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CALCULATION POLICY – MULTIPLICATION AND DIVISION Multiplication Division Solve practical problems in a real or role play Understand sharing as giving everyone the same Foundation context e.g. amount e.g. Stage How many shoe lace holes are there on this 6 grapes are shared equally between 2 people. How Aim by end of shoe? many grapes does each one get? year: Put 5 cherries on each cake. How many cherries -All can count in do you need? 2s, 5s and 10s and solve practical Oral counting in twos, fives and tens. problems in a real or role play Count repeated groups of the same size. Solve practical problems in a real or role play context. context e.g. -All understand How many pairs of socks are there in the sharing as giving drawer? Can you cut the cake in half? How many everyone the pieces are there? same amount and Share objects into equal groups and count how solve problems by many in each group – e.g., ask three children to sharing objects share 6 sweets – can you share these sweets into equal groups. between you? Observe number patterns in the environment – e.g., odd and even numbers on doors Sing nursery rhymes with number patterns Solve practical problems that involve combining Understand sharing as giving everyone the same Year 1 groups of 2, 5 and 10 e.g. amount e.g. Aim by end of year: -All can count in How many fingers are there on 4 hands (draw round 6 grapes are shared equally between 2 people. twos, fives and tens own hands and numbers underneath) How many grapes does each one get? and can derive You have 12 wheels, how many cars can you multiples of 2,5 and make? (draw a car to go with each group of 4 10. wheels until 12 wheels have been used) -All can solve real problems involving Count in 2s, 5s and 10s to derive the multiples of 2,5 combining groups. -All understand and 10. sharing as giving everyone the same Link to arrays. amount and solve Model number sentences in context. problems by sharing objects into equal groups. Understand multiplication as repeated addition e.g. (See Framework – section 5 p49) Year 2 There are 5 pencils in one packet, how many pencils Understand division as Sharing equally Aim by end of in 4 packets? E.g. 6 sweets are shared equally between 2 people. year: lllll lllll lllll lllll = How many sweets does each one get? -Most know 2x,5x 5+5+5+5 and 10x tables or and be able to 4 lots of 5 derive division or facts. 4x5 and as Grouping (this is repeated subtraction) -Most understand E.g. There are 15 apples in a box. How many bags of 5 multiplication as This can also be shown as repeated jumps on a apples can be filled? I.e. How many groups of 5 can you repeated addition number line (modelling on bead bar is useful image). make from 15? and describing an Link to array. – arrays. Most understand the different 0 5 10 15 20 Grouping should also be modelled on a number line. interpretations of Use prepared number lines and children draw own as Understand multiplication as describing an array. division. appropriate ●●●●● -In preparation e.g. 8 children are put into teams of 2. How many teams are ● ● ● ● ● 5 x 4 = 20 (explained a 5 four times) for repeated there? (i.e. How many groups of 2 are there in 8?) ●●●●● subtraction ●●●●● approach for 0 2 4 6 8 4 x 5 = 20 (explained as 4 five times) 82=4 Page 1 May 2009 CALCULATION POLICY – MULTIPLICATION AND DIVISION calculating and Relate to real life contexts. Make links between recording when arrays and number lines. 8 cakes are put into boxes of 4. How many boxes are there? using more formal I.e. How many groups of 4 are there in 8? 