Smyrna School District - General district information and links to individual school sites. John Bassett Moore Intermediate School - Events, clubs and staff directory. Smyrna High School - News and links. North Smyrna Elementary School - Includes staff directory, school calendar, lunch menu, handbook, and information on the library. Smyrna Elementary School - Includes staff directory, school calendar, lunch menu, supplies list, and information on the library. Smyrna Middle School - Includes staff directory, school calendar, lunch menu, sports schedule, and information on the library.