We describe an investigative laboratory module designed to give college undergraduates strong practical and theoretical experience with recombinant DNA methods within 3 weeks. After deducing restriction enzyme maps for two different plasmids, students ligate the plasmids together in the same reaction, transform "E. coli" with this mixture of ligated DNA, and plate the cells on media that specifically select for hybrid plasmids. The main goal of the assignment is for students to deduce the gene map of one hybrid "Frankenplasmid" using the LacZ phenotype of its transformants, PCR, and restriction mapping. Our protocol results in a number of possible outcomes, meaning that students are mapping truly unknown plasmids. The open-ended nature of this assignment results in an effective module that teaches recombinant DNA procedures while engaging students with its investigative approach, increasing complexity, and puzzle-like quality. Moreover, the modular design of the activity allows it to be adapted to a more limited schedule, introductory courses, or more advanced courses. (Contains 2 figures and 1 table.)