λόγος·interactive explainers

Hard ideas,
made to click.

A small, growing shelf of single-page explainers — each one turns something intimidating into a thing you can poke, drag, and feel until it clicks.

Browse the shelf — or click anywhere
113 reads to start

Pick a rabbit hole.

Each one is a single page — no sign-up, no setup. Open it, start playing, and walk away understanding something you didn't an hour ago.

⛰️ Machine learning · playable

How machines learn — by walking downhill

No equations — just a hiker lost in the fog, feeling for the way downhill. Drop a ball, tune the step size, and meet the one quiet habit that powers almost all of modern AI.

Take the descent
🎲 Simulation · playable

Monte Carlo — estimating with randomness

When the math is too hard to solve, throw dice at it. Random sampling turns intractable problems into a loop and a counter — watch darts pin down π, then learn why repetition beats algebra and where the trick breaks.

Throw the darts
🥧 The number π · playable

Meet π — the number hiding in every circle

Roll a wheel one full turn and it travels π — about 3 and a bit. Then chase the number people have hunted for 4,000 years: measure real circles, peel a disc into πr², squeeze it with Archimedes' polygons, add up a sum that never ends, and even find π by tossing needles on the floor.

Roll the wheel
🏛️ History · playable

Ancient Greece — a journey through time

Hundreds of tiny city-states that argued, sailed, and invented half the modern world. Drag a marble marker across 2,000 years, explore a sea ringed with Greek cities, meet the twelve gods of Olympus, match the great heroes to their monsters, weigh Athens against Sparta, vote in the very first democracy, build a temple column by column, and carve your own name in Greek.

Sail into the past
🩺 Probability · playable

Bayes' theorem — why a positive test isn't a verdict

A test that's 99% accurate says you have a rare disease — so you're 99% doomed, right? Not even close. Drag two dials across 1,000 little people and watch a wall of false alarms swamp the handful of real cases, until a scary positive turns out to be a gentle nudge, not a verdict.

Run the test
📏 Numbers · playable

The number line — an anime quest

Zero is home base — step right into the light, left into the shadow realm. Drag a chibi hero down the line, read negatives, line up the party from smallest to largest, dodge a comparison trap, hop through plus and minus, measure distance from home, then zoom past fractions into decimals. Survive a boss-battle quiz — and see the same humble ruler run temperature, money, game HP, sea level, and maps.

Start the quest
🌍 Religion · explorable

What is religion? — a friendly world tour

Every people, in every corner of the world, has asked the same big questions. Tap a glowing land to meet its beliefs, drag the hand of time from the first cave-painters to today, and spin a wheel of life's great moments.

Tour the world of belief
🌡️ Climate · playable

Why Earth can't cool off — the sky's one-way door

Sunlight zooms in like it owns the place — but the heat it leaves behind can barely get out. Tap the sky, meet the gases, then turn the dials and cool the planet back down.

Open the sky
🔁 Nature of science · playable

The scientific method — the loop that never ends

Ask, predict, test, look, decide — then loop back and go again. Spin a glowing cycle, run real fair tests, walk through worked investigations, order the steps, and bust the myth that science is a straight line.

Take a lap
🔍 Nature of science · playable

Research questions — ask what you can actually test

Two questions, one lab bench. "Does temperature change how fast sugar dissolves?" beats "How does sugar work?" every time — because you can actually measure the answer. Sort the weak from the strong, diagnose why fuzzy questions fail, and rewrite a vague wondering into a fair test.

Sort the questions
🌱 Nature of science · playable

Writing a hypothesis — if, then, because

A hypothesis is just a guess with a reason attached. Spin three dropdowns to build one — If I…, then…, because… — run a health check on real examples, and watch a good idea sprout. The 'because' is the secret ingredient.

Build a hypothesis
🎛️ Nature of science · playable

Variables — change one, measure one, lock the rest

Every experiment has three roles: the one thing you change, the one thing you measure, and everything you keep the same. Drag the oven dial, run a fair test on two paper planes, plot your finding on a graph, and feel why scientists lock the recipe.

Run the experiment
⚖️ Nature of science · playable

Fair testing — change just one thing

Flip switches between two sugar-dissolving setups and watch a balance of trust swing from green to red. Fix a broken experiment, meet the variables by name, and learn why one trial is never enough. Change one thing and you know the cause; change two and the result keeps its secret.

