Fun math for young, bored kids?

Solution 1:

I immediately thought of the work of Martin Gardner.

You can see some of his work for free here.

Also worth mentioning is that the MAA is selling the entire collection of his Scientific American articles on a CD here.

Solution 2:

I am not a teacher , but I would have used problems mainly relating to the pigeon-hole principle or Dirichlet's box principle.In fact, for such students, Mathematical Circles would have been a fantastic resource.(That's my opinion as a student) http://www.amazon.com/Mathematical-Circles-Russian-Experience-World/dp/0821804308

You may like to organise math tournaments later on(various formats are suggested at the back of the book).I must say that the chapters on parity and inequality are really good. In fact, the book is aimed at bright 12-13 year olds and is therefore not heavy on notation or anything that is likely to put off students.

Solution 3:

How is your German? I once did a similar workshop for a similar age group, and I taught them some proof techniques. Then, we spent a lot of time solving fun puzzles. The notes are here, here and here. Most of this might be more suitable for later classes, though.

You can teach them Euler characteristics, that's pretty hands on stuff and the result is astonishing. Also, there are lots of entertaining things one can do with probability, such as the Monty Hall problem (I wouldn't expect an average 16 year old to already know it), or the famous trick that if there are 30 people in a room, then you are fairly safe to bet that some two of them have their birthday on the same day of the year.