--- title: "Online Maths Circle UK: University Clubs and a Weekly Circle" description: "Online maths circles in the UK: what a circle is, the free Oxford, Cambridge and King's programmes and who can join, plus a weekly circle-style class online." canonical: https://learn.modernagecoders.com/online-maths-circle-uk source: src/pages/online-maths-circle-uk.html --- > Online maths circles in the UK: what a circle is, the free Oxford, Cambridge and King's programmes and who can join, plus a weekly circle-style class online. What is a maths circle, and can my child join one online in the UK? King's College London Mathematics School, which runs the Axiom circles, defines a maths circle as "a group of students who come together to grapple with intriguing puzzles, discover and explore exciting ideas and learn to think like mathematicians." UK pupils can join several free, partly online programmes: Axiom maths circles from Year 7, with places prioritised by published criteria; the University of Oxford's Online Maths Club, a weekly Thursday livestream open to all; and Cambridge's STEP Support Programme, free online modules for sixth formers. Modern Age Coders, which has no link to any of them, runs a weekly online circle-style class for ages 10 to 18 on our competition maths course, with groups of 15 to 20 pupils or a private teacher. Where to begin ## Three courses that run like a circle Each card opens a syllabus of problem themes rather than exam topics. [![Maths Olympiad & Competition Course course thumbnail](/images/olympiad-competition-maths.webp) CU / 01 The weekly maths circle Number theory, counting, geometry and proof, a long problem at a time, for ages 11 to 18. Open the syllabus →](/courses/olympiad-competition-mathematics-mastery)[![Maths Through Coding course thumbnail](/images/maths-through-coding.webp) CU / 02 Circle problems with code Python to test a conjecture on thousands of cases before proving it, for ages 10 to 15. Open the syllabus →](/courses/maths-through-coding)[![TMUA and STEP Preparation (Oxford MAT Now TMUA) course thumbnail](/images/tmua-mat-step-prep.webp) CU / 03 Sixth-form problem solving The circle habit turned towards TMUA and STEP for students applying to read maths. Open the syllabus →](/courses/tmua-mat-step-preparation-course) What a circle is ## What is a maths circle? A circle is a community and a pace, not a course. The same pupils meet week after week, a problem may stay on the table for a month, and nobody is graded. ### Three things that make a circle Continuity. The Axiom page puts it plainly: "Axiom is a long-term programme and students who join in year 7 will be guaranteed a place on the programme for their entire school journey." A circle builds over years. Open problems. Questions are chosen because they lead somewhere, not because they appear on a paper. Peers. Pupils talk to each other more than to the leader, and the leader asks rather than tells. ### How it differs from a class or a club A tuition class moves through a syllabus and checks progress. A school maths club often runs puzzles that end in a session. A masterclass series is a short, intense block. A circle is slow on purpose: ideas get time to go wrong and come back. King's says the pupils who most enjoy its circles "are high-attainers who love problem-solving and imaginative, creative thinking", which is a description of temperament as much as attainment. | | Tuition class | Masterclass series | Maths circle | | --- | --- | --- | --- | | Time horizon | A term or an exam | Six weeks or so | Years | | What sets the agenda | The syllabus | The speaker | The problem and the group | | Assessment | Regular | None | None, but written explanations | | One problem can last | Minutes | A session | Several weeks | Quotations from [King's College London Mathematics School, Axiom maths circle](https://www.kingsmathsschool.com/outreach/axiom-maths-circle), read 31 October 2026. The comparison table is ours. Our [maths masterclasses page](/maths-masterclasses-for-able-students-uk) covers the Royal Institution series. UK programmes ## Which maths circles and university programmes can UK pupils join online? Several, and most are free, but each has a stage and an entry rule. This table is built from each organiser's own page; check the page before applying, since rules change. | Programme and organiser | Stage | Format | Who can join | | --- | --- | --- | --- | | Axiom maths circles, King's College London