The aim of this study is to investigate task design for differentiated instruction in mathematics in professional learning communities. Based on the cultural-historical activity theory, we conceptualize a professional learning community as an activity system and use the analytical construct of contradictions to give an account of structures that bring forward the teachers' work. Eight Swedish upper secondary teachers, engaged in designing tasks for differentiated instruction in mixed-ability mathematics classrooms, are studied. The analysis outlines three contradictions, manifested as three dilemmas, and shows how the teachers, by noticing a dilemma and making it an explicit object of inquiry, came to address a diversity of issues related to differentiated instruction in mathematics. For example, the teachers addressed students' different learning needs, problem-solving activities for a mixed-ability classroom, and design of tasks that are challenging for all students. With input from our findings on the three dilemmas, we then discuss the design of a task analysis guide as a means for facilitating the development of a professional learning community that is inquiry-oriented with a strong content focus on designing tasks for differentiated instruction in mixed-ability mathematics classrooms.