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A MORE USEFUL
MATHS
DICTIONARY
Chris Guest
Written by Chris Guest, an experienced teacher of
mathematics up to GCSE level, this unique, crossreferencing maths dictionary is designed to help
children aged 6 to13+ improve their maths skills,
whilst also acting as an invaluable guide for
parents. This dictionary is much more useful than
any internet search engine, since it shows all the
key maths vocabulary and methods children need
to know, put together in one handy reference book.
Knowledge of the maths within this dictionary, will
significantly help students prepare for all maths
examinations up to GCSE level.
How to use this maths dictionary
If a word in the definition is in both bold and
slanted font, you can find its meaning crossreferenced in this dictionary; a helpful feature,
which makes this dictionary more useful for
reference, than all other available resources.
ABACUS: a simple machine with beads on
a frame, used for counting
ACCURACY: the state of being correct or
precise
ACCURATE: correct in all details; exact
ACRE: an area measurement,
approximately equal to half of a
full sized football pitch
ACROSS: from one side to the other of
something e.g. the width of a football pitch
ACUTE ANGLE: describes an angle
less than a right angle (90 degrees: 90°)
ADD, ADDITION: plus, join, count on,
bond, how many more, how much more,
increase, sum of, total, make more
The symbol for add is +
See number bonds and column addition.
ADJACENT: next to. Adjacent angles on
a straight line total 180°
150°+30°=180°
ALGEBRA: a branch of mathematics
using symbols (usually letters) to replace
numbers. The letter is the most common
letter used in algebra.
e.g.
+
= 10 (The letter
represents 5.)
e.g. t + 3 = 7 so the letter t must be worth 4
ALTERNATE: every other one.
The alternate number pattern shown below,
uses multiples of 2 and 5:
2, 5, 4, 10, 6, 15, 8, 20, 10, 25, 12, 30
ALTITUDE: height above the earth’s
surface or sea level
A.M. (a.m): ante meridiem. Any time
between midnight and midday (noon).
AMOUNT: quantity, number of, total,
size
ANALOGUE: analogue time is showing
the time on a normal clock face,
whereas digital time only uses
digits. This clock shows the
analogue time: ten minutes to
two (1:50 digital time).
The angle between each hour number
is 30°. For example, there are 120° between
the 2 and the 6, if you turn clockwise.
ANGLE: a turn either clockwise or
anticlockwise. An angle less than 90° is
acute. An angle more than 90°, but less
than 180° is obtuse. An angle more than
180°, but less than 360° is reflex.
A quarter turn = 90º. (right angle)
A half turn = 180º.
A three quarter turn = 270º.
A full turn = 360º.
Angles on a straight line total 180°.
Angles in a triangle total 180°.
Angles around a point total 360°.
Angles in a quadrilateral total 360°.
Opposite angles are equal (the same).
Exterior angles of any polygon total 360°.
ANGULAR: having, forming or consisting
of an angle or angles. The letter Z is angular.
ANSWER: a solution to a problem or
calculation.
ANTICLOCKWISE: the opposite of
clockwise
APEX: the highest point ↓
APPROXIMATE: about equal to
APPROXIMATELY: about equal to.
The symbol for approximately equal to
is or
APPROXIMATION: a rough answer
e.g. 27 + 32 is approximately equal to 60
ARC: part of circle’s circumference
AREA: surface space
The area of square, rectangle, rhombus or
parallelogram = base x height
area of triangle = half of (base x height).
ARITHMETIC: branch of mathematics
that includes + - x ÷, numbers, fractions,
decimals and percentages
ASCENDING ORDER: arranged in
order from smallest to largest. The
ascending order of the first twelve square
numbers is:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
AS THE CROW FLIES: in a straight
line direction (The shortest distance
between two points.)
ASYMMETRICAL: not symmetrical
This teapot is asymmetrical.
ATTRIBUTE: a characteristic of
something e.g. shape, size or colour
AVERAGE: a measure used to find what
seems to be about the middle of a set of
data (see mean, median and mode)
AVERAGE SPEED:
average speed = distance ÷ time
AXES: plural (more than one) of axis
AXIS: the horizontal (x axis) or vertical
(Y axis) lines of a graph (see coordinates)
AXIS OF SYMMETRY: mirror line
dividing something into 2 equal images or
parts
BALANCE: having the same weight on
either side of scales or equalling the same
on both sides.
e.g. a balanced equation: 4 + 6 = 7 + 3
BAR CHART or BAR GRAPH:
a graph using bars
BAR LINE CHART: a graph using lines
BASE: the lowest part of something,
opposite to apex
In mathematical numeral systems,
the base is the number of digits,
including zero, that a positional numeral
system uses to represent numbers.
BASE TEN: a number system based on a
place value of ten:

Millions, Hundred Thousands, Ten Thousands, Thousands, Hundreds, Tens, Units
M
HTh
TTh
TH
H
T U
The TEN base system is known as DENARY.
e.g. 2,325,168 means:
two million, three hundred and twenty five
thousand, one hundred and sixty eight
BASE TWO: binary (see BINARY)
BEARING: A bearing is an angle,
measured clockwise from the north
direction. Three figures are always given
as shown in the diagram below, the bearing
of B from A is 038° and the bearing of A from
P is124° .
The four key words/phrases about bearings
are:1) north line, 2) clockwise
3) three figures 4) from (see example above)
BI- to do with the number 2
BIDMAS: (see BODMAS) stands for the
initial (first) letters of the following words:
Brackets Indices Divide Multiply Subtract Add Subtract
BILLION: a thousand million
1,000,000,000 or in USA, a million, million.
BINARY: The base 2 number system
only uses the digits 1 and 0 to show
numbers. Our standard number system is
base 10 or denary.
TH←(10x100)H←(10X10)T ←(10X1)U
Binary (base 2) is shown using the following
place values: doubling starting from 1.
512, 256, 128, 64, 32, 16, 8, 4, 2, 1
This is an example of a binary number:
64
1
32 16
0
8
4
2
1
0 1 1 0 1 = 77 (64 + 8 + 4 + 1)
BIRD’S EYE VIEW: the view of
something seen looking straight down
vertically (a plan view)
BISECT: cut in half or 2 equal sized parts
If you bisect a right angle (90°), each
angle = 45°.
BODMAS: BODMAS stands for the
initial (first) letters of the following six words:
Brackets Indices Divide Multiply Subtract Add Subtract
and is used to show the correct order of
doing a calculation with more than one
symbol. The word other means other things,
apart from brackets, division, multiplication,
addition or subtraction e.g. %
e.g. 4 + 6 X 2 = 16. A more complicated
example is shown next. The bold underlined
numbers in each line of workings, show the
answers to what has to be done at that
stage.
A more complicated example of BODMAS is:
3² - (50% of 20) + 6 x 40 ÷ 2
B 3²- 10 + 6 x 40 ÷ 2
O 9 - 10 + 6 x 40 ÷ 2
D 9 - 10 + 6 x 20
M 9 – 10 + 120
A 129 – 10
S 119
BOND: an addition sum e.g. 6 + 4 is a
bond of 10. The most important number
bonds are those from 1 to 20. (see number
bonds)
BOUNDARY: a line around the outside
edge. The distance around the outside
edge is called the perimeter. The boundary
of a circle is called the circumference.
BRACKETS: used to show parts of a sum
that should be treated as together or should
be worked out first. The symbols for
brackets are ( ). In arithmetic and algebra,
operations within brackets must be
calculated first.
e.g. 2 x (3 + 4) = 14 since the brackets must
be done first, which makes: 2 X 7 = 14
BREADTH: the width (distance across)
CALCULATE: work out
CALCULATION: the workings resulting
in an answer e.g. 8 + 10 - 6 = 12
CALIBRATED: having calibrations
CALIBRATIONS: the lines on a scale.
This part of a ruler shows centimetre and
millimetre calibrations.
CANCEL: to reduce to lowest or
simplest terms
12
2
e.g
cancels to , since 6 is the highest
18
3
number that divides into both 12 and 18.
CAPACITY: volume (amount of space
taken up by a 3D object or liquid).
volume of cube or cuboid = length x width x height
CARROL DIAGRAM: a sorting diagram
invented by Lewis Carroll (author of ‘Alice in
Wonderland’)
A Carrol diagram, sorting numbers.
CELSIUS CENTIGRADE:
a measurement of temperature.
