You can construct models of the different types of volcanoes (composite, cinder cone, and shield) using clay. Sheets of clay would represent lava flows and small balls of clay (or layers of sand) would represent fragmented lava or ash.

This model of a stratovolcano was made using clay. Strips of clay were plastered in a radial pattern. Then the summit was carved to make a somma (a collapsed area) and a cone of clay was add added inside the somma. The eruption column was made from a cone of aluminum foil. It is held in place by a stick (a chopstick is perfect). The model is about five inches across.

To make the model look more volcanic is was spray painted black. Then it was covered in spray glue and black sand (older pyroclastic deposits) and baking soda (new ash deposit) were sprinkled over the volcano. The make the eruption column look more volcanic it was given a light coat of paint, then covered in spray glue and finally sprinkled with baking soda.

This simple model is a shield volcano with a central caldera and two recent lava flows. Both of these models cost a total of $2 to make (all for the clay).

The very simple model in the photo shows a pile of clay balls that make a cone. This could be used as a very simple model of a cinder cone.