Bonus puzzles & labs
Fun math that isn't tied to any one grade level — puzzles, patterns, and labs you can explore alongside the graded lessons. This section is being translated activity by activity; new ones are added regularly.
🌀 Patterns & sequences
Pascal's Triangle Lab
Add the two numbers just above to build the triangle, then color odd and even numbers to reveal a fractal pattern.
Open English lesson → 🌀Fibonacci Sequence & Spiral Lab
Watch squares sized by the Fibonacci sequence trace out a spiral, and see the ratio approach the golden ratio.
Open English lesson → 🔢Arithmetic & Geometric Sequences Lab
Change the first term and common difference (or ratio) with sliders and see why the sum formulas work, including a compound-interest example.
Open English lesson → 🌻Fibonacci in Nature
Adjust the angle seeds grow at and see why 137.5°, the golden angle, packs them in with no overlap.
Open English lesson → 🔁Collatz Conjecture Lab
Halve evens, triple-plus-one odds — follow the still-unproven "3n+1 problem" step by step with sliders.
Open English lesson →❄️ Drawing & geometry
Fractal Zoom Lab
Explore the Koch snowflake, Sierpiński triangle, dragon curve, and more — zoom in and increase the depth to see self-similarity.
Open English lesson → 🌀Spirograph Lab
Change two circles' radii and a pen position to draw spinning patterns, and see how the number ratio decides the shape.
Open English lesson →🚪 Probability & chance
The Monty Hall Problem Lab
Play the 3-door and 10-door versions yourself and watch why switching doors doubles your odds.
Open English lesson → 🎯Monte Carlo Pi Lab
Scatter random points inside a square and estimate pi from the fraction that land inside a circle.
Open English lesson → 🎂Birthday Paradox Lab
See why the odds of a shared birthday pass 50% with just 23 people, with sliders and a live simulation.
Open English lesson →🔷 3D shapes
Platonic Solids Lab
Adjust the angle gathered at a vertex to discover why there are exactly 5 Platonic solids, then rotate each in 3D.
Open English lesson → 🎀Möbius Strip & Klein Bottle Lab
Draw a line on a Möbius strip and fill a Klein bottle with water to see a surface with no inside or outside.
Open English lesson → 🌐Sphere Volume Lab — Archimedes' Proof
Slice a hemisphere and a cylinder-minus-cone shape at the same height to see why a sphere's volume is (4/3)πr³.
Open English lesson →🧩 Shapes & puzzles
Magic Square Lab
Fill in the blanks with 1–9 so every row, column, and diagonal adds up to the same total.
Open English lesson → 🗼Tower of Hanoi Lab
Move a stack of disks to another peg and watch the minimum move count explode as you add disks.
Open English lesson →🎲 Number games
24 Game Lab
Drag the four operations between four numbers and try to make exactly 24.
Open English lesson → 🎲Four Fours
Use the digit 4 four times, with square roots, factorials, and grouping, to build any number from 0 to 32.
Open English lesson → 🧩Mini Sudoku Lab
Solve 4×4 and 6×6 sudoku puzzles by process of elimination — no number repeats in a row, column, or box.
Open English lesson → 🔷Tangram Lab
Drag, rotate, and flip seven classic pieces to build a square, a triangle, or a shape of your own.
Open English lesson →🕵️ Logic & deduction
Number Baseball Lab
Gather strike and ball clues to deduce a secret number made of different digits.
Open English lesson → 🔍Number Detective
Check clues one at a time and cross off suspects by process of elimination to find the secret number.
Open English lesson →⚫ Strategy games
👀 Optical illusions
✋ Number tricks
🔢 Number systems
Number Base Lab
Group the same count of stars by 2s, 3s, 5s, or 10s and see how the number written changes with the base.
Open English lesson → 🔁Curious Digit Numbers Lab
Palindromes, happy numbers, narcissistic numbers — numbers that follow surprising rules just from playing with their own digits.
Open English lesson → 🔗Divisor Chain Numbers Lab
Perfect numbers, amicable numbers, sociable numbers — repeatedly summing proper divisors sometimes loops back to the starting number.
Open English lesson → 🔐Elliptic Curve Cryptography Lab
From the curious rule for adding points on an elliptic curve to the hard problem that turns it into a real-world cipher.
Open English lesson →⚡ Speed & practice
📚 Stories
🚧 More on the way