Glossary
The glossary draws on the NSW syllabus glossaries, the glossaries developed by the Australian Curriculum, Assessment and Reporting Authority, and the Macquarie Dictionary.
Aboriginal Peoples are the first peoples of Australia and are represented by more than 250 language groups, each associated with a particular Country or territory. Torres Strait Islander Peoples are represented by 5 major island groups, and are associated with island territories to the north of Australia’s Cape York which were annexed by Queensland in 1879.
An Aboriginal and/or Torres Strait Islander person is someone who:
- is of Aboriginal and/or Torres Strait Islander descent
- identifies as an Aboriginal person and/or Torres Strait Islander person, and
- is accepted as such by the Aboriginal and/or Torres Strait Islander community(ies) in which they live.
A recognised dialect of English which is the first, or home language, of many Aboriginal people. It differs from other dialects of English, such as Standard Australian English, in systematic ways including sounds, grammar, words and their meanings, and language use. Aboriginal English is a powerful vehicle for the expression of Aboriginal identity. Aboriginal English is not a target language study option for NSW Aboriginal Languages syllabuses.
Texts that describe landscapes and directions of the tracks forged in lands, waters and skies by Creator Spirits during the Dreaming.
In a measurement, half of the smallest unit of the measuring device. The smallest unit is called the precision of the device.
Content for students with significant intellectual disability who are working towards the Early Stage 1 outcomes. Teachers can use the access content points on their own, or in combination with the content for each outcome.
The extent to which a system, environment or object may be used irrespective of a user’s capabilities or abilities. For example, the use of assistive technologies (AT) to allow people with disability to use computer systems, or the use of icons in place of words to allow young children to use a system.
The extent to which measurements are considered to be close to the true value.
An angle smaller than a right angle, between 0° and 90°.
Extended in Mathematics Advanced and Extension 1: In circular measure, an angle lying in the interval
Has different meanings for different mathematical contexts. For example, adjacent vertices in a network are joined by an edge and adjacent faces in a solid have a common edge. In trigonometry, the adjacent side of a right-angled triangle is the side next to the angle to which the trigonometric ratio is referring.
Angles that share a vertex and an arm. They do not overlap.
Extended in 7–10: Two angles at a point are called adjacent if they share a common ray and a common vertex and lie on opposite sides of the common ray.
A mathematical statement formed by combining numbers and algebraic symbols using arithmetic operations, e.g. .
A fraction in which the numerator and/or the denominator are algebraic expressions.
Forms a 'separable' part of some other algebraic expression. For example, and are terms in the inequality , and 2, , are terms of the polynomial .
In each diagram below, the 2 marked angles are called alternate angles (since they are on alternate sides of the transversal).
If the lines and are parallel, then each pair of alternate angles is equal.
Formed by 2 straight lines meeting at a common endpoint, called the vertex. An angle can describe the amount of turn between its 2 arms (lines).
The angle between horizontal and the line of sight from an observer to an object that is lower than the observer.
The angle between horizontal and the line of sight from an observer to an object that is higher than the observer.
The angle a straight line makes with the positive -axis.
An estimate of a number or an amount to a particular accuracy. For example, and 3.1416 are approximate values, or approximations, for the number .
A part of a circle’s circumference.
Extended in Mathematics Extension 1: A part of a curve.
One of several different arrangements that can be used to model multiplicative situations. It is made by arranging a set of objects, such as counters, into columns and rows. Each column must contain the same number of objects as the other columns, and each row must contain the same number of objects as the other rows.
A device or system whose primary purpose is to maintain or improve an individual's functioning and independence to facilitate participation and enhance overall wellbeing. This includes technologies specifically designed to meet an individual's needs, eg eye gaze technology, as well as more general technologies that can be used by anyone, eg speech-to-text applications. Assistive technology can also be referred to as inclusive technology.
When more than 2 numbers are added or multiplied, the result is unchanged regardless of how they are grouped or associated. For example, addition of numbers is associative, and the corresponding associative law is: for all numbers , and .
Multiplication is also associative: for all numbers , and .
A straight line (or another curve) that a curve approaches as tends to , or to some particular value.
For example, the curve has an asymptote as tends to , and the curve has asymptotes and as tends to and respectively.
A quality, feature or characteristic of an object or shape.
An umbrella term that encompasses the communication methods used to supplement or replace speech or writing. AAC can be unaided, such as gestures, body language and sign language, or aided such as pictures, symbols, objects or speech generating devices.
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A number expressing a central or typical value in a set of data. While it usually refers to the arithmetic mean, that is, the sum of a set of numbers divided by the number of numbers in the set, it may also refer to other measures of centre.
Has different meanings for different mathematical contexts. A base is a number that is raised to a power and the base of a solid is the face the object rests on.
A direction from one point on the Earth’s surface to another. Two types of bearings may be used: compass bearing and true bearing.
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A systematic favouring of certain outcomes more than others, due to unfair influence (knowingly or otherwise).
An algebraic expression with 2 terms. For example, is a binomial expression in the 2 terms and .
Data relating to measurement of 2 variables. It can be categorical data, numerical data or a combination of both.
A synonym for a box-and-whisker plot. A graphical display of a 5-number summary of data. The ‘box’ covers the middle 50% of scores. The ‘whiskers’ extend to the maximum and minimum values in the dataset.
In a box plot, the 'box' covers the interquartile range (IQR). A vertical line in the box is used to indicate the location of the median.
The box plot below has been constructed from the 5-number summary of the resting pulse rates of 17 students.
Generally refers to the amount a container can hold.
A term used to describe how much a container will hold. It is often used in relation to the volume of fluids. Units of capacity (volume of fluids or gases) include litres and millilitres.
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A system that specifies the position of each point in a plane, formed by the intersection of 2 perpendicular number lines called axes. Each point is represented by an ordered pair of real numbers called the coordinates of the point. The point where the axes meet is called the origin and has coordinates .
