How to pedagogically integrate the four STEM (science, technology, engineering, and mathematics) disciplines is a main discussion issue in STEM education. Inquiry-based learning, mathematical modeling, and tool-based pedagogy could go hand in hand to provide a possible integrated STEM pedagogical framework for mathematics and science. This discussion paper explores such a boundary pedagogy via the proposal of an inquiry-based modeling pedagogical cycle. The cycle is used as a lens to analyze a sequence of tool-based mathematics school lessons conducted as a science experiment on the topic of estimation. The lesson design is seen through the proposed pedagogical cycles and selected students' work is presented to illustrate students' different problem-solving tracks in a minimalist instruction environment. Pedagogical features that characterize a STEM boundary pedagogical approach are identified. The paper concludes with a discussion on some core values of STEM education.