This paper, part of a series of working papers published to provide documentation of research and development efforts associated with the Indigenous Mathematics Project of Papua New Guinea, discusses the role of problem solving in the mathematics curriculum and types and characteristics of good problems, with illustrations. Reasoning by analysis and synthesis are presented in some detail, with attention to ends-means analysis and structured problem solving. In the next section, the search for problem solutions is discussed, including suggestions for organizing problem solving sessions. Polya's four-step plan is described, with comments on each step. Several problem-solving strategies are illustrated, with a sample problem worked for each: guesstimation, work backwards, reduce to a simpler case, conduct an experiment, and add elements to the problem situation. In the final section, classroom activities are presented, such as whole-class problem-solving warm-ups and three problems with solutions. A bibliography is included. (MNS)