The purpose of this paper is to analyze how didactic material applied with an intervention program favors understanding the Decimal Numeration System (DNS). Building processes of the SDN are described, interpreted, analyzed, and evaluated using a qualitative methodology of children in the third grade of Gran Colombia school before, during and after the application of an intervention program. Criteria covered includes conventional aspect of the number, numeric transcodification, aspect related to series, packing, numeric order, correspondence, aspect related to greater than but less than, and transitivity. Data was collected, systematized, and analyzed qualitatively using different tools. Results show important advances in the processes of structure the DNS that are explained as the result of the implementation of a specifically designed intervention program. Moreover, it shows that didactic material may be a tool that favorably helps learning of mathematics in children with low academic performance