England · Key Stage 3 · Ages 11–14

Key Stage 3 maths:
three years, one programme,
and no national exams

A parent's map of Key Stage 3 maths in England — why there is no year-by-year curriculum at secondary school, what the three years usually cover, how sets and setting work, and why these are the years that decide how GCSE feels.

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The short answer

What is Key Stage 3 maths?

Key Stage 3 is Years 7, 8 and 9 in England — ages 11 to 14, the first three years of secondary school. Maths is compulsory throughout, and there are no national tests at any point in the key stage.

The important structural difference from primary school: the national curriculum sets out maths year by year only for key stages 1 and 2. For key stage 3 there is a single programme of study covering all three years, and each school decides its own order and must publish its own year-by-year curriculum. That is why two children in Year 8 at different schools can be doing completely different topics, and why any website offering "the Year 8 maths curriculum" is describing one school's scheme.

The programme has six areas: number, algebra, ratio, proportion and rates of change, geometry and measures, probability and statistics. Its stated aim is to build on key stage 2 and develop fluency, mathematical reasoning and the ability to solve increasingly sophisticated problems.

These three years are not a warm-up before the real thing. A large part of what is examined at GCSE is met here for the first time — see below.

Source: the key stage 3 programme of study, published by the Department for Education.

Year by year

What each year of Key Stage 3 maths usually covers

There is no statutory year-by-year split. This is the shape of the DfE's own non-statutory sample framework, which many of the schemes we see resemble — your child's school publishes its own.

Year 7 (ages 11–12)

Mostly consolidating primary number while introducing the language of algebra, ratio and the coordinate grid.

  • Place value, factors, multiples, primes and prime factorisation
  • The four operations with integers, decimals and fractions, positive and negative
  • Algebraic notation, forming expressions, collecting like terms, the distributive law
  • Coordinates in four quadrants, perimeter and area
  • Multiplicative relationships: fractions and ratio
  • Transformations: translation, rotation, reflection, enlargement
The thing that comes back

Algebraic notation: 3a means 3 × a.

A child who thinks 3a + 2b is 5ab will get every simplifying question wrong for a term, and every equation wrong after that.

Where it usually goes wrong The transition itself is often harder than the maths. Our Year 7 maths page covers sets, CATs and what changes from primary school.

Year 8 (ages 12–13)

Algebra becomes a method rather than a notation, and percentages become multiplicative.

  • Rounding to decimal places and significant figures; estimation
  • Sequences, arithmetic sequences and the nth term
  • Straight-line graphs, and solving linear equations of increasing complexity
  • Percentage change, proportion, and compound units
  • Averages, spread, and constructing and interpreting statistical representations
  • Perimeter, area and volume including circles; angles in polygons; constructions
The thing that comes back

15% off £80 as 0.85 × 80.

The multiplier method. Building up from 10% works now and fails at reverse percentages and compound interest.

Where it usually goes wrong The quietest year in school: no transition, no exam, no national test. Our Year 8 maths page covers where gaps start without anyone noticing.

Year 9 (ages 13–14)

The geometry and algebra that GCSE leans on hardest — or, in many schools, the start of the GCSE course itself.

  • Similarity, congruence and Pythagoras' theorem
  • Trigonometry in right-angled triangles
  • Expanding products of binomials, factorising, rearranging formulae
  • Non-linear sequences; standard form
  • Probability — which the sample framework places here, though many schools introduce it earlier
  • Modelling and interpreting situations graphically
The thing that comes back

(x + 3)(x + 5) = x² + 8x + 15

Expanding and factorising are the most load-bearing skills in GCSE algebra, and this is where they are taught properly.

Where it usually goes wrong Many schools start GCSE content in Year 9. Our Year 9 maths page covers three-year GCSE courses and how tier decisions get made.

The six areas are from the key stage 3 programme of study (Department for Education). The year-by-year split broadly follows the DfE's non-statutory sample key stage 3 curriculum framework, published in 2021 with the NCETM, which schools are free not to follow.

Why the order varies

Why every school's Key Stage 3 looks different

Because schools are only required to teach the key stage 3 programme by the end of the key stage. Within that, schools choose the order, and they are required to publish their own year-by-year curriculum on their website — which is the document to look at if you want to know what your child will meet and when.

