Allow different start/end times for each group

Could you allow teachers to activate quizzes between a certain period, with different periods for each group of students. For example, say the class is from 8:00 - 8:40 (Yeah we have 40 minute periods...) Could you make is so the teacher can have the quiz active to a group of students during that time period? That way the teacher can monitor. Then have a different open and close time for another group of students on the course.