# Maths A to Z

Our Maths A to Z glossary provides straightforward explanations and illustrated examples of maths terms used in the classroom.

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## A

### Accuracy of measuring

All measurements are approximations.

The accuracy of the measurement depends on the quality of the instrument being used and the person measuring.

### Acute angle

An angle less than 90 degrees.

#### Example

The red lines illustrate some angles that are acute (less than 90 degrees).

### Acute angled triangle

A triangle with all interior angles less than 90 degrees.

#### Example

• The process of combining collections of objects into a larger collection.
• This is the opposite of subtract.

#### Example

Combining a collection of things together:

The process of combining collections of objects into a larger collection.

This is the opposite of subtraction.

• Two lines, or sides that share a common point (vertex).

### Algebra

A strand of mathematics that substitutes symbols or letters for unknown numbers.

#### Example

A simple algebraic equation could be:

2x + 3 = 15

2x = 12

x = 6

### Algorithm

A step-by-step method for solving problems in mathematics.

### Alternate angles

When two lines are cut by a third line (transversal) alternate angles are between the pair of lines on the outside of the transversal. If the two lines are parallel, the alternate angles are equal.

### Analog clock

A clock with a face and two rotating hands – the minute hand (long) and the hour hand (short) – also sometimes another hand for seconds.

### Angle

The measure of turn between two straight lines that meet.

A protractor is used to measure an angle. Angles are measured in degrees.

### Apex

The highest point or vertex in a plane shape, polyhedron or geometric solid.

### Arc (of a circle)

Part of the circumference of a circle.

### Area

The amount of surface inside a closed flat (2D) shape.

#### Example

The area of this rectangle is 2 × 4 = 8 square units.

### Arms of an angle

The two lines that form the angle.

### Array

A rectangular diagram divided into rows (horizontal) and columns (vertical).

#### Example

This array has 3 rows and 4 columns.

### Ascending order

Increasing from smallest to largest.

#### Example

These numbers are in ascending order.

1, 2, 3, 4, 5, 6...

### Attribute

The attributes of a 2D shape are its size or shape. A 2D shape can have more than one attribute.

### Average

• The average of a set of scores is the total of the scores divided by the number of scores.
• It is called a measure of central tendency.
• Average and mean are often used as interchangeable terms.
• The average (mean) is represented by the symbol x.

#### Example

For the scores 1, 2, 3, 4, 5, 5, 6, 9, and 10:

• the mean = (1 + 2 + 3 + 4 + 5 + 5 + 6 + 9 + 10) ÷ 9
• the mean = 5.

## B

### Bar chart

A graph in which the information is summarised into columns for easy comparison. Bar chart and column graph are interchangeable terms.

### Base

The side of a 2D shape or face of a 3D object that is considered on the bottom of that shape.

### Base ten blocks

Blocks used to help children visualise the value of numbers. Except for the individual unit blocks, all other blocks are based on tens, hence the reason why they are often referred to as 'base ten blocks'. Multi-attribute blocks and base ten blocks are interchangeable terms.

To cut in half.

### Box-and-whisker plot

A diagram that indicates the middle 50% of the scores, with a box with lines (whiskers) drawn to the extremes (end scores).

## C

### Calendar

A system of organising time into days, weeks, months and years.

### Capacity

The amount a container can hold.

#### Example

This container holds 2 litres – its capacity is 2 litres.

### Cardinal number

A number expressing how many of something exist.

#### Examples

• There are 2 birds on the balcony.
• There are 7 days in the week.
• There are 112 ants on my sandwich.

### Categorical data

Information that can be put into different non-numerical groups.

#### Example

• Hair colour (brown, red, black, blonde)
• Gender (male, female).

### Census

A survey of the entire population.

### Centre

The point inside the circle which is the same distance from all points on the circumference.

### Chance

• The likelihood of something occurring.
• See 'Probability'.

### Chord

A line that joins two points on a curve.

### Circumference

The boundary line or perimeter of a circle.

### Clock

An instrument used to keep and display the time.

There are many different kinds of clocks, but the two most common are analog with 'hands' for hours, minutes and seconds, and digital, which displays only digits (numbers).

### Cluster

Where most of the scores are grouped in a set of scores.

#### Example

The scores are clustered around the scores 3 and 4.

### Co-interior

When two lines are cut by a third line (transversal) co-interior angles are between the pair of lines on the same side of the transversal. If the lines are parallel the co-interior angles are supplementary (add up to 180 degrees).

Co-interior

### Column

A vertical arrangement of items.

#### Example

A column of numbers:

23
45
67
92
64
83

### Column graph

A graph in which the information is summarised into columns for easy comparison. Bar chart and column graph are interchangeable terms.

### Common fraction

Fraction shown with one number over another with a dividing line, e.g. ½.

### Commutative law

• Demonstrates that numbers can be added in any order or multiplied in any order and the answer will be the same.
• Commutative law, commutativity and turn-around facts are interchangeable terms.

### Compass directions

The directions shown on a compass. Some examples include: North (N), South (S), East (E), West (W). Also North East (NE), South East (SE), South West (SW) and North West (NW).

### Compensation strategy

One number is rounded to simplify the calculation then the answer is adjusted to compensate for the original change.

#### Example

52 + 39...

Think 52 + 40 = 92, then subtract the extra 1 added to 39 at the start.

So, 52 + 40 − 1 = 91

### Complementary angles

Angles that add to 90 degrees.

### Complementary event

• Not the event but the opposite of the event.
• If an event is represented as E, the complimentary event is represented as E and called, 'not E'.
• Calculated by P(E) = 1 − P(E).

#### Examples

• When rolling a die, the complimentary event of getting a 6 is getting a 1, 2, 3, 4, or 5.
• When tossing a coin, the complementary event of getting a head is getting a tail.

