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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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Vocabulary introduced and used in year 2:
Numbers and the number system
COUNTING, PROPERTIES OF NUMBERS
AND NUMBER SEQUENCES
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
PLACE VALUE AND ORDERING
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
ADDITION AND SUBTRACTION
+, 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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Vocabulary introduced and used in year 3:
Numbers and the number system
COUNTING, PROPERTIES OF NUMBERS
AND NUMBER SEQUENCES
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
PLACE VALUE AND ORDERING
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
ADDITION AND SUBTRACTION
+, 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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MULTIPLICATION AND DIVISION
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
MAKING DECISIONS AND REASONING
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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Vocabulary introduced and used in year 4:
Numbers and the number system
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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MULTIPLICATION AND DIVISION
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
MAKING DECISIONS AND REASONING
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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Vocabulary introduced and used in year 5:
Numbers and the number system
PLACE VALUE, ORDERING AND ROUNDING
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:
>, greater than, more than, larger than, biggerthan
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Calculations
ADDITION AND SUBTRACTION
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
MULTIPLICATION AND DIVISION
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
MAKING DECISIONS AND REASONING
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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Vocabulary introduced and used in year 6:
Numbers and the number system
PLACE VALUE, ORDERING AND ROUNDING
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:
>, greater than, more than, larger than, biggerthan
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MULTIPLICATION AND DIVISION
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
MAKING DECISIONS AND REASONING
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
Using similar methods, children will:
add several numbers with different numbers of digits;
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
Using similar methods, children will:
add several numbers with different numbers of digits;
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.
+ - + - + - + - + - + - +