NELSON PRIMARY SCHOOL WRITTEN CALCULATIONS POLICY Date written / last reviewed: October 204 Date approved by Curriculum and Achievement Committee: 204 Date adopted by Governors: 204 Date of next review: October 206 Pre-stage EYFS) Number bonds to 0 : correspondence *Children begin to add/count on mentally using rhymes and begin to record in the context of play or practical activities e.g; Recording with marks, stamps or objects the ways you can put 5 apples in 2 bowls. *Combine 2 groups of objects to find a total. *Use the language of more by adding one to a group e.g tower of cubes *Adding stories and role play, encouraging use of language for addition. *Begin to record in the context of play or practical activities e.g; counting rhymes that count back. *Remove objects from a group e.g. I have 5 apples and a take one away how many are left? *Use the language of less by taking from a group e.g tower of cubes *In take away stories such as role play encouraging use of language of subtraction. *Children begin to count in groups of 2, 5 and 0 using objects, recite counting, songs and rhymes. *They count related groups of the same size in games and practical activities. *Links are also made to problem solving activities. *Practical division as grouping e.g. buttons, beads etc *Children share objects practically into equal groups e.g; Share the cakes between the three bears. How many cakes will they each have? *Links are made to problem solving activities. *Use a numbered large number lines (number tiles) to identify one more. Children combine 2 groups of objects. *Through cutting and sticking and picture representation of an addition sentence *Use a numbered, large number line (floor tiles) to identify one less. *Picture representation of a subtraction sentence 3 and 2 makes 5 5 take away leaves 4
Year ) Memorise and reason number bonds to 0 and 20 in several forms e.g. 9 + 7 = 6; 6-7 = 9; 7 = 6-9 *Adding by counting on. First by finding more, then in steps of. *Children can count on from the first number using fingers, objects, themselves etc. * The adult should model drawing jumps on the numbered number line to support understanding of the mental method. *Learn that addition can be done in any order and are taught that it is more efficient to put the larger number first. *Children need to understand the concept of equality before using the = sign. Calculations should be written either side of the equality sign so that the sign is not just interpreted as the answer. E.g. 2 =+ and 2+3 = 4+ *Children begin to record addition number sentences using + and =. *Missing numbers need to be placed in all possible places within the number sentence. 4+ = 7 + 2= 8 Also cover up operations as well as numbers. *Use addition in terms of how many more to calculate the difference. *Children learn to represent and use number bonds to 0 and 20. *Children begin to add 3 single digit numbers, by looking for pairs of numbers or doubles to aid mental calculation. *Children are taught to use the hundred square to find 0 more by looking at the number underneath. *Children begin to learn place value of 2 digit numbers to add in tens and ones. *Counting back in steps of then 0. Identify missing numbers in a number line. *Adding by counting back. First by finding less, then in steps of. *Children can count back from the first number using fingers, objects, themselves etc. *The adult should model drawing jumps on the numbered number line to support understanding of the mental method. *Learn that subtraction must start with the larger number and count back the smaller number. *Children begin to record subtraction number sentences using - and =. * Missing numbers need to be placed in all possible places within the number sentence. *Also cover up operations as well as numbers. *Children should be taught to find the difference using subtraction 8-5=3 *Children are taught to use the hundred square to find 0 less by looking at the number above. *Children learn to represent and use the subtraction facts related to number bonds to 0 and 20. *Children begin to subtract to solve simple word problems. *Begin to recognise that subtraction is the inverse of addition. *Children group objects in 2, 5 and 0. *Children start to use visual images as repeated addition. 2 + 2 + 2 + 2 + 2 = 0 *Model this as jumps on a number line. *Practically double numbers to 0 and link this with multiplying by 2. *Solve practical problems involving such as: There are 4 bikes. Each bike has 2 wheels, how many wheels is that? *Show visual representation of a calculation using arrays, with support from an adult. *Make connections between arrays, numbers patterns and counting in twos, fives and tens *Halving to match doubling and understand it is the opposite. *Sort a set of objects by grouping equally into 2 s, 3 s, 4 s etc. *Use practical grouping to solve word problems. e.g. There are 2 daffodil bulbs. Plant 3 in each pot. How many pots are there? *Show visual representation of a division calculation using arrays, with support from an adult. 8 4 = 2 8 2 = 4