### Composite number

Has more than two factors.

#### Examples

• 15 has the factors 1, 3, 5, and 15.
• 36 has the factors 1, 2, 3, 4, 6, 9, 12, 18, and 36.

### Compound interest

Interest is calculated on the sum invested (principal) as well as on any interest earned.

If an event is represented as 'E', the complimentary event is

#### Example

A = P(1+R)n and I = A-P where:

• A is the value of the investment after n time periods.
• P is the principal
• R is the interest rate per time period as a decimal or fraction.
• n is the number of time periods
• I is the interest.

• A quadrilateral that contains a reflex angle.
• One or more of its diagonals lies outside the figure.
• Often referred to as a non-convex quadrilateral.

### Cone

A 3D (three-dimensional) object with a circular base and an apex.

### Congruent

The same size and the same shape.

### Continuous data

Quantitative (numerical) data that is obtained by measuring.

Examples:

• temperature
• height
• weight
• length.

### Conversion graphs

Used to convert from one unit to another.

#### Example

Convex quadrilaterals have the diagonals inside the figure.

### Coordinates

A set of numbers and/or letters that shows the position of a point or space on a map or grid.

The horizontal direction is always read first.

#### Examples

• The image on the left represents the coordinates E3.
• The image on the right represents the coordinates (2, 4).

### Corresponding angles

When two lines are cut by a third line (transversal) corresponding angles are in corresponding positions (i.e. on the same side of the transversal and both above or both below the pair of lines). If the lines are parallel, the corresponding angles are equal.

### Cross-section

The shape you get when a solid is cut through parallel to the base.

The cross-sections of prisms are uniform, which means they are the same size and shape as the base.

#### Examples

The cross-sections of pyramids and cones have the same shape

### Cube

A cube is a square prism, which is a particular type of prism with faces that are all congruent squares. It has 6 faces, 12 edges and 8 corners (or vertices).

### Cube root

• A number that when multiplied by itself three times equals a given number.
• The opposite operation of cubing.
• Indicated by the mathematical symbol ∛

#### Example

∛125 = 5 since 5 × 5 × 5 = 125

### Cubed

• Means to multiply a number by itself three times.
• It is shown by writing a small 3 to the top right of a number.
• The small number is called a power or index.

#### Example

53, pronounced 'cubed', gives 5 × 5 × 5 = 125.

### Cumulative frequency histogram and polygon

• The cumulative frequency histogram is represented by the columns.
• The cumulative frequency polygon is represented by the line.
• The polygon is also called an ogive.
• The scores (x) are always on the horizontal axis.
• The cumulative frequency (cf) is always on the vertical axis.
• The height of each column shows the cumulative frequency (how many scored that number or less).

### Cylinder

A three-dimensional (3D) object with two circular bases that are opposite each other in position and are the same size and same shape.

## D

### Decagon

A polygon with 10 straight sides and 10 interior angles. If all sides and angles are equal, it is called a regular decagon. If not, it is called an irregular decagon

### Decimal

A fraction that is made by dividing a whole into tenths (10 equal parts), hundredths (100 equal parts) or thousandths (1000 equal parts). A fraction uses a decimal point when written.

Decimal and decimal fraction are interchangeable terms.

#### Examples

• 1⁄2 as a decimal fraction (or just decimal) is 0.5 which is the same as 5 parts out of 10.
• 1⁄4 as a decimal is 0.25.

### Decrease

• Taking one number or amount away from another.
• This is the opposite of increase.
• Decrease, subtract, subtraction and take away are related terms.

### Degree (angles)

A measurement used for angles shown by the degrees symbol °.

Degrees is the plural of degree.

### Degrees (Celsius)

A unit of measurement used for temperature. The symbol is °C.

#### Examples

• Water freezes at 0°.
• Water boils at 100°C.

### Denominator

The number below the line in a fraction that shows the number of parts a whole has been divided into.

#### Example

The 8 in the fraction 7⁄8.

### Depreciation

Depreciation occurs when an item loses value over time.

#### Example

D = P(1 − r)n

Where:

• D is the depreciated value
• P is the principal
• r is the rate of depreciation as a fraction or decimal per time period
• n is the number of time periods.

### Descending order

Numbers getting smaller. Decreasing from largest to smallest.

#### Example

These numbers are in descending order:

• 20, 19, 18, 17, 16...

### Diagonal

A line that joins any two vertices (corners) of a polygon or polyhedron, where the vertices are not next to each other.

### Diameter

An chord across a circle through the centre (twice the radius).

### Difference

The result of subtraction.

#### Example

The difference between 10 and 16 is 6 (i.e. 16 – 10 = 6)

### Digit

A symbol used to write a numeral. The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are used to write all the numbers in our number system.

#### Example

• 23 is a 2 digit number
• 387 is a 3 digit number

### Digital

#### What is it?

Digital means the binary format of 1s and 0s (on or off). Digital can also refer to electronic products, such as a digital camera, MP3 player or eBook reader.

#### How does it work?

A digital product such as a camera transforms an analog image into data (a series of 1s and 0s) which is then transferred into a storage device and reassembled so that you see the original image. Analog cameras store the image onto film, which is then processed into prints. You can make a huge variety of changes to digital imagery which you cannot make to photo prints.

An eBook is a digital representation of a book and can only be displayed on a computer, or an e-reader device, such as a Kindle.

#### Why is it useful?

The invention of digital and the development of electronic products and services have led to a revolution that, in general, has made products more widely available and easier to use.

#### What do you need to keep in mind about your children and digital?

Digital development will continue to create many new and amazing new careers for your child to consider in the future.

