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Maths glossary

Maths at school comes with its own words, and some have changed since you were at school: "carrying" is now usually "exchanging", and "units" are now "ones". This glossary explains the words your child is likely to meet from Reception to Year 6, each with an example you can try together.

The year in brackets is when most children first meet the word, following the National Curriculum in England. Your child's school may use it a little earlier or later. For what each year covers in full, see the Learn home page.

A B C D E F G H I K L M N O P Q R S T U V W X Z

A

a.m. and p.m.

a.m. means the hours after midnight and before midday (noon). p.m. means the hours after midday and before midnight. Example: 7:30 a.m. is breakfast time and 7:30 p.m. is the evening. (Year 3.) More on telling the time.

Acute angle

An angle smaller than a right angle, so less than 90°. Example: at 1 o'clock the hands of a clock make an acute angle of 30°. (Year 4.) More on shape and geometry.

Addend

Each of the numbers being added together. Example: in 6 + 2 = 8, the addends are 6 and 2, and 8 is the sum. (Not a National Curriculum word, but many schools now use it from Year 1 or 2.)

Addition

Putting amounts together to find how many there are altogether, using the + sign. Example: 4 apples and 3 more apples make 7 apples: 4 + 3 = 7. (Reception, with the + sign written from Year 1.) More on addition and subtraction.

Analogue clock

A clock with hands that move round a numbered face. The short hand shows the hour and the long hand shows the minutes. Example: the short hand pointing at 3 and the long hand pointing at 12 shows 3 o'clock. (Children read clocks from Year 1; the word "analogue" usually comes in Year 3.)

Angle

The amount of turn between two lines that meet at a point. Angles are measured in degrees (°). Example: each corner of a square is an angle of 90°. (Year 3; measured in degrees from Year 5.)

Anticlockwise

Turning the opposite way to the hands of a clock. Example: turning from 12 round to 9 anticlockwise is a quarter turn. (Year 2.)

Area

The amount of flat space a shape covers, measured in squares. Example: a rectangle 5 cm long and 3 cm wide covers 15 squares of 1 cm by 1 cm, so its area is 15 cm² (5 × 3 = 15). (Year 4 by counting squares; square centimetres in Year 5.) More on measurement.

Arithmetic

Working with numbers by adding, subtracting, multiplying and dividing. Example: the arithmetic paper of the Key Stage 2 SATs, taken in May of Year 6, has questions such as 6,040 − 2,375 and 345 × 12. (Every year group.)

Array

Objects set out in equal rows and columns, used to show multiplication. Example: 3 rows of 4 counters make 12, which shows that 3 × 4 = 12 and also 4 × 3 = 12. (Year 1.) More on multiplication and division.

Average

One number that stands for a typical value in a set of data. In primary school the average children learn is the mean. Example: scores of 4, 6 and 8 have a mean of 6. (Year 6.)

Axis

One of the two straight lines along the bottom and up the side of a graph, marked with labels or a scale. The plural is axes. Example: on a bar chart of favourite fruits, the horizontal axis lists the fruits and the vertical axis counts the children. (Year 3, with bar charts. See also x-axis and y-axis.)

B

Bar chart

A chart that uses bars of different lengths to show and compare amounts. Example: if the bar for "dogs" reaches 8 on the scale, 8 children chose dogs. (Year 3; Year 2 children draw block diagrams.) More on data and graphs.

Bar model

A drawing of rectangles (bars) that shows how the numbers in a problem fit together, so a child can see which calculation to do. Example: "Sam had 15 stickers and gave 6 away." Draw a bar for 15 split into a part of 6 and an unknown part. The unknown part is 15 − 6 = 9. (Often from Year 1 or 2. It is widely used, though the National Curriculum doesn't name it.) More on addition and subtraction.

Base 10 blocks

Blocks for showing place value: small cubes for ones, rods (10 cubes long) for tens and flats (10 rods) for hundreds. They are often called Dienes. Example: 243 is 2 flats, 4 rods and 3 cubes. (Year 1 or 2.) More on counting and place value.

Block diagram

A simple chart where each thing counted is one block, stacked into columns. Example: 5 blocks above "red" means 5 children chose red. (Year 2.)

Borrowing

An older word for exchanging in column subtraction. Most schools now say "exchange". Example: in 52 − 27, you exchange 1 ten for 10 ones so that you can work out 12 − 7. (Year 3.)

Bus stop method

A nickname for short division, because the way it is set out looks like numbers waiting at a bus shelter. Example: 852 ÷ 4 = 213 worked out with the bus stop method. (Year 5.)

C

Capacity

The most a container can hold. Example: a bucket might have a capacity of 10 litres, even when there are only 3 litres of water in it. (Year 1.) More on measurement.

Carroll diagram

A table for sorting things by whether they have, or don't have, two properties. Example: with columns "even" and "not even", and rows "less than 10" and "not less than 10", the number 4 goes in "even, less than 10" and 15 goes in "not even, not less than 10". (Usually Year 2 or 3.)