A variable whose values belong to exactly one of a number of categories. A categorical variable describes a quality or characteristic of something. Sometimes called a discrete variable. There are 2 types of categorical variables: nominal and ordinal. For example, your home state or blood type are categorical variables.
Two variables with a relationship which indicates that one event is the result of the occurrence of the other event.
A possibility of something happening.
A line segment (interval) joining 2 points on a circle.
All points equal to a given distance from a fixed point, the centre. When used to describe a shape, a circle includes all points inside the boundary.
A path that begins and ends on the same vertex. Vertices can be repeated.
The boundary of a circle. The length of the circumference is given by , where is the diameter. Alternatively, it is given by , where is the radius.
A shape enclosed by all its sides with no gaps.
A pair of angles that lie between a pair of parallel lines cut by a transversal and have a sum of 180 degrees or 2 right angles.
In each diagram the 2 marked angles are called co-interior angles.
If the 2 lines are parallel, then co-interior angles add to give 180° and so are supplementary.
Co-interior angles formed by parallel lines are supplementary. In the diagram below the angles ∠CGF and ∠AFG are supplementary. If the lines and are parallel then :
Conversely, if a pair of angles are supplementary, then the lines are parallel.
A numerical quantity that multiplies a variable in an algebraic expression, e.g. 5 is the coefficient of . Variables with no specified coefficient have a coefficient of 1.
Describes points that lie on the same straight line.
The various ways a group of items can be arranged without regard to order.
The sum or percentage paid for services, e.g. to an agent or salesperson.
A factor of each element of a set of numbers or an algebraic expression. Also known as common divisor. For example, 6 is a common factor of 24, 54 and 66, and is a common factor of and .
The ways people communicate and the communicative behaviours they use. Communication forms can be non-symbolic and/or symbolic. Non-symbolic forms include sounds, gestures, facial expressions and eye movements. Symbolic forms can be aided or non-aided. Aided forms of symbolic communication include objects, symbols, photographs and drawings. Aided forms can be digital. Non-aided forms of symbolic communication include formal gestures; speech; and signs, such as Key Word Sign.
Commutativity (commutative property) of addition or multiplication means that 2 numbers can be added or multiplied in any order and the solution will be the same.
Commutative law, commutativity and turn-around facts are interchangeable terms.
Angles either side of north or south. For example, a compass bearing of N50°E is found by facing north and moving through an angle of 50° to the east.
Two adjacent angles that form a right angle, i.e. the sum of the angles measured in degrees is 90°.
Two mutually exclusive outcomes in a probability experiment, such that where is the probability of event and the probability of event .
Extended in Mathematics Standard and Advanced: Two mutually exclusive events that make up the sample space.
A non-zero natural number that has a factor other than 1 and itself. For example, all even numbers besides 2 are composite numbers. Some odd numbers are composite (e.g. 21) but not all are composite (e.g. 11).
A shape that is formed by combining other plane shapes. Composite shapes are often described as 'complex' when they are made up of many and different shapes.
The interest earned by investing a sum of money (the principal) when each successive interest payment is added to the principal for calculating the next interest payment.
Indicates whether the curve ‘opens’ up (concave up) or ‘opens’ down (concave down). For example, the parabola is concave up and the parabola is concave down.
Consideration of whether the knowledge of the occurrence of one event, A, affects the probability of occurrence of another event, B.
Extended in Mathematics Advanced: The probability of an event occurring, given that another event has occurred, notated as (read as ‘probability of given ’).
An exact match between every part of one figure with the corresponding part of another figure, i.e. congruent figures can be exactly superimposed on each other.
In the Cartesian plane, 2 points are connected if there is a line or curve that joins them. In a network, a set of points is connected if every point can be reached from another point. A set of points that is not connected is called disconnected.
Examples of a connected network and a disconnected network respectively are shown below:
Not created or destroyed.
A fixed numerical value. For example, in the algebraic expression , the number 11 is a constant.
Constant difference refers to a common difference between pairs of numbers. For example, the difference between 3 and 7 is 4, and another pair of numbers that has a difference of 4 is 2 and 6.
Objects such as bottles, jars and tubs.
A numerical variable that can take any value that lies within an interval. The values taken are subject to the accuracy of the measuring instrument used to obtain these values. For example, height, reaction time to a stimulus and systolic blood pressure.
If one relationship is true, then the opposite is also true.
The converse of a statement ‘If then ' is 'If then '. For example, the converse of Pythagoras’ theorem is that if the sum of the squares of 2 sides of a triangle is equal to the square of the third side, then the triangle is right-angled.
Extended in Mathematics Extension 2: The converse of is or .
A set of values that define the position of a point or an object in a space. The coordinate system being used will govern the nature of the coordinates.
The protection provided to the creators of original works and makers of sound recordings and films, that offers a legal framework for the control and reproduction or transmission of their literary, dramatic, artistic or musical works.
Angles that lie in the same relative position at the points of intersection where a pair of lines is cut by a transversal.
If the lines are parallel, then each pair of corresponding angles is equal.
Conversely, if a pair of corresponding angles is equal, then the lines are parallel.
The ratio of the length of the base, , of a right-angled triangle to the length of its hypotenuse, , for a given base angle theta, . In any right-angled triangle, , where .
Country is used to describe a specific area of a nation or clan including physical, linguistic and spiritual features. Aboriginal communities’ cultural associations with their Country may include or relate to languages, cultural practices, knowledge, songs, stories, art, paths, landforms, flora, fauna and minerals. These cultural associations may include custodial relationships with particular landscapes such as land, sea, sky, rivers as well as the intangible places associated with the Dreaming(s). Custodial relationships are extremely important in determining who may have the capacity to authentically speak for their Country.
