculationmethod

jottinganswerright, correct, wrong

what could we try next?how did you work it out?number sentencesign, operation, symbol, equationMONEY

moneycoin, notepenny, pence, pound ()price, costbuy, bought, sell, soldspend, spent

paychangedear, costs more, more/most expensivecheap, costs less, cheaper, less/least expensivehow much? how many?total, amountvalue, worth


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units, ones

tens, hundreds, thousandsten thousand, hundred thousand, milliondigit, one-, two-, three- or four-digit numbernumeralteens numberplace, place valuestands for, representsexchangethe same number as, as many asequal toOf two objects/amounts:



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Calculations


add, addition, more, plus, increasesum, total, altogetherscoredouble, near doublehow many more to make?

subtract, subtraction, take (away), minus,decreaseleave, how many are left/left over?difference betweenhalf, halvehow many more/fewer is than?how much more/less is?equals, sign, is the same astens boundary, hundreds boundaryunits boundary, tenths boundaryinverse


lots of, groups oftimes, multiply, multiplication, multiplied bymultiple of, productonce, twice, three times ten timestimes as (big, long, wide and so on)repeated additionarrayrow, column

group in pairs, threes tensequal groups ofdivide, division, divided by, divided intoremainderfactor, quotient, divisible byinverseone each, two each, three eachdouble, halveshare, share equally

USING A CALCULATOR

calculatordisplay, key, enter, clearconstant


pattern, puzzlecalculate, calculationmental calculationmethod, strategy

jottinganswerright, correct, wrong

what could we try next?how did you work it out?number sentencesign, operation, symbol, equation

MONEY

moneycoin, notepenny, pence, pound ()price, costbuy, bought, sell, sold

spend, spentpaychangedear, costs more, more/most expensivecheap, costs less, cheaper, less/least expensivehow much? how many?total, amount, value, worthdiscountcurrency


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units, ones

tens, hundreds, thousandsten thousand, hundred thousand, milliondigit, one-, two-, three- or four-digit numbernumeralteens numberplace, place valuestands for, representsexchangethe same number as, as many asequal toOf two objects/amounts:



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lots of, groups oftimes, multiply, multiplication, multiplied bymultiple of, productonce, twice, three times ten timestimes as (big, long, wide and so on)repeated additionarray, row, column

double, halveshare, share equallyone each, two each, three eachgroup in pairs, threes tensequal groups ofdivide, division, divided by, divided intoremainderfactor, quotient, divisible byinverse

USING A CALCULATOR

calculator, display, keyenter, clear, sign changeconstant, recurring, memory, operation key

Solving problems


pattern, puzzlecalculate, calculationmental calculation

method, strategyjottinganswerright, correct, wrongwhat could we try next?how did you work it out?number sentencesign, operation, symbol, equation

MONEY

money

coin, notepenny, pence, pound ()price, costbuy, bought, sell, soldspend, spentpaychangedear, costs more, more/most expensivecheap, costs less, cheaper, less/least expensivehow much? how many?total, amount, value, worthdiscount, profit, losscurrency


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PROGRESSION THROUGH CALCULATIONS FOR ADDITION

MENTAL CALCULATIONS

(ongoing)These are a selectionof mental calculation strategies:

Mental recall of number bonds6 + 4 = 10 + 3 = 1025 + 75 = 100 19 + = 20

Use near doubles6 + 7 = double 6 + 1 = 13

Addition using partitioning and recombining

34 + 45 = (30 + 40) + (4 + 5) = 79

Counting on or back in repeated steps of 1, 10, 100, 100086 + 57 = 143 (by counting on in tens and then in ones)460 - 300 = 160 (by counting back in hundreds)

Add the nearest multiple of 10, 100 and 1000 and adjust24 + 19 = 24 + 20 1 = 43458 + 71 = 458 + 70 + 1 = 529

Use the relationship between addition and subtraction (the inverse operation)36 + 19 = 55 19 + 36 = 5555 19 = 36 55 36 = 19

MANY MENTAL CALCULATION STRATEGIES WILL CONTINUE TO BE USED. THEY

ARE NOT REPLACED BY WRITTEN METHODS.

