Newton's cradle is often discussed in science classrooms as a clear example of the laws of conservation of momentum and energy although it has been shown that this use is somewhat misleading. Approaches to understanding the behaviour of this apparatus are often over-simplified and deficient or over-complex and with little impact among teachers. In this paper, basic principles of mechanics are used to explain the behaviour of ideal cradles of various lengths and to use a simple model by which to simulate its operation. The purpose is to demonstrate that the real behaviour of Newton's cradle provides a rich source of application of those principles in coming to terms with how the apparatus behaves and experiencing the process of modelling in physics. [For "Understanding Newton's Cradle. II: Exploring a Real Cradle," see EJ1286996.]