To convert Celsius centigrade to
Fahrenheit, multiply the temperature by 2
and then add 30 for an approximate
conversion.
e.g. 20ºC is approximately equal to 70ºF
(20 x 2 + 30 =70)
CENTI- one hundredth 1/100
CENTIGRADE: see CELSIUS CENTIGRADE
CENTILITRE: one hundredth of a litre
CENTIMETRE: one hundredth of a metre
CENTRE: middle point
CENTURY: one hundred years
CHART: a sheet of information in the form
of a table, graph or diagram
CHORD: a line across a circle, NOT
passing through its centre (see segment)
CHUNKING DIVISON: expanded division
Chunking division is a slow method of dividing
and should not be used in timed test situations.
CIRCLE: a perfectly round
2D (two dimensional) shape
CIRCULAR: in the shape of a circle
CIRCUMFERENCE: the perimeter of a
circle
CLASSIFY: put into classes or groups
CLOCKWISE: the direction a clock turns
COLUMN: a vertical arrangement
Below is a column addition and a column
subtraction calculation.
COMMON: sharing the same
characteristics or properties
COMMON FACTOR: a number that will
divide into two or more numbers exactly
e.g. 3 is a common factor of 9, 12, 15 and 18.
COMMON MULTIPLE: a number that
is a multiple of two or more numbers.
e.g. 24 is a common multiple of 2, 3, 4, 6, 8
and 12
COMPARING DECIMALS: see
ordering decimals
COMPARING FRACTIONS:
to compare and order fractions with different
denominators, make all the denominators
the same by finding their LCD as show here:
3 2 5 3
e.g Compare: , , , The LCD = 60
4 3 6 5
45 40 50 36
,
60 60 60 60
So now the fractions can be compared and
3 2 3 5
ordered, smallest to biggest: , , ,
5 3 4 6
COMPASS: The 8 points of the compass
are shown below. The smallest angle
between each of the 4 main directions:
North, East, South, West is 90° (a right
angle) and the smallest angle between each
of the 8 directions is 45° as shown below.

A compass is also a geometric
instrument used for drawing circles.
COMPLEMENTARY ANGLES: either
of two angles which total 90°
COMPOSITE: made up of several parts
This is a composite shape; it can be
separated into 2 rectangles, as shown.
Notice that the 2cm side can be found by subtracting
the 7cm side from the 9cm side.
Likewise, the 4cm side can be found by subtracting
the 6cm side from the 10cm length.
COMPOUND: a mixture of two or more
parts. See composite.
CONCENTRIC: the word used to describe
circles that have the same centre
CONE: a 3D (three dimensional) shape
A cone has 2 faces, 1 edge and 1 vertex.
CONGRUENT: identical in size and
shape.
These scalene triangles are congruent.
CONSECUTIVE: one after the other, in
order e.g. 2, 4, 6, 8, 10 etc
CONVERSION: a change from one
thing to another
CONVERT: change one amount to
another equivalent amount of a different
unit value
COORDINATES: positions in quadrants
A = (-3, 2) B= (4,-3)
A is in the 2nd quadrant and B is in
the 4th quadrant. TIP: Go along the corridor
(+ is forwards and - is backwards) and up (+)
or down (-) in the lift, not the stairs, since
stairs go diagonally.
CORNER: the point where lines meet.
Another word for corner is vertex.
Corners are called vertices
CORRECT: not having any errors.
COUNTER-CLOCKWISE: anticlockwise (Used in USA)
COUPLE: a quantity of two
CRESCENT: a curved segment of a circle
CRISS-CROSS: lines that cross over
each other
CRITERIA: what must be included
CROSS SECTION: a view seen, as if a
cut has been made straight through the
middle of something
CUBE: a square 3D (solid looking) shape
A cube has 6 faces, 12 edges and 8
vertices.
Cube also means to multiply by itself,
again and again. e.g. 2 x 2 x 2 = 8
CUBED: multiplied by itself and
then by itself again or to the power of 3.
e.g. 4³ means 4 x 4 x 4 (see cube number)
(4³ means 4 to the power of 3)
CUBE NUMBER: a number made by
multiplying three of the same numbers
together e.g. 8 is a cube number since
2 x 2 x 2 = 8 or 2³ = 8 (³ means multiplied
by itself and then multiplied by itself again; it
does not mean multiplied by 3; a common
mistake!)
CUBE ROOT: a number, which when
multiplied by itself and then by itself again,
gives another number. The cube root is the
opposite of a cube number.
e.g. The cube root of 125 is 5 = 5

The symbol for cube root is:
CUBIC CENTIMETRE: cm³
a standard unit for measuring volume
1 cubic centimetre = 1 millilitre 1cm³ = 1ml.
A three-dimensional (3D) space
equivalent to a cube of edge length 1cm.
One cubic centimetre = one millilitre.
1ml is equivalent to a droplet of liquid, as
shown above.
This little measuring spoon holds either
5cm³ (5ml) or 2.5cm³ (2.5ml) of medicine.
CUBIC METRE: m³ a standard unit for
measuring volume. A three dimensional
(3D) space, equivalent to a cube having
edge lengths of one metre.
CUBOID: a rectangular 3D (solid looking)
shape.
A cuboid has 6 faces, 12 edges and
8 vertices.
CURRENCY: the kind of money used in a
country
CURVE: a line not straight or angular
CYLINDER: a circular prism, a round
tube shape. A cylinder has 3 faces, 2 edges
and no vertices.
DATA: information collected
DATABASE: a means of storing sets
of data
DAY: 24 hours
There are 7 days in a week and 365 days in a
year (366 days in a leap year).
DECADE: ten years (one tenth of a
century or 10% of a century)
DECAGON: a 2D shape with 10 straight
sides. The example shown below is a
regular decagon, since all its angles and
sides are the same length.
DECAHEDRON: a polyhedron with 10
faces
DECIMAL: a fraction of a unit, with a
denominator as a power of ten and whose
numerator is expressed by figures placed
to the right of a decimal point. e.g. The
numbers in bold on the right of the decimal
point are decimal figures: 25.637
To add decimals and money amounts,in
column addition and subtraction, it is very
important to position the decimal points
underneath one another, as shown.
To multiply decimals, multiply the numbers
together without the decimal point and then
put it into the answer, by counting back from
the unit end of the number, the number of
decimal places in the actual numbers you
started with.
e.g.0.8 x 0.0 3 = 0.024 There are 3 decimal
placed digits in 0.8 x 0.0 3, so count back 3
places from 24, gives 0.024
To divide decimals, you must make sure the
number you are dividing by (the divisor) is
a whole number. If it is not, you first have to
multiply it by 10, 100 or 1000 (see multiply)
and then do the same to the dividend.
e.g. 2.4 ÷ 0.04 = 240÷4=60 The divisor,
0.04 had to be multiplied by 100 to make it
into a whole number (4); therefore, 2.4 also
had to be multiplied by 100 (240).
To multiply or divide decimal numbers by
10, 100 or 1,000 see multiply and divide.
DECIMAL FRACTION: a fraction out of
ten, hundred, thousand, ten thousand,
hundred thousand or million e.g.
DECIMAL PLACES: a position of a digit
to the right of the decimal point.
e.g. 2.5 has one decimal place
1.2 5 has two decimal places
3.1 2 7 has 3 decimal places
DECIMAL POINT: a dot which separates
whole numbers from decimal digit values
e.g. 2.3 means 2 units and 3 tenths
DECIMALS: fractions in tenths,
hundredths and thousandths etc
e.g. 0.283 means 2 tenths, 8 hundredths
and 3 thousandths or 283 thousandths
DECOMPOSITION: a vertical or
column method of subtraction. The
number in the top line is broken down with
exchanging, to help calculation.
e.g. 642 - 387 is worked out as shown below.
DECREASE: go down in amount or size
DEDUCT: take away
DEGREE: a unit of turn used in the
measurement of angles. The symbol for
degrees is °
One whole turn is equal to 360 degrees,
written as: 360° (see angles)
DENARY: BASE 10
The number place value system we use
Th H T U is base 10 or the denary system.
DENOMINATOR: the bottom number of
a fraction
5
has a denominator of 8.
8
DESCEND: to go down
DESCENDING ORDER: going down in
size or value e.g. 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
DIAGONAL: a sloping line or line joining
vertices (corners) of a polygon (2D shape
with straight sides)
A pentagon has 5 diagonals.
