INTRODUCTION: Since 2006, when Jeannette Wing popularized the term "Computational Thinking" as an essential skill for people in the twenty-first century, there is great interest from the scientific community and governments of various countries in the Computational Thinking exploration in K-12. Although Wing describes Computational Thinking as a process of problem solving that is based on the limits of computing, and more fundamentally addresses the question "What is computable?", little attention has been given to this question in practice. OBJECTIVES: The primary objective of this study was to present a theoretical reflection about the importance of the notion of computability for Computational Thinking, and present a game project for its introduction in K-12. METHODS: Through the bibliographical research method, a study was carried out on the Computational Thinking, Theory of Computation and technologies used in the exploration of Computational Thinking. RESULTS: Based on the studies carried out, the design of a logic game inspired by computational models was elaborated. CONCLUSION: The game proposed in this article may represent a new strategy for the Computational Thinking exploration in K-12, because in addition to bringing notions of computability to the fore, it leads to a thinking way based in states changes, which represents an adequate model of the brain conscious functioning.