Make it fair
📊 Nature of Science & Scientific Skills

Graphing data — same numbers, different outfits

One little table can dress up as a line, a bar chart, or a scatter of dots. Toggle between them and watch the answer pop into focus — then learn to pick the outfit that tells the story fastest.

Try the toggle
📏 Nature of science · playable

Measurement & units — the world's shared yardsticks

A metre is a metre in every country on Earth — that's the quiet superpower of units. Drag a converter to watch one length wear four different names, hop the decimal point between kilo, centi and milli, and play a guess-the-unit game. Science's shared language for size and amount.

Grab the ruler
🎯 Nature of science · playable

Accuracy vs precision — bullseye vs. tight cluster

Two sets of darts can both miss — in totally different ways. Throw darts at a board (or pick a classic pattern) and watch a live readout decide: accurate, precise, both, or neither? Then meet science's sneakiest mistake — a scale that's always wrong by exactly the same amount.

Throw some darts
🔍 Nature of science · playable

Observation vs inference — what you saw vs what you figured out

Play detective. An observation is what your senses actually report; an inference is the story your brain builds on top. Sort a deck of statement cards about a drawn scene into Observed and Inferred, catch an inference sneaking into a sentence, and learn why muddling the two quietly wrecks an experiment.

Play detective
🌿 Biology · playable

Photosynthesis — the leaf is a solar kitchen

A leaf is a tiny solar-powered kitchen: it cooks sunlight, air and water into sugar and breathes out the oxygen in your lungs. Drag the sun and the rain, shine red, blue and green light on a leaf, flip night to day — and watch the kitchen speed up, slow down, and stop.

Step inside the leaf
🔬 Biology · playable

Cell structure — every cell is a tiny factory

Zoom past skin and leaves and you find cells: minute, busy little factories, each with workers doing different jobs to keep it alive. Tap an exploded, labelled cell to meet every part — then flip from animal to plant and watch the wall, the green chloroplasts and the big water-tank vacuole pop into place.

Step inside a cell
🔬 Biology

The microscope — a window into the hidden world

Everything around you is stitched together from cells far too small to see. A microscope is the window that opens onto that hidden world. Slide a focus knob until blurry blobs snap into crisp cells, turn up the light, and zoom from ×40 to ×400 — then learn the one tiny sum that tells you how much bigger you are really seeing.

Look through the eyepiece
🌸 Biology · playable

Diffusion & osmosis — how a cell eats & drinks for free

Spray perfume in one corner and soon the whole room smells of it — that's diffusion, particles wandering from crowded to empty all on their own. Drop a crowd of dots and watch them spread, then meet osmosis: the picky membrane that only lets water through. It's how every cell feeds and drinks without spending a drop of energy.

Set the dots loose
🔬 Biology

Cell division — how one becomes two

Every cell copies its contents and pinches in two. Click through the split step by step and watch one become two become four — the doubling that grows a whole you from a single cell.

Watch it split
🫀 Biology · playable

Circulatory system — your body's delivery network

Your heart is a tireless pump, and your blood vessels are a delivery network long enough to wrap around the whole planet. Speed the heartbeat from rest to a sprint, watch red and blue blood race around the loop, then step through the double journey: heart to lungs to heart to body.

Start the heartbeat
Biology · playable

The nervous system — your body's lightning-fast messaging network

Touch the hot stove and watch a spark race from your hand to your brain and back — that's a reflex, faster than thinking. Then play the reaction-time game and catch your own quarter-second in milliseconds.

Race a signal
🍽️ Biology · playable

Nutrition & a balanced diet — food is fuel and building blocks

Carbs are fuel, protein builds and repairs, fats store and protect, and tiny helpers, fibre and water keep the whole machine humming. Meet each food group, tap to see the job it does, then drag foods onto a plate and watch the balance read back — no calorie-counting, just a great mix.

Build a balanced plate
🌳 Biology · playable

Classifying life — one giant family tree

Millions of living things, all filed onto a single branching family tree by the features they share. Open the glowing tree of life branch by branch, climb the levels from kingdom down to species, then sort dolphins, bats and sharks into their real groups.

Open the tree of life
🕸️ Biology · playable

Food chains & webs — the safety net of who-eats-whom

Energy flows from the Sun through grass to grasshoppers, frogs, snakes and hawks — and every chain is knotted into a web. Trace a sunbeam into a hawk, watch energy thin out up the pyramid, then pull one thread and feel the whole net wobble.

