Relations among patterns of conceptual and procedural knowledge and grade were examined in 90 six- to eight-year-olds in order to explore addition and subtraction development. Conceptual knowledge was assessed by examining children's responses to pairs of problems reflecting various part-whole relations. Children solved related problems as part of a Problem-solving Task, judged, and explained part-whole relations in a Judgement Task. Children also solved a random set of addition and subtraction problems. Distinct profiles of problem-solving were derived from an analysis of children's speed, accuracy and self-reported problem-solving procedures on unrelated problems. Problem-solving profiles were associated with individual differences in part-whole knowledge and grade level but grade and part-whole knowledge were not related. Findings suggest that identifying profiles of procedural and conceptual knowledge is important for understanding children's mathematical development.