Reference
Maths Dictionary
Over 280 words, 160 formulae and 40 symbols from Year 1 to Year 11, each explained in plain English. Search for any of them, or read them A to Z.
285 words
also modulus
How far a number is from zero, ignoring its sign, written |x|. The absolute value of -5 is 5.
An angle smaller than 90 degrees.
also add, plus, adding
Putting numbers together to find the total. The answer is called the sum.
Next to. In a right-angled triangle, the adjacent side runs from the angle you are using to the right angle.
Maths that uses letters to stand for numbers, so a rule can be written once and used for any value.
A clock with hands that move round a numbered face.
The amount of turn between two lines that meet at a point, measured in degrees.
also approximate, approximately, roughly
A value close enough to be useful, without being exact.
Part of the edge of a circle.
The amount of surface a flat shape covers. For a rectangle, area = length × width.
Working with numbers by adding, subtracting, multiplying and dividing.
Objects set out in rows and columns, used to show multiplication.
also ascending order, smallest to largest
Going up: smallest first, largest last.
An operation where the grouping does not matter. Addition and multiplication are associative; subtraction and division are not.
A single value that stands for a whole set. Usually the mean: mean = total of the values ÷ how many values.
also axes, x-axis, y-axis
The numbered lines running across and up a graph.
A chart that uses bars of different heights to compare amounts.
A direction given as three digits, measured clockwise from north.
also order of operations, BODMAS
The order for working things out: Brackets, Indices, Division and Multiplication, Addition and Subtraction.
also borrow, exchange
An older name for exchanging in subtraction: one ten becomes ten ones when a column cannot subtract. See exchange.
also bracket, parentheses
Grouping symbols showing what to work out first.
How much a container can hold.
also carry, exchange
An older name for exchanging in addition: ten ones become one ten, carried into the next column. See exchange.
A unit of length: 100 cm = 1 m and 1 cm = 10 mm.
A straight line joining two points on a circle.
A flat shape where every point on the edge is the same distance from the centre. Circumference = π × diameter and area = π × radius².
The distance all the way round a circle: circumference = π × diameter, or 2 × π × radius.
The number in front of a letter in algebra. In 5x it is 5.
A factor that two or more numbers share.
A multiple that two or more numbers share.
An operation that gives the same answer either way round. Addition and multiplication are; subtraction and division are not.
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.
also composite shape
A shape made by joining simpler ones.
A solid with one circular face and one curved surface that narrows to a point, called the apex. Volume = π × radius² × height ÷ 3.
Exactly the same shape and size.
A number on its own in an expression, which does not change.
Data that can take any value in a range, such as height or time.
also convert
Changing a measurement from one unit to another.
also coordinate
A pair of numbers giving a position on a grid.
also cos
One of the three trigonometric ratios. In a right-angled triangle, cos of an angle = adjacent ÷ hypotenuse.
What a shop pays for an item before selling it on: profit = selling price - cost price.
A solid with six square faces, all the same size. Volume = side × side × side, written side³.
also cubed
A number multiplied by itself twice: n × n × n, written n³. 27 is 3 cubed.
The number that, cubed, gives the number you started with: ∛x = a when a × a × a = x. The cube root of 64 is 4.
A solid with six rectangular faces. Opposite faces are the same size. Volume = length × width × height.
The money a country uses.
A solid with two circular ends and one curved surface. Volume = π × radius² × height.
Facts or measurements that have been collected.
A unit of time. There are 24 hours in a day and 7 days in a week.
A flat shape with ten straight sides.
A number written with a decimal point.
also d.p.
A position to the right of the decimal point. 3.14 has two decimal places.
The dot that separates whole numbers from parts of a whole.
also degrees
The unit for measuring angles: a full turn is 360°, and a right angle is 90°.
The bottom number of a fraction: how many equal parts the whole is split into.
How much mass is packed into each unit of volume: density = mass ÷ volume.
A straight line across a circle through its centre: diameter = 2 × radius.
also how far apart
The result of a subtraction, a - b: how far apart two numbers are.
A single number symbol, 0 to 9.
A clock that shows the time in numbers, such as 2:30.
Two quantities that change together: double one and the other doubles too. y = kx for a fixed number k.
also signed number, positive and negative numbers
A number with a sign, so positive or negative.
Data that can only be certain separate values, such as the number of pets.
How far it is from one place to another. At a steady speed, distance = speed × time.