84=2 written methods, children should be 0 4 8 able to subtract 84=2 10 from any Count forwards and backwards. number and begin Record simple mental divisions in a number sentence to be able to using the and = signs. subtract multiples e.g. ‘Share 18 between 2’ could be recorded as 18 2 of 10 (20/30 etc) Derive and recall facts for 2x, 10x and 5x tables. Explain methods and reasoning orally this includes from any number. Begin to know their 3x table. being able to interpret division number sentences Also know how to manipulate number trios – e.g., 2, 6, e.g. 20 4 could mean 12: If £20 is shared between 4 people how much 2 x 6 = 12 would each get? 6 x 2 = 12 There are 20 children and they sit in tables of 12 ÷ 6 = 2, 4. How many tables will we need? 12 ÷ 2 = 6 Record simple mental multiplications in a number sentence using x and = signs. Recognise the use of symbols such as □ or ∆ to Recognise the use of symbols such as Δ or Ο to stand for an unknown number e.g. stand for unknown numbers e.g. 12 2 = □ □ = 12 2 □ 2 =6 12 = 6 6 = 2 6 = 12 6 x Δ = 12 Δ x 2 = 12 ∆ = 10 etc 6x2=Δ Δ x Ο = 12 20 = Δ x 5 20 = 4 x Δ etc. Begin to interpret situations as multiplications Understand the relationship between multiplication calculations and explain reasoning e.g. and division and therefore be able to derive division How many wheels are there on 3 cars? facts for 2x, 5x and 10x tables. Katy’s box is 5 cm wide. Mary’s box is twice as E.g. 5 x 10 =50 so 50 10 = 5 wide as Katy’s box. How wide is Mary’s box? 10 x 5 = 50 50 5 = 10 etc. Understand multiplication as: (See Framework – section 5 p49) Year 3 Understand the operation of division as Aim by end of repeated addition Sharing equally year: 13 x 3 Grouping -All can derive x10 As Y2, but use appropriate numbers and recall facts x1 x1 x1 also that for 2, 3, 4, 5, 6 Division is the inverse of multiplication. and 10x tables. 0 30 33 36 39 Ensure that grouping continues to be modelled by -All understand adults and children on prepared and blank number the three aspects describing an array lines. E.g. of multiplication ●●●●●●●●●●●●● 13 x 3 How many 5s make 35? (repeated ●●●●●●●●●●●●● = 10 x 3 + 3 x 3 addition, ●●●●●●●●●●●●● = 30 + 9 = 39 describing an 0 5 10 15 20 25 30 35 array and scaling) -All recognise all 3 x 13 = Seven 5s make 35 multiples of 2, 5 = 3 x 10 +3x3 and 10 up to = 30 +9 Count forwards or backwards 1000. = 39 -All understand Begin to develop informal ways of calculating and Use practical and informal methods to support division as recording: 13 x 3 division of larger numbers to encourage chunking. grouping or 13 sharing 52 4 = 13 -All solve division calculations by 10 x3 3 x3 x 10 x1 x1 x1 grouping on blank number lines. 30 9 -All can round up 0 40 44 48 52 or down after 39 division depending scaling on the context e.g. Make a tower 3 times taller then this. -All can derive Draw a line 4 times longer than this. and recall Page 2 May 2009 CALCULATION POLICY – MULTIPLICATION AND DIVISION multiplication and Know 2x, 3x, 4x 5x, 6x, 10x times tables. Record simple mental divisions in a number sentence division facts for Recognise multiples of 2, 5 and 10 up to 1000 using the and = signs. 2, 3,4,5,6 and 10 Make links to multiplication square. e.g. ‘Divide 25 by 5’ times tables. Be able to count in steps of 2,3,4,5, 6, 8 and 10. Record mental multiplications in a number sentence Interpret division number sentences using x and = signs. e.g. 24 4 could mean If 24 tulips are shared equally between 4 plant pots, Recognise the use of symbols such as Δ or Ο to how many will be in each pot? or There are 55 stand for unknown numbers e.g. children and they are put in teams of 5. How many 6 x Δ = 18 Δ x 3 = 18 teams can we make? 6 x 10 = Δ Δ x Ο = 24 64 2 20 = Δ x 5 20 = 4 x Δ etc. ‘I halved 60 to get 30, then halved 4 to get 2, then I recombined the numbers to get 32.’ Round up or down after division, according to the context. To provide the children with skills for Y4 written Recognise the use of symbols such approaches, the objective ‘Use knowledge of number as □ or ∆ to stand for an unknown number. E.g. facts and place value to multiply or divide mentally’ 16 4 = □ □ = 24 4 is important i.e. multiply a single digit by 1,10 or 100. □ 3=6 35 □ = 7 dvide a three digit multiple of 100 by 10 or 100. 8 □ = 2 8 = 16 □ double any multiple of 5 up to 50. □÷∆=5 halve any multiple of 10 to 100. 