Mobile eye-tracking research has provided evidence both on teachers' visual attention in relation to their intentions and on teachers' student-centred gaze patterns. However, the importance of a teacher's eye-movements when giving instructions is unexplored. In this study we used mobile eye-tracking to investigate six teachers' gaze patterns when they are giving task instructions for a geometry problem in four different phases of a mathematical problem-solving lesson. We analysed the teachers' eye-tracking data, their verbal data, and classroom video recordings. Our paper brings forth a novel interpretative lens for teacher's pedagogical intentions communicated by gaze during teacher-led moments such as when introducing new tasks, reorganizing the social structures of students for collaboration, and lesson wrap-ups. A change in the students' task changes teachers' gaze patterns, which may indicate a change in teacher's pedagogical intention. We found that teachers gazed at students throughout the lesson, whereas teachers' focus was at task-related targets during collaborative instruction-giving more than during the introductory and reflective task instructions. Hence, we suggest two previously not detected gaze types: contextualizing gaze for task readiness and collaborative gaze for task focus to contribute to the present discussion on teacher gaze.