Year 6

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4) Divide

Formal Division as repeated subtraction, short and long division.
(Please view in full page in order to see correct formatting)
 

Year 4

Children will develop their use of repeated subtraction to be able to subtract multiples of the divisor.
Initially, these should be multiples of 10s, 5s, 2s and 1s ; numbers with which the children are more familiar.
 
To find    72 ÷ 5    we must subtract 5s repeatedly.              
 
   -2     -5     -5      -5       -5     -5     -5      -5      -5    -5      -5     -5      -5     -5     -5       
0      2      7      12      17     22     27     32     37     42     47     52     57     62     67     72
 
 There are 14 bundles of 5 with 2 left over, so    72 ÷ 5    =   14 r2
 
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       62 ÷ 8 is 7 remainder 6,
but whether the answer should be rounded up to 8 or rounded down to 7 depends on the context.

 

e.g. I have 62p. Sweets are 8p each. How many can I buy?

Answer: 7 (the remaining 6p is not enough to buy another sweet)

 or

Apples are packed into boxes of 8. There are 62 apples. How many boxes are needed?

Answer: 8 (the remaining 6 apples still need to be placed into a box)

 

Children should link and use their knowledge of times-tables with multiplication and division.

 

 

Year 5

Children will continue to use written methods to solve short division TU ÷ U.

Children can start to subtract larger multiples of the divisor, e.g. 30x

 

Short division HTU ÷ U

196 ÷ 6

                         0 3 2 r 4

6 ) 1 19 16

 

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.

 

Division should be taught ÷ sign as well as / and should be short division for most pupils and Long division for the more able.

 

In Short division, when the divisor will not go into the first (or second etc.) digit, a zero or line must be put above that digit e.g.

                  0  9  2  r3

        4)     3 37 11

or continued through to a decimal answer by including decimal points and zeros

                0  9  2.  2  5

        4) 3 37 11. 30 20 

 

Appropriate reoccurring symbols should be taught

                    .                                                       .   .

3.333etc =3.3             and                2.245245245etc = 2.245

 

Any remainders should be shown 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 it’s lowest terms).

 

 

Year 6

 

Some children will learn long division. (The numbers in red are 'brought down' from the question.)

 

     0 9  2. 2  5

 4) 3  7   1. 0

  - 3  6  

        1  1

   -        8

            3   0

        -   2   8

                 2  0

              - 2   0

                      0

 

Children will continue to use written methods to solve short division TU ÷ U             HTU ÷ U             and              HTU ÷ TU.
 
They will be encouraged to work through to decimal places rather than leaving remainders.

 

Children can simplify division calculations by understanding that

260 ÷ 16         is equal to       130 ÷ 8       and also equal to       65 ÷ 4

 

By the end of year 6, children will have a range of calculation methods, mental and written.

 

Children should not be made to go onto the next stage if:

1) they are not ready.

2) they are not confident.

Children should be encouraged to approximate their answers before calculating.

Children should be encouraged to check their answers after calculation using an appropriate strategy.

Children should be encouraged to consider if a mental calculation would be appropriate before using written methods.

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