Elementary school contains the primary grades - K-4. and those rowdy kids in grades 5 through 7 as well. At least, they do in Canada. Some countries have weird junior high stuff going on that I'm not even going to touch.

After elementary school comes secondary school, aka high school.

In the United States, a school consisting of Kindergarten and Grades 1 through 5 and sometimes 6.

See middle school, junior high school, high school.