What are some dense elements I can use for a demonstration?

Here is a table I made for you listing the elements with a density higher than $10 \frac{\mathrm{g}}{\mathrm{cm}^3}$ and their approximate price per kg:

I couldn't find any prices for Einsteinium or Actinium and some of the other prices might come from poor sources, but take it as a rough guide.

Now you only have to figure out how much you need and your budgetetary constraints, and choose the densest you can afford. As I have learned from the political debate in the US, teachers are apparently raking in big cash, so I suggest you go with osmium or rhenium.

Note: Some of these might be unsuitable/infeasible for other reasons than their price.

There is a rather lovely looking set of spheres available now through an indiegogo campaign - these are 1 kg objects of different densities. It is a more visual way of driving home the message that you wanted to show with your demonstration:

At $890 for the set it is beautiful, but rather expensive for a science demonstration - more something for a CEO's corner office.

However, there is a set of "density cubes" you can buy on Amazon - probably more in line with what you are looking for. It is sold by Midwest Tungsten Service (in case the Amazon link rots).

Here, the volume is constant but the different densities make it interesting. Note - the title says "Tungsten carbide" (density $\rm{15.6~ g/cm^3}$) but the engraving suggests "tungsten" (density $19.3 ~\rm{g/cm^3}$). At $130 for the set it is less out-of-reach.

DISCLAIMER: I have no relationship to either of these vendors and am providing the links purely as a convenience to people visiting this site. These links may not last...