In the Foundation Stage and Key Stage (KS) 1, children are taught mental calculationswhich are systematically built on throughout KS 2.

During the foundation stage and KS1, children are taught about the operation of additionand learn key facts such as number bonds to ten and twenty, and mentally adding numberstogether. For example, foundation children will find out one more than a given number andundertake addition such as: There are 2 cars in the garage. Letscount them. How manycars are there now? A great deal of work uses concrete materials, counting together andsaying rhymes. This work is extended in year 1 and 2 using larger numbers and writtenmethods.


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By the end of year 5, children will have been taught, and be secure with, a compactstandard written method for addition.

THE FOLLOWING ARE STANDARDS THAT WE EXPECT THE MAJORITY OF

CHILDREN TO ACHIEVE.

Foundation

Children count reliably with numbers from one to twenty, place them in order and saywhich number is one more or one less than a given number. Using quantities and objects,they add and subtract two single digit numbers and count on or back to find the answer.They solve problems including doubling, halving and sharing.

Children need to be able to count confidently. Number games and number songsfamiliarise children with numbers. Addition starts by counting and combining groups ofobjects, for example 1 car add two cars is how many cars?

Year 1

Children are encouraged to develop a mental picture of the number system in their headsto use for calculation. They develop ways of recording calculations using pictures, etc.

They use numberlines and practical resources (e.g. dienes) to support calculation andteachers demonstratethe use of the numberline alongside the use of practical equipment

3 + 2 = 5

___________________________________________0 1 2 3 4 5 6 7 8 9

+1 +1


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Children then begin to use numbered lines to support their own calculations using anumbered line to count on in ones8 + 5 = 13

Bead strings or bead bars can be used to illustrate addition

This includes bridging through ten by counting on 2 and then counting on 3.

Children are introduced to partitioning, i.e. are taught that, for example, 13 is the sameas 10 +3. Partitioning is used in general classroom teaching throughout KS1 and LKS2, and

for children in UKS2 where appropriate.In year 1, children focus on teen numbers, and are taught the meaning of tens andunits. The term units is repeatedly used so that children are familiar with this maths

term. For example, the integer 7 is 7 units; 13 is one ten and 3 units.

Children memorise and reason with number bonds to 10 and 20 in several forms (forexample, 9 + 7 = 16; 16 7 = 9; 7 = 16 9). They should realise the effect of adding orsubtracting zero. This establishes addition and subtraction as related operations.

Children are also shown how to solve missing number problems such as 7 = ? 9 by countingon or back using a number line.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

+1 +1 +1 +1 +1


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Y2

Children will use Dienes as a concrete method of addition, by combining the tens

together and the units together.

34 + 23 =

+ = +

The language used will reflect that there are 3 tens and 2 tens = 5 tens or 50 added to 4units and three units = 7 units.

This method will be revisited when partitioning is used in year 3 and the links between thetwo methods will be made explicit.

Children will begin to use empty number lines themselves, being explicitly shown thatefficient addition starts with the larger number and counting on. Dienes will again be used

to show the connection between the two methods

First counting on in tens and ones.

34 + 23 = 57

34 44 54 55 56 57

+1+1+1

+10+10


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Then helping children to become more efficient by adding the units in one jump

34 + 23 = 57

34 44 54 57

Followed by adding the tens in one jump and the units in one jump.

34 + 23 = 57

34 54 57

Bridging through ten can help children become more efficient.

37 + 15 = 52

37 47 50 52

Y3

+10 +10+3

+20 +3

+10+3 +2


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Children will continue to use empty number lines with increasingly large numbers, includingcompensation where appropriate.

Count on from the largest number irrespective of the order of the calculation. Dienes will also be used to support the core skill of bridging the 100s boundary. For

instance, with 38 + 86, the tens are combined so there are 11 tens. The units arecombined, so there are 14 units.

