Methodology of using interactive methods in solving arithmetical problems

New pedagogical technologies are the product of goal-oriented forms, methods and tools of education, in particular, mathematics education. Observations show that in most cases, the teacher works alone during the lesson, and students remain observers. In this work, one of the teaching methods to connect the teaching of mathematics with life, to develop students' thinking skills, to increase the effectiveness of teaching is to talk about the "Case-study" method, examples of which are given and related to mathematics. Examples are given on the compilation of cases from the topic “Detecting of indefiniteness, L’Hopital’s rule” on the subject of “Mathematical Analysis.