20 – 14 = □ 5 multiply a 2-digit multiple of 10 up to 50, by 2, 3, 4, 5 or 10. multiply a 2-digit number by 2, 3, 4 or 5 without crossing tens boundary ( e.g. 23 x 3 using partitioning) Begin to develop informal ways of calculating and Understand the concept of a remainder. E.g. recording by partitioning and recombining. e.g. How many lengths of 10 cms can you cut from 51 cm 17x5 of tape? How many will be left? 10 x 5 = 50 7 x 5 = 35 50 + 35 = 85 0 10 20 30 40 50 51 Answer: 5 lengths and 1 cm left over. Interpret situations as multiplication calculations Understand the relationship between multiplication and explain reasoning e.g. and division and therefore be able to derive division A baker puts 6 buns in each of 4 rows. How facts for 2, 3, 4, 5 and 10x tables. Begin to know many buns does she make? division facts for 6 and 8 x tables. Lee has 4 stickers. Ian has three times as many e.g. 8 x 4 =32 so 32 4 = 8 etc. as Lee. How many stickers does Ian have? In preparation for repeated subtraction approach for calculating and recording when using more formal written methods, children should be competent at subtracting multiples of 10 from any number e.g. 117 – 20/30 etc. Derive and recall multiplication facts up to 10 x 10 Understand the operation of division as: Year 4 (including multiplication by 0 and 1). Grouping Aim by end of Be able to complete quickly. Sharing year: e.g. The inverse of multiplication (and use this to -All are confident 60 x 2 = x 4 = 160 check results) with the grid 8x = 32 Δ x = 120 etc method way of See Y2/3 examples recording Understand that division is the inverse of multiplication and multiplication and use this to check results. are able to Further develop informal written methods (see EITHER REPEATED ADDITION METHOD explain reasoning Y2/3) e.g. partitioning Continue to model grouping on prepared or blank -All can derive It is important that children are taught to always number lines (and expect children to explain and and recall approximate first in order to get a sensible idea of model it also) e.g. multiplication what the answer must be 72 5 = 14 remainder 2 facts up to 10 x Begin with ‘teens’ numbers e.g. 13 x 8, then progress 10 (including rapidly on to multiples of ten e.g. 23 x 8 (approx. 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 72 multiplication by 0 answer - between 160 and 200) leading to: and 1) ‘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, Page 3 May 2009 CALCULATION POLICY – MULTIPLICATION AND DIVISION Partitioning bead bar is excellent resource). 23 x 8 e.g. 72 5 20 x 8 = 160 3 x 8 = 24 10x5 x1 x1 x1 x1 0 50 55 60 65 70 72 23 x 8 = 160 + 24 = 184 Answer: 14 r. 2 or 23 x 8 = (20 x 8) + (3 x 8) = 160 + 24 = 184 This can be written vertically. 72 5 or (10) 50 (see Framework - section 6 p66) ( 4) 20 23 70 x 7 + 2 (remainder) 20 x 8 160 72 3x8 24 Answer: 14 r 2 184 OR REPEATED SUBTRACTION METHOD and Grid method (see Framework- Section 6 p66 – 0 2 7 12 17 22 27 32 37 42 47 52 57 62 67 72 Method A) leading to: x 20 3 8 160 24 =184 ‘chunking’ ie.10 times the divisor is calculated in one ‘chunk’ because it is quicker and more efficient (do 23 x 8 = 184 not push children on to this without understanding, bead bar is excellent resource). 23 x 8 x1 x1 x1 x1 x 10 20 x 8 = 160 3 x 8 = 24 160 + 24 = 184 0 2 7 12 17 22 72 leading to: (See Framework – section 5 p68) 72 5 72 - 50 10 (10 groups of 5) 22 - 20 4 (4 groups of 5) 2 14 Answer: 14 r.2 Children should be taught to approximate first to gain a sensible idea of what the answer must be. Progress to vertical expanded recording, multiplying Record division calculations in a number sentence by the most significant digit first. (see Framework – where appropriate e.g. Section 6 p66 - Method B) How many lengths of 10 cm. Can you cut from 183 Record like this: cm? 23 x 7 Could be recorded as 183 10 approx. ans. – bit larger than 140 23 x 7 140 (20 x 7) 21 ( 3 x 7) 161 When appropriate, still using expanded recording, begin