That gifted doesn't mean the kid will answer all the questions, be the first one to be done with the work or readily show they are truly advanced to the teachers. My child likes to hide her abilities. You won't know she is gifted if you keep giving her grade level work because she checks out and appears slower/dumber (sorry couldn't think of a good word)than her peers. When she says day after day that recess is her favorite part of school, that just means that she finds the academic portions of the day really boring.
I personally don't even care if the school doesn't teach her much. I just don't want them to try to fit her in a box and kill her creativity and her love for learning and exploration.