Enrichment · Ages 9 to 16 · England, Scotland, Wales, Northern Ireland

Maths masterclasses for able students in the UK

A maths masterclass is a long, hands-on session on one idea that school maths never reaches. The best known in the UK are the Royal Institution Masterclasses, free six-week series that children join only when a teacher nominates them. Modern Age Coders is not part of the Ri. We teach masterclass-style enrichment maths live online, every week, through our olympiad and competition course, in a group or one to one. This page explains how the Ri series work, how places are given, what a session feels like, and gives two sample sessions and a practice set we wrote.

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Built from the Royal Institution and University of Oxford pages, read 31 October 2026 · Not connected with the Ri or any university

What are the Royal Institution Maths Masterclasses?

Ri Masterclasses are extracurricular workshops in mathematics or computer science run by the Royal Institution with regional volunteer groups across the UK. A series usually lasts six weeks in term time; secondary sessions tend to be 2.5 hours on Saturday mornings, and primary ones are shorter. They cost nothing, and a child attends only after a teacher nominates them and the Ri sends a letter of acceptance. The Ri says places are normally for 9 and 10 year olds and 13 and 14 year olds. Modern Age Coders has no link with the Ri; we teach the same kind of beyond-the-syllabus maths live online each week, through our competition maths course, in a batch of 15 to 20 or 1-on-1.

Where to begin

Three courses for a child who wants maths beyond the syllabus

Pick by age. Each card opens the full syllabus, so you can see the ideas we explore before booking.

Maths Olympiad & Competition Course course thumbnail

MAS / 01

Competition and enrichment maths

Proof, number theory, combinatorics and geometry, one rich problem at a time, for ages 11 to 16.

Open the syllabus →
Maths Through Coding course thumbnail

MAS / 02

Maths through coding

Python used to test a conjecture on thousands of cases, the way a computer science masterclass works, for ages 10 to 15.

Open the syllabus →
Reasoning and Readiness for Young Thinkers (Ages 6 to 9) course thumbnail

MAS / 03

Reasoning for young thinkers

Patterns, spatial puzzles and number sense for ages 6 to 9, the years before a primary masterclass.

Open the syllabus →

The Ri series

How do the Royal Institution Masterclasses work?

A series is a run of weekly workshops led by speakers from universities, schools and industry, organised locally by volunteers and coordinated by the Ri. Everything in the table comes from the Ri's own page.

Ri Masterclasses at a glance, from the Royal Institution page read on 31 October 2026
QuestionWhat the Ri says
What are they?Hands-on, interactive extracurricular workshops in mathematics or computer science
Who attends?Students a teacher nominates for an emerging interest in STEM; it is "normally available for 9/10 year old and 13/14 year old students", and some groups work with other ages
How long is a series?"Generally Ri Masterclass series run for six weeks, during term time"
How long is a session?Secondary sessions "tend to be 2.5 hours on Saturday mornings"; primary ones are usually shorter and often during or just after school hours
What does it cost?Nothing to attend
Can a parent apply?No. A teacher registers interest, and students "cannot attend Masterclasses unless they have a letter of acceptance from the Ri"
Is there an online version?Yes, for some: "online Masterclasses can be provided for state schools that cannot access nearby series"
Older students?Science communication projects and volunteering for students aged 16 and over

Where the idea came from

The Ri traces the programme to the televised CHRISTMAS LECTURES of 1978, titled "Mathematics into Pictures". Secondary mathematics masterclasses followed in 1981.

The Ri adds: "Mathematics Masterclasses for primary school students launched in 1998, and secondary school Computer Science Masterclasses launched in 2014. Engineering Masterclasses ran from 2010 to 2020."

Who makes a series happen

Each local series is run by volunteers and collaborators: school teachers, university staff and outreach specialists acting as organisers, supervisors, helpers and speakers. The Ri trains its speakers, and regular volunteers need a DBS check.

That model explains the rationing. A series exists only where a team has formed, and seats go to the schools that team can reach.

Our arithmetic from the Ri's figures: six Saturday sessions of about 2.5 hours give a secondary student roughly 15 hours of masterclass maths in a series. That is a rich block of time, and it is one block. Many families who search for masterclasses are really asking how to keep that kind of maths going for the other 46 weeks of the year.

Source: Royal Institution, Ri Masterclasses, read 31 October 2026. CHRISTMAS LECTURES is the Ri's registered trademark. The Royal Institution is an independent charity; we have no connection with it or with any local series.

Getting a place

How does a child get a place on a maths masterclass?

Through school. Neither a parent nor a pupil can sign up directly; the route runs from a regional organiser to a teacher and then to the Ri.

