Preparing a student with project skills is one of the urgent tasks facing education. At present, the general education school of Russia is moving to new educational standards, which provide for the mandatory formation of students' skills in using project activities. The article contains an analysis of the experience of involving students of different age groups in project activities during their acquaintance with the basic topological concepts within the framework of the author's elective discipline "Get to know topology".At the preparatory stage of teaching, the content of the modern section of mathematics was reasonably selected, different types of practical tasks were modeled, the topic of projects, possible options for the product of project activities, assessment criteria were selected, questionnaires were developed.The article describes the results of experimental teaching, which was carried out for three years in educational institutions of different levels. The article is illustrated with examples of methods of organizing project activities in the course "Get to know topology" and approaches to evaluating project products; the analysis of questionnaires of different groups of students was carried out. The results of the study confirm that project-based learning increases the involvement and interest of schoolchildren in mathematics, allows them to understand a new problem, contributes to the development of communication and cooperation skills of students, creates conditions for the development of students' creativity.