The key to implementing the fundamental task of establishing moral education is how the abstract and broad physical education and health curriculum core literacy is translated into concrete and visible physical education and health subject curriculum and teaching practice. This paper firstly explains the framework for the realization of core literacy in PE and health curriculum in teaching and learning, specifically from three perspectives: context, health behavior, and physical virtue. Secondly, the abstract core literacy of physical education and health curriculum is transformed into a side problem of ordinary differential equation with unknown parameter initial values by using the method of ordinary differential error approximation, which can obtain the parametric expressions of the approximation of function values at the nodes and realize the concretization. The experimental results show that there is a significant difference between the core literacy of physical education and health curriculum based on the ordinary differential error approximation method before and after the application of the core literacy in teaching, in which the comprehensive improvement of motor ability is 23.7%, the comprehensive improvement of health behavior is 19.2%, and the comprehensive improvement of physical morality is 26.6%. This paper successfully visualized the core literacy issues of physical education and health curriculum based on the ordinary differential error approximation method, which provided a reference for physical education teaching, improved the professional competence and quality of school physical education teachers, and formed the characteristics of school physical education and health curriculum.