– Math & Science Done Right

Master concepts by solving fascinating problems

Thousands of fun, guided exercises on everything from logical reasoning to machine learning. See courses →


Math – The Fractal Foundation Educator’s Guide

The Fractal Foundation

A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over.

For a simple description of fractals, please download our “One Pager” (380Kb).

For more detailed info, please download our 20 page “Educators’ Guide” (7.5Mb).

Fractal Triangle – Fractal Foundation

Mathigon – Textbooks come to life

mathigon-for-teachersMathigon contains amazing content for the entire mathematics curriculum. Simply pick a chapter and tell your students to work through it – as a homework assignment, or on within a flipped classroom setting. A teacher dashboard shows detailed analytics on their progress and mastery.

Mathigon works on tablets and laptops, and every student will automatically get a highly interactive and personalised experience. Our content is aligned to mathigonthe Common Core (US) and other national curricula.

Every chapter comes with a corresponding lesson plan for teachers, and we have a library of all the interactive games and components to use.


About Mathigon

Everything in our world follows mathematical laws: from the motion of stars and galaxies to the transmission of phone signals, bus timetables,


weather prediction and online banking. Mathematics lets us describe and explain all of these examples, and can reveal profound truths about their underlying patterns.

Unfortunately the school curriculum often fails to convey the incredible power and great beauty of mathematics. In most cases, school mathematics is simply about memorising abstract concepts: a teacher (or a video, or a mobile app) explains how to solve a specific kind of problem, students have to remember it, and then us

e it to solve homework or exam questions. This has changed very little during the last century, and is one of the reasons why so many students dislike mathematics.

“It is a miracle that curiosity survives formal education.”

– Albert Einstein

In fact, the process of studying mathematics is often much more important than the actual content: it teaches problem solving, logical reasoning, generalising and abstra

ction. Mathematics should be about creativity, curiosity, surprise and imagination – not memorising and rote learning.

Mathigon is part interactive textbook and part virtual personal tutor. Using cutting-edge technology and an innovative new curriculum, we want to make learning mathematics more active, personalised and fun.

Active Learning

Rather than telling students how to solve new kinds of problems, we want them to be able to explore and “discover” solutions on their own. Our content is split into many small sections, and students have to actively participate at every step before the next one is revealed: by solving problems, exploring simulations, finding patterns and drawing conclusions.

We built many new types of interactive components, which go far beyond simple multiple choice questions or textboxes. Students can draw paths across bridges in Königsberg, run large probability simulations, investigate which shapes can be used to create tessellations, and much more.


As users interact with Mathigon, we can slowly build up an internal model of how well they know different related concepts in mathematics: the knowledge graph. This data can then be used to adapt and personalisethe content – we can predict where students might struggle because they haven’t mastered all the prerequisites, or switch between different explanations based on students’ preferred learning style.

virtual personal tutor guides you step-by-step through explanations and gives tailored hints or encouragement in a conversational interface. Students can even ask their own questions.


Using Mathigon requires much more effort and concentration from students, compared to simply watching a video or listening to a teacher. That’s why it is important make the content has fun and engaging as possible.

Mathigon is filled with colourful illustrations, and every chapter has a captivating narrative. Rather than teaching mathematics as a collection of abstract facts and exercises, we use real life applications, puzzles, historic context, inter-disciplinary connections, or even fictional stories to make the content come alive. This gives students a clear reason why what they learn is useful, and makes the content itself much more memorable.

All these goals are difficult to achieve in a classroom, because a single teacher simply can’t offer the individual support required by every student. Of course, we don’t want to replace schools or teachers. Mathigon should be used as a supplement: by students who are struggling and need additional help, students who want to go beyond what they learn at school, or even by teachers in a blended learning environment.

Get the Math – Math Challenges


The Challenges

Get the Math Challenges



The Setup

This video introduces professionals who will pose real-world math challenges to the teams.

Math in Music: Introduction

DobleFlo talks about using math in music production and presents an algebra challenge related to one of their new singles.

Math in Music: Take the challenge

Match the electronic beat to the instrumental sample by calculating the correct tempo in beats per minute.

Math in Music: Try other music challenges

Choose from different instrumental samples and electronic drum tracks to create a new track and figure out the correct tempo in beats per minute.

Math in Fashion: Introduction

Chloe Dao explains how she uses math as a fashion designer and sets up a math challenge involving one of her designs.

