Issue 2 October 2015

Maths Calculation

Explanation Handbook

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3

Introduction 5

Mathematics Curriculum overview 6

Mental maths 7

Mental calculations infants 8

Mental calculations juniors 11

Recording work 19

Addition 20

Adding decimals 23

Adding amounts of money 24

Adding fractions 25

Subtraction 26

Subtracting decimals 29

Calculating change 31

Subtracting fractions 32

Multiplication 33

Multiplying decimals 39

Multiplying fractions 40

Division 41

Apply knowledge to solve problems 46

Useful websites 47

Development of pencil & paper procedures 48

Contents

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5

At Laxton Junior School we provide a curriculum through daily mathematics teaching that promotes enjoyment and enthusiasm for learning through practical activity, exploration and discussion. The children’s growing knowledge and understanding takes place through the development of key skills, concepts, strategies and personal qualities enabling them to become confident mathematicians. We appreciate the need for repetition and consolidation as well as extension and it is important to us that the appropriate teaching for each child’s learning needs is delivered. Within all topics we give the children opportunities to develop their ability, to think logically and solve problems, through decision making and reasoning, enabling them to understand and appreciate the use of mathematics in their everyday lives.

In the early years it is essential that the basics taught are secure. This, in turn, provides a firm foundation on which your child can build. Throughout the school the children are taught according to their own personal learning needs, rather than merely by their age. In each topic, a child must understand the basics before they can progress. Jumping stages will leave gaps in their learning. The temptation to ‘get ahead’ in terms of covering written techniques needs to be resisted. All topics are revisited each year, from Reception up to Year Six. Each time the children’s knowledge, skills and understanding are reinforced and then further developed and extended.

This booklet will:

• give you an overview of how the Maths Curriculum is put together

• explain what pupils are expected to know, regarding their number facts, by the end of each Year group.

• provide you with a greater understanding of the progression of how the four rules of addition, subtraction, multiplication and division are introduced at LJS.

Introduction

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Mathematics Curriculum Overview A variety of Mathematics schemes are used to implement the National Curric-ulum for Mathematics. We teach mathematics as an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are organised into distinct domains that are revisit-ed throughout the year and concepts are consolidated and further extended as the children move through the school. (

In upper Key Stage 2, children are also taught about:

Proportion Algebra At all levels, pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving in-creasingly sophisticated problems. They should also apply their mathematical knowledge to other areas of the curriculum.

Number Measurement Geometry Statistics

Number and place value Addition and subtraction Multiplication and division Fractions, deci-mals and percentages.

Length and height Weight Capacity Time Money

Properties of shapes Angles Position and direction Co-ordinates Refection and translation

Interpret and present data using tables and graphs Probability

Ration & Proportion Algebra

Scaling Reduction

Using simple formulae Solving formulae Substitution

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Maths is not just about sums on a page; a great deal of learning takes place verbally and practically. It is important to recognise that the ability to calculate mentally lies at the heart of what we do. The concept of mental maths means being able to give an answer to a maths question after thinking about it rather than making notes on paper or using calculators. Mental maths can be used as a way to calculate and estimate quickly, using number facts that a child has committed to memory. The ability to work sums in your head is an important skill that we help the children de-velop throughout the school. Each mathematics session begins with a starter that helps children develop their mental recall and skills using diAerent equipment to support their learn-ing. Knowing a variety of number facts helps to develop mental strategies for solving number problems and children will be encouraged to use a variety of strategies relative to their ability. When learning number facts it is essential that each level is achieved comfortably before moving on. Mental maths can and should be practised orally, regularly and for short bursts—this can be done an-ywhere. Equipment used during mental starterEquipment used during mental starterEquipment used during mental starterEquipment used during mental starter

• Interactive whiteboard • Individual whiteboards • Flip flops • Number fans or number up cards • Place value cards • Songs and stories • Movement • Number square or number track • Hangers with pegs • Loop cards • Games We make all activities as multi-sensory as we can to ensure that we cater for all of the learning styles in the classroom.

Mental Maths

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Mental Calculations in the Infants EYFSEYFSEYFSEYFS By the end of Reception children should be able to:By the end of Reception children should be able to:By the end of Reception children should be able to:By the end of Reception children should be able to: • Orally count to 100 • Count reliably up to 20 objects • Recognise numbers up to 20 and place in order • Say which number is one more or one less than a given number • Use quantities and objects to add and subtract two single digit numbers • Count on or back to find answers • Solve problems, including doubling, halving and sharing • Use a range of strategies for addition and subtraction including some

mental recall of number bonds • Write numbers to at least 10

Key Stage 1Key Stage 1Key Stage 1Key Stage 1 By the end of Year 1 children should be able to:By the end of Year 1 children should be able to:By the end of Year 1 children should be able to:By the end of Year 1 children should be able to: • Estimate and count reliably 30 objects and beyond Addition • Know number bonds 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 • Add 10 to any given 2-digit number • Use number facts to add 1-digit numbers to 2-digit numbers e.g. Use 4 + 3 to work out 24 + 3, 34 + 3 • Add by putting the larger number first and counting on Subtraction • Count back in 1s from any 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 • Know by heart all pairs of numbers that make 10, e.g. 3 + 7, 8 + 2 and

related subtraction facts e.g. 10-7=3, 10-3=7, 10-8=2, 10-2=8 • Find change from 10p and 20p

