Free Higher Math Resources
I don't know if it would be recognized by researchers or your average teacher's college, but I personally split math into two main categories: arithmetic is the playing around with real numbers, and higher order math involves concepts, algebraic thinking, geometry, and most high school math. I always included both when I taught my own children and in the classroom, and tried to think of them as separate subjects to ensure that I didn't fall behind on one.
If you are trying to teach a comprehensive math curriculum, and not just arithmetic facts, I recommend visiting my Free Comprehensive Math Curriculum recommended page.
Placement Tests
If you aren't sure what skills your student already has, a placement test is the best place to start. This will tell you any "holes" they may have, and what they are already solid on.
It's not free, so you won't see it on this site, but I think that hands down the absolute BEST elementary school math curriculum is Math Mammoth. I used it will all three of my children, and may or may not have committed a little copyright fraud and used it as a supplement when I was teaching in the classroom (if you purchase it, it is, of course, only for personal use within one family). If you're trying to gauge your student's level as a parent, teacher, or tutor, I highly recommend using their placement tests (which are really just the end-of-year tests). They are LONG, so you do not want to make a child do them all in one sitting. Do a page or two at a time, while your student is fresh and rested. Then you can go back and fill in any gaps.
And, seriously, if you're going to purchase one educational resource, it should be Math Mammoth.