  1. Ahead of a series, a regional organiser sends nomination packs to the schools near it. A few London series are run by the Ri team itself.
  2. A teacher chooses a small group of students with an emerging interest in STEM, usually in Year 5 or 6 at primary age, or Year 9 or 10 at secondary age, and returns the nomination.
  3. The Ri, or the local group, confirms places with a letter of acceptance. Without it a child cannot attend.
  4. If a school has never received a pack, the Ri asks the teacher, not the parent, to email and register interest on behalf of the school.
  5. Where no series runs nearby, the Ri can discuss starting one, and state schools that cannot reach a series may be offered online masterclasses.

A university series works the same way

The University of Oxford's Mathematical Institute runs Oxfordshire Mathematics Masterclasses for Years 9 to 11. Teachers at local state schools receive a pack each October asking them to nominate Year 9 students, and the classes run on Saturdays in the spring, usually January to March.

Oxford adds that "Participants are then invited back in Year 10 and Year 11", so one nomination can lead to three springs of sessions.

If your child was not chosen

Nominations are a teacher's judgement about a handful of places, often two to six per school, and they say nothing final about a child. A pupil who loves maths and was not picked this year is in very good company.

Ask the maths department whether the school receives packs at all, and whether a computer science series runs nearby. Meanwhile the ideas themselves are open to anyone, and the practice set below is a fair start.

The "two to six" figure is our own rough estimate of how many pupils a school usually puts forward, not a number the Ri publishes. For a pupil who prefers a competition route, our maths olympiad training guide sets out the UKMT ladder, which any pupil can enter through school.

Sources: Royal Institution, Ri Masterclasses; University of Oxford, Oxfordshire Mathematics Masterclasses (page last updated 3 February 2026). Both read 31 October 2026.

Inside a session

What happens in a maths masterclass session?

A speaker poses one question, the room experiments in pairs, a pattern appears, and the last half hour asks whether the pattern is really true. Below are two sessions in that style, written by us; neither is an Ri session.

Sample session for ages 13 to 14 (ours): count the corners

Start with solids the class can hold. A cube has 8 corners, 12 edges and 6 faces. A square-based pyramid has 5, 8 and 5. A triangular prism has 6, 9 and 5. Ask the room to find one calculation that gives the same answer for all three. Someone always finds it: corners minus edges plus faces is 2 every time, since 8 minus 12 plus 6, 5 minus 8 plus 5 and 6 minus 9 plus 5 all make 2.

This is Euler's formula. The second hour tries to break it. Build a square picture frame from four bevelled bars: it has 16 corners, 32 edges and 16 faces, and 16 minus 32 plus 16 is 0. The formula fails because the frame has a hole. Now the pupils have discovered something real: the number depends on the shape's holes, not its size.

Sample session for ages 9 to 10 (ours): the five mind-reading cards

Write the numbers 1 to 31 on five cards. Card A holds every number whose binary form has a 1 in the ones place, card B the twos place, then fours, eights and sixteens. A child picks a secret number and says which cards show it. Add the smallest number on each of those cards and the secret appears.

If the cards are the 16, 4 and 2 cards, the number is 22. The session then asks why it works, and the children rebuild binary from scratch: every number is a sum of different powers of two in exactly one way. A computer science masterclass in miniature, with paper only.

Euler's count for five solids, our worked table
SolidCornersEdgesFacesCorners minus edges plus faces
Tetrahedron4642
Cube81262
Square-based pyramid5852
Triangular prism6952
Square picture frame1632160

Notice what is missing from both sessions: no exam technique, no worksheet of twenty similar questions, no mark scheme. That is the defining feature of masterclass maths, and it is why a child who finds school maths easy can still find a masterclass hard. The national curriculum for England asks for exactly this kind of stretch, saying that pupils who grasp concepts quickly should meet rich and sophisticated problems before they are accelerated through new content.

Both sessions, the frame count and the table are ours. Curriculum wording from National curriculum in England: mathematics programmes of study.

Practice set

Masterclass-style problems to try at home

Six problems we wrote, each with the reasoning a speaker would draw out. Try each for ten minutes before reading the answer; the struggle is the point.

1. Handshakes (ages 9 and up)

Eight people each shake hands once with everyone else. How many handshakes? Each person shakes 7 hands, giving 56, but that counts every handshake twice, so 28. Ask what happens with 100 people: 100 times 99 halved, 4,950.

2. The painted cube (ages 9 and up)

Paint a 3 by 3 by 3 cube, then cut it into 27 small cubes. How many have paint on exactly two faces? One in the middle of each of the 12 edges, so 12. Then 8 corners, 6 face centres and 1 hidden cube make up the rest.

