intermediate school

from the GNU version of the Collaborative International Dictionary of English.

• noun A school having grades at a level between the lower primary grades and the upper secondary grades, being variously grades 4 through 6, or grades 7 through 9, etc.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun education A school for children that serves grades between primary school and high school. This grades vary from anywhere from grade 4 to grade 8.