Elementary school is a school for students in their first school years, where they get primary education before they enter secondary education. The exact ages vary by country. In the United States, elementary schools usually have 6 grades with pupils aged between 6 and 12 years old, but the age can be up to 10 or 14 years old as well. In Japan, the age of pupils in elementary school ranges from 6 to 12, after which the pupils enter junior high school.
Elementary school is usually only one part of compulsory education, especially in Western countries.
Students leave nursery school at 4 years old and start primary school for the next 7 years which would be primary 1 (ages 4 to 5) and so on until primary 7 which would be the last year at primary school (ages 10 to 11) then after that off to high school (ages 11 to 12.)