KEY STAGE 1 |
|||||
Children in Years 1 and 2 will be given a really solid foundation in the basic building blocks of mental and written arithmetic. Through being taught place value, children will develop an understanding of how numbers work, so that they are confident with 2-digit numbers and beginning to read and say numbers above 100. | |||||
Addition and Subtraction: A focus on number bonds, first via practical hands-on experiences and subsequently using memorisation techniques, enables a good grounding in these crucial facts, and ensures that all children leave Year 2 knowing the pairs of numbers which make all the numbers up to 10 at least. Children will also have experienced and been taught pairs to 20. Children’s knowledge of number facts enables them to add several 1-digit numbers, and to add/subtract a 1-digit number to/from a 2-digit number. Another important conceptual tool is the ability to add/subtract 1 or 10, and to understand which digit changes and why. This understanding is extended to enable children to add and subtract multiples of 10 to and from any 2-digit number. The most important application of this knowledge is the ability to add or subtract any pair of 2-digit numbers by counting on or back in 10s and 1s. Children may extend this to adding by partitioning numbers into 10s and 1s. | Multiplication and Division: Children will be taught to count in 2s, 3s, 5s and 10s, and will relate this skill to repeated addition. Children will meet and begin to learn the associated ×2, ×3, ×5 and ×10 tables. Engaging in a practical way with the concept of repeated addition and the use of arrays enables children to develop a preliminary understanding of multiplication, and asking them to consider how many groups of a given number make a total will introduce them to the idea of division. Children will also be taught to double and halve numbers, and will thus experience scaling up or down as a further aspect of multiplication and division. | Fractions: Fractions will be introduced as numbers and as operators, specifically in relation to halves, quarters and thirds. | |||
Year 1 |
|||||
Mental calculation |
Written calculation |
Default for ALL children |
|||
Y1 |
Number bonds (‘story’ of 5, 6, 7, 8, 9 and 10)
Count on in 1s from a given 2-digit number Add two 1-digit numbers Add three 1-digit numbers, spotting doubles or pairs to 10 Count on in 10s from any given 2-digit number Add 10 to any given 2-digit number Use number facts to add 1-digit numbers to e.g. Use 4 + 3 to work out 24 + 3, 34 + 3 Add by putting the larger number first |
Pairs with a total of 10
Count in 1s Count in 10s Count on 1 from any given 2-digit number |
|||
Y1 |
Number bonds (‘story’ of 5, 6, 7, 8, 9 and 10)
Count back in 1s from a given 2-digit number Subtract one 1-digit number from another Count back in 10s from any given 2-digit number Subtract 10 from any given 2-digit number Use number facts to subtract 1-digit numbers from 2-digit numbers e.g. Use 7 – 2 to work out 27 – 2, 37 – 2 |
Pairs with a total of 10
Count back in 1s from 20 to 0 Count back in 10s from 100 to 0 Count back 1 from any given 2-digit number |
|||
Y1 |
Begin to count in 2s, 5s and 10s
Begin to say what three 5s are by counting in 5s, or what four 2s are by counting in 2s, etc. Double numbers to 10 |
Begin to count in 2s and 10s
Double numbers to 5 using fingers |
|||
Y1 |
Begin to count in 2s, 5s and 10s
Find half of even numbers to 12 and know it is hard to halve odd numbers Find half of even numbers by sharing Begin to use visual and concrete arrays or |
Begin to count in 2s and 10s
Find half of even numbers by sharing |
|||
Year 2 |
|||||
Mental calculation |
Written calculation |
Default for ALL children |
|||
Y2 |
Number bonds – know all the pairs of numbers which make all the numbers to 12, and pairs with a total of 20
Count on in 1s and 10s from any given 2-digit number Add two or three 1-digit numbers Add a 1-digit number to any 2-digit number using number facts, including bridging multiples of 10 e.g. 45 + 4 Add 10 and small multiples of 10 to any given 2-digit number Add any pair of 2-digit numbers |
