We study the potential of mathematical folding as an invitation to mathematize what is literally in your hands. In the reported study, 16–18-year-old pre-university students (n = 19) develop formulas to describe a pattern in a folded strip. As part of design-based research, we designed a lesson based on the theories of didactical situations and embodied cognition. In this lesson, there is no dichotomy between folding and mathematizing; teacher-guided progressive mathematization and a gradual introduction of mathematical notation are fostered, as well as language derived from the actions and folded artifacts of the students. Students reached multiple but different mathematical layers of the folding tasks in the studied implementation. We conclude that this makes the lesson design suitable for students with different work attitudes and grades.