How advanced are we talking here? Highschool or university? What sources do you have access to? What detector setup - Geiger counter, scintillator, germanium detector? Do you have some kind of supervisor? This changes my suggestions a bit.
I have a few ideas: You can should look at different sources - the shielding requirements for α, β and γ radiation differs a lot. Where you are may change what you can do here, but if you're at a university, you could probably get access to all of the above emitters. If you're in high-school, maybe only γ. In principle, you can get 241Am from a domestic smoke detector, but I don't suggest you try unless you really know what you're doing. (But 241Am has alphas and gammas, so it would be neat for showing the effect of shielding).
You can also look at the effect of γ energy on the required shiedling - does a low energy γ need as much shielding as a high energy γ? You will likely have to correct for the efficiency of the detector to investigate this.
You could also look at the geometry of the shielding. And radiation the off of the shielding - different materials will show different Compton Scattering spectra, and you'll see x-rays off of the material. You need something more sophisticated than a geiger counter for this, obviously.
You should also show the 1/r2 dependence. One thing that will be important for you to control is geometry.
Something really great be with a neutron source (AmBe) and looking at shielding neutrons. I suppose that would be easiest measured doing a neutron activation experiment (that way you don't have to have a neutron detector). But really really only do this with expert supervision. That means someone who is a radiation worker, has a dosimiter badge, and understands how to safely handle hot sources. Really really.
... So many ideas!
