England · Key Stage 3 · Year 9, ages 13 to 14

Year 9 maths tutor online

Year 9 is a strange year for maths. It is the final year of Key Stage 3, so the programme of study expects everything it lists to be known by the summer, yet many schools are already teaching GCSE topics and talking about sets. It is also the options year, when families spend weeks on subject choices, and maths is the one subject nobody chooses because it is compulsory. This page explains what the end of Key Stage 3 actually requires, why the options process changes less for maths than parents expect, which Year 9 topics GCSE leans on hardest, and how to run a short audit before Year 10 begins. Three worked examples and a practice set, all written by us, show the level.

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Live teaching since 2020 · 10,000+ students · Built from the DfE Key Stage 3 and GCSE maths documents

In short

Year 9 maths in England is the final year of Key Stage 3, for students aged 13 to 14, taught from the Department for Education's Key Stage 3 programme of study. There is no national maths test in Year 9; GCSE Mathematics follows in Years 10 and 11. Modern Age Coders teaches Year 9 maths live online through its GCSE Maths: Foundation and Higher course, either 1-on-1 or in a batch of 15 to 20 students, and closes Key Stage 3 gaps before any new GCSE topic. We are independent of schools, the DfE and every exam board.

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Three courses a Year 9 student might join

Most Year 9 students join the first. The second suits a student whose Key Stage 3 arithmetic or algebra is shaky; the third suits one who is racing ahead.

GCSE Maths course thumbnail

Y9 / 01

GCSE Maths: Foundation and Higher

Starts where Key Stage 3 ends, at a pace set by the audit rather than by the calendar.

Open the syllabus →
Middle School Mathematics Mastery course thumbnail

Y9 / 02

Lower secondary maths

For a Year 9 student who needs fractions, negatives and equations rebuilt before GCSE.

Open the syllabus →
Maths Olympiad & Competition Course course thumbnail

Y9 / 03

Competition maths

Rich problems for a fast student, in line with the curriculum's preference for depth before acceleration.

Open the syllabus →

The end of Key Stage 3

What should a Year 9 student know in maths by the end of the year?

Everything in the Key Stage 3 programme of study. The DfE document, dated September 2013, says so in one sentence, and it is worth reading slowly.

The national curriculum sets the target for the whole key stage, not for each year: "By the end of key stage 3, pupils are expected to know, apply and understand the matters, skills and processes specified in the relevant programme of study." Year 9 is where that sentence comes due. Whatever was missed in Years 7 and 8 is still on the list in June of Year 9, and nothing in the curriculum moves it to Year 10.

The programme of study is a nine-page document, organised under six content headings: number; algebra; ratio, proportion and rates of change; geometry and measures; probability; and statistics. Above them sit three aims that run through every topic: to become fluent, to reason mathematically, and to solve problems. In practice the aims matter as much as the topics, because GCSE papers reward the second and third almost as heavily as the first.

Year 9 in the national curriculum, from gov.uk's national curriculum guide
YearAgeKey stageNational assessment in that year
Year 913 to 14Key Stage 3, final yearNot applicable (no national test)
Year 1014 to 15Key Stage 4Some children take GCSEs
Year 1115 to 16Key Stage 4Most children take GCSEs or other national tests

Because there is no national test, Year 9 maths is judged entirely by the school: its own end-of-year exams, its setting decisions and its report. The gov.uk guide adds one duty that families can use: "By the end of each summer term the school must write a report on your child's progress and talk it through with you." The Year 9 summer report is the most useful one to read carefully, because it is usually written by the person deciding the Year 10 set.

What is statutory, and what is not

The programme of study includes example content in square brackets. The DfE is explicit that "Schools are not required by law to teach the example content in [square brackets] or the content indicated as being 'non-statutory'."

So when a school skips a bracketed example, it is not breaking a rule. What it cannot skip is the main statement around the brackets.

Who has to follow it

Maintained schools follow the national curriculum. The gov.uk guide notes that "Other types of school, like academies and private schools, do not have to follow the national curriculum", though academies must still teach maths.

In practice almost every school in England teaches something close to it, because GCSE is built on the same content.

Sources: DfE, Mathematics programmes of study: key stage 3 (September 2013, reference DFE-00179-2013) and gov.uk, The national curriculum, both read on 31 October 2026.

The options year

Do you choose maths in Year 9 options?

No. Maths is a core subject at Key Stage 4, so it is never on the options form. What Year 9 does decide is the shape of the maths that follows.