Multiplying a number by a sum gives the same answer as multiplying by each part and adding.
also divide, share, dividing
Sharing or grouping a number into equal parts. The answer is called the quotient.
A flat shape with twelve straight sides.
A line where two faces of a solid meet.
also enlarge
Making a shape bigger or smaller by a scale factor, keeping its proportions.
A flat shape with nineteen straight sides.
A statement that two things are equal, with something to find.
A triangle with three equal sides and three equal angles of 60°.
also the same as, equal in value
Different in appearance but equal in value. 12 and 24 are equivalent.
Fractions that look different but are worth the same, made by multiplying or dividing the top and bottom by the same number.
Ratios that describe the same relationship, such as 2 : 3 and 4 : 6.
also rough answer
A sensible answer worked out quickly, without full calculation.
also even
Numbers that divide exactly by 2. They end in 0, 2, 4, 6 or 8.
Something that might happen, made up of one or more outcomes.
also borrowing, carrying, regrouping
Swapping ten of one place value for one of the next, when adding or subtracting.
How much of one currency you get for one unit of another: amount in the new currency = amount × exchange rate.
also multiply out
Multiply out brackets.
also power, index
Another name for an index: the small raised number showing a power. See index.
A piece of algebra with no equals sign, such as 3x + 2.
A flat surface of a solid shape.
A number that divides into another exactly.
Write an expression as a product, the opposite of expanding.
also formulae, formulas
A rule connecting quantities, where you put values in.
A number written as one value over another, showing parts of a whole.
How many times something happens.
A table showing how often each value comes up.
A rule that turns each input into exactly one output.
also slope, steepness
How steep a line is: how far it rises for each step across. Gradient = change in y ÷ change in x.
A unit of mass: 1,000 g = 1 kg.
How tall something is, measured straight up from the bottom.
Half a sphere: a curved surface and one flat circular face. Volume = 23 × π × radius³.
A flat shape with eleven straight sides, sometimes called an undecagon.
A flat shape with seventeen straight sides.
A flat shape with seven straight sides.
A flat shape with sixteen straight sides.
A flat shape with six straight sides.
also HCF
The largest factor two numbers share.
A chart for grouped data where the area of each bar, not its height, shows the frequency.
Parts made by splitting one whole into 100 equal pieces.
The longest side of a right-angled triangle, opposite the right angle. By Pythagoras' theorem, hypotenuse² = a² + b².
A flat shape with twenty straight sides.
A statement true for every value, not just some.
Older units still used in Britain, such as miles, feet, inches, pounds and pints.
also top-heavy fraction
A fraction worth one or more, with the top number at least as large as the bottom.
also indices, power, exponent
The small raised number showing a power: aⁿ means a multiplied by itself n times. In 4³ the index is 3.
A statement that one thing is larger or smaller than another.
A whole number, positive, negative or zero.
Where a line crosses an axis. In y = mx + c, the y-intercept is c.
Money added to a saving or a loan, worked out as a percentage of the amount: simple interest = amount × rate × number of years.
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°.
also opposite operation, undo
The operation that undoes another. Subtraction is the inverse of addition.
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.
also isosceles
A triangle with two equal sides and two equal angles.
A unit of mass: 1 kg = 1,000 g.
A unit of length: 1 km = 1,000 m.
A four-sided shape with two pairs of equal sides that are next to each other.
How long something is from one end to the other.
Terms with exactly the same letters, which can be added together. 3a and 5a are like terms.
A straight path with no width, going on for ever in both directions.
A graph where points are joined by lines, usually to show how something changes over time.
A line that splits a shape into two halves that mirror each other.
An equation whose graph is a straight line. The unknown is not squared or cubed, so it can be written y = mx + c.
A unit of capacity: 1 l = 1,000 ml.
also loci
All the points that satisfy a rule, such as every point 3 cm from A.
also LCM
The smallest multiple two numbers share.
The ratio between a distance on a map and the real distance: real distance = map distance × the scale number.
How much matter something contains. Measured in grams and kilograms.
also average
Add all the values, then divide by how many there are: mean = total ÷ number of values.
Finding the size or amount of something in standard units.
The middle value once the data is in order.
The main unit of length: 1 m = 100 cm and 1,000 m = 1 km.
The system of units based on tens: metres, grams and litres.
The point exactly halfway between two points: midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2).
A unit of capacity: 1,000 ml = 1 l.
A unit of length: 10 mm = 1 cm and 1,000 mm = 1 m.
