The aim of the study informing this paper was to investigate pre-service teachers' (PSTs') approaches to task design, posing the research question: How do pre-service teachers respond when they are asked to design an exploratory task using GeoGebra for 8th grade students? The research study and this paper focus on the PSTs' design stories rather than their task formulations. Drawing on multiple case study design, the study's sample consisted of 54 PSTs from a Norwegian teacher education program in mathematics for lower secondary school. Once an initial analysis and coding of the tasks was complete, a group of 13 PSTs were interviewed about their own task design, with some of these PSTs taking part in a focus group discussion as well. In this paper, six representative cases of PST task design are presented and analyzed together with additional support from the rest of the interviews and focus groups. Findings revealed four key themes in their design stories: the knowledge of 8th graders, guiding or exploring, use of context or not, and the role of GeoGebra. Each of these themes is discussed with an aim of highlighting key implications for PST task design and the education of new mathematics teachers.