The gov.uk guide lists the Key Stage 4 core plainly: "Core subjects are: English maths science". Every student in a maintained school in England continues maths into Years 10 and 11 and, in almost every case, sits GCSE Mathematics. The options booklet a family receives in Year 9 is about the other subjects. That is why parents are sometimes surprised that the options evening has nothing to say about maths.

Three maths-shaped questions still sit inside the options year, and they are the ones worth asking the school about before the form goes in.

A second maths qualification

Some schools offer GCSE Statistics, or a Level 2 Further Maths course for a top set, alongside GCSE Maths. These usually sit inside options blocks or after-school slots, so they appear in Year 9 even though maths itself does not.

Subjects that lean on maths

Computer Science, physics and the separate sciences, geography and economics all use Key Stage 3 algebra, graphs and statistics. A student weighing those options should know how secure their own algebra is.

The set for Year 10

Many schools reset maths groups at the start of Key Stage 4. The set is not the GCSE tier, but it often decides which content is taught first and how quickly Higher-only topics arrive.

GCSE Maths has two tiers. AQA's specification describes them in one line: a Foundation tier for grades 1 to 5 and a Higher tier for grades 4 to 9, and the other boards in England use the same split. Nobody is entered for a tier in Year 9; that happens late in Year 11. But the Year 9 audit below is the earliest honest evidence of which tier a student is heading towards, and it is far easier to change that direction at 13 than at 15.

If a student is thinking about Computer Science

Our page on choosing GCSE Computer Science in Year 9 covers that decision on its own terms.

The maths link is real: sequences, algebraic notation and logic all reappear in programming, and a student comfortable with nth-term rules usually finds loops less mysterious.

If a second maths GCSE is offered

Ask when it is taught and how it is examined. A Statistics GCSE in the options block costs a full option; one taught after school does not.

A student still consolidating Key Stage 3 number is usually better served by one strong maths GCSE than by two thin ones.

Key Stage 3 to GCSE

Which Year 9 topics does GCSE Maths build on most?

Nearly all of them. The Key Stage 4 programme of study, dated July 2014, says Key Stage 3 and Key Stage 4 together are the whole GCSE.

The sentence that ties the two stages together is in the Key Stage 4 document: "Together, the mathematical content set out in the key stage 3 and key stage 4 programmes of study covers the full range of material contained in the GCSE Mathematics qualification." The DfE's GCSE subject content then adds that GCSE outcomes "may reflect or build upon subject content which is typically taught at key stage 3", and that "There is no expectation that teaching of such content should be repeated during the GCSE course where it has already been taught effectively at an earlier stage." Read together, those lines carry a quiet warning: if a Key Stage 3 topic was not learned the first time, the GCSE course is not obliged to teach it again.

Eight Key Stage 3 statements and what GCSE adds on top (statements quoted from the KS3 programme of study; the right-hand column is our summary of the DfE GCSE subject content)
Key Stage 3 statement (DfE, 2013)AreaWhat GCSE adds
interpret and compare numbers in standard formNumberCalculating with standard form, not just reading it
use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notationNumberError intervals from truncation, then upper and lower bounds
recognise arithmetic sequences and find the nth termAlgebraQuadratic sequences and their nth term at Higher
use algebraic methods to solve linear equations in one variableAlgebraQuadratics, simultaneous equations and inequalities
solve problems involving percentage change, including ... original value problemsRatioCompound growth and decay, repeated percentage change
solve problems involving direct and inverse proportionRatioProportion written as equations, with constants found
use Pythagoras' Theorem and trigonometric ratios in similar trianglesGeometryExact trigonometric values, then the sine and cosine rules at Higher
generate theoretical sample spaces for single and combined eventsProbabilityTree diagrams, Venn diagrams and conditional probability

Every row in that table is a Year 9 topic that becomes a GCSE topic with more weight on top. A student who leaves Year 9 unable to find an original value after a percentage change does not just lose that question; they arrive at compound interest, reverse percentages and growth and decay without the step those topics stand on. The same is true of linear equations, which hold up most of GCSE algebra.

Depth before speed

The programme of study has a view on fast students: they "should be challenged through being offered rich and sophisticated problems before any acceleration through new content in preparation for key stage 4."

For a strong Year 9 student, that argues for harder problems on Key Stage 3 content, not an early start on Higher-only topics.

Consolidation before moving on

For the rest it is equally direct: those "not sufficiently fluent should consolidate their understanding, including through additional practice, before moving on."

Year 9 is the last year where consolidation can happen without a GCSE scheme of work pulling the class forward.

