To bridge through a multiple of 10 eg =

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1 ADDITION Foundation Stage Year 1 Year 2 Year 3 Begin to represent numbers using fingers, marks on paper or pictures. Begin to relate addition to combining 2 groups of objects. Eg. Practical activities, counting songs and number stories. In practical activities and discussion begin to use the vocabulary involved in adding Find the total number of items in two groups by counting them all. Adults model use of number tracks and number lines to show how you arrive at another point when something is added. Use developing mathematical ideas and methods to attempt to solve practical problems. Record simple mental addition in a number sentence using the + and = signs, particularly all number bonds to 10 then 20 Record opposite way round e.g. 6+4 = 10, 10 = 6+4 Be able to complete number sentences where a missing number is shown by a symbol eg = = = 7 7 = =7 7 = 2 + etc. Record addition by: - showing jumps on prepared number lines - drawing own number line = Using the empty number line to add 10 to a single digit number. Eg = Begin to use empty number lines Use a number line to add a pair of single digit numbers to bridge through 10 eg = Bridge through a multiple of 10 to add, explaining method eg = Represent number line calculations in a number sentence. Solve simple problems explaining methods and reasoning. Good activities for plenary/paired work. Record mental addition in a number sentence using the + and = signs. Recognise the use of symbols such as Ο to stand for unknown numbers and complete number sentences. 9 + = = = = 400 etc Extend to 3 numbers eg = 13 Use prepared number lines then progress on to drawing own empty number lines to count in tens/multiples of 10s, eg To bridge through a multiple of 10 eg = Partition 2 digit numbers eg (not crossing the tens or hundreds barrier) using different methods of recording A) Number line: eg = B) Not using number line eg OR = = = = = 58 Add 9 or 11 by adding 10 and adjusting by 1. Begin to add 19 or 21 adding 20 and adjusting by 1. Demonstrate number line, record jottings eg = =36 Solve problems explaining methods and reasoning orally and where appropriate in writing. Continue to develop recording of equations using +and =with larger numbers. 1 Recognise the use of symbols such as Ο to stand for unknown numbers and complete number sentences = = 33 Use 3 numbers eg = O = = 447 Autumn and Spring term: A) Partitioning using empty number lines with increasingly difficult numbers (crossing tens and 100 barrier) B) Partitioning not using number line: = OR = = = = = = =783. Summer Term: Present calculations vertically using partitioning skills. Least significant digit first (expanded method) (7+4) 80 (60+20) 91 Add a near multiple of 10 to a two digit number and show on a number line, record jottings eg = =64 Solve problems explaining methods and reasoning orally and where appropriate in writing. Aim: By end of Y3 all children to add two 2-digit numbers, some children should be able to add 2 and 3-digit numbers showing method used.

2 ADDITION Year 4 Year 5 Year 6 Use symbols and missing numbers:- Continue to develop as in Y1, 2 and 3 but with appropriate numbers. Use symbols and missing numbers:- Continue to develop as in Y1, 2, 3 and 4 but with appropriate numbers. Use symbols and missing numbers:- Continue to develop as in earlier years but with appropriate numbers (including decimals). 2 Continue to develop use of empty number lines, partitioning and other informal recording methods developed in Y1,2 and 3 to support and explain calculations where appropriate. A) Using Number Lines: Eg B) Not using number lines OR = = = = = 82 Continue with standard written method. Least significant digit first. Start with expanded, move on to carrying below the line (compact recording). See Guidance Paper Calculation (8+3) (50+70) (300+0) 431 Emphasise vocabulary when adding (e.g., 5 tens add 7 tens) Solve problems explaining methods and reasoning orally and in writing. AIM: By the end of Year 4 Most children should be able to use compact method when appropriate to add two 3- digit numbers or several numbers. Note: compact method is not appropriate for adding two 2-digit numbers this is a mental KLO. Develop use of empty number lines, partitioning and other informal recording methods developed in Y1,2,3 and 4 to support and explain calculations where appropriate (including decimals). Use compact carrying method For children that have not yet mastered compact method, use expanded. Addition of decimals (teach expanded method first to ensure understanding.) Ensure that children know the importance of lining up the decimal points particularly when adding mixed amounts eg 16.4 m m m. 1 1 Solve problems explaining methods and reasoning orally and in writing. AIM: By the end of Year 5 most children are able to use compact method, when appropriate, (numbers up to 10,000 and decimals). Develop use of empty number lines, partitioning and other informal recording methods developed in earlier years to support and explain calculations where appropriate (including decimals). As Yr 5 but extend to any number of digits and decimal places. For children that have not yet mastered compact method, use expanded. Do not re-teach expanded if children are competent at carrying. Solve problems explaining methods and reasoning orally and in writing. AIM: By the end of Year 6 Children should be able to use carrying method, accurately and reliably when appropriate.

