Maths Dictionary

Over 280 words, 160 formulae and 40 symbols from Year 1 to Year 11, explained in plain English with examples.

A

16 of 285 terms

Absolute value
How far a number is from zero, ignoring its sign, written |x|. The absolute value of -5 is 5.
Example
Acute angle
An angle smaller than 90 degrees.
Example
Addition
Putting numbers together to find the total. The answer is called the sum.
Example
Adjacent
Next to. In a right-angled triangle, the adjacent side runs from the angle you are using to the right angle.
Example
Algebra
Maths that uses letters to stand for numbers, so a rule can be written once and used for any value.
Example
Analogue clock
A clock with hands that move round a numbered face.
Example
Angle
The amount of turn between two lines that meet at a point, measured in degrees.
Example
Approximation
A value close enough to be useful, without being exact.
Example
Arc
Part of the edge of a circle.
Example
Area
The amount of surface a flat shape covers. For a rectangle, area = length × width.
Example
Arithmetic
Working with numbers by adding, subtracting, multiplying and dividing.
Example
Array
Objects set out in rows and columns, used to show multiplication.
Example
Ascending
Going up: smallest first, largest last.
Example
Associative
An operation where the grouping does not matter. Addition and multiplication are associative; subtraction and division are not.
Example
Average
A single value that stands for a whole set. Usually the mean: mean = total of the values ÷ how many values.
Example
Axis (axes)
The numbered lines running across and up a graph.
Example

B

5 terms

Bar chart
A chart that uses bars of different heights to compare amounts.
Example
Bearing
A direction given as three digits, measured clockwise from north.
Example
BIDMAS
The order for working things out: Brackets, Indices, Division and Multiplication, Addition and Subtraction.
Example
Borrowing
An older name for exchanging in subtraction: one ten becomes ten ones when a column cannot subtract. See exchange.
Example
Brackets
Grouping symbols showing what to work out first.
Example

C

26 terms

Capacity
How much a container can hold.
Example
Carrying
An older name for exchanging in addition: ten ones become one ten, carried into the next column. See exchange.
Example
Centimetre (cm)
A unit of length: 100 cm = 1 m and 1 cm = 10 mm.
Example
Chord
A straight line joining two points on a circle.
Example
Circle
A flat shape where every point on the edge is the same distance from the centre. Circumference = π × diameter and area = π × radius².
Example
Circumference
The distance all the way round a circle: circumference = π × diameter, or 2 × π × radius.
Example
Coefficient
The number in front of a letter in algebra. In 5x it is 5.
Example
Common factor
A factor that two or more numbers share.
Example
Common multiple
A multiple that two or more numbers share.
Example
Commutative
An operation that gives the same answer either way round. Addition and multiplication are; subtraction and division are not.
Example
Compound interest
Interest worked out on the original amount and on the interest already added, so it grows faster each year: final amount = start amount × (1 + rate)ⁿ for n years.
Example
Compound shape
A shape made by joining simpler ones.
Example
Cone
A solid with one circular face and one curved surface that narrows to a point, called the apex. Volume = π × radius² × height ÷ 3.
Example
Congruent
Exactly the same shape and size.
Example
Constant
A number on its own in an expression, which does not change.
Example
Continuous data
Data that can take any value in a range, such as height or time.
Example
Conversion
Changing a measurement from one unit to another.
Example
Coordinates
A pair of numbers giving a position on a grid.
Example
Cosine
One of the three trigonometric ratios. In a right-angled triangle, cos of an angle = adjacent ÷ hypotenuse.
Example
Cost price
What a shop pays for an item before selling it on: profit = selling price - cost price.
Example
Cube
A solid with six square faces, all the same size. Volume = side × side × side, written side³.
Example
Cube number
A number multiplied by itself twice: n × n × n, written n³. 27 is 3 cubed.
Example
Cube root
The number that, cubed, gives the number you started with: ∛x = a when a × a × a = x. The cube root of 64 is 4.
Example
Cuboid
A solid with six rectangular faces. Opposite faces are the same size. Volume = length × width × height.
Example
Currency
The money a country uses.
Example
Cylinder
A solid with two circular ends and one curved surface. Volume = π × radius² × height.
Example