Sources: DfE, Mathematics programmes of study: key stages 3 and 4 and DfE, GCSE mathematics: subject content and assessment objectives, read on 31 October 2026. The middle column of the table and the summaries in it are ours.

The Year 9 audit

How can you tell if a Year 9 student is ready for GCSE Maths?

Run a short audit of the Key Stage 3 statements that GCSE leans on. This is our method; it takes one lesson and leaves a list, not a label.

Our audit uses twelve short questions, one for each of twelve Key Stage 3 statements, chosen because each is the base of a heavier GCSE topic. The student answers without a calculator first, then with one where the statement allows it, because the programme of study warns that "Calculators should not be used as a substitute for good written and mental arithmetic." Each answer is marked secure, shaky or missing. The audit is ours, and it is a teaching tool, not a predicted grade.

  1. Number sense. Order a mix of negative numbers, decimals and fractions on one line, and explain one placement aloud.
  2. Fractions as operators. Find three fifths of 45 and 35% of 60 by hand.
  3. Standard form. Compare 3.2 × 104 with 4.1 × 103 and say which is bigger and roughly how many times.
  4. Estimation. Round each number in a two-step calculation to one significant figure and estimate the answer.
  5. Expressions. Expand and simplify two brackets, then factorise a simple expression.
  6. Linear equations. Solve an equation with the unknown on both sides and a fraction in it.
  7. Sequences. Find the nth term of an arithmetic sequence and test whether a given number belongs to it.
  8. Straight-line graphs. Read the gradient and intercept from y = mx + c, then sketch the line.
  9. Ratio and percentage. Share an amount in a ratio, and find an original amount after a percentage reduction.
  10. Angles and shapes. Use angle facts on parallel lines and give the reason for each step.
  11. Right-angled triangles. Find a missing side with Pythagoras' theorem and decide when to use it.
  12. Probability and data. List a sample space for two events and compare two data sets using a mean and a range.

The pattern of the marks matters more than the count. Shaky fractions and equations usually mean a student will find Foundation algebra hard and Higher algebra very hard. Shaky Pythagoras and sequences on their own are quick fixes. Shaky reasoning, where the answer is right but the student cannot say why, is the gap that costs most at GCSE, because the DfE weights reasoning (AO2) at 30% of Higher marks and 25% of Foundation marks, and problem solving (AO3) the same again.

Worked examples

Three Year 9 questions we wrote, with every step shown

Our own questions, at the level of the end of Key Stage 3. None is taken from a school, a board or a published test.

Example 1, ratio and percentage: an original value

Question (ours). After a 15% cut, a school uses 340 kilowatt hours of electricity a week. How much did it use before the cut?

Think first. 340 is not the starting amount; it is 85% of the starting amount. So the old figure is the unknown, and 340 is what is left after the cut.

Working. 100% − 15% = 85%, so 0.85 × original = 340. Original = 340 ÷ 0.85 = 400 kilowatt hours.

Check. 15% of 400 is 60, and 400 − 60 = 340. The common wrong answer, 340 + 15% of 340 = 391, fails the check at once.

Example 2, algebra: is it in the sequence?

Question (ours). A sequence begins 7, 11, 15, 19. Is 150 a term of the sequence?

Working. The difference is 4, so the nth term is 4n + c. When n = 1 the term is 7, so c = 3, giving 4n + 3.

Test. Solve 4n + 3 = 150, so 4n = 147 and n = 36.75. A term number must be a whole number.

Answer. No, 150 is not in the sequence. The 36th term is 147 and the 37th is 151, which confirms it.

Example 3, geometry: Pythagoras with a decision

Question (ours). A 5 metre ladder leans against a wall with its foot 1.4 metres from the wall. How high up the wall does it reach, to the nearest centimetre?

Think. The ladder is the hypotenuse, because it is opposite the right angle at the foot of the wall. So we subtract squares, not add them.

Working. h² = 5² − 1.4² = 25 − 1.96 = 23.04. h = 4.8 metres exactly, which is 4.80 m to the nearest centimetre.

Sense check. The height must be less than 5 m, the ladder's length. An answer of 5.19 m would come from adding the squares and is impossible.

What the three examples share

Each one has a moment before any arithmetic where the student decides what the numbers mean: which amount is the whole, what the term number must be, which side is the hypotenuse.

That moment is the reasoning the curriculum asks for, and it is the step most often skipped. We teach students to write it as a short sentence before they calculate.

