Working between versions

Hello,

I am a digital television major in college and we have just started using Final Cut Pro X. To help with school, I bought FCPX for my computer at home, but it is the newer version. Can I work on projects at home on the newer version of FCPX and then bring them to school on an external hard drive and continue to work on them on the older version of FTPX? And vice versa? I'm sure I sound like a newb, but I am a student after all and have only been using FTP for a couple weeks.

Thank You