The use of a step-by-step procedure for sequencing materials from concrete objects to paper and pencil can provide kindergarten teachers with a defensible means for showing that children are progressing in their mathematical competencies even though they may not be doing paper-and-pencil activities. Developmental characteristics of young children are first described; of particular importance is the fact that they have developed many mathematical concepts through informal learning before they come to school. They deal best with concepts through activities involving concrete materials and need opportunities to continue to actively construct their own knowledge through involvement with things in their environment. A six-step guide is then outlined which provides a sequence for moving from concrete materials to paper and pencil: manipulation of real objects, real objects and pictorial representations used in combination, manipulation of pictorial representations, manipulation of card sets or cut-up workbook pages, laminated workbook pages or other activities, paper-and-pencil activities. A specific example is given to illustrate this procedure. A number of references are included. (MNS)