A unit of time equal to 60 seconds. There are 60 minutes in an hour.
The line a shape is reflected in. Each point and its image are the same distance from it.
A whole number and a fraction together, such as 2 12.
also most common
The value that appears most often.
Coins and notes. 100 pence make £1.
A unit of time. There are 12 months in a year.
The result of multiplying by a whole number. 12 is a multiple of 3.
also multiply, times, multiplying
Combining equal groups to find the total. The answer is called the product.
also counting number
A counting number: 1, 2, 3 and so on.
also minus number, below zero
A number less than zero, written with a minus sign.
A flat shape that folds up into a solid.
A flat shape with nine straight sides.
also position-to-term rule
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).
also bond, number bonds, pairs that make 10
A pair of numbers that add to a given total. 6 and 4 are bonds to 10.
A line with numbers marked along it in order, used for counting and calculating.
The top number of a fraction: how many parts you have.
An angle between 90 and 180 degrees.
A flat shape with eighteen straight sides.
A flat shape with eight straight sides.
also odd
Numbers that do not divide exactly by 2. They end in 1, 3, 5, 7 or 9.
In a right-angled triangle, the side facing the angle you are using.
also order, put in order
Putting numbers or objects in order, usually smallest to largest.
A number that gives a position: 1st, 2nd, 3rd.
The point (0, 0) where the axes cross.
One possible result, such as rolling a 4.
A value that is far away from the rest of the data.
Lines the same distance apart all along, which never meet.
Two or more lines that stay the same distance apart and never meet.
A four-sided shape with two pairs of parallel sides. Opposite sides are equal and opposite angles are equal. Area = base × height.
also split up, break apart
Split a number into parts, usually by place value.
Something that repeats or changes in a predictable way.
A flat shape with fifteen straight sides.
A flat shape with five straight sides.
also percent, %
Out of one hundred. 25 per cent means 25 out of 100, or 25100.
A number of parts per hundred: x% = x ÷ 100, so 50% = 0.5.
How much a value has gone up or down, as a percentage of what it started at: percentage change = change ÷ original value × 100.
Taking a percentage off a value: percentage decrease = decrease ÷ original value × 100.
Adding a percentage on to a value: percentage increase = increase ÷ original value × 100.
also distance around
The distance all the way round a shape: add up every side length. For a rectangle, perimeter = 2 × (length + width).
At right angles to each other.
Lines that cross at a right angle.
also π, 3.14
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.
A chart that uses pictures to show amounts. A key says what each picture stands for.
A circle split into slices, where the size of each slice shows its share of the whole.
What a digit is worth because of where it sits. The 3 in 30 is worth thirty.
A flat shape with straight sides. Its interior angles add up to (n - 2) × 180°, where n is the number of sides.
A factor that is also a prime number.
also prime
A number with exactly two factors, itself and 1.
A solid with the same cross-section all along its length. Volume = area of the cross-section × length.
also chance, likelihood
How likely something is, from 0 to 1: probability = ways it can happen ÷ total possible outcomes.
The result of a multiplication: a × b.
The money made when something sells for more than it cost: profit = selling price - cost price.
A fraction worth less than one, with the top number smaller than the bottom.
A part compared with the whole, or two quantities that change together.
also square-based 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.
also Pythagoras
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.
One of the four regions a coordinate grid is split into by its axes.
A flat shape with four straight sides.
The result of a division: a ÷ b.
also radii
The distance from the centre of a circle to its edge: radius = diameter ÷ 2.
The largest value minus the smallest: range = largest value - smallest value.
How much of one thing there is for each unit of another, such as miles per hour: rate = amount ÷ time.
A comparison of two or more amounts, written with a colon.
Explaining why an answer is right, using maths rather than guessing.
1 divided by the number. The reciprocal of 4 is 14.
A four-sided shape with four right angles. Opposite sides are equal. Area = length × width and perimeter = 2 × (length + width).
A decimal where a digit or group of digits repeats for ever.
also reflect, flip
Flipping a shape over a line, like a mirror.
An angle larger than 180 degrees.
also left over
What is left over after a division.
also diamond
A four-sided shape with all four sides equal. Opposite angles are equal.
also square corner
An angle of exactly 90 degrees, a quarter turn.
A triangle with one right angle. The longest side, opposite the right angle, is the hypotenuse, and a² + b² = c².
