Mathematics is essentially a process of thinking that involves building and applying abstract, logically connected networks of ideas. These ideas often arise from the need to solve problems in science, technology, and everyday life—problems ranging from how to model certain aspects of a complex scientific problem to how to balance a checkbook.

This chapter presents recommendations about basic mathematical ideas, especially those with practical application, that together play a key role in almost all human endeavors. In Chapter 2, mathematics is characterized as a modeling process in which abstractions are made and manipulated and the implications are checked out against the original situation. Here, the focus is on seven examples of the kinds of mathematical patterns that are available for such modeling: the nature and use of numbers, symbolic relationships, shapes, uncertainty, summarizing data, sampling data, and reasoning.