Carrying

An older word for exchanging in column addition. Example: in 38 + 25, 8 + 5 = 13 ones, so you write 3 and carry (exchange) 1 ten into the tens column. The answer is 63. (Year 3.)

Centimetre (cm)

A unit of length. There are 100 centimetres in 1 metre. Example: a fingernail is roughly 1 cm wide, and a school ruler is usually 30 cm long. (Year 2.)

Change

The money you get back when you pay with more than the price. Example: pay for a £3.40 book with a £5 note and your change is £1.60, because £5 − £3.40 = £1.60. (Year 2.) More on money.

Chunking

A way of dividing by taking away big "chunks" (multiples) of the number you are dividing by. Example: for 96 ÷ 4, take away 40 (ten 4s) to leave 56, take away 40 again to leave 16, then take away 16 (four 4s) to leave 0. That is 10 + 10 + 4 = 24 fours, so 96 ÷ 4 = 24. (Usually Year 4 or 5. Some schools use it before short division; others don't use it at all.)

Circumference

The distance all the way round a circle: its perimeter. Example: the circumference of a circle is always a little more than 3 times its diameter, so a plate 20 cm across is about 63 cm round. (Year 6, when children name the parts of a circle. Working it out with a formula comes at secondary school.) More on shape and geometry.

Clockwise

Turning the same way as the hands of a clock. Example: turning from 12 round to 3 clockwise is a quarter turn. (Year 2.)

Column method

A written method where the numbers are lined up by place value (ones under ones, tens under tens) and worked out one column at a time, starting with the ones. Example: 347 + 285: 7 + 5 = 12, so write 2 and exchange 1 ten; 4 + 8 + 1 = 13 tens, so write 3 and exchange 1 hundred; 3 + 2 + 1 = 6 hundreds. The answer is 632. (Year 3 for adding and subtracting; Year 4 for multiplying.) More on addition and subtraction.

Common factor

A number that is a factor of two or more numbers. Example: the factors of 12 are 1, 2, 3, 4, 6 and 12, and the factors of 18 are 1, 2, 3, 6, 9 and 18, so the common factors of 12 and 18 are 1, 2, 3 and 6. (Year 5.)

Common multiple

A number that is a multiple of two or more numbers. Example: 12 and 24 are both in the 4 times table and the 6 times table, so they are common multiples of 4 and 6. (Year 6.)

Commutative

When you can swap the order of the numbers and still get the same answer. Adding and multiplying are commutative; subtracting and dividing are not. Example: 3 + 5 = 5 + 3 and 4 × 6 = 6 × 4, but 8 − 3 is not the same as 3 − 8. (Year 2.)

Compensation

A mental maths strategy: change a number to make the calculation easier, then adjust the answer to make up for it. Example: for 46 + 9, add 10 to get 56, then take away the extra 1 to get 55. (Usually Year 2 or 3.) More on mental maths.

Composite number

A whole number with more than two factors, so it is not a prime number. Example: 6 is composite because its factors are 1, 2, 3 and 6. The number 1 is neither prime nor composite. (Year 5.)

Cone

A 3D shape with a flat circular face that narrows to a point, called the apex. Example: a party hat or an ice-cream cone. (Usually Year 2.)

Convert

To change a measurement into a different unit without changing its size. Example: 2.5 kg = 2,500 g, and 3 m = 300 cm. (Year 4.)

Coordinates

A pair of numbers in brackets that gives the position of a point on a grid: first how far across, then how far up. Example: (3, 5) means 3 along and 5 up. Children often remember "along the corridor, then up the stairs". (Year 4; all four quadrants, including negative numbers, in Year 6.) More on shape and geometry.

Counting on and counting back

Starting at one number and counting forwards to add, or backwards to subtract. Example: for 9 + 4, start at 9 and count on 4: 10, 11, 12, 13. For 13 − 4, start at 13 and count back 4: 12, 11, 10, 9. (Reception and Year 1.)

Cube

A 3D shape with 6 identical square faces, 12 edges and 8 vertices. Example: an ordinary dice. (Year 1.)

Cube number

A number multiplied by itself, and then by itself again. It is written with a small 3, like 2³. Example: 2³ = 2 × 2 × 2 = 8. The first five cube numbers are 1, 8, 27, 64 and 125. (Year 5.)

Cuboid

A 3D shape with 6 rectangular faces (some of them can be square), 12 edges and 8 vertices. Example: a cereal box or a brick. (Year 1.)

Cylinder

A 3D shape with two flat circular faces joined by one curved surface. Example: a tin of beans. (Year 1 or 2.)

D

Data

Information that has been collected, often as numbers or counts. Example: the colours of the cars that pass the school gate in 10 minutes. (Year 2.) More on data and graphs.