#### Want to know more?

To learn more about digital as a topic, you can search the internet for specific digital products and services to find websites that explain its benefits and how it works.

### Digital clock

Displays the time in digits.

### Directed number

A positive or negative number.

A number showing both sign and size.

-7.5, + 612, -3

### Directed number line

The directed number line extends indefinitely in two directions to show both positive and negative numbers.

### Discrete data

• Quantitative (numerical) data that is obtained by counting.
• 'In-between' values are not possible.

#### Example

An example of discrete data is the number of goals scored in a netball game.

### Divide

To share into equal groups or parts

#### Example

Divide 6 chocolates between 3 children and they get 2 each

### Divided bar graph

A rectangle cut into pieces representing the parts of a whole.

#### Example

Favourite colours

### Divisibility tests

A quick test to see if a number can be divided by another without remainder.

#### Examples

• A number ending in 5 or 0 is always divisible by 5.
• A number ending in 0 is always divisible by 10.

### Division

Partitioning into equal groups.

Represented by the symbol ÷

### Dodecahedron

A three-dimensional (3D) object with 12 faces.

### Dot plot

A number line with dots drawn above the numbers to represent the scores.

## E

### Euler’s formula

A relationship between the number of vertices (V), edges (E) and faces (F) of polyhedra. The relationship is V + F – E = 2.

#### Example

In a rectangular prism, 8 vertices + 6 faces – 12 edges = 2.

### Edge

The line where two flat surfaces meet.

### Empty number line

An unmarked number line that shows mental calculations.

#### Examples

An unmarked number line

Using an empty number line (below) to show a jump strategy for addition and subtraction

### Equal groups

Putting objects together in equal groups helps to understand multiplication and division. Equal groups contain the same number of items or objects

#### Example

12 is divided into 3 equal groups giving 4 in each group

OR

3 equal groups with 4 in each gives 12 altogether.

### Equals

Has the same value as.

Often shown by using the equals = sign (symbol).

### Equal sign (=)

Symbol used to show that two or more amounts have the same value.

eg. 5 + 6 = 12 – 1

### Equation

A mathematical statement using the equal sign to show one side has the same value as the other side.

eg. 20 = 5 × 4

### Equilateral triangle

A triangle with all sides equal in length and all angles equal (60°).

### Equivalent

Has the same value.

### Equivalent fractions

Fractions that are equal in value but have different names.

### Estimate

A type of measure which uses non-standard units such as hand spans, footsteps or pattern blocks to measure length, area, etc.

Estimate and informal measurement are interchangeable terms.

### Even number

Any whole number ending in 0, 2, 4, 6, or 8 is even.

Any number that can be divided by 2 and give no remainder.

#### Example

the numbers 2, 4, 6, 8, 10, 12...

### Expanded notation

Shows the amount each digit is worth because of its place in a number.

#### Example

Expanded notation for 287 is 2 hundreds, 8 tens and 7 ones or 200 + 80 + 7.

## F

### Face

One of the flat surfaces of a 3D (three dimensional) object.

### Fact family

Groups of related facts in addition and subtraction, and multiplication and division.

Helps students understand the relationship between operations.

#### Example

3 + 7 = 10

7 + 3 = 10

10 − 3 = 7

10 − 7 = 3

Multiplication and Division

3 × 4 = 12

4 × 3 = 12

12 ÷ 3 = 4

12 ÷ 4 = 3

### Factor

A factor of a given number is a whole number that divides into it exactly.

#### Example

The factors of 12 are 1, 2, 3, 4, 6 and 12

...1 × 12, 2 × 6 and 3 × 4 all equal 12.

### Factor tree

A factor tree can be used to express a number as a product of its prime factors.

### Fibonacci sequence

Numbers following a sequence in which each subsequent number is the sum of the previous two numbers.

#### Example

This sequence starts with 1:

The numbers 1,1, 2, 3, 5, 8, ...

1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13

### Flip

Turn over to give the mirror image – a reflection.

### Formal measurement

Using a standardised measure such as metres, litres or kilograms.

### Fraction

A fraction is one or more parts of a whole that has been broken into equal parts.

A fraction is shown by putting one number over another with a dividing line between them.

#### Example

This shape has been broken into 4 parts and 3 of them have been coloured. The coloured fraction is 3-quarters or 3⁄4 .

### Fraction notation

A number in the form a⁄b where a and b are numbers and b is not equal to zero.

### Frequency histogram

• A type of column graph used in statistics without gaps between the columns.
• The scores (x) are always on the horizontal axis.
• The frequency (f) is always on the vertical axis.
• The height of each column indicates how many times that score occurs.

### Frequency polygon

• A type of line graph used in statistics usually drawn on the same axes as the frequency histogram.
• The scores (x) are always on the horizontal axis.
• The frequency (f) is always on the vertical axis.
• The height of the point indicates how many times that score occurs. The point is positioned in the centre of its histogram column.
• Always starts and finishes on the horizontal axis.

## G

### Globe

A perfectly round 3D object. Globe and sphere are interchangeable terms.

### Graph

A visual way of showing a collection of information.

#### Example

##### Line graph

*The line graph should only be used for continuous data.

### Greater than sign

The sign > is used to show that the first number is greater than (more than) the second number.

The open (bigger) part is beside the bigger number, the small pointed end points to the smaller number.

#### Example

85 is greater than 37 is written: 85 > 37.

'Is 85 greater than 37?' is written: is 85 > 37?

### Grouping

Putting objects together in groups helps to understand multiplication and division. Groups contain the same number of items or objects

#### Example

12 is divided into 3 groups giving 4 in each group

OR

3 groups with 4 in each gives 12 altogether.

## H

### Hindu-Arabic number system

• The system of numerals we use today.
• Uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with place value.

