The focus is on the problem-solving behaviors of primary age children on one-step verbal or story problems involving addition and subtraction. When children are given a simple word problem for which they have not learned the necessary algorithms, they are often able to derive a solution on their own. This report focuses on the child-invented processes pupils use on word problems that would normally be solved through use of an addition or subtraction algorithm. Much of the data comes from a three-year longitudinal study of about 100 first-grade pupils from one public and one parochial school in the Madison, Wisconsin area serving middle to upper-middle class neighborhoods. It was felt that invention was a rearrangement of elements into similar structures. The data suggested that instruction has a bearing upon changes in invented behavior. Thus, any characterization of children's formal or invented mathematics concepts and procedures needs to consider the role of instruction. (MP)