Let me know if you figure it out because DD's teacher is having the same problem (although I don't think she thinks it's a problem or cares about improving). DD has to do the regular grade-level math curriculum but gets an "enrichment packet" with higher level thinking skills (NOT computations) to work on during the sections of math lecture that she already knows. This is nice, but she gets NO help with the math packet and no instruction on advanced concepts. She may as well be learning on her own at home.
For reading, during independent reading time she picks books that are about 2 grade levels ahead. She doesn't even have to answer questions. Again, no instruction. She still does the common core stuff.
And she gets advanced spelling words along with some of the other kids, but this can easily be done in any class. The teacher reads a word for one group, then the word for the other group, and goes down the list.
I think Davidson has a forum and resources for interested educators. Ah yes, try this link
http://www.davidsongifted.org/edguild/Article/Educators_Guild___Presentations_431.aspx
Isn't there a book on this? Teaching Gifted Kids in the Regular Classroom, or something?