This work is primarily based on the educational strategy of discovery and the methods of research based learning, which in the second portion is applied to the solving of concrete mathematical tasks. In the investigational method, special attention is payed to the methodical and didactical principles so that the student could solve a problem with his own capabilities. In the teaching the proces, the student is allowed to investigate and research everything that is possible by proposing hypotheses and coming to conclusions. This approach is therefore both fun and challenging and will increase a student's self-confidence in his problem solving capabilities and his capacity for succes in math. The acctivities proposed in this essay are ment to increase the amount od research and add enjoyment, as well as encourage curiosity amongst the students so that they can find ways to solve problems that they may encounter in real life, not just those in the textbooks. It is mainly done in groups because the interaction of students with each other and together with the teacher enriches the quality of these activities.