Know pairs of numbers which make each total up to 10
Add two 1-digit numbers Add a 1-digit number to a 2-digit number by counting on in 1s Add 10 and small multiples of 10 to a 2-digit number by counting on in 10s |
|||
Y2 |
Number bonds – know all the pairs of numbers which make all the numbers to 12
Count back in 1s and 10s from any given 2-digit number Subtract a 1-digit number from any 2-digit number using number facts, including bridging multiples of 10 e.g. 56 – 3 Subtract 10 and small multiples of 10 from any given 2-digit number Subtract any pair of 2-digit numbers by counting back in 10s and 1s or by counting up |
Know pairs of numbers which make each total up to 10
Subtract a 1-digit number from a 2-digit number by counting back in 1s Subtract 10 and small multiples of 10 from a |
|||
Y2 |
Count in 2s, 5s and 10s
Begin to count in 3s Begin to understand that multiplication is repeated addition and to use arrays e.g. 3 × 4 is three rows of 4 dots Begin to learn the ×2, ×3, ×5 and ×10 tables, seeing these as ‘lots of’ e.g. 5 lots of 2, 6 lots of 2, 7 lots of 2 Double numbers up to 20 Begin to double multiples of 5 to 100 Begin to double 2-digit numbers less than 50 with 1s digits of 1, 2, 3, 4 or 5 |
Count in 2s, 5s and 10s
Begin to use and understand simple arrays e.g. 2 × 4 is two lots of four Double numbers up to 10 Double multiples of 10 to 50 |
|||
Y2 |
Count in 2s, 5s and 10s
Begin to count in 3s Using fingers, say where a given number is in the 2s, 5s or 10s count e.g. 8 is the fourth number when I count in 2s Relate division to grouping e.g. How many groups of 5 in 15? Halve numbers to 20 Begin to halve numbers to 40 and multiples of 10 to 100 Find ^{1}/_{2}, ^{1}/_{3, }^{1}/_{4} and ^{3}/_{4} of a quantity of objects and of amounts (whole number answers) |
Count in 2s, 5s and 10s
Say how many rows in a given array e.g. How many rows of 5 are in an array of Halve numbers to 12 Find ^{1}/_{2} of amounts |
|||
LOWER KEY STAGE 2 |
|||||
In Lower Key Stage 2, children build on the concrete and conceptual understandings they have gained in Key Stage 1 to develop a real mathematical understanding of the four operations, in particular developing arithmetical competence in relation to larger numbers. | |||||
Addition and subtraction: Children are taught to use place value and number facts to add and subtract numbers mentally and they will develop a range of strategies to enable them to discard the ‘counting in 1s’ or fingers-based methods of Key Stage 1. In particular, children will learn to add and subtract multiples and near multiples of 10, 100 and 1000, and will become fluent in complementary addition as an accurate means of achieving fast and accurate answers to 3-digit subtractions. Standard written methods for adding larger numbers are taught, learned and consolidated, and written column subtraction is also introduced. | Multiplication and division:This key stage is also the period during which all the multiplication and division facts are thoroughly memorised, including all facts up to 12 × 12. Efficient written methods for multiplying or dividing a 2-digit or 3-digit number by a 1-digit number are taught, as are mental strategies for multiplication or division with large but ‘friendly’ numbers, e.g. when dividing by 5 or multiplying by 20. | Fractions and decimals: Children will develop their understanding of fractions, learning to reduce a fraction to its simplest form, as well as finding non-unit fractions of amounts and quantities. The concept of a decimal number is introduced and children consolidate a firm understanding of 1-place decimals, multiplying and dividing whole numbers by 10 and 100. | |||
Year 3 |
|||||
Mental calculation |
Written calculation |
Default for ALL children |
|||
Y3 |
Know pairs with each total to 20
