This research tests a model of the computational role of three cortical regions in tasks like algebra equation solving. The model assumes that there is a left parietal region-of-interest (ROI) where the problem expression is represented and transformed, a left prefrontal ROI where information for solving the task is retrieved, and a motor ROI where hand movements to produce the answer are programmed. A functional magnetic resonance imaging (fMRI) study of an abstract symbolmanipulation task was performed to articulate the roles of these three regions. Participants learned to associate words with instructions for transforming strings of letters. The study manipulated the need to retrieve these instructions, the need to transform the strings, and whether there was a delay between calculation of the answer and the output of the answer. As predicted, the left parietal ROI mainly reflected the need for a transformation and the left prefrontal ROI the need for retrieval. Homologous right ROIs showed similar but weaker responses. Neither the prefrontal nor the parietal ROIs responded to delay, but the motor ROI did respond to delay, implying motor rehearsal over the delay. Except for the motor ROI, these patterns of activity did not vary with response hand. In an ACT-R model, it was shown that the activity of an imaginal buffer predicted the blood oxygen level-dependent (BOLD) response of the parietal ROI, the activity of a retrieval buffer predicted the response of the prefrontal ROI, and the activity of a manual buffer predicted the response of the motor ROI.