Mathematics School | From Year 7, for the whole school journey | Some online, some in person; Mondays and Thursdays 16:30 to 17:30, all year | Places prioritised under widening-participation criteria the school publishes | | GCSE+ Maths, King's College London Mathematics School | Years 9 to 11 | "An extensive programme of enrichment" | Apply through the school's outreach pages | | Oxford Online Maths Club, University of Oxford | Mainly sixth form | Weekly livestream, Thursdays at 5pm UK time, recorded | Everyone; "there's no registration needed" | | Problem Solving Matters, University of Oxford with MEI | Year 12 | A course in problem-solving mathematics | State-funded schools and colleges; home-educated students welcomed | | STEP Support Programme, University of Cambridge | Year 12 and Year 13 | Free online modules with hints and solutions | "The resources are free and open to everyone." | | NRICH, University of Cambridge | Primary and secondary | Free problems online; Maths Club webinars | Open online | ### The year at the Oxford club Oxford describes its club as "free, interactive, casual, and relaxed". From January to June it covers super-curricular maths; from June to December it hosts the Oxford Maths Admissions Test Livestream, which in 2026 focuses on the TMUA and maths interviews. It is "mostly aimed at people about to apply to university or about to start a Maths course", so a Year 8 pupil will find much of it hard, but the recordings can be watched at any pace. ### The dates King's has published King's outreach page for autumn 2026 says Axiom Maths Circles and GCSE+ Maths sessions continue from the week beginning 21 September 2026, with Extension Mathematics: University Admissions Prep from 7 September 2026. King's says all its student events are free. Places on the long-term circles are limited, and the school sets out who is prioritised. The pattern across the table is plain. Free circles exist, but the ones aimed at younger pupils are few and rationed, while the open-to-all programmes lean towards sixth form and university admissions. A curious Year 6 to Year 10 pupil outside the priority groups is the child most likely to find no circle at all, and that is the gap our weekly class is built for. For the sixth-form end, our [STEP preparation page](/step-maths-preparation) goes further. Sources: [King's Maths School outreach](https://www.kingsmathsschool.com/outreach); [Oxford Online Maths Club](https://www.maths.ox.ac.uk/outreach/oxford-online-maths-club); [Oxford, Problem Solving Matters](https://www.maths.ox.ac.uk/outreach/problem-solving-matters); [STEP Support Programme](https://step.maths.org/); [NRICH](https://nrich.maths.org/). All read 31 October 2026. We are not connected with any of them. A three-week arc ## What does one problem look like across three circle sessions? Here is a circle arc we wrote and run, for ages 11 to 15. It is ours, not taken from any programme above. The problem fits on one line; the thinking fills three weeks. **The question.** A post office sells only 3p and 5p stamps. Which postage amounts can you not make exactly? ### Week 1: explore Pupils list amounts from 1p upwards. 3, 5, 6, 8, 9 and 10 work; 1, 2, 4 and 7 do not. From 8 onwards every amount works, because 8, 9 and 10 do, and adding a 3p stamp reaches the next three. The largest impossible amount is 7. ### Week 2: conjecture Change the stamps to 4p and 7p and the largest impossible amount is 17. With 2p and 5p it is 3. Someone notices that 3 times 5 minus 3 minus 5 is 7, 4 times 7 minus 4 minus 7 is 17, and 2 times 5 minus 2 minus 5 is 3. The circle has a conjecture. ### Week 3: test and explain Does it always work? Try 4p and 6p: every odd amount is impossible, so there is no largest one. The rule needs stamps with no common factor. The session ends on why the formula holds for such pairs, written in pupils' own words. ***Our check: the largest impossible postage for two stamp values**Python* ``` def largest_impossible(a, b, limit=200): can = [False] * (limit + 1) can[0] = True for n in range(1, limit + 1): can[n] = (n >= a and can[n - a]) or (n >= b and can[n - b]) missing = [n for n in range(limit + 1) if not can[n]] return missing[-1] if missing else None for a, b in [(3, 5), (4, 7), (2, 5), (5, 8)]: print(a, b, largest_impossible(a, b), a * b - a - b) ``` Run it and each line prints two equal numbers: 7, 17, 3 and 27. The code does not prove the rule, and a good circle says so