e.g. 2 + 6 = 8, 12 + 6 = 18, 7 + 8 = 15 Know pairs of multiples of 10 with a total of 100 Add any two 2-digit numbers by counting on in 10s and 1s or by using partitioning Add multiples and near multiples of 10 and 100 Perform place-value additions without a struggle e.g. 300 + 8 + 50 = 358 Use place value and number facts to add a e.g. 104 + 56 is 160 since 104 + 50 = 154 and 6 + 4 = 10 676 + 8 is 684 since 8 = 4 + 4 and 76 + 4 + 4 = 84 Add pairs of ‘friendly’ 3-digit numbers e.g. 320 + 450 Begin to add amounts of money using partitioning |
Use expanded column addition to add two or three 3-digit numbers or three 2-digit numbers
Begin to use compact column addition to add numbers with 3 digits Begin to add like fractions e.g. ^{3}/_{8} + ^{1}/_{8} + ^{1}/_{8} Recognise fractions that add to 1 e.g. ^{1}/_{4} + ^{3}/_{4 } |
Know pairs of numbers which make each total up to 10, and which total 20
Add two 2-digit numbers by counting on in 10s and 1s e.g. 56 + 35 is 56 + 30 and then add the 5 Understand simple place-value additions e.g. 200 + 40 + 5 = 245 Use place value to add multiples of 10 or 100 |
||
Y3 |
Know pairs with each total to 20
e.g. 8 – 2 = 6 Subtract any two 2-digit numbers Perform place-value subtractions without a struggle e.g. 536 – 30 = 506 Subtract 2-digit numbers from numbers > 100 by counting up e.g. 143 – 76 is done by starting at 76. Then add 4 (80), then add 20 (100), then add 43, making the difference a total of 67 Subtract multiples and near multiples of 10 and 100 Subtract, when appropriate, by counting back or taking away, using place value and number facts Find change from £1, £5 and £10 |
Use counting up as an informal written strategy for subtracting pairs of 3-digit numbers
e.g. 423 – 357 Begin to subtract like fractions e.g. ^{7}/_{8} – ^{3}/_{8} |
Know pairs of numbers which make each total up to 10, and which total 20
Count up to subtract 2-digit numbers e.g. 72 – 47 Subtract multiples of 5 from 100 by counting up e.g. 100 – 35 Subtract multiples of 10 and 100 |
||
Y3 |
Know by heart all the multiplication facts in the ×2, ×3, ×4, ×5, ×8 and ×10 tablesMultiply whole numbers by 10 and 100Recognise that multiplication is commutativeUse place value and number facts in mental multiplicatione.g. 30 × 5 is 15 × 10 Partition teen numbers to multiply by a 1-digit number e.g. 3 × 14 as 3 × 10 and 3 × 4 Double numbers up to 50 |
Use partitioning (grid multiplication) to multiply 2-digit and 3-digit numbers by ‘friendly’ 1-digit numbers |
Know by heart the ×2, ×3, ×5 and ×10 tables
Double given tables facts to get others Double numbers up to 25 and multiples of 5 to 50 |
||
Y3 |
Know by heart all the division facts derived from the ×2, ×3, ×4, ×5, ×8 and ×10 tables
Divide whole numbers by 10 or 100 to give whole number answers Recognise that division is not commutative Use place value and number facts in mental division e.g. 84 ÷ 4 is half of 42 Divide larger numbers mentally by subtracting the 10th multiple as appropriate, including those with remainders e.g. 57 ÷ 3 is 10 + 9 as 10 × 3 = 30 and Halve even numbers to 100, halve odd numbers to 20 |
Perform divisions just above the 10th multiple using horizontal or vertical jottings and understanding how to give a remainder as a whole number
Find unit fractions of quantities and begin to find non-unit fractions of quantities |
Know by heart the division facts derived from the ×2, ×3, ×5 and ×10 tables
Halve even numbers up to 50 and multiples of 10 to 100 Perform divisions within the tables including those with remainders e.g. 38 ÷ 5 |
||
Year 4 |
|||||
Mental calculation |
Written calculation |
Default for ALL children |
|||
Y4 |
Add any two 2-digit numbers by partitioning or counting on
Know by heart/quickly derive number bonds Add to the next 100, £1 and whole number e.g. 234 + 66 = 300 Perform place-value additions without a struggle e.g. 300 + 8 + 50 + 4000 = 4358 Add multiples and near multiples of 10, 100 and 1000 Add £1, 10p, 1p to amounts of money Use place value and number facts to add 1-, 2-, 3- and 4-digit numbers where a mental calculation is appropriate e.g. 4004 + 156 by knowing that 6 + 4 = 10 and that 4004 + 150 = 4154 so the total is 4160 |
Column addition for 3-digit and 4-digit numbers
