This research examined the effects of two instructional treatments on training performance in solid volume measurement and potential effects on solving capacity and displaced volume problems by two related studies. Fifty-three fifth-graders from a public elementary school in Taipei, Taiwan, participated. In the Phase 1 study, the children (n = 27) who received a curriculum that integrated geometric knowledge with concepts of volume measurement (GKVM) showed greater competence in solving problems than did those (n = 26) who received a curriculum that emphasized measurement procedures and volume calculation (VM). In the subsequent Phase 2, the same two groups received identical instruction in capacity, and the group that received the GKVM curriculum showed better problem-solving performance than did the other group. The one-on-one interview data showed that the children’s prior knowledge of solid volume measurement had a critical influence on the solving of advanced problems involving capacity and volume displacement concepts.