The primary aim of this guide is to aid teachers in planning and preparing a senior high school mathematics course for students preparing for college work. It is divided into separate one-semester courses of seven chapters each. The first-semester course consists of a traditional approach to the introduction of trigonometry and trigonometric functions. The second-semester course represents a new approach, treating algebra, trigonometry, analytic geometry, and calculus in a unified manner rather than as four separate sections. Fundamental notions of the subject are unified into a sequence of topics beginning with the consideration of the real number system and the algebraic operations. Emphasis is placed on the importance of being able to visualize and graphically represent mathematical expressions. Ideas of algebra and geometry are presented in the study of linear, quadratic, and general polynomial functions. Permutations, combinations, and probability are treated as additional topics. For both courses, behavioral objectives are stated for each chapter and a set of abbreviated daily lesson plans is presented. (JP)