### Hefting

Holding objects to judge weight.

### Heptagon

A polygon with 7 edges and 7 angles. If all sides and angles are equal, it is called a regular heptagon. If not, it is called an irregular heptagon.

### Hexagon

A polygon with 6 edges and 6 angles. If all sides and angles are equal, it is called a regular hexagon. If not, it is called an irregular hexagon.

### Hexagonal prism

A solid with 2 parallel ends that are hexagons of the same size and shape (ie are congruent).

### Hexagonal pyramid

A solid with a hexagon as its base. Its other faces are triangles that meet at a common point (vertex).

### Hexahedron

A 3D (three-dimensional) object with 6 faces.

### Highest common factor

The highest common factor (HCF) of two or more whole numbers is the largest number that will divide exactly into each of them.

#### Examples

• 2 is the HCF of 4 and 6
• 5 is the HCF of 15 and 20.

### Horizontal

Parallel to the line or surface.

### Hundreds chart

An organised grid of the numbers 0-99 or 1-100 to see and understand patterns in numbers to 100.

### Hundredth

One part of a whole divided into 100 equal parts.

### Hypotenuse

The longest side of a right-angle triangle that is also opposite to the right angle.

## I

### Icosahedron

A 3D (three-dimensional) object with 20 faces.

### Improper fraction

A fraction where the numerator is equal to, or larger than, the denominator.

### Index

An index is more commonly called a power.

It is the small number written to the top right of a number in mathematics. Shows the number of times to multiply a number by itself.

Indices is the plural of index.

#### Example

• in 32, the index is 2,  so 32 = 3 × 3 = 9
• in 53, the index is 3, so 53 = 5 × 5 × 5 = 125

### Index notation

A number written with a power.

### Informal measurement

A type of measure which uses non-standard units such as hand spans, footsteps or pattern blocks to measure length, area, etc.

Estimate and informal measurement are interchangeable terms.

### Integer

Any whole number. An integer can be positive or negative.

• +5
• -6

### Interquartile range

• The difference between the upper quartile and the lower quartile.
• Represents the middle 50% of scores in a set of scores.
• Is not affected by outliers.

#### Example

Interquartile range = upper quartile − lower quartile

### Intersection

The point where lines meet or the line where two or more planes meet.

intersection

### Interval

Part of a line that has a definite start and end point.

### Inverse operation

The function that reverses another one. This is a way of checking if answers are correct.

Addition and subtraction are inverse operations.

Multiplication and division are inverse operations.

#### Examples

• The inverse of adding 7 is subtracting 7.
• The inverse of multiplying 3 is dividing by 3.

### Isometric grid paper

Grid paper used to draw 3D figures. The grid is a series of dots or lines which form equilateral triangles and allow for the drawing of a solid showing 3 or more faces.

#### Example

isometric grid paper

### Isosceles triangle

A triangle with two sides equal in length and two angles that are equal.

## J

### Jump strategy

Mental calculation method jumping from one number (usually the largest number) either forwards (addition) or backwards (subtraction) to the answer.

#### Example

can have any number of digits 23 + 35; 23 + 30 = 53, 53 + 5 = 58

## L

### Length

The longest dimension of an object.

### Less than sign

The sign < is used to show that the first number is smaller than the second number. The pointed end points to the smaller number.

#### Example

• 37 is less than 85 and is written: 37 < 85

### Line

A line is a collection of points. A line does not have a start or end point, it go on forever.

### Line graph

• Has horizontal and vertical axes.
• The points show the quantity.
• Points are joined by lines.
• Reading between the points has meaning.

### Line of symmetry

A line that divides a shape in half so that one half is the mirror image of the other. There can be more than one line of symmetry.

### Long division

Any written method used to divide by a number with two or more digits.

#### Example

An example of long division may look like this:

### Lowest common multiple (LCM)

The lowest common multiple or least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of them.

#### Example

The LCM of 10 and 12 is 60 as 60 is the smallest number that divides both 10 and 12 with no remainder.

## M

### Mass

The amount of matter in something.

### Mean

• The average of all scores.
• The sum of a set of scores divided by the number of scores.
• A measure of central tendency.
• Average and mean are often used interchangeably.

#### Example

For the scores 1, 2, 3, 4, 5, 5, 6, 9, and 10:

• the mean = (1 + 2 + 3 + 4 + 5 + 5 + 6 + 9 + 10) ÷ 9
• the mean = 5.

### Measurement

Using a standardised measure such as metres, litres or kilograms.

### Measuring angles

An angle is the measure of turn between two straight lines which meet at a common point. A protractor is used to measure angles. Angles are measured in degrees °.

### Median

The middle score of an ordered data set.

#### Example

• For the scores: 1, 2, 3, 4, 5, 5, 6, 9, 10, the median is 5.
• For the scores: 5, 7, 8, 9, 10, 12, the median is the average of 8 and 9 (i.e. 8.5).

### Mixed numeral

A number made up of a whole number and a proper fraction.

• 112
• 338

### Mode

The score that occurs the most in a data set.

#### Example

For the scores 1, 2, 3, 4, 5, 5, 6, 9,10

Mode = 5

### Multi-attribute blocks (MAB)

Blocks used to help children visualise the value of numbers. Except for the individual unit blocks, all other blocks are based on tens, hence the reason why they are often referred to as 'base ten blocks'. Multi-attribute blocks and base ten blocks are interchangeable terms.

### Multiple

The product of any quantity and a whole number.

#### Example

The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24...

### Multiplication

The process of repeatedly adding the same number a given amount of times (this only relates to whole numbers).

