How do I play copied games on XBox 360?

[json4639]

I work for a charity that helps house sick kids receiving treatment in the hospital and their families(Ronald McDonald House). We are setting up a video game room for the residents and are going to set up a couple X-box consoles. We have had problems with theft (yes, people will steal from a charity) and want to make sure that we don't waste our money buying games and having them stolen a week later. Is there a way to either A) copy the games to a larger HD and play them from it, or B) make copies of the games and install a modchip(or flash the existing firmware) that can play the copies.

We fully intend to buy the games and only make copies for backup purposes, so please, no comments about copyright violation etc. etc.