My 12-year-old got interested on topology puzzles and thought it would make a great presentation for his school assignment. I myself am not familiar with topology so am of little help. Basically, he wants to do an introduction to topology that he and his age group could easily grasp and appreciate. Would you have suggestions on what topics and puzzles he can include in his 20-minute presentation? So far, we're thinking he can introduce puzzles in the beginning, make the introduction to topology (definition, genus, etc.) with some slides, explain some real-life applications of topology, and then
One thing that your son might consider talking about is the winding number. One example that I sometimes give involves garden hoses. When the hose is nicely coiled on the ground and you try to drag it (staying along the ground) to the garden, you develop kinks in the hose. One way of interpreting this is that the winding number is being preserved.
Of course, there are ways of unkinking the hose, but they involve 3 dimensional movement. (In particular that loops on the 2-sphere can be contracted --- $\pi_1(S^2)=0$ --- unlike the case of the unit circle.)