This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways according to the teacher's requirements and the needs of the students. It gives students a contextual and hence a practical application of the previously mentioned work. The investigation is punctuated with dividers which indicate possible breaks where teachers could assess or monitor student progress. (Contains 2 figures.)