Unlike the time dilation expression, the derivation of this mass relationship requires a knowledge of calculus, and is probably beyond the ability of most high school physics students. (Notice the similarity, though!) The effect this mass increase has on fast-moving objects is sufficiently interesting that you should ask your students to accept the expression without a derivation, and plow ahead!
The first obvious consequence is that only particles with zero rest mass can achieve the speed of light. In accelerating a massive particle, the closer you get to light speed the more massive the particle, and therefore the greater the force required to continue accelerating. At Light speed the mass would be infinite, and thus we say no massive particle can be accelerated to the speed of light. This is not the same as saying nothing can move faster than light. If a particle were somehow created moving faster than light, it could never cross the 'light barrier' in the other direction! Physicists call such particles 'tachyons', though there is no evidence for their existence.
Another interesting consequence is that as you continue to add energy to a particle travelling near light speed, the particle stores this energy as an increase of mass rather than an increase in velocity. Protons entering Fermilab's Tevatron with 150 billion electron volts (GeV) of energy are already travelling at 0.99998 times the speed of light and have a mass of about 150 times their rest mass. When they leave, the energy and mass have increased by a factor of more than 6, while their speed has barely changed. Indeed, "accelerator" is really a misnomer for these big machines; Leon Lederman, in his excellent book "The God Particle", has suggested "ponderator" would be more descriptive.