A mathematics course teaching students how to calculate the area of complex figures with circles was designed using learning trajectories. We conducted a teaching experiment to examine the learning conditions and problem-solving performance of students and understand their misconceptions and difficulties in different areas of learning. Teacher journals review teaching techniques and effective teaching methods to assist students in forming complete and systematic concepts of circles and in solving problems. The subjects in this study comprised a sixth-grade class of students at a public elementary school in Central Taiwan and their homeroom teacher. The course content focused on the concepts of determining the area of complex figures with circles, as introduced in sixth-grade mathematics in the Grade 1-9 Curriculum Guidelines. We referred to math teaching materials and guidelines to design the course. The collected and analyzed data included: (1) teacher-student interactions during class, (2) the math worksheet performance of students, and (3) after-class interview records. We verified teaching effectiveness by using the worksheet scores and qualitatively analyzed the misconceptions of students. The findings of this study indicate the following: (1) the teaching materials designed using learning trajectories include the Basic Composing Elements of Circles, Understanding the Circle Area Formula, Cutting and Shifting Techniques to Calculate Area, Understanding the Distributive Law and Marking Areas with Symbols, and Filling in and Other Strategies, (2) students with different levels of cognition displayed varying performance on the area worksheets, and (3) after retrospective reflections on the teaching experiment, the teacher’s behavior changed with regard to understanding the conceptions of the students, teaching methods, and curricular design