NCEA Level 1 Pāngarau key terms

The Māori word for mathematics; the learning area covering number, algebra, geometry, measurement, and statistics. In NCEA it names the subject and the standards assessed in te reo Māori.

A level or standard in the NCEA framework. Level 1 is the first year of the qualification, and each achievement standard sits at a stated taumata that determines its credit value and difficulty.

A credit awarded for achieving an achievement or unit standard. Credits accumulate towards the qualification; a standard is usually worth between two and six credits depending on the workload it represents.

An achieved grade. It is the lowest of the three passing grades for an achievement standard, showing the candidate has met the standard, and it earns the credits attached to that standard.

The merit grade for an achievement standard. It sits above achieved and below excellence, and signals solid, secure understanding of most of the skills and concepts being assessed.

The excellence grade for an achievement standard. It is awarded when a candidate shows comprehensive, accurate, and insightful work, often including justification or application beyond routine procedures.

A number. In Pāngarau it covers whole numbers, decimals, fractions, and integers, and the operations performed on them such as addition, subtraction, multiplication, and division.

An integer: a whole number that may be positive, negative, or zero, with no fractional part. Integers are closed under addition, subtraction, and multiplication but not always under division.

A fraction. It represents part of a whole or a quotient of two numbers, written with a numerator and denominator, and can be expressed as an equivalent decimal or percentage.

A percentage: a number expressed as a fraction of one hundred. Percentages are used to compare proportions, calculate discounts, and describe increase or decrease in everyday contexts.

A rate: a ratio comparing two quantities with different units, such as kilometres per hour or dollars per kilogram. Rates allow quantities to be compared on a common scale.

A ratio: a comparison of two or more quantities of the same kind. Ratios can be written with a colon, as a fraction, or in words, and are used in scaling and proportion problems.

Proportion or proportional reasoning. It involves recognising that two quantities change together at a constant relative rate, allowing unknown values to be found by scaling up or down.

An equation: a mathematical statement showing two expressions are equal. Solving an equation means finding the value or values of the variable that make the statement true.

An expression: a combination of numbers, variables, and operations without an equals sign. Expressions can be simplified, expanded, or factorised but are not solved for a value.

A variable: a symbol, usually a letter, standing for an unknown or changing number. Variables let general rules be written and relationships between quantities be described.

A power or exponent: the number showing how many times a base is multiplied by itself. For example, in three to the power four, four is the exponent and three is the base.

A square root or root of a number: a value that, when multiplied by itself a given number of times, gives the original number. The square root of nine is three.

A set: a collection of distinct objects, numbers, or outcomes. Sets are described by listing their elements or by a rule, and are used in probability and algebra.

A combination or selection, where the order of chosen items does not matter. It is one of the counting ideas used when working out how many different groupings are possible.

Probability: a number between zero and one describing how likely an event is. It can be found from equally likely outcomes, from experiments, or from theoretical reasoning.

An outcome or event in probability. An event is a set of outcomes, and its probability is calculated by comparing favourable outcomes with the total number of equally likely outcomes.

Statistics: the branch of Pāngarau dealing with collecting, displaying, summarising, and interpreting data. It includes measures such as the mean, median, mode, and range.

Data: information collected through measurement, surveys, or observation. Data may be numerical or categorical, and its type determines how it can be displayed and analysed.

The mean or average of a data set, found by adding all values and dividing by how many there are. It is one measure of the centre of a distribution.

The median: the middle value when a data set is ordered from smallest to largest. If there is an even number of values, the median is the mean of the two middle values.

Shape: a two- or three-dimensional figure studied in geometry. Shapes are described by properties such as the number of sides, angles, symmetry, and whether sides are equal.

An angle: the amount of turn between two lines meeting at a point, measured in degrees. Angles are classified as acute, right, obtuse, straight, or reflex.

A triangle: a three-sided polygon. Its interior angles add to one hundred and eighty degrees, and triangles are classified by side lengths or by angle sizes.

A quadrilateral or four-sided polygon, including squares, rectangles, parallelograms, and trapeziums. Its interior angles add to three hundred and sixty degrees.

Area: the amount of two-dimensional space inside a shape, measured in square units. Formulas for area depend on the shape, such as length times width for a rectangle.

Volume: the amount of three-dimensional space an object occupies, measured in cubic units. It is calculated from dimensions such as length, width, and height.

Perimeter: the total distance around the outside of a two-dimensional shape, found by adding the lengths of all its sides. It is measured in linear units.

To multiply, or multiplication. It combines equal groups into a total and is the inverse operation of division; the result is called the product.

To divide, or division. It splits a quantity into equal parts or finds how many groups of a given size fit into it, and is the inverse operation of multiplication.

A graph or line on a graph, including the plotted line representing a relationship between two variables. The steepness of the line shows the rate of change.

A table used to organise and display data or values in rows and columns. Tables make patterns easier to spot and are often the first step before drawing a graph.

A pattern or a sample. In algebra it refers to a repeating numerical or spatial pattern and its rule; in statistics it means a subset of a population chosen for study.