Despite reforms in mathematics education, many teachers remain reluctant to incorporate challenging (i.e., more cognitively demanding) tasks into their mathematics instruction. The current study examines how lesson structure shapes teacher perceptions of teaching with challenging tasks. Participants included three Year 1/2 classroom teachers who observed the researcher (first author) deliver two units of mathematical work. Teacher-participants were given an opportunity to observe the use of challenging tasks to both launch lessons (Task-First Approach) and extend student thinking (Teach-First Approach). It was revealed that teacher-participants perceived both the Task-First Approach and the Teach-First Approach to teaching with challenging tasks to have particular strengths. Specifically, the Task-First Approach was viewed as engaging and empowering for students, providing an opportunity to build student persistence whilst fostering student mathematical creativity. Teachers also placed value on the quality of the mathematical discussion which emerged, and the value of the Task-First Approach for supporting an authentic assessment of student mathematical knowledge. By contrast, the Teach-First Approach was viewed as highly focussed, and an efficient approach to learning. It was also perceived as providing an opportunity for lower-achieving and less confident students to be successful. Although there appear to be distinct advantages to both the Task-First and Teach-First Approaches, the study revealed that the most dramatic shift in teaching practice for some teachers may be the incorporation of more cognitively demanding tasks into their mathematics instruction in any capacity.