out loud; it only makes the conjecture worth proving. That distinction, between evidence and proof, is the most valuable thing a circle teaches, and it takes weeks rather than minutes to sink in. The problem framing, the three-week plan, the code and the outputs are ours. The underlying result is a classical one in number theory, often called the Frobenius coin problem for two values. Problems ## Circle problems to start at home Five problems we wrote, each one able to fill a session. Answers and the key idea follow each; resist reading them for at least a quarter of an hour. ### A. Locker doors (ages 10 and up) A corridor has 100 closed lockers. Pupil 1 opens all of them; pupil 2 toggles every second; pupil 3 every third; and so on to pupil 100. Which stay open? Exactly the square numbers, 1, 4, 9 up to 100: only squares have an odd number of factors. ### B. Staircase sums (ages 11 and up) Which numbers are a sum of two or more consecutive whole numbers? 9 is 4 plus 5, and 10 is 1 plus 2 plus 3 plus 4. Test up to 32. The ones that fail are 1, 2, 4, 8, 16 and 32: the powers of two. ### C. Knight's reach (ages 11 and up) On an endless chessboard, what is the fewest knight moves to reach the square one step to the right? Three. Each knight move changes the square colour, so an odd number is needed, and one move cannot do it. ### D. Cutting a cake (ages 12 and up) Three cuts across a round cake: what is the most pieces you can make? Seven. With n straight cuts the maximum is 1 plus n times n plus 1 over 2, so 2 cuts give 4 and 4 cuts give 11. The circle conversation is why each new cut adds one more piece than the cut before it. ### E. Digit reversal (ages 12 and up) Take any three-digit number with different first and last digits, reverse it, and subtract the smaller from the larger: 742 minus 247 is 495. The answer is always a multiple of 99. Write the number as 100a plus 10b plus c, and the difference is 99 times the gap between a and c. All five problems and explanations are written by Modern Age Coders and are not taken from Axiom, NRICH, STEP Support or any other programme. Choosing well ## How do you tell a good online maths circle from a tuition class with a new name? Ask five questions. A real circle, free or paid, should answer yes to most of them. 1. Does one problem ever last more than one session? 2. Do pupils speak to each other during the session, not only to the leader? 3. Is there no test, no grade and no homework sheet of similar questions? 4. Are pupils asked to write explanations, and does someone read them? 5. Does the same group meet for months, so pupils know each other's ideas? ### Free first, if your child qualifies If your child fits the stage and entry rules of a free programme in the table, apply. A long-term free circle with a university or a specialist school behind it is a fine thing to be part of. Our class is for the many pupils who do not fit those rules, or want an extra weekly session alongside. ### What our circle adds A fixed weekly time with the same pupils and teacher, ages from 10, and a teacher who reads every written explanation and returns comments before the next session. Sixth formers who want the same habits aimed at admissions can move on to our [BMO](/british-mathematical-olympiad-bmo-preparation) or STEP preparation. Stages ## Four stages in a circle Our stages; pupils move up when the habit, not the topic, is secure. | Stage | Typical age | Secure when | | --- | --- | --- | | 1. Explorer | 10 to 12 | Lists cases carefully and spots when a list is complete | | 2. Conjecturer | 11 to 14 | States a pattern precisely and tries to break it | | 3. Explainer | 13 to 16 | Writes a convincing argument a classmate can follow | | 4. Problem poser | 15 to 18 | Invents the next question and leads part of a session | ### Mixed ages work Circles mix ages comfortably because the problems have many entry points. We group by stage, so a confident 11-year-old may sit with 13-year-olds. ### Competition as a side effect Circle pupils often enjoy the [UKMT olympiad ladder](/maths-olympiad-training-uk), but we never turn a circle into exam practice. The competition route has its own pages. All related courses ## Courses for circle-minded pupils Grouped by stage, each with a full syllabus. I ### Starting out Ages 6 to 11 UK / CU / 01 #### Reasoning for young thinkers Pattern and spatial play, ages 6 to 9. [Open the syllabus](/courses/reasoning-and-readiness-course-for-young-thinkers) UK / CU / 02 #### Mental maths for kids The number fluency that circle problems lean on. [Open the syllabus](/courses/mental-maths-mastery-kids)II ### The circle years Ages 10 to 16 UK / CU / 03 #### Weekly maths circle Long problems, written explanations. [Open the syllabus](/courses/olympiad-competition-mathematics-mastery) UK / CU / 04 #### Circle problems with code Evidence by Python, proof by hand. [Open the syllabus](/courses/maths-through-coding) UK / CU / 05 #### Junior competitions For pupils who like a timed challenge too. [Open the syllabus](/courses/middle-school-math-competitions-course)III ### Sixth form Ages 16 to 18 UK / CU / 06 #### TMUA and STEP preparation Admissions problem solving. [Open the syllabus](/courses/tmua-mat-step-preparation-course) UK / CU / 07 #### A level Further Maths The content behind harder problems. [Open the syllabus](/courses/a-level-further-maths-course) UK / CU / 08 #### Algorithmic problem solving The computing cousin of a circle. [Open the syllabus](/courses/problem-solving-dsa-masterclass-teens) How our circle runs ## The same group, the same time, every week Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. Times are set in UK time. Our teachers work from India, so their working day overlaps the UK afternoon and evening comfortably. Weekday after school Circle groups for ages 10 to 15. Weekday evening Sixth-form problem solving. Weekend morning Circles and 1-on-1 sessions. ### One problem, many weeks A problem stays open until the group can explain it. ### Breakout pairs Pupils think in pairs on screen before the whole group meets. ### A shared board Every idea goes up where everyone can see and test it. ### Written follow-up A short explanation after each arc, read and commented on. ### Stable groups 15 to 20 pupils who stay together, or 1-on-1. ### Code as a lab Python tests a conjecture when hand cases run out. Student work ## Built by students in our classes Maths and code projects from our learners. See more in [student labs](/student-labs). ![NutriLife AI nutrition coach project screenshot](/images/projects/nutrilife.webp) AI and ML #### NutriLife An AI nutrition coach that reads what you eat and works you toward a target. by Bhavya · [Open it](https://nutrilife-bhavya.lovable.app) ![Misti AI chatbot for maths and coding screenshot](/images/projects/misti.webp) AI and ML #### Misti A chatbot that answers mathematics and programming questions, built and deployed by a student. by Harshit · [Open it](https://misti.modernagecoders.com) ![GuardianX AI internet safety assistant screenshot](/images/projects/guardianx.webp) AI and ML #### GuardianX An assistant that helps a young person recognise unsafe situations online. by Vivaan · [Open it](https://guardianx-cybersaver.lovable.app) ![SkyCast weather forecast application screenshot](/images/projects/skycast.webp) Web app #### SkyCast A weather forecasting site with live conditions for any location. by Krish Fees ## Fees for the online circle A single monthly fee, priced for UK learners, with no contract for the year, so a pupil can try the circle for a month and decide. The first session is free. Free first class USD 0 no card required - A full circle session - A suggested stage and group - Booked with a phone number only Book it Group batch USD 100 a month, billed in US dollars - 15 to 20 pupils at one stage - A long problem each few weeks - Explanations read and returned - The same teacher all year Start here One to one USD 150 a month, billed in US dollars - One pupil, one teacher - Problems chosen for the pupil - Ideal for a pupil far ahead of peers Enquire What families say ## Rated 4.9 across 547 Google reviews Family reviews from our Google profile, word for word. ★★★★★ "The one step solution for my son. Modern Age Coders make learning coding so simple that kids love it. The teachers explain complex concepts clearly with practical exercises and interactive content." Ria Mukherjee Parent ★★★★★ "Modern Age Coders has been a game-changer for me. I struggled to grasp IT concepts and coding before joining, but their classes transformed everything. I can now confidently write complex programs with ease." Samriddha Mondal Student ★★★★★ "One of the most wonderful education centres out there. Education is not limited to school syllabus but focuses on skill development." Vansh Agarwal Student ★★★★★ "My child Dhairya is really enjoying the Modern Age Coders classes. This