Key terms & definitions

A comparison made by dividing one quantity by another, or expressing their relative sizes using a colon.

A comparison of quantities by division, written using a colon, such as $2:5$.

A comparison of quantities in a stated order. For example, $A:B=2:3$ means there are two units of A for every three units of B.

A comparison of quantities in a stated order, such as $2:3$.

A logical, evidence-based interpretation that is realistic and flexible.

A decision made by weighing perceived advantages against disadvantages; in Carlen’s explanation, crime becomes an option when its expected benefits outweigh its costs.

The scientific reason for carrying out an investigation in a particular way, including what is being tested and why.

The scientific purpose and reasoning behind an investigation, including what is being tested and why the chosen approach can provide relevant evidence.

The scientific reason for carrying out an investigation in a particular way.

An explanation based on natural processes rather than supernatural forces; it is not necessarily scientifically correct.

A quotient of two polynomials, such as $\frac{x^2-4}{x+3}$, defined only where its denominator is non-zero.

An explanation used to make troubling behaviour seem reasonable or acceptable.

To rewrite a fraction with no surd in its denominator without changing its value.

Rewriting a fraction so that its denominator contains no surd while keeping its value unchanged.

Authority accepted because it rests on shared impersonal rules, laws and recognised offices.

A number that can be written as $\frac{p}{q}$, where $p$ and are integers and . Integers are also rational numbers.

Government limits on the quantities of scarce goods that individuals can buy, intended to share available supplies more fairly.

The colon used to separate the parts of a ratio; for example, $3:5$ is read as “three to five”.

Food allowances distributed by the government. Dependence on these supplies gave officials leverage over Native American families.

One of the equal-sized units represented by the numbers in a ratio.

A comparison of a length on a drawing with the corresponding real length, expressed using the same units, such as 1 : 25 000.

Original measurements, counts, responses or observations before they have been organised or calculated.

Original measurements or observations before any calculations are carried out.

Data as originally collected or recorded, before checking, cleaning or further processing.

Measurements or observations in their original form, before they have been processed or summarised.

Information collected during research before it has been organised, summarised and interpreted.

An unfinished cut edge of fabric, which may fray as yarns become loose.

A naturally occurring material from which useful products are made; metal ores are finite raw materials.

A starting material used to make a material or product, such as a metal ore or crude oil.

A basic material used to make a product, such as fruit used to make juice.