Give group members the technical permissions to upload content to a folder that only their group can access.
Select the Resources tool from the Tool Menu of your site.
Use Actions > Edit Details to access the Availability and Access area for a folder. See How do I create a group folder in Resources? for complete steps.
After assigning the folder to a specific group, change the permissions of the folder to allow students (that can access the folder) to upload and edit content.
Use Actions > Edit Folder Permissions to access the Permissions area for the folder. See How do I allow all students to upload content to a specific folder? for complete steps.