Solution:

The class has 7 children. The first child shakes hands with the other 6 children. The second child has already shaken hands with the first child, and so has to shake hands with only the other 5 children. In this manner, the second-last child has to shake hands with only one child, and the last child has already met all the children. Thus, the number of handshakes is

6 + 5 + ........ + 2 + 1 = 21.

If there were 7 children in the class, then there were 21 total handshakes.

Food for thought:

It is obviously assumed that each child shakes hands with every other child once and only once.

More importantly, is there a quick way to add
6 + 5 + ........ + 2 + 1 ?
Indeed, there is! It simply equals 6 × 7 / 2. Can you show why such a formula holds? Click here to find out more.