There are several reasons why mistakes occur when subtraction requires exchanging. The most common is due to treating subtraction as if it were commutative and switching the digits around instead of exchanging. This is particularly common when zero is in the top line of the calculation.

Once pupils understand the need to exchange, the exchanging may be incorrectly carried out.

In these two examples, the exchanged ten has been incorrectly written to the right of the 3 units, which transforms those 3 units into 3 tens, making 31. In the first example, this mistake may go unnoticed, as the pupil has read the 31 as ‘thirteen’ and thus got the correct answer. This indicates an underlying insecurity with teen numbers. In the second example, the pupil has continued to calculate 31 – 5 = 26, leading to a complete loss of place value.

Here, the exchanged ten has been added to the 3 as if it were a unit. This means that exchanging has to be repeated, with a further 1 being added to the units, before the subtraction is possible.

When such mistakes are made, using base 10 equipment to physically move the ten and see the result of doing so, will reinforce the understanding of how place value is retained in the written calculation.

See our How To video for an example of this.