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Maths Glossary of Terms
Term
analogue clock
angle
anticlockwise
array
axis of symmetry
bar chart
binary operation
block graph
capacity
cardinal number
Carroll diagram
chart
chronological
Description
A clock usually with 12 equal divisions labelled ‘clockwise’ from the top 12, 1, 2, 3 and so on up
to 11 to represent hours.
An angle is a measure of rotation.
In the opposite direction from the normal direction of travel of the hands of an analogue
clock.
An ordered collection of counters, numbers etc. in rows and columns.
A line about which a geometrical figure, or shape, is symmetrical or about which a
geometrical shape or figure is reflected in order to produce a symmetrical shape or picture.
A format for representing statistical information. Bars, of equal width, represent
frequencies and the lengths of the bars are proportional to the frequencies (and often equal
to the frequencies). Sometimes called bar graph. The bars may be vertical or horizontal
depending on the orientation of the chart.
A rule for combining two numbers in the set to produce a third also in the set. Addition,
subtraction, multiplication and division of real numbers are all binary operations.
A simple format for representing statistical information. One block represents one
observation. Example: A birthday graph where each child places one block, or colours one
square, to represent himself / herself in the month in which he or she was born.
Capacity – the volume of a material (typically liquid or air) held in a vessel or container.
Units include litres, decilitres, millilitres; cubic centimetres (cm3) and cubic metres (m3). A
litre is equivalent to 1000 cm3.
A cardinal number denotes quantity, as opposed to an ordinal number which denotes position
within a series.
1, 2, 5, 23 are examples of cardinal numbers
First (1st), second (2nd), third (3rd) etc denote position in a series, and are ordinals.
A sorting diagram named after Lewis Carroll, author and mathematician, in which numbers
(or objects) are classified as having a certain property or not having that property
Example: Use the diagram below to classify all the integers from 1 to 33
Another word for a table or graph
Relating to events that occur in a time ordered sequence.
clockwise
column graph
concrete objects
consecutive
diagram
difference
digit
digital clock
edge
equivalent fractions
even number
face
inverse operations
mass
missing number
problems
multiple
number bond
number line
number sentence
number square
numeral
ordinal number
partition
pattern
pictogram
In the direction in which the hands of an analogue clock travel.
A bar graph where the bars are presented vertically.
Objects that can be handled and manipulated to support understanding of the structure of a
mathematical concept.
Materials such as Dienes (Base 10 materials), Cuisenaire, Numicon, pattern blocks are all
examples of concrete objects.
Following in order. Consecutive numbers are adjacent in a count. Examples: 5, 6, 7 are
consecutive numbers.
A picture, a geometric figure or a representation.
In mathematics (as distinct from its everyday meaning), difference means the numerical
difference between two numbers or sets of objects and is found by comparing the quantity
of one set of objects with another.
e.g. the difference between 12 and 5 is 7; 12 is 5 more than 7 or 7 is 5 fewer than 12.
Difference is one way of thinking about subtraction and can, in some circumstances, be a
more helpful image for subtraction than ‘take-away’ – e.g. 102 - 98
One of the symbols of a number system most commonly the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8
and 9. Examples: the number 29 is a 2-digit number; there are three digits in 2.95. The
position or place of a digit in a number conveys its value.
A clock that displays the time as hours and minutes passed, usually since midnight. Example:
four thirty in the afternoon is displayed as 16:30.
A line segment, joining two vertices of a figure. A line segment formed by the intersection
of two plane surfaces. Examples: a square has four edges; and a cuboid has twelve edges.
Fractions with the same value as another. For example: 4/8, 5/10, 8/16 are all equivalent
fractions and all are equal to ½.
An integer that is divisible by 2.
One of the flat surfaces of a solid shape. Example: a cube has six faces; each face being a
square
Operations that are opposites of each other. Examples: addition and subtraction are inverse
operations. Multiplication and division are inverse operations
A characteristic of a body, relating to the amount of matter within it. Mass differs from
weight, the force with which a body is attracted towards the earth’s centre. Whereas,
under certain conditions, a body can become weightless, mass is constant. In a constant
gravitational field weight is proportional to mass.
A problem of the type 7 = ☐ − 9 often used as an introduction to algebra.
A number that is in the times table of a given number.
Example: 14, 49 and 70 are all multiples of 7 because 14 = 7 x 2, 49 = 7 x 7 and 70 = 7 x 10.
A pair of numbers with a particular total, e.g. number bonds for ten are all pairs of whole
numbers with the total 10.
A line where numbers are represented by points upon it.
