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Brough Primary School Division Calculation Policy DIVISION STEPS EYFS Early Learning Goal Children develop an awareness of number names through their enjoyment of action rhymes and Children count reliably with numbers from one songs that relate to their experience of numbers. to 20, place them in order and say which Children need to : number is one more or one less than a given •Knows that numbers identify how many objects number. Using quantities and objects, they add are in a set. and subtract two single-digit numbers and count • Compares two groups of objects, saying when on or back to find the answer. They solve they have the same number. problems, including doubling, halving and • Create opportunities for children to separate sharing. objects into unequal groups as well as equal groups. BIG MATHS ‘Learn Its’ Term 1 1 + 1 = 2, 2 +2 = 4 Term 2 5 + 5 = 10, 4 + 4 = 8, 3 + 3 = 6 Term 3 2 + 1 = 3, 2 + 3 = 5 (to prepare for inverse – switchers) Say multiples of 10 EYFS vocabulary Twenty….nineteen…..eighteen ….to zero, hundred…ninety…..eighty….to zero, count, count back (from, to) count in ones, twos... tens..., how many times? Even. Pair, pattern, estimate ,halve, sort, equal, sets of, share DIVISION STEPS Year 1 Count on or back in ones, twos, fives and tens and use this knowledge to derive the multiples of 2, 5 and 10 to the tenth multiple Solve one step practical problems involving division of 2, 5 or 10 with support Mental Methods Practical Methods Doubling and Halving Find half of even numbers to 12, including it is hard to halve odd numbers Begin to count in 2s, 5s, and 10s Spider counts in tens (the ones stay the same) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Grouping Begin to use visual and concrete arrays and ‘sets of’ objects to find the answers to such questions as ‘How many towers of 3 can I make with twelve cubes?’ Sharing Find half of even numbers by sharing E.g. find half of 14 cubes by giving one each repeatedly to two children Key Vocabulary problem, solution, calculate, calculation, number sentence, answer, method, explain, money, coin, pence, penny, pound, pay, change, buy, sell, price, spend, number sequences, count back (from, to) in ones, twos...fives….. tens...less, few, many, odd, even, how many times? pair, multiple, half, halves, share DIVISION STEPS Year 2 Count on or back in ones, twos, threes, fives and tens and use this knowledge to derive the multiples of 2,3, 5 and 10 to the tenth multiple Solve problems involving division Calculate mathematical statements for division and write them using the ÷ and = signs Show that division of one number by another cannot be done in any order (commutative) Mental Methods Count in 2s, 5s and 10s Practical/Written Methods Say how many rows in a given array e.g. How many rows of 5 are in an array of 3 × 5? Doubling and Halving Find half of numbers up to 40 realising that half of and odd number gives a remainder of 1 or an answer containing a half E.g. half of 11 Begin to count in 3s Using fingers, say where a given number is in the 2s, 5s or 10s count e.g. 8 is the fourth number when I count in 2s Relate division to grouping e.g. How many groups of 5 in 15? Grouping Relate division to multiplication by using arrays or towers of cubes to find answers to division. e.g. How many towers of five cubes can I make from fifteen cubes? _ x 5 = 15 and also as 15 ÷ 5 = _ Begin to halve numbers to 40 and multiples of 10 to 100 Find 1/2, 1/3, 1/4 and 3/4 of a quantity of objects and of amounts (whole number answers) 24 divided into groups (chunks) of 6. There are 4 groups of 6 in 24. Using Number Facts Sharing Begin to find a quarter of a quantity using sharing Know half numbers to 24 Know x2, x5, x 10 division facts Begin to know x3 division facts ÷ = signs and missing numbers (Switchers and Fact Families- Big Maths) 6÷2= =6÷2 6÷=3 3=6 ÷ ÷2=3 3=÷2 ÷=3 3=÷ 2x3=6 3x2=6 e.g. find a quarter of 16 by sorting the piles into four piles Find ½, ¼, ¾ of small quantities Key Vocabulary (Y2) calculate, calculation, inverse, answer, explain, method, sign, operation, symbol, number sentence, number line, mental calculation, written calculation, informal method, jottings, diagrams, pictures, images, grouping, halve, share, share equally, one each, two each, three each... group in pairs, threes... tens , equal groups of, ÷ sign, divide, divided by, divided into, left ,left over, remainders DIVISION STEPS Year 3 Recall and use division facts for the 2, 3, 4, 5, 8 and 10 times-tables Divide two-digit numbers by one -digit numbers Solve problems, including missing number