This study was concerned with the verification of a learning hierarchy for the mathematical task of adding fractions, when group learning procedures involving teacher-student interaction were used. Through a task analysis procedure a hierarchy of 13 subordinate skills was hypothesized, behavioral objectives were specified, and a curriculum sequence was developed. Test materials were constructed directly from the behavioral objectives to yield pass-fail information on each subskill and on the final task. The classes of five fifth-grade teachers participated. A pretest indicated that although some children had prior knowledge of some lower subskills, none were able to perform the final task. The final task and subordinate skills posttest showed a significant attainment of the task and the skills by the sample. Two different methods were used to examine the children's achievement patterns in order to determine if the hierarchy had been validated; the investigator concluded that, under both methods, the values calculated from posttest results exceeded the minimum criterion established for validity. Validation based on daily quiz performance yielded similar results. (Author/DT)