This article reports on an investigation of the design/re-design processes of a French grade 10 e-textbook (including its associated resources), which has been designed by the French Sésamath teacher association. These processes have been fostered by new 'digital' possibilities: platforms; discussion lists, etc. The object of the study has been the French Sésamath association, which mainly involved secondary school mathematics teachers designing various kinds of online teaching resources. The focus has been on their design of a Grade 10 e-textbook, more precisely the chapter on 'functions'. This design has been considered as a documentation work, and the analysis conducted with the theoretical perspective provided by Cultural-Historical Activity Theory. The authors studied the activity system of the e-textbook designer community, with particular focus on the resources, the rules and the division of labour in this system, their evolutions, and the factors of evolution. Three moments were identified, corresponding to three successive objects of the activity: a full-web e-textbook; interactive exercises; and finally a digital textbook. For lack of space, only one of these moments is presented, as an example. There is evidence that there were particular resources crucial for this collaborative work.