Representing a situation or solving a problem pictorially means doing so using drawings or representations of actual objects. A visualization of the situation and solution takes place rather than an actual concrete experience of the situation and solution.   (Learn Alberta)

When performing the same operation with the same value to both sides of the equation the equality is preserved. AB ED Parent Communication

In order for equations to be equivalent, the same operations have to be performed on each side where the value of the variable does not change. E.g., 3n + 1 = 7 and 3n = 6 are equivalent equations because 1 is subtracted from each side in the first equation to make the second equation. This is called ‘preservation of equality’. NewFoundland Grade 6 Math Curriculum Guide, page 108

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.  

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 results in a total of twenty-one apples.
• Thirteen blocks of concrete plus eight blocks of concrete results in a total of twenty-one blocks of concrete.
• Thirteen houses plus eight houses results in a total of twenty-one houses.

And so on.       (Learn Alberta)