e.g. Add like fractions e.g. ^{3}/_{5 }+ ^{4}/_{5 }= ^{7}/_{5} = 1 ^{2}/_{5} Be confident with fractions that add to 1 and fraction complements to 1 e.g. ^{2}/_{3} + _ = 1 |
Add any 2-digit numbers by partitioning or counting on
Number bonds to 20 Know pairs of multiples of 10 with a total of 100 Add ‘friendly’ larger numbers using knowledge of place value and number facts Use expanded column addition to add 3-digit numbers |
||
Y4 |
Subtract any two 2-digit numbers
Know by heart/quickly derive number bonds to 100 Perform place-value subtractions without a struggle e.g. 4736 – 706 = 4030 Subtract multiples and near multiples of 10, 100, 1000, £1 and 10p Subtract multiples of 0·1 Subtract by counting up e.g. 503 – 368 is done by adding Subtract, when appropriate, by counting back or taking away, using place value and number facts Subtract £1, 10p, 1p from amounts of money Find change from £10, £20 and £50 |
Use expanded column subtraction for 3- and 4-digit numbersUse complementary addition to subtract amounts of money, and for subtractions where the larger number is a near multiple of 1000 or 100e.g. 2002 – 1865Subtract like fractionse.g. ^{4}/_{5 }– ^{3}/_{5 }= ^{1}/_{5} Use fractions that add to 1 to find fraction complements to 1 e.g. 1 – ^{2}/_{3 }= ^{1}/_{3} |
Use counting up with confidence to solve most subtractions, including finding complements to multiples of 100
e.g. 512 – 287 |
||
Y4 |
Know by heart all the multiplication facts up to 12 × 12Recognise factors up to 12 of 2-digit numbersMultiply whole numbers and 1-place decimals by 10, 100, 1000Multiply multiples of 10, 100 and 1000 by 1-digit numberse.g. 300 × 6 e.g. 4000 × 8 Use understanding of place value and number facts in mental multiplication e.g. 36 × 5 is half of 36 × 10 Partition 2-digit numbers to multiply by a 1-digit number mentally e.g. 4 × 24 as 4 × 20 and 4 × 4 Multiply near multiples by rounding e.g. 33 × 19 as (33 × 20) – 33 Find doubles to double 100 and beyond using partitioning Begin to double amounts of money e.g. £35·60 doubled is £71·20 |
Use a vertical written method to multiply a 1-digit number by a 3-digit number (ladder method)
Use an efficient written method to multiply a 2-digit number by a number between 10 and 20 by partitioning (grid method) |
Know by heart multiplication tables up to 10 × 10Multiply whole numbers by 10 and 100Use the grid method to multiply a 2-digit or a 3-digit number by a number ≤ 6 |
||
Y4 |
Know by heart all the division facts up to 144 ÷ 12Divide whole numbers by 10, 100, to give whole number answers or answers with 1 decimal placeDivide multiples of 100 by 1-digit numbers using division factse.g. 3200 ÷ 8 = 400Use place value and number facts in mental division e.g. 245 ÷ 20 is half of 245 ÷ 10 Divide larger numbers mentally by subtracting the 10th or 20th multiple as appropriate e.g. 156 ÷ 6 is 20 + 6 as 20 × 6 = 120 and Find halves of even numbers to 200 and beyond using partitioning Begin to halve amounts of money e.g. half of £52·40 is £26·20 |
Use a written method to divide a 2-digit or a 3-digit number by a 1-digit numberGive remainders as whole numbersBegin to reduce fractions to their simplest formsFind unit and non-unit fractions of larger amounts |
Know by heart all the division facts up to 100 ÷ 10Divide whole numbers by 10 and 100 to give whole number answers or answers with 1 decimal placePerform divisions just above the 10th multiple using the written layout and understanding how to give a remainder as a whole numberFind unit fractions of amounts |
||
UPPER KEY STAGE 2 |
|||||
Children move on from dealing mainly with whole numbers to performing arithmetic operations with both decimals and fractions. | |||||
