If you want to begin solving real math problems in your head, I think you would enjoy reading Lewis Carroll's "The Mathematical Recreations of Lewis Carroll: Pillow Problems and a Tangled Tale (Dover Recreational Math)".
These are math problems that he thought up and solved while lying in bed. It has inspired me to do similar things. One thing it has inspired me to do is to never write down any of my solutions to problems herebefore entering them; instead, I work them out as I enter them.
You can find it here: