The relevance of the research is due to the opportunities of using live worksheets for increasing the cognitive activity of students in the school course of mathematics and improving the effectiveness of the "flipped classroom" technology. The research problem is determined by contradictions: between the opportunities provided by live worksheets to support cognitive activity of students in the process of solving practice-oriented tasks with the 'flipped classroom" technology and actual forms of teaching at school; between the need to provide resources for automating calculations, solving problem character tasks in terms of the digital transformation of society and the insufficient level of mathematical competence of graduates. The purpose of the study is to substantiate theoretically and test experimentally the effectiveness of using live worksheets in the organization of teaching mathematics with the "flipped classroom" technology. The research methodology is based on the analysis of scientific works and interactive educational tools, generalization of the empirical data processing results and materials from interactive resources. The study was conducted in Kirov schools with in-depth study of some subjects. The experiment involved 100 students of 5-6 grades in 2019-2020. Live worksheets are implemented in the Wizer.me service - a free resource that supports feedback and display of work results in an electronic journal. Statistical verification of the results reliability is made using the Fisher test. The author clarified the essence of “live worksheet” concept and described the characteristic features of using the “flipped classroom” technology for learning mathematics. It is noted that there is a potential of live worksheets for the formation of mathematical competence, for getting the practice of computing, and the support of cognitive activity in the framework of the “flipped classroom” learning technology. The opportunities of live sheets are shown by the example of solving practice-oriented tasks in basic school. The article summarizes the didactic potential of using live worksheets when implementing the “flipped classroom” technology to enhance interaction and cognition in the formation of competencies that are in demand in a digital society. The materials of the article may be used for reviving cognitive interest, involving students in mathematical research activities, and for the control of their actions assessment.