Practice set (ours, answers at the end). (1) Write 0.000 47 in standard form. (2) Solve 5x − 3 = 2x + 18. (3) Share 84 in the ratio 3 : 4. (4) After a 20% cut, a bus journey takes 72 minutes; how long did it take before? (5) Find the nth term of 2, 9, 16, 23. (6) A right-angled triangle has shorter sides 9 cm and 12 cm; find the hypotenuse. (7) Two fair coins are flipped; what is the probability of exactly one head? Answers: (1) 4.7 × 10−4; (2) x = 7; (3) 36 and 48; (4) 90 minutes; (5) 7n − 5; (6) 15 cm; (7) one half, from the sample space HH, HT, TH, TT.

A Year 9 plan

How should a Year 9 student spend the year in maths?

Our three-term outline for the year, written around the way most English schools run Year 9: options in the spring, end-of-year exams and the summer report in the summer.

  1. Autumn term: audit and repair. Run the twelve-line audit in the first weeks. Spend the term on the two or three weakest lines, retesting each one a fortnight after it is taught.
  2. Autumn half-term: written arithmetic. A short daily habit of non-calculator work, fractions and negative numbers especially, because GCSE has a full non-calculator paper.
  3. Spring term, before options: a conversation. Ask the school how maths groups are set for Year 10 and whether a second maths qualification is offered. Use the audit, not a feeling, to decide whether to ask for a change.
  4. Spring term, after options: reasoning. Move from getting answers to explaining them: angle reasons, why a number is or is not in a sequence, what a gradient means in a context.
  5. Summer term: the school exam. Revise from the audit list, sit the school's end-of-year paper, and keep the marked paper.
  6. After the summer report: the handover. Re-run the audit. The lines still shaky become the first weeks of Year 10, before GCSE content builds on them.

The plan is ours and it is deliberately modest. It does not try to finish GCSE topics in Year 9. It tries to make sure that when Year 10 starts, the base is solid enough that new content can be added rather than patched. For a student who is already secure on all twelve lines, the curriculum's own advice applies: richer problems, more proof and reasoning, and perhaps further maths later, rather than a sprint through the Higher specification.

Progression

Four rungs from Year 9 into Year 10

A rung is reached when the audit says so, not when the calendar does.

What should be true by each point
RungWhenWhat should be true
1. Gaps namedFirst weeks with usThe audit has been run and the shaky lines are written down
2. Arithmetic by handBy Christmas of Year 9Fractions, negatives and percentages done without a calculator
3. Algebra secureBy the options deadlineLinear equations, brackets and nth terms solved and checked
4. Reasons writtenBy the summer reportEvery geometry and sequence answer comes with a sentence saying why

Why the first rung matters

Families often arrive with a worry and leave the first class with a list. The list is shorter than the worry, almost always.

Our Key Stage 3 maths page covers Years 7 and 8 if the gaps go back further.

Why the fourth rung matters

GCSE marks reasoning and problem solving on both tiers. A student who writes reasons in Year 9 is practising for every GCSE paper.

We send families a short note on the audit each month.

The catalogue

Nine courses around Year 9 maths

Grouped by what a Year 9 student usually needs: repair, the GCSE itself, or stretch.

I

Repair

Key Stage 3 foundations

UK / Y9A / 01

Lower secondary maths

Number, geometry and early algebra, rebuilt in order.

Open the syllabus

UK / Y9A / 02

Algebra Foundations

From expressions to equations with the unknown on both sides.

Open the syllabus

UK / Y9A / 03

Mental maths

Number sense for students whose written arithmetic is slow.

Open the syllabus
II

The GCSE ahead

Starting at the right pace

UK / Y9B / 01

GCSE Maths

Foundation and Higher content once the base is secure.

Open the syllabus

UK / Y9B / 02

Statistics and probability

Sample spaces, averages and spread, taken further.

Open the syllabus

UK / Y9B / 03

Maths through coding

Sequences and straight-line graphs turned into short Python programs.

Open the syllabus
III

Stretch

For the fastest Year 9s

UK / Y9C / 01

Competition maths

Problems that reward depth on familiar content.

Open the syllabus

UK / Y9C / 02

Proof and problem solving

Longer arguments for students who enjoy hard questions.

Open the syllabus

UK / Y9C / 03

Python for teens

A first programming language, useful for a Computer Science option.

Open the syllabus

How lessons work

Live Year 9 maths classes, set in UK time

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Teachers work from India and every lesson is timetabled in UK time.

After school

A good slot for a 13 or 14 year old.

Early evening

After homework and clubs.

Weekend mornings

Unhurried time for the audit.

Audit first

Twelve Key Stage 3 lines checked in the first lesson, so teaching starts at the real gap.