problems with positive integer scaling problems and correspondence problems which n objects are connected to m objects Mental Methods Know by heart all the division facts derived from the ×2, ×3, ×4, ×5, ×8 and ×10 tables Written Methods Perform divisions just above the 10th multiple using horizontal or vertical jottings and understanding how to give a remainder as a whole number e.g. 41 ÷ 4 = 10 r1 Divide whole numbers by 10 or 100 to give whole number answers +40 +1 10 groups Recognise that division is not commutative e.g. 16 ÷ 8 does not equal 8 ÷ 16 Use place value and number facts in mental division e.g. 84 ÷ 4 is half of 42 Divide larger numbers mentally by subtracting the 10th multiple as appropriate, including those with remainders e.g. 57 ÷ 3 is 10 + 9 as 10 × 3 = 30 and 9 × 3 = 27 Halve even numbers to 100, halve odd numbers to 20 78 35 4 39 Use division facts to find unit fractions of quantities and begin to find non-unit fractions of quantities e.g. ¾ of 48 is 3 x (48 ÷ 4) Halve even numbers up to 50 and multiples of 10 to 100. Perform divisions within the tables including those with remainders e.g. 16 ÷ 3 0 3 6 9 12 15 16 Relate division to multiplication with missing digits e.g. x 5 = 30 is the same calculation as 30 ÷ 5 = ? Key Vocabulary problem, solution, calculate, calculation, inverse, answer, method, explain, predict, estimate, reason, operation, symbol, number sentence, equation, mental calculation, written calculation, informal method, jottings, number line, pound ( ), penny/pence (p), note, coin, units of measurement and their abbreviations, share, share equally ,one each, two each, three each. group in pairs, threes... tens , equal groups of ,÷ sign, divide, division , divided by, divided into, left, left over, remainder, inverse DIVISION STEPS Year 4 Recall and derive division facts up to 12 × 12 Use place value, known and derived facts to divide mentally, including x by 0 and 1 Recognise and use factor pairs and commutativity in mental calculations Mental Methods Know by heart all the division facts up to 144 ÷ 12 Divide whole numbers by 10, 100, to give whole number answers or answers with 1 decimal place Divide multiples of 100 by 1-digit numbers using division facts e.g. 3200 ÷ 8 = 400 Use place value and number facts in mental division e.g. 245 ÷ 20 is half of 245 ÷ 10 Divide larger numbers mentally by subtracting the 10th or 20th multiple as appropriate e.g. 156 ÷ 6 is 20 + 6 as 20 × 6 = 120 and 6 × 6 = 36 Written Methods Use a written method to divide a 2-digit or a 3-digit number by a 1-digit number Numberline chunking e.g. 64 ÷ 4 = 10 groups of 4 0 Column Chunking e.g. 64 ÷ 4 = 16 65 3 68 Begin to halve amounts of money e.g. half of £52·40 is £26·20 40 1 group of 4 = 16 groups of 4 60 64 64 - 40 (10 groups of 4) 24 - 20 ( 5 groups of 4) 4 - 4 ( 1 group of 4) 0 Short division method 98 ÷ 7 = 14 53 ÷ 4 = 14 r 2 ( Give remainders as whole numbers) Refer to as a ‘chocolate box’ (There are 98 chocolates in a box to share between 7 people. How many will they get each?) e.g. Find halves of even numbers to 200 and beyond using partitioning 136 5 groups of 4 14 7 9 28 1 4r2 4 5 18 Begin to reduce fractions to their simplest forms e.g. 6/9 = 2 /3 or ¼ Find unit and non-unit fractions of larger amounts e.g. 7/8 of 56 is 7 x (56 ÷ 8) Divide whole numbers by 10 and 100 to give whole number answers or answers with 1 decimal place e.g. 643 ÷ 10 = 64.3 Find unit fractions of amounts e. g. 2/3 of 60 = 40 Key Vocabulary (Y4) calculate, calculation, equation, operation, symbol, inverse, answer, method, explain, predict, reason, reasoning, pattern, relationship, decimal, decimal point, decimal place, pound ( ), penny/pence (p), units of measurement and abbreviations, degrees Celsius share, share equally ,halve, one each, two each, three each... group in pairs, threes... tens ,equal groups of, divide, division, divided by, divided into, divisible by, remainder, factor, quotient, inverse DIVISION STEPS Year 5 Identify multiples and factors Know and use vocabulary of prime numbers, prime factors and composite(non-prime number) Divide numbers mentally using known facts Divide numbers up to 4 digits by a 1-digit number using formal written method of short division and interpret remainders appropriately for the context Divide whole numbers involving decimals by 10, 100 and 1000 Solve ÷ problems using knowledge of factors and multiples, squares and cubes Solve ÷ problems including scaling by simple fractions and problems involving simple rates Mental Methods Know by heart all the division facts up to 144 ÷ 12 Divide whole numbers by 10, 100, 1000, 10 000 