D

20 terms

Data
Facts or measurements that have been collected.
Example
Day
A unit of time. There are 24 hours in a day and 7 days in a week.
Example
Decagon
A flat shape with ten straight sides.
Example
Decimal
A number written with a decimal point.
Example
Decimal place
A position to the right of the decimal point. 3.14 has two decimal places.
Example
Decimal point
The dot that separates whole numbers from parts of a whole.
Example
Degree
The unit for measuring angles: a full turn is 360°, and a right angle is 90°.
Example
Denominator
The bottom number of a fraction: how many equal parts the whole is split into.
Example
Density
How much mass is packed into each unit of volume: density = mass ÷ volume.
Example
Diameter
A straight line across a circle through its centre: diameter = 2 × radius.
Example
Difference
The result of a subtraction, a - b: how far apart two numbers are.
Example
Digit
A single number symbol, 0 to 9.
Example
Digital clock
A clock that shows the time in numbers, such as 2:30.
Example
Direct proportion
Two quantities that change together: double one and the other doubles too. y = kx for a fixed number k.
Example
Directed number
A number with a sign, so positive or negative.
Example
Discrete data
Data that can only be certain separate values, such as the number of pets.
Example
Distance
How far it is from one place to another. At a steady speed, distance = speed × time.
Example
Distributive
Multiplying a number by a sum gives the same answer as multiplying by each part and adding.
Example
Division
Sharing or grouping a number into equal parts. The answer is called the quotient.
Example
Dodecagon
A flat shape with twelve straight sides.
Example

E

16 terms

Edge
A line where two faces of a solid meet.
Example
Enlargement
Making a shape bigger or smaller by a scale factor, keeping its proportions.
Example
Enneadecagon
A flat shape with nineteen straight sides.
Example
Equation
A statement that two things are equal, with something to find.
Example
Equilateral triangle
A triangle with three equal sides and three equal angles of 60°.
Example
Equivalent
Different in appearance but equal in value. 12 and 24 are equivalent.
Example
Equivalent fraction
Fractions that look different but are worth the same, made by multiplying or dividing the top and bottom by the same number.
Example
Equivalent ratios
Ratios that describe the same relationship, such as 2 : 3 and 4 : 6.
Example
Estimate
A sensible answer worked out quickly, without full calculation.
Example
Even numbers
Numbers that divide exactly by 2. They end in 0, 2, 4, 6 or 8.
Example
Event
Something that might happen, made up of one or more outcomes.
Example
Exchange
Swapping ten of one place value for one of the next, when adding or subtracting.
Example
Exchange rate
How much of one currency you get for one unit of another: amount in the new currency = amount × exchange rate.
Example
Expand
Multiply out brackets.
Example
Exponent
Another name for an index: the small raised number showing a power. See index.
Example
Expression
A piece of algebra with no equals sign, such as 3x + 2.
Example

F

8 terms

Face
A flat surface of a solid shape.
Example
Factor
A number that divides into another exactly.
Example
Factorise
Write an expression as a product, the opposite of expanding.
Example
Formula
A rule connecting quantities, where you put values in.
Example
Fraction
A number written as one value over another, showing parts of a whole.
Example
Frequency
How many times something happens.
Example
Frequency table
A table showing how often each value comes up.
Example
Function
A rule that turns each input into exactly one output.
Example

G

2 terms

Gradient
How steep a line is: how far it rises for each step across. Gradient = change in y ÷ change in x.
Example
Gram (g)
A unit of mass: 1,000 g = 1 kg.
Example

H

11 terms

Height
How tall something is, measured straight up from the bottom.
Example
Hemisphere
Half a sphere: a curved surface and one flat circular face. Volume = 23 × π × radius³.
Example
Hendecagon
A flat shape with eleven straight sides, sometimes called an undecagon.
Example
Heptadecagon
A flat shape with seventeen straight sides.
Example
Heptagon
A flat shape with seven straight sides.
Example
Hexadecagon
A flat shape with sixteen straight sides.
Example
Hexagon
A flat shape with six straight sides.
Example
Highest Common Factor (HCF)
The largest factor two numbers share.
Example
Histogram
A chart for grouped data where the area of each bar, not its height, shows the frequency.
Example
Hundredths
Parts made by splitting one whole into 100 equal pieces.
Example
Hypotenuse
The longest side of a right-angled triangle, opposite the right angle. By Pythagoras' theorem, hypotenuse² = a² + b².
Example

I

13 terms

Icosagon
A flat shape with twenty straight sides.
Example
Identity
A statement true for every value, not just some.
Example
Imperial
Older units still used in Britain, such as miles, feet, inches, pounds and pints.
Example
Improper fraction
A fraction worth one or more, with the top number at least as large as the bottom.
Example
Index (indices)
The small raised number showing a power: aⁿ means a multiplied by itself n times. In 4³ the index is 3.
Example
Inequality
A statement that one thing is larger or smaller than another.
Example
Integer
A whole number, positive, negative or zero.
Example
Intercept
Where a line crosses an axis. In y = mx + c, the y-intercept is c.
Example
Interest
Money added to a saving or a loan, worked out as a percentage of the amount: simple interest = amount × rate × number of years.
Example
Interior angle
An angle inside a shape, between two of its sides. The interior angles of a polygon with n sides add up to (n - 2) × 180°.
Example
Inverse
The operation that undoes another. Subtraction is the inverse of addition.
Example
Inverse proportion
Two quantities where one goes up as the other goes down: double one and the other halves. y = k ÷ x for a fixed number k.
Example
Isosceles triangle
A triangle with two equal sides and two equal angles.
Example

K

3 terms

Kilogram (kg)
A unit of mass: 1 kg = 1,000 g.
Example
Kilometre (km)
A unit of length: 1 km = 1,000 m.
Example
Kite
A four-sided shape with two pairs of equal sides that are next to each other.
Example

L

9 terms

Length
How long something is from one end to the other.
Example
Like terms
Terms with exactly the same letters, which can be added together. 3a and 5a are like terms.
Example
Line
A straight path with no width, going on for ever in both directions.
Example
Line graph
A graph where points are joined by lines, usually to show how something changes over time.
Example
Line of symmetry
A line that splits a shape into two halves that mirror each other.
Example
Linear equation
An equation whose graph is a straight line. The unknown is not squared or cubed, so it can be written y = mx + c.
Example
Litre (l)
A unit of capacity: 1 l = 1,000 ml.
Example
Locus (loci)
All the points that satisfy a rule, such as every point 3 cm from A.
Example
Lowest Common Multiple (LCM)
The smallest multiple two numbers share.
Example

M

18 terms

Map scale
The ratio between a distance on a map and the real distance: real distance = map distance × the scale number.
Example
Mass
How much matter something contains. Measured in grams and kilograms.
Example
Mean
Add all the values, then divide by how many there are: mean = total ÷ number of values.
Example
Measurement
Finding the size or amount of something in standard units.
Example
Median
The middle value once the data is in order.
Example
Metre (m)
The main unit of length: 1 m = 100 cm and 1,000 m = 1 km.
Example
Metric
The system of units based on tens: metres, grams and litres.
Example
Midpoint
The point exactly halfway between two points: midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2).
Example
Millilitre (ml)
A unit of capacity: 1,000 ml = 1 l.
Example
Millimetre (mm)
A unit of length: 10 mm = 1 cm and 1,000 mm = 1 m.
Example
Minute
A unit of time equal to 60 seconds. There are 60 minutes in an hour.
Example
Mirror line
The line a shape is reflected in. Each point and its image are the same distance from it.
Example
Mixed number
A whole number and a fraction together, such as 2 12.
Example
Mode
The value that appears most often.
Example
Money
Coins and notes. 100 pence make £1.
Example
Month
A unit of time. There are 12 months in a year.
Example
Multiple
The result of multiplying by a whole number. 12 is a multiple of 3.
Example
Multiplication
Combining equal groups to find the total. The answer is called the product.
Example

N

8 terms

Natural number
A counting number: 1, 2, 3 and so on.
Example
Negative number
A number less than zero, written with a minus sign.
Example
Net
A flat shape that folds up into a solid.
Example
Nonagon
A flat shape with nine straight sides.
Example
nth term
A rule for finding any term in a sequence from its position, n. For a sequence going up in equal steps of d, nth term = dn + (first term - d).
Example
Number bond
A pair of numbers that add to a given total. 6 and 4 are bonds to 10.
Example
Number line
A line with numbers marked along it in order, used for counting and calculating.
Example
Numerator
The top number of a fraction: how many parts you have.
Example