DIAGONALLY: in a slant
DIAGRAM: a picture which explains
information
DIAMETER: a line through the centre of a
circle, touching the circumference
Half of a diameter is called a radius.
DIFFERENCE: the amount between
two numbers.
e.g.The difference between 4 and 10 is 6,
the difference between -5 and 3 = 8
The result of a subtraction
The amount by which, one number or value,
is greater than another
DIGIT: another word for figure. Words are
made of letters but numbers are made using
digits or figures. e.g. 1,000,000 has 7 digits
TIP: The word ‘million’ has 7 letters and the
number ‘million’ has 7 digits (figures).
DIGITAL: using digits
DIMENSIONS: refers to length, width
(breadth) and height. e.g. a cuboid has
length, width and height
DIRECTED NUMBERS: negative and
positive numbers
e.g. -5, -4, -3, -2, -1, 1, 2, 3, 4, 5
When calculating with positive and
negative numbers, you must follow the rules
below; the word signs in the rules, just
refers to + and 2 signs the same, make a + answer, when
multiplying, dividing or when they are next to
each other.
2 different signs, make a - answer, when
multiplying, dividing or when they are next to
each other. Below are lots of examples:
8 + - 3 = 5, 12 - - 3 = 15, - 5 x 3= -15
- 4 x -3=12, 20 ÷ - 5 = - 4, -10 ÷ - 2 = 5
- 4 - 3 = -7, - 4 + 10 = 6, - 9 + 5 = - 4
-12 - - 7 = -5, 30 ÷ -10 = -3, - 20 ÷ - 5 = 4
DIRECTION: the line or course on which
something is going (see compass directions)
DISTANCE: the length between two
points
DIVIDE: separate or repeated subtraction.
The symbol for divided by is ÷
e.g. 15 ÷ 3 = 5. See short division.
To divide a number by 10, move the digits
together, one place value position smaller.
To divide a number by 100, move the digits
together, two place value positions smaller.
To divide a number by 1000, move the
digits together, three place value positions
smaller.
e.g. 45÷10=4.5 256÷100=2.56 8÷10=0.8
360÷100=3.6 73÷1000=0.073, 60÷100=6
63.2÷1000=0.0632, 8÷1000=0.008
DIVIDED INTO: The symbol for divided
into is
(See short division and long division)
DIVIDEND: the number used to divide
another number into.
e.g. 8÷4 =2 The dividend is 8
DIVISIBILITY RULES:
A number is divisible by 2, if it’s even (ends
with 0, 2, 4, 6, 8). A number is divisible by
10, if it ends with 0. A number is divisible
by 5, if it ends with 5 or 0. A number is
divisible by 4, if the last two digits are
divisible by 4.e.g. 71, 928. A number is
divisible by 3, if the total of its digits is
divisible by 3. e.g. 2781 (The digits total 18
which is a multiple of 3) A number is
divisible by 6 if the total of its digits is
divisible by 3 and it’s also even. e.g. 798.
A number is divisible by 9, if the total of the
digits can be divided by 9. e.g. 7281.
There is no quick and simple rule for testing
divisibility by 7 or 8.
DIVISIBLE: can be divided by
e.g. 12 is divisible by the following numbers:
1, 2, 3, 4, 6 and 12
DIVISION: sharing or grouping into equal
parts or taking away the same number any
number of times
DIVISOR: the number which divides into
another number
e.g. 8 ÷ 4 = 2 (The divisor is 4)
DODECAGON: a polygon with 12
straight sides and 12 angles
DODECAHEDRON: a 12 sided
polyhedron
DOUBLE: multiply by 2
DOUBLING: multiplying by 2
e.g. doubling one:
1, 2, 4, 8, 16, 32, 64,128, 256, 512, 1024 etc
DOUBLING and HALVING: a quick
method of multiplying by doubling and
halving e.g. 15 X 24 = 30 X 12 = 360
See halving and doubling.
DOZEN: twelve
e.g. a dozen eggs = 12 eggs
EDGE: line joining faces of a 3D shape
(polyhedron)
e.g. a cuboid has 12 edges
EIGHTH: one equal sized part out of eight
To find an eighth of a number, halve it,
halve it again and then halve it again, or
divide it by 8.
ELEVATION: a view seen from the front,
plan (top) or side
A plan view is a bird’s eye view.
 height above a given level, especially
sea level
ELLIPSE: an oval shape
ENLARGE: make bigger
ENLARGEMENT: the action or state of
enlarging or being enlarged
EQUAL: the same amount or size
EQUALS: is the answer to
e.g. 3 times 4 equals 12 or 3 x 4 = 12.
The symbol for equals is =
EQUATION: a mathematical statement
containing an equals sign (=) with two or
more terms a + b = 8 or 3 + 5 = 8
EQUIDISTANT: at equal distances
EQUILATERAL: having equal angles
and equal sides e.g. an equilateral triangle
The little line symbols
across each side mean the sides are the
same length.
EQUIVALENT: equal to
EQUIVALENT FRACTION: a fraction
which is equal to another fraction
9
3
e.g.
=
(The numerator (9) and
12
4
denominator (12) both divide by 3.)
ERROR: a mistake
ESTIMATE: guess as an approximation
(work out a rough answer)
EULER’S THEOREM: F + V - E = 2
Faces + Vertices – Edges = 2
an equation for checking the faces,
vertices and edges of a polyhedron
EURO: € is the currency used by the
Institutions of the European Union
EVALUATE: work out
EVEN: only multiples of 2 are even.
Even numbers always end with the digits:
0, 2, 4, 6 or 8.
EXACT: not approximate in any way;
precise
EXPRESSION: numbers and symbols
grouped together that show the value of
something e.g. 2 + 3 x 4 is an expression
EXTERIOR: outside
EXTERIOR ANGLES: outside angles.
The exterior angles of any polygon always
total 360º.
e.g. A pentagon’s exterior angles shown
below: 1+2+3+4+5 = 360 º.
FACE: the side (flat or curved part) of a
3D shape. The 3 visible faces of this cuboid
are shown in 3 different shades.
FACTOR: a number that divides exactly
into a number e.g. The factors of 12 are:
1, 2, 3, 4, 6 and 12, since they all divide
exactly into 12.
FACTORISE: show a number or
expression as a product of factors
e.g. 18 = 2 x 9 which equals 2 x 3 x 3
30 = 2 x 15 which equals 2 x 3 x 5
FARENHEIT: a measurement of
temperature. To convert Fahrenheit to
Celsius centigrade, divide the temperature
by 2 and then halve the answer for an
approximate conversion.
FEET: more than one foot (the plural of
foot)
FEW: a small number
FIBONACCI SEQUENCE: a number
sequence in which each number is the sum
of the two numbers before it.
e.g. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 etc
FIGURE: another word for digit.
e.g. 164 has 3 digits. Words are made with
letters, numbers are made up of figures or
digits. A figure can also mean a shape.
FINGER CALCULATOR:
a very useful finger tip calculator for working
out the harder 6, 7,8 and 9 times table
products. The following example shows how
to work out 8 x 7:
Hold your hands facing towards you with
your fingers spread apart. In your head,
number your fingers on each hand, starting
at your little finger and working up along the
other fingers: 6, 7, 8 and 9, as shown in the
picture. The example shows how to work out
8 x 7 by touching together finger numbers 8
and 7. Simply, count the fingers touching
and below, as the tens of the answer: this
shows 5 fingers which equals 50. Then
multiply the top pairs (left and right hand) of
fingers together (2 x 3) which equals 6.
Finally add together 50 and 6, so the
answer is 56. Practise this method and it will
really help you learn the harder tables facts.
FLAT: being level (horizontal) or smooth.
A tennis court must be flat.
FLIP: turn over
FOOT: an imperial measurement which is
approximately equal to 12 inches or 30 cm,
as shown below, with this standard length
ruler.
FORMULA: a mathematical relationship or
rule shown using symbols.
e.g.The formula for calculating the area of a
triangle is: (base x height) ÷ 2
FORTNIGHT: 2 weeks (14 days)
FRACTION: an equal sized part of a
whole e.g. A shape cut into quarters has
4 equal parts. To find a fraction of a number,
divide it by the denominator and then
multiply the answer by the numerator.
e.g. ¾ of 12 = 9 (12 ÷ 4 = 3 and then 3 x 3 = 9)
To add or subtract fractions, the
denominators must be the same:
e.g.
In the next example, the lowest common
denominator had to be calculated first, in
order to make the fractions have the same
denominators.