to record the least significant digit first, in order to prepare children for teaching the ‘Compact Standard Method i.e. 23 x 7 23 21 leading to x7 140 16 1 161 2 Page 4 May 2009 CALCULATION POLICY – MULTIPLICATION AND DIVISION Interpret situations as multiplication calculations Explain methods and reasoning orally and in writing, and explain reasoning e.g. including whether to round up or down after division There are 6 eggs in a box. How many in 45 (involving remainders) depending on the context boxes? (single step problem) (using pencil and paper jottings or mental There are 4 stacks of plates. Three stacks have strategies). e.g. 15 plates each. One stack has 5 plates. How 320 = 80 240 6 = many plates are there altogether? (multi- step 30 = 8 (25 ) + 2 = 7 problem) ( 5) – 2 = 3 Recall quickly multiplication facts up to Understand the different aspects of division and Year 5 10 x 10, including multiplication by 0 and 1. use as appropriate. (see Y2/3/4 examples) Aim by end of Complete written questions e.g. year: 160 x 2 = x 2 = 290 -All use an 0.9 x = 6.3 Δ x = 1600 etc efficient and Understand that division is the inverse of appropriate multiplication and use this to check results. written method Continue to teach children to approximate answers Continue to develop method of recording division for multiplication first. from Year 4 progressing to -All recall quickly (See Framework Section 6 p 67) HTU U, ‘chunking’ 20x and 30x the divisor, where multiplication Continue to use informal methods of recording to appropriate. facts up to 10 x support and explain mental methods where the This can be modelled on a blank number line e.g. 10 and use them numbers are appropriate. 256 7 to multiply pairs It is important to ensure that children continue to REPEATED ADDITION METHOD of multiples of 10 use informal methods of recording to support and 20x7 10x7 5x7 1x7 r.4 and 100. explain their mental methods where the numbers are -All quickly derive 0 140 210 245 252 256 appropriate the corresponding = 36 r 4 i.e. they do not use formal recording where it is division facts. inappropriate. E.g. 47 x 5 - All can use the leading to: 40 x 5 = 200 ‘chunking’ method 7 x 5 = 35 200 + 35 = 235 140 (20) division (using 20/30x the 70 (10) Begin with the ‘grid’ method. E.g. 72 x 38 210 divisor, if ans. approx. 70 x 40 = 2800 42 (6) appropriate) and the schools’ 252 x 70 2 4 (remainder) chosen method of 30 2100 60 2160 256 recording with 8 560 16 576 + Answer: 36 r.3 HTU U 2736 calculations. - Those who cannot WHEN READY MOVE FROM REPEATED Only progress to compact recording for children are able to use ADDITION TO REPEATED SUBTRACTION. for whom it is appropriate. It is important to 10x the divisor. show links to the grid method. -All can explain r4 x6 x10 x20 (see Framework – section 6 p67) methods and 72 72 reasoning and 0 4 46 116 256 x 38 x 38 whether to round 30 x 70 2100 72 x 30 2160 (see Framework – section 6 p69) up or down after 30 x 2 60 leading to 72 x 8 576 division depending leading to: 8 x 70 560 2736 on context. 8x2 16 1 256 7 256 2736 - 140 (20) 1 116 - 70 (10) 46 - 42 (6) 4 Answer: 36 r.4 leading to: 256 7 256 - 210 ( 30) 46 - 42 (6) 4 Answer: 36 r 4 Page 5 May 2009 CALCULATION POLICY – MULTIPLICATION AND DIVISION Children should be taught to approximate first to Children should be taught to approximate first to gain a sensible idea of what the answer must be gain a sensible idea of what the answer must be. Interpret situations as multiplication calculations and explain reasoning e. g. I think of a number, then divide it by 15. The answer is 20. What was my number? There are 8 shelves of books. Six of the shelves hold 25 books each. Two of the shelves have 35 books each. How many books are there altogether on the shelves? Extend to simple decimals, with one decimal place, Explain methods and reasoning orally and in writing, multiplied by a single digit. Approximate first. E.g. including whether to round up or down after division 4.9 x 3 is approx. 