Assignment-type pages do not have the option to restrict the number of times an item can be submitted that quiz-type pages do. In order to work around this, there are different options you can choose from depending on which you feel will best suit your classroom.
Use a Quiz-Type Page for an Assignment
If you wish to restrict the number of submissions for an assignment, you can always use a quiz-type page. For example, you can use the instructions area of the quiz to house the instructions for the assignment. Then, you can create one single question type that matches an assignment submission type as follows:
Quiz Question Type = Assignment Submission Type
1) File Upload question type = File Upload submission type
2) Essay question type = Text Entry submission type
3) Essay question type = Website URL submission type
Since you would not want to restrict the number of submissions in the platform for No Submission or On Paper submissions types, the only assignment submission type that you cannot recreate is the External Tool.
If you are creating a copy of an assignment that uses an External Tool, we recommend not using this in a quiz-type page. These external tools will not display the students' coding work, only their grade, in the course for the teacher to view. In order for this to be displayed, it must be used in an assignment-type page.
Only Count the First Submission for an Assignment
You can also set a policy in your classroom that you will only count the first submission for an assignment. This way, no matter how many times a student resubmits the assignment, you can just accept and grade the first submission.
You can toggle between and view the submissions by opening the student's assignment in SpeedGrader. When a student has submitted multiple submissions, you can view them by clicking the drop-down button.
Select the submission you'd like to view.
If you view an older submission, SpeedGrader will alert you that the submission you are viewing is not the most recent version.
If you have already graded an assignment that a student has resubmitted, you have the option of using the same grade for the resubmission without doing any additional work. To apply the same grade to the new assignment, click the "Use this same grade for the resubmission" link as shown below.