United States · Grades 3 to 12 · Math circles

Online math circle for kids: explore, argue, discover

A math circle is not a class and not a tutoring session. It is a small group of children and a mathematician working on one rich problem, arguing about it, getting stuck and finding a way through. Many children who find school math too easy discover in a circle that math is actually hard, and wonderful. This guide explains what math circles are, in the words of the US Math Circle Network, how to find one near you or online, and gives you a complete circle-style exploration to try at the kitchen table.

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Teaching math and coding live since 2020 · 10,000+ students · ages 6 to 67

In short

A math circle is a community focused on the enjoyment of mathematical problem solving, where students meet regularly with mathematicians to explore challenging problems together. In the US, the Math Circle Network, a project of the American Institute of Mathematics, maps hundreds of circles, some online. Modern Age Coders is not a math circle, but we teach in the same spirit: live online problem-solving classes in our olympiad and competition math course, as a group of 15 to 20 or one to one.

Problem solving, every week

Three courses for a child who loves a hard problem

Each puts discussion and reasoning ahead of speed, the way a good circle does.

Maths Olympiad & Competition Course course thumbnail

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Olympiad and competition math

Rich problems, proof and contest skills for grades 6 and up.

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Middle School Math Competitions course thumbnail

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Middle school competition math

MATHCOUNTS and AMC 8 problem solving for grades 5 to 8.

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Problem Solving and Computational Thinking for Kids course thumbnail

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Problem solving for younger kids

Logic, patterns and puzzles for grades 3 to 6.

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What a circle is

What is a math circle?

The Math Circle Network defines it simply: "Math Circles are communities focused on the enjoyment of mathematical problem solving." Meetings, it says, are lively, interactive and often "funstrating": challenging, but rewarding.

Three kinds of circle

The network describes Math Student Circles (after-school programs for students), Math Teacher Circles (professional learning for teachers and mathematicians) and Family Math Circles for parents and families who want to do mathematics together.

For children, a student circle is the usual door. Some circles welcome a parent alongside a younger child, which is a lovely way to start.

Where the idea comes from

According to the network, the model of students meeting regularly with mathematics professionals to solve problems "originated in Eastern Europe more than 100 years ago".

In the United States, the first student circles began "in Boston in 1994 and in the San Francisco Bay Area (Berkeley and San Jose) in 1998". The first Math Teacher Circle was founded in 2006 at the American Institute of Mathematics.

Math circle, school class and tutoring compared (our summary)
QuestionMath circleSchool classTutoring
Main aimEnjoying hard problemsCovering the syllabusFixing gaps, homework
Typical problemOne rich question for a whole sessionMany short exercisesWhatever is due
Who talks mostThe studentsThe teacherBoth
Getting stuckExpected and welcomeOften a problemThe reason to book

Source: Math Circle Network, About, read 31 October 2026. Modern Age Coders is not a math circle and has no connection with the Math Circle Network, the American Institute of Mathematics or any circle named on this page.

Find one

How do I find a math circle near me or online?

Start with the Math Circle Network's map, which lists circles by level and marks those that meet online. University math departments run many of the longest-running circles too.

The national network

The Math Circle Network calls itself "A National Network of Local Math Communities". It is "a project of the American Institute of Mathematics (AIM), a nonprofit mathematical sciences research institute supported by the National Science Foundation".

The network says "There are hundreds of Math Circles around the U.S." Its map lets you filter by elementary, middle and high school, and some entries are tagged Online. In 2020 AIM also became host of the National Association of Math (Student) Circles.

Starting your own

If there is no circle nearby, the network helps people start one. Its organizer pages offer planning toolkits and a 2026 New Math Circle Training and Mentoring Cohort for new leadership teams.

It also says "Our network provides free resources for all U.S.-based Math Circles", including an activities database and MathCircular, which it describes as "a free semi-annual magazine".

Two university math circles, from their own pages (read 31 October 2026)
CircleWhen and whereOnline?Note from its page
Stanford Math Circle (Stanford Pre-Collegiate Studies)Quarter-long, after-school sessions, weekly on Tuesdays, Wednesdays or ThursdaysYes: "Students from any geographic location are welcome to enroll in the online classes."Emphasizes "discussion and group problem solving"
Berkeley Math CircleWeekly on Wednesday evenings at UC BerkeleyMainly in person"Emulating famous Eastern European models"; the BMC-Upper group will not run in fall 2026 and spring 2027

Sources: mathcircles.org (home, map and organizer pages), Stanford Math Circle and Berkeley Math Circle, read 31 October 2026. Schedules change by term; check each circle before applying.