Decimal

A number with a decimal point. The digits after the point are tenths, hundredths and so on. Example: 3.7 means 3 ones and 7 tenths, and £2.45 is 2 pounds and 45 pence. (Year 4, after tenths in Year 3.) More on decimals and percentages.

Decimal place

A position after the decimal point. The number of decimal places is how many digits come after the point. Example: 4.25 has two decimal places: 2 tenths and 5 hundredths. Rounded to one decimal place, it is 4.3. (Year 4; rounding to one decimal place in Year 5.)

Degree (°)

The unit for measuring angles. A full turn is 360°. Example: a right angle is 90° and the angle on a straight line is 180°. (Year 5. Degrees Celsius for temperature, also written °, come in Year 2.)

Denominator

The bottom number of a fraction. It says how many equal parts the whole is split into. Example: in ¾ the denominator is 4, so the whole is split into 4 equal parts. (Year 3.) More on fractions.

Diameter

A straight line from one side of a circle to the other, passing through the centre. It is twice as long as the radius. Example: a circle with a radius of 5 cm has a diameter of 10 cm. (Year 6.)

Difference

How much bigger or smaller one number is than another. You can find it by subtracting, or by counting on from the smaller number. Example: the difference between 12 and 9 is 3. (Year 1.)

Digit

One of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 that we use to write every number. Example: 507 is a three-digit number; its digits are 5, 0 and 7. (Year 1 or 2.)

Digital clock

A clock that shows the time in digits instead of hands. Example: 08:45 on a digital clock is quarter to nine in the morning. (Year 3.)

Dividend

The number being divided. Example: in 20 ÷ 4 = 5, the dividend is 20, the divisor is 4 and the quotient is 5. (Often heard from Year 4.)

Division

Sharing an amount out equally, or splitting it into equal groups, using the ÷ sign. Example: 12 ÷ 3 = 4: share 12 sweets between 3 people and each gets 4, or put 12 sweets into bags of 3 and you fill 4 bags. (Year 1 with objects; the ÷ sign in Year 2.) More on multiplication and division.

Divisor

The number you divide by. Example: in 20 ÷ 4 = 5, the divisor is 4. (Often heard from Year 4.)

Double

Twice as many, which is the same as multiplying by 2. Example: double 7 is 14. (Reception.)

E

Edge

The line where two faces of a 3D shape meet. Example: a cube has 12 edges. (Year 2.) More on shape and geometry.

Equals sign (=)

The sign = means "is the same value as". It doesn't mean "the answer comes next". Example: 5 + 3 = 8, 8 = 5 + 3 and 4 + 4 = 5 + 3 are all true. (Year 1.)

Equation

A number sentence with an equals sign, often with a missing number to find. Example: 3 + □ = 10, so □ = 7. In Year 6 a letter can stand for the missing number: in 2n + 1 = 15 (where 2n means 2 × n), n = 7. (Missing-number problems from Year 1; the word "equation" and letters mostly in Year 6.) More on algebra and ratio.

Equilateral triangle

A triangle with all three sides the same length. All three of its angles are 60°. Example: a triangle with sides of 5 cm, 5 cm and 5 cm. (Year 4.)

Equivalent fractions

Fractions that look different but are worth the same. You find them by multiplying or dividing the top and bottom by the same number. Example: ½ = ²⁄₄ = ⁴⁄₈ (multiply the top and bottom of ½ by 2, then by 2 again). (Year 3; Year 2 children see that ²⁄₄ is the same as ½.) More on fractions.

Estimate

A sensible guess at an answer, often found by rounding, used to check that a calculation makes sense. Example: 298 + 405 is about 300 + 400 = 700, so an answer of 703 looks right. (Year 2 for measuring; Year 3 for checking calculations.)

Even number

A whole number that can be split into two equal groups with none left over. Even numbers end in 0, 2, 4, 6 or 8. Example: 34 is even, because 34 = 17 + 17. (Year 2.)

Exchange

Swapping 10 of one place value for 1 of the next one up, or 1 for 10 of the next one down. It used to be called carrying (in adding) and borrowing (in subtracting). Example: for 52 − 27 in columns, you can't take 7 from 2, so exchange 1 ten for 10 ones: 52 becomes 4 tens and 12 ones. 12 − 7 = 5 and 4 − 2 = 2, so the answer is 25. (Year 2 with blocks; Year 3 in the written column method.)

F

Face

A flat surface of a 3D shape. Example: a cube has 6 faces, all squares. A cylinder has 2 flat faces and one curved surface. (Year 2.)

Fact family

A set of linked addition and subtraction facts (or multiplication and division facts) that use the same three numbers. Example: 3, 5 and 8 give 3 + 5 = 8, 5 + 3 = 8, 8 − 3 = 5 and 8 − 5 = 3. (Year 1 or 2.)

Factor

A whole number that divides exactly into another number with nothing left over. Example: the factors of 12 are 1, 2, 3, 4, 6 and 12. (Year 4.)

