England and Scotland · Reception to Year 11 · ages 4 to 16

UK maths year by year: what is taught in each year, Reception to Year 11

Parents usually meet school maths one year at a time, through a homework sheet or a letter about a test. This page lays all twelve years out together, from the Department for Education's own programmes of study and assessment calendar, so you can see when the times tables are due, where algebra first appears and which years carry a national check. Each section then points to the page for one year or one check.

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Live teaching since 2020 · 10,000+ students · Built from DfE programmes of study and assessment calendars

In short

In England, school maths runs from Reception (age 4 to 5) to Year 11 (age 15 to 16) across five stages: the EYFS, Key Stages 1 and 2 with a list for every year, then Key Stages 3 and 4, which are each one programme. National checks fall in Reception, Year 2 (optional), Year 4, Year 6 and Year 11. Modern Age Coders teaches every one of these years live online, in a group or 1-on-1, with Elementary Maths, Middle School Maths and GCSE Maths courses. We are not connected with the DfE, STA or any exam board.

Courses by stage

Three courses that cover the years on this page

One for primary, one for the first secondary years, one for the GCSE years. The catalogue below adds early number for the youngest.

Elementary Maths for Grades 1-5 course thumbnail

YY / 01

Elementary Maths

Years 1 to 6: place value, the four operations, fractions to percentages, shape.

Open the syllabus →
Middle School Mathematics Mastery course thumbnail

YY / 02

Middle School Maths

Key Stage 3: algebra, proportion, negatives and geometry.

Open the syllabus →
GCSE Maths course thumbnail

YY / 03

GCSE Maths

Years 10 and 11, either tier, any English board.

Open the syllabus →

The year map

What maths is taught in each year in England?

One row per school year. Ages and checks come from gov.uk's year table; the content column is our short pick from that year's statutory statements.

The government describes the shape simply: "The national curriculum is organised into blocks of years called 'key stages' (KS)." Reception has early learning goals, not a programme of study. Years 1 to 6 each have their own statutory list. Years 7 to 9 share one Key Stage 3 programme and Years 10 and 11 one Key Stage 4 programme, so for those five rows the split by year is our illustration, not a legal one.

Maths in England, year by year (ages and checks from gov.uk; content selected by us from the DfE programmes of study and the EYFS framework)
YearStageAgeHeadline maths that yearNational check
ReceptionEYFS4 to 5Numbers to 10 and how each is made; subitising up to 5; counting aloud past 20; comparing quantities up to 10Reception baseline (first 6 weeks); EYFS profile (April to June)
Year 1KS15 to 6Counting to and across 100; one more and one less; halves and quarters; adding and subtracting in one stepNone in maths
Year 2KS16 to 7Addition and subtraction facts to 20 recalled fluently; the 2, 5 and 10 tables; thirds and quarters; time to five minutesOptional KS1 tests, May
Year 3Lower KS27 to 8The 3, 4 and 8 tables; column addition and subtraction; counting in tenths; perimeter; clock numerals I to XIINone
Year 4Lower KS28 to 9All tables to 12 × 12; counting back through zero; decimal forms of a quarter, a half and three quarters; Roman numerals to C; area by counting squares; first-quadrant coordinatesMultiplication tables check, June
Year 5Upper KS29 to 10Numbers to at least 1 000 000; square and cube numbers; primes; long multiplication; thousandths; percentagesNone
Year 6Upper KS210 to 11Numbers to 10 000 000; long division; ratio; first algebra with simple formulae; the mean; parts of a circle; all four quadrantsKS2 national tests, May
Year 7KS311 to 12Algebra used to generalise arithmetic; the four operations with negatives, fractions and mixed numbers; prime factors (order set by the school)None
Year 8KS312 to 13Linear equations; percentages above 100%; proportion; straight-line graphs; angle facts (order set by the school)School check of maths progress expected (no start year yet)
Year 9KS313 to 14The nth term of arithmetic sequences; standard form; Pythagoras' theorem and trigonometric ratios (order set by the school)None
Year 10KS414 to 15Quadratic and simultaneous equations; vectors; for higher attainers, surds and the sine and cosine rulesSome take GCSEs
Year 11KS415 to 16The rest of the KS4 programme, then revision for three GCSE papersGCSE Maths, May and June

Sources: gov.uk, The national curriculum (year, age and assessment table); DfE, Mathematics programmes of study for key stages 1 to 4; DfE, EYFS statutory framework from September 2026. All read on 1 November 2026.