An exploration

What does a math circle problem look like? The hundred lockers

A circle problem is easy to state, impossible to finish by guessing, and has a beautiful reason behind the answer. This one is a classic of the genre; the walkthrough and wording are ours.

The problem

A hallway has 100 closed lockers, numbered 1 to 100. Student 1 opens every locker. Student 2 changes every second locker (closes it if open, opens it if closed). Student 3 changes every third locker, and so on, up to student 100.

When all 100 students have passed, which lockers are open? A circle leader would not let anyone answer yet. First: try it with 10 lockers.

Explore small cases (ours)

With 10 lockers, children usually find that lockers 1, 4 and 9 end up open. Someone says "those are square numbers!" That is a conjecture, not yet an answer.

Now the circle question: why squares? Locker 12 is changed by students 1, 2, 3, 4, 6 and 12, its six factors. Six changes means open, closed, open, closed, open, closed: it ends closed.

  1. The key idea (ours). A locker ends open only if it is changed an odd number of times, so only if its number has an odd number of factors.
  2. Why factors usually pair up. Factors come in pairs: for 12, 1 with 12, 2 with 6, 3 with 4. Pairs make an even count.
  3. The exception. For 36, the pair 6 x 6 uses the same number twice, so 6 is counted once. 36 has 9 factors: an odd number. Only perfect squares have an unpaired factor.
  4. The answer. The open lockers are the squares 1, 4, 9, ..., 100: ten lockers. We checked it by simulating all 100 students in Python.
  5. Extend it. Which lockers are changed exactly twice? (The primes.) A good circle ends with a new question.

A session

What happens in a math circle session?

Most circles follow a similar rhythm: a problem is posed, students work on it in small groups, ideas are shared and argued over, and the leader helps the group turn a pattern into an explanation. The timings below are our own sketch of a 75-minute session.

A 75-minute circle-style session (our sketch)
PartMinutesWhat happens
Warm-up10A quick puzzle everyone can start
The big problem5Stated simply, with no method given
Explore in pairs25Small cases, drawings, tables
Share and argue20Groups present conjectures; others test them
Why it works10The group builds the explanation together
One more question5An extension to take home

What makes it work

Silence is allowed. Leaders wait rather than rescue, because the stuck moment is where the learning happens.

Wrong ideas are valuable. A conjecture that fails on the next case teaches the whole room why we test before we believe.

Is my child ready?

Readiness is about attitude more than level. A child who enjoys a puzzle, can stay with it for twenty minutes and likes talking about ideas is ready, whatever their grade.

Children who are used to always being right sometimes find the first circle hard. That is normal, and usually the start of something good.

Try these

What problems can we explore at home like a math circle?

Pick one per evening. Explore small cases first, look for the pattern, then ask why. The problems and answers are ours, each checked in Python.

Five circle-style explorations with answers (ours)
ExplorationStart withAnswer
You climb 10 stairs, taking 1 or 2 steps at a time. How many different ways?Count for 1, 2, 3 and 4 stairs; each total is the sum of the two before89
Twelve people each shake hands once with everyone else. How many handshakes?Each person shakes 11 hands; every handshake is counted twice66
Cut two opposite corners off a chessboard. Can 31 dominoes cover the rest?Color the squares; each domino covers one black and one whiteNo
What is the 2026th odd number?The nth odd number is 2n - 14051
In the locker problem, how many lockers stay open with 100 students?Count the perfect squares up to 10010
  1. Week 1 (our plan for families). One exploration, done together, with paper and colored pens. No hints for the first ten minutes.
  2. Week 2. Your child explains the answer to someone who was not there. Explaining is half of mathematics.
  3. Week 3. Look on the Math Circle Network map for a local or online circle, and try a session.
  4. Week 4. Decide: a circle, a weekly problem-solving class, or both.

If your child also enjoys contests, see our middle school math competitions guide, MATHCOUNTS preparation and Math Kangaroo USA.

Where your child is

Four stages from puzzle fan to mathematician

Our own way of describing how children grow in a circle.

