As a home-schooling parent, I scan this digest in search of activities of just this sort. If you have access to the World Wide Web, you might find something of interest at the MegaMathematics site. (URL is http://www.c3.lanl.gov/mega-math/index.html) They offer lesson plans dealing with map coloring, graph theory, knots, algorithms, logical analysis, and infinity paradoxes. All come with background information, suggested activities, references for further study, and tie-ins to the NCTM standards
Unfortunately, the section on infinity does not offer much in the way of "active" exploration. It does, however include a story, "The Hotel Infinity," based on Ganow's paradoxes, and suggests that students try to illustrate it.