#### Example

Multiplication, times, products of, lots of, product, square, of (i.e. 1/4 of 8, 3 groups of 6)

### Multiplication tables

• The products of numbers 0 to 10 multiplied by each other. Students are encouraged to learn and appreciate a range of mental strategies to work out the answers.
• Multiplications may be shown in an organised way (such as the examples below) to assist in memorising the answers.
• Multiplication tables and times tables are interchangeable terms.

#### Example

The 5 times tables are:

1 × 5 = 5

2 × 5 = 10

3 × 5 = 15

4 × 5 = 20

5 × 5 = 25

6 × 5 = 30

7 × 5 = 35

8 × 5 = 40

9 × 5 = 45

10 × 5 = 50

## N

### Negative index

A number raised to a negative power is the reciprocal of that number raised to the positive power.

### Net

A flat shape that can be folded up into a solid.

### Nonagon

A polygon with 9 straight sides and 9 angles. If all sides and angles are equal, it is called a regular nonagon. If not, it is called an irregular nonagon.

### Number line

The line can start and end on any number. A line is used to visualise number sequences or aid in computation.

#### Examples

The position of 43 on the numberline:

Numberlines can represent fractions:

### Number sentence

Using numbers and symbols in an equation.

#### Example

Number sentence for 3 birds which have 6 eggs each: 3 × 6 = 18 or 6 + 6 + 6 = 18

### Numerator

The number above the line in a fraction which shows how many parts are being considered.

The 7 in 7/9.

## O

### Object

An object has 3 dimensions – length, width and depth.

### Oblique solids

Solids drawn or shown on a slant. The sides are not perpendicular to the base.

### Obtuse angle

An angle measuring between 90° and 180°.

#### Example

Angles D and C are obtuse. Angles A and B are acute.

### Obtuse angled triangles

A triangle with one angle that is obtuse (greater that 90 degrees).

### Octagon

A polygon with 8 straight sides and 8 angles. If all sides and angles are equal, it is called a regular octagon. If not, it is called an irregular octagon.

### Octagonal prism

A solid with 2 parallel bases that are octagons of the size and same shape.

### Octagonal pyramid

A solid with an octagon as its base. Its other faces are triangles that meet at a common point (vertex).

### Octahedron

A three-dimensional (3D) object with 8 faces.

### Odd number

Any number ending in 1, 3, 5, 7 and 9 is odd.

#### Examples

The numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, ...

### One-dimensional

Having one dimension ie length.

#### Example

A line has only one dimension (i.e. length)

### Order of symmetry

This is the number of times a shape matches the original in one full rotation.

#### Example

An equilateral triangle can be turned 3 times and match its original shape exactly. It also has a rotational symmetry order of 3.

### Ordinal number

Tells the position of something in a sequence.

#### Example

1st, 2nd, 15th, 100th

### Outlier

A value that 'lies outside' (is much smaller or larger than) most of the other values in a set of data.

#### Example

In this data set: 1, 1, 3, 4, 5, 5, 6, 9, 10, 25

25 is an outlier

## P

### Pascal’s triangle

A triangular array of numbers in which each number in the triangle is the sum of the two directly above it.

### Palindromic numbers

Numbers that are the same if read forwards or backwards.

• 44
• 121
• 3,993
• 23,532.

### Parallel

Lines on the same plane that are the same distance apart and never meet.

### Parallelogram

A polygon with 4 straight sides. The opposite sides are parallel and equal. The opposite angles are equal.

### Pattern

A pattern is made up of a number of elements that repeat.

#### Example

This is a pattern – 2 elements repeat

### Pentagon

A polygon with 5 straight sides and 5 angles. If all sides and angles are equal, it is called a regular pentagon. If not, it is called an irregular pentagon.

### Pentagonal prism

A solid with 2 parallel ends that are pentagons of the same size and shape (ie are congruent). All its other faces are rectangular.

### Pentagonal pyramid

A 3D (three-dimensional) object with a pentagon as its base. Its other faces are triangles that meet at a common point (vertex).

### Per annum

For each year (ie the interest rate on the mortgage was 7% per annum). Also referred to as p.a.

### Per cent

Means parts per 100 and is shown by the symbol %. A grid of 100 is used to show per cent. Per cent can also be expressed as percent, percentage or simply with the symbol %.

#### Example

30 out of the 100 squares have been shaded, so 30% is shaded

### Percentage

Means parts per 100 and is shown by the symbol %. A grid of 100 is used to show per cent. Per cent can also be expressed as percent, percentage or simply with the symbol %.

### Perimeter

The distance around the boundary of a 2D (two-dimensional) shape. Calculating the perimeter of a shape is equal to the sum of the length of all sides.

#### Example

Perimeter of this trapezium is 6cm + 4cm + 3cm + 4cm = 17cm

### Perpendicular

At 90° to the given line.

### Perpendicular height

The height measured at 90° from the base to the vertex at the top.

### Place value

The amount a digit is worth due to its position in a number, ie, ones, tens, hundreds, thousands, etc.

#### Examples

• the digit 2 in 42 is worth 2
• the digit 2 in 269 is worth 200.

A tool for showing the value of each digit in a whole number. Can be used to help with addition and subtraction.

#### Example

The whole number 521 can be shown on a chart as:

Hundreds Ten Ones
5 2 1

521 + 47 can be shown on chart as:

Hundreds Ten Ones
5 2 1
+ 4 7
5 6 8

### Place value chart – decimal fractions

A tool for showing the value of each digit in decimal fractions. Can be used to help with addition and subtraction of decimal fractions.

#### Example

The decimal fraction 0.34 can be shown on the chart as:

Ones Tenths Hundredths
0 3 4

### Plane

Any flat two-dimensional (2D) surface. Also known as face.