Each primary stage opens with a one-line aim. Key Stage 1 seeks "confidence and mental fluency with whole numbers, counting and place value"; lower Key Stage 2 wants pupils to "become increasingly fluent with whole numbers and the four operations"; upper Key Stage 2 is meant to "develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio". From Year 7 the order is the school's, since the KS3 text says "Decisions about progression should be based on the security of pupils' understanding". And gov.uk adds that "Other types of school, like academies and private schools, do not have to follow the national curriculum."

National checks

Which school years have a national maths test or check?

Reception (two of them), Year 2 (optional), Year 4, Year 6 and Year 11. The dates below are those published for 2026 to 2027.

gov.uk puts it in one line: "Your child will be tested at the end of some key stages." The DfE's assessment calendar adds that "Assessment arrangements for the academic year 2026 to 2027 will remain unchanged", and that "Schools must keep these periods free for administering the assessments." GCSE dates come from the exam boards; the Year 11 row uses AQA's.

National assessments that include maths, school year 2026 to 2027 (dates from DfE Primary assessments: future dates and the AQA 8300 key dates page)
YearAssessmentMaths content and formatWhen in 2026 to 2027
ReceptionReception baseline assessmentA short task, designed to take around 20 minutes, on early maths and language; no expected standard and no pass or failFirst 6 weeks after a child enters Reception
ReceptionEYFS profileTeacher judgement against the early learning goals, including Number and Numerical PatternsApril to June 2027, completed no later than 30 June
Year 2Optional KS1 testsMaths Paper 1 arithmetic (about 20 minutes) and Paper 2 reasoning (about 35 minutes)Recommended during May 2027
Year 4Multiplication tables check25 on-screen questions, 6 seconds each, tables 2 to 12Two weeks from Monday 7 June 2027
Year 6KS2 national testsPaper 1 arithmetic, Papers 2 and 3 reasoningMaths on Wednesday 12 May and Thursday 13 May 2027
Year 11GCSE Mathematics (AQA 8300 as example)Three papers of 1 hour 30 minutes, Paper 1 without a calculator; Foundation grades 1 to 5, Higher 4 to 914 May, 27 May and 14 June 2027, mornings

Sources: DfE, Primary assessments: future dates, updated 12 October 2026; STA optional KS1 and tables check guidance; AQA, GCSE Mathematics 8300 key dates. Edexcel and OCR sit on the same three mornings.

Only the KS2 tests and GCSE carry real weight for a family. KS2 results are scaled scores, which the STA says "are used to report national curriculum test outcomes", and they pass to the secondary school. The Year 2 papers are the school's choice, and the times tables check is brief: the STA leaflet says "On average, the check should take no longer than 5 minutes to complete." The DfE already lists the 2028 KS2 tests for Monday 8 May to Thursday 11 May 2028.

Primary

Primary, Reception to Year 6: which page covers which year?

Thirteen pages: seven for single year groups, two for Key Stage 1, and four that follow one strand across years.

The early years and Key Stage 1

Start with Reception maths online if your child is four or five. It reads the early learning goals line by line and makes the case for play with a grown-up over formal lessons.

Year 1 maths is about the step from counting objects to working with numbers to 100, including why a missing-number sum such as 7 + ? = 12 is hard at six. Year 2 maths picks up where that leaves off, with subtraction checked by addition and the first three times tables.

For both years together, KS1 maths tuition sets out what a seven year old should know when Key Stage 1 ends, and KS1 SATs maths explained takes apart the optional Year 2 papers, including what a scaled score means.

Lower Key Stage 2

Year 3 maths is the first year of written column methods. That page shows how column addition and subtraction are taught in school.

Year 4 maths covers the whole Year 4 list, of which the tables are one part. Two narrower pages sit beside it. Multiplication tables check practice is only about the June check and the six-second design behind it, while times tables tutoring follows the tables from Year 2 to Year 4 and counts how few facts are truly hard.

Upper Key Stage 2

Year 5 maths is written for the year when numbers jump to a million and fractions start turning into decimals and percentages. In grammar school areas it is also the 11+ run-up.

Year 6 maths handles the last primary year as a calendar: ratio and algebra in the autumn, the SATs in May, and what the secondary school receives afterwards. The test itself, paper by paper, has its own page: KS2 SATs maths papers explained.

