A. k. a. elementary school or primary school.
A school which encompases the first six to eight grades of a child's education (in the US, at least). The word "grammar" is used not in the sense of "the study of how words are strung together to make sentences"; but "grammar" meaning "dealing with the basic principles of knowledge".
I've always liked the term "grammar school" better than "elementary school" or "primary school" because it's got that nice, archaic Laura Ingalls Wilder/Anne of Green Gables ring to it.
Grammar school is fun. A lot funner than Junior High School or High School. I mean homework usually involves coloring with Crayons or making stuff with Play-Doh. In retrospect, the only bad thing about grammar school was that I didn't get to play with girls enough. Oh well. Priorities change.