This handbook is intended to assist postsecondary Kentucky vocational education instructors in determining the mathematics competencies that they should address in their courses. The competency listings and resource information included in the handbook are based on information obtained from 109 postsecondary vocational instructors throughout the state. The first section describes the development of the handbook and the importance of math competencies throughout the continuum of technical and nontechnical vocational education programs. The second section includes listings of accepted competencies for the following program areas: air conditioning, auto body, auto mechanics, carpentry, drafting, electricity, electronics, graphic arts, machine shop, masonry, and welding. Section 3 provides additional competencies and comments obtained at several points throughout the project. The fourth section lists resources for teaching math (including texts, audiovisual materials, and computer software), and the fifth section discusses ways in which the information provided can be used to improve vocational programs. Appendixes include the 10 surveys used to develop the handbook, tabulations of the survey responses, lists of competencies that were not selected, examples of competencies, and evaluation forms. (MN)