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Multiplication • 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 Division • Find half of even numbers to 12 by sharing • Know it is hard to halve odd numbers • Begin to use visual and concrete arrays or ‘sets of’ to find how many sets of

a small number make a larger number By the end of Year 2 children should be able to:By the end of Year 2 children should be able to:By the end of Year 2 children should be able to:By the end of Year 2 children should be able to: Addition • Number bonds—know all the pairs of numbers which make all the num-

bers 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 e.g. 38 + 7 • Add 10 and small multiples of 10 to any given 2-digit number • Add any pair of 2-digit numbers Subtraction • 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 e.g. 53 - 5 • 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 Multiplication • Count in 2s, 5s and 10s • Begin to count in 3s

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• Begin to understand that multiplication is repeated addition and to use ar-rays

e.g. 3 x 4 is three rows of 4 dots • Begin to learn the x2, x3, x5 and x10 tables, seeing these as ‘lots of’ e.g. 5 lots of 2, 6 lots of 2, 7 lots of 2 • Double numbers 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 Division • 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 ½, ¹⁄₃, ¼ and ¾ and of a quantity of objects and amounts (whole

number answers)

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Key Stage 2Key Stage 2Key Stage 2Key Stage 2 By the end of Year 3 children should be able to:By the end of Year 3 children should be able to:By the end of Year 3 children should be able to:By the end of Year 3 children should be able to: Addition • 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 confidently e.g. 300 + 8 + 50 = 358 • Use place value and number facts to add a 1-digit or 2-digit number to a 3-

digit number e.g. 104 + 56 is 160 since 104 + 50 = 154 and 6 + 4 = 10 e.g. 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 Subtraction • Know pairs with each total to 20 e.g. 8 - 2 = 6, 18 - 6 = 12, 15 - 8 = 7 • Subtract any two 2-digit numbers • Perform place-value subtractions confidently 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 diAerence 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 Multiplication • Know all the multiplication facts in the x2, x3, x4, x5, x8 and x10 tables • Multiply whole numbers by 10 and 100 • Recognise that multiplication is commutative

Mental Calculations in the Juniors

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• Use place value and number facts in mental multiplication e.g. 30 x 5 is 15 x 10 • Partition teen numbers to multiply by a 1-digit number e.g. 3 x 14 as 30 x 10 and 3 x 4 • Double numbers up to 50 Division • Know all the division facts derived from the x2, x3, x4, x5, x8 and x10 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 (Introducing Chunking) e.g. 57 ÷ 3 is 19 19 19 19 as 10101010 x 3 = 30 and 9999 x 3 = 27 • Halve even numbers to 100, halve odd numbers to 20 By the end of Year 4 children should be able to:By the end of Year 4 children should be able to:By the end of Year 4 children should be able to:By the end of Year 4 children should be able to: Addition • Add any two 2-digit numbers by partitioning or counting on • Know by heart/quickly derive number bonds to 100 and to £1 • Add to the next 100, £1 and whole number e.g. 234 + 66 = 300 e.g. 3.4 + 0.6 = 4 • 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 a 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 Subtraction • 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

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• Find change from £10, £20 and £50 • 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 368 + 2 + 30 + 100 + 3 (so we added 135) • Subtract, when appropriate, by counting back or taking away, using place

value and number facts • Subtract £1, 10p, 1p from amounts of money Multiplication • Know all the multiplication facts up to 12 x 12 • Recognise factors up to 12 of 2-digit numbers • Multiply whole numbers and 1-place decimals by 10, 100 and 1000 • Multiply multiples of 10, 100 and 1000 by 1-digit numbers e.g. 300 x 6 e.g. 4000 x 8 • Use understanding of place value and number facts in mental multiplica-

tion e.g. 36 x 5 is half of 36 x 10 e.g. 50 x 60 • Partition 2-digit numbers to multiply by a 1-digit number mentally e.g. 4 x 24 as 4 x 20 and 4 x 4 • Multiply near multiples by rounding e.g. 33 x 19 as (33 x 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 Division • Know all the division facts up to 144 ÷ 12 • Divide whole numbers by 10 or 100 to give whole number answers or an-

swers with 1 decimal place • Divide multiples of 100 by 1-digit numbers using division facts e.g. 3200 ÷ 8 = 400 • Use 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 x 6 = 120 and 6 x 6 = 36

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• 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

By the end of Year 5 children should be able to:By the end of Year 5 children should be able to:By the end of Year 5 children should be able to:By the end of Year 5 children should be able to: Addition • 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 e.g. 23000 + 47000 • Add 1– or 2-digit multiples of 10, 100, 1000, 10000 and 100000 e.g. 8000 + 7000 e.g. 600000 + 700000 • Add near multiples of 10, 100, 1000, 10000 and 100000 to other numbers e.g. 82472 + 30004 • Add decimal numbers which are near multiples of 1 or 10, including money e.g. 6.34 + 1.99 e.g. £34.59 + £19.95 • 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. 2059 + 44 Subtraction • Subtract numbers with 2 significant digits only, using mental strategies e.g. 6.2 - 4.5 e.g. 72000 - 47000 • Subtract 1– or 2-digit multiples of 10, 100, 1000, 10000 and 100000 e.g. 8000 - 3000 e.g. 60000 - 20000 • Subtract 1– or 2-digit near multiples of 10, 100, 1000, 10000 and 100000