Place is a space mapped out by physical or intangible boundaries that individuals or groups of Torres Strait Islander Peoples occupy and regard as their own. It is a space with varying degrees of spirituality.
The intersection of a solid with a plane. May differ for a given solid depending on the orientation of the slicing plane. For example, the cross-section of a sphere will be a circle (of different radius depending on the slicing plane), while the cross-section of a cube could be a square or other polygon (e.g. triangle, hexagon) depending on the orientation of the slicing plane.
An object with 6 equal square faces and 12 edges.
The inverse or opposite of cubing a number. For example, the cube root of 8 is 2 because . In symbols it is written .
Having the form of a cube or being of the third power or degree.
The customs, habits, beliefs/spirituality, social organisation and ways of life that characterise different groups and communities. Cultural characteristics give a group or individual a sense of who they are and help them make sense of the world in which they live. Culture is a shared system but inherently diverse – there can be individual and group differences within cultures. Everyone has culture – it is a lens through which we see the world.
A one-dimensional figure that is not straight.
Surface of an object that is not flat, e.g. a cylinder has one curved surface.
In Aboriginal communities, an individual charged with maintaining and passing on particular elements of cultural significance, eg language, stories, songs, rituals and imagery.
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A trail that finishes on the vertex it begins on. No vertex is repeated.
A quadrilateral with every vertex (corner point) on a circle’s circumference.
An object that has parallel circular discs of equal radius at the ends that are joined by a curved surface.
When referring to deaf people who belong to a linguistic and cultural minority known as the Deaf community, the 'D' may be capitalised in reference to the individual, the group, or the culture in order to accord respect and deference, for example, the Deaf community. When referring simply to audiological status or when cultural affiliation is not known, as in the case of a person with a hearing loss in general, the lowercase 'd', as in 'deaf' is the more common usage.
Facts or units of information collected together.
A collection of numbers or values relating to a particular subject. Datasets are normally presented in tables or represented by graphs. For example, the test scores of each student in a particular class.
A cultural identity for people with hearing loss who share a common culture and who usually have a shared sign language.
Used to describe aspects of the base-10 number system. The decimal point (. or ,) separates the whole number part of a number from its decimal part.
The degree of a vertex is the number of edge ends at that vertex.
A unit for measuring an angle. Angles are measured as a proportion of a full turn, which is equivalent to 360 degrees, so that one degree, written as is equal to of a full turn.
Comes from Latin, meaning ‘that which gives a name’ [de- “completely”; nomen “name”]. The denominator of a fraction identifies the name of the fractional parts (e.g. thirds, quarters or fifths).
Extended in 7–10: In the fraction , b is the denominator.
An event that relies on another event to happen first. One event influences the probability of another event.
The variable used to represent the output values of a function. A dependent variable is generally represented on the vertical axis of a graph.
A decrease in value due to wear and tear, decay, decline in price etc.
A chord passing through the centre of a circle. The word is also used for the length of the diameter.
The difference of 2 numbers is the result of subtracting one from the other. You can use subtraction or addition to find the difference between 2 numbers.
For example, to find the difference between 15 and 21, you can:
- add 5 up from 15 to get to 20, then add one more to get to 21, so the difference is 6
- start with 21 and count back to find the difference of 6.
A proportional relationship where one quantity directly varies with respect to a change in another quantity. This implies that if there is an increase (or decrease) in one quantity then the other quantity will experience a proportionate increase (or decrease).
An umbrella term for any or all of the following components:
- impairments: challenges in body function or structure
- activity limitations: difficulties in executing activities
- participation restrictions: challenges an individual may experience in involvement in life situations. (World Health Organization)
Individual and countable items that can be listed.
Extended in Mathematics Advanced: Also known as a discrete random variable.
The spread of data which can be shown graphically or in a table.
Multiplication of numbers is distributive over addition because the product of one number with the sum of 2 others equals the sum of the products of the first number with each of the others. For example, the product of 3 with gives the same result as the sum of and :
and
The distributive law is expressed algebraically as follows:
, for all numbers , and .
Differences that exist within a group, for example, age, sex, gender, gender expression, sexuality, ethnicity, ability/disability, body shape and composition, culture, religion/spirituality, learning differences, socioeconomic background, values and experiences.
The number that is divided or distributed in a division problem. For example, in , 12 is the dividend.
The set of allowable values of in a function or relation.
Extended in Mathematics Advanced, Extension 1 and Extension 2: For a function or relation, it is the set of real numbers on which the function or relation is defined.
Doubling and halving is a strategy that can make solving multiplication problems easier, e.g. solving 4 x 12 is the same as solving 2 x 24.
Doubling and halving is also a strategy used to find factors of a number. For example, to find the factors of 24, start with 1 x 24 then double and halve, 2 x 12, 4 x 6, 8 x 3.
The Dreaming has different meanings for different Aboriginal groups. The Dreaming can be seen as the embodiment of Aboriginal creation which gives meaning to everything; the essence of Aboriginal beliefs about creation and spiritual and physical existence. It establishes the rules governing relationships between the people, the land and all things for Aboriginal Peoples. The Dreaming is linked to the past, the present and the future. Where appropriate, refer to Aboriginal names for the Dreaming.
The line segment formed by the intersection of two faces of a polyhedron, e.g. a cube has 6 faces and 12 edges.
A line that joins vertices to each other in a network diagram.
The custodians of knowledge and lore. They are chosen and accepted by their own communities as people who have the permission to disclose cultural knowledge and beliefs. Recognised Elders are highly respected people within Aboriginal communities. Proper consultation with local Aboriginal communities will often direct schools to recognised Elders.
A member of a set. For example, is a member of the set of natural numbers . This relation can be written more concisely as (' is an element of the set ').
A type of transformation that increases or decreases the size of an image without changing its shape, depending on the size of the enlargement factor.
A balance where the distance from the support point (middle) to the arms at each end is equal.
An event for which all outcomes have the same probability of occurring. For example, in tossing a fair coin, the outcome ‘head’ and the outcome ‘tail’ are equally likely. In this situation, 𝑃(head)=𝑃(tail)=0.5.
In mathematics, the equals sign is used to indicate equivalence, e.g. 5 + 1 = 2 + 4 and to show that two or more amounts have the same value.
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An expression showing the equality of 2 quantities, using the = sign between them. A mathematical formula asking for a solution so that the 2 expressions in that variable are equal, e.g. .
When the angles of one polygon are equal to the corresponding angles of another polygon.
Two things are equivalent if they have the same value.
See Loading , Loading .
Extended in Mathematics Advanced, Extension 1 and Extension 2: Two things are equivalent if they have the same value, function or meaning. For example, and are equivalent. Statements and are equivalent if implies and implies .
Fractions that are different representations of the same value, e.g. .
Two fractions and are equivalent if they are equal, that is, .
Situations that occur in the everyday context, e.g. having lunch. In the context of probability, the set of possible outcomes.
Extended in 7–10: A subset of the sample space for a random experiment. For example, the set of possible outcomes from tossing 2 coins is , where H represents a 'head' and T is a 'tail'. For example, if is the event 'at least one head is obtained', then .
A relationship in which the independent variable occurs as an exponent (or power/index) with a positive base. For example, is an exponential relationship where is the independent variable. The graph of an exponential relationship is an exponential curve.
Two or more numbers or variables connected by operations. For example, , , are all expressions. Expressions do not include an equals sign.
Extended in Mathematics Advanced, Extension 1 and Extension 2: The result of combining numbers, variables and operations in a meaningful way. For example, is an expression, but is not a validly formed expression.
Occurs when the fitted model, such as a line of best fit, is used to make predictions using values that are outside the range of the original data upon which the fitted model was based.
A flat surface of a 3-dimensional geometric object (polyhedron) with only straight edges.
A bounded region in a network.
A number that divides another number without a remainder. For example, 1, 2, 3 and 6 are factors of 6 but 4 and 5 are not.
Extended in 7–10: Numbers or algebraic expressions are factors (or divisors) of another number if they multiply to give that number. For example, 3 and 4 are factors of 12 as . This can be written algebraically as and are factors of , if .
If is a polynomial and for some number , then is divisible by . The factor theorem can be used to obtain factors of a polynomial.
To express a number or algebraic expression as a product. For example, 15 is factorised when expressed as a product: and is factorised when written as a product: .
The first language(s) that a person learns to speak.
A method for summarising a dataset using 5 statistics: the minimum value, the lower quartile, the median, the upper quartile and the maximum value.
The result of a division. For example, 2 divided by 4 produces quarters. Fractions also represent:
- a relationship or ratio
- parts when a whole is partitioned into equal parts
- numbers between whole numbers
- units of measure.
The number of times that a particular value occurs in a dataset. For grouped data, it is the number of observations that lie in that group or class interval. For example, when rolling a dice 20 times, ‘the frequency of a 6’ means how many times the number 6 comes up.
A visual display that organises and presents frequency counts of scores so that the information can be interpreted more easily.
Frequency distributions can be displayed in tabular or graphical form.
A function assigns to each element of one set precisely one element of a second set .
The functions most commonly encountered in elementary mathematics are real functions of real variables. For such functions, the domain are sets of real numbers.
Functions are usually defined by a formula for in terms of . For example, the formula , defines the ‘squaring function’ that maps each real number to its square .
The total value of an investment or annuity at the end of a specified term, including all contributions and interest earned.
The slope of a line. It is calculated as the gradient of a line segment it contains. If and are 2 distinct points on a line, the gradient of the line (or line segment ) is given by .
A visual representation of statistical data or of a relationship between variables. Ordered pairs of values () that represent the function or relation are plotted to form a graph. Graphs of statistical data include dot plots, box plots, column graphs, divided bar graphs and histograms.
Extended in Mathematics Advanced, Extension 1, Extension 2: For a function , its graph consists of all ordered pairs for in the domain of .
The Gregorian calendar is the most widely used solar dating calendar. It was introduced in 1582 as a modification of the Julian calendar.
Grouping (quotitive) division requires finding how many groups are formed, e.g. if I have 12 marbles and each child gets 4, how many children will get marbles?
When grouping, the quotient represents the number of groups within the shared quantity.
A common unit of land measure in the metric system equal to 10 000 square metres (approximately 2.47 acres).
Testing the weight of an object by lifting and/or balancing it.
Half of a sphere.
The common divisor of a given set of natural numbers that is greater than each of the other common divisors. For example, 1, 2, 3 and 6 are common factors of 24, 54, and 66, and 6 is the highest common factor.
The graph of produces what is called a rectangular hyperbola. The - and - axes are asymptotes.
The longest side in a right-angled triangle that is opposite the right angle.
A supposition or proposed explanation made on the basis of limited evidence as a starting point for further investigation.
Two events are independent if knowing the outcome of one event tells us nothing about the outcome of the other event.
A variable used to represent values in the domain (input values) of a function. Generally represented on the horizontal axis of a graph.
Also called ‘exponent’. The power to which a number or algebraic expression is to be raised. The index or exponent is written as a superscript. Positive integral exponents indicate the number of times a term is to be multiplied by itself.
The plural of the term index.
An internationally recognised term for the first peoples of a land. In NSW the term Aboriginal person/Peoples is preferred.
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Includes, but is not limited to, objects, sites, cultural knowledge, cultural expression and the arts, that have been transmitted or continue to be transmitted through generations as belonging to a particular Indigenous group or Indigenous people as a whole or their territory.
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A statement that one number or algebraic expression is less than (or greater than) another. There are 4 types of inequalities:
- is less than is written
- is greater than is written
- is less than or equal to is written
- is greater than or equal to is written .
