Understanding measurement units is critical to mathematics and science learning, but it is a topic that American students find difficult. In 3 studies, we investigated the challenges underlying this difficulty in kindergarten and second grade by comparing performance on different versions of a linear measurement task. Children measured crayons that were either aligned or shifted relative to the left edge of either a continuous ruler or a row of discrete units. The alignment (aligned, shifted) and the measuring tool (ruler, discrete units) were crossed to form 4 types of problems. Study 1 showed good performance in both grades on both types of aligned problems as well as on the shifted problems with discrete units. In contrast, performance was at chance on the shifted ruler problems. Study 2 showed that performance on shifted discrete unit problems declined when numbers were placed on the units, particularly for kindergarteners, suggesting that on the shifted ruler problems, the presence of numbers may have contributed to children's difficulty. However, Study 3 showed that the difficulty on the shifted ruler problems persisted even when the numbers were removed from the ruler. Taken together, these findings suggest that there are multiple challenges to understanding measurement, but that a key challenge is conceptualizing the ruler as a set of countable spatial interval units.