The urgency of the problem stated in the article is due to the fact that the traditional method of teaching mathematics to students of physics and mathematics generally considers mathematical problems that do not require large computing and constructions, while solving complex problems requires more time, which is usually done at the expense of time that is to be spent on other branches of mathematics, so there is a need to study some sections of mathematics with the help of information technology. The purpose of the article is to develop methods of using information technologies in teaching elementary mathematics to students of physics and mathematics department. The leading method in the study of this problem is a design method aimed at selection and structuring of the contents of the computer tutorial under the heading “Polygons” in the system “Mathematics”. The designed computer tutorial for students of physics and mathematics includes a classification of polygons based on their historical information, method of construction, basic properties, the use of polygons in life, in construction, etc. The developed computer tutorial is aimed at improving students’ knowledge of elementary geometry, it promotes the formation of the students’ abilities to create computer textbooks (workshops), which they can use in their professional activity thus endowing them with the skills necessary to modern highly qualified teachers.