The article is devoted to the problem of finding effective ways and means of organization teaching mathematics process to modern students grades 5-6. On the basis of the researched psychological and pedagogical features of digital generation Z representatives to which modern schoolboys belong, the ways of realization of the applied orientation of teaching mathematics to students of 5-6 grades are considered. According to Theory of Generations, the generations of modern students are strikingly different from all previous ones. To organize effective cooperation, a modern school must respond to the changes that have taken place in the psychology and behavior of children and take them into account when organizing the learning process. The analysis of the psychological scientific literature shows that modern students have an active life position, unlimited opportunities to search for information, mainly visual perception, clip thinking. They perceive information quickly, but find it more difficult to memorize and quickly switch their attention, prefer an activity-based approach to learning, and depend on their own performance. The effectiveness of teaching mathematics to students in grades 5-6 is influenced by the level of development of their thinking, and such mental processes as perception, memory, attention, thinking, imagination. The specifics of the content of the subject "mathematics" requires increased attention and cognitive activity of students, so in the learning process it is important to encourage them to consciously and thoughtfully immerse themselves in learning, self-control, responsibility and independence by involving them in practice-oriented learning activities. By offering students tasks whose plots resonate with the modern life of students and their interests, the teacher has the opportunity to awaken students' interest in learning, encourage them to feel the need for new knowledge, organize purposeful learning activities and thus build a comfortable relationship between participants in the educational process. , which are most likely representatives of different generations.