The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related to addition and subtraction, and coded strategy data for a set of verbal addition and subtraction problems administered in an interview setting. Eleven children starting third grade in Tasmania, Australia were involved in the study. The data suggested two notions: (1) there is a group of children who have the capacity to reason about quantitative problems, know the basic procedures of addition and subtraction, but see little reason to use those algorithmic procedures to find answers to verbal problems; (2) there is a second group of children whose capacity to reason about quantitative problems is suspect: they do not know the basic procedures to addition and subtraction and have not acquired other skills like modeling or counting which would help them solve verbal problems. It is suggested that educators need to reexamine the relationships between the algorithm and its application. (MNS)