to give whole number answers or answers with 1, 2 or 3 decimal places Use doubling and halving as mental division strategies e.g. 34 ÷ 5 is (34 ÷ 10) × 2 Use knowledge of multiples and factors, as well as tests for divisibility, in mental division e.g. 246 ÷ 6 is 123 ÷ 3 e.g. We know that 525 divides by 25 and by 3 Halve amounts of money by partitioning e.g. 1/2 of £75·40 = 1/2 of £75 (£37·50) plus half of 40p (20p) which is £37·70 Divide larger numbers mentally by subtracting the 10th or 100th multiple as appropriate e.g. 96 ÷ 6 is 10 + 6, as 10 × 6 = 60 and 6 × 6 = 36 e.g. 312 ÷ 3 is 100 + 4 as 100 × 3 = 300 and 4 × 3 = 12 Know tests for divisibility by 2, 3, 4, 5, 6, 9 and 25 Written Methods Short division of 3- and 4-digit numbers by 1-digit numbers e.g. 145 ÷ 4 3 6r1 4 1 425 Give remainders as whole numbers or as fractions Find non-unit fractions of large amounts e.g. 3/5 of 265 is 3 x (265 ÷ 5) = 159 Choose the most efficient method in any given situation Divide whole numbers by 10, 100 or 1000 to give answers with up to 1 decimal place Use an efficient written method to divide numbers ≤ 1000 by 1-digit numbers Know square numbers and cube numbers Reduce fractions to their simplest form Key Vocabulary (Y5) calculate, calculation, equation, operation, symbol, inverse, answer, method, strategy, explain, predict, reason, reasoning, pattern, relationship, decimal, decimal point, decimal place, estimate, approximate, pound ( ), penny/pence (p), units of measurement and abbreviations, degrees Celsius share, share equally , halve, one each, two each, three each... group in pairs, threes... tens, equal groups of, divide, divided by, divided into, divisible by, remainder, factor, quotient, divisible by, inverse DIVISION STEPS Year 6 Divide numbers up to 4 digits by a 2-digit whole number using formal method of long division or short division, and interpret remainders as whole number remainders, fractions, or by rounding up or down appropriately Identify common factors, common multiples and prime numbers Use knowledge of the order of operations to carry out calculations involving the four operations Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy Multiply simple pairs of proper fractions, writing the answer in the simplest form Divide numbers by 10, 100 and 1000 giving answers to 3 decimal places Divide proper fractions by a whole number Mental Methods Know by heart all the division facts up to 144 ÷ 12 Divide whole numbers by powers of 10 to give whole number answers or answers with up to 3 decimal places Identify common factors, common multiples and primes numbers and use factors in mental division e.g. 438 ÷ 6 is 219 ÷ 3 which is 73 Use tests for divisibility to aid mental calculation Use doubling and halving as mental division strategies, for example to divide by 2, 4, 8, 5, 20 and 25 e.g. 628 ÷ 8 is halved three times: 314, 157, 78·5 Divide 1- and 2-place decimals by numbers up to and including 10 using place value e.g. 2·4 ÷ 6 = 0·4 e.g. 0·65 ÷ 5 = 0·13 e.g. £6·33 ÷ 3 = £2·11 Halve decimal numbers with up to 2 places using partitioning e.g. Half of 36·86 is half of 36 (18) plus half of 0·86 (0·43) Know and use equivalence between simple fractions, decimals and percentages, including in different contexts Recognise a given ratio and reduce a given ratio to its lowest terms Written Methods Use short division to divide a number with up to 4 digits by a 1-digit or a 2-digit number e.g. 145 ÷ 4 3 6r1 4 1 425 Use long division to divide 3-digit and 4-digit numbers by 2-digit numbers e.g. 4176 ÷ 13 300 + 20 + 1, r1 4176 ÷ 13 = 321 r 3 13 4176 - 3900 276 - 260 16 -13 3 Give remainders as whole numbers or as fractions or as decimals Use place value to divide a 1-place or a 2-place decimal number by a number ≤ 12 using multiples of the divisors e.g. 3· 65 ÷ 5 as (365 ÷ 5) ÷ 100 = 0·73 Divide proper fractions by whole numbers Use an efficient written method, involving subtracting powers of 10 times the divisor, to divide any number of up to 1000 by a number ≤ 12 e.g. 836 ÷ 11 as 836 – 770 (70 × 11) leaving 66 which is 6 × 11, giving the answer 76 Key Vocabulary (Y6) calculate, calculation, equation, operation, symbol, inverse, answer, method, strategy, explain, predict, reason, reasoning, pattern, relationship, decimal, decimal point, decimal place, estimate, approximate, pound ( ), penny/pence (p), units of measurement and abbreviations, degrees Celsius, halve, share, share equally, one each, two each, three each... group in pairs, threes... tens, equal groups of, divide, division, divided by, divided into, remainder, factor, quotient, divisible by, inverse, integer