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All professions use a particular language to convey specific meanings. As educational professionals, school leaders and teachers use certain words and terms with specific and precise meanings to ensure shared understandings. This glossary explains terms used within the mathematics standards and their illustrations.

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Additive: a term used to describe a range of problem-solving strategies that use the properties of addition and subtraction to partition (split) and combine numbers.

Addition facts: the basic facts of addition; equations in which two single-digit numbers are combined by addition to give a sum. For each basic addition fact (for example, 7 + 9 = 16), there are one or two related basic subtraction facts (for example, 16 − 7 = 9 and 16 − 9 = 7).

Algebraic equation: a statement of equality between variables that uses letters, the equals sign, and operation symbols to describe the relationship (for example, y = 3x + 2).

Algorithm: a series of steps that can be followed mechanically to find a solution. There are standard written algorithms used for addition, subtraction, multiplication, and division.

Array: an arrangement or tessellation of objects in rows and columns, for example, an arrangement of unit squares to measure the area of a rectangle. Such an arrangement is a useful representation for illustrating the properties of multiplication and division.

Attribute blocks: plastic blocks that have two sizes, three colours, five geometric shapes, and two thicknesses and that are useful for developing ideas about classification.

Axes: the horizontal and vertical reference lines for a geometric figure; the x and y axes of a number plane.

Bar graph: a chart that displays the frequency of category or number variables as bars of varying height (but equal width).

Bearings: the direction or position of something relative to a fixed point, usually measured in degrees, clockwise from north.

Capacity: fluid volume, that is, how much liquid a container can hold.

Category data: non-numeric data (for example, colours, genders, flavours) that can be organised into distinct groups.

Cluster: a grouping or concentration of data points in a display (for example, of pulse rates between 70 and 90 beats per minute).

Comparison question: a question that compares two or more subsets of data (for example, male and female) in relation to a common variable (for example, age).

Compensation: rounding to tidy numbers (for example, 5, 10, 20, 100) to perform an operation and then compensating for the rounding by adding or subtracting so that an exact answer or a better estimate is obtained.

Co-ordinates: the position of a point in relation to a set of axes or grid lines and usually described using ordered pairs (for example, 3,10).

Counting all: solving simple addition or subtraction problems by counting all of a set of objects from one (the first object).

Counting back: an early subtraction strategy in which students solve problems by counting back by ones (for example, for 8 – 3, counting back from 8: 7, 6, 5).

Counting on: an early addition strategy in which students solve problems by counting up from a number (for example, for 5 + 3, counting on from 5: 6, 7, 8).

Cuboid: a rectangular prism, that is, a 3-dimensional solid with six rectangular faces. Note that a cube is a special case of a cuboid.

Data cards: cards used to collect data, usually with several variables to a card. Data cards can be sorted to reveal patterns and differences.

Dimensions: the measures of the length, width, and height of an object.

Dot plot: a graph in which each value of a numeric variable is represented by a dot.

Doubling and halving: a multiplication strategy in which one number is halved and the other is doubled (for example, 50 x 40 = 100 x 20). Note that the answer remains unchanged.

Equal dealing: equal sharing (see below) in which an equal number of objects is given to each subset over a number of cycles.

Equal sharing: dividing a set of objects into equal subsets.

Equilateral triangle: a triangle with all sides equal.

Equivalent fractions: fractions that represent the same value.

Frequency table: a table that uses numbers to show how many items are in several categories or how often several things occur (for example, the number of students with black, brown, red, and blonde hair).

General rule: a generalisation that describes how two variables are related and that may be expressed in words or as an equation (for example, “You get the next number by doubling the first number” or y = 2x).

Half-turn symmetry: rotational symmetry of 180 degrees: if you turn the object halfway, it maps onto itself.

Histogram: a type of bar graph used to display the distribution of measurement data in equal intervals across a continuous range.

Imaging: visualising physical objects and the movement of the objects mentally.

Interval: a section of the range of measurement data (for example, heights grouped into intervals of 150–160 cm, 160–170 cm, and so on).

Inverse relationship: the relationship between two operations in which the effects of one reverse those of the other and vice versa (for example, multiplication and division).

Isometric view: a 2-dimensional drawing of a 3-dimensional object in which the three axes are at an angle of 120 degrees to each other.

Knowledge: information that a person can recall or access without significant mental effort (for example, basic addition or multiplication facts).

Line graph: a graph in which data points are joined by straight lines, typically used to represent time-series data, with the horizontal axis representing time.

Linear relationship: a relationship between two variables in which the value of one variable is always the value of the other multiplied by a fixed number plus or minus a constant (for example, y = 2x + 3). The graph of a linear relationship is a straight line.

Making tens: a mental calculation strategy that uses combinations of numbers that add up to 10 (for example, 53 + 7 = 60 because 3 + 7 = 10).

Mixed operations: problems that involve more than one arithmetic operation (+, –, x, ÷), for example, 4 x 7 – 3.

Multiplication facts: the basic facts of multiplication: the products of single-digit numbers (for example, 8 x 9 = 72). For each basic multiplication fact, there are one or two related basic division facts (for example, 72 ÷ 9 = 8 and 72 ÷ 8 = 9).

Multiplicative strategies: a range of problem-solving strategies that use the properties of multiplication and division.

Multivariate category data: a data set in which data for two or more variables is collected for each item or person (for example, gender, eye colour, and favourite television programme).

Net: a 2-dimensional figure that can be cut and folded to form a 3-dimensional object.

Number Framework: a set of progressions, in both number strategies and knowledge, that outline a growth path for students over time.

Ordinal position: the place of a number in the whole-number counting sequence from 1 (for example, ninth, twenty-fifth).

Outcome: the result of a trial in a probability activity or a situation that involves an element of chance.

Parallelogram: a 4-sided polygon in which both pairs of opposite sides are parallel.

Partitioning: the breaking up of numbers, shapes, or objects into parts (for example, by place value) to facilitate understanding, calculation, or problem solving.

Part–whole strategy: a strategy for solving difficult problems that involves partitioning (splitting) numbers into manageable components and then recombining them to get a final result (for example, 38 + 46 might be calculated as (30+ 40) + (8 + 6)).

Perimeter: the distance around the outside of a shape.

Perspective view: a 2-dimensional drawing that gives a 3-dimensional view of an object.

Pictograph: a graph of category or whole-number data in which pictures or symbols represent the number in each category or grouping.

Pie chart: a graph that represents category data by splitting a circle into sectors, the size of each sector being proportional to the frequency of the data it represents.

Place value: the value of a digit in a number, as determined by its place (for example, the 4 in 47 is in the tens place, giving it a total value of 4 x 10 or 40).

Place value partitioning: splitting numbers by the place values of the digits that compose them to perform calculations (for example, 234 – 70 can be thought of as 23 tens minus 7 tens plus 4).

Plan view: a 2-dimensional drawing (projection) of an object that shows how it would look from above.

Polygon: a closed 2-dimensional figure with three or more straight sides.

Prism: a 3-dimensional solid that has a regular cross-section (for example, a triangular prism has a triangular cross section).

Probability: the likely occurrence of an event (a particular outcome), which can be represented by a number from 0 (impossible) to 1 (certain).

Projections: 2-dimensional drawings of a 3-dimensional object that show how the object looks from different directions, for example, from the top (the plan view), the front, or the side.

Proportional thinking: using equivalent fractions to solve problems that involve fractions, percentages, decimals, or ratios.

Rectangular prism: a solid that has a regular rectangular cross-section.

Recursive rule: a rule that describes the connection between a term and the next term in a number sequence (for example, + 4 for the sequence 6, 10, 14, ...).

Reflective symmetry: the regularity of a pattern or shape in which one half of the figure is a mirror image of the other half.

Relationship question: a question about the link between two variables in a set of data.

Right-angled triangle: a triangle with one interior angle of 90 degrees.

Rotation: a turn about a point.

Rotational symmetry: the regularity of a pattern or shape that allows the figure to be mapped onto itself by a less than 360 degree turn about a point.

Scalene triangle: a triangle that has no equal sides.

Skip-counting: counting in amounts other than ones (for example, 2s, 5s, or 10s).

Solids: 3-dimensional objects.

Spatial patterns: patterns in which figures or objects are arranged in consistent ways in relation to position or distance.

Spread: the difference between the lowest and highest values in a data set. Spread may be measured by calculating the range.

Standard units: units of measurement that are universally accepted, such as the units of the metric system, as opposed to informal, non-standard units, such as hand spans.

Statistical enquiry cycle: an investigative cycle for data-based enquiry.

Stem-and-leaf graph: a graph used to display discrete number data for the purpose of a summary (a single graph) or a comparison (a back-to-back graph). The 'stem' is created from a common place value in the numbers (for example, tens), and the 'leaves' represent the remaining place value, typically, ones.

Strategy: a way of working out the answer to a problem.

Subtraction facts: the basic facts of subtraction: equations in which two numbers are combined by subtraction. Subtraction facts are related to the addition of single-digit numbers (for example, 8 + 6 = 14 leads to the subtraction facts 14 – 6 = 8 and 14 – 8 = 6).

Summary question: an investigative question about the distribution of a single variable (for example, “How long does it typically take a year 6 student to run 100 metres?”).

Symmetry: in geometry, the regularity of a figure or object that maps onto itself by reflection or rotation. Using symmetry is important in Number, for example, when sharing by equal dealing or when finding doubles and halves by equal partitioning (for example, 4 + 4 is a symmetrical partitioning of 8).

Tally chart: a method of recording frequency of data using stroke marks (for example, //// ).

Tessellate: cover a surface with repeats of the same shape without gaps or overlaps.

Tidy numbers: numbers that are easy to work with for a given calculation (for example, 5 instead of 4.95 or 20 instead of 19).

Time-series data: a set of data gathered over time to investigate time-related trends.

Transformation: the mapping in space of every point in a figure or object onto a new location. Common transformations are reflection, rotation, translation, and enlargement.

Translation: a transformation that moves every point in a figure a given distance in the same direction.

Trial: one instance of carrying out an experiment (for example, flipping a coin ten times).

Unit conversion: changing from one unit of measurement to another unit for the same attribute so that both represent the same quantity (for example, from 1.5 litres (L) to 1500 millilitres (mL)).

Variable: a numerical value that can vary, for example, across data or in describing a mathematical relationship (for example, in the equation y = 4x, x and y are variables).

Vertical algorithm: a standard written working form that organises calculations into columns to make use of place value.

Volume: the amount of space occupied by a 3-dimensional object.

Weight: the measure of the heaviness of an object (in scientific terms, the force of gravity acting on a mass).

Whole numbers: all numbers in the set that includes zero and the counting numbers (for example, 0, 1, 2, 3 ...).

Written algorithm: see algorithm; the written recording of a series of steps for calculating an answer.

Published on: 19 Oct 2009