The Department for Education has published a non-statutory sample key stage 3 curriculum framework, written with the NCETM, which sets out one possible order term by term across the three years. It is guidance, not a requirement, and it says its material can be used whether or not a school teaches in the order suggested.

That framework is also explicit about time: it exemplifies a three-year key stage 3, and it does not recommend condensing the content into two years, on the grounds that the necessary depth of understanding is unlikely to be reached in a shorter time. Schools that begin GCSE in Year 9 take a different view, and both are common.

For a parent this matters in one practical way. If you are buying a workbook or a website subscription "for Year 8", it may not match what your child's school is teaching this term. Ask the school for its curriculum map first.

Assessment

What is actually assessed in Key Stage 3

Nothing national. Everything that happens in these three years is the school's own.

Detail
National testsNone. The last statutory tests are the key stage 2 tests in Year 6; the next are GCSEs in Year 11
Baseline testingMany secondary schools test in the first weeks of Year 7 — their own maths paper, a cognitive abilities test such as CAT4, or both. GL Assessment, which publishes CAT4, says it is used by over half of UK secondary schools
School assessmentsEnd-of-unit and end-of-year tests, set by the school. These are usually what set changes are based on
SettingThe large majority of English secondary schools set for maths at some point, according to the Education Endowment Foundation's evidence summary, commonly from Year 7. Sets are reviewed during the key stage
ReportingSchools report progress in their own way — grades, bands, flight paths, or working-towards descriptors. There is no national scale at KS3
Tier decisionsFoundation or higher tier is a GCSE decision, usually taken in Year 10 or 11, not in key stage 3

Because there is no national key stage 3 assessment, a school's grades and bands mean what that school says they mean. It is always worth asking what a reported number is measured against.

Why it matters

Why Key Stage 3 decides how GCSE feels

The national curriculum states that the key stage 3 and key stage 4 programmes of study together cover the full range of material in GCSE mathematics. In practice, much of what a foundation-tier candidate is examined on in Year 11 is first taught between Year 7 and Year 9.

So the three years without an exam in sight are the years in which most of the GCSE content is met for the first time. Arriving in Year 10 fluent with fractions, algebra and ratio turns Years 10 and 11 into an extension of what is already known. Arriving without them turns the same two years into a first encounter, with an exam in the way.

That is not an argument for panic in Year 7. It is an argument for taking a Year 8 gap seriously when it appears, rather than waiting for a Year 10 report to say so.

There are four things worth being secure in by the end of Year 9, and they are the same four every year: fractions, ratio and proportion, algebraic manipulation, and negative numbers. Almost everything else at GCSE leans on them.

Signs of a gap

How a Key Stage 3 gap shows itself

There is no test to catch it, so it usually shows up in what a child says rather than in a mark.

What to listen for

The words children use for "I stopped understanding this" are rarely those words.

  • "Maths is boring this year" — often means lost, three weeks ago
  • "I don't need it, I'm not going to do maths after GCSE"
  • "The teacher goes too fast" — sometimes true, and sometimes a gap making normal pace feel fast
  • Homework done quickly and always green on the school platform
  • "I'm in set 4, so" — a placement being used as a self-description
Try this at home

Ask what this week's topic is called, then ask them to explain one homework question to you.

Both answers are informative, and neither needs you to know the maths.

Where it usually goes wrong Homework platforms that let a child retry until the screen goes green. Persistence is rewarded; understanding is not measured.

What to check

Four questions that find most key stage 3 problems, whatever year your child is in.

  • ⅔ × ¾, and ¾ ÷ ½ — fractions
  • Share £60 in the ratio 2:3 — ratio
  • Simplify 3a + 2b + a, and solve 4x − 3 = 17 — algebra
  • 7 − (−3), and (−3) × (−4) — negative numbers
The answers

½; 1½; £24 and £36; 4a + 2b; x = 5; 10; 12.

Hesitation on any of these matters more than this week's topic, whichever year they are in.

Where it usually goes wrong If two or more are shaky, the current topic is not the problem. Fixing the foundation is faster than keeping up without it.

At home

How to support Key Stage 3 maths

You do not need to be able to do the maths. Most of this is asking the right questions.

How we help

How ClassArc supports a Key Stage 3 student

Weekly one-to-one classes, following the school's own scheme of work, with the same teacher throughout the key stage wherever we can arrange it.

We work from the school's order

With nothing statutory to follow year by year, the school's scheme is the only sensible plan — so that is the one we teach to.