3 SUBTRACTION Foundation Stage Year 1 Year 2 Year 3 Encourage children to record what they have done e.g. by mark making. Begin to relate subtraction to taking away In practical activities and discussion begin to use the vocabulary involved in subtracting Adults model use of number tracks and number lines to show how you arrive at another point when something is taken away. Record simple subtraction in a number sentence using the and = signs eg. There were 8 cakes on a plate. Mary ate 3 of them. How many were left? 8 3 = 5 Be able to complete number sentences where a missing number is shown by a symbol eg. 6-2 = = 6-2etc. Use a marked, partly marked or empty number line to count back (take away) or to count on (find the difference) (counting back) - marked line What is the difference between 17 and 12? (counting on) marked line What is the difference between 12 and 17? (counting on) empty line Children need to begin to understand when it is sensible to count back eg 18 5 and when it is sensible to count on eg Record mental subtraction in a number sentence using the and = signs eg 18 4 = 14 Extend to = 20- etc. Recognise the use of symbols such as or to stand for unknown numbers and complete number sentences = 9-4 = 9 Extend to: = - 10 Use marked, partly marked or empty number lines to count back (take away) or to count on (find the difference) see Y1 but use appropriate numbers. Understand when it is sensible to count back and when to count on. Eg 43 5 (count back) (count on) Use empty number lines to Bridge through a multiple of 10 eg 22 5 = 17(counting back) Bridge through a multiple of 10 eg = 5(counting on) Partition 2 digit numbers eg (not crossing the tens or hundreds barrier) using different methods of recording A) Number line: eg = B) Not using number lines: Partitioning both numbers partitioning the second number only =20 OR 71-20= = = = 25 Subtract 9 or 11. Begin to subtract 19 or 21. Show number line, demonstrate jottings = = = 36 Record mental subtraction in a number sentence using the and = signs, using appropriate numbers. Recognise the use of symbols such as or to stand for unknown numbers and complete number sentences = - 15 = = 5 etc Autumn and Spring term: Develop counting on or counting back with an empty number line (see Y1 and 2) eg Extend to three digit numbers. Summer term: Begin to record calculations in preparation for an efficient standard method. Expanded decomposition. Use and not +. (No exchange first) and 7-40 and 3 10 and 4 = 14 Include HTU - TU and 50 and 7-0 and 40 and and 10 and 4 = 114 Then exchange (tens/units). Eg = 80 and 1 = 70 and and 7 50 and 7 20 and 4 =24 Subtract a near multiple of 10 from a two digit number. As Yr 2 with appropriate numbers. 3 Use developing mathematical ideas and methods to attempt to solve practical problems. Explain methods and reasoning orally. Explain methods and reasoning orally and by using any of recording methods shown above eg 45 9 I subtracted 10 from that was too much so then added 1 and got 36. Explain methods and reasoning orally and by using any of recording methods shown above or in Y1 or 2. Aim: by the end of Y3 all children should be able to use a number line to subtract 2 and 3-digit numbers. Some should be able to use expanded decomposition as shown.

