How about a job interview? However, instead of you interviewing them for a job, they have to interview you. You come up with a job title (the more ridiculous the better), and they have to interview for that job. I used to do this with my adult one-to-one students, with some amusing consequences. It really helps you find out how inventive your students can be, as well as whether they have the vocabulary for all sorts of different topics.
My favourite experience of this was being interviewed for a job as a coal miner. Once I'd got my student to understand what that was, she reduced me to tears of laughter with her very first question - "Do you like getting dirty in the dark?"
The reason I did it this way round was that students get very used to being asked questions, and they can frequently fumble their way through an answer by using bits and pieces of answers they know they've given in the past. If you reverse the situation, not only do they need different vocabulary, but they need to know the correct word order for questions.
I think this would work for the 15-year-old at least.