The goal of this study was to describe characteristic stages in the development of children's understanding of place value. Sixty children (15 in each grade, 2 through 5) at 5 elementary schools in Butte County, California, were individually administered 18 tasks designed to reveal their thinking about place value and part-whole relations. On six tasks children were to identify the number of objects represented by the individual digits in a two-place numeral. Seven fifth-graders, seven fourth-graders, two third-graders, and no second-graders were successful on all six tasks; 28 children failed to convincingly demonstrate any understanding of the tens digit. Success on prerequisite tasks measuring rational counting by tens, identifying the tens and ones places, partitioning collections into a tens part and a ones part, and conserving grouped number were all found to be necessary for success on more than four digit-correspondence tasks. Understanding of part-whole relations as reflected by success on arithmetic word problems and on logical classification tasks was necessary for success on more than two digit-correspondence tasks. A five-stage model of the development of children's understanding of place value was then proposed. A three-page bibliography concludes the document. (MNS)