This report illustrates a network of procedures which can be used to solve problems involving the addition and subtraction of fractions. This network, which is based on a skills hierarchy, is used to classify seven levels of student competency. The determination of student competency depends upon the careful construction of error-diagnostic tests. Several examples of student response patterns are used to illustrate a procedure to construct a few selected items for such a test so that it will have both content and construct validity. Similar examples of student misconceptions and incomplete knowledge are included to illustrate the difficulty/futility in using test scores to assess student performance. The report includes several lists of projected errors which are either predicted from the nodes of the procedural network or are based on classroom observations of junior high school students. These errors have been classified by the node best representing the misconception or incomplete information. Complete tests which were used to assess student knowledge have been included in the report. (Author)