Mathematical Terms

Common multiple

A counting number which is a multiple of two or more other numbers. e.g. The multiples of 3 are 3, 6, 9, 12, ... and the multiples of 4 are 4, 8, 12, 16, ... so the common multiples of 3 and 4 are 12, 24, 36, 48, ...

Cent (c)

A currency or money unit of one-hundredth of a dollar.

Closed curve

A curve that has no end points. A simple closed curve does not intersect itself.

Abacus

A device with beads on wires, used to perform calculations.

Ascending order

An ordered arrangement according to number or size, beginning with the smallest.

Adjacent angles

Angles in the same plane with a common side and common vertex.

Composite number

Any counting number having more than two factors; i.e. 4, 6, 8, 9, 10, ...

Congruent figures

Figures having exactly the same shape and size.

Complementary addition

Finding the missing addend e.g. What must be added to 7 to get 10? i.e. 7 + ? = 10

Complementary angles

Two angles that together make a right angle.

Bearing

The direction of an object measured by its angle from the north in a clockwise direction by means of a compass.

Breadth (Width)

The distance across.

Circumference

The distance around a circle or the length of a circle; i.e. the perimeter of a circle.

Compass

An instrument used for drawing circles. An instrument for finding directions (has a magnetised needle that always points to the north).

Class interval

A category of grouped data where the intervals are generally bounded by limits referred to as the class limits, but for some categories there are no limits; e.g. for the data listed here the 'Over 30' class interval does not have an upper limit.

Calendar

A chart showing the days, weeks and months of the year.

Circle

A circle is the set of all points in a plane that are the same distance from a centre point.

Arrowhead (Chevron, Dart, Delta)

A concave quadrilateral with two pairs of congruent adjacent sides. [Can be considered as a concave kite].

Concave

A concave shape is curved inwards like the inside of a bowl.

Common factor

A counting number which divides two or more counting numbers without a remainder is a common factor of those numbers e.g. The factors of 6 are 1, 2, 3, 6 and the factors of 9 are 1, 3, 9; so 1 and 3 are common factors of 6 and 9.

Bar graph

A diagram that uses horizontal or vertical bars to represent information; also called a 'Column graph' if the bars are vertical.

Arrow diagram

A diagram where arrows are used to show the relationship between members of two sets. An arrow diagram may also be used to solve problems involving combinations.

Algebra

A generalised form of arithmetic where letters are used to represent numbers.

Box and whisker plot (Boxplot)

A graphical summary of data that shows five aspects of the data; the lower and upper quartiles (hence inter-quartile range), the median, and the lowest and highest values.

Carroll diagram

A grid-like structure for categorising results. [Named after its inventor, Lewis Carroll - a pen-name for the logician Charles Dodgson.]

Combination

A grouping. E.g. In selecting two or more letters from a, b, c there are four possible combinations: ab, ac, bc, abc.

Cumulative frequency graph (Ogive)

A line graph connecting the midpoints of the tops of the cumulative frequency bars. [Ogive refers to the shallow S-shape of such graphs.]

Chord

A line segment joining two points of a circle.

Axis (plural: axes)

A linear direction, usually vertically or horizontally; e.g. a bar or column graph and a line graph each have both vertical and horizontal axes to represent quantities.

Are

A metric unit of area equivalent to 100m2.

Common denominator

A name which can be used for several fractions e.g. A common name for the fractions 1/2 and 1/3 is sixths, because 1/2 and 1/3 can be renamed as 3/6 and 2/6 respectively - thus 6 is a common denominator for halves and thirds, as are 12, 18, 24, 30, ...

Co-interior angles

A pair of angles formed by the transversal of two parallel lines. They are supplementary (add to 180 degrees).

Cone (Circular pyramid)

A pyramid with a circular base.

Arithmetic progression (AP)

A sequence of numbers where the next term is generated by addition and/or subtraction with one or more of the previous terms. e.g. 4, 8, 12, 16, .... and 20, 15, 11 and 8, ... are both APs.

Attribute blocks

A set of plastic or wooden blocks consisting of differing attributes of shape, colour, size and thickness such that no two blocks in the set are the same, and used for classification purposes.

Algorithim

A step-by-step method for calculating a result.

Attribute

A trait or characteristic e.g. one attribute of a quadrilateral is that it has four sides.

Acute-angled triangle

A triangle where all three angles are acute; i.e. less than 90 degrees.

Centimetre (cm)

A unit of length which is one-hundredth of a metre.

Categorical variable

A variable whose categories are separate/distinct; e.g. makes of vehicles in a car park.

Column

A vertical arrangement of objects; i.e. in an up-and-down layout.

BC

Abbreviation for Before Christ and applied to dates. [BCE, for Before Common Era, is now often used.] e.g. The Roman emperor Julius Caesar was born in the year 100 BC.

AD

Abbreviation for the Latin "anno Domini" (year of our lord) applied to the years after the birth of Christ. [CE, for Common Era, is now often used.]

am (a.m.)

Abbreviation for the Latin words "ante meridiem", meaning before noon.

Cartesian product

All the possible matchings of the members of one set with the members of another set, illustrating multiplication e.g. The 2 cups and the 3 saucers can be matched in 2 x 3 = 6 ways.

Column graph

Also called a bar graph, where results are represented by columns or bars.

Acute angle

An angle of size less than 90 degrees. [Acute means sharp]

Approximate

An approximate number or measure is based on an estimate.

Array

An arrangement of objects into rows and columns.

Algebraic expression

An expression involving numbers, variables and operations. (An Algebraic expression is not an equation.) e.g. 2x + 5y

Addend

Any number to be added e.g. in the sentence 4+5=9, both 4 and 5 are addends.