Tug a thread
🧬 Biology · playable

DNA & genes — the recipe book in every cell

Almost every cell carries the same instruction manual, written in a four-letter alphabet. Unzip a glowing double helix, zoom from your whole body down to a single gene, build the matching strand yourself, then flip one letter and watch a trait change.

Unzip the helix
🦋 Biology · playable

Natural selection — the colour that gets to stay

Camouflage is a survival game: the moths that blend into the bark are harder to spot, so they live to have more babies. Set the bark from pale to sooty, run the generations, and watch a whole population change colour — without a single moth ever repainting itself.

Run the generations
🧊 Chemistry · playable

States of matter — same stuff, three outfits

Ice, water, and steam are all the same particles — heat just decides how tightly they pack. Drag the heat slider to freeze, melt, and boil a box of particles, click through the six changes of state, and sort everyday things into solid, liquid, and gas.

Turn up the heat
🧊 Chemistry

Changes of state — the same stuff in three outfits

Ice, water, and steam are one substance wearing three different costumes, and heat is the costume-changer. Drag the temperature slider and watch the particles switch their dance.

Turn up the heat
🧂 Chemistry · playable

Compounds — when a poison meets a metal

Sodium is a metal wild enough to catch fire in water. Chlorine is a green, choking gas. Bond them and you get the harmless white salt on your chips. Press the button, watch two dangerous elements snap into one safe new substance, and meet the big rule: the whole is more than its parts.

Bond them!
⚛️ Chemistry · playable

Atomic Structure — the tiny solar system inside everything

Zoom inside an atom and it looks like a miniature solar system: a dense, glowing core of protons and neutrons, with electrons whizzing around it. Add one proton and the whole atom becomes a brand-new element — hydrogen, helium, carbon, on and on. Build atoms, take the challenge, and meet the three tiny particles that make up absolutely everything.

Build an atom
🧪 Chemistry · playable

The periodic table — chemistry's seating chart

Where an element sits tells you how it behaves — and neighbours act alike. Read a tile, stack up protons, recolour all 118 elements by family or by state, and watch whole columns light up.

Take a seat
🧪 Chemistry

Molecules & formulas — the recipe card for atoms

H₂O means two hydrogen, one oxygen — a formula is just a recipe card telling you which atoms and how many. Snap atoms together and watch the formula count itself, live.

Build a molecule
⚛️ Chemistry · playable

Chemical reactions — same atoms, a new build

Hit React! and watch hydrogen and oxygen tear their bonds apart and snap back together as water — while an atom counter quietly proves not a single atom vanished. Then play spot-the-signs: colour change, bubbles, heat, and light, each with a familiar example. Atoms are just LEGO bricks, taken apart and rebuilt into something new.

Break some bonds
🍋 Chemistry · playable

Acids & bases — the kitchen detective game

Sour or slippery? Lemon and vinegar are acids; soap and baking soda are bases — chemical opposites, with plain water sitting neutral between them. Be the kitchen detective: sort a deck of household substances into Acid, Neutral and Base bins, then slide a 0–14 colour strip to see exactly where each one lands.

Start sorting
🧪 Chemistry · playable

The pH scale — sour to slippery in colour

Drag a slider down a rainbow ruler from 0 to 14 and watch a beaker change colour: fiery red for sour acids, calm green for neutral water, deep purple for slippery bases. Dip indicator papers, neutralise an acid, and find out why each step is a tenfold jump. Lemon, soap and bleach all get a home on the line.

Slide the colour ruler
⚗️ Chemistry · playable

Separation techniques — the right tool for every mixture

A mixture keeps its parts whole, so you can always pull them back out — you just need the right tool. Match sand-in-water, salt water, alcohol and a black ink dot to filtering, evaporation, distillation or chromatography, then watch one black spot climb wet paper and split into its hidden colours.

Match the method
🛟 Chemistry · playable

Density — why a log floats but a pebble sinks

A tiny pebble sinks, but a giant log floats — and it isn't about size or weight, it's how tightly the stuff is packed. Squeeze marbles into a box to feel that density = mass ÷ volume, then drop cork, ice, steel and lead into a water tank and watch the float rule decide who swims and who sinks.

Drop it in the tank
🧲 Physics

Forces — the invisible pushes and pulls

Every push and pull is really an arrow you just can't see. Drag glowing arrows onto an object and watch it start, speed up, slow, stop, or turn.

Grab an arrow
🪐 Physics · playable

Gravity — the pull that's everywhere

Gravity is the invisible tug between any two lumps of stuff — and it isn't the same everywhere. Drop the same object on the Moon, Mars, Earth, Jupiter and the Sun to watch its strength change, find out why you'd weigh different amounts on each, and prove that a feather and a hammer fall together.