2 Year 2) use addition and subtraction facts to 20 fluently, and derive and use related facts up to 00 use and division facts for the 2, 5, 0 tables. Children can link x0 to place value and x5 to the divisions on an analogue clock face. *Children learn to count on in tens and ones on the number line. *Add 9 and by adding 0 and adjusting by. *Children add 2 digit numbers on the hundred square by counting on in tens down the hundred square and then across in ones. *They then draw blank number lines and draw how many they are counting on. 23+5 23 33 34 35 36 37 38 *Continue with using a range of equations as in, but with larger numbers such as multiples of 0, a two-digit number and ones, a two-digit number and tens, two two-digit numbers, adding three one-digit numbers 70 + = 20 + *Children begin to round up to the nearest multiple of ten. *Find the difference by counting on with larger numbers on the number line. *Know that subtraction is the inverse of addition and use known number facts to calculate mentally. *Show that addition of two numbers can be done in any order (commutative) *Begin to add by bridging through 0 where necessary. *Children begin to add larger 3 digit numbers by partitioning and recombining into hundreds, tens and ones. 2+27 = 0 + 20 = 30 = 2 + 7 = 9 = 30 + 9 = 39 extend to 2+ 27 = 00 + 0 + 20 = 30 = 2 + 7 = 9 = 39 *Children learn to count back in tens and ones on the number line. *Subtract 9 and by subtracting 0 and adjusting by using the hundred square. *Children subtract 2 digit numbers on the hundred square by counting back in tens up the hundred square and then back in ones. *They then draw blank number lines and draw how many they are counting back. 38-5 33 34 35 36 37 38 *This would then progress to jumping in tens then ones. *Subtract by bridging through 0 where necessary. *Continue with using a range of equations as in year, but with larger numbers such as multiples of 0, a two-digit number and ones, a two-digit number and tens, two two-digit numbers, adding three one-digit numbers 00 - = 40 *Find the difference by counting on with larger numbers on the number line. *Know that subtraction is the inverse of addition and use known number facts to calculate mentally. *Show that subtraction of two numbers cannot be done in any order and is not commutative. *Children begin to subtract larger 2 digit numbers by partitioning the second number only. 37 2 = 37 0 = 27 = 27 2 = 25 *Subtract by bridging through 0 where necessary. *Children use repeated addition number sentences to calculate ; 4x3 = 3+3+3+3 *Continue to show visual representation of this using an array. 3x4 = 2 4x3=2 *Explore the fact that, like addition, can be done in any order (commutative). *Children are taught to calculate questions by jumping in groups on a number line. *Children begin to record number sentences using x and =. *They are then taught to develop an understanding of the families of numbers to work out the missing numbers e.g. 7 x 2 = = 2 x 7 7 x = 4 4 = x 7 x 2 = 4 4 = 2 x x = 4 4 = x *Use to solve more complex word problems in a context. Children begin to relate division to fractions of numbers and shapes e.g. ½ and ¼ is the same as dividing by 2 and dividing by 4 respectively. *Children continue to use grouping of objects practically and relate to real life situations. Progressing to grouping numbers into equal sets with a remainder. * Continue to show visual representation of this using an array. 2 3=4 2 4=3 *Children show division as repeated subtraction. *Then begin to divide a number by counting back in equal steps model this on a number line. *Children begin to record their practical division as a written calculation using and = in a number sentence. *Explore the fact that division, like subtraction, cannot be done in any order (is not commutative). *Children learn that division is the inverse of. *They are then taught to use the and division facts to work out missing numbers. e.g; 2 = 4 *Children use division to solve more complex word problems in a context.
