The relation between skill in simple addition and subtraction and more general math achievement in elementary school is well established but not understood. Both the intrinsic importance of skill in simple calculation for math and the influence of conceptual knowledge and cognitive factors (working memory, processing speed, oral language) on simple calculation and math are plausible. The authors investigated the development of basic calculation fluency and its relations to math achievement and other factors by tracking a group of 259 United Kingdom English children from second to third grade. In both grades the group did not retrieve the solutions to most problems, but their math achievement was typical. Improvement in basic calculation proficiency was partially predicted by conceptual knowledge and cognitive factors. These factors only partially mediated the relation between basic calculation and math achievement. The relation between reading and math was wholly mediated by number measures and cognitive factors. (Contains 9 tables and 1 footnote.)