Extended in Advanced, Extension 1, Extension 2: An order relation between one number or algebraic expression and another.
A conclusion reached on the basis of evidence and reasoning.
A chart, diagram or illustration (as in a book or magazine or on a website) that uses graphic elements to present information in a visually striking way.
A whole number, positive, negative or zero, e.g. −3, −2, −1, 0, 1, 2 …
Extended in Advanced, Extension 1, Extension 2: The set of integers is usually denoted by ℤ.
Non-material assets such as forms of cultural expression that belong to a particular individual or community. Intellectual property rights refer to the rights that the law grants to individuals for the protection of creative, intellectual, scientific and industrial activity, such as inventions.
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The point at which a curve or function crosses an axis or other curve in a plane. The point at which a curve crosses the -axis is called the -intercept and the point at which a curve crosses the -axis is called the -intercept.
Extended in Advanced and Extension 1: The - and -intercepts are sometimes taken to mean the signed distance from the point at which the curve crosses the axis to the origin, e.g. for the line , the -intercept is .
When referring to polygons, the inner angles formed by 2 adjacent sides.
When referring to a transversal cutting through a pair of straight lines, the 4 angles formed are called interior angles.
A measure of how much a container can hold.
Making predictions between known data values. For example, working between 2 known points on a graph to predict a value in between these points.
A measure of the spread within a numerical dataset. It is equal to the upper quartile minus the lower quartile ; that is, .
The IQR is the width of an interval that contains the middle 50% (approximately) of the data values.
A continuous subset of the real number line. For example, ‘the set of all real numbers greater than or equal to 10’.
The operation that reverses the effect of another operation.
Examples:
- Addition and subtraction are inverse operations. When you add 3 to 7 you get 10. If you then subtract 3, you get back to 7.
- Multiplication and division are inverse operations. When you multiply 6 by 2 you get 12. If you then divide by 2 you get back to 6.
When one variable increases as the other variable decreases. For example, if is said to be ‘inversely proportional’ to , the equation is of the form , where is a constant of variation (or proportion). Also known as inverse proportion.
A number that cannot be expressed as a fraction in the form , where and are integers and is non-zero. The decimal form of irrational numbers does not terminate and is non-recurring.
A mental calculation method that involves jumping from one number (usually the largest number) either forwards (addition) or backwards (subtraction) to the solution.
A communication strategy that incorporates signing with speech. It is used to support language development for people with communication difficulties. Although Key Word Sign uses a simplified form of manual signing, it is different to Auslan, as it is not a signed language.
A key aspect of Aboriginal cultures and values. It includes the importance of all relationships and of being related to and belonging to the land.
An Aboriginal community identified with a common language, both verbal and nonverbal, and with a particular territory. Used in preference to the term ‘tribe’.
The process and range of strategies for increasing knowledge and use of a language that is no longer spoken fluently across all generations in the context of language loss or language dispossession caused by colonisation. Aboriginal Languages and Torres Strait Islander Languages are being revived through community initiatives, linguistic research and school programs. ‘Language revival’ may be used as an overarching term that could also include ‘reclamation’, ‘revitalisation’, ‘renewal’ and ‘reawakening’.
Measure of an object from end to end.
A one-dimensional figure that is straight, has no thickness and extends endlessly.
A line drawn through a scatter plot of data points that represents the nature of the relationship between 2 variables.
An equation involving linear expressions. The general form of a linear equation in one variable is where and are constants.
is a linear function of if where and are constants.
The graph of a linear function is a straight line, where is the gradient and is the -intercept.
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A pattern created by the regular repetition of units with the same difference between terms.
Two variables and are in a linear relationship (or form a linear function) if they are connected by an equation of the form . Graphically, is the gradient and is the intercept with the vertical axis of the corresponding linear graph.
A number of items, typically presented one after the other.
An equation that contains mostly letters, such as , where each variable represents a quantity ‘literally’. Formulas are literal equations.
A local Aboriginal community is constituted by those people who are Aboriginal and who reside in the near locality. Aboriginal communities will have a rich and diverse history that has been seriously affected by dispossession and relations, which sees families with spiritual connection to Country residing beside those who have been forced to move from other locations. The notion of locality is complex and multilayered: schools should seek advice from a range of people and/or organisations representing local interests.
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The logarithm of a positive number is the power to which a given number , called the base, must be raised in order to produce the number . The logarithm of , to the base is denoted by .
Algebraically: is equivalent to .
A scale where successive endpoint values of intervals increase by a constant factor (multiplicatively). Contrast with linear scales in which the increase is a constant amount.
The size or absolute value of a number. For example, 4 and 4 have a magnitude of 4.
Extended in Mathematics Extension 1 and Mathematics Extension 2: For a vector, the magnitude is its length, given by for 2D vectors and for 3D vectors.
The amount of matter in an object.
The sum of values in a dataset divided by the total number of values in the dataset. Also called the average.
A statistic that is used to summarise a dataset. There are 3 common measures of centre for a dataset: mode, median and mean.
In statistics, different methods of calculating the variability of a set. The most commonly used measures of spread are the range, interquartile range and standard deviation.
The value in a set of ordered data that divides the data into 2 parts. It is frequently called the 'middle value'.
Extended in Mathematics Standard and Advanced: If the number of values in the ordered dataset is even, it is the average of the two middle values. If the number of values in the dataset is odd, the median is the middle value.
A point on a line segment or interval that divides the segment into 2 equal parts.
Let and be points in the Cartesian plane. Then the midpoint of line segment has coordinates .
This can be seen from the congruent triangles below.
The most frequently occurring value in a set of data.
Extended in 7–10: There can be more than one mode. When there are 2 modes, the dataset is said to be bimodal.
A polynomial in which the coefficient of the leading term is 1.