Factor pair

Two whole numbers that multiply together to make a given number. Example: the factor pairs of 12 are 1 × 12, 2 × 6 and 3 × 4. (Year 4.)

Formula

A rule for working something out, written in words or letters. The plural is formulae (or formulas). Example: area of a rectangle = length × width, so a rectangle 6 cm by 4 cm has an area of 24 cm². (Year 6.)

Fraction

A part of a whole that has been split into equal parts. Example: cut a pizza into 4 equal slices and one slice is ¼ (one quarter) of the pizza. (Year 1.) More on fractions.

G

Gram (g)

A small unit of mass. There are 1,000 grams in 1 kilogram. Example: a paperclip weighs about 1 g. (Year 2.)

Greater than (>) and less than (<)

Signs for comparing two numbers. The wide, open end always faces the bigger number. Example: 9 > 4 (9 is greater than 4) and 4 < 9 (4 is less than 9). (Year 1 in words; the signs in Year 2.)

Grid method

A way of multiplying by splitting numbers into tens and ones, multiplying each part in a grid, then adding the answers. Example: 23 × 4: 20 × 4 = 80 and 3 × 4 = 12, so 23 × 4 = 80 + 12 = 92. (Usually Year 3 or 4, before the formal column method.)

H

Half

One of two equal parts. Halving means dividing by 2. Example: half of 10 is 5. (Year 1.)

Hexagon

A 2D shape with 6 straight sides and 6 vertices. Example: each cell in a honeycomb is a hexagon. A regular hexagon has 6 equal sides and 6 angles of 120°. (Year 2.)

Horizontal

Going straight across, level like the horizon. Example: the top of a table is horizontal. (Year 3.)

Hundredth

One of 100 equal parts of a whole, written 0.01 or ¹⁄₁₀₀. Example: 1p is one hundredth of £1, and 0.07 is 7 hundredths. (Year 4.) More on decimals and percentages.

I

Imperial units

Older units of measurement that are still used in the UK, such as inches, feet, pounds, stones, pints and miles. Example: 1 inch is about 2.5 cm, and a pint of milk is about 568 ml. (Year 5; miles and kilometres in Year 6.)

Improper fraction

A fraction whose numerator is the same as or bigger than its denominator, so it is worth 1 or more. Example: ⁷⁄₄ is an improper fraction. It is the same as the mixed number 1¾. (Year 5.)

Integer

A whole number, which can be positive, negative or zero, with no fraction or decimal part. Example: −3, 0 and 12 are integers; 2.5 and ½ are not. (Mostly a secondary school word, though some schools use it in Year 6.)

Inverse

The opposite operation, which undoes another one. Adding and subtracting are inverses, and so are multiplying and dividing. Children use the inverse to check answers. Example: 6 × 4 = 24, so 24 ÷ 4 = 6. (Year 2.)

Isosceles triangle

A triangle with two sides the same length. The two angles opposite those sides are also equal. Example: a triangle with sides of 6 cm, 6 cm and 4 cm. (Year 4.)

K

Kilogram (kg)

A unit of mass equal to 1,000 grams. Example: a bag of sugar weighs 1 kg. (Year 2.)

Kilometre (km)

A unit of length equal to 1,000 metres. Example: walking 1 km takes most adults about 15 minutes. (Year 4.)

L

Leap year

A year with 366 days instead of 365, because 29 February is added. Leap years come round every four years. Example: 2024 and 2028 are leap years. (Year 3.)

Line graph

A graph where points are joined with straight lines, often to show how something changes over time. Example: the temperature in the garden, measured every hour from 9 a.m. to 3 p.m. (Year 5; Year 4 children start with simple time graphs.) More on data and graphs.

Line of symmetry

A line that splits a shape into two halves that match exactly, like a mirror image. It is also called a mirror line. Example: a square has 4 lines of symmetry, and the capital letter A has 1. (Year 2; shapes in different positions in Year 4.)

Litre (l)

A unit of capacity. There are 1,000 millilitres in 1 litre. Example: a large carton of juice holds 1 litre. (Year 2.)

Long division

A written method for dividing by a two-digit number, with every step written down. Example: 432 ÷ 12: 12 goes into 43 three times (36) with 7 left over; bring down the 2 to make 72; 12 goes into 72 six times. The answer is 36. (Year 6.)

Long multiplication

A written column method for multiplying by a two-digit number. Example: 24 × 13: 24 × 3 = 72 and 24 × 10 = 240, then 72 + 240 = 312. (Year 5.)

M

Mass

How heavy something is, measured in grams and kilograms. At home we usually call it weight. Example: a large bag of flour often has a mass of 1.5 kg, which is 1,500 g. (Year 1 compares heavier and lighter; grams and kilograms in Year 2.) More on measurement.

