Machine Learning and Neural Networks for High School Students
For high school kids, I think the most important goal is to make sure they're impressed by what they've accomplished. To do that the task needs to be inherently useful. Classic things like the XOR problem or pixel counting aren't going to do the trick, because you're relying on the students to connect the dots and realize that this means you can build it into something cool. You need them to build a system 


that does something cool,
which can't easily be accomplished with a handbuilt algorithm,
that seems to behave intelligently.


A few ideas:


Make an environment where agents play a game. Something like tic-tac-toe or rock-paper-scissors is probably best. At the end of the course, you can let the agents that the students have made battle each other in a tournament.
Create a simple a-life environment with 2D creatures with simple sensors and joints. Let students create the neural network for the creatures, so they learn to walk. You can also let them evolve the network topology when creatures mate.
A car driver. Again, this is best with an artificial environment, but you can probably get a dataset somewhere too. This is an example from Tom Mitchell's machine learning where they did this with an actual car and a human driver for the network to learn from.