The number system that uses letters: I, V, X, L, C, D and M.
also rotate, turn
Turning a shape about a fixed point.
A shape has rotational symmetry if it fits onto itself before a full turn. The order is how many times it fits.
also round, round off
Replacing a number with a nearby, simpler one.
How real distances are shrunk on a map, plan or model, written as a ratio such as 1 : 100.
An accurate drawing where every length is the real length multiplied by the same scale.
The number a shape or amount is multiplied by when enlarging or shrinking: new length = original length × scale factor.
A triangle with no equal sides and no equal angles.
A graph of dots showing two measurements at once, to see if they are linked.
The basic unit of time. There are 60 seconds in a minute.
A slice of a circle, between two radii.
Half a circle, made by cutting a circle along a diameter. Area = π × radius² ÷ 2.
An ordered list of numbers, called terms, where a rule says how to get from each term to the next.
also s.f., sig figs
The digits that carry the size of a number, counted from the first non-zero one.
The same shape but a different size.
also simplest form
Write something in its shortest equal form.
Dividing every part of a ratio by the same number until no smaller whole numbers work.
also sin
One of the three trigonometric ratios. In a right-angled triangle, sin of an angle = opposite ÷ hypotenuse.
Find the value of the unknown that makes an equation true.
How far something travels in a set time, such as kilometres per hour: speed = distance ÷ time.
A perfectly round solid, like a ball. Volume = 43 × π × radius³.
A four-sided shape with four equal sides and four right angles. Area = side × side and perimeter = 4 × side.
also squared
A number multiplied by itself: n × n, written n². 16 is 4 squared.
The number that, squared, gives the number you started with: √x = a when a × a = x. The square root of 36 is 6.
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.
A way of writing very large or very small numbers, as a × 10ⁿ where a is at least 1 and less than 10.
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.
Put numbers in place of letters.
also subtract, take away, minus
Taking one number away from another. The answer is called the difference.
The result of an addition: a + b.
A root that cannot be written exactly as a fraction, such as √2.
Asking a group of people the same question and recording the answers.
Information set out in rows and columns.
A table where each item is counted with a tally mark. Every fifth mark is drawn across the other four.
also tan
A line that touches a circle at exactly one point. Also one of the three trigonometric ratios: tan of an angle = opposite ÷ adjacent.
Money paid to the government, often as a percentage of what you earn or spend.
How hot or cold something is, measured in degrees Celsius.
Parts made by splitting one whole into 10 equal pieces.
One number in a sequence, or one part of an algebraic expression.
The rule for getting from one term in a sequence to the next.
A decimal that stops, such as 0.25.
A flat shape with fourteen straight sides.
How long something takes, measured in seconds, minutes, hours, days and years.
also times tables, multiplication table
The list of multiples of a number in order.
also altogether, sum
The amount you get when everything is added together.
A change to a shape’s position or size: a translation, reflection, rotation or enlargement.
also translate, slide
Sliding a shape to a new position without turning it.
A four-sided shape with one pair of parallel sides. Area = (a + b) × height ÷ 2, where a and b are the parallel sides.
A flat shape with three straight sides and three angles. The angles add up to 180°, and area = base × height ÷ 2.
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.
A flat shape with thirteen straight sides, also called a triskaidecagon.
also SOHCAHTOA
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.
also trig
Using the ratios between the sides and angles of triangles to find missing lengths and angles.
The standard amount something is measured in, such as a metre or a gram.
A fraction with 1 on top, such as 15.
also missing number
A value you do not know yet, shown by a letter.
A letter that stands for a number that can change.
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.
A movement with a size and a direction, written as a column: across on top, up or down underneath.
Overlapping circles that sort things into groups. Anything in both groups goes in the overlap.
also vertices, corner
A corner, where edges meet. The plural is vertices.
The amount of space a solid takes up. For a cuboid, volume = length × width × height.
A unit of time equal to 7 days.
also how heavy
How heavy something is. In everyday life, weight and mass are used to mean the same thing.
A number with no fraction or decimal part: 0, 1, 2, 3 and so on.
The horizontal axis on a graph, running left to right.
The first number in a coordinate pair: how far across.
The vertical axis on a graph, running bottom to top.
The second number in a coordinate pair: how far up.
Where a line crosses the y-axis. In y = mx + c, it is c.
A unit of time equal to 12 months, or 365 days (366 in a leap year).
also nought, nil, none
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.
A zero that keeps the other digits in the right column, showing there is nothing in that place.