In the article some aspects of the development of divergent thinking of primary school students during mathematics studies are considered, the principles which teachers should take into account when preparing and conducting mathematics lessons are given. The authors describe the specifics of the formation of divergent thinking in studying and constructing graphs of functions by pupils of the main school. In our opinion, the most effective forms of educational activity for the formation and development of divergent thinking of students in mathematics lessons include: situational modeling, discussion of questions, project method, problem teaching, problems of practical content, etc. An important form of work is, in particular, the solution of so-called divergent problems. One of the most important topics taught in the algebra school course is the graphs of functions that accompany a person throughout their lives. The analysis of the properties of a function and the choice of an appropriate algorithm for constructing its schedule, the reproduction of the properties of a function according to a known schedule is the very educational material that promotes the development of divergent thinking of students. Such tasks are appropriate to offer students to practice skills: to recognize the quadratic function among others; determine the coordinates of the vertex and the direction of the branches; to analytically investigate its properties, as well as to apply schemes of execution of the basic types of geometric transformations of graphs of functions. Divergent tasks for the development of function graphs develop creative search activity, graphic culture, independence of thinking, attention and initiative of students, their solving forms cognitive interest and skills of teamwork and cooperation.