A mathematical sentence involving numbers. Examples: 3 + 6 = 9 and 9 > 3
A square grid in which cells are numbered in order.
A symbol used to denote a number. The Roman numerals I, V, X, L, C, D and M represent the
numbers one, five, ten, fifty, one hundred, five hundred and one thousand. The Arabic
numerals 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are used in the Hindu-Arabic system giving numbers in
the form that is widely used today.
A term that describes a position within an ordered set. Example: first, second, third, fourth
… twentieth etc.
1. To separate a set into subsets.
2. To split a number into component parts. Example: the two-digit number 38 can be
partitioned into 30 + 8 or 19 + 19.
A systematic arrangement of numbers, shapes or other elements according to a rule.
A format for representing statistical information. Suitable pictures, symbols or icons are
used to represent objects. For large numbers one symbol may represent a number of objects
and a part symbol then represents a rough proportion of the number.
pictorial
representations
place value
product
property
quarter turn
repeated addition
rotation
rule
sequence
share (equally)
sign
sort
sum
symbol
symmetry
table
tally
total
turn
unit
vertex
weight
Pictorial representations enable learners to use pictures and images to represent the
structure of a mathematical concept. The pictorial representation may build on the
familiarity with concrete objects. E.g. a square to represent a Dienes ‘flat’ (representation
of the number 100). Children may interpret pictorial representations provided to them or
create a pictorial representation themselves to help solve a mathematical problem.
The value of a digit that relates to its position or place in a number.
Example: in 1482 the digits represent 1 thousand, 4 hundreds, 8 tens and 2 ones
respectively.
The result of multiplying one number by another. Example: The product of 2 and 3 is 6 since
2 × 3 = 6.
Any attribute. Example: One property of a square is that all its sides are equal.
A rotation through 90º or a right angle turn.
The process of repeatedly adding the same number or amount. One model for multiplication.
Example 5 + 5 + 5 + 5 = 5 x 4.
In 2-D, a transformation of the whole plane which turns about a fixed point, the centre of
rotation.
Generally a procedure for carrying out a process. In the context of patterns and sequences
a rule, expressed in words or algebraically, summarises the pattern or sequence and can be
used to generate or extend it.
A succession of terms formed according to a rule. There is a definite relation between one
term and the next and between each term and its position in the sequence. Example: 1, 4, 9,
16, 25 etc.
One model for the process of division.
A symbol used to denote an operation. Examples: addition sign +, subtraction sign −,
multiplication sign ×, division sign ÷, equals sign = etc.
To classify a set of entities into specified categories.
The result of one or more additions.
A letter, numeral or other mark that represents a number, an operation or another
mathematical idea. Example: L (Roman symbol for fifty), > (is greater than).
A plane figure has symmetry if the effect of the reflection or rotation produces an
identical-looking figure in the same position..
An orderly arrangement of information, numbers or letters usually in rows and columns.
Make marks to represent objects counted; usually by drawing vertical lines and crossing the
fifth count with a horizontal or diagonal strike through.
A Tally chart is a table representing a count using a Tally
1. The aggregate. Example: the total population - all in the population.
2. The sum found by adding.
A rotation about a point: a quarter turn is a rotation of 90°. A half turn is a rotation of 180°,
a whole turn is a rotation of 360°.
A standard used in measuring e.g. the metre is a unit of length; the degree is a unit of
turn/angle, etc.
The point at which two or more lines intersect. Plural: vertices.
In everyday English weight is often confused with mass. In mathematics, and physics, the
weight of a body is the force exerted on the body by the gravity of the earth, or any other
gravitational body.
English Glossary of Terms
Term
adjective
Description
The surest way to identify adjectives is by the ways
they can be used:
 before a noun, to make the noun’s meaning more
specific (i.e. to modify the noun), or
 after the verb be, as its complement.
adverb
The surest way to identify adverbs is by the ways
they can be used: they can modify a verb, an
adjective, another adverb or even a whole clause.
apostrophe
Apostrophes have two completely different uses:
 showing the place of missing letters (e.g. I’m for
I am)
 marking possessives (e.g. Hannah’s mother).
A compound word contains at least two root words
joined to make a new word; e.g. whiteboard,
superman.
A conjunction links two words or phrases together.
There are two main types of conjunctions:
 co-ordinating conjunctions (e.g. and) link two
words or phrases together as an equal pair
 subordinating conjunctions (e.g. when) introduce
a subordinate clause.
compound,
compounding
conjunction/
joining word
Example
The pupils did some really good work.
