## Long division

When attempting long division, there are many opportunities for pupils to make mistakes.

The first difficulty that pupils face is a seemingly long and complicated process, which bears little resemblance to short division. Confidence can be promoted by showing how long division works in exactly the same way as short division, just with a bit of extra recording to make it easier to calculate with the larger numbers involved. This can be seen in our 'Linking short division to long division' video. If the link to short division isn’t made, pupils may attempt to partition and calculate with the divisor as they would in column multiplication. Here the pupil has divided just by the units digit and has then been unsure how to divide by the tens. Pupils may misuse commutativity when dividing, as this will initially seem to be an easier calculation to work out. Here the pupil worked out 13 ÷ 4 (instead of 4 ÷ 13) and then 13 ÷ 11. This then led to 13 ÷ 29, at which point the pupil switched back to 29 ÷ 13.

The aspect of long division that pupils can find the most difficult, is calculating the multiples of the 2-digit divisor. In addition to making mistakes with this, pupils may become so focussed on calculating the multiples that they forget to write the actual answer above the box as they progress.

If mistakes are consistently made in the column subtraction part of the calculation, a subtraction diagnostic sheet can be used to identify where support is needed. Once the subtraction is completed, pupils may not see this answer as the remainder and can forget what to do next. This leads to confusion about where to look for the next number to divide. Again, highlighting the link with short division will help pupils proceed correctly. 