Some of the CC math I've heard discussed is monkey motion intended to teach by an attempt to systematize "tricks of the trade" which I believe are best learned after a student has solid experience with proven, straightforward methods of obtaining correct answers.
The problem I see with doing it the other way around is proving correctness of the tricks of the trade brings in more overhead than is necessary.
For example, by "number sense" I know 2.99567 times 3.0004012 is going to be quite close to 9. Question: How do you show this "number sense" answer to be correct without actually calculating the answer? It's easy for me, but I don't think I'll show my proof to my third grader nephew.
