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You may wish to explore the private school option. Possibly if enough other parents also choose to do this, it may provide an opportunity to carpool. It may also signal to the public middle school that additional challenge is needed to keep students learning and prevent planting the seeds of underachievement.

The extra length of commute may reduce the amount of time available for your daughter's extracurricular activities.

As a family you may wish to discuss the options you are most comfortable with (those which help you feel most resilient versus stressed to the max and unable to handle the next curve ball life may toss at you). Determine which options will stay on the table for further discussion and consideration.

It is great to be prepared with lists of questions to compare each potential school. The questions to ask when seeking information that will help predict a good educational fit may be different for each family. In general, when selecting a school parents may want to ask about:
1) anything that you have been trying to put in place in your children's current learning environment,
2) details for anything described on the potential new school's website,
3) anything mentioned or observed during the school tour.

A parent may wish to consider their children's current learning experience and ask questions that would help them compare/contrast how the students' learning experience in the new school would be the same/different from what they have now. For example: How are children grouped for instruction? Would it be easier to advocate for having the child's needs met at the new school?

There are more ideas in the book "A Parent's Guide to Gifted Children", which has Chapter 14 dedicated to "Finding a Good Educational Fit".

There are lists of considerations and questions for choosing a school found online at Davidson database, greatschools website, and other websearch results.

Information at the following links on the Davidson Database may be of interest...
1- Advocacy - Working with your child's school http://www.davidsongifted.org/db/Articles_id_10558.aspx
2- Choosing the right school for your gifted child http://www.davidsongifted.org/db/Articles_id_10511.aspx
3- Basic educational options for gifted children http://www.davidsongifted.org/db/Articles_id_10270.aspx
4- Guidebook - Advocating for Exceptionally Gifted Young People, plus lists of other resources http://www.davidsongifted.org/db/browse_resources_165.aspx

If it does not seem like a good fit, you may wish to visit/tour other schools, have your daughter shadow, and work toward choosing the learning environment with the best (or least-worst) "fit".