Counting
Counting means saying one number for each thing in a group, in order, to find out how many there are. The last number you say is the total.
Learning Wiki
Maths
Numbers, shapes, measuring and data, from counting to Pythagoras.
Around ages 3–7
First steps
Around ages 5–11
Primary
Addition
Addition is putting amounts together to find a total. The sign is +, and the answer is called the sum or total, so 4 + 3 = 7.
2D shapes
2D shapes are flat shapes with length and width but no thickness, like circles, triangles, squares and hexagons. You can draw them on paper.
Number bonds
Number bonds are pairs of numbers that add up to a given total, like 3 and 7 making 10. Knowing them by heart makes adding and subtracting much faster.
Odd and even numbers
Even numbers can be split into two equal groups or pairs with none left over (2, 4, 6…). Odd numbers always leave one left over (1, 3, 5…).
Pictograms
A pictogram shows data using small pictures or symbols. A key tells you what each picture is worth, such as one apple standing for 2 apples. In the US it is often called a picture graph.
Subtraction
Subtraction is taking one amount away from another, or finding the difference between two numbers. The sign is −, so 9 − 4 = 5.
Telling the time
To tell the time on a clock, read the short hand for the hour and the long hand for the minutes. When the long hand points to 6, it is half past the hour.
Length and measuring
Length is how long, tall or far something is. It is measured with a ruler or tape in units such as millimetres, centimetres, metres and kilometres (or inches, feet and miles).
Money
Money maths means counting coins and notes, adding up prices and working out change. Most currencies split one unit into 100 smaller ones, like 100 pence in a pound.
Number line
A number line is a straight line with numbers marked at equal steps, smallest on the left and biggest on the right. It helps you count, compare, add and subtract.
3D shapes
3D shapes are solid shapes with length, width and height, like cubes, spheres, cylinders and pyramids. They have faces, edges and vertices.
Capacity
Capacity is how much a container can hold, usually measured in millilitres (ml) and litres (l). A large bottle of water often holds 2 litres, which is 2000 ml.
Fractions
A fraction is part of a whole that has been split into equal parts. In ¾, the bottom number says how many equal parts and the top says how many you have.
Mass and weight
Mass is how much stuff is in an object, measured in grams and kilograms. Weight is the pull of gravity on that mass. In everyday life people say weight for both.
Place value
Place value means a digit's value depends on its position in a number. In 352, the 3 is worth 300, the 5 is worth 50 and the 2 is worth 2.
Division
Division is sharing into equal groups, or finding how many groups fit. The sign is ÷, so 12 ÷ 3 = 4. The answer is called the quotient.
Multiplication
Multiplication is adding equal groups quickly. 4 × 3 means 4 groups of 3 (or 3 groups of 4), which makes 12. The answer is called the product.
Times tables
Times tables are lists of the multiplication facts for a number, such as 3 × 1 = 3 up to 3 × 12 = 36. Knowing them by heart speeds up almost all later maths.
Bar charts
A bar chart shows data using bars of different lengths. The longer the bar, the bigger the number. In the US it is usually called a bar graph.
Estimation
Estimating means making a sensible guess at an answer, usually by rounding the numbers first. It tells you roughly what to expect and helps you spot mistakes.
Symmetry
A shape has symmetry when one half is a mirror image of the other (line symmetry), or when it looks the same after being turned (rotational symmetry).
Sequences
A sequence is a list of numbers or shapes that follows a rule, like 3, 7, 11, 15 (add 4 each time). Each item is called a term.
Equivalent fractions
Equivalent fractions look different but are the same size, like 1/2, 2/4 and 4/8. You make them by multiplying or dividing the top and bottom by the same number.
Perimeter
Perimeter is the total distance all the way around the outside of a flat shape. For a rectangle 5 cm long and 3 cm wide, it is 5 + 3 + 5 + 3 = 16 cm.
Rounding
Rounding means replacing a number with a simpler one that is close to it, such as 47 rounded to the nearest ten being 50. It makes numbers easier to work with.
Angles
An angle measures the amount of turn between two lines that meet at a point. Angles are measured in degrees (°); a right angle is 90° and a full turn is 360°.
Decimals
Decimals are numbers with a decimal point. Digits after the point show tenths, hundredths and so on, so 2.5 means two and five tenths.
Area
Area is the amount of flat space inside a shape, measured in square units like cm² or m². A rectangle 4 cm by 3 cm has an area of 4 × 3 = 12 cm².
Coordinates
Coordinates are a pair of numbers that give an exact position on a grid, like (3, 5). The first number is how far across (x) and the second is how far up (y).
Factors and multiples
Factors are numbers that divide exactly into a number (the factors of 12 are 1, 2, 3, 4, 6 and 12). Multiples are the numbers in its times table (12, 24, 36…).
Negative numbers
Negative numbers are numbers less than zero, written with a minus sign, like −3. You meet them in cold temperatures, bank overdrafts and floors below ground.
Percentages
A percentage is a number out of 100, written with the sign %. So 25% means 25 out of every 100, which is the same as one quarter.
Prime numbers
A prime number is a whole number greater than 1 that has exactly two factors, 1 and itself. The first primes are 2, 3, 5, 7, 11 and 13.
Square numbers
A square number is what you get when you multiply a whole number by itself, like 4 × 4 = 16. The first square numbers are 1, 4, 9, 16, 25 and 36.
Volume
Volume is the amount of space a 3D object takes up, measured in cubic units like cm³ or m³. A box 4 cm by 3 cm by 2 cm has a volume of 24 cm³.
Order of operations
The order of operations is the agreed order for working out calculations: brackets, then powers, then × and ÷, then + and −. UK pupils learn it as BIDMAS; US pupils as PEMDAS.
Around ages 11–16
Secondary
Probability
Probability measures how likely something is to happen, on a scale from 0 (impossible) to 1 (certain). A fair coin landing heads has a probability of 1/2.
Mean, median and mode
Mean, median and mode are three kinds of average. The mean shares the total out equally, the median is the middle value in order, and the mode is the most common value.
Ratio
A ratio compares two or more amounts, written with a colon. A ratio of 2:3 means for every 2 of one thing there are 3 of the other.
Algebra
Algebra is maths that uses letters, like x or n, to stand for numbers we don't know yet or numbers that can change. For example, if n + 3 = 10, then n = 7.
Equations
An equation says two things are equal, using an = sign, like 2x + 1 = 9. Solving it means finding the value of the letter that makes it true, here x = 4.
Pi (π)
Pi (π) is the number you get when you divide any circle's circumference by its diameter. It is about 3.14, and its digits go on forever without repeating.
Powers and indices
A power (also called an index or exponent) is a small raised number showing how many times to multiply a number by itself. So 2⁴ means 2 × 2 × 2 × 2 = 16.
Square roots
The square root of a number is the value that, multiplied by itself, gives that number. The square root of 25 is 5, because 5 × 5 = 25. The sign is √.
Pythagoras' theorem
Pythagoras' theorem says that in a right-angled triangle, a² + b² = c², where c is the longest side (the hypotenuse). For sides 3 and 4, the hypotenuse is 5.