is his first online class and he eagerly looks forward to it. I can already see his improvement, and the teachers are very cooperative." Sonam Oswal Parent of Dhairya ★★★★★ "Modern Age Coders have wonderful teachers who teach in a clear, easy and practical way. The teacher boosts students' confidence and inspires them to learn without hesitation." Sonu Goyal Parent ★★★★★ "I highly recommend this computer coding class! The teachers are incredibly knowledgeable and passionate about coding." Ritu Kedia Parent Maths circle questions ## What families ask about maths circles ### What is a maths circle? A small group that meets regularly to work on rich problems with no syllabus and no grades, often staying on one problem for weeks. King's College London Mathematics School describes its Axiom circles as students coming together to grapple with puzzles and learn to think like mathematicians. ### Are there maths circles in the UK? Yes. The Axiom circles run by King's College London Mathematics School are a long-term programme from Year 7, partly online. University outreach such as the Oxford Online Maths Club and Cambridge's STEP Support Programme works in a similar spirit for older pupils. ### Can my child join a maths circle online? Some free programmes run online, but most have an age range or priority rules. The Oxford Online Maths Club needs no registration and suits sixth formers best. Our own weekly circle runs online for ages 10 to 18 and is open to any family. ### Is the Oxford Online Maths Club free? Yes. Oxford says it is free, needs no registration and is recorded. It streams on Thursdays at 5pm UK time, and from June to December it hosts the Oxford Maths Admissions Test Livestream, which now focuses on the TMUA. ### Who gets a place on Axiom maths circles? King's says a pupil who joins in Year 7 keeps a place for their whole school journey. Places are prioritised for students who meet the widening-participation criteria the school publishes on its Axiom page, so read that page before applying. ### What age should a child start a maths circle? Many circles start around age 10 or 11, the Year 6 to Year 7 point, once a child can explain their thinking in words. Younger children do well with reasoning and puzzle lessons first. ### Is a maths circle the same as olympiad training? No. Olympiad training works towards a paper on a fixed date. A circle has no paper at all, although circle pupils often enjoy olympiads because they are used to long, unfamiliar problems. ### Is STEP Support a circle? Not quite. The STEP Support Programme is free online modules, designed to be studied weekly over about six months from Year 12, with hints and full solutions. Working through it with friends gives it some of a circle's feel. ### Are you connected with Oxford, Cambridge or King's? No. We run our own classes and answer to no university or school. We describe these programmes from their own pages so families can find them, and we have no link with any of them. ### When does your circle meet? 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. Related pages ## More enrichment for keen mathematicians Masterclasses, competitions and admissions maths. ### [Maths masterclasses](/maths-masterclasses-for-able-students-uk) The Royal Institution series and how places work. ### [Maths olympiad training](/maths-olympiad-training-uk) The UKMT ladder from junior to British olympiad. ### [STEP preparation](/step-maths-preparation) Sixth Term Examination Papers in detail. ### [Team Maths Challenge](/ukmt-team-maths-challenge-practice) Maths as a team sport. ### [Maths tuition in Oxford](/maths-tuition-in-oxford) Local options around the university city. ### [Coding classes in the UK](/coding-classes-in-united-kingdom) All our UK pages. ## Related pages in this guide Part of the guide: [UK maths enrichment, competitions and able pupils](/uk-maths-enrichment-and-competitions-guide) ### Enrichment and able pupils - [Online maths summer school](/online-maths-summer-school-uk) - [Maths masterclasses for able students](/maths-masterclasses-for-able-students-uk) - [Gifted and talented maths and coding](/gifted-and-talented-maths-and-coding-uk) - [Maths for home-educated children](/maths-for-home-educated-children-uk) - [Duke of Edinburgh Skills section coding](/duke-of-edinburgh-skills-section-coding) ### Maths competitions - [Maths olympiad training in the UK](/maths-olympiad-training-uk) - [Primary Maths Challenge