I typed up a sheet with many text boxes with the number of students in my class. I make many copies and cut them apart and keep a basket full on my desk. I assign the children a number on the first day of school. I have 21 this year so I just cross off the extra.
The first student finished their work gets an empty folder and an assignment sheet. They write the name of the assignment and attach it to the folder. I like the slash clear folders so the kids can see the papers inside. As they pass in their work, they cross off numbers...easy! I can quickly put their papers in numeric order and make sure that I have every one's papers. I will sometimes make a list of missing assignments on the board with just the numbers.
I used to line them across my desk but found an expandable file holders that I keep on the side of my desk or counter. Look how neat my desk is now!!!!