[adjective used before a noun, to modify
it]
Their work was good. [adjective used
after the verb be, as its complement]
Usha soon started snoring loudly.
That match was really exciting!
We don’t get to play games very often.
Fortunately, it didn’t rain.
I’m going out and I won’t be long.
[showing missing letters]
Hannah’s mother went to town in Justin’s
car. [marking possessives]
blackbird, blow-dry, bookshop, icecream, English teacher, inkjet, one-eyed,
bone-dry, baby-sit, daydream
James bought a bat and ball. [links the
words bat and ball as an equal pair]
Kylie is young but she can kick the ball
hard. [links two clauses as an equal pair]
Everyone watches when Kyle does backflips. [introduces a subordinate clause]
Joe can’t practise kicking because he’s
injured. [introduces a subordinate
clause]
co-ordinate,
co-ordination
digraph
grapheme
graphemephoneme
correspondences
(GPC)
homophone
Words or phrases are co-ordinated if they are
linked as an equal pair by a co-ordinating conjunction
(i.e. and, but, or).
In the examples on the right, the co-ordinated
elements are shown in bold, and the conjunction is
underlined.
The difference between co-ordination and
subordination is that, in subordination, the two
linked elements are not equal.
A type of grapheme where two letters represent
one phoneme.
Sometimes, these two letters are not next to one
another; this is called a split digraph
A letter, or combination of letters, that
corresponds to a single phoneme within a word.
The links between letters, or combinations of
letters (graphemes) and the speech sounds
(phonemes) that they represent.
In the English writing system, graphemes may
correspond to different phonemes in different
words.
Two different words are homophones if they sound
exactly the same when pronounced.
Susan and Amra met in a café. [links the
words Susan and Amra as an equal pair]
They talked and drank tea for an hour.
[links two clauses as an equal pair]
Susan got a bus but Amra walked. [links
two clauses as an equal pair]
Not co-ordination: They ate before they
met. [before introduces a subordinate
clause]
The digraph ea in each
The digraph sh in shed
The split digraph i–e in line
The grapheme t in the words ten, bet
and ate corresponds to the phoneme /t/.
The grapheme ph in the word dolphin
corresponds to the phoneme /f/.
The grapheme s corresponds to the
phoneme /s/ in the word see, but…
…it corresponds to the phoneme /z/ in
the word easy.
hear, here
some, sum
noun
The surest way to identify nouns is by the ways
they can be used after determiners such as the: for
example, most nouns will fit into the frame “The __
matters/matter.”
Nouns may be classified as common (e.g. boy, day)
or proper (e.g. Ivan, Wednesday),
noun phrase
A noun phrase is a phrase with a noun as its head,
e.g. some foxes, foxes with bushy tails.
Our dog bit the burglar on his behind!
My big brother did an amazing jump on
his skateboard.
Actions speak louder than words.
a book, two chocolates, one day, fewer
ideas, money, some chocolate, less
imagination , Marilyn, London, Wednesday
Adult foxes can jump. [adult modifies
foxes, so adult belongs to the noun
phrase]
Almost all healthy adult foxes in this
area can jump. [all the other words help
to modify foxes, so they all belong to the
noun phrase]
past tense
phoneme
phrase
Verbs in the past tense are commonly used to:
 talk about the past
 talk about imagined situations
Most verbs take a suffix –ed, to form their past
tense, but many commonly-used verbs are irregular.
A phoneme is the smallest unit of sound that signals
a distinct, contrasting meaning. For example:
 /t/ contrasts with /k/ to signal the difference
between tap and cap
 /t/ contrasts with /l/ to signal the difference
between bought and ball.
It is this contrast in meaning that tells us there are
two distinct phonemes at work. There are around 44
phonemes in English. A single phoneme may be
represented in writing by one, two, three or four
letters constituting a single grapheme.
Tom and Chris showed me their new TV.
Antonio went on holiday to Brazil.
I wish I had a puppy.
A phrase is a group of words that are grammatically
connected so that they stay together, and that
expand a single word, called the ‘head’. The phrase
is a noun phrase if its head is a noun, a preposition
phrase if its head is a preposition, and so on; but if
the head is a verb, the phrase is called a clause.
Phrases can be made up of other phrases.
She waved to her mother. [a noun
phrase, with the noun mother as its
The word cat has three letters and
three phonemes.
The word catch has five letters and
three phonemes.
