The Assignment tool allows you to keep manage the announcing and collecting of assignments in the class.
You can set Assignments for different modes of submissions under the "Student Submissions" option. When you select "Inline and Attachments", students can submit assignments electronically. You can also set this option for "Non-electronic".
When you create the assignment, there is a box to check to have scores posted to the Gradebook under the "Grading" option.