The aim of this study is to examine students’ mathematical reasoning, suggested by Lithner (2008), to see how reasoning sequences will unfold in actual classroom situations. We visited two classrooms in an upper secondary school and observed two student groups in each classroom for the time it took them to complete a task, constructed and presented to them by their teacher. Initial analysis showed that there were two interesting dimensions to regard, group characteristics (i.e., motivation and persistence) and task design (i.e., reasoning promoted by the task). We recorded conversations between the students and after transcribing we utilized Lithner’s (2008) framework of mathematical reasoning to analyze students’ reasoning. We classified the moments (vertices) when the students’ reasoning took a new trajectory and characterized the segment (edge) between two such vertices according to the students’ reasoning (i.e., either creative mathematically founded reasoning or algorithmic reasoning). We then visualized the students’ reasoning in graphs (see Figure 10) and analyzed the patterns, the progress and types of reasoning, as well as how the group characteristics and task design would influence reasoning and progress. The result showed that task design is important for which reasoning the students will use. Although an algorithmic-task does not exclude creative reasoning, it only occurs in our data if the students have difficulties and strive to handle them by themselves. We also observed that group characteristics were important for the chosen reasoning type.