Drop something
🛷 Physics

Friction — the invisible grip between surfaces

Friction is the quiet force that grabs whenever two surfaces rub, slowing things down and making heat. Slide a block from ice-smooth to sandpaper-rough and watch it stop after a long glide or a short one — then find out why brakes bite and ice is slippery.

Slide the block
🚀 Physics · playable

Newton's laws — three rules that run everything that moves

Three simple rules secretly steer your bike, a car crash, every step you take, and a rocket. Nudge a frictionless puck, push a loaded cart, and fire a rocket to feel inertia, F = ma, and action–reaction with your own hands.

Set things in motion
🎢 Physics · playable

Energy transfer & conservation — the roller-coaster energy bank

Energy never vanishes — a roller coaster just keeps swapping height for speed and back again. Drag the first hill, hit Go, and watch the height and motion bars trade places while the total holds steady. Then flip on friction to see where the 'missing' energy really goes.

Ride the energy
⚖️ Physics · playable

Simple machines — trade distance for force

A machine never makes you stronger — it lets you swap one short, hard push for a long, easy one. Drag a lever's pivot and tilt a ramp to watch the effort drop while the distance grows, and discover why the work you do barely changes either way.

Make work easier
🔦 Physics · playable

Reflection & refraction — aim a ray of light

Light knows only two tricks: it bounces, and it bends. Grab a glowing beam, fire it at a mirror and into water, dip a straw, trap light in a pipe, and split white light into a rainbow — and finally understand why a straw looks broken in your glass.

Aim the light
🌈 Physics · playable

Colour & the spectrum — white light, unmasked

White light is wearing a disguise: it's secretly every colour at once. Fire a white beam through a prism and watch it fan into a rainbow, see why one hangs in the sky after rain, then shine coloured light on an apple and catch it turning black. Colour was never in the object — it's in the light.

Split the light
🔊 Physics

Sound — vibrations you can suddenly see

Poke the air and watch it ripple. Sound is just a shiver travelling through stuff — air, water, even steel — which is exactly why outer space is dead silent. Hit vibrate, switch the medium, and see the wave spread.

See the ripple
💡 Physics · playable

Electric circuits — one path, or many?

Untangle a box of fairy lights and you've met the whole idea: a circuit is a loop, and current only flows when the loop is complete. Build a glowing board, wire bulbs in series or parallel, flip the switch, then unscrew a bulb — and watch one string go dark while the other shrugs it off.

Build a circuit
🧲 Physics · playable

Magnetism — the force field you can see

A magnet pushes and pulls without ever touching — through an invisible field wrapped around it. Drag a bar magnet through a cloud of iron filings to make that field snap into view, add a second magnet to watch fields combine, then shove two magnets together to feel like poles repel and opposites attract.

Reveal the field
🌍 Earth & Space Science

Structure of the Earth — from thin crust to iron heart

Our planet is layered like an onion. Click a cutaway of the Earth and journey down from the thin ground under your feet — through hot rock and molten metal — to a solid iron ball as hot as the surface of the Sun.

Take the journey down
🗺️ Earth & Space · playable

Plate Tectonics — Earth's cracked, drifting shell

The ground under your feet is a giant raft of rock, drifting about as fast as your fingernails grow. Set an animated map of plates in motion and watch mountains rise, new ocean floor spread, and earthquakes crackle wherever the plates meet.

Set the plates moving
💧 Earth & Space · playable

The water cycle — the water you drank today is ancient

Turn up the Sun and watch the whole planet's water move: it evaporates off the sea, condenses into clouds, falls as rain and snow, and runs back down to the ocean — over and over, forever. Drive the loop, follow a single drop on its journey, and find out why we never run out.

Turn up the Sun
🪐 Earth & Space · playable

The Solar System — our cosmic neighbourhood

One star, eight wildly different planets, and a whole lot of empty space — all held in their lanes by the Sun's gravity. Spin a glowing (not-to-scale) model, weigh yourself on other worlds, stretch the map to true distances, and see exactly where Earth sits in the crowd.

Take a spin
🪐 Earth & Space Science

The Planets — eight wildly different worlds

Four small rocky worlds, four giant gas and ice worlds. Click from scorching Mercury to frozen Neptune and see each planet's stats and a hand-drawn portrait.

