Advocating was very hard for me- I kept hoping that the school would observe DS and figure it out on their own. That turned out to be a bit of a disaster-- in all fairness, even I can't "figure it out" with DS and I am his mother, I after school him, and have all of his test scores:)
My best advice is to be straightforward with the school- bring convincing, but not overwhelming documentation (IQ and/or achievement test scores). Ask some straightforward, specific questions about differentiation (how, when, etc.).
DS doesn't go to public school but I (think) that schools who have several methods for differentiation, depending on a student, do it best. Subject acceleration, grade acceleration, pull out gifted, or separate school HG gifted. I know many districts don't deal with gifted very well, but due to a couple of near misses with a job transfer, I have interviewed a couple of different districts. There are some out there that are getting it right.
For my particular DS, he is in a Montessori school that is gradually transitioning to a traditional classroom. It's an ideal learning environment both for his needs and his particular learning style. We had to transfer schools to find it- but I don't think that's too unusual, Even we weren't aware of how advanced he was when he first started school- and some schools "do things like they do things" and aren't willing to adjust. That didn't work for us.