3. Last digits (ages 11 and up)

What is the last digit of 7 to the power 100? Powers of 7 end 7, 9, 3, 1 and then repeat every four. 100 is a multiple of 4, so the last digit is 1. A cycle turned a huge number into a tiny one.

4. Chessboard squares (ages 11 and up)

How many squares of any size are on a chessboard? 64 small ones, 49 of size 2, 36 of size 3, down to 1 of size 8. The sum of the first eight square numbers is 204. Most people guess 64.

5. Odd sums (ages 12 and up)

Add the first few odd numbers: 1, then 1 plus 3 is 4, then 9, then 16. Every total is a square. Draw it: each new odd number wraps an L shape around the previous square. A picture becomes a proof.

6. Domino tiling (ages 13 and up)

Remove two opposite corners from a chessboard. Can 31 dominoes cover the rest? No. Each domino covers one black and one white square, but the two removed corners share a colour, leaving 32 of one colour and 30 of the other.

In our lessons each of these becomes a full session: the first answer is the start, and the rest of the hour is spent on the general case, a written explanation and a harder cousin of the problem. Pupils keep a notebook of the patterns they found and the arguments that made them certain, which is a habit university mathematicians recognise.

All six problems, answers and explanations are written by Modern Age Coders. None is taken from an Ri, UKMT or university resource.

Choosing a route

Masterclass, olympiad or weekly class: which suits an able child?

They do different jobs, and many keen pupils do more than one. The table gives the facts and our view of who each suits; the choice is yours.

Three kinds of maths enrichment in the UK, facts from each organiser and our own judgements
Ri Masterclass seriesUKMT challenges and olympiadsWeekly online enrichment (ours)
EntryTeacher nomination and Ri letterEntered through school; olympiads by qualifying scoreBook a free first lesson
AgesUsually 9 to 10 and 13 to 14Primary to sixth form, by paper6 to 18, by course
RhythmSix weeks, once a yearOne paper at a time, set datesEvery week, all year
FeelExploration, no assessmentTimed problems, written proof at olympiad levelExploration plus written explanations
Who it suits (our view)Any curious child lucky enough to be nominatedA pupil who enjoys a hard testA pupil who wants this kind of maths to be regular

Take the masterclass if offered

If your child is nominated, say yes. Meeting a working mathematician in a room full of other keen pupils is worth a great deal, and the series costs nothing.

Nothing we teach replaces that, and we would never suggest a family turn down a place for our lessons.

Where a weekly class fits

Before a nomination, between series, or where none runs nearby. It also suits pupils who need longer than one Saturday to get comfortable with open problems, and those who want to write up their reasoning and have it read every week.

Our junior olympiad page and team challenge page cover the competition side in detail.

Stages

Four stages from curious to independent

Our stages for enrichment maths, matched loosely to the two ages the Ri usually works with.

Our enrichment stages
StageAgesSecure when
1. Notice6 to 9Spots a pattern and says it aloud before being asked
2. Test9 to 11Checks a guess on several cases and tries to break it
3. Explain11 to 14Writes why a pattern holds, in full sentences
4. Extend14 to 16Asks the next question unprompted and generalises

Why the stages are about habits

Masterclass topics change every week, so content is a poor ladder. The habits underneath, noticing, testing, explaining and extending, are what carry over.

We place children by which habit is secure, not by school year.

Where it leads

At sixth-form age the same habits feed into university admissions maths; see our STEP preparation page.

For computing, the British Informatics Olympiad rewards the same patience.

All related courses

Courses for able and curious pupils

Grouped by age. Every card opens a syllabus with the topics in order.

I

Primary

Ages 6 to 11

UK / MAS / 01

Reasoning for young thinkers

Pattern, shape and number puzzles for ages 6 to 9.

Open the syllabus

UK / MAS / 02

Mental maths for kids

Number sense that makes bigger ideas reachable.

Open the syllabus

UK / MAS / 03

Coding for kids

Scratch projects with logic at their heart.

Open the syllabus
II

Lower secondary

Ages 11 to 14

UK / MAS / 04

Competition and enrichment maths

Rich problems, then the written argument.

Open the syllabus

UK / MAS / 05

Maths through coding

Test a conjecture on a thousand cases in Python.

Open the syllabus

UK / MAS / 06

Junior competitions

Kangaroo-style problems for ages 11 to 14.

Open the syllabus
III

Upper secondary

Ages 14 to 18

UK / MAS / 07

Problem solving for teens

Logic and algorithms, the computing side.