Products formed using the same base number multiplied by different whole numbers, e.g. 3, 6, 9, 12 …
The number of times a particular number is a zero for a given polynomial or a root for a polynomial equation.
Two events that cannot have simultaneous outcomes in the same chance experiment. For example, when a fair coin is tossed twice, the events 'HH' and 'TT' cannot occur at the same time and are, therefore, mutually exclusive.
In a Venn diagram, as shown below, mutually exclusive events do not overlap.
Extended in Mathematics Advanced: For a random experiment two events and are mutually exclusive if , that is, they cannot occur simultaneously.
A diagram showing the pattern of connected faces and the edges of an unfolded polyhedron (a solid with all faces polygons).
One possible net for a cube is shown below.
A set of points (vertices or nodes) some of which are joined by lines or curves (edges) that sometimes enclose regions (faces). For example, road networks, a family tree or the edges lining a tennis court.
Functions or graphs that cannot be represented by a straight line or a linear function.
Combinations (pairs) of numbers that add to a given number, e.g. 8 + 2, 6 + 4, and 7 + 3 all bond to form 10.
A table that lists numbers in numerical order. There are different types of number charts.
For example:
- a 1–120 or 0–99 chart
- a calendar display for a month.
A number line is used to represent numbers according to their distance from a zero point. The representation of a number line can start and end on any number.
A number sentence uses numerals and mathematical symbols. A number sentence may be used instead of the word equation. For example, instead of writing 6 apples plus 7 apples equals 13 apples, the number sentence would be 6 + 7 = 13.
In the fraction , is the numerator. If an object is divided into equal parts, then the fraction represents of these parts all together. For example, if a line segment is divided into 5 equal parts, each of these parts is one-fifth () of the whole and 3 of these parts taken together corresponds to the fraction .
Variables whose values are numbers and for which arithmetic processes, such as adding and subtracting or calculating an average, make sense.
A discrete numerical variable is a numerical variable, each of whose possible values is separated from the next by a definite 'gap'. The most common numerical variables have the counting numbers 0, 1, 2, 3, … as possible values. Others are prices, measured in dollars and cents. For example, the number of children in a family or the number of days in a month.
A three-dimensional solid.
An angle bigger than a right angle (90°) but smaller than a straight angle (2 right angles, or 180°).
Taking place away from Aboriginal land or Country of origin.
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Taking place on Aboriginal land or Country of origin.
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Display of data using objects and pictures where one object or picture represents one data value.
The process of combining numbers or expressions. Operations are arithmetic – addition, subtraction, multiplication and division – and also include exponentiation and substitution.
The point of intersection of the - and -axes on the Cartesian plane.
Possible result from an experiment or trial.
A data value that appears to stand out from the other members of the dataset by being unusually high or low.
Each Aboriginal Language is recognised as belonging to a particular geographical area and thus to the people who can claim a connection to that area. Aboriginal community members acquire ownership of their language(s) at birth. Language proficiency is not essential for ownership.
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The graph of . The point is called the vertex of the parabola and the -axis is the axis of symmetry of the parabola.
Some other parabolas are the graphs of where .
Two distinct lines, rays or line segments in the same plane that have no points of intersection and so necessarily have the same gradient (slope).
The symbol is used to express that one line, ray, or line segment is parallel to another.
Partitioning is dividing a quantity into parts.
In the early years, it commonly refers to treating whole numbers as made up of 2 parts (number bonds), e.g. 10 is 8 and 2.
In later years, it refers to dividing both continuous and discrete quantities into equal parts (equi-partitioning) when learning about fraction and division concepts.
A sequence of consecutive edges in a graph. The length of the path is the number of edges traversed.
A pattern in mathematics is made up of a number of elements that repeat or follow a rule.
Examples:
- a repeating pattern is square, triangle, square, triangle
- a growing pattern is 2, 4, 6, 8, 10.
A polygon with 5 sides.
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The absolute error of a measurement expressed as a percentage of the recorded measurement.
Two lines, rays, line segments, vectors, planes or other objects that intersect at a 90° angle (a right angle).
The ratio of the circumference of any circle to its diameter. It is denoted by the Greek letter (pi). Approximate values are or .
Display of data using images, symbols or pictures to represent data in categories.
Employment where a worker is paid a fixed rate for each item produced or action performed regardless of the time taken.
The place value system has 4 properties: positional, base-ten, additive and multiplicative.
The value of a digit is determined by its position in a number relative to the ones (or units) place. For example, in the number 924, the 4 denotes 4 ones, the 2 denotes 2 tens or 20 ones, and the 9 denotes 9 hundreds, 90 tens or 900 ones.
A connected graph that is drawn within a plane whose edges do not cross.
Representation of a location in space that has zero dimensions. Lines, curves, shapes, surfaces and objects are constructed from sets of points. Points in the Cartesian plane are specified by coordinates.
Plane shape bounded by 3 or more line segments.
An expression made up of non-negative integer powers of the same variable and coefficients combined using addition, subtraction and multiplication.
The complete set of individuals, objects, places, etc., that we want information about.
Extended in Mathematics Standard and Mathematics Extension 1: In statistics it is the entire dataset from which a statistical sample may be drawn.
A prime factor of a natural number is a factor of that is a prime number. For example, the prime factors of 330 are 2, 3, 5 and 11.
The total amount of money borrowed or invested on which interest is calculated. Also referred to as present value ().
The chance of something happening shown on a scale from 0 and 1 (inclusive). For example, the probability that a fair coin toss will come up ‘heads’ is 0.5.
A letter or symbol that is used to represent a value in a problem that can vary or change. Also known as a variable.
A rigorous mathematical argument that demonstrates the truth of a given statement or proposition. A mathematical statement that has been established by means of a proof is called a theorem.
A constant ratio between corresponding elements of 2 sets. For example, the circumference and diameter of a circle are in proportion as their ratio is the constant (pi).
