to give lessons;  to lecture;  to teach
As it's almost time to teach, all teachers left the meeting-place
He lectures twice a week
to go on to the next form;  to move up to the next form/grade;  to be admitted to the next year/class;  to be allowed into the next year / class
This boy cannot move up unless he works harder
To move up to the tenth grade
to moralize;  to sermonize;  to lecture;  to preachify
This soothsayer likes to sermonize about human behaviour
sanctimonious;  sententious;  didactic;  holier-than-thou