The Encouraging Persistence Maintaining Challenge (EMPC) Project has been working with secondary teachers in Melbourne as they seek to build persistence in students, during work on challenging mathematics tasks. The authors have developed sequences of tasks in various topic areas for Years 7 and 8, which require students to connect different aspects of mathematics, to devise solution strategies for themselves and to explore more than one pathway to solutions. There is an expectation that students record the steps in their solutions, and justify their thinking to the teacher and other students. The authors have surveyed teachers on their strategies for encouraging student persistence, before and after the experience of teaching some challenging tasks which have been provided to them. This article provides examples of the kinds of challenging tasks teachers are using with students, and share teacher insights on helpful strategies.