Pattern, Functions and relationships. It is frequently written that mathematics is the study of patterns and relationships. Pattern is seen as a wide-ranging concept that covers patterns encountered all around us, such as those in musical forms, nature, traffic patterns, etc. It is argued by Senechal (1990) that our ability to recognize, interpret, and create patterns is the key to dealing with the world around us. The human capacity for identifying relationships and for thinking analytically undergirds mathematical thinking. Algebra - beyond symbolic manipulation - provides a tool for representing relationships between amounts through the use of tables, graphs, symbols, and words. The ability to generalize and to characterize functions, relationships between variables, is a crucial gateway to understanding even the most basic economic, political or social analyses. A basic level numeracy task might require someone to describe how items are arranged in a package; developing a formula for an electronic spreadsheet would put a higher level of demand on the individual.

Data and chance. Data and chance encompass two related but separate topics. Data covers "big ideas" such as variability, sampling, error, or prediction, and related statistical topics such as data collection, data displays, and graphs. Modern society demands that adults interpret and produce organizers of data such as frequency tables, pie charts, graphs and to sort out relevant from irrelevant data. Chance covers "big ideas" related to probability, subjective probability, and relevant statistical methods. Few things in the world are 100% certain; thus the ability to attach a number that represents the likelihood of an instance is a valuable tool whether it has to do with the weather, the stock-market, or the decision to board a plane. In this mathematical category, a simple numeracy skill might be the interpretation of a simple pie chart; a more complex task would be to infer the likelihood of an occurrence, such as predicting the weather, based upon past information.

Change. This term describes the mathematics of how the world changes around us. Individual organisms grow, populations vary, prices fluctuate, objects traveling speed up and slow down. Change and rates of change help provide a narration of the world as time marches on. Additive, multiplicative, exponential patterns of change can characterize steady trends; periodic changes suggest cycles and irregular change patterns connect with chaos theory. Describing weight loss compares as a simple task to calculating compounded interest.

3.4 Facet 4: Representations of mathematical information

Mathematical information in an activity or a situation may be available or represented in many forms. It may appear as concrete objects to be counted (e.g., people, buildings, cars, etc.) or as pictures of such things. It may be conveyed through symbolic notation (e.g., numerals, letters, and operation or relationship signs). Sometimes, mathematical information will be conveyed by formulas, which are a model of relationships between entities or variables.

Mathematical information may be encoded in visual displays such as a diagram or chart; graphs and tables may be used to display aggregate statistical or quantitative information (by displaying objects, counting data, etc.). Similarly, a map of a real entity (e.g., of a city or a project plan) may contain information that can be quantified or mathematized.