Psychological regularities in the organization of common activity connected with looking for a solution of an academic problem requiring to find the trajectory of a complex movement are considered. Orienting behavior of children has been of particular interest. Two groups of orienting operations, each with a specific object, have been established in 5 experimental series which required different division and re-combination of individual activities. The first group was guided by the task of looking for a correspondence between the result of the common activity and the given form of the trajectory, the second - by the very task of finding the proper method of coordination of shared operations.