Take the tour
🌙 Earth & Space · playable

The Moon & its phases — the Moon never changes, your view does

Half the Moon is always lit by the Sun — you just can't always see that half. Drag the Moon around its orbit to watch every phase appear from Earth, name them in a quiz, see why we only ever spot one face, and learn why phases are not the Earth's shadow.

Drag the Moon
🌑 Earth & Space · playable

Eclipses — a cosmic game of shadows

An eclipse is just a shadow landing in the right place. Drag the Moon around its orbit to line up the Sun, Earth and Moon, watch the shadows connect into a solar or lunar eclipse, and discover why we don't get one every single month.

Line them up
🔢 Maths thinking · playable

Patterns & generalising — from 2, 4, 6, 8 to the rule 2n

Maths is really the science of patterns. Extend a growing dot pattern with your own hands and watch the nth-term rule (2n) appear, build rules for all sorts of sequences, and see why turning a few examples into one rule that works forever is the very heart of algebra.

Extend the pattern
🔵 Maths thinking · playable

Sets & Venn diagrams — collections you can see

A set is just a collection of things — your friends, your favourite songs, the even numbers. Drag people into two overlapping circles and watch ∈, ∩, and ∪ stop being scary squiggles and start meaning something. The middle slice is smaller than you think.

Drag the circles
🎯 Maths thinking · playable

Estimation — your built-in answer-checker

Is 49 × 51 closer to 2,500 or 25,000? Estimation is the quiet superpower that catches silly mistakes before they bite. Round to friendly numbers, fire off a ballpark guess, then reveal the exact answer and see how close you got.

Take a ballpark guess
🪜 Maths thinking · playable

Order of operations — the rulebook everyone shares

Is 2 + 3 × 4 equal to 14 or 20? Without an agreed order, the same sum gives different answers — so maths everywhere follows one rulebook: BIDMAS. Tap a step-by-step highlighter that lights up the operation you do next and marches an expression all the way to its answer.

Light up the next step
🔍 Maths thinking · playable

Logic & conditionals — the detective's "if… then…"

Every "if… then…" is a tiny promise. "If a shape is a square, then it's a rectangle" is always true — but flip it around and the promise breaks. Sort a deck of statements into Always, Sometimes, and Never true, then test what happens when you turn a true claim backwards.

Start sorting
📱 Mathematical Thinking & Problem-Solving Skills

Mathematical modelling — turning a real choice into maths

A phone plan, a recipe, a journey — modelling turns a real situation into maths you can solve, then reads the answer back out. Drag a slider and watch two cost lines cross to see which plan wins.

Find the crossover
🔢 Number · playable

Prime numbers — the indivisible building blocks

A prime has exactly two factors: itself and 1. So 7 is prime, but 8 isn't. Run an interactive Sieve of Eratosthenes to cross out every multiple until only the primes glow, build factor rectangles, and meet the unbreakable building blocks that every other number is made from.

Run the sieve
🌳 Number · playable

Prime factorisation — every number's secret DNA

Every whole number bigger than 1 breaks into one and only one bunch of primes — its number-DNA. Grow an animated factor tree until only primes are left, write the answer with little indices like 2² × 3, and watch those exact primes power HCF and LCM.

Grow the tree
📄 Number · playable

Powers & indices — how small numbers grow explosively

An index is just shorthand for repeated multiplication: 2⁴ means 2 × 2 × 2 × 2 = 16. Fold a sheet of paper and watch it shoot past the edge of space, race plain adding against doubling, crack the laws of indices, and feel why tiny numbers can grow astonishingly fast.

Start folding
🔭 Number · playable

Standard form — writing the universe in powers of ten

Galaxies are too big to write out and atoms are too small — so we fold the zeros into a power of ten, and 4,500,000 becomes 4.5 × 10⁶. Slide from a single atom to the whole Milky Way and watch the notation keep up, hop a decimal point to build your own, compare cosmic sizes, then learn the one rule (1 ≤ a < 10) that trips everybody up.

Zoom the scales
♾️ Number · playable

Rational & irrational numbers — the digits that end, and the ones that never do

Every number belongs to one of two secret families. Reveal a fraction's decimal and watch it lock into a repeating block — then line it up beside √2, the troublemaker whose digits never end and never repeat. Sort the suspects, bust the myth that π is exactly 22/7, and learn to call any number on sight.