### Platonic solids

A set of five regular polyhedra. All the faces are congruent regular polygons and the same number of faces meet at each vertex. The platonic solids are: the cube (hexahedron), dodecahedron, icosahedron, octahedron, and tetrahedron.

### Plus

• The process of combining collections of objects into a larger collection.
• This is the opposite of subtraction.

#### Example

Combining a collection of things together:

### Point

A point is a position in space. It has no length, width or height. Where two lines intersect. A point is named using a capital letter.

### Polygon

A two-dimensional (2D) shape having three or more straight sides. It can be a regular polygon – where all sides are the same length and all angles are the same size – or an irregular polygon.

### Polyhedron

• A three dimensional (3D) object in which each face is a polygon.
• It can be a regular polyhedron – all faces are identical regular polygons – or an irregular polyhedron – where all faces are not regular polygons.
• Polyhedra is the plural of polyhedron.

### Population

All the items under consideration.

#### Example

If data on the opinions of Year 8 is required, then the population is all of Year 8.

### Position

The location of an object in relation to oneself or another object.

#### Example

The tree is to my left, the station is south-west of the school.

### Prime factor

A factor that is a prime number cannot be divided again by a number other than itself or one.

#### Example

Prime factors of 12 are 3 × 2 × 2 or 3 × 22

### Prime number

A number that has only 2 factors.

(Note that 1 is not a prime number as it only has one factor – the number 1.)

#### Example

7 has only 2 factors: 1 and 7

### Principal

The original amount of money borrowed or invested.

### Prism

• A 3D (three-dimensional) object with two facing ends or bases (polygons) that are the same size and the same shape (ie they are congruent).
• All its other faces are rectangular.
• A prism is named according to the shape of its base, eg one with a hexagonal base is called a hexagonal prism.

### Probability

• The likelihood of something occurring.
• The probability of an event occurring equals the number of desired outcomes divided by the total number of outcomes.
• Probability and chance are related terms.

#### Examples

It may rain today but raining money is impossible.

P(red marble) = 15. The probability of randomly selecting a red marble from the bag is 1 in 5.

### Product

The answer when 2 or more numbers are multiplied together.

#### Example

15 is the product of 3 and 5

### Proper fraction

The numerator (top number) is smaller than the denominator (bottom number) in a fraction.

### Protractor

A tool used to measure angles.

### Pyramid

• A 3D (three-dimensional) object with any polygon as its base.
• Its other faces are triangles that meet at a common point (vertex).
• A pyramid is named by the shape of its base, eg a pyramid with a rectangular base is called a rectangular pyramid.

### Pythagoras' theorem

A famous result named after the Greek mathematician Pythagoras.

The theorem says that in any right angled triangle, the square of the length of the longest side is the same as the sum of the squares of the lengths of the other two sides: a2+b2 = c2.

#### Example

A set of three integers (whole numbers) that obey Pythagoras' theorem.

That is the sum of the squares of the two smaller numbers is the square of the largest number.

## Q

A quarter of a circle or quarter of its circumference.

#### Example

• A polygon with 4 straight sides.
• The sum of the angles in a quadrilateral is 360°.
• The special types of quadrilaterals include the:
• kite
• rhombus
• square
• rectangle
• trapezium
• parallelogram.

### Quantitative data

• Numerical data.
• Information represented by numbers.

#### Example

• Number of children in family
• Heights of students in class.

### Quotient

The answer when one number is divided by another.

#### Example

The quotient when 18 is divided by 6 is 3.

## R

### Roman numerals

An ancient number system represented by characters such as I(1), V(5), X(10), L(50), C(100), D(500) and M(1000).

#### Examples

• 7 in Roman numerals is Vll
• 65 in Roman numerals is LXV

The distance from the centre of the circle to the circumference of the circle. Radii is the plural of radius.

### Range

• The difference between the highest score and the lowest score in a data set.
• A measure of the spread of the distribution.

#### Example

For the scores 1, 2, 3, 4, 5, 5, 6, 9, 10. The range is 10 – 1 = 9.

### Rate

A rate is used to compare quantities that are measured in different types of units.

#### Example

A typist might type at a rate of 45 words per minute. This is written as 45 words/min.

### Ratio

ratio is a comparison of two or more quantities.

#### Example

The ratio of stars to hearts is 4:3

### Reciprocal of a fraction

The reciprocal of a fraction (not equal to 0) can be made by interchanging the numerator and the denominator.

#### Example

The reciprocal of 2/3 is 3/2.

### Rectangle

• A polygon with 4 straight sides and 4 angles that are equal.
• The opposite sides are equal in length and parallel.

### Rectangular prism

• A solid with 2 parallel faces that are rectangles of the same size and shape (ie are congruent).
• All its other faces are rectangles.

### Rectangular pyramid

• A 3D (three-dimensional) object with a rectangle as its base.
• Its other faces are triangles that meet at a common point (vertex)
• All the other faces are triangular and meet at a common vertex.

### Reflect

To flip over or appear as a figure would look if shown in a mirror.

### Reflex angle

An angle between 180° and 360°.

### Remainder

The amount left over after a quantity has been divided onto another.

#### Example

12 / 5 = 2 with remainder 2

### Revolution

An angle measuring 360°. A complete turn.

### Rhombus

A quadrilateral with all sides equal, opposite angles equal and opposite sides parallel.

### Rhythmic counting

Counting with emphasis on rhythm or counting to a beat.

#### Example

1, 2, 3, 4, 5, 6, 7, 8, 9 (all numbers are spoken, but the bold numbers are said more loudly).

### Right angle

An angle that measures 90°.

#### Example

Right angles are shown like this:

### Right angled triangle

A triangle with one right angle (90°).

