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Maths Calculation Policy DUNCHURCH BOUGHTON C of E (VA) JUNIOR SCHOOL Maths Calculation Policy Recognising its historic foundation, the school will preserve and develop its religious character in accordance with the principles of the Church of England and in partnership with the church at parish and diocesan level. The Christian Faith, and its practical expression, form a major part of the whole school ethos. The school aims to give children both knowledge and understanding of the Christian Faith while respecting and understanding other religions and cultures. The school aims to: School Aim Statement: Review History: ensure that all children receive their entitlement to a broad, balanced National Curriculum, encouraging them to have high expectations in all areas of the curriculum and to reach their full potential. provide a secure and relaxed environment in which the children are encouraged to have a healthy lifestyle, to be tolerant and to grow in confidence and self-esteem. ensure that pupils develop an open and enquiring mind and are encouraged to be creative, imaginative and inventive. work in partnership with parents and the wider community. Reviewed by Governors: April 2006, April 2008, April 2011 Next review date: Issue Date: th Printed: 11 July 2012 Page 1 DUNCHURCH BOUGHTON C of E (VA) JUNIOR SCHOOL Maths Calculation Policy Purpose This policy has been developed to enable a consistent approach to be taken in the teaching and learning of written mathematical calculations. This should ensure that the methods taught allow progression in dealing with larger numbers and are consistent with mental strategies taught. The strategies adopted are taken from the National Numeracy strategy following advice from The Warwickshire County Council Numeracy advisor. To ensure familiarity with traditional calculations, children will be shown alternative methods, where appropriate, before they complete Key Stage 2. Aims For children to be taught one clear method to complete each calculation type. For methods taught to link to mental strategies taught. For children, teachers and parents to all use the same calculation methods. Multiplication Children should know and use multiplication facts to 10x10. When sufficient facts are known children may progress to multiplying larger numbers as shown below. Questions should initially be written horizontally to enable children to make a sensible estimate before calculating. 16 x 5 (Partition 16 into 10 + 6, then set the calculation out as below.) X 5 10 50 6 30 = 80 The steps within the calculation are as follows 10 x 5 =50 6 x 5 = 30 50 + 30 = 80 Hence 16 x 5 = 80 3 digit x 1 digit (HTU X U ) 256 X 8 is approximately 260 x 10 = 2600 X 8 200 1600 50 400 6 48 = 2048 ( The final calculation of 1600 + 400 + 48 can be done mentally or with appropriate jottings, or using the method children are using for addition. ) Decimals with one decimal place multiplied by a single digit integer. 4.9 X 3 is approximately 5 x 3 = 15 X 3 th Printed: 11 July 2012 4 12 0.9 2.7 Page 2 = 14.7 DUNCHURCH BOUGHTON C of E (VA) JUNIOR SCHOOL Maths Calculation Policy 2 digit x 2 digit (TU x TU) 23 X 37 is approximately 20 x 40 = 800 X 30 7 20 600 140 3 90 21 = 690 = 161 + 851 Add numbers from left to right Then total. (Children should be aware that whichever order they add the numbers the answer will be the same because of the commutivity of addition. Eg 600 + 140 + 90 + 21 = 851 ) 3 digit x 2 digit (HTU X TU) 324 X 43 X 40 3 300 12000 900 20 800 60 4 160 12 = 12960 = 972 + 13932 Care should be taken when selecting numbers in calculations. For example, when multiplying decimals for the first time using the grid method, use numbers such as 4.5 x 5. Children who do not know all of their tables can use the grid method to multiply larger numbers based on tables they should be familiar with. Eg 253 x 4 requires knowledge of 2, 5 and 3 times tables and understanding of place value. Subtraction This method, also called complementary addition, builds on mental methods taught. It is based on finding the difference between 2 numbers by counting on from the smallest to the largest. The two numbers being subtracted are positioned at each end of a number line. An addition to the smallest number is made to the nearest 10, this is noted on the line. Further additions are made, and noted, until the second of the two numbers being subtracted is reached. All the additions are then added mentally, giving the final answer. th Printed: 11 July 2012 Page 3 DUNCHURCH BOUGHTON C of E (VA) JUNIOR SCHOOL Maths Calculation Policy 56 – 27 (TU –TU) This is approximately 56 – 30 = 26 +3 +10 + 10 +6 = 29 --------------------------------------------27 30 40 50 56 The size of jump may vary according to confidence. The next stage in the understanding of this calculation would be to make a more efficient jump of 20 from 30 to 50. . 