4 SUBTRACTION Year 4 Year 5 Year 6 Continue to use counting up method, with informal notes or jottings, when appropriate eg When subtracting from multiples of 100 or 1000 Finding a small difference by counting up eg =7. (can be modelled using an empty number line or jottings) Continue to use counting up method, with empty number lines, informal notes or jottings, when appropriate eg When subtracting from multiples of 100 or 1000 Finding a small difference by counting up eg = (can be modelled using an empty number line or jottings) Continue to use counting up using an empty number line, informal notes or jottings when appropriate (see Y4 and 5 examples) and with appropriate numbers eg To support or explain mental calculations eg Explaining the subtraction of the nearest multiple of 10 and adjusting (see Y2/3 examples) Do not use Compensation Method.Teach expanded decomposition leading to compact decomposition. (see Guidance Paper Calculation) Note: when partitioning numbers use and as in Y3 example eg 700 and 50 and 4 Begin with exchange from tens to units only, then hundreds to tens, then both. Demonstrate with HTU equipment = 700 and 50 and and = 700 and 40 and and 6 = 600 and 140 and and and 60 and 8 = 668 When children are secure in the expanded method, move on to compact method and teach alongside at first. Extend to decimals as appropriate. Eg money knowing that the decimal points should line up under each other. Explain methods orally or using any informal recording methods. AIM: By the end of Year 4 most children should be able to use compact decomposition when appropriate ie 3-digit 3- digit or 3-digit 2-digit. But continue to use counting up method, with jottings, where appropriate. Note compact method is not appropriate for subtracting two 2- digit numbers this is a mental KLO Using known number facts and place value to subtract eg = To support or explain mental calculations To support or explain the subtraction of the nearest multiple of 10 or 100 then adjust. Do not use Compensation Method. Continue to develop compact decomposition with different numbers of digits and decimals. Children should understand the importance of lining up units digits under units digits, tens under tens etc '7 6 4.' Children who have not mastered compact decomposition in Y4 continue to use preferred, reliable method, but teach again when appropriate. Extend to include calculations up to two decimal places. e.g '7 6 4.' Explain methods orally or using any informal or formal recording methods. AIM: By the end of Year 5 most children should be able to use compact decomposition with all types of numbers, including decimal, where appropriate. But should continue to use counting up method, with jottings, where appropriate. Children should also be able to add and subtract whole numbers and decimals with up to two places Subtracting the nearest multiple of 10,100, 1000 Subtracting from any multiple of 1000, 10,000 etc ie where using decomposition would be very complicated. Do not use Compensation Method.Continue to develop compact decomposition with different numbers of digits and decimals. Children should understand the importance of lining up units digits under units digits, tens under tens Explain methods orally or using any informal or formal recording methods. AIM: By the end of Year 6 children should be able to use compact decomposition method accurately when appropriate. But should be able use counting up method, with jottings, where appropriate.

5 5 Foundation Stage Count orally in 1s, 2s, 5s, 10s. Count repeated groups of the same size. Clifton Primary School Recording and Written Calculations Policy MULTIPLICATION Year 1 Year 2 Year 3 Oral counting on and back in small steps Eg. 2 s, 5 s and 10 s (Understand multiplication as repeated addition eg There are 5 pencils in one packet. How many pencils in 4 packets? lllll lllll lllll lllll = or 4 lots of 5 or 4 x 5 This can also be shown as repeated jumps on a number line Record simple mental multiplications in a number sentence using the x and = signs. Recognise the use of symbols such as Δ or Ο to stand for unknown numbers eg.6 x Δ = 12 Δ x 2 = 12 6 x 2 = Δ Δ x Ο = = Δ x 5 20 = 4 x Δ Understand multiplication as repeated addition eg There are 5 pencils in one packet. How many pencils in 4 packets? lllll lllll lllll lllll = or 4 lots of 5 or 4 x 5 This can also be shown as repeated jumps on a number line Understand multiplication as describing an array. 5 x 4 = 20 4 x 5 = 20 Know 2x,5x and10x tables Be able to count in steps of 2, 5, 10. Begin to interpret situations as multiplications calculations and explain reasoning. Eg.How many wheels are there on 3 cars? Record mental multiplications in a number sentence using the x and = signs. Recognise the use of symbols such as Δ or Ο to stand for unknown numbers eg. 6 x Δ = 18 Δ x 3 = 18 6 x 10 = Δ Δ x Ο = = Δ x 5 20 = 4 x Δ Understand multiplication as: repeated addition describing an array (see Y2 examples of these, but use appropriate numbers for Y3 children) Also: Scaling eg Make a tower 3 times taller then this. Draw a line 4 times longer than this. Know their 2x, 3x, 4x 5x 6xand 10x tables and begin to know their 6x *.Be able to count in steps of 2,3,4,5,6,10 Interpret situations as multiplication calculations and explain reasoning. Eg.A baker puts 6 buns in each of 4 rows. How many buns does she make? Begin to develop informal ways of calculating and recording eg 17 x 5 by partitioning and recombining. For example: 10 x 5 = 50 7 x 5 = = 85 In order to provide the children with some of the pre-requisite skills for Year 4 written approaches, the objective Use knowledge of number facts and place value to multiply or divide mentally is important. Eg Multiply a single digit by 1,10 or 100. Double any multiple of 5 up to 50/ halve any multiple of 10 to 100. Multiply a 2-digit number by 2, 3, 4 or 5 without crossing the tens boundary (eg 23 x 3). AIM: All children know 2x, 5x and 10x tables. Most know 3x and 4x tables. All children understand the three aspects of multiplication.

