Within the commognitive perspective, ritual and explorative routines are used in a very particular way to distinguish students’ routines according to whether they are driven by socialreward or by generating a substantiated narrative. Explorative routines in this theorisation mayrefer not to inquiry-based activity but to the result of a student’s routine moving from beingprocess-oriented to becoming outcome-oriented, a deritualisation. Choice of tasks as well asa teacher’s moves ofer students diferent opportunities to engage in rituals, explorative routines and deritualisations. Through nuancing the space spanned by opportunities to engage inrituals and explorative routines respectively, we describe and contrast classroom practices inthree lessons from three contexts. The lessons share a commonality in encouraging explorativeroutines as a starting point, yet being adapted towards ritual activity through decreased openings for student agentivity, fewer invitations for students’ own substantiations or both. We arguethat such adaptations are driven by the teachers’ commitment to reach mathematical closure ina lesson, to balance considerations of the classroom community and individual students and tomeet curricular requirements. Our model helps interrogate the nature and relevance of hybridsof explorative routines and rituals.