157 –78 (HTU – TU) +2 +20 +57 = 79 ----------------------------------------78 80 100 157 763 – 285 (HTU – HTU) +15 +400 +63 = 478 ----------------------------------285 300 700 763 12.5 – 3.6 (Decimals to 1 decimal place) +0.4 +8.5 = 8.9 ------------------------------ 3.6 4.0 12.5 8.37 – 3.59 (Decimals to 2 decimal places) +0.41 +4.37 = 4.78 --------------------------------3.59 4.0 8.37 It may be appropriate for some children at the end of year 6 to investigate other methods of subtraction, including decomposition. Division The aim is that children should know and use multiplication facts to 10x10, and know and use the corresponding division facts. However, children need to be dividing even when they don’t know the number facts ie tables. Children should be able to count on, for example, in 2`s even if they don’t know by heart their 2 x tables. As children move on from counting on in groups of the divisor, they need to use key facts to help them. The key facts needed, will be 10x, 5x and 2x. Known facts can be used to make fewer steps. This enables children to more efficient in their calculations, and eliminates the need to always start counting on from zero. The number being divided is positioned at the right end of a number line, 0 is placed at the other end. Jumps along the line are made in multiples of the divisor (the th Printed: 11 July 2012 Page 4 DUNCHURCH BOUGHTON C of E (VA) JUNIOR SCHOOL Maths Calculation Policy number being divided by), 7 in the example below. The number of jumps is totaled and recorded along with any remainder. 68 7 7 7 7 7 7 7 7 7 7 “ nine sevens are sixty three remainder 5” (R5) ----------------------------------------------------0 7 14 21 28 35 42 49 56 63 68 68 7 = 9 R 5 A more efficient method would be to use key facts as a starting point. “I know that 5 x 7 = 35, so that will be my first jump”. 5 x7 7 7 7 7 (R5) x1 x1 x1 x1 ------------------------------------------------------0 35 42 49 56 63 68 As confidence increases children may use other known tables facts to help them in their calculation. I know 7 x 7 = 49 and I know 2 x 7 = 14 68 7 7 x7 2 x7 R5 -------------------------------------------------------0 49 63 68 68 7 = 9 R 5 Leading to 3 digits divided by 2 216 13 10 x13 5 x13 1 x13 R8 216÷13 = 16R8 ------------------------------------------------------------------------0 130 195 208 216 The remainder can alternatively be recorded as a quotient 216 ÷ 13 = 16 8/13 This method of recording the answer should be clearly modeled to support understanding. Addition Children will be taught to mentally add number bonds for all numbers to 10, then 20. As they progress to adding two 2 digit numbers, they will be taught to partition the numbers, then add. th Printed: 11 July 2012 Page 5 Maths Calculation Policy DUNCHURCH BOUGHTON C of E (VA) JUNIOR SCHOOL Addition sums should be written horizontally, initially. Each mental step in the calculation should be recorded on a separate line. A number of steps will be taught, confidence with one is necessary before moving to the next. Some children will not progress to step 5. The method used is based on understanding of partitioning and recombining numbers. E.g. 13 + 16 = is 10 + 3 + 10 + 6 so 10 + 10 = 20 3+6=9 20 + 9 = 29 Step 1 48 + 53 =101 40 + 50 = 90 8 + 3 = 11 90 + 11 = 101 Partition each number then add tens, then units Mentally add the sum of the two partitioned parts When children are confident with this method and can apply it to 3digit numbers, and can use it to solve problems, subsequent steps can be taught. Step 2 48 + 53 = 101 The process of step 1 along side the usual addition layout 48 (40 + 8) + 53 (50 + 3) -------------90 (40+50) The most significant digit is added first i.e. 10’s 11 (8 + 3) -------------101 The answer is then transferred to complete the original sum Step3 48 + 53 = 101 The process of step 2 not showing the partitioning. 48 and adding the most significant digits first + 53 --90 + 11 --101 Step 4 48 + 53 =101 As step 3 but adding the least significant digits first 48 + 53 ---11 + 90 ---101 th Printed: 11 July 2012 Page 6 Maths Calculation Policy DUNCHURCH BOUGHTON C of E (VA) JUNIOR SCHOOL Step 5 48 + 53 = 101 The compact method 48 + 53 ---101 ---Children will be at different stages in their understanding of the process and should move on when they are secure at using a particular stage. Care should be taken when selecting numbers for calculations as progression is important. Numbers that do not bridge 10 Numbers that bridge 10 Numbers that do not bridge 100 Numbers that bridge 100 Numbers that bridge both 10 and 100 All calculation methods taught will be modeled to support children`s understanding so that they have a good sense of the size of numbers and a clear understanding of the operations being used. th Printed: 11 July 2012 Page 7