The Small Magellanic Cloud is a crucial galaxy to understand many aspects of the formation and evolution of galaxies. We propose to collect deep photometry in sixteen fields located at galactocentric distances from R_gc=2 to 4 degrees, in order to obtain color- magnitude diagrams reaching the oldest main sequence turnoff stars with high signal-to-noise ratio. These will allow us to derive accurate life- time star formation histories through comparison with synthetic color magnitude diagrams. The main outcome of this work will be a representative characterization of the time and space variations of the star formation history across the outer disk of the SMC. The range of galactocentric distances has been selected such that the density of SMC stars is enough to populate the color-magnitude diagrams of each observed MOSAIC field with over 50,000 stars, enough for a robust star formation history determination. We describe our plan for the near future to obtain the necessary data for other ranges of galactocentric distances, using the most suitable instruments for each case.