6 MULTIPLICATION Year 4 Year 5 Year 6 Know by heart multiplication facts for 2,3,4,5,6,7,8,9 and10 x tables (including multiplication by 0 and 1) Complete quickly 60 x 2 =?? x 4 = x?=? = 120 etc Understand that division is the inverse of multiplication and use this to check results. Develop informal written methods eg partitioning. Teach children to approximate first in order to get a sensible idea of what the answer must be. Begin with teens numbers eg 13 x 8, then progress rapidly on to multiples of ten eg 23 x x 8= x 8= = 184 AND Grid Method x =184 Know by heart all multiplication facts up to 10 x 10, including multiplication by 0 and 1. Complete written questions eg.160 x 2 =?? x 2 = x? = 6.3 Δx? = 1600 etc Understand that division is the inverse of multiplication and use this to check results. Continue to use informal methods including Grid method of recording to support and explain mental methods where the numbers are appropriate Eg 47 x 5 Know by heart all multiplication facts up to 10 x 10, including multiplication by 0 and 1. Complete written questions eg. 0.7 x 20 =?? x 20 = x? = 3.6 Δx? = 2.4 etc Understand that division is the inverse of multiplication and use this to check results Continue to use informal methods including grid method of recording to support and explain their mental methods where the numbers are appropriate Eg 8.6 x 7. 6 Short Multiplication - Progress as appropriate to vertical expanded recording, multiplying by the least significant digit first. 23 leading to compact 23 x 7 when appropriate x 7 21 (7x3) (7x20) When moving from expanded to compact, teach side by side. Interpret situations as multiplication calculations g. There are 6 eggs in a box. How many in 45 boxes? (single step and multistep problems.) AIM: By end of Y4 most children are confident with the vertical, expanded way of recording multiplication and are able to explain reasoning. Some are able to use the compact standard method (carrying below the line).they know 2,3,4,5,6,7,8,9,and 10 x tables. Short Multiplication Compact Standard Method of recording to children for whom it is appropriate (HTU x U). 346 x For those who cannot use this method reliably continue to use partitioning, grid or expanded methods as necessary (see Y4). Continue to teach children to approximate answers first. Long multiplication begin with the grid method. Eg. 72 x 38 (ans. approx. 70 x 40 = 2800) x Only progress to vertical recording for children for whom it is appropriate. Use expanded method first, least significant digit first. 72 leading to 72 x 38 only when x38 16 (8x2) appropriate 576 (8x72) 560 (8x70) 2160 (30x72) 60 (30x2) (30x70) 2736 Extend to simple decimals, with one decimal place, multiplied by a single digit. Approximate first Use expanded method first. x (3x0.9) 12.0 (3x4) 14.7 Interpret situations as multiplication calculations Eg.I think of a number, then divide it by 15. The answer is 20. What was my number? AIM: By the end of Year 5 most children are able to use compact method for short multiplication of HTU x U and for simple decimals. Most are able to use grid method for long multiplication. They know all table facts up to 10 x10 (multiplication and division) Short multiplication teach compact method to children who have not grasped it in Y5. Children should be able to multiply ThHTU x U (Doesnt mention Th in framework) Continue to teach children to approximate answers first. Long multiplication teach expanded method first. Only move on to compact for children for whom it is appropriate, extending to HTU x TU. Children can continue to use grid method if it is more reliable and better understood. Extend to decimals, with up to 2-decimal places, multiplied by a single digit Interpret situations as multiplication calculations Eg.There are 35 rows of chairs. There are 28 chairs in each row. How many chairs are there altogether? AIM: By the end of Year 6 all children can use compact short multiplication method with any number of digits and decimals. They use their preferred method for long multiplication. They know all tables up to 10 x 10 (multiplication and division)

7 Foundation Stage Share objects into equal groups and count how many in each group. Clifton Primary School Recording and Written Calculations Policy DIVISION Year 1 Year 2 Year 3 Solve problems practically, for example, involving 2, 5, or 10 or sharing into equal groups. * We need to put 12 cakes into boxes of 3 or 4. How many boxes will we have? Understand the operation of division as Sharing equally Eg 6 sweets are shared equally between 2 people. How many sweets does each one get? Record simple mental divisions in a number sentence using the and = signs. Eg. Share 18 between 2 could be recorded as 18 2 Recognise the use of symbols such as or to stand for an unknown number. Eg 12 2 = = 12 2 Understand the operation of division as Sharing equally Eg 6 sweets are shared equally between 2 people. How many sweets does each one get? And Understand the operation of division as Grouping Eg There are 15 apples in a box. How many bags of 5 apples can be filled? ie. How many groups of 5 can you make from 15? Record simple mental divisions in a number sentence using the and = signs. Eg. Divide 25 by 5 Recognise the use of symbols such as or to stand for an unknown number. Eg 16 4 = = 24 4 Understand the operation of division as Sharing equally Grouping (see Y2 examples, but use appropriate numbers) Also that division is the inverse of multiplication. Ensure that grouping continues to be modelled by adults and children on prepared and blank number lines. Eg How many 5s make 35? 