For this assignment, you should try to find a partner from the class, so you can get your own portrait taken as well. By doing this you get to put yourself into the shoes of the subject, which helps a lot with the 5th element - learning how to direct and pose the subject.
Talk to your partner and get to know him/her and find an interesting aspect about the person to base your portrait on. Normal portraits simply show you waht a person looks like, but environmental portraits specifically highlight some aspect about the person, such as their work, skills, unique attributes, or interest.
If you haven't found a partner yet, check the discussion thread in the google groups, or send out an email on the group.
I'd highly recommended coming up with some kind of theme to base your portrait session around - it sort of serves as a creative catalyst and gives direction when you're planning out the shots you want. Get to know your partner, and come up with an aspect about the person or even a whole persona that you want to represent in the portrait.
When we talk about your photos in a couple of weeks, you'll come up and present your photos - talk about the theme you chose, and what you did/tried to do with each of the five elements listed above.
On another note, if you want, shoot in RAW - we'll start talking about post-processing and what you can do with RAW files vs. your ordinary jpeg files next week.
Assignment Summary: