Canvas assignments, quizzes and graded discussions can be assigned to everyone, a section of students or individual students in a course. By default, Canvas will set ‘Everyone’ in the “Assign to” field. Please see an example in the screenshot below. 

assign to

“Assign to” in Canvas

To add another section with a different due and availability dates, click the Add button, then type and select the name of a section in the new Assign to field. You can add individual students using the same way. Please see an example in the screenshot below.

Assign to

Assign to a section with different dates