I'm starting off with the order of operations because I feel that this is the beginning of math. Yes, there are the actual operations of addition, subtraction, multiplication, division, and exponents. Those are what I consider pre-math.
The purpose of the order of operations is to simplify an expression (hint, if you ever come across a question on a homework or test that says "simplify" or "simplify the expression," this is what it is talking about). In other words, we want to make something ugly into something pretty.
In order to do that, we use the order of operations, which is:
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction