# K–10Mathematics K–10 Syllabus

## 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.

A measurement result that is considered to be close to the true value.

An angle smaller than a right angle between 0° and 90°.

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 fraction in which the numerator and/or the denominator are algebraic expressions.

In each diagram below, the 2 marked angles are called alternate angles (since they are on alternate sides of the transversal).

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.

A part of a circle’s circumference.

An array is one of several different arrangements that can be used to model multiplicative situations involving whole numbers. 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.

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 bearings and true bearings.

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A systematic favouring of certain outcomes more than others, due to unfair influence (knowingly or otherwise).

The distribution of a set of data that has 2 modes. The term 'bimodal' is also used if the graph of the distribution has 2 distinct peak values, which may not be equal.

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 data set.

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 (named after French mathematician René Descartes) that describes the exact location of any point in a plane using an ordered pair of numbers, called coordinates. It is defined by the intersection of a horizontal and vertical number line at a point called the origin. The coordinates of the origin are (0, 0). Positions are represented by an ordered pair of real numbers (x, y). Also known as the rectangular coordinate system, or Cartesian plane.

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.

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.

Conversely, if a pair of angles are supplementary, then the lines are parallel.

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, for example to an agent or salesperson.

A factor of each element of a set of numbers or an algebraic expression. Also known as common divisor.

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.

Commutative property of addition or multiplication means that two 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.

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 (for example, 21) but not all are composite (for example, 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.

Consideration of whether the knowledge of the occurrence of one event, A, affects the probability of occurrence of another event, B.

An exact match between every part of one figure with the corresponding part of another figure, ie 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.

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.

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.

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 (eg triangle, hexagon) depending on the orientation of the slicing plane.

An object with 6 equal square faces and 12 edges.

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, eg 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.

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 (eg thirds, quarters or fifths).

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 two numbers is the *result* of subtracting one from the other. You can use subtraction or addition to find the difference between two 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.

The spread of data which can be shown graphically or in a table.

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.

Doubling and halving is a strategy that can make solving multiplication problems easier, eg 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, eg a cube has 6 faces and 12 edges.

A line which 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 scaling of a figure in which the corresponding lengths in the transformed figure are increased or decreased in proportion to the original figure. The 2 figures are similar.

A balance where the distance from the support point (middle) to the arms at each end is equal.

In mathematics, the equals sign is used to indicate equivalence, eg 5 + 1 = 2 + 4 and to show that two or more amounts have the same value.

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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.

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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 which divides another number without a remainder. For example, 1, 2, 3 and 6 are factors of 6 but 4 and 5 are not.

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 data set. 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.

The total value of an investment or annuity at the end of a specified term, including all contributions and interest earned.

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, eg 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 100 acres, or 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 longest side in a right-angled triangle which 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 the input values of the 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 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 eg -3, -2, -1, 0, 1, 2 …

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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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.

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.

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.

A pattern created by the regular repetition of units with the same difference between terms.

A number of items, typically presented one after the other.

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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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 amount of matter in an object.

The sum of values in a data set divided by the total number of values in the data set. Also called the average.

A statistic that is used to summarise a data set. There are 3 common measures of centre for a data set: 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'.

A point on a line segment or interval that divides the segment into 2 equal parts.

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, eg 3, 6, 9, 12 …

Two events which 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.

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) which 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, eg 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.

Examples:

- 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.

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.

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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Partitioning is dividing a quantity into parts.

In the early years it commonly refers to treating whole numbers as made up of two parts (number bonds), eg 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 five 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).

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.

The sum of several terms that contain different powers of the same variable.

The complete set of individuals, objects, places, etc, that we want information about.

For example, the prime factors of 330 are 2, 3, 5 and 11.

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 proposition. A mathematical statement that has been established by means of a proof is called a theorem.

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 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 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 part of a line that starts at a point and continues in a particular direction to infinity.

A four-sided shape (quadrilateral) with opposite sides of equal length and all four interior angles equal (right angles).

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, ie 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.

A correspondence (map) between the elements of 2 sets, eg ‘favourite colour’ related to the set of students in a class (the domain) and the set of colours (the co-domain).

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 heads is {HH, HT, TH, 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.

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 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 two 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.

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).

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 which 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.

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, eg 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 four interior angles equal (right angles).

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.

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.

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.

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 3-dimensional shape or object. For example, the surface area of a cube with side length 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.

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 which has a finite number of non-zero digits, eg 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.

A closed shape with exactly three straight sides and three interior angles.

The relationships between the angles and sides of right-angled triangles, and the 3 basic trigonometric ratios, sine, cosine and tangent.

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.

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 7–10: 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.

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.