Mean

A kind of average: add up all the values, then divide by how many values there are. Example: 4, 6 and 8 add up to 18, and 18 ÷ 3 = 6, so the mean is 6. (Year 6.) More on data and graphs.

Median

The middle value when a set of numbers is put in order. The median is not part of the primary National Curriculum: children meet it at secondary school (Key Stage 3), along with the mode (the most common value) and the range (the biggest value take away the smallest). Example: for 2, 5, 9, 10 and 11, the median is 9. (Secondary school.)

Mental maths

Working things out in your head, sometimes with quick jottings, using facts you know and handy strategies. Example: for 99 + 47, add 100 to get 147, then take away 1 to get 146. (Every year group.) More on mental maths, or try these mental maths strategies.

Metre (m)

A unit of length equal to 100 centimetres. There are 1,000 metres in a kilometre. Example: a door is about 2 m tall. (Year 2.)

Millilitre (ml)

A small unit of capacity. There are 1,000 millilitres in 1 litre. Example: a medicine spoon holds 5 ml. (Year 2.)

Millimetre (mm)

A small unit of length. There are 10 millimetres in 1 centimetre. Example: the tiny marks between the centimetres on a ruler are millimetres, so 4.5 cm is the same as 45 mm. (Year 3.)

Minuend and subtrahend

In a subtraction, the minuend is the number you start with and the subtrahend is the number you take away. Example: in 15 − 6 = 9, 15 is the minuend, 6 is the subtrahend and 9 is the difference. (Not National Curriculum words, but some schools use them from Year 1 or 2.)

Mixed number

A whole number and a fraction together. Example: 2½ is a mixed number. It is the same as the improper fraction ⁵⁄₂. (Year 5.)

Multiple

A number in a times table: what you get when you multiply a number by a whole number. Example: the multiples of 5 are 5, 10, 15, 20 and so on. (Year 1, when children count in 2s, 5s and 10s.)

Multiplication

Adding equal groups, using the × sign. Example: 3 bags with 4 sweets in each is 4 + 4 + 4 = 12 sweets, which can be written 3 × 4 = 12 or 4 × 3 = 12. (Year 1 with objects; the × sign in Year 2.) More on multiplication and division.

Multiplication Tables Check (MTC)

A check taken on screen in June of Year 4. Children answer 25 times tables questions up to 12 × 12, with 6 seconds for each one. There is no pass mark. Example: a question might be 7 × 8 (the answer is 56). (Year 4.) Times tables practice ideas.

N

Near doubles

Using a double you know to work out the sum of two numbers that are close together. Example: 6 + 7 is double 6 plus 1 more, which is 12 + 1 = 13. (Year 1 or 2.) More on mental maths.

Negative number

A number less than zero, written with a minus sign. Example: −3 °C is 3 degrees below zero. Counting up from −2 to 5 is 7 steps. (Year 4; calculating across zero in Year 6.)

Net

A flat shape that can be folded up to make a 3D shape. Example: 6 squares joined in a cross shape fold up into a cube. (Year 6.)

Number bond

Two numbers that add together to make a given number. Example: number bonds to 10 include 7 + 3 and 6 + 4; a number bond to 100 is 65 + 35. (Reception for bonds to 5 and some to 10; Year 1 for bonds to 20.) Number bonds to 20.

Number line

A line with numbers marked in order at equal spaces, used for counting on and back. Example: for 8 + 5, jump 2 to reach 10, then 3 more to land on 13. (Year 1.)

Number sentence

A calculation written with numbers and signs. Example: 4 + 5 = 9 and 12 − □ = 7 are both number sentences. (Year 1.)

Numeral

A symbol, or group of symbols, that stands for a number. Example: 7 is the numeral for "seven"; in Roman numerals it is VII. (Year 1.)

Numerator

The top number of a fraction. It says how many of the equal parts you have. Example: in ¾ the numerator is 3: you have 3 of the 4 equal parts. (Year 3.) More on fractions.

O

Obtuse angle

An angle bigger than a right angle but smaller than a straight line, so between 90° and 180°. Example: at 4 o'clock the hands of a clock make an obtuse angle of 120°. (Year 4.)

O'clock and half past

Time words for whole hours and half hours. At o'clock the long hand points to 12; at half past it points to 6. Example: 4 o'clock is 4:00, and half past 4 is 4:30. (Year 1.) More on telling the time.

Octagon

A 2D shape with 8 straight sides. Example: a stop sign is an octagon. (Usually Year 2 or 3.)

Odd number

A whole number that can't be split into two equal groups of whole numbers: there is always 1 left over. Odd numbers end in 1, 3, 5, 7 or 9. Example: 27 is odd, because 13 + 13 = 26 with 1 left over. (Year 2.)

Ones

The place value column on the right of a whole number, for amounts less than ten. Schools used to call them units. Example: 46 is 4 tens and 6 ones. (Year 1 or 2.) More on place value.

