Any project/learning ideas for a 14-16 year old kid to do for a week?

To cut a long-story short, I'll be working with a kid on work experience for a week, and I'm trying to come up with the best way to utilise this time.

I've worked with kids in the past, albeit child-genius types that have written search engines at the age of 12, and are doing consulting work while at school. In this case it was pretty easy - we gave them an internal project to work on, and at the end of the week they demo'd it to the team. If they were really smart, we'd have them pair program with another developer on a real-life project, so they'd get to say "you see that feature? I built that".

I'd do something similar, but I have no idea what base level of knowledge this kid is going to have, so it's best to assume that they have limited experience.

The main thing I want for this kid is for them to have fun, and to get a taste of what writing software for a living is like.

Have any of you been in a similar position before? If you've had to teach a kid to program or have mentored a kid, what meaningful projects did you give them to work on? Also, if you were in a similar position as a kid, do you have any fond memories of projects that you worked on?