Use colored dots to make groups easy. Put a different colored dot on each desk in a group. When you need to have a student from each table do something, you can simply ask for all the green dots to bring you the papers from their group.
Instant feedback: As you go over each question as a class, have students colour in the square if they had that question wrong. Collect each strip afterwards and tape them to a manilla folder. Voila! Instant data on areas of difficulty to cover later.