Applying and adapting a variety of appropriate heuristic strategies is one of the accepted standards of problem solving (NCTM, 2000). Thinking through a solution to a non-routine mathematical task, experts in problem solving call into play many sophisticated strategies (almost) without conscious efforts, while novices need to be taught how to do so. The purpose of this article is to present examples of heuristic-oriented activities (HOA) that invite the use of "working forward" and "working backward strategies."