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