Perhaps one of the contents in mathematics with greater difficulties, both for students and teachers, is the teaching and learning of the division. It is for this reason that the present research work described as a concrete and judicious form, some instrumentalization processes for the teaching of the division mediated with an instrument. An analysis that is sold in the traditional way of teaching in the classroom of mathematics and overflows to the use of the Instrument of the mackinder box, where in a natural way, it is also possible to formalize introductory concepts of the theory of numbers. A research work for the account of historical, didactic and innovative aspects for the teaching of architecture, considering different readings in a sequence of activities for fourth grade students in two educational institutions, where their arguments, processes and concludes if in effect, the Instrument enhances their learning and, in addition, generates significant learning.