Stages of mathematical exploring (ours)
StageWhat it looks like
1. Answer hunterWants the answer fast, unsure what to do when stuck
2. Case tryerTries examples and draws pictures without being told
3. ConjecturerSpots a pattern, says it clearly and tests it
4. ExplainerGives a reason the pattern must hold, and asks the next question

For parents

Praise the trying, not the speed. "I like how you made a table" does more than "you're so smart".

If your child asks you the answer, ask them what they have tried. Then wait.

For students

When you are stuck, make the problem smaller: 10 lockers instead of 100.

A pattern is a guess until you can say why. Always ask why.

The catalogue

Problem-solving math courses for grades 3 to 12

Live courses that put exploration and reasoning first.

I

Young explorers

Grades 3 to 5
II

Middle school

Grades 6 to 8
III

High school

Grades 9 to 12

How lessons run

Circle-style problem solving, live 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.

Weekdays

An evening problem session after school.

Weekends

Longer explorations with time to argue.

1-on-1

For a child who wants a personal mentor.

One rich problem

Depth over a long worksheet.

Students talk

Ideas shared and tested.

Problems we chose

Original write-ups, never copied.

Why, always

Every pattern gets a reason.

No contest promises

We teach thinking; results are theirs.

Size

A batch of 15 to 20, or just your child.

Student work

What our young mathematicians make

Explorations, simulations and puzzle games from students in our classes. More at student labs.

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Fees

Fees

Problem-solving classes run month to month with no term contract, so a family can try circle-style math for a few weeks and stay only if the spark is there.

Free first class

USD 0

no card required

  • A free first class
  • A puzzle to start
  • No card needed
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Group batch

USD 100

a month, billed in US dollars

  • Fifteen to twenty learners
  • The same teacher each week
  • Pick your batch
  • Monthly
Start here

One to one

USD 150

a month, billed in US dollars

  • One teacher, one child
  • Problems chosen for them
  • Flexible times
Enquire

What families say

Rated 4.9 across 547 Google reviews

Reviews from parents on Google, reproduced exactly.

★★★★★

"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

Questions from families

Math circles: questions answered

What is a math circle for kids?

It is a group where children meet regularly with mathematicians to explore challenging problems together. The Math Circle Network describes math circles as communities focused on the enjoyment of mathematical problem solving.

How do I find a math circle near me?

Use the map on mathcircles.org, run by the Math Circle Network. You can filter by elementary, middle and high school, and some circles are marked as meeting online.

Are there online math circles?

Yes. Some circles on the national map meet online, and the Stanford Math Circle says students from any geographic location are welcome to enroll in its online classes.

What age is a math circle for?

Circles exist for elementary, middle and high school students, and the network also describes family circles where parents join in. Readiness depends more on enjoying puzzles than on grade.

Where did math circles start?

The Math Circle Network says the model originated in Eastern Europe more than 100 years ago. The first US student circles began in Boston in 1994 and in the San Francisco Bay Area in 1998.

Is a math circle the same as math tutoring?

No. Tutoring usually fixes gaps or helps with homework, while a circle explores one rich problem for the joy of it. Many children benefit from both at different times.

How is your class different from a math circle?

We are an online school, not a community circle. Our problem-solving classes follow a planned course with the same teacher each week, but they borrow the circle habits of discussion, exploration and proof.

Can I start a math circle?

Yes. The Math Circle Network offers organizer toolkits, free resources for US-based circles and a 2026 training and mentoring cohort for new circle leadership teams.

What times 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.

Are you connected with the Math Circle Network?

No. Modern Age Coders is independent and has no link to the Math Circle Network, the American Institute of Mathematics, Stanford or the Berkeley Math Circle.

Elsewhere on this site

Related pages

More math enrichment for US children.

Middle school math competitions

Contests for puzzle lovers.

MATHCOUNTS preparation

Contest problem solving for middle schoolers.

Math Kangaroo USA

A friendly first contest.

Math League contests

School-based contests by grade.

Accelerated math online

Working ahead with understanding.

Beast Academy help

For families using that curriculum.

Related pages in this guide

Part of the guide: US math and coding competitions guide

Math contests

Coding and robotics

Projects and next steps

More guides: US state math tests by state · US gifted and selective school tests · US math placement and college readiness tests · Homeschool and school math curricula guide

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Let us know what grade your child is in and the last puzzle they could not put down. The teacher will bring a problem pitched just above that.

You could first read about our teaching or look through our courses.

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