Share 6 objects in half.

Division Strategies These notes show the stages in building up to a compact, efficient method for division. Our aim is that children use mental methods when appropriate but for calculations that they cannot do in their heads they choose an appropriate written method which they can use accurately and with confidence. Time must be taken building up to the most efficient method to ensure complete understanding at each stage. Division should be taught alongside its inverse, multiplication. Reception Class Practical division Pupils should - Solve problems including halving and sharing. - Children will start by counting out all the objects and then sharing them into 2 equal groups. (halving) Share 6 objects in half. Reliably count objects up to 20. Recognise numerals up to 20. share, halve, total, equals. Children should: 1. Use practical objects such as dinosaurs, toy cars, toy sheep etc. 2. Use mathematical representations of numbers e.g. numicon, counters, unifix cubes 1

Class 1 Pupils should: - solve one-step problems involving division, by calculating the answer using concrete objects, pictorial representations and arrays, with support from the teacher. Grouping and Sharing: Practical Division Children should have plenty of opportunity to use objects, diagrams and pictorial representations to solve problems. Children should be able to find half of a group of objects by sharing it into 2 equal groups. They should also be able to share into 4 equal groups to find a quarter of a quantity. Share 8 into half. Count in multiples of 2s, 5s and 10s. halve numbers and quantities Find simple fractions of objects, numbers and quantities. Share, share equally, one each, two each, group, groups of, lots of, half, quarter. Share 10 objects into 2s 10 shared into 2s = 5 groups 2

Class 2 Pupils should consolidate understanding from the previous years. Pupils should be taught to: recall and use division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication ( ), division ( ) and equals (=) signs show that the division of two numbers has to be done in a specific order. solve problems involving division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts. Count in steps of 2,5 and 10. Grouping and Sharing: Practical Division Children should have plenty of opportunity to use objects, diagrams and pictorial representations to solve problems involving both grouping and sharing. Children should be taught to understand the difference between grouping and sharing (how many groups of 2 can you make with 6 sweets? Understand division as grouping. Understand that division is the inverse of multiplication. Solve one step problems involving division. Share these 6 sweets between 2 people). Children should be able to find half of a group of objects by sharing it into 2 equal groups. They should also be able to find 1/3, ¼, 2/4 and ¾ of a set of objects. Share, share equally, one each, two each, group, groups of, lots of, half, quarter, third. array, divide, division. e.g. Group these 12 sweets into 4s (how many groups of 4 in 12?): e.g. Share these 12 sweets equally between 4 people: 3

Repeated Addition: Arrays Children should be introduced to using arrays for division at the same time as using them for multiplication. e.g. 40 5 can be asked as how many 5s in 40? This can be linked back to grouping. Children can then draw this as an array: Example without a remainder 40 5 = 8 (Phrase this as how many 5s in 40? ) 4

Repeated Addition: Number lines Children should be taught to link their array to a number line using practical apparatus. This can then be recorded on an empty number line: 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 40 0 5 10 15 20 25 30 35 40 40 5 = 8 Children can use Cuisenaire or Numicon to work this out using grouping. Example with a remainder This should first be done practically using Cuisenaire or Numicon as above. 38 5 = 7 r 3 +5 +5 +5 +5 +5 +5 +5 +3 = 7 fives with a remainder of 3 0 5 10 15 20 25 30 35 38 5

Class 3 Pupils should consolidate understanding from the previous years. Pupils should be taught to: recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables. write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods. solve problems, including missing number problems division. Short Division When children have a secure understanding of all the previous steps from year 2, they can move onto short division. No remainder 81 3 Recall all multiplication facts and related division facts for 3x,4x and 8x. Understand place value and use this to divide and multiply by 10, 100 and 100. Relate division to fractions. Understand division and multiplication as the inverse. Find fractions of quantities where the numerator is 1. Children use their knowledge of the 3 times table to find, How many 3s in 80 where the answer is a multiple of 10? This gives 20 threes (since 30 threes would be too many), with 20 remaining (2 tens are carried over to the next column) Now ask: How many threes in 21?. Share, share equally, one each, two each, group, groups of, lots of, half, array, divide, division, fraction, inverse, remainder, quotient (the answer), divisor (number you are dividing by), dividend (number you are dividing into), decimal. 6

