As a result, it includes the use of variables, modeling relationships both algebraically and graphically, and appropriate use of functions. Number and Numeration Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas. Although number and numeration deal heavily with number concepts of whole numbers, fractions, decimal fractions, ratios, percents, integers, and irrational numbers, this key idea also includes procedures for ordering numbers and applying them to real-world situations. Operations Students use mathematical operations and relationships among them to understand mathematics. Often considered to be primarily procedural, operations includes the expectation that students understand the concepts of addition, subtraction, multiplication, and division in order to be successful with problem solving.
Problem solving often requires the selection of appropriate computational or operational methods.
The concepts of ratio and proportion must be understood in order to recognize and solve problems that are proportional in nature. Patterns and Functions Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently. The study of patterns and functions is one of the central themes of mathematics. Patterns are a major part of mathematics study in the elementary grades. Astudy of patterns requires the conceptual understanding of recognizing, describing, and generalizing patterns.