What follows are some suggestions upon module developments designed to provide problem-solving experiences in developing a sequence of trigonal,numerical arrays, JE(n), which in turn give rise to sequences of discrete, fair probability spaces, P(m(JE(n))), with practical suggestions for open-ended model building. Hopefully these module developments will give some insight into teaching and learning some aspects of problem-solving, as well as naturally generating probability spaces which are discrete and fair. The intent is that the module will contribute to the student's overall ability to understand probability and statistics at a more mature level of sophistication. These ideas were initiated about 1983 by the author, have been field tested with two groups of fifth grade students successfully, and many teachers at the public school level and university level have benefited from workshops based upon these modules.