Common fraction (Fraction)

Any numeral (number name) for a rational number and having a numerator and denominator. [Fraction is from the Latin "fractus" (to break). Common fractions are sometimes called vulgar fractions.]

Alternate angles

Any pair of angles on the opposite side of a transversal that cuts two parallel lines.

Annulus

Area enclosed between two concentric circles.

Classification

Arrangement into groups according to particular attributes. E.g. 1: The set of whole numbers may be classified as odd or even. E.g. 2: Attribute blocks may be classified by colour, shape, size and thickness.

Concentric circles

Circles having the same centre.

Balance

Equipment using a pivoted beam to compare the masses of objects, or to weigh objects.

Complementary events

Events that have no outcomes in common and that together contain all the outcomes of the experiment. Example: When rolling a dice, 'getting an even number' and 'getting an odd number' are complementary events.

Altitude

Height or vertical distance e.g. the helicopter was flying at an altitude of 300 metres.

Additive inverse (Opposite)

If the sum of two numbers is zero, then they are additive inverses or opposites of each other. E.g. 3 and -3 are additive inverses or opposites because 3 + -3 = 0.

Binomial

In algebra, an expression consisting of two terms showing either a sum or a difference [from Latin and meaning 'two names']. e.g. 2b + c or x - y2

Base

In the number 4 cubed, the base is 4. In a place value system of numeration, the base indicates the grouping; i.e. in the decimal system the base is 10. The base of a 3-D object is the horizontal face it stands on. In 2-D, the base is the horizontal line from which the height of the figure is determined.

Anticlockwise (Counterclockwise)

In the opposite direction to the movement of the hands of a clock.

Clockwise

In the same direction as the movement of the hands of the clock.

Binary

Involving two possibilities such as yes/no, true/false, 0/1, etc.

Bivariate data

Relates to two variables; e.g. height and arm span.

Commutative property of addition

Numbers may be added in any order without affecting the result (sum). e.g. 7 + 3 = 3 + 7

Commutative property of multiplication

Numbers may be multiplied in any order without affecting the result (product). e.g. 5 x 2 = 2 x 5, 3 x 5 x 7 = 7 x 3 x 5

Binary numbers

Numbers that are powers of two and usually referring to the base two numeration system which uses 0s and 1s and is the basis of all digital systems.

Annual (Annually)

Occurring once each year.

Century

One hundred, usually referring to 100 years e.g. This is the 21st century AD.

Billion

One thousand million; i.e. 1 000 000 000.

Arc

Part of a circle.

Brackets (Parentheses)

That is { }, ( ) and [ ].

Capacity

The amount a container can hold, usually related to liquids or gases e.g. the capacity of the bottle is 1L.

Area

The amount of surface.

Cardinal number (Whole number)

The answer to the question, 'How many?'. [0, 1, 2, 3, ... is the set of whole numbers.

Class boundary

The border between two class intervals e.g. The boundary between the intervals 31-35 and 36-40 is 35.5.

Chance (Probability)

The likelihood of an event occuring. Assigned a probability of 0 (for never) to 1 (for always). e.g. If you toss a coin you have the same chance of scoring a head as scoring a tail; i.e. the chance of scoring a head is 1/2.

Angle of elevation

The line of sight as inclined above the horizon when looking at an object.

Angle of depression

The line of sight as inclined below the horizon when looking at an object.

Basic number facts

The number facts needed to be able to carry out all calculations; i.e. the addition facts from 0 + 0 to 9 + 9 and the related subtraction facts, together with the multiplication facts from 0 x 0 to 9 x 9 and the related division facts.

Coefficient

The number of each variable in a mathematical expression. E.g. In the expression 3x + 4y, 3 is the coefficient of x and 4 is the coefficient of y.

Absolute value [ ]

The numerical value of a number, ignoring the sign. [From the Latin "absoluere" (to free from), hence to free from its sign.] e.g. the absolute value of both +7.5 and -7.5 is 7.5.

Addition (+)

The operation of combining two or more addends to produce another number called a sum.

Arithmetic

The part of mathematics involving the study of numbers and their operations and properties.

Centre

The point in the interior of a circle (or sphere) that is the same distance from all points on the circle (or sphere).

Celsius (C)

The scale on a thermometer where the freezing point of water is 0 degrees and the boiling point is 100 degrees. [Named after its 18th century inventor, Anders Celsius.]

Apex

The top vertex of an object or figure.

Collinear

Three or more points in the same line.

Bisect

To halve, usually referring to an object or a figure; e.g. to bisect an angle.

Angle

Two rays with a common end point called a vertex, and the extent of rotation about a point.

Bicentenary

Two-hundredth anniversary e.g. 1988 was the bicentenary of the first European settlement in Australia.

Calculate

Use a mathematical procedure to determine a number, quantity or expression.

Calculator

Usually meaning an electronic calculating device, which can range in power from basic to graphing to computer algebra system (CAS) capability.

Associative property of addition

When adding three or more numbers, the grouping does not affect the sum e.g. 2 + (3+4) = (2+3) + 4

Associative property of multiplication

When multiplying three or more numbers, the order in which they are multiplied does not affect the product e.g. 3 x (5 x 6) = (3 x 5) x 6

Addition property of zero

When zero is added to any number, the sum is that number e.g. 7 + 0 = 7.

Asymmetry

Where an object or figure has no reflection symmetry.

Base ten blocks (Place Value Blocks)

Wooden, plastic or foam materials, consisting of four different pieces called units, longs, flats and blocks, to represent place values in the decimal system of numeration.