Managing student participation is a key interactional and instructional task in any classroom. This is even more relevant in language classrooms, as students need to demonstrate understanding, knowledge and proficiency through the production of lexical, phrasal, clausal or sentential elements. Question-Answer-sequences have been the focus within the Initiation-Response-Feedback pattern; however, another kind of initiation is that of turns with incomplete turn-constructional-units which students need to complete in the next sequential slot. This study explores elicitations designed as incomplete in five secondary EFL classrooms in the South of Chile. Analysis follows a multimodal Conversation Analytic approach. Results show that teachers mobilise turn-completion not only through gaze and gestures to explicitly signal to students that the floor is open, but also to project turn completion and index the relevance of the teaching materials. This study contributes to the understanding of teachers' practices to manage participation and the progression of the pedagogical project in general, and to previous research on designedly incomplete utterances, in particular.