[Objective] This article describes heuristics used by 8 and 9 year-old students to solve four non-routine problems that promote the development of arithmetic thinking from two perspectives: number distribution under a graphical representation, and use of arithmetic operations in the positional decimal system. [Methodology] The analysis included the formulation of categories that made it possible to characterize a priori the heuristics that could arise when solving each problem. These categories were used in the implementation of a mixed methodological approach with an exploratory and descriptive orientation. Qualitative analysis was carried out through a case study that helped to identify key actions based on written results provided by students. Quantitative analysis was carried out using implicative analysis, which includes a similarity tree and identification of significant classes. [Results] The results point to the importance of using simple heuristics in finding solutions to non-routine arithmetic problems, and confirm the presence of some characteristics of heuristic reasoning, such as attention, reduction, and change of assumptions. Likewise, implicative relationships were identified among some heuristics that share common characteristics, depending on the type of problem. [Conclusions] The results of this study show that, even in incorrect or incomplete answers, it is possible to recognize logical processes for the elaboration of partial answers and intuitive approaches, which are consistent with the action of simplifying or facilitating the search for a solution.