Ten of the units are swapped for one ten, using the language of fair swaps. Now

there are 12 tens and 4 units or 120 add 4 = 124

The two different ways of using the number line will be shown to aid understanding ofbridging the 100 boundary:

Method one counting on to the nearest multiple of 10

38 + 86 = 124

+4 + 10 +10 +10 + 4

86 90 100 110 120 124

Progressing to: Method 2

+10 +10 +10 +4 +4

86 96 106 116 120 124

Counting on using a number line is then extended to count on in larger multiples of 10:

86 116 120 124

Compensation

+30+4 +4


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49 + 73 = 122

73 122 123

Children will begin to use informal pencil and paper methods (jottings) to support, recordand explain partial mental methods building on existing mental strategies.

Children will then move on to setting out calculations horizontally first and then vertically,as a precursor to using the formal standard method

Horizontal method:

67 + 24 =60 + 20 = 807 + 4 = 11 80 + 11 = 80 + 10 +1 = 91

The concrete method of using dienes is explicitly linked to partitioning until the childrenare secure in their understanding of fair swaps.

Vertical method:

Adding the least significant digits first.In years 3 & 4, place value column headings need to be added to the calculation, i.e. HTU(Hundreds, Tens, Units). The value of each digit needs to be made explicit, for example60 + 20 = 6 tens + 2 tens = 8 tens = 80

TU HTU

67 267+ 24 + 851 1 ( 7 + 4) 12 ( 7 + 5)80 (60 + 20) 140 (60 + 80)91 200

352

Chn begin to estimate their answers prior to calculating them, by rounding each

number to the nearest multiple of 10.

+50

-1


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E.g 67 + 24E = 70 + 20 = 90Chn then check that their answer is close to their estimate

Y4


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From this, children will begin to carry below the line, extending this method to includenumbers with at least four digits

HTU HTU HTU

625 783 367+ 48 + 42 + 85

673 825 4521 1 1 1

The number carried over to the next column is crossed out when it has been added on.

The value of the digit needs to be made explicit when carrying.

HTU

679+ 63

742

1 1

In the above example, there are 14 tens or one hundred and four tens or 140. So we carry onehundred into the hundreds column and place the four tens in the tens column

Chn continue to estimate their answers prior to calculating them, by rounding each

number to the nearest multiple of 10.

E.g 679 + 63

E = 680 + 60 = 740

Chn then check that their answer is close to their estimate

Using similar methods, children will:

add several numbers with different numbers of digits;

begin to add two or more three-digit sums of money, with or without adjustment

from the pence to the pounds;

know that the decimal points should line up under each other, particularly whenadding or subtracting mixed amounts, e.g. 3.59 + 78p.

Y5

Children should extend the carrying method to numbers with four or more digits.


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587 3587+ 475 + 675

1062 42621 1 1 1 1



begin to add two or more decimal fractions with up to three digits and the same

number of decimal places;

know that decimal points should line up under each other, particularly when adding

mixed amounts, e.g. 3.2 m 280 cm. Such amounts would be converted first into like

units of measurement, e.g.

3.2m + 280cm = 3.2m + 2.8m = 6m

7648 6584 42+ 1486 + 5848 6432

9134 12432 7861 1 1 1 1 1 3

+ 468111944

1 2 1

Chn continue to estimate their answers prior to calculating them, by rounding eachnumber to the nearest multiple of 10 or 1 in the case of decimals

E.g 2.1 + 13.8E = 2 + 14 = 16

Y6


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By year 6, children apply their previous learning of addition methods to solve a range ofquestions. In addition, their knowledge of decimal addition is extended to include decimalsup to 3dp

Chn are shown how to estimate by rounding to the most significant figureExample: 3.451 + 2.123E = 3.5 + 2.1 = 3.6



begin to add two or more decimal fractions with up to four digits and up to 3 decimal

places;

know that decimal points should line up under each other when adding mixed amounts,

e.g. 401.2 + 26.85 + 0.71.

+ - + - + - + - + - + - +

revised addition policy

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