Across the whole of primary

Many English primary schools plan maths with a published scheme, and the one parents ask about most is White Rose. White Rose Maths help at home explains how its years, blocks and small steps fit together and how to help at home. We are not affiliated with White Rose Education.

Secondary

Secondary, Year 7 to Year 11: how does maths build towards GCSE?

One page per secondary year, each built around what that year is for, since no year owns its own list.

  1. Year 7, the reset year. Year 7 maths compares the Year 6 list with the start of Key Stage 3 and what a new school knows about a pupil in September.
  2. Year 8, the middle. Year 8 maths is about equations, graphs and proportion, and about the government's new expectation that schools check maths progress in Year 8.
  3. Year 9, the audit. Year 9 maths treats the end of Key Stage 3 as a checklist: which statements GCSE leans on hardest, and why maths is never one of the Year 9 options.
  4. Year 10, the first GCSE year. Year 10 maths shows how the GCSE content is printed in three typefaces, how weighting shifts towards algebra at Higher tier, and how to read a mock as a diagnosis.
  5. Year 11, the exam year. Year 11 maths lays out the June 2027 papers for all three English boards, the contingency day and results day, and what grade 4 means afterwards.

Key Stage 3 quietly turns arithmetic into algebra; the DfE's phrase is "use algebra to generalise the structure of arithmetic". A child who knows 7 + 5 = 5 + 7 is ready for a + b = b + a.

GCSE Maths has two tiers: AQA's 8300, for example, sets Foundation for grades 1 to 5 and Higher for grades 4 to 9. For all three KS3 years at once see KS3 maths tuition; for the boards side by side, our AQA, Edexcel and OCR comparison.

Scotland

How does maths work year by year in Scotland?

Scotland does not use year groups or key stages. It uses stages (P1 to P7, then S1 upwards) and Curriculum for Excellence levels, and there is no national maths exam before the senior phase.

In Scotland a child works through numeracy and mathematics at Early, First, Second, Third and Fourth level. Progress is reported at four stages, which also sit the online National Standardised Assessments.

Scottish stages, expected CfE level and numeracy results, 2024-25 (Scottish Government, Achievement of CfE Levels 2024-25, published 9 December 2025)
StageExpected levelNumeracy: share achieving it, 2024-25National Standardised Assessment
P1Early level85 per centYes, numeracy and literacy
P4First level78 per centYes
P7Second level79 per centYes
S3Third level or better91 per centYes
S3Fourth level68 per centSame assessment

Sources: Scottish Government, Achievement of CfE Levels 2024-25, chapter 1, tables 1 and 2; National Standardised Assessments for Scotland, parents and carers page and questions and answers page. All read on 1 November 2026.

Those percentages are "based on teachers' professional judgements", not on a test score, and the standardised assessments have no pass mark. The question-and-answer page for those assessments is blunt about it: "There is no pass or fail." Nor are the Benchmarks a tick list: Education Scotland says "They should not be ticked off individually for assessment purposes."

Primary in Scotland

Scottish primary maths tutoring covers P1 to P7, Early to Second level, and explains why there are no P7 maths past papers.

S1 to S3

S1 to S3 maths tutoring explains Third and Fourth level and why S3 shapes the S4 course. The exam itself is on our National 5 maths page.

One idea, five stages

How does one maths idea grow from Year 2 to GCSE?

Most topics return each year, deeper. Here is one thread of ours, three quarters, through the programmes of study.

  1. Year 2: a part of a whole. The Year 2 list includes finding thirds and quarters "of a length, shape, set of objects or quantity". Our question: three quarters of 8 sweets. Thinking: 4 equal groups of 2; 3 groups is 6.
  2. Year 4: a decimal. Year 4 asks children to "recognise and write decimal equivalents to" a quarter, a half and three quarters. Thinking (ours): a quarter of 100 hundredths is 25 hundredths, so three quarters is 0.75.
  3. Year 6: a percentage and a ratio. Year 6 expects pupils to "recall and use equivalences between simple fractions, decimals and percentages" and to solve "problems involving the relative sizes of two quantities". Our question: three quarters of a class walk to school; give the percentage and the ratio of walkers to the rest. Thinking: 75%, and 3 : 1.
  4. Key Stage 3: an operator above 100%. The KS3 programme asks pupils to "work with percentages greater than 100%" and to "interpret fractions and percentages as operators". Our question: a plant is 40 cm tall and grows to 175% of that height. How tall is it? Thinking: 175% is 1.75, so 40 × 1.75 = 70 cm.
  5. Key Stage 4: an exact value. At GCSE, higher-attaining students learn to "change recurring decimals into their corresponding fractions". Our question: show that 0.7575... (75 repeating) is 25/33. Thinking: let x = 0.7575...; then 100x = 75.7575...; subtracting gives 99x = 75, so x = 75/99 = 25/33.