from other numbers e.g. 82472 - 30004

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• Subtract decimal numbers which are near multiples of 1 or 10, including money

e.g. 6.34 - 1.99 e.g. £34.59 - £19.95 • 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 e.g. 1000—782 • Recognise fraction complements to 1 and to the next whole number e.g. 1 ²⁄₅+ ³⁄₅ = 2 Multiplication • Know by heart all the multiplication facts up to 12 x 12 • Multiply whole numbers and 1– and 2 -place decimals by 10, 100 and 1000 • Use knowledge of factors and multiples in multiplication e.g. 43 x 6 is double 43 x 3 e.g. 28 x 50 is half of 28 x 10 • Use knowledge of place value and rounding in mental multiplication e.g. 67 x 199 as (200 x 67) - 67 • Use doubling and halving as a strategy in mental multiplication e.g. 58 x 5 is half of 58 x 10 e.g. 34 x 4 is 34 doubled twice • Partition 2-digit numbers, including decimals, to multiply by a 1-digit num-

ber mentally e.g. 6 x 27 as 6 x 20 (120) plus 6 x 7 (42) e.g. 6.3 x 7 as 6 x 7 (42) plus 0.3 x 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 Division • Know by heart all the division facts up to 144 ÷ 12 • Divide whole numbers by 10, 100, 1000 or 10000 to give whole number

answers or answers with 1, 2 or 3 decimal places • Use doubling and halving as mental division strategies e.g. 34 ÷ 5 is (34 ÷ 10) x 2 • Use 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 by 3

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• Halve amounts of money by partitioning • e.g. half of £75.40 = half of £75 (£37.50) plus half of 40p (20p) which is

£37.70Divide larger numbers mentally by subtracting the 10th or 100th multiple as appropriate

e.g. 96 ÷ 6 is 10 + 6 as 10 x 6 = 60 and 6 x 6 = 36 e.g. 312 ÷ 3 is 100 + 4 as 100 x 3 = 300 and 4 x 3 = 12 • 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 By the end of Year 6 children should be able to:By the end of Year 6 children should be able to:By the end of Year 6 children should be able to:By the end of Year 6 children should be able to: Addition • Know by heart number bonds to 100 and use these to derive related facts e.g. 3.46 + 0.54 • Derive quickly and without diZculty, 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. 34000 + 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 e.g. 0.74 + 0.33 • Add positive numbers to negative numbers e.g. Calculate a rise in temperature or continue a sequence beginning with a negative number Subtraction • 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

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• 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 e.g. 4.63 - 1.02 • 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 Multiplication • Know by heart all the multiplication facts up to 12 x 12 • Multiply whole numbers and decimals with up to 3 places by 10, 100 and

1000 e.g. 234 x 1000 = 234000 e.g. 0.23 x 1000 = 230 • • Identify common factors, common multiples and prime numbers and use

factors in mental multiplication e.g. 326 x 6 is 652 x 3 which is 1956 • Use place value and number facts in mental multiplication e.g. 4000 x 6 = 24000 e.g. 0.03 x 6 = 0.18 • Use doubling and halving as mental multiplication strategies, including to

multiply by 2, 4, 8, 5, 20, 50 and 25 e.g.28 x 25 is a quarter of 28 x 100 = 700 • Use rounding in mental multiplication e.g. 34 x 19 as (34 x 20) - 34 • Multiply 1– and 2– place decimals by numbers up to and including 10

using place value and partitioning e.g. 3.6 x 4 is 12 + 2.4 e.g. 2.53 x 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) Division • Know by heart all the division facts up to 144 ÷ 12 • Divide whole numbers by powers of 10 to give whole number answers or

answers with up to 3 decimal places • Identify common factors, common multiples and prime numbers and use

factors in mental division e.g. 438 ÷ 6 is 219 ÷ 3 which is 73

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• Use tests of divisibility to aid mental calculation • Use doubling and halving as mental division strategies, for example to di-

vide by 2, 4, 8, 5, 20 and 25 e.g. 628 ÷ 8 is halved three times: 314, 157, 78.5 • 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 usi9ng 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 per-

centages, including diAerent contexts • Recognise a given ratio and reduce a given ratio to its lowest terms

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Recording Work During EYFS and Key Stage One, emphasis will be placed upon developing the

skills of mental calculation. However mental calculation is not at the exclusion

of written recording; it should be seen as complementary to and not as

separate from it. Therefore all children will be given regular opportunities to

record and explain their mathematical thinking.

Learning may be recorded, formally and informally, using:Learning may be recorded, formally and informally, using:Learning may be recorded, formally and informally, using:Learning may be recorded, formally and informally, using: • Photographs • Displays • Whiteboards • iPads • Workbooks • Squared books Developing recording skillsDeveloping recording skillsDeveloping recording skillsDeveloping recording skills • Teachers will model diAerent ways of recording on a regular basis. • Children will be given opportunities to select and use diAerent methods of

recording. • Teachers and children will discuss the eZciency of diAerent methods of

recording. • Teachers will support children in moving towards using more eZcient

methods. Children will use:Children will use:Children will use:Children will use: • Practical equipment to physically add groups together or to take away

objects from a group. • Number lines to hop forwards or backwards. • Hundred squares to add and subtract larger numbers. Progressing to:Progressing to:Progressing to:Progressing to: • Adding or taking away units without aids. • Putting the largest number in your head then counting on or back. • Estimating answers of more complex addition and subtraction questions to

ensure the final answer is appropriate.