4
11
+
The LCD of 9 and 12 is 36.
9
12
16
33 49
13
+
=
=1
36 36 36
36
is worked out by dividing 36 by 9 and then
multiplying the answer by the numerator 4.
So 36 ÷ 9 = 4 and then 4x4=16.
To subtract fractions, do the same as above,
but take away the numerators, rather than
adding them.
To multiply fractions, simply multiply the
numerators and denominators together.
Remember to simplify your answer to
lowest terms as shown below.
3
5 15 5
x =
=
4
6 24 8
To divide fractions, turn the second fraction
upside down and then multiply the two
fractions together, as shown below.
2 3 2
4 8
÷ =
x =
3 4 3
3 9
To add, subtract, multiply or divide mixed
numbers to other mixed numbers, fractions
or whole numbers, first change the mixed
numbers into improper fractions and then
work out as explained above. Look at these
examples below.
3
5 11 23 33 46 79
7
e.g. 2 + 3 = +
=
+ = =6
4
6 4
6 12 12 12
12
2
3 14 3 42
12
4
x =
x =
=2 =2
3
5
3 5 15
15
5
You must always simplify fraction
answers to lowest terms.
e.g. 4
To change a fraction to a decimal, divide
the numerator by the denominator as
shown below.
FRACTION, DECIMAL AND
PERCENTAGE CONVERSION
CHART
1/2 = 0.5 = 50%
1/4 = 0.25 = 25%
3/4 = 0.75 = 75% (see division calculation above)
1/5 = 0.2 = 20%
1/10 = 0.1 = 10%
1/20 = 0.05 = 5%
1/100 = 0.01 = 1%
One whole unit = 1.0 = 100%
FREQUENCY: the number of
FUNCTION MACHINE: a Function
Machine is a diagram that represents a
machine that takes an input, applies a rule
such as a set of operations and delivers the
answer as an output
GALLON: an imperial measurement
approximately equal to 4.5 litres
Petrol containers often hold about a gallon.
GEOMETRY: maths about solids,
surfaces, points, lines, curves, angles and
their relationship
GRADIENT: a slope
how steep something is
gradient = vertical ÷ horizontal
GRAM: one thousandth of a kilogram kg.
A standard size paper clip weighs
approximately one gram.
GRAPH: a mathematical diagram showing
information, usually with an x and Y axis
e.g.
GREATER THAN: more than. This is the
symbol > e.g. 8 > 5
GRID: an arrangement of perpendicular lines
This is a 10 x 10 grid.
GRID MULTIPLICATION: a method of
multiplying multi-digit numbers
e.g. 35 x 26 is shown next:
GUESSTIMATE: an estimate
HALF: one of 2 equal sized pieces.
Halves are 2 equal sized (congruent)
pieces.
HALF A DOZEN: half of 12 = 6
e.g. half a dozen eggs = 6 eggs
HALFWAY: at or to a point equidistant
between two others. To calculate a number
halfway between two numbers, simply add
them both together and then halve the
answer. e.g. To calculate the number
halfway between 15 and 45: 15 + 45 = 60
and then 60 ÷ 2 = 30, so 30 is the halfway
number.
HALVE: divide into 2 equal size pieces or
divide by 2 (÷2)
HALVES: 2 equal amounts or parts
HALVING: dividing by 2
e.g. 128 ÷ 2 = 64 then 64 ÷ 2= 32 then
32 ÷ 2 = 16 then 16 ÷ 2= 8 then 8 ÷ 2 = 4
then 4 ÷ 2= 2 then 2 ÷ 2= 1
HALVING and DOUBLING: a fast
method of multiplying by halving and
doubling numbers.
e.g. 24 x 15 = 12 x 30 = 360
See doubling and halving
HANDSPAN: distance across a fully
stretched open hand from thumb tip to little
finger tip
HAPPY NUMBER: a number which,
when you square its digits and then add
them together in a sequence, you eventually
end up with the digit 1, as shown below
The first ten happy numbers are:
1, 7, 10, 13, 19, 23, 28, 31, 32, 44
e.g. 19 is happy, as the sequence follows as
shown:
HAPPY NUMBER 19:
12 + 92 = 82 (1 + 81)
82 + 22 = 68 (64 + 4)
62 + 82 = 100 (36 + 64)
12 + 02 + 02 = 1 (1 + 0 + 0)
HCF: Highest Common Factor means the
highest number which will divide into two or
more numbers.
e.g. The HCF of 8 and 12 is 4.
The HCF of 6 and 9 is 3.
HECTARE: 2.471 acres or 10,000 square
metres
HEIGHT: vertical length.
Height should be measured perpendicular
to a horizontal.
HEMISPHERE: half of a sphere
HEPTAGON: a seven sided
two dimensional (flat) shape (polygon)
This is an irregular heptagon.
HEXAGON: a 6 sided 2D (flat) shape
This is a regular hexagon.
HIGHEST COMMON FACTOR (HCF)
The highest number which divides into
two or more numbers.
e.g. The HCF of 18 and 30 is 6.
HORIZONTAL: level (not sloping in any
way).
This arrow points to a horizontal line:↓
______________________________
HORIZONTALLY: across a level
HOUR: a measurement of time equal to
60 minutes. There are 24 hours in a day.
HUNDRED: ten X ten or one hundred
units
HUNDREDTH: a fraction equal to one
part out of a hundred equal sized parts of a
whole 1/100
ICOSAHEDRON: a polyhedron made up
of 20 congruent triangular faces
IDENTICAL: exactly the same
IMPERIAL MEASUREMENTS:
old fashioned British measurements used
before metric measurements
IMPROPER FRACTION:
(top heavy fraction) A fraction which has a
bigger numerator than denominator
e.g. 11
4
To convert an improper fraction to a mixed
number, divide the numerator by the
denominator.
e.g. 11 = 2 ¾ (11÷ 4 = 2 rem 3)
4
INCH: an imperial measurement equal to
approximately 2.5cm as shown on below.
INCLUDE: contain as part of a whole
INCREASE: make bigger
INDEX: see POWER: the little number
written in the air after a number
e.g. 5² means 5 x 5 (It does not mean 5 x 2)
4³ means 4 x 4 x 4 (It does not mean 4 x 3)
INDICES: the plural of index
INFINITE / INFINITY: unable to be
counted because goes on forever
e.g. recurring decimal figures:
1÷3 shown below
INITIAL: first
The first letters of your names are called initials.
INTEGER: a positive or negative number
without any fractions or decimals
e.g. -8, -4, 2, 5, 7, 13 etc
INTERCEPT: where a straight line
crosses the Y axis of a graph
INTERIOR: inside
INTERIOR ANGLES: angles inside a
shape. The interior angles of a triangle
total 180°. The interior angles of a
quadrilateral total 360°. The interior angles of
any polygon = (number of sides – 2) x 180
INTERSECT: to cross over one another.
In a Venn diagram, the sets often intersect
as shown in the shaded area shaded below.
INTERVAL: distance or time between
INVERSE OPERATION: the opposite
operation. The opposite or inverse
operation of + is – and the opposite or
inverse operation of x is ÷
IRREGULAR: having unequal angles
and unequal sides
This is an irregular heptagon.
ISOMETRIC: having equal dimensions
or measurements
ISOSCELES: having two equal angles
and two equal sides.
e.g. an isosceles triangle
Notice the little lines showing the two equal
sides.
Below is an isosceles trapezium.
ITEM: a single thing or unit, especially one
that is part of a list, collection or set
JOTTINGS: workings out
KILO: one thousandth 1/1000
KILOGRAM: one thousand grams
1,000g = 1kg
KILOLITRE: one thousand litres
1,000L=1kl
KILOMETRE: one thousand metres
1,000m = 1km
KITE: a quadrilateral which looks like the
classic flying kite shape
LCD: Lowest Common Denominator
The lowest number that the bottom
numbers of fractions will all divide into
5
7
e.g. The LCD of
and
is 18, since 6 and
6
9
9 both divide into 18.
LCM: Lowest Common Multiple.
The LCM means the lowest number that two
or more numbers will divide into.
e.g. The LCM of 4 and 6 is 12.
The LCM of 6 and 9 is 18.
The LCM of 8 and 10 is 40.
The LCM of 9 and 12 is 36.
The LCM of 2,3,4,5,6,12 and 15 is 60.
