A central component in the young child's construction of a number system is an understanding of correspondence. Although current research demonstrates that preschool children use correspondence in a variety of tasks, the nature of the relationship between the use of correspondence action patterns and the use of correspondence as a quantifier is still not understood. This paper reports on three studies of 4- to 5-year-olds that were designed to determine whether preschool children know that correspondence can be used to measure quantity. Children were given number conservation, addition and subtraction, and division tasks. Only the division task varied across the three studies. Children were asked to divide a clump of 11 cookies into 2 equal parts. Whole cookies were used in the first study, and wholes and halves were used in the second and third studies. In most cases, children used several strategies on a trial, and correspondence was one of them. Children rarely used counting on all trials. Performance on the addition and subtraction tasks suggested that young children can use correspondence effectively to make equivalence judgments. However, most children were not successful in making judgments based on the differences in absolute numerosity between the two arrays. Additional findings suggested that children's use of correspondence precedes their understanding that correspondence can be used to measure quantity. Eight statistical tables are included. Contains 6 references. (LB)