Reveal the digits
🦘 Number · playable

Adding & subtracting integers — the number-line hopscotch

The number line is a hopscotch board: adding hops you right, subtracting hops you left, and a negative flips the direction — which is exactly why subtracting −5 is the same as adding 5. Build a calculation like 3 + (−5) or 2 − (−4), press Go, and watch a hopper jump the right way to land on the answer. Then light up the sign rules and dodge the famous 'two minuses make a plus' trap.

Make it hop
🍯 Number · playable

Factors & multiples — two directions on one idea

Factors divide a number exactly; multiples count outward in steps — two directions on the very same idea. Type any number into the factor-finder and watch its dots snap into every rectangle it can make (so you see why factors come in pairs), then skip-count multiples along a track that never runs out.

Find the factors
🟩 Number · playable

Square numbers & square roots — building a square out of tiles

Squaring a number just means building a square out of tiles: 5² is a 5-by-5 grid holding 25 of them. Grow the grid side by side and watch n² appear, then run it backwards — a square root asks 'what side made this square?' Rebuild squares to find their roots, and see why √10 hides between 3 and 4.

Build a square
🍕 Number · playable

Fractions — a fair slice of the whole

A fraction is just a fair way to share a pizza: the bottom says how many equal slices, the top says how many you take. Slice a live pizza and bar yourself, watch ½ and 2⁄4 line up to the exact same width, and settle once and for all why a bigger bottom number means a smaller piece.

Slice it up
🎭 Number · playable

Fractions, decimals & percentages — three costumes, one value

½, 0.5 and 50% aren't three different numbers — they're one value wearing three outfits. Spin a live three-way converter (change any one and the other two follow), watch a 100-square grid fill up, then play a matching game to line up the equivalent forms.

Switch the costume
💯 Number · playable

Percentages — just a score out of 100

“Per cent” means “per hundred,” so 30% is simply 30 little squares shaded in a grid of 100. Drag a slider to shade the grid, click squares to set your own, then work out what 30% off a £40 jacket really saves you. Scores, discounts, statistics — it's all out of 100.

Shade the grid
🥤 Number · playable

Ratio — a recipe for a mix

A ratio is a recipe, not a total. Pour squash and water 1:4 and watch the glass blend — make it 1:2 and the drink turns stronger and more orange right in front of you. Then share a pile of sweets in a ratio, with every step worked out live: add the parts, divide, multiply. Bust the 1:4-means-a-quarter trap for good.

Mix the squash
🔵 Number

Highest common factor — the biggest block two numbers share

Every number is built from prime bricks. Drop two numbers into a Venn diagram, watch the bricks they share slide into the middle, and see their product light up as the HCF.

Find the shared bricks
🧊 Number

Cube numbers — a number you can stack

Cube a number and you get the volume of a real cube — stack the little blocks yourself and watch it grow. Then run it backwards: the cube root is just the length of one side.

Stack the cube
🏷️ Number

Percentage change — the maths behind every price tag

Every sale sticker, tip, and tax is one small multiplication in disguise. Drag a slider from a deep discount to a markup and watch the new price tag flip in real time.

Drag the price slider
⚖️ Algebra · playable

Solving equations — keep the scale balanced

An equation is a balance, and the equals sign is the point it tips on. Tip a scale to find x by feel, then keep one perfectly level while you undo operations — one-step and two-step — doing the very same thing to both sides until the unknown stands alone.

Balance the scale
⚙️ Algebra · playable

Function machines — drop a number in, watch it transform

Feed in 4, the rule says “× 3,” and out pops 12. Build your own function machine and watch numbers fall in and pop out changed — then chain two together, run one backwards, and crack hidden rules. This tidy little in–rule–out box is the doorway to algebra.

Feed the machine
📈 Algebra · playable

Linear graphs — watch an equation become a line

Give a rule like y = 2x + 1 a coordinate grid and it turns into a perfectly straight line. Drag two sliders and watch it redraw live: m tilts it, c slides it up and down. Plot points, match lines to equations, read a taxi-fare graph, and dodge the classic 'steeper means bigger c' trap.

Draw the line
📐 Algebra · playable

Gradient — turning steepness into a number

Gradient is just steepness with a number on it: how much a line climbs for every step across. Tilt a line with your finger and watch rise, run and gradient update live, sort real ramps and ski slopes from gentle to scary, link it to y = mx + c, and bust the myth that a longer line is a steeper one.

Tilt the line
📦 Algebra · playable

Substitution — drop a number into the box

A letter is just a labelled box. Slide a real number into x and watch 2x + 1 spring to life — 2(4) + 1 = 8 + 1 = 9 — with every step shown. Then plug two values into a real formula and read the answer straight off.