The appropriate ways of behaving, communicating and showing respect for diversity of history and culture. This involves appreciation of the knowledge, standing and status of people within the local Aboriginal community and the school community. Protocols inevitably vary between communities, and between people within a community. In establishing a partnership between schools and Aboriginal communities, it is especially important that protocols are acknowledged and respected.
The square of the length of the hypotenuse, , of a right-angled triangle equals the sum of the squares of the lengths of the other 2 sides, and , such that .
An equation of the form , where , and are constants.
An expression of the form , where , and are constants.
The roots of a quadratic equation where are given by the quadratic formula:
.
The amount a digit represents in a number. For example, the quantity value of the five in 546 is 500, and the quantity value of the four is 40.
The values that divide an ordered dataset into 4 (approximately) equal parts. There are 3 quartiles. The first, the lower quartile , divides off (approximately) the lower 25% of data values. The second quartile is the median. The third quartile, the upper quartile , divides off (approximately) the upper 25% of data values.
The result of dividing one number or algebraic expression by another.
The distance from the centre of a circle to any point on its perimeter. It is equal to half of the circle’s diameter.
A number whose value is governed by chance. For example, the number of dots showing when a fair die is tossed. The value of a random number cannot be predicted in advance.
The set of values of the dependent variable for which a function is defined.
The difference between the highest and lowest values in a dataset.
A comparison of magnitudes of sets, quantities of the same kind, or algebraic expressions. It is often used as a comparison of the size of 2 (or more) quantities relative to each other.
An element of the infinite set of numbers {, where and are integers and 0}. It may be expressed in decimal form, e.g. and
The part of a line that starts at a point and continues in a particular direction to infinity.
If is any real number, then the reciprocal of that number will be . For example, the reciprocal of 4 is .
A four-sided shape (quadrilateral) with opposite sides of equal length and all 4 interior angles equal (right angles).
A decimal expansion of a number that contains a finite sequence of digits that repeats indefinitely, such as The repeating sequence is often designated by a bar over it, such as . Every recurring decimal is the decimal expansion of a rational number.
A transformation of a shape formed by creating a mirror image on the other side of a given line.
An angle that measures between 180 and 360 degrees, i.e. between 2 and 4 right angles.
A two-dimensional polygon with all sides and all interior angles equal. A square is an example of a regular shape.
An association between the elements of one set, , and the elements of another set, . It may be represented as a set of ordered pairs , where is in , is in and is related to .
Given by the ratio , where is the frequency of occurrence of a particular data value or group of data values in a dataset, and is the number of data values in the dataset.
The part 'left over' when dividing a number into equal groups. The remainder forms part of the next group.
Extended in 7–10: The amount left over when one number or algebraic quantity is divided by another . If is divisible by , then the remainder is 0. For example, when 68 is divided by 11, the remainder is 2, because 68 can be expressed as .
Extended in Mathematics Extension 1: What is left over after a division. When division of a polynomial by a non-zero polynomial gives , where the degree of is less than the degree of , then is the remainder.
An early strategy for solving multiplication problems used to add groups of the same quantity. For example, 3 + 3 + 3 + 3 to solve 4 groups of 3.
A term used commonly in NSW Aboriginal communities to refer to the way an individual treats others. Showing respect occurs in many ways, such as waiting to speak, listening and demonstrating understanding, not asking too many direct questions, ensuring that people are not made to feel uncomfortable or uneasy, and generally showing regard for others’ ideas, beliefs and culture.
Rhythmic counting refers to the repeated sound pattern that students may use to vocalise the count – creating a beat to emphasise the pattern.
The process for approximating a value that lies between 2 known values. It is used to specify a number correct to a given accuracy. For example, 4.027 becomes 4.03 when rounded to 2 decimal places.
A subset of a population used to estimate characteristics of the population. For example, a randomly selected group of 8-year-olds (sample) selected to estimate the height of 8-year-olds in Australia (population).
The set of all possible outcomes of a chance experiment. For example, the set of outcomes (also called sample points) from tossing 2 identical coins at the same time is {HH, HT, TT}, where H represents a ‘head’ and T a ‘tail’.
A visual representation of bivariate numerical data using the position of each dot on the horizontal and vertical axis to indicate the numerical values for an individual data point. Scatter plots are used to observe relationships between variables.
A way of writing numbers that are too big or too small to be written in an accessible way. It uses powers of 10. For example, the scientific notation for 34 590 is .
The straight line passing through 2 points on the graph of a function.
The plane figure enclosed by 2 radii or a circle and the arc between them.
A plane figure enclosed by a chord and the arc joining the endpoints of a chord.
A collection of objects or elements, usually specified by listing its elements, e.g. ; by describing it in words, e.g. ‘the set of primes’; or by using a rule such as .
Extended in Mathematics Advanced, Extension 1 and Extension 2: A collection of distinct, unordered objects, referred to as members or elements of the set.
A two-dimensional closed figure.
Sharing (partitive) division requires finding how many are in each group, eg if 12 marbles are shared between 3 students, how many does each student get?
When sharing, the quotient represents the quantity of shared objects in each group.
A side is the line segment joining 2 vertices of a two-dimensional shape.
Hand signs (or hand talk) used to supplement or replace oral language. Signs form part of nonverbal communication for Aboriginal and Torres Strait Islander Peoples and may be used by people who are hearing, or d/Deaf or hard of hearing. Aboriginal and Torres Strait Islander Sign Languages may be used in some areas. Some Sign Languages may be associated with sacred ceremonial practices.
The use of words, graphic designs and/or symbols used to communicate a message, eg information signs, plaques, warning signs, road signs, signs that show direction.
Each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first non-zero digit. For example, has 2 significant figures and when 123,456 is rounded to 3 significant figures, the result will be 123 000.
