In this article, we focus on the use of mental tools of computational thinking (CT) to solve selected problems in school mathematics. We suggest how to expand and enrich some of the traditional school mathematics topics through the use of CT, and as a result, obtain solutions that use and are supported by the power of informatics as a discipline and computers as computational tools. We show how addressing the computational complexity of problems can help also with developing mathematical thinking (MT). Although the problems are mathematical in nature, they do not appear in teaching mathematics in Poland according to the actual core curriculum, but they do appear in selected informatics classes (All references to the core curriculum in this paper are to the National Core Curriculum approved by the Ministry of National Education of Poland in 2017/2018). In the first part of the work, we briefly refer to computational thinking, mathematical thinking and general problem-solving strategies.