Slide a number in
📦 Algebra · playable

Expanding brackets — unwrap the parcel

A bracket is a parcel, and expanding is how you unwrap it: multiply everything inside by what's outside, so 3(x + 2) becomes 3x + 6. Drag sliders on a split-rectangle area model and watch the answer build itself, then check it by plugging in a number — the parcel and the unwrapped form always agree.

Unwrap a bracket
📏 Algebra · playable

Inequalities — when the answer is a whole range

Not every question has one tidy answer. ‘x is at least 13’ describes a whole crowd of numbers, not just one. Slide along a number line to shade the solution, plant an open or closed circle on the boundary, test which numbers belong — then solve inequalities just like equations.

Shade the number line
🪜 Algebra · playable

Sequences & the nth term — teleport to the 100th term

In an arithmetic sequence the same amount is added each time — a steady staircase. Set the first term and the step, watch the nth-term rule build itself, then jump straight to term 100 without counting a single step in between.

Build the rule
📍 Algebra · playable

Coordinates — a treasure-map address for every point

Two crossing number lines give every point on a page its own exact address — two numbers, like a map reference. Click the grid and watch the (x, y) read out live (along the corridor, then up the stairs), meet the four quadrants and negative coordinates, then play a plot-the-point game with a running score.

Drop a pin
🧩 Algebra

Factorising — putting the bracket back

Expanding runs a bracket out into terms. Factorising runs it backwards: pull out what every term shares and repackage 6x + 9 as 3(2x + 3). Slide, snap, and watch the tiles line up.

Pull out the factor
📈 Algebra

Reading graphs — every line tells a story

A flat line means you stopped. A steep line means you flew. Learn to read a distance-time graph out loud like a story — then match graphs to stories and win.

Read the line
📐 Geometry · playable

Angles in a triangle — three corners, always 180°

Stretch it, squash it, spin it — a triangle's three inside corners always add up to exactly 180°. Drag the corners and watch the total refuse to budge, tear the corners off and line them up into a straight line, then race the missing-angle puzzles.

Drag the corners
📐 Geometry · playable

Pythagoras' theorem — the squares that always balance

Draw a square on each side of a right-angled triangle, and the two smaller ones together hold exactly as much space as the biggest: a² + b² = c². Drag the legs and watch the three squares stay in perfect balance, then use the rule to find any missing side.

Build the squares
🦋 Geometry · playable

Symmetry — fold it, spin it, watch it land on itself

Draw a mirror line on a shape and see if the two halves match. Spin a square and feel it click back into place four times in one turn. Then complete the other half across a mirror, count the lines of symmetry hiding in everyday shapes, and spot it all again in letters, snowflakes, faces and logos.

Draw a mirror line
Geometry · playable

Polygon angles — two rules that never break

Build a shape side by side and watch its angles obey two unbreakable patterns. The inside angles climb by a tidy formula, (n−2)×180°. The corner-turns you make walking around the outside always add up to a single full spin: 360°. Add sides forever — the rules hold.

Build a polygon
📦 Geometry · playable

Nets & 3D shapes — unfold a solid

Every solid is a flat shape in disguise. Fold a cube net up on the screen, count faces, edges and vertices, sort the nets that actually work, and meet the F − E + V = 2 pattern hiding inside every flat-faced solid.

Fold the net
🔄 Geometry · playable

Transformations — slide, flip and spin

Three ways to move a shape without changing its size: slide it along a vector, flip it across a mirror line, or spin it around a centre. Set the parameters and watch the object glide to its image on the grid — then play a spot-the-move game and meet the one move that breaks the rules.

Move the shape
🕒 Geometry · playable

Types of angles — acute, right, obtuse, straight, reflex

An angle is just an amount of turn — and its size hands it a name. Grab the arm of a full-circle protractor and swing it: watch the degrees climb while the label flips from acute to right to obtuse to straight to reflex. Then play name-that-angle and see how fast your eye gets.

Swing the arm
🛤️ Geometry · playable

Angles in parallel lines — spot the F, Z and C

Cross two parallel lines with one straight road and eight angles spring up — but only ever two sizes, and they always add to 180°. Tilt the road, light up the F (corresponding), Z (alternate) and C (co-interior) pairs, and hunt down missing angles with the rules.

Tilt the road
🎯 Geometry · playable

Parts of a circle — all measured from the centre

Radius, diameter, circumference, chord, arc, sector — every part of a circle is secretly defined by its distance from one point: the centre. Click each part to light it up, slide the radius and watch the diameter stay exactly double, then race the label-the-part game.

