Both of your DDs sound a bit like mine.

DYS DD10 seems to have a love-hate relationship with math. While she hates extra math work and becomes bored in math very easily, she seems to take some pride in being "good at" math. While she is extremely strong verbally (via testing it is usually her extreme strength), she also tests well in math. She complains school math is too easy/boring, but AoPS...not sure that is working, either. She is in a class right now and is not thrilled about having to do any math work outside of school (which is not making homeschooling ever look like a great option, in case I was wondering

). To be fair, AoPS classes move at a pretty quick pace and require more work than I'd realized (not easy to sell during summer, but this seemed like the only time to really try it). I, too, am trying to figure out how to best help this kid!!!
DD, too, loves science...so I see math as important for her.
greenlotus - I think that DD would like the "friend," but I'm not sure who I'd recruit. Most of DD's friends on not even in her leveled math class at school.