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Addition Adding using number linesAdding using number linesAdding using number linesAdding using number lines Children will begin to independently use ‘empty number lines’, starting with the larger number and counting on. Begin first by counting on in tens and units 34 + 23 = 57

Children become more eZcient by adding the tens in one jump and the units in one jump. 34 + 23 = 57

Children should understand that numbers can be added in any order to give the same answer and should therefore count on from the largest number irrespective of the order of the calculation.

+20

+3

34 54 57

33334444 44444444 55554 4 4 4 55555555 55556666 55557777

++++10 10 10 10 ++++10101010

++++1 1 1 1 ++++1 1 1 1 ++++1111

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Adding using partitioningAdding using partitioningAdding using partitioningAdding using partitioning Children becoming more confident with place value and can use their knowledge to add using partitioning. e.g. 35 + 46 = 81

33335 5 5 5 + + + + 44446666 ==== 30 30 30 30 ++++ 40 40 40 40 = 70 = 70 = 70 = 70 5 5 5 5 ++++ 6 6 6 6 = 11= 11= 11= 11 70 + 11 = 8170 + 11 = 8170 + 11 = 8170 + 11 = 81

Partitioning can be used to add larger numbers. e.g. 322 + 236 = 558

333322222 2 2 2 + + + + 222233336666 ==== 300 + 200 300 + 200 300 + 200 300 + 200 = 500 = 500 = 500 = 500 20 20 20 20 ++++ 30 30 30 30 = 50 = 50 = 50 = 50 2 2 2 2 ++++ 6 6 6 6 = 8= 8= 8= 8 500 + 50 + 8 = 558500 + 50 + 8 = 558500 + 50 + 8 = 558500 + 50 + 8 = 558

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Adding using the expanded methodAdding using the expanded methodAdding using the expanded methodAdding using the expanded method Children need to use their knowledge of partitioning to expand the numbers.

365 300 60 5 + 129 + 100 20 9 400 80 14 = 494 354 300 50 4 + 241 200 40 1 + 362 300 60 2 800 150 7 = 957 Adding using the compact method of column additionAdding using the compact method of column additionAdding using the compact method of column additionAdding using the compact method of column addition The compact method is taught alongside the expanded method to develop a clear understanding of carrying.

466 + 238 = 400 60 6 + 200 30 8 100 10 700 00 4 = 704 466 + 238 11 704

NOTE: NOTE: NOTE: NOTE: We carry above the line so that the carried numbers are not forgotten.

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When adding decimals, children can use either mental strategies, a number line, partitioning or column addition. Using a number line Using a number line Using a number line Using a number line e.g. 3.8 + 2.4 = 6.2

Using partitioningUsing partitioningUsing partitioningUsing partitioning

3333....8888 + + + + 2222....4 4 4 4 ==== 3 + 2 3 + 2 3 + 2 3 + 2 = 5 = 5 = 5 = 5 0.8 0.8 0.8 0.8 ++++ 0.4 0.4 0.4 0.4 = 1.2= 1.2= 1.2= 1.2 5 + 1.2 = 6.2 5 + 1.2 = 6.2 5 + 1.2 = 6.2 5 + 1.2 = 6.2 Using column additionUsing column additionUsing column additionUsing column addition

3333....8888 + 2222....4 4 4 4 1111 6666....2222

++++2222....0000

++++0000....2222

3333....8 8 8 8 4444....0 0 0 0 6666....0 0 0 0 6666....2222

++++0000....2222

Adding decimals

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Using the expanded methodUsing the expanded methodUsing the expanded methodUsing the expanded method Children need to use their knowledge of money to partition correctly.

£14.64 + £8.78 + £12.26

£14 60p 4p £ 8 70p 8p + £12 20p 6p £34 150p 18p = £35.68 Using the compact method of column addition Using the compact method of column addition Using the compact method of column addition Using the compact method of column addition Children must ensure that the decimal points are kept lined up in all amounts that are being added and in the answer.

£15.68 + £27.86 = 15.68 +27.86 11.1 43.54 = £43.53

Adding amounts of money

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Adding fractions with the same denominatorAdding fractions with the same denominatorAdding fractions with the same denominatorAdding fractions with the same denominator Denominators remain the same, add the numerators.

Adding related fractionsAdding related fractionsAdding related fractionsAdding related fractions Initially change fractions to equivalent fractions that have the same denominator. Then add as before. Adding unlike fractionsAdding unlike fractionsAdding unlike fractionsAdding unlike fractions Identify a common denominator and change to equivalent fractions with that denominator. Then add as before. Adding mixed numbersAdding mixed numbersAdding mixed numbersAdding mixed numbers Keep whole numbers whole. Add fractions as above.