Order of operations

The rule for which part of a calculation to do first: brackets, then multiplying and dividing, then adding and subtracting. Some schools use the memory word BODMAS or BIDMAS. Example: 2 + 3 × 4 = 14 (do 3 × 4 first), but (2 + 3) × 4 = 20. (Year 6.)

P

Parallel

Lines that always stay the same distance apart and never meet, however long they get. Example: the two rails of a railway track, or the opposite sides of a rectangle. (Year 3.)

Parallelogram

A four-sided shape whose opposite sides are parallel and the same length. Example: a rectangle pushed over to one side. A rectangle is a special kind of parallelogram. (Year 4.)

Part-whole model

A diagram, usually of circles, that shows a whole number split into its parts. Example: a circle with 10 in it joined to two circles with 6 and 4 shows that 6 + 4 = 10, 10 − 6 = 4 and 10 − 4 = 6. (Reception or Year 1.) More on addition and subtraction.

Partition

To split a number into parts, usually by place value, to make it easier to work with. Example: 357 = 300 + 50 + 7, or 300 + 40 + 17. (Year 2.) More on place value.

Pentagon

A 2D shape with 5 straight sides. Example: a simple drawing of a house, a square with a triangle roof on top, is a pentagon. (Year 2.)

Percentage (%)

A number of parts out of 100. "Per cent" means "out of a hundred". Example: 25% means 25 out of 100, which is the same as ¼. 50% of 40 is 20. (Year 5.) More on decimals and percentages.

Perimeter

The total distance all the way round the edge of a flat shape. Example: a rectangle 5 cm long and 3 cm wide has a perimeter of 5 + 3 + 5 + 3 = 16 cm. (Year 3.) More on measurement.

Perpendicular

Lines that meet or cross at a right angle. Example: the two lines of a plus sign (+), or the bottom and side edges of a sheet of paper. (Year 3.)

Pictogram

A chart that uses pictures or symbols to show amounts. A key says what each picture stands for. Example: if one picture stands for 2 children, 4 pictures show 8 children and half a picture shows 1 child. (Year 2.) More on data and graphs.

Pie chart

A circle split into slices to show how a whole is shared out. Example: if half the circle is labelled "walk", half the class walks to school. (Year 6.)

Place value

The value a digit has because of where it is in a number. Example: in 352 the 5 is worth 50, but in 523 the 5 is worth 500. (Year 2.) More on counting and place value.

Polygon

A flat, closed shape with straight sides. Example: triangles, squares, pentagons and hexagons are polygons; a circle is not, because it has no straight sides. (Year 2; regular and irregular polygons in Year 5.)

Prime factor

A factor of a number that is also a prime number. Example: 12 = 2 × 2 × 3, so the prime factors of 12 are 2 and 3. (Year 5.)

Prime number

A whole number with exactly two factors: 1 and itself. Example: the prime numbers up to 20 are 2, 3, 5, 7, 11, 13, 17 and 19. The number 1 is not prime, because it has only one factor, and 2 is the only even prime. (Year 5.)

Prism

A 3D shape with two identical ends joined by flat sides, so it is the same shape all the way through. Example: a cuboid is a prism. A triangular prism, shaped like a tent, has 2 triangular faces and 3 rectangular faces. (Usually Year 2 or 3.)

Product

The answer when you multiply numbers together. Example: the product of 6 and 7 is 42. (Year 2 or 3.)

Protractor

A tool, usually a clear half-circle, for measuring and drawing angles in degrees. Example: put the centre cross on the corner of the angle and the 0° line along one arm, then read where the other arm crosses the scale, counting up from 0. (Year 5.)

Pyramid

A 3D shape with a flat base and triangular faces that meet at a point. Example: a square-based pyramid has 5 faces, 8 edges and 5 vertices. (Year 1.)

Q

Quadrilateral

Any 2D shape with 4 straight sides. Example: squares, rectangles, kites and trapeziums are all quadrilaterals. (Year 2; sorted and named in more detail in Year 4.)

Quarter

One of four equal parts. Example: a quarter of 12 is 3. (Year 1.) More on fractions.

Quarter past and quarter to

15 minutes after the hour, and 15 minutes before the hour. Example: quarter past 2 is 2:15, and quarter to 3 is 2:45. (Year 2.) More on telling the time.

Quotient

The answer to a division. Example: in 20 ÷ 4 = 5, the quotient is 5. (Often heard from Year 4.)

R

Radius

The distance from the centre of a circle to its edge. It is half the diameter. The plural is radii. Example: a circle with a diameter of 8 cm has a radius of 4 cm. (Year 6.)

Ratio

A way of comparing two amounts, saying how much of one there is for every amount of the other. Example: a recipe uses 2 cups of flour for every 1 cup of sugar, a ratio of 2 : 1. With 6 cups of flour you need 3 cups of sugar. (Year 6.) More on algebra and ratio.

