Mathematical content/information/ideas
Four key areas of mathematical content, information and ideas are covered by the numeracy assessment in PIAAC .

Quantity and number
Quantity is an outgrowth of people’s need to quantify the surrounding world. It encompasses attributes such as the number of features or items, prices, size (e.g. length, area and volume), temperature, humidity, atmospheric pressure, populations and growth rates, revenues and profit, etc. Number is fundamental to quantification. Different types of numbers constrain quantification in various ways. Whole numbers can serve as counters or estimators; fractions, decimals and percents can offer expressions of greater precision, parts or comparisons; and positive and negative numbers can serve as directional indicators. In addition to quantification, numbers are used as organisers and identifiers (e.g. telephone numbers or postal codes). In calculations, operations (i.e. the four main operations of +, –, x, ÷ and others, such as squaring) are performed on quantities and numbers. Facility with quantity, number and operations on numbers requires a good “sense” of magnitude. Thus, contextual judgment is necessary when deciding how precise one should be or which tool to use (mental arithmetic, a calculator or a computer). Since mathematics is ubiquitous in every adult’s life, the good management of money and time depends on a good sense of number and quantity.

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Dimension and shape
Dimension includes the “big ideas” related to the description of “things” in space, such as projections, lengths, perimeters, areas, planes, surfaces, location, etc. The capacity to operate with spatial dimensions requires a sense of “benchmarks” and estimation, direct measurement and derived measurement skills. Shape involves a category describing real images and entities that can be visualised in two or three dimensions (e.g. houses and buildings, designs in art and craft, safety signs, packaging, snowflakes, knots, crystals, shadows and plants). An awareness of direction and spatial location is a fundamental skill required when reading, interpreting or sketching maps and diagrams. This content area requires an understanding of units and systems of measurement, both informal and standardised, such as the metric and imperial systems.

Pattern, relationships and change
Mathematics is often described as the study of patterns and relationships. Pattern covers regularities encountered in the world, such as those in musical forms, nature, traffic, etc. The capacity to analyse and identify patterns and relationships underpins much mathematical thinking. Relationships and change relate to the mathematics of how things in the world are associated or develop. Individual organisms grow, populations vary over time, prices fluctuate, and moving objects speed up and slow down. Some characteristics or values can change directly in proportion or relation to another change, while other characteristics may change in the opposite direction or in a different way. Change and rates of change describe the evolution of values in time. This domain includes the ability to develop and/or use mathematical formulae relating the different variables involved in a situation, together with the capacity to understand, use and apply a sense of proportional reasoning.

Data and chance
Data and chance encompass two separate but related topics. Data covers the “big ideas” related to variability, sampling, error, prediction and statistical topics, such as data collection, data displays and graphs. Chance covers the “big ideas” related to probability and relevant statistical methods. Few things in the world are certain; thus, the ability to attach a number to the likelihood of an event is a valuable tool, whether it has to do with the weather, the stock market or the decision to board a plane.

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