A child who stalls at step four usually has a gap at step two. When Year 8 goes wrong, the fix is often a Year 4 idea, and the map shows where to look.

How to choose

How do you find the right year page for your child?

Five steps, in order.

  1. Confirm the school year, not just the age. gov.uk says "Most children start reception full-time in September after their fourth birthday." Our reading: a year group runs on birthdays from September to August.
  2. Check which nation's curriculum applies. The map on this page is England's. Scotland is above; Wales and Northern Ireland are not covered here.
  3. Find the next national check. A Year 3 child has the tables check next; a Year 9 student has GCSE two years out.
  4. Read the row before your child's row. If the previous year's headline content is not secure, start there.
  5. Then open the year page, or book a free class. A free class shows which row your child is really working at.

A worked example (ours). A child was born in March 2018. Which year are they in during 2026 to 2027, and which national check comes next? They turned 4 in March 2022, so under the gov.uk rule they started Reception in September 2022. Counting on one year each September gives Year 1 in 2023 to 2024, Year 2 in 2024 to 2025, Year 3 in 2025 to 2026 and Year 4 in 2026 to 2027. The Year 4 row carries the multiplication tables check, which the DfE lists in the two weeks from Monday 7 June 2027, so the pages to open are Year 4 and the tables check.

What is changing

Is the maths curriculum in England changing?

Yes, but not this school year.

The November 2025 government response says it will "publish the final revised national curriculum by spring 2027" and implement it "for first teaching from September 2028". For maths it promises to review Key Stages 1 to 3 "with a particular focus on resequencing content (particularly in the 'number' domain)", so some rows above may move. GCSEs are to be updated "for first teaching from 2029 onwards".

Announced changes and their timing (Government response to the Curriculum and Assessment Review, November 2025; DfE Primary assessments: future dates, October 2026)
ChangeTiming as publishedWho it affects first (our reading)
2026 to 2027 assessmentsUnchangedEvery year group this school year
Revised curriculum first taughtSeptember 2028Schools from that September
Year 8 maths progress check by schoolsExpectation announced; no start year in the text we readFuture Year 8 groups
Updated GCSEs first taught2029 onwardsYear 7 or below in 2026 to 2027, at the earliest

The last column is our arithmetic: a child in Year 8 now reaches Year 10 in September 2028 and sits GCSE on the current specification. On Year 8 itself the response says: "We will expect all schools to assess pupil progress in writing and maths in Year 8".

Stages

Four stages of school maths, and what each one asks

Our grouping of the twelve years into the four shifts we see most in class.

What a child should be able to show at the end of each stage (our summary of the programmes of study)
StageYearsWhat secure looks like
1. Count and composeReception to Year 2Place value to 100, bonds to 20 recalled, halves and quarters
2. CalculateYears 3 and 4Tables to 12 × 12, column methods, tenths and hundredths
3. ConnectYears 5 and 6Fraction, decimal and percentage as one amount; long methods; first ratio
4. GeneraliseYears 7 to 11Letters for any number; equations solved and checked; proportion

Stages, not ages

Families who teach at home may find our home education maths page useful for planning across stages.

Stage 4 is the long one

Students who reach it early can stretch with UKMT challenge tutoring.

Catalogue

Nine maths courses arranged by school stage

From first counting to GCSE, plus three for extra depth.

I

Early years and primary

Reception to Year 6

UK / YY1 / 01

Early Maths Foundations

Concrete, playful number for ages 4 to 7.

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UK / YY1 / 02

Elementary Maths

The primary years, strand by strand.

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UK / YY1 / 03

KS2 SATs Maths

The three Year 6 papers, taught calmly.

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II

Secondary

Year 7 to Year 11

UK / YY2 / 01

Middle School Maths

Key Stage 3 algebra, proportion and geometry.

