Year 1Add with numbers up to 20
Use number tracks, practical methods & numbered number lines to add by counting on in ones & using the addition (+) & equals (=) signs.
Encourage to start with the larger number & count on:
Examples:
8 + 3 =
15 + 4 =
5 + 3 + 1 =
Children are encouraged to record by drawing jumps on prepared lines. / Key vocabularyadd, more, plus, and make, altogether, total, equal to, equals, double, most, count on, number line
Key number skills
Read and write numbers to 100 in numerals, incl 1-20 in words.
Recall bonds to 10 & 20, & addition facts within 20.
Count to & across 100.
Count in multiples of 1,2,5 & 10.
Year 2Add with 2 digit numbers
Add 2 digit numbers & tens:
27 + 30 = 27 + 10 + 10 + 10 = 57
Add pairs of 2 digit numbers (add tens & then units, starting with the largest number):
23 + 12 = 23 + 10 + 2 = 35
23 33 35
Lead to expanded column method, only introducing examples that cross tens boundary when ready.
20 + 3
30 + 4
50 + 7 = 57 / Key vocabularyas before + sum, tens, ones, partition, addition, column,tens boundary
Key number skills
Add a 2-digit number & ones (e.g. 27+6)
Add a 2-digit number & tens (e.g. 23+40)
Add pairs of 2-digit numbers (e.g. 35+47)
Add 3 one-digit numbers (e.g. 5+9+7)
Know that adding can be done in any order.
Recall bonds to 20 & bonds of tens to 100 (30+70)
Understand the place value of 2 digit numbers (tens & ones)
Compare & order numbers to 100 using the ‹ › & = signs.
Read & write numbers to at least 100 in numbers & words.
Year 3Add up to 3-digit numbers
Expand column method adding ones first (example 1)
Progressing to the compact column method using “carrying” (example 2)
1) 236 2) 236
73 + 73 +
9 (6+3) 309
100 (30+70) 1
200 (200+0)
309n / Key vocabulary as before + hundreds boundary, increase, vertical, “carry”, expanded, compact
Key number skills
Read & write numbers to 1000 in numerals & words.
Add 2-digit numbers mentally, incl those exceeding 100
Add a 3-digit number & ones mentally (175+8)
Add a 3-digit number & tens mentally (249+50)
Add a 3-digit number & hundreds mentally (381+400)
Estimate answers using inverse to check
Recognise place value of digits in 3-digit numbers
From Year 3 onwards, teachers need to follow the methods specified in grade-level standards for end of KS2 (Year 5 & 6Calculation Policy Document). Children should be developing their capacity to use formal written methods for all four number operations.
Year 4 Add numbers with up to 4 digits
Using the compact column method, adding ones first & “carrying” numbers underneath the calculation. Children should also add money & measures.
e.g. 3517 + 396 = 3913 3517
396 +
3913
1 1 / Key vocabulary as before + thousands, hundreds, digits, inverse
Key number skills
Select most appropriate method: mental, jottings or written & explain why.
Recognise place value of each digit in a 4-digit number.
Round any number to the nearest 10, 100 or 1000.
Estimate & use inverse operations to check answers.
Find 100 more or less than a given number.
Year 5Add number with more than 4 digits
Add numbers including money, measures & decimals with different numbers of decimal places.
£ 23.59 23.481 19.01
7.55+ 1.362 + 3.65
£ 31.14 24.843 0.70 +
1 1 1 1 23.36
1 1 / Key vocabularyas before + decimal places, decimal point, tenths, hundredths, thousandths
Key number skills
Add numbers mentally with increasingly large numbers.
Use rounding to check answers & accuracy.
Read, write, order & compare numbers to at least 1 million & determine the value of each digit.
Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 & 100,000.
Year 6Add several numbers of increasing complexity
Add “zeros” where needed to show the place value of decimals.
23.361 81059
9.080 3668
59.770 15301
1.300 + 20551 +
93.511 120579
2 1 2 1 1 1 1 / Key vocabulary as before
Key number skills
Perform mental calculations, including with mixed operations & large numbers.
Use estimation to check answers to calculations & determine, in the context of a problem, levels of accuracy.
Read, write, order & compare numbers up to 1 million & determine the value of each digit.
Round any whole number to a required degree of accuracy.
