This study proposes to describe and analyse the dynamics of didactic interactions in the lessons on addition and multiplication in Z and to interpret their effects. At the end of this study, we have concluded that verbal and non-verbal didactic interactions contribute to the appropriation of knowledge in the seventh year. However, many of them are held back in overcrowded classes, mainly those related to proxemia and kinesis. Thus, the theorical model chosen is one of joint action verbalo-active. The usage of this model in overcrowded classes has given satisfying results. The movement and spread of interactions allowed us to identify the procedures used by teachers in both classes. These are the procedures of motivation, recall, activation, reformulation, validation, institutionalization through the procedure of support and/or mediation in class. These processes have led students to appropriate their knowledge through hesitation, silence, doubt, trial and error, speeches and peer support during interaction. As regards the rules of the signs, the movement of the interactions also enabled the teacher to transpose the rules of the signs by the process of breaking these rules into different stages. This led the students to use a portrait of knowledge in the application of the rules of signs. Future research will be able to examine students' assimilation of each knowledge.