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In order to promote more efficient and quality education in this period of pandemic, this article presents an adaptation of an Active methodology called Hybrid Teaching, in particular, the Flipped Classroom model. In this way, it was sought to enrich the pedagogical practice through an unprecedented methodological approach with the integrated use of digital technologies aiming at the personalization of Remote Teaching through a Didactic Sequence applied to a 2nd year high school class at a private institution in the State of Rio de Janeiro. The research is quantitative and qualitative, where the data collected sought to investigate the performance and reactions of students amid the concepts of Combinatorial Analysis. The results showed that the Flipped Classroom Adapted to Remote Education can, in fact, contribute to the learning of the theme proposed in this period of social isolation, with the development of autonomy and critical sense as well as the argumentative and socializing capacity of the students. [ABSTRACT FROM AUTHOR]

The one-to-one correspondence has been revealed between a set of cosets of the Mathieu group M11, a set of blocks of the Steiner system S(4, 5, 11) and 11-vertex equi-edged triangulated clusters. The revealed correspondence provides the structure interpretation of the S(4, 5, 11) system: mapping of the biplane 2-(11, 5, 2) onto the Steiner system S(4, 5, 11) determines uniquely the 11-vertex tetrahedral cluster, and the automorphisms of the S(4, 5, 11) system determine uniquely transformations of the said 11-vertex tetrahedral cluster. The said transformations correspond to local reconstructions during polymorphic transformations in metals. The proposed symmetry description of polymorphic transformation in metals is consistent with experimental data. [ABSTRACT FROM AUTHOR]