Functions represent the systematic dependence of one quantity on another. Students use functions to represent and model problem situations and to analyze and interpret relationships. Equations arise as a way of asking and answering questions involving functional relationships. Students work in many situations to set up equations and use a variety of methods to solve these equations. Techniques for working with functions and equations are essential in understanding underlying relationships.
Many processes underlie all content areas in mathematics.
Students continue to build on this foundation as they expand their understanding through other mathematical experiences. Students study algebraic concepts and the relationships among them to better understand the structure of algebra. The study of functions, equations, and their relationship is central to all of mathematics. Students perceive functions and equations as means for analyzing and understanding a broad variety of relationships and as a useful tool for expressing generalizations. Students perceive the connections between algebra and geometry and use the tools of one to help solve problems in the other.