O

10 terms

Obtuse angle
An angle between 90 and 180 degrees.
Example
Octadecagon
A flat shape with eighteen straight sides.
Example
Octagon
A flat shape with eight straight sides.
Example
Odd numbers
Numbers that do not divide exactly by 2. They end in 1, 3, 5, 7 or 9.
Example
Opposite
In a right-angled triangle, the side facing the angle you are using.
Example
Ordering
Putting numbers or objects in order, usually smallest to largest.
Example
Ordinal number
A number that gives a position: 1st, 2nd, 3rd.
Example
Origin
The point (0, 0) where the axes cross.
Example
Outcome
One possible result, such as rolling a 4.
Example
Outlier
A value that is far away from the rest of the data.
Example

P

30 terms

Parallel
Lines the same distance apart all along, which never meet.
Example
Parallel lines
Two or more lines that stay the same distance apart and never meet.
Example
Parallelogram
A four-sided shape with two pairs of parallel sides. Opposite sides are equal and opposite angles are equal. Area = base × height.
Example
Partition
Split a number into parts, usually by place value.
Example
Pattern
Something that repeats or changes in a predictable way.
Example
Pentadecagon
A flat shape with fifteen straight sides.
Example
Pentagon
A flat shape with five straight sides.
Example
Per cent
Out of one hundred. 25 per cent means 25 out of 100, or 25100.
Example
Percentage
A number of parts per hundred: x% = x ÷ 100, so 50% = 0.5.
Example
Percentage change
How much a value has gone up or down, as a percentage of what it started at: percentage change = change ÷ original value × 100.
Example
Percentage decrease
Taking a percentage off a value: percentage decrease = decrease ÷ original value × 100.
Example
Percentage increase
Adding a percentage on to a value: percentage increase = increase ÷ original value × 100.
Example
Perimeter
The distance all the way round a shape: add up every side length. For a rectangle, perimeter = 2 × (length + width).
Example
Perpendicular
At right angles to each other.
Example
Perpendicular lines
Lines that cross at a right angle.
Example
Pi
The number you get when you divide any circle’s circumference by its diameter. It is the same for every circle, a little over 3.14, and it is written with the Greek letter π.
Example
Pictogram
A chart that uses pictures to show amounts. A key says what each picture stands for.
Example
Pie chart
A circle split into slices, where the size of each slice shows its share of the whole.
Example
Place value
What a digit is worth because of where it sits. The 3 in 30 is worth thirty.
Example
Polygon
A flat shape with straight sides. Its interior angles add up to (n - 2) × 180°, where n is the number of sides.
Example
Prime factor
A factor that is also a prime number.
Example
Prime number
A number with exactly two factors, itself and 1.
Example
Prism
A solid with the same cross-section all along its length. Volume = area of the cross-section × length.
Example
Probability
How likely something is, from 0 to 1: probability = ways it can happen ÷ total possible outcomes.
Example
Product
The result of a multiplication: a × b.
Example
Profit
The money made when something sells for more than it cost: profit = selling price - cost price.
Example
Proper fraction
A fraction worth less than one, with the top number smaller than the bottom.
Example
Proportion
A part compared with the whole, or two quantities that change together.
Example
Pyramid
A solid with a flat base and triangular faces that meet at a point, called the apex. Volume = area of the base × height ÷ 3.
Example
Pythagoras’ theorem
In a right-angled triangle, the square of the hypotenuse equals the squares of the other two sides added together: a² + b² = c², where c is the hypotenuse.
Example

Q

3 terms

Quadrant
One of the four regions a coordinate grid is split into by its axes.
Example
Quadrilateral
A flat shape with four straight sides.
Example
Quotient
The result of a division: a ÷ b.
Example

