Secondary School Mathematics offers a variety of options to complement the problem solving lesson. This article shows several problem-solving problems that need to be solved through exploration and experimentation. The solution is demonstrated, including proof that is an integral part of these solutions of tasks. Here is how experimentation in problem solving and hypothesis proving can enrich the teaching of mathematics at the secondary level. This enhances the mathematical thinking of students and increases their relationship to mathematics. Solving problem problems increases pupils' engagement in teaching, thus supporting heuristic approaches to teaching.