In the current national course of study for Mathematics 1 and Mathematics A, task-based learning was newly added.  Since many students in Japan are not interested in mathematics, it is important that we develop teaching materials for task-based learning that interest them.

　　 In this paper, we describe a series of studies on task-based learning as follows:

　　 First, why we have selected Euler’s polyhedron theorem and Euler’s number as the theme of teaching materials for task-based learning.  It is important to develop them with the goal of giving each student the best curriculum possible.  We are conscious of the meaning of task-based learning, namely, relationship of real lives, development, interest and concern of students, and mathematical activities.  To ensure this outcome, we feel that Euler’s polyhedron theorem and Euler’s number are sufficient for the purpose of task-based learning.

　　 Second, how we have developed teaching materials for task-based learning since 2012.  We have developed them by assuming the students’ questions about this theorem, for example, what is the figure two at the righthand side of the formula in this theorem, and have practiced them for college students.  As the result, it turned out that some teaching materials were useful in terms of cost-effectiveness, the degree of interest, and the level of difficulty.

　　 Third, we describe the results of practice for high school students.  We had an opportunity to practice a teaching material for high school students, and selected Euler’s number of figures made with lines and triangles by students as the teaching material, but it was not always equal to two.  Interpreting the results of questionnaires, this teaching material for task-based learning is useful for high school students.