R

18 terms

Radius
The distance from the centre of a circle to its edge: radius = diameter ÷ 2.
Example
Range
The largest value minus the smallest: range = largest value - smallest value.
Example
Rate
How much of one thing there is for each unit of another, such as miles per hour: rate = amount ÷ time.
Example
Ratio
A comparison of two or more amounts, written with a colon.
Example
Reasoning
Explaining why an answer is right, using maths rather than guessing.
Example
Reciprocal
1 divided by the number. The reciprocal of 4 is 14.
Example
Rectangle
A four-sided shape with four right angles. Opposite sides are equal. Area = length × width and perimeter = 2 × (length + width).
Example
Recurring decimal
A decimal where a digit or group of digits repeats for ever.
Example
Reflection
Flipping a shape over a line, like a mirror.
Example
Reflex angle
An angle larger than 180 degrees.
Example
Remainder
What is left over after a division.
Example
Rhombus
A four-sided shape with all four sides equal. Opposite angles are equal.
Example
Right angle
An angle of exactly 90 degrees, a quarter turn.
Example
Right-angled triangle
A triangle with one right angle. The longest side, opposite the right angle, is the hypotenuse, and a² + b² = c².
Example
Roman numerals
The number system that uses letters: I, V, X, L, C, D and M.
Example
Rotation
Turning a shape about a fixed point.
Example
Rotational symmetry
A shape has rotational symmetry if it fits onto itself before a full turn. The order is how many times it fits.
Example
Rounding
Replacing a number with a nearby, simpler one.
Example

S

28 terms

Scale
How real distances are shrunk on a map, plan or model, written as a ratio such as 1 : 100.
Example
Scale drawing
An accurate drawing where every length is the real length multiplied by the same scale.
Example
Scale factor
The number a shape or amount is multiplied by when enlarging or shrinking: new length = original length × scale factor.
Example
Scalene triangle
A triangle with no equal sides and no equal angles.
Example
Scatter graph
A graph of dots showing two measurements at once, to see if they are linked.
Example
Second
The basic unit of time. There are 60 seconds in a minute.
Example
Sector
A slice of a circle, between two radii.
Example
Semicircle
Half a circle, made by cutting a circle along a diameter. Area = π × radius² ÷ 2.
Example
Sequence
An ordered list of numbers, called terms, where a rule says how to get from each term to the next.
Example
Significant figures
The digits that carry the size of a number, counted from the first non-zero one.
Example
Similar
The same shape but a different size.
Example
Simplify
Write something in its shortest equal form.
Example
Simplifying a ratio
Dividing every part of a ratio by the same number until no smaller whole numbers work.
Example
Sine
One of the three trigonometric ratios. In a right-angled triangle, sin of an angle = opposite ÷ hypotenuse.
Example
Solve
Find the value of the unknown that makes an equation true.
Example
Speed
How far something travels in a set time, such as kilometres per hour: speed = distance ÷ time.
Example
Sphere
A perfectly round solid, like a ball. Volume = 43 × π × radius³.
Example
Square
A four-sided shape with four equal sides and four right angles. Area = side × side and perimeter = 4 × side.
Example
Square number
A number multiplied by itself: n × n, written n². 16 is 4 squared.
Example
Square root
The number that, squared, gives the number you started with: √x = a when a × a = x. The square root of 36 is 6.
Example
Standard deviation
A measure of how spread out a set of values is around the mean: the square root of the mean of the squared differences from the mean.
Example
Standard form
A way of writing very large or very small numbers, as a × 10ⁿ where a is at least 1 and less than 10.
Example
Straight line graph
The graph of a linear equation. Its equation can be written y = mx + c, where m is the gradient and c is the y-intercept.
Example
Substitute
Put numbers in place of letters.
Example
Subtraction
Taking one number away from another. The answer is called the difference.
Example
Sum
The result of an addition: a + b.
Example
Surd
A root that cannot be written exactly as a fraction, such as √2.
Example
Survey
Asking a group of people the same question and recording the answers.
Example