Addition and subtraction: Children will consolidate their use of written procedures in adding and subtracting whole numbers with up to 6 digits and also decimal numbers with up to 2 decimal places. Mental strategies for adding and subtracting increasingly large numbers will also be taught. These will draw upon children’s robust understanding of place value and knowledge of number facts. Negative numbers will be added and subtracted. | Multiplication and division: Efficient and flexible strategies for mental multiplication and division are taught and practised, so that children can perform appropriate calculations even when the numbers are large, such as 40000 × 6 or 40 000 ÷ 8. In addition, it is in Years 5 and 6 that children extend their knowledge and confidence in using written algorithms for multiplication and division. | Fractions, decimals, percentages and ratio:Fractions and decimals are also added, subtracted, divided and multiplied, within the bounds of children’s understanding of these more complicated numbers. Children will also calculate simple percentages and ratios. | |||
Year 5 |
|||||
Mental calculation |
Written calculation |
Default for ALL children |
|||
Y5 |
Know number bonds to 1 and to the next whole number
Add to the next 10 from a decimal number e.g. 13·6 + 6·4 = 20 Add numbers with 2 significant digits only, using mental strategies e.g. 3·4 + 4·8 Add 1- or 2-digit multiples of 10, 100, 1000, 10 000 and 100 000 e.g. 8000 + 7000 Add near multiples of 10, 100, 1000, 10 000 and 100 000 to other numbers e.g. 82 472 + 30 004 Add decimal numbers which are near multiples of 1 or 10, including money e.g. 6·34 + 1·99 Use place value and number facts to add two or more ‘friendly’ numbers, including money and decimals e.g. 3 + 8 + 6 + 4 + 7 e.g. 0·6 + 0·7 + 0·4 e.g. 2056 + 44 |
Use column addition to add two or three whole numbers with up to 5 digits
Use column addition to add any pair of 2-place decimal numbers, including amounts of money Begin to add related fractions using equivalences e.g. ^{1}/_{2} + ^{1}/_{6} = ^{3}/_{6} + ^{1}/_{6} Choose the most efficient method in any given situation |
Add numbers with only 2 digits which are not zeros
e.g. 3·4 + 5·8 Derive swiftly and without any difficulty number bonds to 100 Add ‘friendly’ large numbers using knowledge of place value and number facts Use expanded column addition to add pairs of |
||
Y5 |
Subtract numbers with 2 significant digits only, using mental strategies
e.g. 6·2 – 4·5 Subtract 1- or 2-digit multiples of 10, 100, 1000, 10 000 and 100 000 e.g. 8000 – 3000 Subtract 1- or 2-digit near multiples of 10, 100, 1000, 10 000 and 100 000 from other numbers e.g. 82 472 – 30 004 Subtract decimal numbers which are near multiples of 1 or 10, including money e.g. 6·34 – 1·99 Use counting up subtraction, with knowledge of number bonds to 10, 100 or £1, as a strategy to perform mental subtraction e.g. £10 – £3·45 Recognise fraction complements to 1 and to the next whole number e.g. 1 ^{2}/_{5} + ^{3}/_{5} = 2 |
Use compact or expanded column subtraction to subtract numbers with up to 5 digits
Use complementary addition for subtractions where the larger number is a multiple or near multiple of 1000 Use complementary addition for subtractions of decimal numbers with up to 2 places, including amounts of money Begin to subtract related fractions using equivalences e.g. ^{1}/_{2} – ^{1}/_{6} = ^{2}/_{6} Choose the most efficient method in any given situation |
Derive swiftly and without difficulty number bonds to 100
Use counting up with confidence to solve most subtractions, including finding complements to multiples of 1000 e.g. 3000 – 2387 |
||
Y5 |
Know by heart all the multiplication facts up to 12 × 12Multiply whole numbers and 1- and 2-place decimals by 10, 100, 1000, 10000Use knowledge of factors and multiples in multiplicatione.g. 43 × 6 is double 43 × 3e.g. 28 × 50 is ^{1}/_{2} of 28 × 100 = 1400 Use knowledge of place value and rounding in mental multiplication e.g. 67 × 199 as 67 × 200 – 67 Use doubling and halving as a strategy in mental multiplication e.g. 58 × 5 is half of 58 × 10 e.g. 34 × 4 is 34 doubled twice Partition 2-digit numbers, including decimals, to multiply by a 1-digit number mentally e.g. 6 × 27 as 6 × 20 (120) plus 6 × 7 (42) e.g. 6·3 × 7 as 6 × 7 (42) plus 0·3 × 7 (2·1) Double amounts of money by partitioning e.g. £37·45 doubled is £37 doubled (£74) plus 45p doubled (90p) giving a total of £74·90 |
Use short multiplication to multiply a 1-digit number by a number with up to 4 digits
