Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times relationship between places in the number system and what happens when numbers are multiplied or divided by powers of ten. Evidence from the research project discussed here suggests that many students have a procedural view of these ideas, and that a conceptual understanding needs to be developed. It is suggested that this may be possible through the use of a device called "The Marvellous Multiplier".