Click the circle
🍕 Geometry · playable

Area of a circle — a rectangle in disguise

Slice a circle into skinny wedges like a pizza, fan them out, and they slot together into a rectangle — height r, width πr. That's the whole secret of πr²: no algebra, just scissors. Drag the slider to add slices and watch the bumpy edge melt into a clean rectangle, then play with the area calculator to see why the radius gets squared — and the diameter doesn't.

Slice the circle
🧊 Geometry · playable

Volume — count the cubes inside

Volume is just how many little cubes fit inside a shape. Pack a box with unit cubes by dragging length, width and height, watch why volume = l × w × h is one base layer stacked up, and see base area × height work for a prism too — all in cubic centimetres.

Fill the box
🧭 Geometry · playable

Bearings — which way, in three figures

A wave of the hand says "over there!" A bearing says it exactly: a three-figure angle measured clockwise from north, so due east is 090°. Spin an interactive compass, then read the bearing from A to B like a real navigator.

Spin the compass
🟩 Geometry & Measurement

Area — count the little squares

How much paint, carpet, or grass covers a shape? Tile a grid with unit squares and watch the count climb. Then meet the formulas that count them for you — l × w for rectangles, ½ × b × h for triangles.

Start tiling
🌀 Geometry & Measurement · playable

Rotation — spin a shape like a clock hand

Pin a point, pick an angle, choose a direction — and watch a shape swing around to its image, just like the hands of a clock. Spin it on a coordinate grid, trace the circles each corner rides, then race the challenge round.

Pin a point and spin
📊 Statistics · playable

Averages — mean, median & mode you can feel

Three ways to squeeze a whole pile of numbers into one. Drag the dots along a number line and watch the mean balance the data like a see-saw — then sneak in one giant outlier and feel the mean lurch while the median barely blinks.

Tip the see-saw
📈 Statistics · playable

Scatter graphs — watch a relationship appear from dots

Plot two things at once and a hidden relationship floats to the surface. Click to drop points on a grid and a line of best fit and a correlation read-out update live — positive, negative or none, strong or weak. Fit a line by eye, predict with it, hunt an outlier, and learn the rule every scientist lives by: correlation is not causation.

Drop some points
📉 Statistics · playable

Misleading graphs — how charts trick your eyes

Same numbers, wildly different picture. Drag a slider to chop a chart's baseline and watch a tiny 10% difference balloon into a fake shock — then snap it back to the honest truth. Squash a pictogram, peek behind a 3D pie, and spot the trick in a gallery of sneaky little charts.

Catch the trick
🥧 Statistics · playable

Pie charts — slices of a whole you can redraw

A whole circle is 360° and 100% — slice it and each wedge shows its share. Change the votes and the pie redraws live, with every slice's angle worked out as (count ÷ total) × 360°. Turn counts into degrees, read which slice wins, build one from a frequency table, and learn the one trap: a pie chart only works when the parts make a whole.

Slice the pie
🎲 Statistics · playable

Probability — from impossible to certain

How likely is it? Every answer lives somewhere on one line — from 0 (impossible) to 1 (certain). Drag everyday events onto the scale, see the same chance written as a fraction, a decimal and a percent, and find out why a 1-in-6 chance is not a promise.

Find the odds
🪙 Statistics · playable

Experimental vs theoretical probability — watch chance settle

Theory says a coin lands heads half the time. So flip one for real — the truth lurches all over the place before it ever settles. Flip hundreds of coins, roll a die, and watch what actually happens close in on what should happen.

Start flipping
🎲 Statistics · playable

Sample space — list every outcome, then just count

Probability sounds spooky until you realise it's mostly counting. A sample space is simply the list of everything that could happen. Lay all 36 two-dice outcomes on a 6×6 grid, pick a condition, and watch the matching squares light up with the exact odds. Spoiler: a 7 really is luckier than a 2.

Light up the grid
🍎 Statistics & Probability

Pictograms — counting with pictures

One little apple can stand for five. Build your own picture-graph, watch rows of icons redraw as you change the counts, meet the half-symbol, and learn to read a pictogram at a glance.

Build a pictogram
🎲 Statistics & Probability

Combined events — count the grid

Two coins, two dice, a coin and a die — when events happen together, every combination fits in a grid. Fill the table, highlight a target like 'both heads' or 'sum = 7', and watch the probability fall right out of the counting.

Build the grid