This article analyzes the use of the software Grid Algebra with a mixed ability class of 21 nine-to-ten-year-old students who worked with complex formal notation involving all four arithmetic operations. Unlike many other models to support learning, Grid Algebra has formal notation ever present and allows students to "look through" that notation and interpret it either in terms of physical journeys on a grid or in terms of mathematical operations. A dynamic fluidity was found between the formal notation, imagery of movements on a grid, and the process of mathematical operations. This fluidity is interpreted as a "dance" between these three. The significant way in which this dynamic took place reflects the scaffolding and fading offered by the software, which was crucial to the students' fluency with formal notation well beyond what has been reported from students of that age.