This paper introduces a model built upon the Method of Varying Inquiry, offering a didactical approach to problem posing and solving activities that stimulates inquiry-based learning in mathematics classrooms. The model combines the inquiry-based framework with the variation theory and with specific didactical and theoretical elements (the mathematics laboratory approach and the construct of virtuous cycle) to support both the design of effective environments for students' inquiry processes and the theoretical justification of this design. By means of an example, we show how the model can provide teachers with specific criteria that could guide them both in designing tasks specifically aimed at engaging students in ongoing inquiry-based learning processes, and in planning effective ways of managing students' interactions during these processes.