Open the syllabus

UK / MAS / 08

TMUA and STEP preparation

University admissions maths at sixth form.

Open the syllabus

How lessons run

One big idea a week, online

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Lessons are booked in UK time; our teachers work from India, which is four and a half hours ahead of UK time in British summer and five and a half in winter.

After school

Group sessions for ages 9 to 14.

Saturday morning

The masterclass hour, for those who like it.

Any agreed time

1-on-1 sessions planned around your week.

Question first

Every session opens on a problem, never on a method to copy.

Pairs, then the room

Pupils try in pairs on screen before ideas are shared.

A written ending

Each session closes with a short written explanation.

Read and returned

The teacher comments on that explanation before next week.

Group or 1-on-1

A batch of 15 to 20 or a teacher for one pupil.

Code when it helps

Python tests patterns on more cases than paper allows.

Student work

What our students have built

Maths and code projects from children in our classes. More in student labs.

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Fees

Fees for enrichment maths

One monthly fee, shown in the currency we use for UK families, with no term to sign up for. The first lesson costs nothing, so a child can see whether open-ended maths suits them.

Free first class

USD 0

no card required

  • A sample session on one big idea
  • Our view of the right stage
  • A phone number is all we ask
Book it

Group batch

USD 100

a month, billed in US dollars

  • 15 to 20 pupils of a similar stage
  • One problem explored each week
  • Written explanations read and returned
  • Same teacher through the year
Start here

One to one

USD 150

a month, billed in US dollars

  • One pupil and one teacher
  • Topics chosen around the pupil
  • Pace set by the pupil
Enquire

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Masterclass questions

What parents ask about maths masterclasses

What are Royal Institution maths masterclasses?

Series of extracurricular workshops in mathematics or computer science, coordinated by the Royal Institution and run by volunteer groups across the UK. A series generally lasts six weeks in term time, and they are free to attend.

How do you get into Royal Institution masterclasses?

Through a teacher. Regional organisers send nomination packs to schools, a teacher nominates a small group, and the Ri confirms with a letter of acceptance. Parents and pupils cannot apply directly; if your school has never had a pack, ask a teacher to email the Ri.

What age are Ri masterclasses for?

The Ri says they are normally for 9 and 10 year olds and 13 and 14 year olds, with some groups working with other ages. Older students aged 16 and over can join science communication projects or volunteer.

Are there primary maths masterclasses?

Yes. The Ri launched primary mathematics masterclasses in 1998. Primary sessions are usually shorter than secondary ones and are often held during or just after school hours, though some run on Saturdays.

How long is each masterclass?

The Ri says secondary sessions tend to be 2.5 hours on Saturday mornings, over a series of about six weeks. By our arithmetic that is roughly 15 hours of masterclass maths in one series.

Are there online maths masterclasses?

The Ri says online masterclasses can be provided for state schools that cannot reach a nearby series, again arranged through the school. Separately, our own weekly online lessons are open to any family and are not Ri masterclasses.

Is there a computer science masterclass?

Yes. The Ri launched secondary computer science masterclasses in 2014, alongside the mathematics series. Ask your school which subjects the nearest series offers.

My child was not nominated. What now?

Places are few and a nomination is one teacher's choice in one year, so it is not a verdict on ability. Ask whether the school receives packs at all, try the practice set on this page, and consider UKMT challenges or a weekly enrichment class.

Are you part of the Royal Institution?

No. Modern Age Coders is an independent online school with no link to the Royal Institution, any local masterclass group or any university. We teach maths in a similar spirit, and we say so plainly.

When do your lessons run?

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 given in UK time.

Related pages

More stretch for keen young mathematicians

Competitions, olympiads and the computing side.

Maths olympiad training

The full UKMT ladder in one place.

Junior Mathematical Olympiad

The first written-proof paper, for Year 8 and below.

UKMT Kangaroo rounds

The multiple-choice follow-on papers.

Maths tuition in London

Where the masterclass story began.

British Informatics Olympiad

Problem solving with code.

Coding classes in the UK

Every UK page from one hub.

Related pages in this guide

Part of the guide: UK maths enrichment, competitions and able pupils

Enrichment and able pupils

Maths competitions

Computing programmes and competitions

More guides: UK maths exam boards and specification codes · UK maths year by year, Reception to Year 11 · UK selective school maths tests: 7+, 11+, 13+ and 16+ · UK university admissions: maths tests and computing applications

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Tell us your child's age and what kind of maths lights them up. We run one session on a single big idea and then suggest a stage and a group.

Want to look first? Each course page lists its topics in order, and how we teach sets out our method in plain words.

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