The integration of History in the educational practice can lead to the development of a series of activities exploiting genetic "moments" of the history of Mathematics. Utilizing genetic ideas that developed during the 14th century (Merton College, N. Oresme), activities are developed and mathematical models for solving problems related to uniform motions are proposed, using the graph of velocity vs. time. The view of the covered distance as the area of the figure between the time axis and the velocity curve allows for the use of concepts and propositions of the Euclidean geometry. The use of simple geometric transformations leads to equivalent motion problems of a real context. This approach, applied to a wider range of problems, can form the basis for the introduction of basic concepts of calculus (such as integral, derivative, and their interrelation), in the context of a program of instruction in Senior High School. [For complete proceedings, see ED489538.]