Guiding pupils to discovery of mathematical relations and creative problem solving is one of the ways to improvement of mathematical education. For these ends it is essential to create such learning environments that are rich in stimuli for pupils’ independent discovery and that naturally activate pupils. The paper describes one possible use of various mathematical models in the process of generalization, namely the discovery of regularities in the environment of geometrical figures constructed in a regular triangle grid and expression of these relations using arithmetic and algebraic means.