Adding fractions

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Children should understand that subtraction is the inverse (opposite) of addition. Unlike addition, when given a subtraction sum, the order of the numbers can not be switched to give the same answer. Subtraction using number linesSubtraction using number linesSubtraction using number linesSubtraction using number lines Begin subtraction with the tens and then units. 47 - 23 = 24

Children become more eZcient by jumping the tens in one jump and the units in one jump. 47 - 23 = 24

Subtraction by counting up (Using Frog)Subtraction by counting up (Using Frog)Subtraction by counting up (Using Frog)Subtraction by counting up (Using Frog) When numbers are close together, it may be appropriate to use Frog to start at the smallest number, end at the largest number and calculate the diAerence. e.g. 300—267 = 33

22224 4 4 4 22225 5 5 5 22226666 22227777 33337777 44447777

----10 10 10 10 ----10101010

----1111 ----1111 ----1111

22224 4 4 4 22227777 44447777

----20202020

----3333

222266667777 222277770000 333300000000

+ + + + 30303030

+ + + + 3333

30 30 30 30 + + + + 3 3 3 3

Subtraction

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Subtraction using partitioningSubtraction using partitioningSubtraction using partitioningSubtraction using partitioning Children becoming more confident with place value and can use their knowledge to subtract using partitioning.

66668 8 8 8 ---- 44442222 ==== 60 60 60 60 ---- 40 40 40 40 = 20 = 20 = 20 = 20 8 8 8 8 ---- 2 2 2 2 = 6= 6= 6= 6 20 + 6 = 2620 + 6 = 2620 + 6 = 2620 + 6 = 26 7000 7000 7000 7000 ---- 2000 2000 2000 2000 = = = = 5000500050005000 7777444499993 3 3 3 ---- 2222000022220000 5555444477773333 90 90 90 90 ---- 20 20 20 20 = = = = 70707070

When using partitioning, a common misconception is that you must always take the smallest digit from the biggest. Children must take care not to change the numbers when partitioning.

e.g. 52—36 ≠ 24

• Children may arrive at this answer by doing

50—30 = 20 and 6—2 = 4

• What the child has actually calculated is 56—32 = 24

• Instead you need to split 52 into 40 and 12

• Therefore allowing you to do

40—30 = 10 and 12—6 = 6

• Producing the correct answer 52—36 = 16

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Subtraction using the expanded method of column subtractionSubtraction using the expanded method of column subtractionSubtraction using the expanded method of column subtractionSubtraction using the expanded method of column subtraction e.g. 726—358 =

600 600 600 600 110110110110 16161616 777722226666 ++++ 700700700700 20202020 6666 ---- 333355558888 ++++ 300300300300 50505050 8888 300300300300 60606060 8888 = 368= 368= 368= 368 Subtraction using the compact method of column subtractionSubtraction using the compact method of column subtractionSubtraction using the compact method of column subtractionSubtraction using the compact method of column subtraction

762 762 762 762 ---- 378 =378 =378 =378 = 666615 15 15 15 12121212 7 7 7 7 6 6 6 6 2222 ---- 3 3 3 3 7 7 7 7 8888 3 3 3 3 8 8 8 8 4444 Using compact column subtraction for large numbersUsing compact column subtraction for large numbersUsing compact column subtraction for large numbersUsing compact column subtraction for large numbers

34685 34685 34685 34685 ---- 16458 =16458 =16458 =16458 = 2222 14141414 7 7 7 7 15151515 3333 4444 6 6 6 6 8 8 8 8 5555 ---- 1111 6666 4 4 4 4 5 5 5 5 8888 1111 8888 2 2 2 2 2 2 2 2 7777

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When subtracting decimals, children can use either mental strategies, a number line, partitioning or column addition. Using a number line to subtract Using a number line to subtract Using a number line to subtract Using a number line to subtract e.g. 4.9 - 2.4 = 2.5

Subtraction by counting on (Frog) Subtraction by counting on (Frog) Subtraction by counting on (Frog) Subtraction by counting on (Frog) e.g. 4.2 - 1.74 = 0.06 + 0.2 + 2 + 0.2 = 2.46

2222....5 5 5 5 2222....9 9 9 9 4444....9999

---- 2222

---- 0000....4444

1111....77774444 1111....8888 2 2 2 2 4444 4444....2222

++++2222

+ + + + 0000....00006 6 6 6 ++++0000....2 2 2 2 ++++0000....2 2 2 2

Subtracting decimals

30

Using column subtractionUsing column subtractionUsing column subtractionUsing column subtraction

3 3 3 3 . . . . 8888 - 2 2 2 2 . . . . 4444 1 1 1 1 . . . . 4444 When using column subtraction to subtract amounts with diAerent When using column subtraction to subtract amounts with diAerent When using column subtraction to subtract amounts with diAerent When using column subtraction to subtract amounts with diAerent numbers of decimal places always line up the decimal pointnumbers of decimal places always line up the decimal pointnumbers of decimal places always line up the decimal pointnumbers of decimal places always line up the decimal point e.g. 24.2—12.74 =

3 1110 2 4 4 4 4 . . . . 2 2 2 2 0 0 0 0 - 1 2 2 2 2 . . . . 7 7 7 7 4444 1 1 1 1 1 . . . . 4444 6666 In the example above, a common error is that the zero in the hundredths is not always thought about and therefore children don’t identify the need to borrow from the tenths column and record the answer in the hundredths column as 4.

Once the decimals have been lined up correctly, zeros can be added to ensure children think about the numbers in that column.