SUBTRACTION / -
Year 1 Subtract from numbers up to 20
Count back in ones on a numbered number line to take away.
Begin to write numbers sentences with - & = signs
11 – 4 = 7
Find the “distance between”, “how many more” & “how many less” by counting on. using practical resources (Numicon & counting beads) / Key vocabulary equal to, take away, less, minus, subtract, leaves, distance between, how many more, how many left, how many less is…?
Key number skills
Give any number, say one more or one less.
Count to & over 100, forward on & back, from any number.
Represent & use subtraction facts to & within 20.
Subtract with 1 & 2-digit numbers to 20 incl 0.
Year 2Subtract with 2-digit numbers
Subtract by counting back gradually using more efficient jumps.
82-49 = 33
Use counting on as a mental strategy where numbers are close together.e.g. 42-38 / Key vocabulary as before + difference, count on, strategy, partition, tens, units
Key number skills
Recognise the place value of each digit in a 2-digit number.
Recall & use subtraction facts to 20 fluently & derive & use related facts up to 100.
Subtract using concrete objects, pictorial. representations, 100 squares & mentally incl a 2-digit & tens, & 2- digit numbers.
Know that subtraction cannot be done in any order.
Recognise & use inverse relationship between addition & subtraction to check calculations & missing number problems.
Year 3 Subtract with 2 & 3-digit numbers
Find a small difference by counting up.
Continue from Year 2 but with appropriate numbers.e.g. 102 – 97 = 5
Subtract mentally a ‘near multiple of 10’ to or from a two-digit number, extending to 3-digit numbers.
Continue as in Year 2 but with appropriate numbers. e.g. 78 – 49 = 78 – 50 + 1
Partitioned column subtraction method:
89 – 35
80 9
- 30 + 5
50 + 4 / Key vocabulary as before + exchange, decrease, hundreds, value, digit
Key number skills
Subtract mentally:
- 3-digit number & ones
- 3-digit number & tens
- 3-digit number & hundreds
Solve problems, incl missing number problems.
Find 10 or 100 more or less than a given number.
Recognise place value of each digit in 3-digit number.
From Year 3 onwards, teachers need to follow the methods specified in grade-level standards for end of KS2 (Year 5 & 6Calculation Policy Document). Children should be developing their capacity to use formal written methods for all four number operations.
Year 4 Subtract with up to 4-digit numbers
Partitioned column subtraction using exchanging method leading to decomposition method.
Subtract mentally a ‘near multiple of 10 or 100 etc.’
Use known number facts and place value to subtract:
6.5 – 0.7 = 5.8
5.8 6.0 6.5
0.2 0.5 / Key vocabulary as before + inverse
Key number skills
Subtract by counting on where numbers are close together or are near to mutiples of `10, 100 etc (87-79, 202-197)
Estimate & use inverse operations to check answers.
Solve addition & subtraction 2-step problems in contexts, choosing which operations & methods to use & why.
Find 1000 more or less than a given number.
Count backwards through zero to include negative numbers.
Recognise the place value of each digit in a 4 digit number.
Round any number to the nearest 10, 100 or 1000.
Year 5 Subtract with at least 4-digit numbers
(see appendix) / Key vocabulary as before + tenths, hundredths, decimal point, decimal
Key number skills
Subtract numbers mentally with increasingly large numbers.
Use rounding & estimation to check answers to calculations.
Solve addition & subtraction mulit-step problems in context, deciding which operations & best methods to use and why.
Read, write, order & compare numbers to at least 1 million & determine the value of each digit.
Count forwards or backwards in steps of 10, 100, 1000, 10,000….
Interpret negative numbers in context, counting forwards & backwards with positive & negative integers through 0.
Round any number up to 1 million to the nearest 10, 100, 1000, 10,000 & 100, 000.
Year 6Subtract with increasingly large & more complex numbers & decimals values
(see appendix) / Key vocabularyas before
Key number skills
Solve addition & subtraction multi-step problems in context, deciding which operations to use & why.
Read, write, order & compare numbers up to 10 million & determine the value of each digit.
Round any whole number to a required degree of accuracy.
Use negative numbers in context, calculating the intervals across 0.
MULTIPLICATION / X
Year 1 Multiply with concrete objects, arrays & pictorial representations
There are 3 sweets in 1 jar.
