Math Relearning/Pre-algebra

I'm using pre-algebra to refer to elementary and maybe middle school math, but I've learned that those years over not only algebra-related topics but also basic geometry, measurement, and statistics. I'm finding that these areas are interrelated, so I'm going to take a cue from elementary school curricula and cycle through them to make it easier to build the concepts on each other.

As I analyze the concepts of pre-algebra and decide how to order them, I have the sense I'm on a journey. My destination is the general math of everyday life and the more formal treatment of these areas covered in the upper grades, and I'm mapping a course through the terrains of the various areas to get there.

Several questions guide my route, directing my attention and reflection: What are numbers? How can we represent them in useful ways? What can we use them for? How can we work with them to achieve these purposes? How do we find the numbers we need in a situation?