There are increasing calls for mathematics teachers to foster computational thinking (CT) skills in their lessons and align them with existing curricula and national educational policies. Algorithmic thinking (AT) and generalization are two key elements of CT that are often underrepresented in traditional mathematics lessons. This study investigated how to address AT and generalization aspects in 12th-grade calculus lessons using the dynamic mathematics software GeoGebra. We present a six-lesson intervention designed by an interdisciplinary team of researchers and teachers with a background in computer science and mathematics education that aims to foster pre-university students’ AT and generalization skills in calculus lessons. We evaluated the intervention in a 15 students classroom in the Netherlands through the analysis of students’ workbooks, files, interviews, and the teacher’s logbook. The findings suggest that the intervention was favorably seen by both the teacher and the students, and that their learning and teaching experience was highly satisfactory. The most common challenges for successfully completing the designed material included issues related to getting familiar with GeoGebra, syntax, and effectively using conditional statements. Finally, we report on the learning and teaching experience and discuss strategies to address AT and generalization aspects for teachers who wish to address such CT aspects in mathematics lessons.