This study was designed to gain information about the understandings children in Israel and the United States have about multiplication and division of whole numbers that may be useful in building accurate understandings of these operations with decimals and the extent to which they hold conceptions about these operations that may interfere with their work with decimals. Data from interviews of the fourth and fifth graders indicate that students of this age already hold misconceptions such as "multiplication always makes bigger." However they also hold conceptions that are prerequisite to understanding the area model of multiplication and the measurement model of division. These early conceptions might be used to build understanding of multiplication and division by decimals. Implications for the content and sequencing of instructional activities are presented.