This paper presents a derivation of all five Lagrange points by methods accessible to sixth-form students, and provides a further opportunity to match Newtonian gravity with centripetal force. The predictive powers of good scientific theories are also discussed with regard to the philosophy of science. Methods for calculating the positions of the Lagrange points are presented. For points L1-3 the author uses a typical graph-plotting package available in schools, and for points L4 and L5 the author uses elementary trigonometry together with a knowledge of circular motion and gravitation. (Contains 13 figures.)