The word caught has six letters and
three phonemes.
head]
She waved to her mother. [a preposition
phrase, with the preposition to as its
head]
She waved to her mother. [a clause, with
the verb waved as its head]
dogs, boxes, mice
plural
A plural noun normally has a suffix –s or –es and
means ‘more than one’.
possessive
apostrophe
A noun followed by an apostrophe, with or without s
Tariq’s book
The boys’ arrival
prefix
A prefix is added at the beginning of a word in
order to turn it into another word.
Contrast suffix.
Verbs in the present tense are commonly used to:
 talk about the present
 talk about the future.
overtake, disappear
present tense
They may take a suffix –s (depending on the
subject).
Jamal goes to the pool every day.
He can swim.
The bus arrives at three.
My friends are coming to play.
Punctuation includes any conventional features of
writing other than spelling and general layout: the
standard punctuation marks . , ; : ? ! - – ( ) “ ” ‘ ’ , and
also word-spaces, capital letters, apostrophes,
paragraph breaks and bullet points. One important
role of punctuation is to indicate sentence
boundaries.
Morphology breaks words down into root words,
which can stand alone, and suffixes or prefixes
which can’t. For example, help is the root word for
other words in its word family such as helpful and
helpless, and helping. Compound words (e.g. helpdesk) contain two or more root words. When looking
in a dictionary, we sometimes have to look for the
root word (or words) of the word we are interested
in.
“I’m going out, Usha, and I won’t be long,”
Mum said.
A sentence is a group of words which are
grammatically connected to each other but not to
any words outside the sentence.
The form of a sentence’s main clause shows whether
it is being used as a statement, a question, a
command or an exclamation.
A sentence may consist of a single clause or it may
contain several clauses held together by
subordination or co-ordination.
John went to his friend’s house. He
stayed there till tea-time.
You are my friend. [statement]
Are you my friend? [question]
Be my friend! [command]
What a good friend you are!
Standard English can be recognised by the use of a
very small range of forms such as those books, I did
it and I wasn’t doing anything (rather than their
non-Standard equivalents). It is the variety of
English which is used, with only minor variation, as a
major world language. Some people use Standard
English all the time. The aim of the national
curriculum is that everyone should be able to use
Standard English as needed in writing and in
relatively formal speaking.
I did it because they were not willing to
undertake any more work on those
houses. [formal Standard English]
I did it cos they wouldn’t do any more
work on those houses. [casual Standard
subordinate
clause
A clause which is subordinate to some other part of
the same sentence is a subordinate clause; for
example, in The apple that I ate was sour, the
clause that I ate is subordinate to apple (which it
modifies). Subordinate clauses contrast with coordinate clauses as in It was sour but looked very
tasty.
That’s the street where Ben lives.
He watched her as she disappeared.
suffix
A suffix is an ‘ending’, used at the end of one word
to turn it into another word. Unlike root words,
suffixes cannot stand on their own as a complete
word.
Contrast prefix
call – called
teach – teacher
terror – terrorise
syllable
A syllable sounds like a beat in a word. Syllables
consist of at least one vowel, and possibly one or
more consonants.
Cat has one syllable.
Fairy has two syllables.
Hippopotamus has five syllables.
punctuation
root word
sentence
Standard
English
played [the root word is play]
unfair [the root word is fair]
football [the root words are foot and
ball]
[exclamation]
English]
I done it cos they wouldn’t do no more
work on them houses. [casual nonStandard English]
tense
In English, tense is the choice between present and
past verbs, which is special because it is signalled by
inflections and normally indicates differences of
time.
The simple tenses (present and past) may be
combined in English with the perfect and
progressive.
He studies. [present tense – present
time]
He studied yesterday. [past tense – past
time]
He studies tomorrow, or else! [present
tense – future time]
He may study tomorrow. [present
tense + infinitive – future time]
He plans to study tomorrow. [present
tense + infinitive – future time]
trigraph
A type of grapheme where three letters represent
one phoneme.
High, pure, patch, hedge
verb
The surest way to identify verbs is by the ways
they can be used: they can usually have a tense,
either present or past (see also future).
He lives in Birmingham. [present tense]
The teacher wrote a song for the class.
[past tense]
He likes chocolate. [present tense; not an
action]
He knew my father. [past tense; not an
action]
word
A word is a unit of grammar: it can be selected and
moved around relatively independently, but cannot
easily be split. In punctuation, words are normally
separated by word spaces. Sometimes, a sequence
that appears grammatically to be two words is
collapsed into a single written word, indicated with a
hyphen or apostrophe (e.g. well-built, he’s).
headteacher or head teacher [can be
written with or without a space] I’m
going out. 9.30 am