5x3 = 15 (involving remainders) depending on the context. Complete written questions (using pencil and paper 4.9 x 3 jottings or mental strategies). E.g. x 4 0.9 3 12 2.7 12 + 2.7 =14.7 54 = 18 186 6 = 40 = 12 leading to 4.9 (125 ) + 2 = 27 ( 5) – 22 = 30 x 3 14.7 2 Use knowledge of place value and multiplication facts Understand the different aspects of division and Year 6 to 10 x 10 to derive related multiplication and use as appropriate. (see Y2/3 examples) Aim by end of division facts involving decimals. year: Complete written questions e.g. -All use an 0.7 x 20 = x 20 = 8000 efficient and 4 x = 3.6 Δ x = 2.4 etc appropriate Understand that division is the inverse of method for multiplication and use this to check results multiplication. Continue to teach children to approximate answers Continue to develop method of recording division -All use first. from Year 5, ‘chunking’ multiples of 10x the divisor knowledge of (See Framework – Section 6 p67) (20/30x etc) – see year 5 examples. place value and Continue to use partitioning ‘grid’ or expanded multiplication fats methods if appropriate (see y4/5) Develop the compact method for short division if to 10 x 10 to It is important to ensure that children continue to appropriate (see Y5). derive related use informal methods of recording to support and Teach long division (HTU TU) using ‘chunking’ multiplication and explain their mental methods where the numbers are method that school prefers i.e. ‘repeated division facts appropriate i.e. they do not use formal recording subtraction’ or ‘counting on’ method. involving decimals. where it is inappropriate Children should approximate answers first e.g. - All can use an e.g. 8.6 x 7 appropriate REPEATED ADDITION (approx. as: between 56 and 63) method for short 977 36 is approximately 1000 40 = 25 division for any 8 x 7 = 56 360 (10) numbers, including 0.6 x 7 = 4.2 56 + 4.2 = 60.2 + 360 (10) decimals. Continue to use ‘grid’ method if it is more reliable 720 -All can explain and better understood. + 180 (5) methods and 372 x 24 900 reasoning and x 300 70 2 + 72 (2) whether to round 20 6000 1400 40 = 7440 972 up or down after 4 1200 280 8 = 1488 + + 5 (remainder) division depending 8928 977 on context. leading to: Answer: 27 remainder 5 -All use 372 knowledge of x 24 REPEATED SUBTRACTION (see Framework – place value and 6000 (300 x 20) section 6 p69) multiplication 1400 (70 x 20) 977 facts up to 10x10 40 (2 x 20) - 360 (10) to derive related 1200 (300 x 4) 617 multiplication and 280 (70 x 4) - 360 10 division facts 8 (2 x 4) 257 involving decimals 8928 - 180 5 e.g., 0.8 x 7, 77 4.8 ÷ 6 leading to: - 72 2 5 27 Answer: 27 remainder 5 Page 6 May 2009 CALCULATION POLICY – MULTIPLICATION AND DIVISION (see framework – Section 6 p67) 372 x 24 7740 (372 x 20) 1488 (372 x 4) 8928 Interpret situations as multiplication calculations When appropriate develop an efficient standard and explain reasoning e.g. method (see Framework - section 6 p 69) e.g. There are 35 rows of chairs. There are 28 chairs in each row. How many chairs are there 972 36 altogether? _____ 27 There is space in a multi-storey car park for 17 36) 972 36) 9 7 2 rows of 30 cars on each of 4 floors. How many - 720 20 -720 cars can park? 252 252 960 marbles are put into 16 bags. There is the - 252 7 - 252 same number of marbles in each bag. How many 0 0 marbles are there in 3 of these bags? Answer: 27 Extend to decimals, with up to 2-decimal places, Extend to decimals with up to 2 decimal places as multiplied by a single digit e.g. appropriate and using school’s chosen method of 4.92 x 3 (answer approx: 15) recording i.e. ‘chunking’ or compact short division. Complete written questions e.g. x 4 0.9 0.02 3 12 2.7 0.06 = 14.76 9.9 = 1.1 6.3 7 = 5 = 0.8 = 12 +2.7 + 0.06 = 14.76 (100 ) + 5 = 7.5 ( 25) – 22 = 30 Leading to: (Framework – section 6 p67) 4.92 x 3 12.00 ( 4x 3) 2.70 (0.9 x 3) 0.06 (0.2 x 3) Page 7 May 2009

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