When I first started, I didn't think about what concepts I wanted to teach. I gave problems. The students learned mental models as they solved the problems. They didn't know what they had learned, and I didn't know what they learned, but as long as they learned, everything was fine.
However, in the course of teaching, I occasionally started with a concept I wanted to teach, and designed my exercise to teach that concept. This got me started on a list of concepts that I teach. And occasionally, I realized afterward what concept I was trying to teach. That added to my list. When I realized I had a list of basic math concepts, I tried to fill in my list.
About My Curriculum
One list below is the list of concepts I would try to teach to a second-grader.
Notice that, at least for the second grader, there aren't many math concepts on the list -- the current list has 14. Perhaps I lack insight. Perhaps there simply aren't that many to teach. Obviously, the list will be longer when I add older children.
However, no matter what age I am teaching, I teach these concepts. Most people are not as good on these concepts as they should be. These are basic concepts. They are important. They usually are not taught well, so most people usually need (at least) some strengthening in the concept.
First Things First: Enjoyment and Aha