Open the syllabus

UK / YY2 / 02

GCSE Maths

Foundation or Higher, any English board.

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UK / YY2 / 03

11 Plus Maths Prep

For families in selective areas, from Year 5.

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III

Beyond the year list

Depth and play

UK / YY3 / 01

Mental maths

Number sense without tricks, ages 5 to 10.

Open the syllabus

UK / YY3 / 02

Problem solving for kids

Puzzles that reward patient reasoning.

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UK / YY3 / 03

Maths through coding

Sequences and graphs explored in Python, ages 10 to 15.

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Lessons

How our maths classes run for any school year

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 are in India; slots are quoted in UK time.

After school

Common for primary children.

Evening

Often chosen by secondary students.

Weekend morning

Good for longer GCSE sessions.

Placed by strand

We find the row your child is really on for each strand before planning.

One year back first

Gaps from the previous year are closed before new content goes on top.

Free first class

One live class, no payment, and a plain view of where to start.

Group or 1-on-1

A same-stage group of 15 to 20, or a tutor for one child.

Student work

Work our students made in class

Ordinary class projects, unmarked. More in student labs.

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Fees

Fees for maths classes, Reception to Year 11

The first class is free. Then one monthly fee, lower in a group than 1-on-1, due only once a course and weekly slot are agreed. No contract.

Free first class

USD 0

no card required

  • A live class at your child's level
  • A check across the main strands
  • Booked with a phone number
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Group batch

USD 100

a month, billed in US dollars

  • 15 to 20 children at the same stage
  • One tutor across the year
  • Short practice between classes
  • A note to parents each term
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One to one

USD 150

a month, billed in US dollars

  • A tutor for one child
  • Planned around the next national check
  • Suited to closing earlier gaps
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Year-by-year questions

Questions parents ask about maths in each school year

What maths is taught in each year in the UK?

In England: numbers to 10 in Reception; place value to 100 and the first tables in Years 1 and 2; written methods and all tables to 12 × 12 in Years 3 and 4; large numbers, percentages, ratio and early algebra in Years 5 and 6; then Key Stages 3 and 4 towards GCSE.

Which year groups have maths tests in England?

Reception has the baseline assessment and the EYFS profile, Year 2 has optional KS1 tests, Year 4 has the multiplication tables check, Year 6 has the KS2 national tests and Year 11 sits GCSE Maths. The other years have no national maths test.

What age is each school year in England?

gov.uk lists Reception as 4 to 5, rising a year at a time to Year 11 at 15 to 16. Most children start Reception in the September after their fourth birthday.

When are the 2027 KS2 SATs and the times tables check?

The DfE lists the KS2 tests from Monday 10 May to Thursday 13 May 2027, with the maths papers on 12 and 13 May. The multiplication tables check runs in the two weeks from Monday 7 June 2027.

Are KS1 SATs still compulsory?

No. They are optional, and the STA recommends May 2027 for schools that use them.

Why is there no Year 7, 8 or 9 maths list?

Key Stage 3 is one programme for all three years, and each school decides the order.

Is there a Year 8 maths test now?

Not a national one. In November 2025 the government said it will expect schools to assess maths progress in Year 8; no start year has been given.

How is Scottish maths different from England?

Scotland uses stages (P1 to P7, then S1 upwards) and CfE levels from Early to Fourth. P1, P4, P7 and S3 take online assessments with no pass or fail.

When are your classes?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Every time is given in UK time.

Are you linked to the Department for Education or an exam board?

No. We are independent of the DfE, the STA, Education Scotland and every exam board, and we promise no grades.

Wider pages

Other maths pages for UK families

Pages that cover a whole key stage, a qualification or a different kind of test.

KS2 maths tuition

Four junior years seen as a single stretch.

KS3 maths tuition

The three-year programme from Year 7.

GCSE maths tuition

The qualification across every English board.

11+ maths tuition

Selective entry tests, which the year map leaves out.

National 5 maths

The first Scottish maths exam after S3.

Our UK hub

Every UK maths and coding page we run.

Every page in this guide

Primary, Reception to Year 6

Secondary, Year 7 to Year 11

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

Start here

Book a free maths class for any school year

Give the year group and a number; we ring at a UK time you pick. The class places your child on the map, strand by strand.

Prefer to read first? The Elementary Maths, Middle School Maths and GCSE Maths course pages list each syllabus, and how we teach describes the method.

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