T

21 terms

Table
Information set out in rows and columns.
Example
Tally chart
A table where each item is counted with a tally mark. Every fifth mark is drawn across the other four.
Example
Tangent
A line that touches a circle at exactly one point. Also one of the three trigonometric ratios: tan of an angle = opposite ÷ adjacent.
Example
Tax
Money paid to the government, often as a percentage of what you earn or spend.
Example
Temperature
How hot or cold something is, measured in degrees Celsius.
Example
Tenths
Parts made by splitting one whole into 10 equal pieces.
Example
Term
One number in a sequence, or one part of an algebraic expression.
Example
Term-to-term rule
The rule for getting from one term in a sequence to the next.
Example
Terminating decimal
A decimal that stops, such as 0.25.
Example
Tetradecagon
A flat shape with fourteen straight sides.
Example
Time
How long something takes, measured in seconds, minutes, hours, days and years.
Example
Times table
The list of multiples of a number in order.
Example
Total
The amount you get when everything is added together.
Example
Transformation
A change to a shape’s position or size: a translation, reflection, rotation or enlargement.
Example
Translation
Sliding a shape to a new position without turning it.
Example
Trapezium
A four-sided shape with one pair of parallel sides. Area = (a + b) × height ÷ 2, where a and b are the parallel sides.
Example
Triangle
A flat shape with three straight sides and three angles. The angles add up to 180°, and area = base × height ÷ 2.
Example
Triangular prism
A prism with two triangular ends and three rectangular faces. Its cross-section is a triangle all along its length, so volume = area of the triangle × length.
Example
Tridecagon
A flat shape with thirteen straight sides, also called a triskaidecagon.
Example
Trigonometric ratio
Sine, cosine and tangent, the three ratios linking an angle of a right-angled triangle to its sides: sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent.
Example
Trigonometry
Using the ratios between the sides and angles of triangles to find missing lengths and angles.
Example

U

3 terms

Unit
The standard amount something is measured in, such as a metre or a gram.
Example
Unit fraction
A fraction with 1 on top, such as 15.
Example
Unknown
A value you do not know yet, shown by a letter.
Example

V

6 terms

Variable
A letter that stands for a number that can change.
Example
VAT
Value Added Tax: a tax added to the price of most things you buy. At the standard 20% rate, price with VAT = price × 1.2.
Example
Vector
A movement with a size and a direction, written as a column: across on top, up or down underneath.
Example
Venn diagram
Overlapping circles that sort things into groups. Anything in both groups goes in the overlap.
Example
Vertex
A corner, where edges meet. The plural is vertices.
Example
Volume
The amount of space a solid takes up. For a cuboid, volume = length × width × height.
Example

W

3 terms

Week
A unit of time equal to 7 days.
Example
Weight
How heavy something is. In everyday life, weight and mass are used to mean the same thing.
Example
Whole number
A number with no fraction or decimal part: 0, 1, 2, 3 and so on.
Example

X

2 terms

x-axis
The horizontal axis on a graph, running left to right.
Example
x-coordinate
The first number in a coordinate pair: how far across.
Example

Y

4 terms

y-axis
The vertical axis on a graph, running bottom to top.
Example
y-coordinate
The second number in a coordinate pair: how far up.
Example
y-intercept
Where a line crosses the y-axis. In y = mx + c, it is c.
Example
Year
A unit of time equal to 12 months, or 365 days (366 in a leap year).
Example

Z

2 terms

Zero
The number that means none, and also a real number with its own place on the number line, between -1 and 1. Adding it leaves a number unchanged and multiplying by it gives none at all: n + 0 = n and n × 0 = 0.
Example
Zero as a place holder
A zero that keeps the other digits in the right column, showing there is nothing in that place.
Example

Maths Dictionary

A

Absolute value

Acute angle

Addition

Adjacent

Algebra

Analogue clock

Angle

Approximation

Arc

Area

Arithmetic

Array

Ascending

Associative

Average

Axis (axes)

B

Bar chart

Bearing

BIDMAS

Borrowing

Brackets

C

Capacity

Carrying

Centimetre (cm)

Chord

Circle

Circumference

Coefficient

Common factor

Common multiple

Commutative

Compound interest

Compound shape

Cone

Congruent

Constant

Continuous data

Conversion

Coordinates

Cosine

Cost price

Cube

Cube number

Cube root

Cuboid

Currency

Cylinder

D

Data

Day

Decagon

Decimal

Decimal place

Decimal point

Degree

Denominator

Density

Diameter

Difference

Digit

Digital clock

Direct proportion

Directed number

Discrete data

Distance

Distributive

Division

Dodecagon

E

Edge

Enlargement

Enneadecagon

Equation

Equilateral triangle

Equivalent

Equivalent fraction