Communicate about the mathematical information given, or the results of one's actions or interpretations to someone else. This can be done orally or in writing (ranging from a simple number or word to a detailed explanation or analysis) and/or through drawing (a diagram, map, graph).

3.3 Facet 3: Mathematical information

Mathematical information can be classified in a number of ways and on different levels of abstraction. One approach is to refer to fundamental "big ideas" in the mathematical world. Steen (1990), for example, identified six broad categories pertaining to: Quantity, Dimension, Pattern, Shape, Uncertainty, and Change. Rutherford & Ahlgren (1990) described networks of related ideas: Numbers, Shapes, Uncertainty, Summarizing data, Sampling, and Reasoning. Dossey (1997) categorized the mathematical behaviors of quantitative literacy as: Data representation and interpretation, Number and operation sense, Measurement, Variables and relations, Geometric shapes and spatial visualization, and Chance. The ALL Numeracy team drew from these three closely tied categorizations to arrive at a set of five fundamental ideas that in their view characterize the mathematical demands met by adults in diverse situations at the beginning of the 21^st century.

Quantity and Number. Quantity is described by Fey (1990) as an outgrowth of people's need to quantify the world around us, using attributes such as: length, area, and volume of rivers or land masses; temperature, humidity, and pressure of our atmosphere; populations and growth rates of species; motions of tides; revenues or profits of companies, etc. Number is fundamental to quantification and different types of number constrain quantification in various ways: whole numbers can serve as counters or estimators; fractions, decimals and percents as expressions of greater precision, parts or comparisons (ratios); and positive and negative numbers as directional indicators. In addition to quantification, numbers are used to put things in order and as identifiers (e.g., telephone numbers or zip codes). Facility with quantity, number, and operation on number requires a good "sense" of magnitude. Contextual judgment comes into play when deciding how precise one should be or which tool (calculator, mental math, a computer) to use. Money and time management, the ubiquitous mathematics that is part of every adult's life, depends on a good sense of number and quantity. A basic level numeracy task might be figuring out the cost of one can of soup, given the cost of 4 for $2.00; a task with a higher cognitive demand could involve more complex numbers such as when figuring out the cost per pound when buying 0.783 kg of cheese for 12,95 Euros.

Dimension and shape. Dimension includes "big ideas" related to one, two, and three dimensions of "things" (using spatial and numerical descriptions), projections, lengths, perimeters, planes, surfaces, location, etc. Facility with each dimension requires a sense of "benchmarks" and estimation, direct measurement and derived measurement skills. Shape is a category describing real images and entities that can be visualized (e.g., houses and buildings, designs in art and craft, safety signs, packaging, snowflakes, knots, crystals, shadows and plants), as well as highly abstract "things" greater than three dimensions. Direction and location are fundamental qualities called upon when reading or sketching maps and diagrams. A basic numeracy task in this fundamental aspect could be shape identification whereas a complex task might involve describing the change in the size of an object when one dimension is changed.