This study investigated the performance of 790 fourth graders from Taiwan for judging the reasonableness of a computational result by using corresponding methods pertaining to whole numbers. A number-sense web-based two-tier diagnostic test was used to assess the number-sense performance of the fourth graders who participated in this study. The results revealed unsatisfactory performance of study participants. Only 25% of them could apply the number-sense-based method to answer problems, and approximately 38% of them had misconceptions regarding various items. This paper discusses several of these misconceptions, as well as the study implications and suggestions for future research.