This study was to design, develop, and investigate instructional units for freshmen with low academic achievement to learn before they study calculus. Because the concepts, skills, and theories of function are fundamental for the calculus course but the below average students were not familiar with the basic knowledge and ability in function when they studied in the high schools and it will affect their learning calculus, the investigator in this study has analyzed the calculus course to find out the relevant functional concepts, skills, and theories and taken some actual research studies as references to deliberately design, compile, and write an instructional unit on function. Then the teaching material was tried out in the classroom. During trying out the unit, the investigator found that students were also unfamiliar with the concepts and operations of numbers and sets. Therefore, the investigator thought that it is indispensable to integrate the content of numbers and sets into the course. Finally the curriculum units including numbers, sets, and functions have been completed to be a basic course for calculus. After preparing the curriculum units, the teaching materials were sent to experts to ask for reviewing and giving feedback for revising the content. Then the curriculum will be tried out again in the beginning of the calculus course to test the degree of appropriateness and find where it should be revised again. During the next year, a formal instruction will be carried out. Finally, it is to complete a set of curriculum units on number systems, sets, and functions for freshmen to take as basic content for calculus course.