Just to be clear: for this assignment I'm looking for your to demonstrate your understanding of both slow and fast shutter speeds. This means that you're going to need to shoot some shots that stop motion, and others that show motion. This will require you to find brightly lit areas for your fast shots, and low-light situations for your slow shutter shots
If you're doing long exposures, you need a tripod. You cannot handhold the camera without introducing handshake into your images.
If you attempt light painting, I don't want you doing it with fire. Use flashlights/LEDs/etc. Save long exposures using fire for your own photography on your own time and with a parent (ideally a parent who's also a volunteer firefighter).