Hand arithmetic

Non-calculator practice in every class, because GCSE has a paper without one.

Reasons in writing

Every answer ends with a sentence that says why it is right.

School work alongside

Homework and school tests are welcome in class; we teach around them.

Free first lesson

One live class to try the format, with nothing paid until a regular time is agreed.

Group or 1-on-1

A batch of 15 to 20 Year 9 students, or a teacher for one student.

Student work

Things students made in our classes

Ordinary class work, not assessed pieces. More in student labs.

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Fees

Fees for Year 9 maths classes

The first lesson is free. After that a single monthly fee, with a group seat costing less than 1-on-1 teaching. There is no contract, and nothing is charged until a weekly slot is fixed.

Free first class

USD 0

no card required

  • A live class with the twelve-line audit
  • A written list of the shaky lines
  • Booked with only a phone number
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Group batch

USD 100

a month, billed in US dollars

  • 15 to 20 Year 9 students
  • The same teacher through the year
  • Hand arithmetic in every class
  • A monthly note on the audit
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One to one

USD 150

a month, billed in US dollars

  • A teacher for one student
  • Built around that student's audit
  • Suits a big gap or a fast learner
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Questions about Year 9 maths

What parents ask about Year 9 maths

What maths is taught in Year 9?

Year 9 finishes the Key Stage 3 programme of study: number, algebra, ratio and proportion, geometry and measures, probability and statistics. Many schools also start some GCSE topics in Year 9, but the Key Stage 3 statements are still the target for the end of the year.

Is there a test at the end of Year 9?

There is no national maths test in Year 9; the gov.uk guide lists the assessment for Year 9 as not applicable. Schools set their own end-of-year exams and must send a written report on progress by the end of the summer term.

Do you pick maths in Year 9 options?

No. Maths is a core subject at Key Stage 4, alongside English and science, so it is not on the options form. Options can still involve maths, for example a GCSE Statistics course or a subject such as Computer Science that uses a lot of algebra.

Is Year 9 maths the start of GCSE?

In many schools, partly. The Key Stage 4 programme of study says Key Stage 3 and Key Stage 4 together cover the whole GCSE, so Year 9 content is GCSE content in its first form. The DfE also says GCSE teaching need not repeat topics already taught well at Key Stage 3.

Does the Year 9 set decide Foundation or Higher?

Not directly. Students are entered for a tier late in Year 11, and the Foundation tier awards grades 1 to 5 while Higher awards 4 to 9. But Year 10 sets often decide which content is taught first, so Year 9 progress shapes the route.

My child is ahead in Year 9. Should they start GCSE early?

The Key Stage 3 programme of study prefers depth: fast students should get rich and sophisticated problems before acceleration through new content. We usually give strong Year 9 students harder problems on familiar topics rather than racing ahead.

What is the most important Year 9 maths topic?

If we had to choose one, solving linear equations, because so much GCSE algebra stands on it. Close behind are fractions and percentages by hand, including original value problems, which lead straight into reverse percentages and compound change.

How do I know if my child has gaps?

A short audit tells you more than a test score. We use twelve questions, each tied to a Key Stage 3 statement, and mark each one secure, shaky or missing; the free first class includes it.

When are classes held?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. All times are set in UK time.

Are you connected with my child's school or the DfE?

No. Modern Age Coders is an independent online school. We teach to the published Key Stage 3 programme of study and the GCSE content, and we do not promise a set, a tier or a grade.

Elsewhere on this site

More for Year 9 and the years after

The key stage around Year 9, and the GCSE questions that come next.

Key Stage 3 maths tuition

Years 7 to 9 together, for gaps that go back further.

GCSE maths tuition

The two years that follow Year 9, in one place.

Foundation or Higher

How the tier choice is made, and by whom.

Comparing the GCSE boards

What changes, and what does not, between AQA, Edexcel and OCR.

Computer Science as an option

A Year 9 choice that leans on maths.

All our UK pages

The UK hub for maths and computing.

Related pages in this guide

Part of the guide: UK maths year by year, Reception to Year 11

Secondary, Year 7 to Year 11

Primary, Reception to Year 6

Scotland

More guides: UK maths exam boards and specification codes · UK selective school maths tests: 7+, 11+, 13+ and 16+ · UK university admissions: maths tests and computing applications · UK maths enrichment, competitions and able pupils

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Book a free Year 9 maths class

Leave a number and we will call at a UK time you choose. The class runs the twelve-line audit and ends with a short written list of what to work on first.

Want to look before booking? The GCSE Maths course page shows the syllabus, and how we teach describes a typical lesson.

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