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A hierarchy for learning to solve different types of addition wit fractions problems was hypothesized on the basis of both content a lysis and psychological considerations. Problem types were defined acco ding to the relationship of the two denominators to each other (e.g., e al, prime, etc.) Students in grades 4 through 8 were each given 45 ad tional problems to perform. Papers which were totally correct or totally, incorrect were deleted leaving a sample of 200. These papers were analyzed using both the Walbesser Technique and Pattern Analysis. No ordering of the tasks was found to yield acceptable levels for all of the Walbesser ratios (consistency, adequacy, completeness). However, with few exceptions, task comparisons yielded acceptable values on two of the three ratios. The empirically determined sequence was analyzed and seven implications for teaching addition with fractions were determined. (SD) * * via the ERIC Document Reproduction Service (EDRS). EDRS is not * responsible for the quality of the original document. Reproductions * * supplied by EDRS are the best that can be made from the original.