One of the most sucessful Mathematica activities that I have is one where first I show the students how to create a chess piece with a solid of revolution, and then I ask them to create a Coke bottle with the same procedure, see the last pages of this PDF: http://homepage.cem.itesm.mx/jose.luis.gomez/data/mathematica/CocaCola.pdf 
This activity is really adictive, students want to continue trying to improve their coke after working several hours on it. Really. And my "students" have been both 18-years old engineering students, and their 40+ years old teachers, all get trapped by this activity. 
First: they learn by doing. Second: they can asses their own work, they can easily say if their revolution solid looks or not like a coke. Third: there is room for creativity (take a picture of a real coke, measure it, try using trigonometric functions, etc) I guess those are some of the elements of an engainging activity.
Regards
Jose, Mexico