How many sweets in 5 jars?
Counting steps using bead string and on prepared number lines.
Counting in multiples using a range of objects, e.g. pairs of legs on animals; fingers in gloves etc.
Counting in rows and columns
Two groups of three is six
Three groups of two is six
So 6 = 2 + 2 +2 or 6 = 3 + 3 / Key vocabulary groups of, lots of, times, array, altogether, multiply, total, count up in….
Key number skills
Count in 2s, 5s & 10s.
Solve 1-step problems involving multiplication by calculating the answer using concrete objects, pictorial representations & arrays with the support of the teacher.
Make connections between arrays, number patterns & counting in 2s, 5s & 10s.
Begin to understand doubling using concrete objects & pictorial representations.
Year 2 Multiply using arrays & repeated addition
Using arrays:
4 x 2
2 x 4
or repeated addition:
4 + 4
2 + 2 + 2 + 2 / Key vocabulary as before & multiplied by, column, row, repeated addition, commutative, sets of, equal groups, times as big as, once, twice, three times etc
Key number skills
Count in steps of 2,3 & 5 from 0 & in 10s from any number.
Recall & use multiplication facts incl recognising odds & evens.
Write & calculate number statements using thex and = signs.
Show that multiplication can be done in any order (commutative).
Solve a range of problems involving multiplication, using materials, arrays, repeated addition, mental methods & multiplication facts.
Year 3 Multiply 2 digits by a single digit number (grid method)
Continue to use repeated addition on number lines as above (where needed) to reinforce how to calculate multiplication facts.
x / 30 / 5
5 / 150 / 25
35 x 5 = 175 32 x 4 = 128 / Key vocabulary as before & partition, grid method, multiple, product, tens, units, value
Key skills
Recall & use multiplication facts for 2,3,4,5, 8 & 10 multiplication tables & multiply multiples of 10.
Write & calculate number statements using the multiplication tables they know, incl 2 digit x single digit drawing upon mental methods & progressing to reliable written methods.
Year 4 Multiply 2 & 3 digit numbers by a single digit (using the grid & partitioning methods)
Use grid method:
x / 20 / 3
7 / 140 / 21
23 x 7 = 161
Use partitioning method:
23 x 7 = 161
23 x 7 = (20 x 7) + (3 x 7)
Use short multiplication:
(see appendix) / Key vocabulary as before & square. Factor. Integer, decimal, short/long multiplication, ‘carry’
Key skills
Count in multiples of 6,7,9,25 & 1000.
Recall multiplication facts for tables up to 12 x 12.
Recognise place value of digits in up to 4 digit numbers.
Use place value, known facts & derived facts to multiply mentally e.g. multiply by 1,10, 100 by 0, or multiply 3 numbers.
Use commutativity in mental calculations:
3 x 6 = 6 x 3
2 x 6 x 5 = 10 x 6
Year 5 Multiply up to 4 digits by 1 or 2 digits
(see appendix) / Key vocabulary as before & cubed, square, factor, integer, decimal, short/long multiplication, ‘carry’
Key skills
Identify multiples & factors using knowledge of tables up to 12 x 12.
Solve problems where larger numbers are decomposed into their factors.
Multiply & divide integers & decimals by 10,100 & 1000.
Recognise & use square & cube numbers & their notation.
Year 6 As Year 5 & multiply decimals with up to 2 decimal places by a single digit
(see appendix) / Key vocabulary as before &
tenths, hundredths
Key skills
Multiply multi digit numbers up to 4 digit numbers, up to 4 digit x 2 digit using long multiplication.
Perform mental calculations with mixed operations & large numbers.
Estimate answers using rounding & approximation & determine levels of accuracy.
Round any digit to a required degree of accuracy.
DIVISION / ÷
Year 1 Group & share small quantities
Using objects, diagrams & pictorial representations to solve problems about both grouping & sharing.
Use of pictures and objects or marks 12 children get into teams of 4 to play a game. How many teams are there?
6 sweets are shared between 2 people. How many do they have each?
Make use of practical activities involving sharing, e.g. distributing cards when playing a game, putting objects onto plates, into cups, hoops etc.
