For this study, the second in the cross sectional series, based on the Conceptual Learning and Development (CLD) model, assessment batteries were developed to determine each child's level of attainment and related use of the concepts "equilateral triangle,""cutting tool,""noun," and "tree." Batteries were designed as paper-and-pencil tasks and were administered to from 349 to 362 children, depending on assessment battery, enrolled in each of four grades: first, fourth, seventh, and tenth. Predictions based on the model about children's conceptual development were strongly supported across concet concepts: (1) The concepts were attained in an invariant sequence at four successive levels: concrete, identity, classificatory, and formal. (2) As the concepts were attained at higher levels, they were used increasingly in cognizing supraordinate-subordinate relationships in a hierarchy, in understanding principles that stated a relationship between the attained concept and one or more other concepts, and in solving problems that required the use of the particular concept. (3) Having the labels of the concept and of its defining attributes facilitated attainment of the concept and mastery of the three uses of the concept. (Author/BW)