### Rotate

• To move around a point by turning.
• Can be done by turns or a given number of degrees.
• Rotate and turn are interchangeable terms.

### Rotational symmetry

A shape has rotational symmetry if an outline of the figure can be rotated or turned about its centre to match its original shape.

#### Example

A regular hexagon comes to rest in 6 identical positions to it original shape

### Rounding

• To increase or decrease to the nearest whole number, ten, hundred, thousand, as a form of estimation.
• 1, 2, 3, 4 round down and for 5, 6, 7, 8, 9 round up.
• With money, rounding increases or decreases the price to the nearest available coin or note.
• With fractions, rounding is to increase or decrease to the nearest whole number, tenth, hundredth, thousandth, ...

#### Examples

• 38 rounded to the nearest ten is 40
• 623 rounded to the nearest hundred is 600, to nearest thousand is 1000
• \$7.99 rounds to \$8
• \$7.97 rounds to \$7.95
• 814 to the nearest whole is 8.

### Row

Items arranged horizontally.

## S

### Sample

A part of the population that has been selected in order to find information about the whole population.

### Sample space

The set of all possible outcomes of a situation or experiment.

#### Example

The possible outcomes when tossing a die are 1, 2, 3, 4, 5 and 6. The set would be {1, 2, 3, 4, 5, 6}.

### Scale drawing

A drawing, which maintains proportions, shown bigger or smaller than real life. Common examples include maps or house plans.

### Scale factor

A measurement of how much a diagram has been enlarged or reduced in a scale diagram.

### Scalene triangle

A triangle which has sides of different lengths and where all angles are different.

### Scientific notation

• Used for writing very large or very small numbers.
• Also called standard notation.

#### Examples

• Population of the Earth in 2010 was about 6.82 × 109
• The mass of an electron is about 9.1 × 10-31kg

### Secant

A straight line that passes through two points on a circle or curve.

### Section

The flat surface you see after cutting through a solid in any direction.

### Sector graph

• A circle divided into sectors to illustrate parts of a whole.
• Commonly called a pie chart.

Sports played:

### Segment

The part of a circle that is between a chord and the circumference.

Half a circle.

### Sharing

To divide into equal or unequal groups.

#### Example

Sharing 10 apples between 5 children gives 2 apples each.

### Significant figures

The digits considered to be significant in reporting a measurement, irrespective of the location of the decimal place.

### Similar figures

Two figures that look the same but one is an enlargement of the other. All proportions are maintained.

### Simple interest

• Simple interest is the interest calculated on the original investment amount or the amount borrowed (the principal).
• Simple interest is also called flat rate interest.

#### Example

I = PRN where:

I = the simple interest

P = the principal

R = the interest rate per period, expressed as a decimal or fraction

N =  the number of time periods.

### Skew lines

Skew lines never touch each other but are not parallel. Skew lines only exist in 3D space.

### Skewed distribution

Most of the data is clustered at one end.

### Skip counting

Counting forwards or backwards in groups or multiples of a particular number.

4, 8, 12, ....

### Slant height

Slant height is the height from the base to the apex along a surface. This is at an angle to the base, not perpendicular.

### Slide

To move the position without rotating it or turning it over. This is also called a translation.

### Solid

Is any 3D (three-dimensional) object. The three dimensions are length, width and depth.

### Sphere

A perfectly round 3D object. Globe and sphere are interchangeable terms.

### Split strategy

Mental computation method where numbers are 'split' according to their place value to make it easier to add them.

#### Example

For 46 + 33 the numbers are split to become:

(40 + 30) + (6 + 3) = 70 + 9 = 79

### Square

A polygon with 4 straight sides where all sides are equal in length and all angles are equal (90°).

### Square number

The result of multiplying a number by itself.

#### Example

16 is a square number. It has 4 rows of 4, so 4 × 4 = 16

### Square prism

• A 3D solid with 2 parallel bases that are squares of the same size and shape (ie are congruent).
• Its other faces are squares or rectangles or parallelograms.
• It is called a cube if all its other faces are also squares.

### Square pyramid

• A 3D (three-dimensional) solid with a square as its base.
• Its other faces are triangles that meet at a common point (vertex).

### Square root

• A positive number that can be multiplied by itself to give this number.
• The converse or opposite operation of squaring.
• Indicated by the square root symbol √.

#### Example

√25 = 5 since 5 × 5 = 25

### Standard deviation

A standard measure of the average spread of the scores about the mean.

### Stem and leaf plot

• A way of representing small data sets.
• It shows the shape of the distribution.
• The left column contains the stem and the right column contains the leaf.

### Step graphs

• A line graph with broken horizontal intervals.
• Used when the values stay the same for a period of time, e.g. parking costs.

### Straight angle

An angle measuring 180°.

### Strategy

A way of working something out using known relationships, patterns and operations.

### Subitising

Immediately recognising the number of objects in a small collection without having to count them.

#### Example

Seeing 5 immediately, without counting 1, 2, 3, 4, 5.

### Subtract

• Taking one number or amount away from another.
• This is the opposite of add.
• Decrease, subtract, subtraction and take away are related terms.

### Subtraction

• Taking one number or amount away from another.
• This is the opposite of addition.
• Decrease, subtract, subtraction and take away are related terms.

### Sum

• The process of combining collections of objects into a larger collection.
• This is the opposite of difference.

#### Example

Combining a collection of things together:

### Supplementary angles

Supplementary angles add up to 180 degrees.

### Surd

• An old-fashioned term for an irrational number.
• A number under a √ sign that has no rational equivalent.

√3 is a surd

### Symmetrical

An object or shape has symmetry or is symmetrical when one half is the mirror image of the other half.

### Symmetrical distribution

The spread of scores or results is symmetrical.

