This case study examined teachers' on-the-fly formative assessment conversations, that is, how teachers collect information from students' thinking and use that information to support their learning during teacher-student interactions. Previous studies have typically analysed whole-class discussions on the level of speaking turns, and have identified means of collecting information (eliciting) and using information (feedback). This study used episode-based analysis to identify both forms and functions of on-the-fly formative assessment conversations during all phases of the inquiry lessons. We video-recorded two teachers' physics lessons for 7th graders (13-14 years). When analysing the forms of on-the-fly formative assessment conversations, we found five types of collecting information, including questioning and other means, and four ways of using the information. We also studied the functions of on-the-fly formative assessment and found four main functions and their sub-functions. The main functions differed according to the purpose of guiding in relation to the flow of student inquiry. Teachers: (1) checked or examined students' thinking; (2) corrected or developed students' present thinking; (3) redirected students' thinking; and (4) reviewed students' thinking. The analysis of forms and functions enabled us to recognise differences in two physics inquiry lessons on the same topic.