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:

Density and prices of heavy elements

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:

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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).

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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...