Realistic Mathematics Education (RME) is a body of educational theory which is a common point of inspiration among mathematics educators focused on reform towards active learning at the undergraduate level. This paper presents the origin and major components of RME theory, placing particular attention on the thought of Dr. Hans Freudenthal, the founder of the theoretical school. The theory is further elucidated through the perspective of a curriculum generating developmental research project, Teaching Abstract Algebra for Understanding (TAAFU or IOAA). Finally, this review is used as a jumping off point for the creation of the outline of a lesson plan for teaching introductory counting methods in a discrete mathematics course. Informed by the research on active learning, TAAFU, and RME theory, this lesson plan focuses on how students can be guided towards a reinvention of the mathematical concepts in the context of an experientially real activity.