A finite state machine and a Turing machine are introduced in a series of four easy examples. Models are defined in a functional language, Miranda^†. The popular problem of a paper-vending machine is considered in all cases. The first, very primitive model, which is presented in full, is refined in consecutive versions. Students are expected to modify functions of the previous model and test them. The experimental session with such models is offered as a 1-hr laboratory exercise in the first semester course for a large group of c. 300 students whose major is in CE, CS and EE. The functions producing an annotated output are also presented in the paper.