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Using Frog to count up Using Frog to count up Using Frog to count up Using Frog to count up e.g. £50—£28.76

Using column subtractionUsing column subtractionUsing column subtractionUsing column subtraction e.g. £78.56 + £27.25 =

7 8 . 5 6 + 2 7 . 2 5 4 3 . 5 4

Children should select an appropriate method. For example, when a number of zeros are involved it is often better to use Frog as this allows less room for error. Children can often be confused when borrowing from a number of columns away.

++++0000....00004 4 4 4 ++++0000....2222 ++++1111 (4p) (20p) (£1)(4p) (20p) (£1)(4p) (20p) (£1)(4p) (20p) (£1)

++++22220000 (£20)(£20)(£20)(£20)

££££22228888....77776666 ££££22228888....88880 £0 £0 £0 £22229 9 9 9 ££££33330 0 0 0 ££££55550000

Calculating change

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Subtracting fractions with the same denominatorSubtracting fractions with the same denominatorSubtracting fractions with the same denominatorSubtracting fractions with the same denominator Denominators remain the same, subtract the numerators.

Subtracting related fractionsSubtracting related fractionsSubtracting related fractionsSubtracting related fractions Initially change fractions to equivalent fractions that have the same denominator. Then subtract as before. Subtracting unlike fractionsSubtracting unlike fractionsSubtracting unlike fractionsSubtracting unlike fractions Identify a common denominator and change to equivalent fractions with that denominator. Then subtract as before. Subtracting mixed numbersSubtracting mixed numbersSubtracting mixed numbersSubtracting mixed numbers Keep whole numbers whole. Subtract fractions as above.

Subtracting fractions

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To begin with children count in 2s, 10s and 5s. Multiplication is taught as: • Repeated addition; e.g. 3 x 5 = 5 + 5 + 5 + 1 5 • Lots of; e.g. 3 x 5 = 3 lots of 5 = 1 5 • ‘groups of’ and ‘sets of’ • Times; e.g. 3 x 5 Children should understand that doubling is like multiplying by 2 and then this knowledge can be extended to knowing that multiplying by 4 is the same as doubling and doubling again. Children initially attempt solving multiplication with apparatus and visual aids.

3 x 4 = 12

Children should know that 3 x 5 has the same answer as 5 x 3. This can be shown on a number line.

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

3 3 3 3 3

5 5 5

Multiplication

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Doubling Doubling Doubling Doubling Find doubles of numbers using partitioning.

48 126

80 16 200 40 12

96 256

This method can also be used to double amounts of money and decimals.

£1.76 9.871

£2 £1.40 12p 18 1.6 0.14 0.002

£3.52 19.742

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Using the grid methodUsing the grid methodUsing the grid methodUsing the grid method In Key Stage 2 the grid method will be introduced to multiply larger numbers. Multiplying TU x U Multiplying TU x U Multiplying TU x U Multiplying TU x U e.g. 23 x 4 = Multiplying HTU x U Multiplying HTU x U Multiplying HTU x U Multiplying HTU x U e.g. 253 x 6 = Multiplying TU x TU Multiplying TU x TU Multiplying TU x TU Multiplying TU x TU e.g. 16 x 48 =

36

Using a vertical written algorithm (ladder method)Using a vertical written algorithm (ladder method)Using a vertical written algorithm (ladder method)Using a vertical written algorithm (ladder method) The ladder method is introduced as a stepping stone between the grid method and the more traditional method of short division. Multiplying HTU x U Multiplying HTU x U Multiplying HTU x U Multiplying HTU x U e.g. 253 x 6 =

3 5 4 x 6

1 8 0 0 6 x 300 3 0 0 6 x 50 + 2 4 6 x 4 1 2 1 2 4 Short multiplicationShort multiplicationShort multiplicationShort multiplication Multiplying HTU x UMultiplying HTU x UMultiplying HTU x UMultiplying HTU x U e.g. 435 x 8 =

4 3 5 x 8 2 4 3 4 8 0

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Long multiplicationLong multiplicationLong multiplicationLong multiplication Multiplying 2, 3 and 4 digit numbers by ‘teen’ numbers.

4 4 x 1 2

4 4 0 10 x 44 8 8 2 x 44 + 1 5 2 8 Multiplying 2, 3 and 4 digit numbers by 2 digit numbers.

4 5 6 3 8 4 4

3 6 4 8 8 x 456 1 1

1 3 6 8 0 30 x 456 1 7 3 2 8

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Multiplication of decimals by whole numbers (including amounts of Multiplication of decimals by whole numbers (including amounts of Multiplication of decimals by whole numbers (including amounts of Multiplication of decimals by whole numbers (including amounts of money)money)money)money) When multiplying decimals or amounts of money, children should select an appropriate method, using mental strategies, partitioning, doubling, the grid method, ladder method or short multiplication. Using the grid methodUsing the grid methodUsing the grid methodUsing the grid method e.g. 6.76 x 4 =

Ladder methodLadder methodLadder methodLadder method e.g. 2.59 x 3 =

2 . 5 9 x 3

6 3 x 2 1 . 5 3 x 0.5 + 0 . 2 7 3 x 0.09 7 . 7 7

Short multiplicationShort multiplicationShort multiplicationShort multiplication e.g. 5 x 1.34 =

1 . 3 4 x 5 1 . 2 6 . 7 0

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When multiplying a decimal by another decimal, take out the decimal When multiplying a decimal by another decimal, take out the decimal When multiplying a decimal by another decimal, take out the decimal When multiplying a decimal by another decimal, take out the decimal point, and then put it back in the answer.point, and then put it back in the answer.point, and then put it back in the answer.point, and then put it back in the answer.

