The essential element of ball games is a competition with a future unknown result (the objective of competition). In such a situation, the players engage in competition tasks to directly achieve their objective. This paper clarifies the relationship between the various activities of learners (extension of concept) and learned contents (intention of concept) through organization of tasks and the processes involved in task-solving. Any type of ball game has one of two distinct objectives: progression of the ball to an objective point, or progression of players to an objective point. Ball or player progression is accomplished either through conflicts between offense and defense or by the personal activities of an individual player. Considering these elements, the processes of task-solving can be classified into four types: “target-shooting”, “breakthrough”, “breakthrough+target-shooting”, and “breakthrough+base-advance”. Each type of task-solving represents a fundamental learning aspect of the ball game. Furthermore, based on the layered structure of the defensive threshold and the method selected for breaking through the structure, three phases of confrontation between offense and defense can be distinguished. Especially in the process of breakthrough task-solving, players select the specific application of ball manipulation (“pass” or “carry”) depending on the ratio between two antagonistic intentions: ball-possession and ball-progression. These findings provide a new perspective for instruction in ball games, which would enable learners to construct the processes as a meaningful experience, rather than merely reproducting solutions for the tasks of the competition.