I'd probably build a solar furnace anyway, just to freak the teacher.
"Okay, let's place the beaker at the focal poi... It's melting... My hand! My hand!"
So, what you need is something which takes advantage of inbound radiation, while minimising outward radiation, convection and conduction.
Minimising convection is easy. Seal the vessel. Sealed vessel = NO convection.
Minimising radiation is harder, but still easy. Highly reflective interior.
Minimising conduction is hardest. Air is a pretty good insulator, so don't bother insulating the sides and top. Mount the apparatus on top of a thick wooden or polystyrene block to insulate it from the ground. Last is the material your apparatus is made from - it needs to admit heat from the outside, but not waste energy heating itself up.
So... I'd use a steel can (not stainless, and certainly not aluminium) with a polished interior - get polishing. If it doesn't polish up, spray it with silver metal spray paint. Spray the exterior of the can with matte black metal spray paint. Also wrap in black card/paper, which will provide an extra barrier to radiation when the metal of the can gets hot.
Get a top for it of the same material - steel, polished on one side, matte black on the other - and seal it tight on. Put a hole in the top and insert some rubber tubing - this will allow the water and thermometer in. Make the hole very tight and seal it in place with rubber sealant. Put a tube-grip on it (small things which fit over a tube and allow you to seal it and unseal it by a small screw) to maintain internal pressure and ensure the water stays liquid - and allowing you to release the pressure gently for insertion of the thermometer (release it slowly, or the energy can vapourise some of the water, which you'll lose). Place the whole apparatus atop a 10cm thick block of polystyrene.
Putting all of this inside a parabolic reflector would be a good move too, so as to increase the received solar radiation by several orders of magnitude. But make sure it isn't TOO high, or you'll burn the cardboard and the steel.
Next step - win.