Teaching Constructions can be fun and frustrating at the same time. A lot of students using a lot of different tools at once can cause chaos. My biggest advice would be do not just show them how to do them and then turn them loose. Solve every problem with them step by step making them all do the same thing at the same time. That way when one student asks a question or messes part of it up you can show the whole class the correction at once.
If you teach them the lesson and then turn them loose you will have one student on an angle bisector problem, another on a perpendicular bisector, and another on an segment bisector. So in reality you could have a bunch of kids all with sharp objects, all getting frustrated, and waiting for your attention. NOT GOOD COMBINATIONS!
Do your self a favor and work through all problems with them together! It is okay to have them do problems on their own but have them all doing the same one problem at the same time. Then when they are all done with that one problem move on.