Use long multiplication to multiply 3-digit and Choose the most efficient method in any given situation Find simple percentages of amounts e.g. 10%, 5%, 20%, 15% and 50% Begin to multiply fractions and mixed numbers by whole numbers ≤ 10 e.g. 4 × ^{2}/_{3} = ^{8}/_{3} = 2 ^{2}/_{3} |
Know multiplication tables to 11 × 11
Multiply whole numbers and 1-place decimals by 10, 100 and 1000 Use knowledge of factors as aids to mental multiplication e.g. 13 × 6 is double 13 × 3 e.g. 23 × 5 is ^{1}/_{2} of 23 × 10 Use the grid method to multiply numbers with up to 4 digits by 1-digit numbers Use the grid method to multiply 2-digit numbers by 2-digit numbers |
||
Y5 |
Know by heart all the division facts up to 144 ÷ 12Divide whole numbers by 10, 100, 1000, 10 000 to give whole number answers or answers with 1, 2 or 3 decimal placesUse doubling and halving as mental division strategiese.g. 34 ÷ 5 is (34 ÷ 10) × 2Use knowledge of multiples and factors, as well as tests for divisibility, in mental division e.g. 246 ÷ 6 is 123 ÷ 3 e.g. We know that 525 divides by 25 and Halve amounts of money by partitioning e.g. ^{1}/_{2} of £75·40 = ^{1}/_{2} of £75 (£37·50) plus half of 40p (20p) which is £37·70 Divide larger numbers mentally by subtracting the 10th or 100th multiple as appropriate e.g. 96 ÷ 6 is 10 + 6, as 10 × 6 = 60 and e.g. 312 ÷ 3 is 100 + 4 as 100 × 3 = 300 and Know tests for divisibility by 2, 3, 4, 5, 6, 9 and 25 Know square numbers and cube numbers Reduce fractions to their simplest form |
Use short division to divide a number with up to 4 digits by a number ≤ 12Give remainders as whole numbers or as fractionsFind non-unit fractions of large amountsTurn improper fractions into mixed numbers and vice versaChoose the most efficient method in any given situation |
Know by heart division facts up to 121 ÷ 11
Divide whole numbers by 10, 100 or 1000 to give answers with up to 1 decimal place Use doubling and halving as mental division strategies Use an efficient written method to divide numbers ≤ 1000 by 1-digit numbers Find unit fractions of 2- and 3-digit numbers |
||
Year 6 |
|||||
Mental calculation |
Written calculation |
Default for ALL children |
|||
Y6 |
Know by heart number bonds to 100 and use these to derive related facts
e.g. 3·46 + 0·54 Derive, quickly and without difficulty, number bonds to 1000 Add small and large whole numbers where the use of place value or number facts makes the calculation do-able mentally e.g. 34 000 + 8000 Add multiples of powers of 10 and near multiples of the same e.g. 6345 + 199 Add negative numbers in a context such as temperature where the numbers make sense Add two 1-place decimal numbers or two 2-place decimal numbers less than 1 e.g. 4·5 + 6·3 Add positive numbers to negative numbers e.g. Calculate a rise in temperature or continue a sequence beginning with a negative number |
Use column addition to add numbers with up to 5 digits
Use column addition to add decimal numbers with up to 3 decimal places Add mixed numbers and fractions with different denominators |
Derive, swiftly and without difficulty, number bonds to 100
Use place value and number facts to add ‘friendly’ large or decimal numbers e.g. 3·4 + 6·6 Use column addition to add numbers with up to Use column addition to add pairs of 2-place decimal numbers |
||
Y6 |
Use number bonds to 100 to perform mental subtraction of any pair of integers by complementary addition
e.g. 1000 – 654 as 46 + 300 in our heads Use number bonds to 1 and 10 to perform mental subtraction of any pair of 1-place or 2-place decimal numbers using complementary addition and including money e.g. 10 – 3·65 as 0·35 + 6 e.g. £50 – £34·29 as 71p + £15 Use number facts and place value to perform mental subtraction of large numbers or decimal numbers with up to 2 places e.g. 467 900 – 3005 Subtract multiples of powers of 10 and near multiples of the same Subtract negative numbers in a context such as temperature where the numbers make sense |
Use column subtraction to subtract numbers with up to 6 digits
