Different models work well for different types of numbers. Can you make this model work for negative numbers? How about fractions? Or is it just for 123s? Try it out and submit pictures.
Chimeras are made out of parts of several different animals. There are a lot of chimeras in myths. Genetics researchers are making real chimeras, too. This three by three table has all chimeras you can make out of three heads and three bodies.
I created a version of this that kids can play with and construct their own versions in Etoys (project at: http://www.squeakland.org/showcase/project.jsp?id=10494). Similar things could be done in a simple paint program (to a point). Also a video demonstrating how to use the project is at: http://www.youtube.com/watch?v=lVHLYMujS4E.