LEANING: sloping (on a slant)
LEAP YEAR: a year with 366 days
LEAST: the smallest amount
LENGTH: the distance: usually the
longest distance e.g. a swimming pool
length
LESS THAN: the symbol for less than is
e.g. 3
8
LEVEL: horizontal (having no slope).
A tennis court should always be level.
LIKELIHOOD: the chance something will
happen (probability)
LINE: a one dimensional (not 2D or 3D),
a continuous mark or path
See horizontal, vertical, diagonal, parallel
and perpendicular lines.
LINE GRAPH: a graph with an angular
line showing data
LINE OF SYMMETRY: axis of symmetry
a line which separates symmetrical parts
LITRE: a liquid measurement of
1,000 millilitres = 1 litre
(1,000ml or 1,000cm³ = 1L)
LONG DIVISION:
an old fashioned, long method of dividing
LONG MULTIPLICATION:
a method of multiplying multi-digit numbers
(not as reliable as Napier’s Multiplication
Abacus, since people often forget the
nought !)
Don’t get caught, remember the nought!
LOTS OF: multiplied by
LOWEST COMMON DENOMINATOR:
(LCD) The lowest number that the bottom
numbers of fractions will all divide into
e.g. The LCD of 2/3, 3/4 and 5/6 is 12, since
3, 4 and 6 all divide into 12.
LOWEST COMMON MULTIPLE:
(LCM) The LCM means the lowest number
that two or more numbers will divide into.
e.g. the LCM of 4 and 6 is 12,
The LCM of 6 and 9 is 18.
The LCM of 8 and 10 is 40.
The LCM of 9 and 12 is 36.
LOWEST TERMS: simplified as far as
18
3
possible e.g.
simplifies to
30
5
since the numerator 18 and denominator 30,
both divide by 6, which is the HCF.
MAGIC SQUARE: a square grid of
numbers which has the same total
horizontally, vertically and diagonally
e.g. All these numbers total 15.
MAPPING: a connection between two sets
MASS: weight (how heavy something is)
MAXIMUM: the highest possible amount
MAXIMISE: to increase or make as
great as possible
MEAN: average. To work out a mean
(average), add together all the numbers
and divide the answer by how many
numbers there are. e.g. The mean of 2, 3, 7
and 8 = 5 (2 + 3 + 7 + 8 = 20 and 20 ÷ 4 = 5)
MEASURE: use of standard units to finout
size or quantity regarding: length, width
(breadth), height, area, mass, weight,
volume, capacity, temperature and time
MEASUREMENT: the size, length or
amount of something
MEDIAN: the middle amount of a list of
numbers arranged in order, smallest to
biggest. If there is an even amount of
numbers, there will be two middle numbers,
so you have to add them both together and
then halve the answer to find the median.
The median of 2, 20, 3, 7 and 30 is: 7
(2, 3, 7, 20, 30)
The median of 3, 7, 10, 12 is 8.5
(half of 7 + 10).
METRE: one hundred centimetres or one
thousandth of a kilometre
METRIC: the metric system is the decimal
system of measurement used in Europe
MIDDAY: noon 12 o’clock
(The middle time in a full day: 24 hours)
MIDDLE: halfway
MIDNIGHT: 12 o’clock at night
MIDWAY: see halfway
MILE: a measurement of distance
approximately equal to 1.6 kilometres
MILLENNIUM: a period of a thousand
years, especially when calculated from the
traditional date of the birth of Jesus Christ.
MILLI: one thousandth 1/1000
MILLIGRAM: mg: one thousandth of a
gram. A grain of sand weighs
approximately one milligram.
MILLILITRE: ml
one thousandth of a litre
A droplet of water is about equal to 1ml
(1cm³). A standard medicine spoon holds
5ml or 2.5ml
MILLIMETRE: mm
one thousandth of a metre or one tenth of
a centimetre 10mm =1cm 1,000mm = 1m
MILLION: one thousand x thousand
1,000 x 1,000 = 1,000,000
MINIMISE: to reduce to the smallest
possible amount
MINIMUM: the lowest possible amount
MINUS: take away, subtract, the
difference, decrease, how many less than,
how much less than. The symbol for minus
is MINUTE: sixty seconds (hour).
MIRROR IMAGE: a reflection
MIXED NUMBER: a number and a
fraction together e.g. 2¾
To convert a mixed number into an
improper fraction, multiply the whole
number by the denominator and add on
the numerator. Then put the answer on top
of the original denominator.
e.g. 2¾ = 11 ( 2 x 4 = 8, 8 + 3 = 11 )
4
MODE: the most common amount
e.g. 3 is the mode of 2, 3, 3, 3, 3, 5, 5, 8
MONEY: The coins we use in the
United Kingdom are:
1p, 2p, 5p, 10p, 20p, 50p, £1 and £2.
The notes we use are: £5, £10, £20 and £50.
100x1p=£1, 50x2p=£1, 20x5p=£1,
10x10p=£1, 5x20p=£1, 2x50p=£1
MONTH: one of the twelve parts of a year:
January = 31 days, February = 28 days
(February has 29 days in a leap year),
March = 31 days, April = 30 days,
May = 31 days, June = 30 days,
July = 31 days, August = 31 days,
September = 30 days, October = 31 days,
November = 30 days, December = 31 days.
30 days have September, April, June and November, all
the rest have 31, except for February alone, which has
28 days clear, but 29 in each leap year.
MORE THAN: the symbol for more than
is > e.g. 8 > 3
MOST: the highest amount
MULTIPLE: a number in a multiplication
table e.g. 5, 10, 15, 20, 25 etc
MULTIPLICATION: a mathematical
operation where a number is added to itself
any number of times
MULTIPLY: lots of.
The symbol for multiply is X
e.g. 3 x 4=12 (3 lots of 4 =12)
To multiply a number by 10, move the digits
together, one place value bigger.
To multiply a number by 100, move the
digits together two place values bigger.
To multiply a number by 1000, move the
digits together three place values bigger.
e.g. 25x10=250 3.4x10=34 0.625x100=62.5
8.7x100=870 0.0148=1000=14.8
9.6x1000=9600 0.425x10=4.25
NAPIER’S MULTIPLICATION GRID:
a recommended and very useful method of
multiplying multi-digit numbers which has
proven success and is becoming
increasingly popular.
The product of 376 and 24 is 9024, which is
calculated by multiplying the top figures (376)
by the figures down the side (24) and then
totalling the digits diagonally from top right to
bottom left, leaving a sum of 9024. Each little
square is split diagonally into Tens and Units.
This method of multiplying is sometimes called
Napier’s Bones.
NATURAL NUMBERS: the counting
numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9 etc
e.g. -9, -8, -7, -6, -5, -4, -3, -2, -1
NEAR DOUBLE: A near double is a way
to help with addition, if you're adding two
numbers that are really close.
e.g. 10 + 11 is really close to: 10 + 10 = 20
so 10 + 11 = 21 which is one unit more.
8 + 9 is really close to 8 + 8 = 16 so
8 + 9 = 17 which is one unit more.
NEGATIVE NUMBERS: these are
numbers that are less than 0, as shown on
the number line below.
Negative temperatures are below
0° (freezing point)
(see directed numbers)
NET: a 3D shape opened out flat
Shown below is the net of a triangular
prism.
These are the 11 nets of a cube.
NONAGON: a 9 sided 2D shape (polygon)
NOON: midday 12 o’clock
(half-way through a full day: 24 hours)
NOTHING: having no value, zero, nought
NOUGHT: 0, zero, nothing
0 lies between -1 and 1
(5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)
NUMBER: a number describes a
quantity or value
NUMBER BONDS: addition sum facts
The key number bonds are shown below:
2+2=4 2+3=5 2+4=6 2+5=7 2+6=8 2+7=9
2+8=10 2+9=11 3+3=6 3+4=7 3+5=8
3+6=9 3+7=10 3+8=11 3+9=12 4+4=8
4+5=9 4+6=10 4+7=11 4+8=12 4+9=13
5+5=10 5+6=11 5+7=12 5+8=13 5+9=14
6+6=12 6+7=13 6+8=14 6+9=15 7+7=14
7+8=15 7+9=16 8+8 =16 8+9=17 9+9=18
10+10=20
NUMBER LINE: a line on which every
point represents a number.
Number lines can be used to add, subtract,
multiply and divide.