Use complementary addition for subtractions where the larger number is a multiple or near multiple of 1000 or 10 000 Use complementary addition for subtractions of decimal numbers with up to 3 places, including money Subtract mixed numbers and fractions with different denominators |
Use number bonds to 100 to perform mental subtraction of numbers up to 1000 by complementary addition
e.g. 1000 – 654 as 46 + 300 in our heads Use complementary addition for subtraction of integers up to 10 000 e.g. 2504 – 1878 Use complementary addition for subtractions of 1-place decimal numbers and amounts of money e.g. £7·30 – £3·55 |
||
Y6 |
Know by heart all the multiplication facts up to 12 × 12Multiply whole numbers and decimals with up to 3 places by 10, 100 or 1000e.g. 234 × 1000 = 234 000 e.g. 0·23 × 1000 = 230Identify common factors, common multiples and prime numbers and use factors in mental multiplication e.g. 326 × 6 is 652 × 3 which is 1956 Use place value and number facts in mental multiplication e.g. 4000 × 6 = 24 000 Use doubling and halving as mental multiplication strategies, including to multiply by 2, 4, 8, 5, 20, 50 and 25 e.g. 28 × 25 is a quarter of 28 × 100 = 700 Use rounding in mental multiplication e.g. 34 × 19 as (34 × 20) – 34 Multiply 1- and 2-place decimals by numbers up to and including 10 using place value and partitioning e.g. 3·6 × 4 is 12 + 2·4 e.g. 2·53 × 3 is 6 + 1·5 + 0·09 Double decimal numbers with up to 2 places using partitioning e.g. 36·73 doubled is double 36 (72) plus double 0·73 (1·46) |
Use short multiplication to multiply a 1-digit number by a number with up to 4 digits
Use long multiplication to multiply a 2-digit number by a number with up to 4 digits Use short multiplication to multiply a 1-digit number by a number with 1 or 2 decimal places, including amounts of money Multiply fractions and mixed numbers by whole numbers Multiply fractions by proper fractions Use percentages for comparison and calculate simple percentages |
Know by heart all the multiplication facts up to 12 × 12Multiply whole numbers and 1- and 2-place decimals by 10, 100 and 1000Use an efficient written method to multiply a1-digit or a teen number by a number with up to 4 digits by partitioning (grid method)Multiply a 1-place decimal number up to 10 by a number ≤ 100 using the grid method |
||
Y6 |
Know by heart all the division facts up to 144 ÷ 12Divide whole numbers by powers of 10 to give whole number answers or answers with up to3 decimal placesIdentify common factors, common multiples and primes numbers and use factors in mental divisione.g. 438 ÷ 6 is 219 ÷ 3 which is 73 Use tests for divisibility to aid mental calculation Use doubling and halving as mental division strategies, for example to divide by 2, 4, 8, 5, 20 and 25 e.g. 628 ÷ 8 is halved three times: Divide 1- and 2-place decimals by numbers up to and including 10 using place value e.g. 2·4 ÷ 6 = 0·4 e.g. 0·65 ÷ 5 = 0·13 e.g. £6·33 ÷ 3 = £2·11 Halve decimal numbers with up to 2 places using partitioning e.g. Half of 36·86 is half of 36 (18) plus half of 0·86 (0·43) Know and use equivalence between simple fractions, decimals and percentages, including in different contexts Recognise a given ratio and reduce a given ratio to its lowest terms |
Use short division to divide a number with up to 4 digits by a 1-digit or a 2-digit numberUse long division to divide 3-digit and 4-digit numbers by ‘friendly’ 2-digit numbersGive remainders as whole numbers or as fractions or as decimalsDivide a 1-place or a 2-place decimal number by a number ≤ 12 using multiples of the divisorsDivide proper fractions by whole numbers |
Know by heart all the division facts up to 144 ÷ 12Divide whole numbers by 10, 100, 1000 to give whole number answers or answers with up to 2 decimal placesUse an efficient written method, involving subtracting powers of 10 times the divisor, to divide any number of up to 1000 by a number ≤ 12e.g. 836 ÷ 11 as 836 – 770 (70 × 11) leaving 66 which is 6 × 11, giving the answer 76Divide a 1-place decimal by a number ≤ 10 using place value and knowledge of division facts |
||