A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a series of exercises that lead each student to see the pattern that is the intended theorem. This article describes a method of using computer projects, by which students can discover classical theorems before they are stated and proved, with the help of leading questions and the software "Groups, Algorithms and Programming" (GAP). The authors illustrate the method with three examples using GAP. Two of the examples are designed as a series of GAP exercises that lead a student to conjecture a theorem in each case. The third example is a professor demonstration that leads the students to predict a theorem.