### Symmetry

An object or shape has symmetry or is symmetrical when one half is the mirror image of the other half.

## T

### Table

A way of presenting information in rows and columns for easy interpretation.

#### Example

What pets do you own?

### Take away

• Taking one number or amount away from another.
• This is the opposite of plus.

### Tangent

A straight line that touches a circle or curve at only one point.

### Ten frame

An empty chart that has 2 rows of 5. This frame helps children to visualise the numbers 1 to 10.

### Tessellating

Fits together without any spaces or overlaps.

### Tetrahedron

A 3D (three-dimensional) object with 4 faces.

### Three-dimensional

• Three-dimensional defines a space as having length, width and depth.
• Three-dimensional and 3D are interchangeable terms.

#### Example

A solid has 3 dimensions

### Three-dimensional object (3D)

Has 3 dimensions – length, width and breadth – and has surfaces that are curved, flat or a combination of both. Flat surfaces that meet at the edges are called faces.

#### Example

A solid has 3 dimensions

### Times tables

The products of numbers 0 to 10 multiplied by each other. Students are encouraged to learn and appreciate a range of mental strategies to work out the answers.

Multiplications may be shown in an organised way (such as the examples below) to assist in memorising the answers.

Multiplication tables and times tables are interchangeable terms

#### Examples

The 5 times tables:

1 × 5 = 5

2 × 5 = 10

3 × 5 = 15

4 × 5 = 20

5 × 5 = 25

6 × 5 = 30

7 × 5 = 35

8 × 5 = 40

9 × 5 = 45

10 × 5 = 50

Changing a quantity into smaller or bigger parts without changing its value. This method is used to make calculations easier.

### Translation

The result of sliding a figure without turning or flipping it, while maintaining its size.

### Transversal

A straight line that crosses two or more other lines.

### Trapezium

A quadrilateral with at least one set of parallel lines.

### Travel graphs

• A travel graph shows a journey.
• The time is marked on the horizontal axis.
• The distance from the starting point is shown on the vertical axis.

#### Example

Dan's walking track

### Tree diagram

A branching diagram used to list all the outcomes in a sequence of events.

### Triangle

A polygon with 3 straight sides and 3 angles. The sum of the angles in a triangle is 180°.

### Triangular numbers

Number that can be represented by a triangular pattern of dots.

#### Example

The first three triangular numbers 1, 3 and 6 can be represented by:

### Triangular prism

• A 3D (three-dimensional) solid with 2 parallel ends that are triangles of the same size and shape (ie are congruent).
• All its other faces are rectangles.

### Triangular pyramid

A pyramid with a triangle as its base. Its other faces are triangles that meet at a common point (vertex).

### Turn

• To rotate around a point.
• Can be done by turns or a given number of degrees.
• Rotate and turn are interchangeable terms.

### Turn around facts

• Turn around facts show you are able to add and multiply numbers in any order (you are able to turn them around) and the answer will not change.
• Commutative law, commutativity and turn around facts are interchangeable terms.

### Twenty-four hour time

• A division of the day into 24 hours, starting from midnight (00:00) through to 11:59pm (23:59).
• 24 hour clock and twenty-four hour time are interchangeable terms.

#### Example

7:30 in the morning is 07:30, but 7:30 at night is 19:30 (midday 12:00 plus 7 1/2 hours).

### Two-dimensional (2D)

Two-dimensional defines a space as having length and width. Two-dimensional and 2D are interchangeable terms

#### Example

A flat shape has 2 dimensions

## U

### Uniform cross-section

A cross section that is the same size and shape throughout a solid.

#### Example

This solid has a uniform cross-section:

This solid does not have a uniform cross-section:

### Unit fraction

A fraction that has a numerator of 1.

### Units of area

Standard area units include:

• square millimetres (mm2)
• square centimetres (cm2)
• square metres (m2)
• square kilometres (km2)

#### Examples

• 102 mm2 = 1cm2
• 1002 cm2 = 1m2
• 10002 m2 = 1km2

### Units of length

Standard length units include:

• millimetres (mm)
• centimetres (cm)
• metres (m)
• kilometres (km)
• nautical miles (nm)
• 10 mm = 1 cm
• 100 cm = 1 m
• 1000m = 1 km
• 1852km = 1 nm

### Units of time

Time is measured in units such as seconds, minutes, and hours:

• 60 seconds = 1 minute
• 60 minutes = 1 hour
• 24 hours = 1 day.

### Units of volume

Standard volume units include:

• centimetres cubed (cm3)
• metres cubed (m3)
• kilometres cubed (km3).

#### Examples

• 103 mm3 = 1cm3
• 1003 cm3 = 1m3
• 10003 m3 = 1km3

## V

### Vertex

• A meeting of 2 or more lines that form an angle.
• The plural of vertex is vertices.

#### Example

A cube has 8 vertices

### Vertical

A line that is at right angles to a horizontal plane.

### Vertical algorithm

A step-by-step method of addition, subtraction, multiplication or division.

### Vertically opposite angles

Vertically opposite angles are created when two lines cross. These angles are equal in size.

#### Example

Angles a and b are vertically opposite angles

### View

Solid shapes look different depending on where they are seen from, eg front view, side view, top view.

#### Example

Different views of this solid

### Volume

The amount of space taken up by an object or substance, measured in cubic units.

#### Example

This shape has a volume of 6 cubic units

## W

### Weight

Mass and weight are interchangeable in everyday usage but weight is a force which changes with gravity, while mass remains constant.

## W

### Whole number

Any number that is not or does not include a fraction or a decimal.

2 or 84 or 6000

## Z

### Zero index

Any non-zero number to the power of zero is equal to one.

#### Example

20 = 1, 50 = 1, 230 = 1