Representing a situation or solving a problem symbolically means doing so using an abstract representation.

The number 13 is a representation for thirteen of any object. It can represent 13 apples, 13 blocks of concrete, 13 houses, etc.

In solving 13 + 8 symbolically, one might use the traditional addition approach shown below.

At no time are any actual "concrete" thirteen or eight objects used to represent the situation, nor are there pictorial representations of objects. 13, 8 and 13 + 8 = 21 are symbolic representations leading to the conclusion that:

• Thirteen apples plus eight apples resuls in a total of twenty-one apples.
• Thirteen blocks of concrete plus eight blocks of concrete resuls in a total of twenty-one blocks of concrete.
• Thirteen houses plus eight houses resuls in a total of twenty-one houses.
• And so on.

Solving a problem symbolically is often the most efficient way to solve a problem.

As well as symbolically, most situations or problems can also be represented concretely and pictorially.