Year 7 maths: the curriculum and the move from primary school

What do children learn in Year 7 maths?

In Year 7 maths, children start the key stage 3 programme of study, which runs from Year 7 to the end of Year 9. The curriculum lists what children should learn across all three years, but it doesn't say which topics come in Year 7. Each school decides its own order, so the best way to find out what your child will cover this year is to ask the school for its maths scheme of work or curriculum map.

What the curriculum does say is where KS3 starts. Its first aim is that children consolidate the number skills they bring from primary school, then extend their understanding of the number system to include decimals, fractions, powers and roots. So the start of secondary school maths can feel familiar, but the same ideas are pushed further and used in new ways.

From Year 6 to Year 7

Children arrive in Year 7 with the KS2 maths curriculum behind them, and most will have taken the KS2 SATs in May of Year 6. The results are given as scaled scores. GOV.UK says one of their purposes is to help teachers see where children may need extra help or support as they move to secondary school. They're one piece of information among many, and your child's maths teacher will get to know how they work in class.

The KS3 programme of study asks schools to build on KS2 rather than start again. This table shows how some of the main ideas from the end of primary school grow at KS3.

At primary school (by the end of Year 6)	At key stage 3 (Years 7 to 9)
Numbers up to 10,000,000, and negative numbers in real situations like temperatures	Numbers of any size, and adding, subtracting, multiplying and dividing with negative numbers
Prime numbers, common factors and common multiples	Prime factors, the highest common factor and the lowest common multiple, powers and roots
The order of operations with brackets	The order of operations with powers and roots too
Adding and subtracting fractions with different denominators, and simple fraction multiplication and division	All four operations with fractions and mixed numbers, positive and negative
Percentages of amounts, like 15% of 360	Percentage change, percentages over 100%, and one amount as a percentage of another
Unequal sharing problems and scale factors	Ratio written as 2:3, simplest form, sharing in a ratio and proportion
Simple formulae, sequences, and letters for missing numbers	Algebra: expressions, expanding brackets, solving equations and the nth term
Area of triangles and parallelograms, angles in triangles, parts of a circle	Area of trapezia and circles, volume of prisms, angles and parallel lines, Pythagoras' theorem
Pie charts, line graphs and the mean	The median, mode and range, grouped data and scatter graphs

Two things are new rather than grown from KS2. Probability isn't in the primary curriculum, so KS3 is where it starts. And algebra, which was a small part of Year 6, becomes one of the biggest areas of secondary school maths.

The year 7 maths curriculum: the six areas of KS3

The KS3 curriculum has six areas. Here's each one in plain words, with an example of the kind of thing children do. Remember that your child's school decides which parts come in Year 7.

Number

Children work with whole numbers, decimals and fractions of any size, positive and negative. For example, −3 + 5 = 2 and 3 × −4 = −12. They write numbers as a product of prime factors, so 36 is 2 × 2 × 3 × 3, and use powers and roots: 5² means 5 × 5.

Algebra

Children use letters to stand for numbers and learn the conventions for writing them: 3y means 3 × y, and ab means a × b. They substitute numbers into expressions (if y is 4, then 3y + 1 is 13), collect like terms, and solve equations.

Ratio, proportion and rates of change

Children write ratios like 2:3, simplify them, and share amounts in a ratio. They solve problems with percentages and with rates such as speed and the price per item.

Geometry and measures

Children work out perimeters, areas and volumes, use angle facts to find missing angles, and draw accurate constructions with a ruler and compasses. Later in KS3 this includes Pythagoras' theorem and trigonometry.

Probability

Children describe how likely things are on a scale from 0 to 1, and learn that the probabilities of all the possible outcomes add up to 1.

Statistics

Children find the mean, median, mode and range of a set of data, and draw and read charts, including charts for grouped data.

Maths words for Year 7

Integer

A whole number. It can be positive, negative or zero, like 7, −3 or 0.

Prime factor

A factor of a number that is also a prime number. The prime factors of 12 are 2 and 3.

Highest common factor (HCF)

The biggest number that divides exactly into two or more numbers. The HCF of 12 and 18 is 6.

Lowest common multiple (LCM)

The smallest number that is a multiple of two or more numbers. The LCM of 4 and 6 is 12.

Power (or index)

The small raised number that says how many times to multiply a number by itself. 2³ means 2 × 2 × 2.

Square root

The number that multiplies by itself to make a given number. The square root of 49 is 7.

Expression

A collection of numbers and letters without an equals sign, like 3y + 1.

Term

One part of an expression. In 3y + 1, the terms are 3y and 1.

Like terms

Terms with exactly the same letters, which can be added together. 2a and 5a are like terms; 2a and 5b aren't.

Substitute

To put a number in place of a letter to work out the value of an expression.

Equation

A statement that two things are equal, with an unknown to find, like y + 4 = 10.

Inverse operation

The operation that undoes another. Adding undoes subtracting, and dividing undoes multiplying.

Ratio

A way of comparing amounts, written with a colon. 2:3 means 2 of one thing for every 3 of another.

Median

The middle value when the data is put in order.

Mode

The value that appears most often.

Range

The biggest value take away the smallest, which shows how spread out the data is.

Probability

How likely something is to happen, given as a number from 0 (impossible) to 1 (certain).

End of year 7 maths tests

There's no national maths test in Year 7. GOV.UK's guide to the national curriculum lists national assessments for the primary years and GCSEs in key stage 4, but none for Years 7, 8 and 9. If your child's school sets an end-of-year maths test or exam, the school writes it and decides what it covers, so ask your child's maths teacher which topics will come up and how the results are used. The school's curriculum map shows what's been taught so far, which is a good guide to what to revise.

For a bit of practice at home, try the Year 7 maths questions below.

Year 7 maths questions to try

These are our own practice questions, not a test from school. They start from things children met at primary school and take them one step further.

1. What is −7 + 12?
2. What is 3 + 4 × 5?
3. Find the highest common factor of 24 and 36.
4. Write 60 as a product of prime factors.
5. Simplify the ratio 12:18.
6. If a is 4, what is 3a + 2?
7. What is ²⁄₃ + ¹⁄₄?

Answers

1. 5
2. 23 (multiply first, then add)
3. 12
4. 2 × 2 × 3 × 5, which can also be written 2² × 3 × 5
5. 2:3 (divide both parts by 6)
6. 14
7. ¹¹⁄₁₂ (change both to twelfths: ⁸⁄₁₂ and ³⁄₁₂)

How to help with Year 7 maths at home

• Ask what they did in maths today. The move to secondary school brings new teachers, new rooms and new ways of working. Talking about the maths, even briefly, helps you see how they're settling in.
• Keep the times tables fresh. Prime factors, fractions, ratio and algebra all lean on quick multiplication facts. The times tables test mixes up every table, and our guide on how to learn times tables has a short routine.
• Don't drop written and mental methods. The KS3 curriculum says calculators shouldn't replace good written and mental arithmetic, so methods like long division still count.
• Ask them to explain the method. Secondary schools may use slightly different methods or words from primary school. Asking "how were you shown this?" helps your child, and stops you teaching a clashing method.
• Ask the school for its curriculum map. It tells you which KS3 topics come up when, so you can talk about them at home.

If you'd like to look back at what came before, our Year 6 maths guide covers the last year of primary school.