Year 3) use addition and subtraction facts to 00 fluently. use and division facts for the 3, 4, 8 tables Connect the 2, 4, 8 times tables through doubling. *Add a near multiple of 0 to a two-digit and then a three-digit number. Children should be taught to add numbers mentally, including: - a 3-digit number and ones - a 3-digit number and tens - a 3-digit number and hundreds *Secure mental methods by using a number line to model the method. e.g. 35 + 9 is the same as 35 + 20. Children need to be secure adding multiples of 0 to any two-digit and three-digit number including those that are not multiples of 0. 48 + 36 = 84 *Partition into hundreds, tens and ones Partition numbers and recombine. Count on by partitioning the second number only e.g. 36 + 53 = 36 + 50 + 3 = 86 + 3 = 89 +50 +3 36 86 89 *Add numbers with up to three-digits using formal written methods of columnar addition. *Horizontal expansion: 83 + 42 80 + 3 + 40 + 2 20 + 5 = 25 *Leading to columnar addition: 83 + 42 83 + 42 25 * Children should be taught to subtract numbers mentally, including: - a 3-digit number and ones - a 3-digit number and tens - a 3-digit number and hundreds *Find a small difference by counting up, particularly over a tens or hundreds boundary. *Secure mental methods by using a number line to model the method. e.g. 35-9 is the same as 35-20 +. *With practice, children will need to record less information for mental jottings and decide whether to count back or forward. It is useful to ask children whether counting up or back is the more efficient for calculations such as 57-2, 86-77 or 43-28 *Complementary addition 84-56 = 28 +4 +20 +4 56 60 80 84 *Add numbers with up to three-digits using formal written methods of columnar addition. *Horizontal expansion: 83-42 80 + 3-30 + 2 50 + = 5 *Leading to columnar subtraction: 83-42 83-32 5 *Children develop efficient mental methods, e.g. using commutativity and associativity (e.g. 4x2x5=5x5x2=20x2=240) and and division facts (e.g. 3x2 = 6, 6 3 = 2 and 2 = 6 3) to derive related facts (e.g., 30x2=60, 60 3=20 and 20 = 60 3) * Continue to understand as repeated addition and continue to use arrays to visualise and illustrate mental. *Grid method (partitioning) x 30 5 2 60 0 60+0 = 75 35x2 = 70 x 30 2 3 90 6 = 96 *Children develop efficient mental methods, e.g. using and division facts (e.g. 3x2 = 6, 6 3 = 2 and 2 = 6 3) to derive related facts (e.g., 30x2=60, 60 3=20 and 20 = 60 3) *Understanding division as sharing and grouping (TU U) 8 3 can be modelled as: How many 3 s make 8? 0 3 6 9 2 5 8 *Remainders 6 3 = 5 r Sharing - 6 shared between 3, how many left over? Grouping How many 3 s make 6, how many left over? e.g. 0 3 6 9 2 5 6
Year 4) Children practise mental methods for +/- with increasingly large numbers to aid fluency Recall and division facts for tables up to 2x2 *Add numbers with up to four-digits using formal written methods of columnar addition. *Horizontal expansion: 393 + 52 300 + 90 + 3 + 00 + 50 + 2 _ 400 + 40 + 5 = 545 *Leading again to columnar addition: 2083 + 452 2083 + 452 3535 *Extend to decimals in the context of money 20.83 + 4.52 20.83 + 4.52 35.35 *Wide range of 2-step problems in contexts, deciding which operations and methods to use and why. *Find a small difference mentally by counting up e.g. 5003 4996 = 7 Children should be encouraged to use known number facts to reduce the number of steps. *Subtract numbers with up to four-digits using formal written methods of columnar subtraction. *Horizontal expansion: *Leading again to columnar subtraction: 754 86 6 4 754-86 668 *Wide range of 2-step problems in contexts, deciding which operations and methods to use and why. *Children continue to practise recalling and using tables and related division facts to aid fluency. *Children practise mental methods and extend this to 3-digit numbers to derive facts e.g. 600 3 = 200 can be derived from 2 x 3 = 6 *Children begin to practise writing statements about the equality of expressions e.g. use the distributive law 39x7 = (30 x 7) + (9x7). This can be linked to their understanding of the grid method. 59 x 3 = x 00 50 9 3 300 50 27 300 50 + 27 477 Answer: 59x3 = 477 *Children practise combining their knowledge of number facts and rules of arithmetic to solve mental and written calculations e.g. 2x6x5 = 0x6 = 60 *Begin to use Long Multiplication (TUxU, HTUxU) 46 X 3 8 20 38 Answer: 46x3 = 38 46 X 3 8 20 300 _ 438 Answer: 46x3 = 438 *Children continue to practise recalling and using tables and related division facts to aid fluency. *Children practise mental methods and extend this to 3-digit numbers to derive facts e.g. 600 3 = 200 can be derived from 2 x 3 = 6 *Sharing and grouping 30 6 can be modelled as: i) grouping groups of 6 placed on no. line and the number of groups counted e.g. +6 +6 +6 +6 ii) sharing sharing among 6, the number given to each person *Remainders 4 4 = 4 = (0 x 4) + Answer: 4 4 = 0 r +6 0 6 2 8 24 30 +40 0 groups *Leading to Long Division (chunking) 72 5 = Answer: 72 5 = 4r2 +
