I was thinking that perhaps the number line would help make a nice illustration of the fact that there are different sizes of infinity. You could explore the natural numbers, the whole numbers, the integers--positive, negative, both, even positive, all evens, etc.--and on and on.
A "parallel" in geometry :) is the length of a line vs. a ray. Both are infinite but of different sizes. And so forth. These seem accessible to students of practically any age.
Just my two cents' worth... Angie
P.S. Let us know what you *do* end up doing!
____________________________________________________________ Angie S. Eshelman 116 Erickson Hall Office: (517) 353-0628 Michigan State University E-Mail: email@example.com East Lansing, MI 48824-1034 ____________________________________________________________
At 12:27 PM 4/17/95, Jill A. Dumesnil wrote: >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. > >--- >Jill A. Dumesnil > >Stephen F. Austin State Univ. > >Dept. of Mathematics and Statistics > >Nacogdoches, TX 75962-3040 >firstname.lastname@example.org