For example: 6.8 x 2.7 = ? (estimate first 7 x 3 = 21)

1. Take out the point so 68 x 27 2. Do the sum using a preferred method of multiplication

68 x 27 = 1836

3. Then, put the point ‘back in!’. There were 2 digits beyond the decimal points in 2 decimal places in the original question, so he have to have 2 decimal places in the answer

Therefore 6.8 x 2.7 = 18.36 (check using estimate).

Multiplying decimals

40

Multiplying fractions by whole numbersMultiplying fractions by whole numbersMultiplying fractions by whole numbersMultiplying fractions by whole numbers

When multiplying fractions by whole numbers multiply the numerator by the whole number. The denominator remains the same.

e.g .

7 x =

You may be asked to give your final answer in an improper fraction as above or change it to a mixed number as shown below.

= 2 Multiplying fractions by fractions Multiplying fractions by fractions Multiplying fractions by fractions Multiplying fractions by fractions

e.g. x =

Multiply the numerators (top numbers) and multiply the denominators (the bottom numbers).

=

Depending on the answer, you may need to simplify the fraction or change an improper fraction to a mixed number.

Multiplying fractions

14141414

14141414

41

Division is taught as:Division is taught as:Division is taught as:Division is taught as: • sharing • the inverse of multiplication • Children are taught to use their knowledge of times tables to help solve

division problems e.g. 20 ÷ 5 = ( 5, 10, 15, 20) 4 Children should understand that halving is like dividing by 2. This knowledge can then be extended to understanding that dividing by 4 is the same as halving and halving again. We have seen that multiplication is introduced as ‘repeated addition’. Similarly division can be shown as repeated subtraction. e.g. 20 ÷ 4 = 5

Grouping and remaindersGrouping and remaindersGrouping and remaindersGrouping and remainders Example: 13 counters are sorted into groups of 4 13 ÷ 4 = 3 r 1 (3 remainder 1)

0 4 8 12 16 20

- 4 - 4 - 4 - 4 - 4

Lots of practice in Year 3 where inverse of multiplication takes place i.e. 5 x 3 = 15 So, 15 ÷ 5 = 3 & 15 ÷ 3 = 5

- 4 - 4 - 4

0 1 5 9 13

- 1

Division

42

HalvingHalvingHalvingHalving Find halves of numbers using partitioning.

48 258 20 4 100 25 4 24 129 This method can also be used to halve amounts money and decimals.

£14.84 £14.84

£5 £2 40p 2p £7 42p £7.42 £7.42

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GroupingGroupingGroupingGrouping Initially using multiples of 10 times the divisor by 1 digit numbers above the tables facts. e.g. 45 ÷ 3 as 10 x 3 (30)and 5 x 3 (15)

45 ÷ 3= x 3 = 45 45 ÷ 3 = 15151515 10 x 3 = 30 15 5 x 3 = 15 0 15 Moving on to using the 10th, 20th, 30th… or 100th, 200th … multiples of the divisor to divide large numbers. e.g. 388 ÷ 9 as 40 x 9 (360) and 3 x 9 (27), remainder 1

388 ÷ 9 = x 9 = 3 8 8 388 ÷ 9 = 43 r 1 40 x 9 = 3 6 0 2 8 3 x 9 = 2 7 1 43

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After children have understood using grouping to divide larger numbers by 1 digit numbers they are then able to move onto the more traditional method of short division. Short division (The Bus Stop Method)Short division (The Bus Stop Method)Short division (The Bus Stop Method)Short division (The Bus Stop Method) Can be used to divide 3 and 4 digit numbers by 1 digit numbers. e.g. 139 ÷ 3

Long division (Chunking)Long division (Chunking)Long division (Chunking)Long division (Chunking) Dividing 3 and 4 digit numbers by 2 digit numbers. e.g. 4176 ÷ 13

4176 ÷ 13 = x 13 = 4 1 7 6 4176 ÷ 13 = 321 r 3 300 x 13 = 3 9 0 0 2 7 6 20 x 13 = 2 6 0 1 6 1 x 13= 1 3 3 321

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Traditional Long Division Traditional Long Division Traditional Long Division Traditional Long Division Can be used to divide 3 and 4 digit numbers by 2 digit numbers. e.g 6570 ÷ 18

0 3

6 5 7 0 1 8 - 5 4

Set out in ‘bus stop’ method style. 18 Doesn’t go into 6 so 0 goes in the thousands column. 18 Goes into 65 3 times and then 54 (3x18) is taken from the total. The three is placed in the hundreds column.

You bring the 7 down and then find how many 18’s there are in 117. There are 6 and then 108 (6x18) is taken from 117. The 6 is placed in the tens column.

