An understanding of measurement and units of measurement is important in mathematics and science. However, children in the United States perform very poorly on measurement items on standardized mathematics tests compared to students in other countries. We examine understanding of linear measurement and units of measurement in 2nd grade students and carry out a training study aimed at improving their understanding, drawing on research showing that structural alignment is important in promoting learning. We find that students do not improve when training consists of measuring items aligned with a ruler, either when discrete units are coordinated with this activity by overlaying them on the ruler or when students engage in aligned ruler measurement and measurement with discrete units separately. However, we do find significant improvement when children measure objects that are misaligned and then aligned with the start of the ruler and discrete units are coordinated with ruler use.