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Calculations Policy This policy was reviewed by the Teachers at Binfield C.E. Primary in September 2012 Binfield C.E. Primary School Calculation Policy Subtraction Multiplication Addition Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways of recording calculations using pictures and concrete apparatus etc. They use number lines, hundred squares and practical resources to support calculation. Teachers demonstrate the use of the number line. Children begin to use number lines themselves starting with the larger number and counting on. First counting on in tens and ones 34 + 23 = 57 +10 +10 +1 +1 +1 Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways of recording calculations using pictures and concrete apparatus etc. They use number lines, hundred squares and practical resources to support calculation. Teachers demonstrate the use of the number line. Children begin to use number lines themselves to support their calculations. First counting back in tens and ones 47 - 23 = 24 -1 -1 -1 -10 -10 Children will experience equal groups of objects, particularly in practical problem solving activities. They will join in with adults counting in 2s, 5s and 10s, and become independent. 24 25 26 34 44 54 55 56 57 Then adding the units in one jump 34 + 23 = 57 +10 +10 +3 44 54 57 Followed by adding the tens in one jump and the units in one jump 34 + 23 = 57 +20 +3 54 Compensation 49 + 73 = 57 +50 57 47 27 37 47 Children will develop their understanding of multiplication and use jottings to support calculation. Repeated addition 3 times 5 = 5 + 5 + 5 = 3 lots of 5 = 5 x 3 Repeated addition can be shown on a number line: 5x3=5+5+5 +5 +5 +5 0 5 15 Commutativity Children should also know that 3 x 5 has the same answer as 5 x 3. This can also be shown on the number line. +5 +5 +5 27 47 Counting on 47 – 23 = 24 +7 +10 5 10 15 +3 +3 +3 +3 +3 Arrays Children should be able to model a multiplication calculation using an array. +7 Children will understand equal groups and share items out in play and problem solving activities. They will join in with adults counting in 2s, 5s and 10s and become independent. Children will develop their understanding of division and use jottings to support calculation. Sharing equally “6 sweets shared between 2 people. How many do they each get?” Grouping or repeated addition “There are 6 sweets. How many children can have 2 sweets each?” Repeated subtraction using a number line 12 ÷ 3 = 4 30 40 0 1 2 3 4 5 6 7 8 9 10 11 12 Repeated subtraction using a number line including remainders 13 ÷ 3 = 4 r 1 5 x 3 = 15 -1 122 123 10 Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways of recording calculations using pictures and concrete apparatus etc. 0 23 73 37 Followed by subtracting the tens in one jump and the units in one jump 47 - 23 = 24 -3 -20 24 34 27 Then subtracting the units in one jump 47 - 23 = 24 -3 -10 -10 24 34 Division Children are encouraged to develop a mental picture of the number system in their heads to use for calculation. They develop ways of recording calculations using pictures and concrete apparatus etc. 47 3 x 5 = 15 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Using symbols to stand for unknown numbers ÷ 10 = 8 26 ÷ = 13 24 ÷ 2 = Binfield C.E. Primary School Calculation Policy Children will begin to use informal pencil and paper methods (jottings) to support, record and explain partial mental methods building on existing mental strategies. Children will begin to use informal pencil and paper methods (jottings) to support, record and explain partial mental methods building on existing mental strategies. Adding least significant digits first 625 + 148 13 5 + 8 60 20 + 40 700 600 + 100 773 Carrying below the line 587 + 475 1062 Partitioning and decomposition 89 - 57 = 80 50 30 + + + 9 7 2 Begin to exchange 60 1 71 - 46 = 70 = 40 20 + + + 1 6 5 = 25 Children will begin to use informal pencil and paper methods (jottings) to support, record and explain partial mental methods building on existing mental strategies. Partitioning 38 x 5 = (30 x 5) + (8 x 5) = 150 + 40 = 190 Grid Method x 30 5 150 8 40 = 190 Children will use the grid method to multiply TU x U, TU x TU, HTU x TU and decimals. 11 Carrying below the line 587 + 475 1062 11 Using similar methods, children will: Add several numbers using different numbers of digits; Begin to add two or more sums of money, with or without adjustment from pence to pounds; Know that the decimal places should line up underneath each other. Children should extend the carrying method to numbers with any number of digits or decimal places. Decomposition 6141 754 – 286 468 Using similar methods, children will: Subtract numbers with different numbers of digits; Begin to subtract two or more sums of money, with or without adjustment from pence to pounds; Know that the decimal places should line up underneath each other. Children should extend the Decomposition method to numbers with any number of digits or decimal places. Children will develop their use of repeated subtraction to be able to subtract multiples of the divisor. 72 ÷ 5 R2 - 5 - 5 -5 -5 - 50 Expanded written method 46 x 32 12 80 180 1200 1472 Compact method 46 x 32 92 1380 1472 Using similar methods, children will: Know that the decimal places should line up underneath each other. Children should extend the Compact method to multiply decimals with up to two decimal places by a single digit number, then two digit numbers. 02 7 12 Chunking 17 22 72 72 ÷ 5 = 14 r 2 -50 (10 x) 22 - 5 (1 x) 17 - 5 (1 x) 12 - 5 (1 x) 7 - 5 (1 x ) 2 Compact Method 3 157 471 3 17 15 21 Short Compact Method 157 3 41721 Using similar methods, children will: Decide what to do after division and round up or down accordingly; Express remainders as fractions or decimals where appropriate. Children should extend the Compact method to divide numbers with decimal places. Binfield C.E. Primary School Calculation Policy