On a more serious note: Other people have recommended very good books that will teach you problem solving so I would like to give you a feeling of what "real" math is. In high school and in most University degrees you only do applied math => how to use math to solve this or that problem. The more math you know, the more tools you have to solve your problem. For a given problem: could I solve it with a partial differential equation? with a Bayesian approach? etc. You can see how the more math you know, the wider your search for a solution can be.
However, most people never get to do "pure" math => to create your own new math. When you read a book or attend to a class you only get to see the finished product. When you see a finished building, they have removed all the scaffolding, the cranes, and all the other tools that were used to build it. If you spend some time creating your own new math you will get a very deep understanding of what math is and it will widen your learning abilities.
Of course I don't expect a high school student to create something truly new, this is just a learning exercise. I just want to provide a 'feeling', I won't be formal or rigorous.
Definition 1: An object of class TIAM is composed of an integer and a set. The set can be empty or contain letters from the English alphabet with no duplicates.
Definition 2: Operation "+" This operation will take two TIAM objects and produce a new TIAM object. The integer part of the new object will be the sum of the cardinalities of the sets. The set part of the new object will be the union of the two sets with all the letters shifted as many places as specified by the integer part of the second TIAM object.
Example 1: [1, {a,b,c}] + [2, {c, d}] = [cardinal({a,b,c}) + cardinal({c,d}), {a,b,c}U{c,d}>>2] = [3+2,{a,b,c,d}>>2] = [5, c,d,e,f]
Example 2: [0,{z}] + [1, {}] = [cardinal({z}) + cardinal({}), {z}U{}>>1] = [1+0,{z}>>1] = [1,{a}]
* TIAM objects are closed under +. (See http://en.wikipedia.org/wiki/Closure_%28mathematics%29). Do you understand why? Can you prove it?
* Is the operation + conmutative or non conmutative? (See http://en.wikipedia.org/wiki/Commutativity) Why? Can you prove that it is / it isn't?
* Can you find a neutral element? (See http://en.wikipedia.org/wiki/Identity_element) I mean, can you find a TIAM object (I will call it TIAM-ZERO) so that TIAM-A + TIAM-ZERO = TIAM-A for any given value of TIAM-A?
Etc.
This is just an example, try to build your own stuff and reason about it. Ask yourself questions about it and answer them. Once you get used to this kind of thinking, you will learn faster and deeper.