The advantages and disadvantages of two common grading methods are presented, and from an analysis of the virtues and vices of these prototypic methods, a set of goals or criteria for grading systems is derived. Percentage and class-curve grading systems are discussed in detail. Criteria for grading systems include the following: obtain relevant norm referencing; avoid instability of small samples; avoid psychological evils of fixed-sum games; provide sense of efficacy; and be defined and interpretable. The concept of anchoring measures to provide an escape from the apparent paradox that emerges from the analysis of the two common grading systems is presented. The statistical processes by which anchor measures are used can be relatively simple and intuitive. Their ease of use is illustrated by the following examples: the use by one instructor of final exams as anchor measures; the teaching of a U.S. history course in a community college by three instructors each teaching one or two sections; and the teaching of a freshman English course in multiple sections by 20 graduate teaching assistants in a large university. Each of the common bases for assigning college grades (percentage and class-curve grading) has only limited meaning and lacks a sound rationale; neither satisfies the major criteria for student grading systems. Anchor measures enable the advantages of norm-referenced grading to be achieved without the negative aspects of class-curve grading. They are recommended for use in assigning college grades. Contains 10 references. (SM)