This is a very interesting and free prompt. You should be thrilled with it! If you are having a hard time thinking about your own answers, think about some movies and literature. Think about "The Invisible Man." If you are into more modern TV shows think about "Dexter's Laboratory" or "Buffy the Vampire Slayer." Buffy learns that you can fool your friends and do things you may be ashamed to do if you are seen, while being invisible.
Maybe there is a place you'd like to go you have never been before but might stand out so you want to just observe? Or maybe you would want to observe someone or something without them knowing you were there.
There are tons of possibilities, but at the same time think about how you would feel at the end of the day where people didn't see you because they couldn't. How would you feel about this? Or think about "The League of Extraordinary Gentlemen." You can wear a trench-coat and make up to seen when you want or take it off when you want the full power of your invisibility.
If I were an English teacher I would not dare to assign this because I wouldn't want to see the answers!
This answer is going to depend a lot on your own personality and the circumstances of your own life.
For me, what I would do if I were invisible would be to watch my kids. It would be so interesting to be able to see what they are like when they do not know I am around (they're 7 and 4). It would add to my understanding of them and it would be a pretty special thing. I have not been able to do that much -- only a couple times when I've gotten somewhere before they expect me and have been able to watch them -- and it is really a nice experience when I get the chance.
This is a prompt for which you should let your imagination run free. I can see that you are a twelfth grader, so you are going to be interested in advantages that are different from those of a young child. Being invisible would confer so many advantages, I would hardly know where to begin myself.
I think the first aspect you should consider is whether you would commit some illegal acts if you were invisible or if you want to focus solely on legal activities! Once you make that decision, you need to consider what you would do if no one could see you.
Obviously, you could probably be a great thief if you were invisible. I don't know about banks because invisibility does not confer the ability to figure out security codes, but you might be able to follow someone into a vault and remain there after the person left. Of course, you would be stuck until someone returned, so you would want to bring a snack with you. Would the snack be visible? You will have to figure that out. But certainly, you could slip in and out of places and take what you want, as long as what you took was invisible, too.
There are some acts that are not necessarily illegal, but which are unethical. These might be a temptation. For example, you could eavesdrop on conversations. You might be able to find out what your teachers, parents, and friends really think of you. You might be able to find out when the next test will be in math class. Being able to listen to the conversations of others when they don't know you are listening is not illegal, just wrong, but it would be a powerful temptation.
On the other hand, you might be able to do some good with your invisibility. If you saw someone being attacked or robbed, you would probably be able to assist that person more easily than if you were visible. After all, how does someone fight against an invisible defender?
Finally, whether you would do good deeds or wicked deeds as an invisible person, you would always want to be very careful when crossing the street!
I hope this gives you some ideas on how to proceed. I have provided a link to a website with information on a real invisibility cloak.