to say what level of a quality something has, or what standard it is
grade something according to something
Pencils are graded according to softness.
All the parks are regularly checked and graded by tourist board inspectors.
2 especially American EnglishSE
to give a mark to an examination paper or to a piece of school work [= mark]:
Ted is grading papers in his office.
to give a particular rank and level of pay to a job