One popular way to illustrate simple one-dimensional collisions in the classroom is our air track. We have two models of air track for larger and smaller rooms, and several demonstration setups for them, including C7-01: Elastic Collisions; C7-02: Inelastic Collisions, and C7-04: Collision Velocity Multiplier.

small and medium carts on an air track, with photocell gates

 In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is still conserved, but kinetic energy is not; energy is lost to friction, internal interactions, etc. 

There are several simulations on the internet that have been developed to help illustrate elastic collisions as well. They can be useful when used in class in conjunction with the demonstration, or to examine such collisions on your own time outside of class.

Andrew Duffy has developed a simulation that simulates the motion of a pair of carts on such a track, and you can see active graphs of the momentum, energy, velocity, or position. You can try it out here:

duffy collision simulation screenshot

Eric Neumann has a simulation with one to three masses colliding with each other and the walls. You can try it out here: 

neumann collision simulation screenshot

In both cases, controls are available to let you adjust variables like mass, velocity, elasticity, etc. Try out different configurations and see if you can replicate your favourite in-class experiments; and see if you can find the limitations of the simulations as well!