7 Grouping should also be modelled on a number line by the teacher and later by pupils. Use prepared number lines and also draw own lines as appropriate eg. 8 children are put into teams of 2. How many teams are there? ie How many groups of 2 are there in 8? 8 2 = Answer: Seven 5s make cakes are put into boxes of 4. How many boxes are there? ie How many groups of 4 are there in 8? 8 2 = Explain methods and reasoning orally. This includes being able to interpret division number sentences eg 20 4 could mean If 20 is shared between 4 people how much would each get? Understand the relationship between multiplication and division and therefore be able to derive division facts for 2x, 5x and 10x tables. Eg 5 x 10 =50 so = 5 etc. Explain methods and reasoning orally and in writing. If 24 tulips are shared equally between 4 plant pots, how many will be in each pot? Understand the relationship between multiplication and division and therefore be able to derive division facts for 2, 3, 4, 5, 6 and 10x tables. Eg 8 x 4 =32 so 32 4 = 8 etc. Understand the concept of a remainder. Eg. How many lengths of 10 cms can you cut from 51 cm of tape? How many will be left? Answer: 5 lengths and 1 cm left over Be able to round remainders up or down depending on context AIM: By end of Yr 3, children will understand the different interpretations of division. They should be ble to derive division facts for 2, 3,4,5 6and 10x tables. Children should be competent at subtracting multiples of 10 from any number eg /30 etc. in preparation for the chunking method.

8 DIVISION Year 4 Year 5 Year 6 Complete written questions (using pencil and paper jottings or mental strategies). Eg 320? = =? Complete written questions (using pencil and paper jottings or mental strategies). Eg 54?= =? Complete written questions (using pencil and paper jottings or mental strategies). Eg9.9?= =? 8 Understand the operation of division as: Grouping/Sharing / inverse of multiplication (and use this to check results) See Y2/3 examples. Continue to model grouping on prepared or blank number lines (and expect children to explain and model it also). Eg.72 5 = 14 remainder This leads on to chunking ie.10 times the divisor is calculated in one chunk because it is quicker and more efficient (do not push children on to this without understanding). Eg x Answer: 14 r. 2 (Demonstrate only. Children record in vertical format). This should be written in vertical format as in the Framework (section 6, p.68). The Framework relates division to repeated subtraction ie )72-50 (5x10) (5x4) Place divisor on left. 2 Answer: 14 r.2 Children should be taught to approximate first to gain a sensible idea of what the answer must be. Explain methods and reasoning orally and in writing, including whether to round up or down after division (involving remainders) depending on the context. AIM: By the end of Year 4 most children are able to use the chunking method of division (using 10x the divisor. Those who cannot are able to chunk in smaller steps. All children are able to explain methods and reasoning and whether to round up or down after division. Most children are able to derive division facts for 2,3,4,5,6,7,8,9and10x tables. Understand the different aspects of division and use as appropriate. (see Y2/3 examples) Continue to develop method of recording division from Year 4 progressing to HTU U, chunking 20x and 30x the divisor, where appropriate ) (7x20) (7x10) (7x6) 4 Answer: 36 r.4 Children should be taught to approximate first to gain a sensible idea of what the answer must be Explain methods and reasoning orally and in writing, including whether to round up or down after division (involving remainders) depending on the context. AIM: By the end of Y5 most children are able to use the chunking method division (using 20/30x the divisor, if appropriate) Those who cannot are able to use 10x the divisor. All children are able to explain methods and reasoning and whether to round up or down after division. All children are able to derive division facts for tables up to 10x10 Understand the different aspects of division and use as appropriate. (see Y2/3 examples) Continue to develop method of recording division from Year 5, chunking multiples of 10x the divisor (20/30/100x etc) see year 5 examples. Teach long division (HTU TU) using chunking method.children should approximate answers first. Eg is approximately = 25 36) (10 x 36) (10 x 36) (5 x 36) (2 x 36) 5 Answer: 27 remainder 5 Extend to decimals with up to 2 decimal places as appropriate. Explain methods and reasoning orally and in writing, including whether to round up or down after division (involving remainders) depending on the context. AIM: By the end of Y6 children should be able to use an appropriate method for short division for any numbers, including decimals. Some children are able to do long division. All children are able to explain methods and reasoning and whether to round up or down after division. All children are able to derive division facts for tables up to 10x10