It's wonderful that you have that kind of relatinship with your DD. Unfortunately, DS rarely lets me teach him anything. However, he will accept an explanation of why something is wrong if I can manage to cough it up in 60 seconds or so.

You are absolutely correct that "teaching to the SAT" would skipped way too much essential background knowledge for higher math. That's part of the reasoning why I agreed with DS that he should repeat Pre-Algebra at school this year even though he was able to get 100% on the ALEKS Pre-algebra over 3-4 weeks in the summer.