For those who see mathematics as an activity and not as a body of knowledge, projects and investigational work are seen as a fundamental part of the study of the subject. After reviewing some of the efforts made over the last twenty years to introduce this kind of work into the curriculum, this paper takes a detailed look at an investigation of ‘number chains’ where each link of the chain is generated in some way by its predecessor (e.g. a new number is formed by taking the sum of the squares of the digits of the preceding number). The paper then goes on to develop a versatile and flexible computer program that can be used to generate data for such chains, leaving the student free to analyse any emerging patterns. The program, written in BASIC on a Commodore PET, is made up of several modules fitted together, and only one or two of the modules need to be changed to produce a new kind of chain.