Class 4 Pupils should consolidate understanding from the previous years. Pupils should be taught to: recall multiplication and division facts for multiplication tables up to 12 12 use place value, known and derived facts to multiply and divide mentally, including dividing by 1 recognise and use factor pairs and commutativity in mental calculations Short Division ( consolidate from year 3) When children have a secure understanding of all the previous steps they can move onto short division. No remainder 81 3 Recall all multiplication facts and related division facts up to 12 x 12. Understand place value and use this to divide and multiply by 10, 100 and 100. Relate division to fractions. Understand division and multiplication as the inverse. Share, share equally, one each, two each, group, groups of, lots of, half, array, divide, division, fraction, inverse, remainder, Children use their knowledge of the 3 times table to find, How many 3s in 80 where the answer is a multiple of 10? This gives 20 threes (since 30 threes would be too many), with 20 remaining (2 tens are carried over to the next column) Now ask: How many threes in 21. Remainders: Once secure, children can use this to find remainders 284 6 = 47 r2 7

Pupils should consolidate understanding from the previous years. Class 5 Pupils should be taught to: multiply and divide numbers mentally drawing upon known facts divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context divide whole numbers and those involving decimals by 10, 100 and 1000 Pupils should consolidate knowledge of short division (see Class 4) Remainders: Once secure, children can use this to find remainders, then remainders as fractions and then remainders as decimals: Recall all multiplication facts and related division facts up to 12 x 12. Understand place value and use this to divide and multiply by 10, 100 and 100. Relate division to fractions. Understand division and multiplication as the inverse. Find fractions of qunatities where the numerator is 1. Share, share equally, one each, two each, group, groups of, lots of, half, array, divide, division, fraction, inverse, remainder, quotient (the answer), divisor (number you are dividing by), dividend (number you are dividing into), decimal. 284 6 = 47 r2 284 6 = 47 2 6 284 4 = 70.5 7 0. 5 4 2 8 2. 2 0 0 8

Pupils should consolidate understanding from the previous years. Class 6 Pupils should be taught to: divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context perform mental calculations, including with mixed operations and large numbers use their knowledge of the order of operations to carry out calculations involving the four operations Recall all multiplication facts and Long Division related division facts up to 12 x 12. When dividing by numbers larger than 12, children will need to use long division. Understand place value and use this to Formal Long Division divide and multiply by 10, 100 and 100. Relate division to fractions. Example with a remainder Example with the remainder as a fraction Example with the remainder as a decimal Understand division and multiplication as the inverse. 2 8 r 12 2 8 r 12 Understand fractions 15 4 4 3 2 15 4 4 3 2 Understand decimals and decimal 3 0 3 0 1 3 2 1 3 2 palce value. 1 2 0 1 2 1 2 0 1 2 Find fractions of quantities where the numerator and denominator could be any number. 432 15 = 28 r12 432 15 = 28 12 15 Children can simplify 12 15 to 4 5 This can then be simplified to short division. Children are encouraged to write out the multiples of the divisor. Eg. 15 = 15, 30, 45, 60, 75, 90, 105, 120. 2 8 r 12 15 4 4 3 2 9 2 8. 8 15 4 4 3 2. 0 3 0 1 3 2 1 2 0 1 2 0 1 2 0 0 432 15 = 28.8 Share, share equally, one each, two each, group, groups of, lots of, half, array, divide, division, fraction, inverse, remainder, quotient (the answer), divisor (number you are dividing by), dividend (number you are dividing into), decimal.

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