The two key pieces of evidence for the Big Bang can be demonstrated in class: the Doppler Shift and microwave background radiation. Demonstrate the Doppler Shift with sound. Take a small buzzer with very long leads to a power supply, a metre length should be fine. Clear a good space and twirl the buzzer round your head. As the buzzer comes towards students the pitch rises and as it goes away it drops. The slight variation in pitch can be heard and the drop in pitch as the buzzer goes away is equivalent to the drop in frequency of the light, the redshift, from receding galaxies. The equivalent to this model with light is described on the Nasa site http:imagine.gsfc.nasa.govdocsteacherslessonsstar_sizestar_velocity.h tml where it has a simulation of the wavelength change happening in a binary star system as viewed from Earth. It makes the wavelength shift very clear.
To demonstrate the microwave background radiation refer to Frank Close's idea in his "Cosmic Onion" 1993 Royal Institution Christmas Lectures. If you leave a TV on and transmission has stopped you are left with a hiss of background noise and a fuzzy picture on the screen. A tiny bit of this hiss is the microwave radiation left from the Big Bang. Look at pictures of the microwave background radiation that bathes the Universe at http:map.gsfc.nasa.govm_mm.html
Go to www.newscientist.comnewsnews.jsp?id=ns99994320 to experience an idea of how the Big Bang sounded. In response to a request from a student, physicist John Cramer took data from the Nasa Wilkinson Microwave Anisotropy Probe to calculate the frequency of sound waves propagating through the Universe when it was very young. It has had to be scaled up to make it audible but is a lovely addition to make the Big Bang come alive.