Rectangle

A four-sided shape with four right angles, whose opposite sides are the same length. A square is a special kind of rectangle. Example: a door or a sheet of paper. (Year 1.)

Reflection

The mirror image of a shape on the other side of a mirror line. Every point ends up the same distance from the line, on the other side. Example: a triangle 2 squares to the left of a mirror line reflects to a triangle 2 squares to the right of it. (Year 5; Year 4 children complete symmetrical shapes.)

Reflex angle

An angle bigger than a straight line (180°) but smaller than a full turn (360°). Example: at 3 o'clock, the angle on the outside of the clock hands is 270°. (Year 5.)

Regular polygon

A polygon with all its sides the same length and all its angles the same size. A polygon that isn't regular is irregular. Example: a square is a regular polygon; a rectangle 6 cm by 2 cm is irregular. (Year 5.)

Remainder

The amount left over when a number can't be divided exactly. Example: 17 ÷ 5 = 3 remainder 2 (written 3 r 2), because 3 × 5 = 15 and 2 is left over. (Usually Year 3 or 4.)

Right angle

A quarter turn, which is 90°. It is often marked with a small square in the corner. Example: the corners of a book or a window. (Year 2 as a quarter turn; Year 3 in shapes.)

Roman numerals

The number system of the ancient Romans: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 and M = 1,000. A smaller numeral in front of a bigger one is taken away. Example: IX = 9, XIV = 14 and MMXXVI = 2026. (Year 3 on clock faces, I to XII; Year 4 up to C, which is 100; Year 5 up to M, which is 1,000, and reading years.)

Rounding

Changing a number to a nearby, simpler number, usually to the nearest 10, 100 or 1,000. If the digit that decides is 5 or more, round up. Example: 47 rounds to 50 (to the nearest 10), 1,250 rounds to 1,300 (to the nearest 100) and 3.6 rounds to 4 (to the nearest whole number). (Year 4.)

S

Scale

The numbers and marks on a measuring tool or on a graph's axis, going up in equal steps. Example: on a jug marked every 50 ml, the mark after 200 ml shows 250 ml. (Year 2.)

Scale factor

How many times bigger (or smaller) a shape is made. Example: a rectangle 2 cm by 3 cm, enlarged by a scale factor of 3, becomes 6 cm by 9 cm. (Year 6.)

Scalene triangle

A triangle with all three sides different lengths, and all three angles different sizes. Example: a triangle with sides of 3 cm, 4 cm and 5 cm. (Year 4.)

Sequence

A list of numbers or shapes that follows a rule. Example: 3, 7, 11, 15 … goes up by 4 each time, so the next number is 19. (Year 2 for patterns; number sequences with rules in Year 6.) More on algebra and ratio.

Short division

A compact written method for dividing by a one-digit number, also called the bus stop method. Example: 852 ÷ 4: 8 ÷ 4 = 2; 5 ÷ 4 = 1 remainder 1, so carry the 1 over to make 12; 12 ÷ 4 = 3. The answer is 213. (Year 5; many schools start it in Year 4.) More on multiplication and division.

Short multiplication

The column method for multiplying by a one-digit number. Example: 236 × 4: 6 × 4 = 24, write 4 and carry 2; 3 × 4 = 12, add the 2 to make 14, write 4 and carry 1; 2 × 4 = 8, add the 1 to make 9. The answer is 944. (Year 4.)

Simplify

To write a fraction using the smallest possible numbers, by dividing the top and bottom by the same number. Example: ⁶⁄₈ simplifies to ¾ (divide both by 2), and ¹²⁄₁₆ also simplifies to ¾ (divide both by 4). (Year 6.) More on fractions.

Sphere

A perfectly round 3D shape, like a ball. It has one curved surface and no edges or vertices. Example: a football or a marble. (Year 1.)

Square

A four-sided shape with four equal sides and four right angles. Example: each little box on squared paper. (Year 1.)

Square centimetre (cm²)

A unit of area: the space covered by a square 1 cm long and 1 cm wide. Example: a rectangle 4 cm by 2 cm has an area of 8 cm². (Year 5.)

Square number

A number multiplied by itself, written with a small 2, like 4². That many dots can be arranged in a square. Example: 4² = 4 × 4 = 16. The square numbers up to 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. (Year 5.)

Subitising

Seeing how many things there are straight away, without counting them. Example: knowing a dice shows 5 from the pattern of the dots. (Reception, for amounts up to 5.)

Subtraction

Taking one amount away from another, or finding the difference between them, using the − sign. Example: 10 − 4 = 6. (Reception, with the − sign written from Year 1.) More on addition and subtraction.

Sum

The total you get when you add numbers together. Children often call any calculation "a sum", but in maths it means the answer to an addition. Example: the sum of 6 and 9 is 15. (Year 1.)

Symmetry

A shape has symmetry when one half is a mirror image of the other. See line of symmetry. Example: a butterfly's wings are symmetrical. (Year 2.)