/ Key vocabulary share, share equally, one each, two each…, group, groups of, lots of, array
Key skills
Solve one step problems, calculating answers using concrete objects, pictorial representations arrays with support.
Through grouping & sharing small quantities, begin to understand division & find simple fractions of objects, numbers/quantities.
Make connections between arrays, number patterns & counting in 2s, 5s & 10s.
Year 2 Group & share using the ÷ sign
Use objects, arrays, diagrams, pictorial representations & repeated addition on a number line.
Use repeated addition on a number line
Use the ÷ & = signs
6 ÷ 2 = 3 6 ÷ 3 = 2 / Key vocabulary as before & inverse, short division, ‘carry’, remainder, multiple
Key number skills
Recall & use multiplication/ division facts for 2,3,4,5,8 & 10 multiplication tables (through doubling, connect the 2,4 & 8s)
Write & calculate number statements for multiplication & division using multiplication tables that they know, incl for 2 digit numbers times 1 digit numbers.
Solve problems in contexts & incl missing number problems involving multiplication & division
Develop efficient mental methods e.g. using multiplication & division facts (e.g. 3 x 2 = 6, 6 ÷ 3 = 2 & 6 ÷ 2 = 3) to derive related facts (30 x 2 = 60, so 60 ÷ 2 = 30 & 20 = 60 ÷ 3)
Year 3 Divide 2 digit numbers by a single digit (no remainders in final answer)
Short division
Remainders carried within the calculation once confident with method.
/ Key vocabulary as before & divide, divided by, divided into, division, grouping, number line, left, left over
Key skills
Count in 2s, 3s & 5s from 0.
Recall & use the multiplication & division facts for the 2, 5 & 10 multiplication tables, recognising odds & evens.
Calculate statements for multiplication & division within the multiplication tables, writing them using x, ÷ & = signs.
Show that division cannot be done in any order.
Solve problems in context using materials, arrays, repeated addition, mental methods, multiplication & division facts.
Year 4 Divide up to 3 digit numbers by a single digit (with remainders)
Short division
/ Key vocabulary as before & divisible by, factor
Key number skills
Recall all multiplication facts up to 12 x 12..
Use place value, known & derived facts to multiply & divide mentally incl multiplying & dividing by 10 & 100.
Use short division with exact answers.
Extend mental methods to 3 digit numbers, deriving facts e.g.
200 x 3 = 600, so 600 ÷ 3 = 200
Solve 2 step problems in contexts, choosing the appropriate operation, working with increasingly harder numbers. (This should include correspondence questions such as 3 cakes shared equally between 10 children)
Year 5 Divide up to 4 digits by a single digit (incl remainders as fractions & decimals)
(see appendix) / Key vocabulary as before & quotient, prime number, prime factors, composite number (non-prime)
Key skills
Recall multiplication/ division facts for all numbers up to 12 x 12.
Identify multiples & factors of any number.
Multiply & divide whole numbers & those involving decimals by 10, 100 & 1000.
Work out if numbers to 100 are prime, recalling primes to 19.
Use multiplication & division as inverses.
Express remainder answers as fractions, decimals or rounded numbers, as appropriate in context to the problem.
Year 6 Divide up to 4 digit numbers by 1 or 2 digits (incl decimals)
(see appendix). / Key vocabulary as before & common factor
Key skills
Use multiplication & division facts for all umbers to 12 x 12 for more complex calculations.
Identify common factors, common multiples & prime numbers.
Solve problems which require answers to be rounded to specified degree of accuracy & remainders to be expressed as rounded numbers, fractions or decimals.
Use estimation to check answers to calculations.
New Mathematics Calculation Policy: Year 5 and Year 6
The exemplification of formal methods here should be taken into account by all Key Stage 2 teachers so children are adequately prepared by Year 5 and into Year 6 to use the means of calculating specified in grade-level standards.
Addition & Subtraction
AS5.1
Columnar
Addition &
Subtraction
Multiplication & Division
MD5.5 Short Multiplication
(DfE, 2013,
Appendix 1)
MD5.7 & ASMD6.2b
Short Division
(DfE, 2013, Appendix 1)
MD5.5 & ASMD6.1 Long
Multiplication
(DfE, 2013,
Appendix 1)
ASMD6.2a
Long Division
(DfE, 2013, Appendix 1)