NUMBER SENTENCE: writing sums
across horizontally e.g. 3 + 4 =7
NUMERAL: symbol used to represent a
number (See Roman Numerals)
NUMERATOR: the top number of a
fraction
3 in this fraction, 3 is the numerator
4
NUMERICAL ORDER: numbers
arranged in consecutive order
OBLIQUE: slanting, sloping
OBLONG: a rectangle which cannot be
square. A quadrilateral with 2 pairs of
parallel sides and 4 right angles.
The two length sides must be longer than
the two width sides as shown here.
OBTUSE: an angle greater than 90°, but
less than 180°
e.g.
OCTAGON: an 8 sided 2D shape
(polygon) This is a regular octagon.
OCTAHEDRON: an 8 sided regular
polyhedron made with 8 equilateral
triangles
ODD: a number which is NOT a
multiple of 2
e.g. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
OF: means multiply or times
3
3
60
e.g. of 20 means X 20 =
=12
5
5
5
OPERATION: one of the 4 arithmetical
rules: + - x ÷
The opposite or inverse operation of + is –
The opposite or inverse operation of x is ÷
OPPOSITE ANGLES: see vertically
opposite angles (opposite angles are equal)
ORDER: arrangement according to size,
amount or value
ORDERING DECIMALS: to order
decimals, smallest to biggest, think of them
as money values, remembering that money
amounts, must always have 2 decimal
placed digits.
e.g. 0.9, 1.1, 0.09, 0.75, 1.5
Money values=90p, £1.10, 9p, 75p, £1.50
So the decimals ordered smallest to biggest
are as follows: 0.09, 0.75,0.9,1.1,1.5
ORDERING FRACTIONS: see
comparing fractions
ORDER OF OPERATIONS: the order
in which mathematical operations should be
done (see BODMAS)
ORIGIN: the point (0, 0) on a coordinate
grid.
The origin is where the horizontal X axis
and vertical Y axis cross over - see below.
OVAL: a curved shape which looks like a
squashed circle
PAIR: two e.g. a pair of shoes or gloves
PARALLEL: equal distance apart.
Parallel lines never meet, since they always
remain an equal distance apart.
Arrows pointing in the same direction are
the mathematical signs for parallel lines.
Parallel lines do not have to be the same
length.
PARALLELOGRAM: a quadrilateral with
2 pairs of parallel sides of equal length
area = base x perpendicular height
PARTITION: split
e.g. 25 partitions into 20 and 5.
25 x 3 can be solved by doing partitioning:
(20 x 3 = 60) + (5 X 3 = 15) totalling 75
PATTERN: a continuing, repetitive or
recurring design or sequence of numbers
e.g. 1, 3, 5, 7, 9, 11, 13......(odd numbers)
PENTAGON: a 5 sided 2D polygon.
This is a regular pentagon since all its
angles and sides are equal.
PERCENT: a fraction of 100
The symbol for percent is %
50% = ½ = 0.5
25% = ¼ = 0.25
75% = ¾ = 0.75
10% = 1/10 = 0.1
20% = 1/5 = 0.2
100% = 1 (one whole)
To work out 10% of a number, simply divide
it by 10 (see divide) e.g 10% of £25 = £2.50
To work out 1% of a number, divide it by
100 (see divide).
PERCENTAGE: see PERCENT
PERIMETER: the total distance around a
2D (two dimensional) shape’s edges
PERPENDICULAR: at right angles to,
lines intersecting or meeting at right
angles
PI: the ratio of a circle's circumference to
its diameter. The symbol for pi is
and is
equivalent to: 3.14159265358979323846...
the decimal digits go on and on, without
repeating.
A rough approximation of pi is or 3.142,
but this is not very accurate. The picture
below shows the position of pi on a number
line.
PICTOGRAM: a chart/graph with
pictures
PIE CHART: a chart showing data
divided into sectors of a circle
PINT: an imperial liquid measurement
equal to just over half of a litre
Glass bottles of milk are usually delivered to
people’s houses in pints.
PLACE VALUE: the value of a digit that
shows its position or place in a number
e.g. in 1,482 the digits represent:
1 thousand, 4 hundreds, 8 tens and 2 units
In 12.34 the digits represent:
1 ten, 2 units, 3 tenths and 4 hundredths.
PLANE: a flat or level surface
PLANE FIGURE: a flat (2D) shape
PLUS: add. The symbol for plus is +
POINT: a mark showing a position
POLYGON: a 2D shape with straight sides
e.g.
POLYHEDRON: a 3D shape with flat
faces e.g. pyramid, cube, triangular prism
and cuboid (a cylinder is not a polyhedron,
since it has a curved face)
POLYHEDRA: plural of polyhedron
POSITION: where something is compared
to another object or its surroundings
POSITIVE: more than zero.
e.g. 1, 2, 3, 4, 5, 6, 7, 8, 9 are all positive
numbers since they are bigger than zero.
POUND: £ an amount of UK currency
which equals 100 pence £1 =100p
POWER: (see index / indices). The power
of a number shows you how many times to
use the number repeatedly in a
multiplication. It is written as a small
number to the right and above the base
number. e.g. 5³ means 5 to the power of 3
(5 x 5 x 5) not 5 x 3.
PRECISE: not approximate in any way;
precise; exact
PREDICT: guess what is going to happen
next
PRIME FACTORS: numbers which are
both factors and also prime.
e.g. The prime factors of 30 are: 2, 3 and 5
PRIME FACTOR TREE:
a prime factor tree is a diagram used to
break down a number, by dividing it by its
factors, until all the numbers left are prime.
The prime factor tree of 48 is shown next:
The product of the prime factors for the
example shown should be written as:
48 = 2 x 2 x 2 x 2 x 3 or x 3. Notice that 4 is
not included, since 4 is not a prime number,
so it’s not in the product calculation.
PRIME NUMBER: a number which can
be divided by just two different numbers,
one and itself. The first ten prime numbers
are: 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29
(2 is the only even prime number).
PRISM: a 3D shape which remains the
same throughout its length, with two
congruent (identical) opposite faces
Examples of prisms are shown below.
PROBABILITY: chance or likelihood
e.g. The probability of a head turning up
when spinning a coin is ½ or 0.5
The probability scale goes from zero to one,
as shown below:
PRODUCT: the answer to a multiplying sum
e.g. The product of 3 and 4 is 12.
PRODUCT OF FACTORS: In the
calculation, 3 x 4 = 12, 3 and 4 are factors
and 12 is the product.
PRODUCT OF PRIME FACTORS:
see prime factors
PROPER FRACTION: a fraction smaller
than one whole e.g. ¾ The numerator
must be smaller than the denominator.
PROPERTIES: a thing or things
belonging to something
PROPORTION: a part to whole
comparison. Proportions are written as
fractions.
1 out of 3 is in proportion to 2 out of 6.
PROTRACTOR: a geometric instrument
used for measuring angles
This shows a 180º protractor.
PYRAMID: a 3D shape of triangles rising
up from its base
This is a square based pyramid. A square
based pyramid has 5 faces, 8 edges and 5
vertices.
QUAD- to do with the number 4
QUADRANT: each of four quarters of a
circle.
A quadrant is also one of the four parts of a
plane, sphere, space, or body divided by
two lines or planes at right angles. In the
diagram below, the four numbered
quadrants are shown in Roman numerals.
QUADRILATERAL: a polygon with
4 straight sides: square, rectangle, kite,
trapezium, rhombus, parallelogram
QUADRUPLE: multiply by 4
QUANTITY: amount or number of
something
QUARTER: one equal sized part of four.
To quarter a number you need to divide it
by 4 or halve it and then halve it again.
e.g. A quarter of 24 is 6, since half of 24 is
12 and half of 12 is 6. Each piece of this
circle is a quarter.
QUOTIENT: the answer to a division
sum
e.g. The quotient of 8 ÷ 4 is 2
RADIUS: the line joining the centre of a
circle to its circumference, half of a
circle’s diameter
RANDOM: chance pick (like drawing
numbers/names out of a hat)
RANGE: the difference between the
lowest and the highest number
e.g. The range of - 5 and 8 is 13 (count from
-5 to 8).
RATIO: comparative amounts. A ratio is a
comparison or relation between quantities
e.g. 20 children split into a ratio of
3:2 boys:girls = 12 boys 8 girls
RECTANGLE: a 4 sided 2D (flat) shape
with 4 right angles and 2 pairs of parallel
sides
area of a rectangle = length x width
A square is a type of rectangle.
