The article discusses the educational potential and special advantages of a mathematical laboratory in the teaching of mathematics at the pre‐calculus level. The laboratory envisaged is equipped with a set of microcomputers or programmable pocket calculators, which play a central role in the teaching process, with particular emphasis on algorithmization. As a typical laboratory subject we concentrate on the approximation of areas to a prescribed accuracy, including the appropriate error analysis. Different types of approximations, with progressively increasing efficiency, are examined and their laboratory implementation discussed. Extensions and generalizations are indicated for more advanced mathematical education.