first grade vs primary school

first grade

noun
  • The first year of grade school, the period in school that comes after kindergarten and before second grade. Children usually begin first grade at age six. 

primary school

noun
  • A formal, obligatory kind of school that typically begins with nursery school or first grade and ends at fifth or sixth grade. 

How often have the words first grade and primary school occurred in a corpus of books? (source: Google Ngram Viewer )