practice](/primary-maths-challenge-practice) - [UKMT Kangaroo rounds practice](/ukmt-kangaroo-rounds-practice) - [UKMT Team Maths Challenge practice](/ukmt-team-maths-challenge-practice) - [Junior Mathematical Olympiad preparation](/junior-mathematical-olympiad-preparation) - [Cayley, Hamilton and Maclaurin olympiad preparation](/intermediate-mathematical-olympiad-cayley-hamilton-maclaurin-preparation) - [British Mathematical Olympiad preparation](/british-mathematical-olympiad-bmo-preparation) - [Mathematical Olympiad for Girls preparation](/mathematical-olympiad-for-girls-preparation) - [Scottish Mathematical Challenge practice](/scottish-mathematical-challenge-practice) ### Computing programmes and competitions - [CyberFirst courses and bursary](/cyberfirst-courses-and-bursary-preparation) - [CyberFirst Girls Competition preparation](/cyberfirst-girls-competition-preparation) - [UK Bebras Challenge practice](/bebras-computational-thinking-challenge-practice-uk) - [British Informatics Olympiad preparation](/british-informatics-olympiad-preparation) - [KS1 coding lessons online](/ks1-coding-lessons-online) - [UK coding, maths and AI competitions calendar](/uk-coding-maths-and-ai-competitions-calendar) More guides: [UK maths exam boards and specification codes](/uk-maths-exam-boards-and-specification-codes) · [UK maths year by year, Reception to Year 11](/uk-maths-year-by-year-guide) · [UK selective school maths tests: 7+, 11+, 13+ and 16+](/uk-selective-school-maths-tests-guide) · [UK university admissions: maths tests and computing applications](/uk-university-admissions-maths-and-computing-guide) Start here ## Try a circle session free Share how old your child is and a problem they enjoyed. We place them in a circle session, then suggest the group that fits. Prefer to read first? Every [course page](/courses) lists its problem themes, and [how we teach](/how-we-teach) describes our sessions. [WhatsApp us](https://wa.me/919123366161?text=Hello%20Modern%20Age%20Coders%2C%20I%20would%20like%20to%20try%20your%20online%20maths%20circle.) · [+91 91233 66161](tel:+919123366161) · [connect@modernagecoders.com](mailto:connect@modernagecoders.com) WhatsApp is the fastest route to us. We answer from India on a +91 number. ### Want a class sooner? Book a priority demo A priority demo is a full class of about 45 to 60 minutes. After the class the mentor sends a written skill report and a personal learning roadmap on WhatsApp. If you enrol, the demo fee is adjusted against your first month's fee. Share your demo Order ID with us on WhatsApp and we take it off. [Book a priority demo](/book-demo) ## Keep exploring Modern Age Coders ### More maths tuition - [Online Maths Classes for Adults in the UK](/online-maths-classes-for-adults-in-uk) - [Online Coding Tutor UK](/online-coding-tutor-uk) - [OCR MEI A Level Maths H640 Help: Comprehension Paper](/ocr-mei-a-level-maths-h640-help) - [Online Maths Tuition for College & Sixth Form in the UK](/online-maths-tuition-for-college-students-in-uk) - [OCR GCSE Maths J560 Help](/ocr-gcse-maths-j560-help) - [Online Maths Tuition for Kids in the UK](/online-maths-tuition-for-kids-in-uk) - [Cambridge A Level Maths 9709 Help: Papers, Routes, Syllabus](/cambridge-a-level-maths-9709-help) - [Common Entrance Maths Tuition](/common-entrance-maths-tuition) - [Cambridge IGCSE Computer Science Tuition](/cambridge-igcse-computer-science-tuition) ### Learn more - [KS2 and 11 Plus Maths Tutor Cost UK 2026: What to Budget](/ks2-and-11-plus-maths-tutor-cost-uk) - [College Maths Course: Calculus, Linear Algebra to Analysis](/courses/college-mathematics-complete-masterclass) - [Group vs One-to-One Maths Tuition: Cost, Evidence, Fit](/group-vs-one-to-one-maths-tuition) - [GCSE Maths Tutor Cost UK 2026: Hourly Rates by Format](/gcse-maths-tutor-cost-uk) ### From the blog - [Maths Learning Guides](/blog/topic/maths) - [Area and Perimeter: The Difference, Explained Simply](/blog/area-and-perimeter-difference) - [What JavaScript to Learn Before React (with Examples)](/blog/javascript-to-learn-before-react) - [IGCSE Computer Science (0478) Explained for Parents](/blog/igcse-computer-science-explained-for-parents) ### Start here - [Real projects built by Modern Age Coders students](/student-labs) - [Browse every live course at Modern Age Coders](/courses) Free class[Priority demo](/book-demo)[Call us](tel:+919123366161) --- *Canonical: https://learn.modernagecoders.com/online-maths-circle-uk*