In this study, we propose to realize a didactic engineering on the notion of arithmetic and geometric succession numbers through the «hidden cages game». We went from the society game called « kede game » seeming the game of marelle, which we transformed in a class game we named « hidden cages game » as a basic didactic situation for the learning of arithmetic and geometric succession numbers. From this basic situation, a didactic progression with pupils’ procedures was conceived and has been subjected to the experimentation in a real class. The transformed game consists of filling in the empty cages of a two-column table, subdivided into 6 cages each, which the learner must complete by performing an arithmetic and geometric succession numbers. We resorted to the group work method during our experimental sessions to implement the four didactic moments: action moment, formation moment, proof or validation moment, institutionalization moment. In confronting the a priori analysis and the posteriori analysis, we validated the didactic progression in question which can be used for teaching and learning of arithmetic and geometric succession numbers. At the end of this study, we concluded that didactic variables from hidden cages game allow us to conceive a didactic progression for the learning of the concept of arithmetic and geometric succession numbers.