Math in Fashion: Take the challenge

Modify Chloe Dao’s design from the video to meet the target retail price of $35 or less.

Math in Fashion: Try other fashion challenges

After solving Chloe’s challenge, use the same skills to modify three more complicated garment designs.

Math in Videogames: Introduction

Julia Detar describes how she uses math to create videogames and presents a math challenge.

Math in Videogames: Take the challenge

Plot a linear path for the spaceship to avoid crashing into the asteroid.

Math in Videogames: Try other videogame challenges

After saving the spaceship, try a more challenging submarine game to test your skills with coordinate graphing and linear equations.


Chef Sue Torres challenges the teams to use algebra to recommend a price for guacamole.

Math in Restaurants: Take the challenge

Choose one of two strategies to make your prediction for avocado prices in the coming year. Then, use Sue’s rule of thumb to come up with a recommended menu price for guacamole.

Math in Restaurants: Try other restaurant challenges

After solving Sue’s guacamole challenge, try additional challenges involving three menu items with different main ingredients: chicken, shrimp, and beef.

Math in Basketball: Introduction

Basketball player Elton Brand presents a challenge about the math behind free throw shots.

Math in Basketball: Take the challenge

Use the three key variables and Elton Brand’s stats to figure out the maximum height the basketball reaches when Elton shoots a free throw.

Math in Basketball: Try other basketball challenges

Choose new sets of stats and sharpen your skills with additional challenges around the math behind free throw shooting.

Math in Special Effects: Introduction

Jeremy Chernick from J&M Special Effects sets up a challenge about lighting for high-speed effects.

Math in Special Effects: Take the challenge

Use light probe readings to figure out the mathematical relationship between intensity and distance.

Math in Special Effects: Try other special effects challenges

Learn how a setting called an f-stop affects the amount of light coming through a camera lens.

Yummy Math – Real Life Math

Yummy Math provides teachers with an easy way to bring real-life into their math classrooms. It is our belief that when math is explored in contexts that are familiar and of interest to students, students will be more engaged to do math, reason, think critically, question and communicate.  Our activities are written to correspond with the NCTM Process Standards and the CCSS Standards for Mathematical Practice. You can read what our users have said here.

We’ve kept the site updated with multiple activities per week since March 2010 at no charge to teachers. If you have used our material, please consider making a donation to help us continue bringing meaningful mathematics to you and your students.

For example, here is a lesson from Sept 2017 about Hurricanes: 


Caribou Math Competition

About Caribou

caribou-mathThe Caribou Mathematics Competition is a world wide online contest that is held six times throughout the school year. Each of these days, five contests are offered, one for each of the grade levels 3/4, 5/6, 7/8, 9/10 and 11/12 and each one in English, French and Persian.

The Caribou Cup is the series of all Caribou Contests in one school year. Each student’s ranking in the Caribou Cup is determined by their performance in their best 5 of 6 contests through the school year.

All of our previous contests are available for free online as previous tests.


The goals of this project are to:

  • To improve student’s problem solving techniques by providing a wide variety of challenging math activities suitable for all students in grades 3-12.
  • Motivate students to get back to their school math when a question needed a technique or formula which they did not remember.
  • Show that mathematical puzzles can be fun and that competing in math contests with interactive questions is exciting.

Upcoming Contests

Contests can be started between 7:30AM and 3:30PM local time. Students are given 60min to complete the test.

Date Grades
18th(Wed) & 19th(Thu) October, 2017 3/4, 5/6, 7/8, 9/10, 11/12
15th(Wed) & 16th(Thu) November, 2017 3/4, 5/6, 7/8, 9/10, 11/12
17th(Wed) & 18th(Thu) January, 2018 3/4, 5/6, 7/8, 9/10, 11/12
14th(Wed) & 15th(Thu) February, 2018 3/4, 5/6, 7/8, 9/10, 11/12
4th(Wed) & 5th(Thu) April, 2018 3/4, 5/6, 7/8, 9/10, 11/12
2nd(Wed) & 3rd(Thu) May, 2018 3/4, 5/6, 7/8, 9/10, 11/12


Details for participation and fees can be found here.


Cash prizes are given out to the top performing students and schools in the Caribou Cup. Additionally, contest and Caribou Cup certificates can be printed after each test is marked. More information regarding prizes and a sample certificate can be found here.

Calcrostic of the Day

Calcrostics are a trademark in a Caribou Contest – one appears in nearly every contest.