Representation is central to the study of mathematics. Students can develop and deepen their understanding of mathematical concepts and relationships as they create, compare, and use various representations.
Representations are ubiquitous in the middle-grades mathematics curriculum proposed here.
The study of proportionality and linear relationships is intertwined both with students' learning to use variables flexibly in order to represent unknowns and with their learning to employ tables, graphs, and equations as tools for representation and analysis. Middle-grades students who are taught with this Standard in mind will learn to recognize, compare, and use an array of representational forms for fractions, decimals, percents, and integers. They also will learn to use representational forms such as exponential and scientific notation when working with large and small numbers and to use a variety of graphical tools to represent and analyze data sets. Students in the middle grades solve many problems in which they create and use representations to organize and record their thinking about mathematical ideas. For example, they use representations to develop or apply their understanding of proportionality when they make or interpret scale drawings of figures or scale models of objects, when they connect the geometric notion of similarity with numerical ratios, and when they draw relative-frequency histograms for data sets.