When dealing with a complex problem, solving it by reduction to simpler problems, or problems for which the solution is already known, is a common method in mathematics and other scientific disciplines, as in computer science and, specifically, in the field of computability. However, when teaching computational models (as part of computability) this topic is not usually explicitly emphasized. The authors believe that developing reductive thinking patterns is an important goal in any scientific discipline, and specifically in Computer Science (CS). Problems that deal with computational models can nicely serve to demonstrate and enable practice of such thinking patterns, especially if these problems are carefully chosen, and have a few possible reductive solutions. In this paper, the authors demonstrate this principle using a number of problems for two computational models: The finite automata model (representing finite state machines with no additional memory) and the pushdown automata model (representing finite state machines equipped with an infinite memory, which may be accessed according to the Last-In-First-Out principle.) Although these problems were used for high school students, appropriate problems can be defined that are suitable for college and university courses. (Contains 13 figures.)