The Teaching of Division at West Byfleet Junior School March 2016

1. Children need to understand that division can be sharing or grouping (repeated subtraction) 6÷2 What is 6 shared by 2? How many groups of 2 can be made from 6?

Division as Sharing In the first stages children naturally start their learning of division as division by sharing, e.g. 6 ÷2.

Division as Grouping (Repeated Subtraction) To become more efficient, children need to develop the understanding of division as grouping, e.g. 6 ÷2.

Division as Grouping (Repeated Subtraction)

2. Children need to have Mental Strategies Counting in steps Halving Doubling Multiplication tables facts up to 12x12 Relate division to multiplication – that division is the inverse of multiplication X and ÷ by 10, 100, 1000

3. Children are taught mental strategies and informal jottings before moving to formal written methods

53÷4= 13r1 Don’t forget the remainder!

-4 10 groups 2 groups 48 ÷ 4 = 12 Before starting the more formal written method of ‘chunking’, children should first use the repeated subtraction on a vertical number line. 48 ÷ 4 = 12 (groups of 4) leading to 48 ÷ 4 = 10 (groups of 4) + 2 (groups of 4) = 12 (groups of 4)

4. Formal written methods Repeated Subtraction (Chunking) Short Division Long Division

Division by Repeated Subtraction (Chunking) TU ÷ U Children will develop their use of grouping (repeated subtraction) to be able to subtract multiples of the divisor, developing the use of the 'chunking' method. Children should write their answer above the calculation to make it easy for them and the teacher to distinguish. Any remainders should be shown as integers, i.e. 14 remainder 2 or 14 r 2.

Division by Repeated Subtraction (Chunking) HTU ÷ U e.g. 196 ÷ 6 Any remainders should be shown as integers, i.e. 14 remainder 2 or 14 r 2. Children need to be able to decide what to do after division and round up or down accordingly. They should make sensible decisions about rounding up or down after division. For example 240 ÷ 52 is 4 remainder 32, but whether the answer should be rounded up to 5 or rounded down to 4 depends on the context. Children can start to subtract larger multiples of the divisor (e.g. 20x 30x).

Division Repeated Subtraction (Chunking) HTU ÷ TU Children may still use the menu box if required, but would also be expected to use larger multiples of the divisor (e.g. 20x, 30x, 40x). Children are taught to show remainders as fractions, i.e. if the children were dividing 32 by 10, the answer should be shown as 3 2 / 10 which could then be written as 3 1 / 5 in its lowest terms. 1x36=36 2x36=72 3x36=108 4x36=144 5x36=180 6x36=216 7x36=252 8x36=288 9x36=324 10x36=360

196÷6 (Repeated Subtraction/Chunking) 1x6=6 2x6=12 3x6=18 4x6=24 5x6=30 6x6=36 7x6=42 8x6=48 9x6=54 10x6=60 20x6=120 30x6=180

972÷36 (Repeated Subtraction/Chunking) 1x36=36 2x36=72 3x36=108 4x36=144 5x36=180 6x36=216 7x36=252 8x36=288 9x36=324 10x36=360

Short Division (Bus stop!!) Is a quick trick method to be used when children are secure in division and formal chunking methods

Short Division

5674÷4 (Short Division)

Key Facts 1x51=51 2x51=102 3x51=153 4x51=204 5x51=255 6x51=306 7x51=357 8x51=408 9x51= ÷51 (Short Division)

Long Division Key Facts; 1x14=14 2x14=28 3x14=42 4x14=56 5x14=70 6x14=84 7x14=98 8x14=112 9x14=126 10x14=140

748÷51 (Long Division) Key Facts 1x51=51 2x51=102 3x51=153 4x51=204 5x51=255 6x51=306 7x51=357 8x51=408 9x51=459

Children are encouraged to approximate before calculating and check whether their answer is reasonable.

By the end of year 6, children will have a range of calculation methods, mental and written. Selection will depend upon the numbers involved. Children should not be made to go onto the next stage if: they are not ready. they are not confident. Children should be encouraged to consider if a mental calculation would be appropriate before using written methods.

 Children need to know number and multiplication facts by heart and be tested regularly.  Children should always estimate first.  Thought should be given as to whether a mental method would be more appropriate.  Attention should be paid to language – referring to the actual value of the digits.  Answers should always be checked, preferably using a different method, e.g. the inverse operation.  Errors need to be discussed; problems should be diagnosed and then worked through – do not simply re-teach the method.  Children who make persistent mistakes should return to the method that they can use accurately until they are ready to move on.  When extending to harder numbers, refer back to expanded methods. This helps reinforce understanding and reminds children that they have an alternative to fall back on if they are having difficulties.