When the enlargement of one figure is congruent to another figure. Similar figures have corresponding lengths in the same proportion, are the same shape and have equal corresponding angles.
The interest accumulated when the interest payment in each period is a fixed percentage of the principal (the initial lump sum of money).
The simple interest formula is given by where is the interest earned, is the principal value invested, is the rate of interest and is the number of time periods over which the interest is applied.
A recreation of random phenomena used to collect probability data through either physical or virtual manipulatives such as spinners, coins and cards or computer-generated simulations that can be performed a large number of times.
A set of 2 or more equations, each containing 2 or more variables whose values can simultaneously satisfy all the equations in the set, the number of variables being equal to or less than the number of equations in the set.
In any right-angled triangle, where .
A measure of asymmetry (non-symmetry) in a distribution of values about the mean of a set of data.
Skip counting is counting forwards or backwards in groups or multiples of a particular number, e.g. 5, 10, 15, 20 ...
Sliding a shape without turning it.
A four-sided shape (quadrilateral and a parallelogram) with all sides of equal length and all 4 interior angles equal (right angles).
The result of multiplying a natural number by itself. For example, , and is an element of the set
A value that when multiplied by itself gives the original number. The positive square root of a given real number is the positive real number such that .
A measure of the variability or spread of a dataset. It gives an indication of the degree to which the individual data values are spread around their mean.
Extended in Mathematics Standard and Advanced: For a random variable, the standard deviation is the square root of its variance.
It provides a measure of the spread of the probability density function.
A method of organising and displaying numerical data in which each data value is split into 2 parts, a 'stem' and a 'leaf'. For example, the stem-and-leaf plot below displays the resting pulse rates of 19 students. The stem is on the left side of the vertical line and the leaves are on the right side.
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In geometry, an angle subtended by an arc or interval is the angle whose 2 rays pass through the endpoints of the arc or interval. A possible synonym for ‘subtends’ is ‘makes’.
To place or lay on top of.
Two adjacent angles that form a straight angle and whose sum is 180 degrees (a straight angle). For example, 45° and 135° are supplementary angles.
A numerical expression involving one or more irrational roots of numbers.
Extended in Mathematics Advanced: An irrational root of a number, e.g. and .
More generally sums involving rational multiples of surds are sometimes also referred to as surds, e.g. .
The flat or curved area of an object. A surface with straight edges is called a face, a surface with a curved boundary is called a curved surface.
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The measure of the total area of the surface(s) of a three-dimensional shape or object. For example, the surface area of a cube with side length of 5 units is 150 square units.
A type of assistive technology that enables people with cognitive and/or physical disability to access a range of devices, including computers and communication devices. Switches can be activated by touch, or triggered without contact, such as through eye gaze, sound or blowing.
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When the 2 sides of the distribution are a mirror image of each other. A normal distribution is a true symmetric distribution of observed values.
An arrangement of information in rows and columns.
A line that intersects a circle at just one point. It touches the circle at that point of contact but does not pass inside it.
Extended in Mathematics Advanced, Extension 1 and Extension 2: For a curve at a given point the tangent can be described intuitively as the straight line that ‘just touches’ the curve at that point. At the curve has ‘the same direction’ as the tangent. In this sense, it is the best straight-line approximation to the curve at point . For a differentiable function the tangent to its graph at the point has slope .
The ratio of the length of the altitude, , of a right-angled triangle to the length of its base, , for a given base angle, theta, .
In any right-angled triangle, , where ° °.
The amount of yearly income that is used to calculate an individual’s or company’s payable income tax.
A decimal expansion of a number that has a finite number of non-zero digits, e.g. 3.125. Every terminating decimal represents a rational number where the denominator is a power of 10.
A walk where no edges are repeated.
A line that intersects 2 other lines obliquely.
A diagram consisting of line segments (edges) connected to points (vertices) like the branches of a tree. It shows the relationship between sets, events or the set of outcomes of a multi-step random experiment.
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A closed shape with exactly 3 straight sides and 3 interior angles.
The relationship between the angles and sides of right-angled triangles. The 3 basic trigonometric ratios are sine, cosine and tangent.
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Measured in degrees clockwise from true north and written with 3 digits to specify the direction. For example, the direction of north is specified as °T, east is specified as °T, south is specified as °T and north-west is specified as °T.
Having length and width only (with no depth).
A common way of displaying the two-way frequency distribution that arises when a group is categorised according to 2 criteria.
Means ‘the same as’. Used to refer to units of the same size used for measuring.
A circle with a radius of 1 unit.
Things that are measurable or observable that are expected to either change over time or between individual observations. They are often designated by symbols, such as , and , to represent members of a set. For example, the variable could represent an unspecified real number.
Something measurable or observable that is expected to change either over time or between individual observations. For example, the age of students, their hair colour or a playing field's length or its shape.
Graphical representations, using several typically overlapping circles, showing elements of sets in relation to properties or attributes. They are drawn for some specified universal set.
Where 2 straight sides of a two-dimensional shape meet.
Extended in 7–12: A vertex is a point in the plane where lines meet and do not extend beyond, or a point in space where several edges meet. A vertex can also refer to a node in a network. It is also the turning point of a parabola.
Determines whether a relation or graph is also a function. If a vertical line intersects or touches a graph at more than one point, then the graph is not a function.
Two pairs of vertically opposite angles formed at the point of intersection of 2 lines in a plane. Vertically opposite angles are equal.
The amount of space occupied by an object.
A sequence of edges and vertices in a network.
The measure of the force of gravity acting on a body with a given mass. An object can be weightless without its mass being zero. The term ‘weight’ is used as a synonym for mass when the concept of gravitational force has not been introduced.
Yarning circles are an important cultural practice for Aboriginal and Torres Strait Islander Peoples to learn within the collective group. Knowledge and information are shared in harmony and respect with all individuals.