The four foundations first

Fractions, ratio, algebraic manipulation and negative numbers get checked in the first classes, because most key stage 3 difficulty sits on one of them.

Methods that scale

Equations solved by balance, percentages by multiplier, expanding by multiplying every term. The shortcuts that work in Year 8 and break in Year 10 are not taught.

Reasons written down

Every answer comes with its method and its reason, in the form secondary marking expects, from Year 7 onwards.

The same teacher, all three years

Wherever we can arrange it, one teacher stays with a student through key stage 3 and into GCSE, so nothing has to be rediscovered each September.

No promises about sets or grades

Neither a tier nor a grade can honestly be predicted from key stage 3. What arrives each term is a plain account of what your child can now do.

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Go deeper

The year your child is in

Each year page covers what is usually taught, where children get stuck, and what to ask the school.

Year 7 maths

The transition from primary, how sets and CATs are decided, and what changes at secondary school.

Year 7 in full

Year 8 maths

Equations, percentages as multipliers, circles and averages — and the year gaps start unnoticed.

Year 8 in full

Year 9 maths

Pythagoras, trigonometry and expanding brackets — plus three-year GCSE courses and tiers.

Year 9 in full

Key Stage 4 maths

Years 10 and 11: the GCSE course, how the two tiers work, and the decision the school makes at the end.

KS4 & Years 10–11

GCSE maths tutor

How we teach Years 10 and 11 across the three boards and both tiers.

GCSE tutoring

Key Stage 3 maths questions

What years are Key Stage 3?
Years 7, 8 and 9 in England, ages 11 to 14 — the first three years of secondary school. Maths is compulsory throughout, and remains compulsory to the end of Year 11.
What maths is taught in Key Stage 3?
Six areas: number, including negative numbers, powers, roots, standard form and percentages; algebra, from notation to equations, sequences and graphs; ratio, proportion and rates of change; geometry and measures, including circles, angle reasoning, constructions, transformations, Pythagoras' theorem and trigonometry; probability; and statistics.
Is there a Year 7, 8 or 9 maths curriculum?
Not a statutory one. The national curriculum is set out year by year only for key stages 1 and 2. Key stage 3 has a single programme of study covering Years 7 to 9, and each school decides its own order and publishes its own year-by-year curriculum. The DfE has published a non-statutory sample framework schools may follow if they choose.
Are there SATs or national tests in Key Stage 3?
No. National tests at key stage 3 were abolished before the current curriculum, and there are none now. The last statutory tests are at the end of Year 6 and the next are GCSEs at the end of Year 11. Any tests your child sits in Years 7 to 9 are set by the school.
How are maths sets decided at secondary school?
It varies. Schools commonly use the key stage 2 results passed on from primary, their own baseline test in the first weeks of Year 7, or a cognitive abilities test such as CAT4 — often more than one, cross-referenced. Sets are reviewed during key stage 3 and children move. Ask the school what its placement was based on and when it is next reviewed.
How does Key Stage 3 relate to GCSE?
Directly. Directly — and the curriculum says so: the key stage 3 and key stage 4 programmes of study together cover the full range of GCSE mathematics. Some schools start the GCSE specification in Year 9 as a three-year course; others begin in Year 10.
What should my child be secure in by the end of Year 9?
Four things above all: fractions, ratio and proportion, algebraic manipulation (expanding, factorising, rearranging), and arithmetic with negative numbers. Almost every GCSE topic assumes them, and they are much cheaper to fix in key stage 3 than in Year 11.
My child says maths is boring this year. Is that a problem?
It can be the polite version of "I stopped understanding this a few weeks ago". Before treating it as attitude, ask what the current topic is called and get them to explain one homework question. If the four foundation checks are shaky, the boredom usually has a cause.
How can a tutor help in Key Stage 3?
By teaching into the school's own scheme rather than a separate one, repairing the primary gaps that secondary maths exposes, and making sure the methods learned are the ones that still work at GCSE. These are also the years with no exam competing for the time, which makes them the easiest years in which to fix something.
What does ClassArc cost in Key Stage 3?
Years 7 and 8 sit in our Years 1–8 band, from £11 per 55-minute one-to-one class on the largest plan; Year 9 sits in the Years 9–11 band, which includes GCSE work and past papers. Full details are on the UK pricing page, and the first class is free.
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