Influential curriculum documents such as the National Statement on Mathematics for Australian Schools recommend that greater emphasis be given to students' informal written computation methods. This raises the question of the nature of these informal methods and the extent to which students can and do use them. The present study explored the informal methods students in a Year 3/4 class used to solve problems for which they had not previously been taught a formal method. The results of the study indicate that, once students can understand the problem, they invariably are able to generate a valid method to solve it. Furthermore, while the sophistication of their methods varied considerably, the students displayed an ownership and understanding of the methods which they do not always have when using formal algorithms. Invalid methods were nearly always associated with attempts to obtain an answer just by symbolic manipulation of the numbers involved. This has important implications for the teaching of written computation in mathematics. In many cases, it may not be necessary to teach the standard algorithms at all and, if they are needed, the students' informal methods could form a valuable basis for this teaching.