I'm an Assistant Professor of Mathematics who has been asked to prepare 45 minutes to an hour of "meaningful enrichment activity" for gifted and talent fifth graders for this friday. The short notice and my inexperience with elementary-aged children has me a bit anxious. All of my experience has been teaching college mathematics.
I'm thinking of doing something basic on the concept of infinity and the different "sizes" of infinity. It's been my (extremely limited) experience that it's "easy" to convince children that there are infinitely many real numbers between 0 and 1 by considering the unitary fractions (with numerator 1). They quickly see that there are infinitely many of these and "many more" numbers than these between 0 and 1. Does anyone have any ideas for activities or materials that I could use? I appreciate your help.