Mental strategies for addition and subraction

Counting forwards and backwards in mental calculations

We have seen that addition could be understood as counting on and subtraction as counting back, and that these ideas were strongly linked with movements along a number line. These ideas are also central to much mental and informal calculation. Doing additions and subtractions on a hundred square provides pupils with a strong image that supports the process of counting on and back in ones and tens. So 57 + 3 done by counting on in ones is associated with a movement to the right along a row: 57 … 56, 55, 54. Then 57 + 30 done by counting on in tens is seen as a movement down a column: 57 …67, 77, 87. And 57 – 30 done by counting back in tens is seen as a movement up a column: 57 …47, 37, 27.

Remember that confidence in counting backwards and forwards in ones, tens and hundreds is an essential prerequisite for effective mental calculation, so these skills should be taught specifically and reinforced frequently.

These are important strategies that can be extended to counting in hundreds and which we combine with other strategies when we become more proficient calculators. A good target for primary-school teachers is that their pupils should be able to count on or back in ones, tens and hundreds from any given number (up to three digits) by about the age of 9 years.