Mental strategies for addition and subraction

How multiples of 5 help in mental additions and subtractions

Multiples of 5 (5, 10, 15, 20, 25, 30, …) are particularly easy to work with. Young children learn to relate simple additions and subtractions to fives. For example, a 5-year-old might think of 6 + 7 as ‘5 and 1 and 5 and 2’, and proceed by first combining the fives. This tendency to relate numbers to multiples of 5 is no doubt related to the way our early experience of counting on our fingers leads us to perceive 6, 7, 8 and 9 as ‘5 and some more’.

It is then reinforced by our experience of handling money. We can exploit this confidence with multiples of 5 in many additions and subtractions done mentally. For example, 37 + 26 could be related to 35 + 25 which we would probably find much easier. This can be taught as a specific strategy. Here are some examples, written out in full to show what would, of course, be a mental process:

37 + 26 = (35 + 25) + 2 + 1 = 60 + 2 + 1 = 63

77 + 24 = (75 + 25) + 2 – 1 = 100 + 2 – 1 = 101

174 – 46 = (175 – 45) – 1 – 1 = 130 – 1 – 1 = 128