0 3 6

6 5 7 0 1 8 - 5 4

1 1 7

- 1 0 8

0 3 6 5

6 5 7 0 1 8 - 5 4

1 1 7

- 1 0 8

9 0

- 9 0

0

Once again you bring down the 0 and then find out how many 18’s there are in 90. There are 5 18’s in 90 (5x18) and you take this away. It leaves you with 0. The five is placed in the units column and then the method is complete. 6570 ÷ 18 = 365

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Applying knowledge to solve problems Learning facts and processes is one part of maths, children must then learn to apply their knowledge to solve problems. Problem solving process can be described as a journey from meeting a problem for the first time to finding a solution, communicating it and evaluating the route. ComprehensionComprehensionComprehensionComprehension This stage is about making sense of the problem, identifying relevant information and creating mental images. This can be helped by encouraging children to re-read the problem several times and record in some way what they understand the problem to be about . RepresentationRepresentationRepresentationRepresentation At this stage children must identify what is unknown and needs finding. • Can they represent the situation mathematically? • Will this problem require a number of steps? • What do they think the answer might be? PlanningPlanningPlanningPlanning This stage is about planning a pathway to the solution. During this process, encourage children to think about whether they have seen something similar before and what strategies they adopted then. This will help them to identify appropriate methods and tools. ExecutionExecutionExecutionExecution During the execution phase children will need to consider how they will keep track of what they have done and how will they communicate their findings. EvaluationEvaluationEvaluationEvaluation Children can learn as much from reflecting on and evaluating what they have done as they can from the process of solving the problem itself. During this phase children can reflect on the eAectiveness of their approach as well as other people’s approaches, justify their conclusions and assess their own learning.

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• activelearnprimary.co.uk • ictgames.com • bbc.co.uk KS1 Maths KS2 Maths KS3 Maths (KS3 work but some useful exercises) • maths-games.org • topmarks.co.uk • IXL Learning, Inc • mathsphere.co.uk • mathsisfun.com • mymaths.com

Useful Websites

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The Development of Pencil and Paper

Procedures EYFSEYFSEYFSEYFS Record numbers, initially by making marks, progressing to simple tallying and writing numerals. Begin to use +, - and = to record mental calculations in number sentences. Year 1Year 1Year 1Year 1 Use +, - and = to record mental calculations in number sentences. Begin to use the x sign, introducing multiplication as repeated addition. Year 2Year 2Year 2Year 2 Use informal pencil and paper methods to support, record and explain TU ± TU. Use counting up as an informal written strategy for subtracting pairs of 2-digit numbers

e.g. 43 – 35 Use x and ÷ and = to record mental calculations in number sentences, un-derstanding the relationship between the two operations. Year 3Year 3Year 3Year 3 Use informal pencil and paper methods to support, record and explain HTU ± TU, HTU ± HTU. Use column addition and subtraction for HTU ± TU. 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 = 1 and 3/5 + 2/5 5 5 5 = 1 = 1 = 1 = 1 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

Use partitioning (grid multiplication) to multiply 2-digit and 3-digit numbers by ‘friendly’ 1-digit numbers

49

x and ÷ of 3 digit numbers by 2 digit numbers. 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 Year 4Year 4Year 4Year 4 Develop and refine written methods for column addition and subtraction of two whole numbers less than 1000 and addition of more than two such numbers. Use informal pencil and paper methods to support, record and explain mul-tiplications and divisions. Develop and refine written methods for TU x U, TU ÷ U. Column addition for 3-digit and 4-digit numbers 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 Use expanded column subtraction for 3- and 4-digit numbers Use complementary addition to subtract amounts of money, and for sub-tractions where the larger number is a near multiple of 1000 or 100

e.g. 2002 – 1865 Subtract like fractions

e.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 a vertical written method to multiply a 1-digit number by a 3-digit num-ber (ladder method) Use an eZcient written method to multiply a 2-digit number by a number between 10 and 20 by partitioning (grid meth-od) Use a written method to divide a 2-digit or a 3-digit number by a 1-digit number Give remainders as whole numbers Begin to reduce fractions to their simplest forms Find unit and non-unit fractions of larger amounts

50

Year 5Year 5Year 5Year 5 Column ± of two integers less than 10,000. Column addition of more than two integers less than 10,000. Column ± of a pair of decimal fractions to one or two decimal places. Short x of HTU or U.t by U. Long x of TU by TU. Short ÷ of HTU by U (with integer remaining). 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 eZcient method in any given situation 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 eZcient method in any given situation 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 4-digit numbers by a number between 11 and 20 Choose the most eZcient 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 Use short division to divide a number with up to 4 digits by a number ≤ 12 Give remainders as whole numbers or as fractions Find non-unit fractions of large amounts Turn improper fractions into mixed numbers and vice versa Choose the most eZcient method in any given situation

51

Year 6Year 6Year 6Year 6 ± of numbers with decimals. x of ThHTU by U. Short x of numbers with decimals. Long x of 3 digit numbers by two digit numbers. Short ÷ of TU or HTU by U and of numbers with decimals. ÷ of HTU by TU (long division). ExtensionExtensionExtensionExtension Standard column ± of numbers and numbers with decimals to 2 decimal places. 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 diAerent denominators

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 diAerent denominators

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

Use short division to divide a number with up to 4 digits by a 1-digit or a 2-digit number Use long division to divide 3-digit and 4-digit numbers by ‘friendly’ 2-digit numbers Give remainders as whole numbers or as fractions or as decimals Divide a 1-place or a 2-place decimal number by a number ≤ 12 using multi-ples of the divisors Divide proper fractions by whole numbers

52

Laxton Junior School, East Road, Oundle, PE8 4BX

T: 01832 277275 E: info@laxtonjunior.org.uk

www.laxtonjunior.org.uk