Calculating with zero

Once you understand zero and its effect in calculations, it is easy to overlook the uncertainty which pupils can feel when calculating with zero, especially if the assumption is made that they are already confident with this. An awareness of this issue means that it can easily be dealt with in a practical way and prevent future mistakes with zero in written calculations.

When pupils begin to add and subtract, it is generally in a very concrete way, physically moving objects such as counters, bricks or fingers. In this way, they are able to realise that, by adding or subtracting zero, the number of objects they began with doesn’t change and that if they begin with zero, they end up with the same number that they added on.

When multiplication is introduced, they then have to realise that 6 + 0 = 6 but 6 x 0 = 0. Again this can be done in a concrete way by asking them to give you six lots of zero bricks, zero bricks six times or six bricks zero times. This reinforces the concept that when zero is involved in multiplication, we always end up with nothing!

Similarly, in 0 ÷ 6, if a pupil is ‘given’ zero bricks and asked to share them between six children or put them into groups of six, they can see that there is nothing to physically share or group.

Once multiplication and division with zero has been introduced, it is important to revisit addition and subtraction with zero, encouraging pupils to use their fingers or other objects to physically reinforce and cement correct understanding. Fingers are invaluable as a convenient method of checking whenever a pupil encounters a zero and is uncertain of the answer!

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Although many of the calculations have an answer of zero, pupils must work carefully to correctly complete the calculations which do not!