Year 5) Children practise mental methods for +/- with increasingly large numbers to aid fluency e.g. 0632 + 2300 = 2932 2462-2300 = 062 Continue to use all the tables to calculate mathematical statements in order to maintain fluency *Add numbers with more than four-digits using formal written methods of columnar addition. * 22083 + 9452 22083 + 9452 3535 *Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy *Wide range of multi-step problems in contexts, deciding which operations and methods to use and why. *Extend to up to two places of decimals (same number of decimals places) and adding several numbers (with different numbers of digits). 72.8 +54.6 27.4 *Find a difference mentally by counting up e.g. 8006 2993 = 503 Children should be encouraged to use known number facts to reduce the number of steps. *Subtract numbers with more than fourdigits using formal written methods of columnar subtraction. *Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy *Wide range of multi-step problems in contexts, deciding which operations and methods to use and why. *Extend to up to two places of decimals (same number of decimals places) and subtracting several numbers (with different numbers of digits). *Children identify multiples and factors, including finding all factor pairs of a number and common factors of two numbers. *Children practise using the vocabulary of prime numbers, prime factors and composite numbers. *Children multiply numbers up to 4-digits by a - or 2-digit number. *Grid Method (partitioning) 2395x4 = x 2000 300 90 5 4 8000 200 450 20 8000 200 450 + 20 9670 Answer: 2395x4 = 9670 *Long Multiplication (ThHTUxTU; HTUxTU) 2 24 X 26 _ 744 2480 _ 3224 Answer: 24x26 = 3224 *Children identify multiples and factors, including finding all factor pairs of a number and common factors of two numbers. * Children divide numbers mentally drawing upon known facts * When working with remainders, the children express the quotients as fractions or decimal fractions 6 4 = 5 ¼ or 5.25 *Children divide up to 4-digits by a -digit number. *Long Division (chunking) *Short Division 847 5 = +40 0 groups 5 groups 256 7 = +20 20+0+6 = 36 Answer: 256 7 = 36r4 256 7 = 36 4 / 7 + Answer: 857 5 = 69r2 (69 2 / 5
Year 6) Children undertake mental calculations with increasingly large numbers and more complex calculations Continue to use all the tables to calculate mathematical statements in order to maintain fluency *Wide range of multi-step problems in contexts, deciding which operations and methods to use and why. *Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy (Children round answers to a specified degree of accuracy, e.g. to the nearest 0, 20, 50 etc. but not to a specified number of significant figures.) *As 5, continue to add numbers with more than four-digits using formal written methods of columnar addition. * 22083 + 9452 22083 + 9452 3535 *Extend to numbers with any number of digits and decimals with, 2 and/or 3 decimal places. 3.86 + 9.48 = 23.34 3.86 + 9.48 23.34 *Find a difference mentally by counting up e.g. 8000 2785 = 525 To make this method more efficient, the number of steps should be reduced to a minimum through children knowing: Complements to, involving decimals to two decimal places ( 0.6 + 0.84) Complements to 0, 00 and 00 *Wide range of multi-step problems in contexts, deciding which operations and methods to use and why. *Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy (Children round answers to a specified degree of accuracy, e.g. to the nearest 0, 20, 50 etc. but not to a specified number of significant figures.) *As 5, continue to subtract numbers with more than four-digits using formal written methods of columnar subtraction. * 22083 9452 22083-9452 263 *Extend to numbers with any number of digits and decimals with, 2 and/or 3 decimal places. 3.86-9.48 = 7 3.86-9.48 4.38 *Children continue to perform mental calculations, including with mixed operations and large numbers. * Children continue to practise identifying common factors, common multiples and prime numbers. * Grid method - Extend to decimals with up to two decimal places. 23.95x4 = x 20 3 0.9 0.05 4 80 2 4.5 0.2 20 3 0.9 + 0.05 23.95 *Children multiply numbers up to 4-digits by a 2-digit number. *Long Multiplication (ThHTUxTU) 3 2 524 X 36 _ 944 45720 _ 54864 Answer: 524x36=54864 *Short Multiplication 274x6 = 274 X 6 6446 4 2 274x6=6446 * Children continue to perform mental calculations, including with mixed operations and large numbers. * Children divide numbers up to 4-digits by a 2-digit number. They interpret remainders as whole number remainders, fraction, or by rounding, as appropriate for the context. *Long Division (chunking) 5 677-500 (00x5) 77-50 (0x5) 27-5 (x5) 2 2 / 5 = 4 / 5 Answer: 677 5 = 4 / 5 *Short Division 432 5 becomes: 45 r 5 496 Answer: 432 5 = 45 /