RECTANGULAR: in the shape of a
rectangle
RECURRING: repeating to infinity (never
ending) e.g.
The dot above the digit 9 means recurring.
REDUCE: make smaller
REDUCTION: the action or state of
reducing or being reduced
REFLECTION: a mirror image
REFLECTIVE SYMMETRY: a type of
symmetry where one half is the reflection of
the other half
The dotted lines on the shapes below are
the axes of reflective symmetry.
REFLEX: an angle greater than 180° but
less than 360°
REGULAR: having equal angles and
sides e.g. a square is a regular
quadrilateral. An equilateral triangle is a
regular triangle.
REMAINDER: what’s left over
e.g . 25 ÷ 7 = 3 remainder 4
REPEATING: continuing again and again,
recurring
REPRESENTS: stand for; symbolize
RESULT: the quantity found after doing
a calculation
RHOMBUS: a slanted square,
a quadrilateral with 4 equal sides and
4 equal angles. The diagonals of a
rhombus always intersect at right-angles.
area of rhombus = base x height
RIGHT ANGLE: a quarter turn an angle
of 90°
Notice the symbol for a right angle shown
above (half a square). The corners of book
pages are all right angles (90°angles).
RIGHT-ANGLED TRIANGLE:
a triangle with a right angle (90° angle)
ROMAN NUMERALS: Roman numbers
I=1, II=2, III=3, IV=4, V=5, VI-6, VII=7, VIII=8,
IX=9, X=10, XI=11, XII=12, XIII=13, XIV=14,
XV=15, XVI=16, XVII=17, XVIII=18, XIX=19,
XX=20, XXX= 30, XL =40,
L=50, C=100, D=500, M=1,000
e.g. 28 = XXVIII, 39= XXXIX, 45= XLV,
54= LIV, 63= LXIII, 96=XCVI
ROOT: a number which when multiplied by
itself a given number of times equals
another number
e.g. The square root of 16 is 4.
The cube root of 125 is 5.
ROTATE: to turn around a point
ROTATION: a turn
ROTATIONAL SYMMETRY: a shape
has rotational symmetry if it can be turned
partly around and looks the same
If a shape has to be turned completely
around (360°), it has NO rotational symmetry.
If a shape has rotational symmetry, we say it
has an order.
e.g. H = order 2, ▲ = order 3
■ = order 4, ₤ = no rotational symmetry
ROUGH: approximate (about equal to)
ROUGHLY: approximately equal to
ROUND: curved or change a number to a
more convenient value.
e.g. rounding 27 to the nearest 10 is 30.
If a number is halfway, it should be rounded
up.
e.g. 25 to the nearest 10, rounds up to 30
350 to the nearest 100 rounds up to 400
4,500 to the nearest 1,000 = 5,000
ROUNDING: changing a number to a
more convenient value which is easier to
calculate with
ROW: a horizontal arrangement
SCALE: series of calibrated marks on a
measuring instrument e.g. a ruler
Most 30cm rulers have mm and cm
SCALE DRAWING: a drawing that is a
reduction or enlargement of the original
SCALENE: having both unequal
(irregular) angles and sides
e.g. a scalene triangle
SCORE: a group of 20 units
SECOND: one sixtieth of a minute; the
next position after first
SECTOR: a fraction of a circle coming
out from its centre
SEGMENT: a fraction of a circle NOT
coming out from its centre
a chord separates the two segments
SEQUENCE: an ordered pattern of
numbers or shapes following a rule
e.g. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 etc (odd numbers)
SERIES: a sequence
SEMI-CIRCLE: a half-circle
SEMI-CIRCULAR: having the shape of a
semi-circle
SET: a group of numbers or things which
have something in common
SET SQUARE: a right–angled triangle
shaped measuring instrument for drawing or
checking perpendicular lines
SHAPE: a form or outline with area or
volume
SHARE: divide
SHORT DIVISION: a very useful method
of dividing quickly, sometimes called the bus
stop or bus shelter method
This example shows 964 divided by 7.
SIDE: the edge of a 2D shape or the face
of a 3D shape
SIGN: symbol; a short way of saying
mathematical words.
The most common mathematical signs or
symbols are: + plus,
minus, x multiply,
÷ divided by,
divided into.
The fraction separating lines: / and – , also
mean divided by e.g. 8/2 = 4 or 8 = 4
2
= equals, ≠ not equal to,
approximately equal to,
> greater than,
≥ greater than or equal to,
< less than
less than or equal to,
% percent
² squared,
square root
³ cubed
cube root
SIMILAR SHAPES: shapes which are
the same shape and have the same angles
but are of different size. These three
triangles are similar.
SIMPLEST TERMS: simplified as far
as possible
e.g. 24 = 12 = 6 = 3
32 16 8 4
SIMPLIFY: cancel to simplest terms
SINGLE: one
SIZE: how big or small something is
SLANTED: sloping
SLOPE: a gradient
SLOPING: diagonal (not horizontal or
vertical)
SOLUTION: the answer to a problem
SOLVE: to work out the answer.
SPACE: area or volume (capacity)
SPEED FORMULA:
speed = distance ÷ time
SPHERE: a 3D perfectly round shape
such as a tennis ball, football, ping-pong ball,
netball etc
SPIRAL: a curve which comes out from a
central point, getting progressively farther
away as it turns around the point.
This is an anticlockwise spiral.
SQUARE: a 2D (flat) shape with 4 right
angles and 4 sides of equal length
area of a square= length X width
 The answer to two of the same
numbers multiplied together.
e.g. The square of 4 is 16 (4² = 16). The first
twelve square numbers are:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100,121,144
SQUARE CENTIMETRE: a square with
one cm long sides
SQUARED: multiplied by itself
e.g. 6 squared = 36 (6x6=36 or 6²=36).
SQUARE KILOMETRE: a square area
having sides of one kilometre in length
SQUARE METRE: a square with sides
of one metre length
SQUARE MILLIMETRE: a square
which has each side of 1 millilitre in length
SQUARE NUMBERS: a product of two
of the same numbers when shown in dots,
forms a square as shown:
e.g. 25 is a square number since 5 x 5=25
The symbol for squared is ² so:
1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25,
6² = 36, 7² = 49, 8² = 64, 9² = 81,
10² = 100, 11² = 121, 12² = 144
The first twelve square numbers are:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
SQUARE ROOT: a number which when
multiplied by itself gives another number
e.g. 6 is the square root of 36
The sign for square root is:
e.g = 6 (6x6=36)
STANDARD: accepted as normal
STRAIGHT: not curved or bent in any way
(the shortest distance between 2 points is a
straight line or as the crow flies)
STRAIGHT LINE ANGLE: straight line
angles total 180° (see ADJACENT ANGLES)
SUBSTITUTE: replace: take the place of
SUBSTITUTION: the action of replacing
something with another thing
SUBTRACT, SUBTRACTION:
The symbol for subtract is –
Minus, take away, the difference
count down, less than, decrease
SUM: the total or whole amount or the
result of adding.
SUPPLEMENTARY ANGLES:either of
two angles whose sum is 180°
SURFACE: the area inside a boundary
SURFACE AREA: the area of a surface
SURVEY: a method of collecting data by
asking people questions or counting different
things
SYMBOLIZE: stand for; represent
SYMBOLS: see signs
SYMMETRICAL: having 2 identical
halves which look as if they can be folded
over on top of each other
This butterfly shape has one vertical
line of symmetry
SYMMETRY: When one half is a mirror
image of the other half.
A rectangle has 2 lines of reflective
symmetry. Symmetrical capital letters are:
A,B,C,D,E,H,I,M,O,T,U,V,W,X,Y
TABLE: a chart showing information of
a set of facts or figures systematically
displayed, especially in columns
TABLES: multiplication calculations
The key tables facts are shown below, since
the other tables facts are easy to work out.
The first twelve sums shown are square
number tables sums.
Key Tables Facts
1x1=1, 2x2=4, 3x3=9 4x4=16 5x5=25
6x6=36, 7x7=49 8x8=64, 9X9=81,
10X10=100, 11X11=121, 12X12=144
--------------------------------------------------------3X4=12, 3X6=18, 3X7=21, 3X8=24,
3X9=27, 4X6=24, 4X7=28, 4X8=32,
4X9=36, 6X7=42, 6X8=48, 6X9=54,
7X8=56, 7X9=63, 8X9=72, 11X12=132
TAKE AWAY: count back, find the
difference, minus, subtract
The symbol for take away is TALLY: using vertical and diagonal lines
to record counting. Each vertical line shows
one and a diagonal line drawn through the
vertical tally marks, means 5 have been
counted.