T

Tally chart

A way of counting with marks. Each thing counted gets one line, and every fifth line is drawn across the four before it to make a bundle of 5. Example: two bundles and 3 more lines show 13. (Year 2.) More on data and graphs.

Temperature

How hot or cold something is, usually measured in degrees Celsius (°C). Example: water freezes at 0 °C and boils at 100 °C. (Year 2.)

Ten frame

A rectangle of 2 rows of 5 boxes for placing counters in, used to show numbers up to 10. Example: 7 counters fill the top row and 2 boxes of the bottom row; the 3 empty boxes show that 7 + 3 = 10. (Reception and Year 1.)

Tenth

One of 10 equal parts of a whole, written 0.1 or ⅒. Example: 10p is one tenth of £1, and 0.3 is 3 tenths. (Year 3.) More on decimals and percentages.

Thousandth

One of 1,000 equal parts of a whole, written 0.001. Example: 1 mm is one thousandth of a metre, and 0.005 is 5 thousandths. (Year 5.)

Three-dimensional (3D) shape

A solid shape with length, width and height, which you could pick up. Example: cubes, spheres, cones and pyramids. (Year 1.) More on shape and geometry.

Times tables

The multiplication facts from 1 × 1 up to 12 × 12. Example: 7 × 8 = 56 is in both the 7 and the 8 times tables. (Year 2 for the 2, 5 and 10 times tables; Year 3 for the 3, 4 and 8; Year 4 for all of them up to 12 × 12.) Times tables practice ideas.

Translation

Sliding a shape to a new position without turning it, flipping it or changing its size. Example: move a triangle 3 squares to the right and 2 squares down. (Year 4.)

Trapezium

A four-sided shape with one pair of parallel sides. The plural is trapeziums or trapezia. Example: the side view of a bucket, wider at the top than the bottom. (Year 4.)

Triangle

A 2D shape with 3 straight sides and 3 corners. Its three angles always add up to 180°. Example: in an equilateral triangle, 60° + 60° + 60° = 180°. (Year 1; the 180° total in Year 6.)

24-hour clock

A way of writing times that counts the hours from 00:00 at midnight to 23:59, so a.m. and p.m. aren't needed. Example: 15:30 is 3:30 p.m. (for times after 1 p.m., take 12 away from the hours). (Year 3; changing between the two in Year 4.)

Two-dimensional (2D) shape

A flat shape with length and width but no thickness, like one drawn on paper. Example: circles, triangles, squares and rectangles. (Year 1.)

U

Unit fraction

A fraction with 1 as its numerator. It means one equal part. Example: ½, ⅓, ⅕ and ⅒ are unit fractions; ⅗ is not. (Year 3.) More on fractions.

Unit of measure

The standard amount we measure in, such as centimetres, kilograms or litres. ("Units" is also the old name for ones in place value.) Example: in "the table is 120 cm long", the unit is centimetres. (Year 2.)

V

Venn diagram

Overlapping circles used for sorting. Things that belong in both groups go in the overlap. Example: sorting numbers into "even" and "multiples of 5": 10 goes in the overlap, 4 goes in "even" only, 15 goes in "multiples of 5" only, and 7 goes outside both circles. (Usually Year 2 or 3.)

Vertex (plural vertices)

A corner of a shape, where sides or edges meet. Example: a triangle has 3 vertices and a cube has 8. (Year 2.)

Vertical

Going straight up and down. Example: a flagpole, or the side of a door. (Year 3.)

Vertically opposite angles

When two straight lines cross, the angles opposite each other are equal. Example: if one angle is 40°, the angle opposite it is also 40°, and the other two are both 140°. (Year 6.)

Volume

The amount of space a 3D object takes up, measured in cubic centimetres (cm³) or cubic metres (m³). Example: a cuboid 3 cm long, 2 cm wide and 4 cm tall has a volume of 3 × 2 × 4 = 24 cm³. (Year 1 for comparing full and empty; cubes and cm³ from Year 5.) More on measurement.

W

Weight

The everyday word for how heavy something is. At school children learn the word mass alongside it. Example: "the apples weigh 500 g" means their mass is 500 g. (Year 1.)

Whole number

A number with no fraction or decimal part: 0, 1, 2, 3 and so on. Example: 8 and 250 are whole numbers; 8.5 is not. (Used throughout primary school.)

X

x-axis and y-axis

On a graph or coordinate grid, the x-axis goes across (horizontal) and the y-axis goes up (vertical). In coordinates, the x number always comes first. Example: the point (4, 2) is 4 along the x-axis and 2 up the y-axis. (Coordinates from Year 4; the names x-axis and y-axis are most used in Year 6.)

Z

Zero

The number 0, meaning none. In place value it is a placeholder that keeps the other digits in the right columns. Example: in 205 the 0 shows there are no tens; without it, the number would read 25. (Reception and Year 1.)