The workplace practices of engineers have changed due to the ubiquity of digital technology. So-called techno-mathematical literacies (TmL), seen as a domain specification of 21st-century skills, are essential for future engineers. How these TmL can be fostered in their education, however, is still unclear. To address this issue, we conducted a design study in which we developed a course in applied mathematics for higher technical professional education with TmL as central learning goals. This paper describes the design and implementation of the course in a first design cycle with 59 chemistry students. We focus on the teaching strategies that the lecturer used to stimulate the development of students' TmL. In classroom discussions, in the so-called feedback hours on which students' collaborative work on TmL was centered, context-based cases were discussed. Results include didactical, process, and inquiry-based learning strategies used by the lecturer.