<p>Well-designed mathematical tasks are central to effective teaching in face-to-face classrooms. However, due to differences in interactions and technological mediation, the extent to which this principle applies to online video lessons remains unclear. This mixed-methods study adapts the Mathematical Tasks Framework to systematically analyze 361 tasks serving multiple instructional roles in online video lessons from Shanghai and England, tracking changes in cognitive demands from the pre-production design stage to the on-screen presentation stage. We find that the cognitive demands of the same task differ across stages, and that the frequency of demand shifts varies by task role. Across distinct cultural contexts, factors associated with the enhancement, maintenance, or decline of high-level cognitive demands may differ. Beyond cross-cultural comparison, our findings highlight prioritizing factors that enhance or maintain high-level cognitive demands (e.g., pressing students for explanations, planned exploration time, and targeted use of digital tools) while avoiding those associated with their decline (e.g., routinizing the problematic aspects). These insights provide actionable guidance for designing high-quality, student-centered online resources that foster mathematical thinking.</p>