TALLY CHART or TABLE: a chart or
table using tally marks (see TALLY)
TEN: ten units = 10
TENTH: one equal part out of ten 1/10
TERM: a number, or letter, if using algebra
This equation has 4 terms: a + b + c = 20
TESSELLATE: joining together with no
gaps
TESSELATION: shapes joining together
with no gaps. This image shows tessellating
hexagons.
TETRAHEDRON: a triangular based
pyramid
e.g.
A tetrahedron has 4 faces, 6 edges and 4 vertices.
THIRD: one equal sized part out of a total
of three
To find a third of a number, divide it by 3.
THOUSAND: ten lots of a hundred
(10 X 100=1,000)
THOUSANDTH:
one part out of a thousand equal parts of a whole
THREE DIMENSIONAL (3D):
solid looking e.g. cube, sphere, cone etc
TIME: interval measured in:
seconds, minutes, hours, days, weeks,
months, years, decades, centuries or
millenniums
TIMES: multiplied by e.g. 3 x 4 =12
The symbol for times is x
 values of time
TIMES TABLE GRID: a grid showing
multiplying products.
(Turn to the end of this book.)
TONNE:1,000 kilograms(1,000kg)
A small car weighs about one tonne.
TOP HEAVY FRACTION: an improper
fraction. A fraction which has a bigger
numerator than its denominator e.g. 47
5
To convert a top heavy fraction into a
mixed number, divide the numerator by the
denominator. e.g. = 13 = 3¼
4
(13 ÷ 4= 3 remainder ¼ )
TOTAL: the answer to an adding sum
e.g. the total of 5 and 3 = 8
TOTAL SURFACE AREA: all of the
face areas of a 3D shape added together
TRANSLATE: move
TRANSLATION: a movement in any
direction, left, right, up, down or diagonally
TRAPEZIUM: a quadrilateral with
2 parallel sides
area formula of a trapezium=
(a + b) ÷ 2 X perpendicular height
TREBLE: triple multiply by 3
TRI- to do with the number 3
TRIAL and ERROR:
experimenting until a solution is found
TRIAL and IMPROVEMENT:
experimenting until a solution is found
TRIANGLE: a 2D (flat) shape with 3
straight sides
The 4 types of triangle are: scalene,
equilateral, isosceles and right-angled
TRIANGULAR: in the shape of a triangle
TRIANGULAR PRISM: a prism with
triangular ends
A triangular prism has 5 faces, 9 edges
and 6 vertices.
TRIANGULAR NUMBERS: a number
that when, shown in dots, forms an
equilateral triangle
The first five triangular numbers are:
1, 3, 6, 10 and 15
TRILLION: a million lots of million
1,000,000,000,000
TRIPLE: treble multiply by 3
e.g. triple 5 = 15 (3X5=15)
TURN: to rotate around a point
TWELVE HOUR TIME: measuring time
by dividing the day into two halves of
12 hours each: a.m. and p.m. (a.m. is before
noon and p.m. is after noon)
TWENTY FOUR HOUR TIME:
measuring time all the way through the
24 hours of the day rather than separating
the day into two halves of a.m. and p.m.
e.g. 7:30 am = 07:30 11:15 am=11:15
1:45pm=13:45 4:20pm=16:20
9:25pm=21:25
TWICE: multiply by 2 e.g. twice 5 = 10
TWO DIMENSIONAL (2D): flat
polygons are 2D shapes
UNEQUAL: not equal (see irregular)
UNIFORM: remaining the same in all
cases and at all times; unchanging in form or
character.
UNIT: another name for: one whole thing
UPRIGHT: vertical
VALUE: numerical amount
VENN DIAGRAM: a way of showing
information using shapes, usually circles
The area where the sets cross over is called
an intersection.
The symbols for Venn diagrams are shown
in the chart below.
VERTEX: a corner of a shape
→
This arrow points to one of the 8 vertices
(corners) of this cuboid.
VERTICAL: upright: not leaning
perpendicular (at right angles) to
the horizontal. Walls of most buildings are
vertical. The leaning tower of Pisa is NOT
vertical!
This fence shows vertical lines:
VERTICALLY: shown as vertical
VERTICALLY OPPOSITE ANGLES:
angles which are opposite each other
opposite angles are equal to each other
VERTICES: the plural of vertex
corners e.g. a triangle has 3 vertices.
All quadrilaterals have 4 vertices.
A cube has 8 vertices.
A cyclinder has NO vertices.
VIEW: 3D shapes can be viewed from
three different elevations: front,
plan (top or bird’s eye view) and side.
(see elevation)
VISUALISE: to picture in your head
VOLUME: a measurement of 3D space
or capacity; the amount of space a 3D
object takes up in the air.
WEEK: seven days. There are 52 weeks in
a year. The first day of a week is Sunday.
WEIGH: to find out how heavy someone or
something is, typically using scales
WEIGHT: the mass; how heavy something is
WHOLE: complete (no parts missing) a
unit is one whole
WHOLE NUMBERS: the set of numbers
that includes zero and all of the natural
numbers: 0, 1, 2, 3, 4, 5, 6 etc
WIDTH: (breadth) distance across
TIP: Think of a swimming pool’s length and
width.
WORKINGS: jottings; writing down sums etc
to help solve a calculation or problem
WORTH: the value of
X AXIS: the horizontal (level) axis of a graph
Y AXIS: the vertical (upright) axis of a graph
(see picture above)
YEAR: 12 months or 52 weeks or
365 days (366 days in a leap year)
ZERO: 0 nothing nought
5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
Any number multiplied by zero = 0
1 x 0 = 0, 2 x 0 = 0, 3 x 0 = 0, 4 x 0 = 0 etc
ZIGZAG: A line or course having sudden
alternate left and right turns. The letter Z is
a zigzag shape.
KEY FACTS






10mm = 1cm, 100cm = 1m, 1000m = 1km
(2.5cm 1 inch, 30cm 1 foot, 1.6km 1 mile)
5 miles = 8 km
1000 milligrams (mg) = 1 gram (g)
1000g = 1kg 1000kg = 1 tonne
1000ml or 1000cm³ = 1L (litre)
(4.5 litres 1 gallon)
30 days have September, April, June and
November, all the rest have 31, except for
February alone, which has 28 days clear, but
29 in each leap year
60 seconds = 1 minute,
60 minutes = 1 hour,
24 hours = 1 day,
7 days = 1 week,
2 weeks = fortnight,
4 weeks is approximately one month
one year =365 days (366 leap year)




or 52 weeks or 12 months
10 years = decade,
100 years = century
1,000 years = a millennium
£1 = 100 x 1p or 50 x 2p or 2 x 50p or 5 x 20p
or 20 x 5p or 10 x 10p
The first 12 square numbers are:
1,4,9,16,25,36,49,64,81,100,121 and 144
The first ten prime numbers are:
2, 3, 5, 7, 11, 13, 17, 19, 23 and
29 (1 is NOT a prime number)
The first five cube numbers are:
1, 8, 27, 64 and 125
TIMES TABLES GRID
X
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
6
7
8
9
10
11
12
2
4
6
8
10
12
14
16
18
20
22
24
3
6
9
12
15
18
21
24
27
30
33
36
4
8
12
16
20
24
28
32
36
40
44
48
5
10
15
20
25
30
35
40
45
50
55
60
6
12
18
24
30
36
42
48
54
60
66
72
7
14
21
28
35
42
49
56
63
70
77
84
8
16
24
32
40
48
56
64
72
80
88
96
9
18
27
36
45
54
63
72
81
90
99
108
10
20
30
40
50
60
70
80
90
100
110
120
11
22
33
44
55
66
77
88
99
110
121
132
12
24
36
48
60
72
84
96
108
120
132
144
Key times tables facts, square numbers first:
1x1=1 2x2=4 3x3=9 4x4=16 5x5=25 6x6=36
7x7=49 8x8=64 9x9=81 10x10=100
11x11=121 12x12=144
----------------------------------------------------------4x3=12 6x3=18 7x3=21 8x3=24 9x3=27
6x4=24 7x4=28 8x4=32 9x4=36 7x6=42
8x6=48 9x6=54 8x7=56 9x7=63 9x8=72
11x12=132