Tag
Numbers
Zero, place value, primes, and numbers below nothing — 84 tiny stories across 9 shelves.
Math
Number ideas with toys — 64 stories.
All math →Putting together
What Does Adding Do?
Adding only gathers — nothing is created. The order makes no difference, which halves what anyone has to memorise, and hard sums split into friendly steps.
Let’s go →Levelling everyone off
What Does an Average Actually Tell You?
An average is what everyone would get if the total were shared out evenly. It is a fact about a group rather than about any one member of it.
Let’s go →A thousand times, not a bit
How Much Bigger Is a Billion Than a Million?
A billion is a thousand millions. Count them in seconds and the gap stops being abstract: a million is eleven days, a billion is thirty-two years.
Let’s go →On and off is enough
How Do Computers Count With Only Two Digits?
A switch is only ever off or on, so computers count with two digits. Place value that doubles each column can still write any number you like.
Let’s go →A 50.7 per cent chance
In a Room of Twenty-Three, Two People Share a Birthday
With 23 people the odds of a shared birthday pass one half, because 23 people make 253 pairs — and it is the pairs, not the people, that get the chances.
Let’s go →The small things add up first
Why Does the Money Run Out Before the Month?
Budgets fail on the small, frequent spending rather than the big purchases you remember — so the number that matters is price times how often.
Let’s go →More orders than atoms nearby
Has Anyone Ever Had This Hand Before?
Adding the numbers one to fifty-two gives a few thousand; multiplying them fills sixty-eight digits. It takes seven riffles to reach that properly.
Let’s go →Objects have no memory
Why Does a Coin Not Owe You Heads?
A coin has no memory, so a long run of tails changes nothing at all about the next throw. The coin does not owe you anything and never did.
Let’s go →Counting up, not taking away
How Do You Work Out Your Change?
Your change is not a distance but a sum of hops counted forwards from the price. That is why the small coins come out first — the order the hops came in.
Let’s go →Two hands, one set of numbers
Why Does the 3 on a Clock Mean Both 3 and 15?
The twelve printed numbers belong to the hour hand alone. The minute hand is counting sixty little marks in between, which is why 3 means 15.
Let’s go →Interest on the interest
Why Does Saved Money Grow Faster Each Year?
Interest is added to your money, and next year you earn interest on that too. The curve accelerates — and it works exactly as hard against you on debt.
Let’s go →Two numbers, one place
How Do You Describe Exactly One Square?
Two numbers in an agreed order, measured from a shared corner, name one exact place and no other — how far across, then how far up.
Let’s go →One thing, one word
How Does Counting Work?
Counting has three rules: one word per object, always the same order, and the last word is the answer. Young children reliably miss the third one.
Let’s go →Count a little, multiply a lot
How Do You Count a Huge Crowd?
Any count taking an hour is counting a different crowd by the end, so one square is counted and the rest is measured. All the error lives in that square.
Let’s go →More ways to get there
Why Is Seven the Commonest Roll?
Two dice do not make every total equally likely. Six different pairs add up to seven, while two and twelve have exactly one route each.
Let’s go →Taking a slice off the top
How Do Shops Work Out a Sale Price?
A discount is a percentage of the old price, so the same thirty per cent off saves wildly different amounts — and two discounts never simply add up.
Let’s go →Fair shares
How Does Division Work?
Division takes one pile and shares it into equal groups, and the answer it hands back is the size of a single group rather than the number of groups.
Let’s go →Two of the same
What Does Doubling Mean?
Doubling adds a copy rather than a fixed amount, so it grows far faster than anyone expects: ten doublings of 1 reach 1,024, and thirty pass a billion.
Let’s go →Balance, not 'the answer'
What Does the Equals Sign Really Mean?
Equals does not mean an answer comes next. It means both sides are worth the same, which is why 7 = 4 + 3 is perfectly correct written that way round.
Let’s go →Close enough on purpose
What Is Estimating?
An estimate trades precision for speed, and it is often the better answer — as well as the check that catches an exact calculation gone badly wrong.
Let’s go →Proved in 1976, by machine
Four Colours Are Always Enough
Four colours suffice for every possible map — a claim that resisted proof for over a century, then fell to a computer checking 1,936 cases no human could.
Let’s go →Bigger bottom, smaller piece
Why Is a Third Bigger Than a Quarter?
The bottom number counts how many pieces the whole was cut into, so a bigger bottom means smaller pieces, and that is why a third beats a quarter.
Let’s go →Seeing beats reading
Why Draw Numbers as a Picture?
Eyes compare lengths far faster than they read columns, so a graph turns numbers into heights — as long as the axis honestly starts at zero.
Let’s go →Comparing
Which Number Is Bigger?
A number is bigger if you reach it later while counting — further right on the number line, whatever the number happens to look like.
Let’s go →Small steps that stop being small
Why Does Doubling Get Out of Hand?
Ten doublings multiply anything by roughly a thousand, which is why one grain per chessboard square ends as more rice than the world has grown.
Let’s go →Two equal shares
What Does Half Mean?
A half is one of two pieces that match exactly. The shape can be anything — straight, wiggly, striped — as long as the amount is the same.
Let’s go →Eratosthenes, about 240 BC
How We Measured the Earth With a Stick
Two noon shadows and one long walk gave Eratosthenes the size of the planet, to within a few per cent, without his ever leaving Egypt.
Let’s go →It reaches past the Sun
What If You Folded Paper Fifty Times?
Every fold doubles the thickness, so fifty folds of ordinary paper would reach three quarters of the way from here to the Sun.
Let’s go →Never running out
What Is Infinity?
Infinity is not a huge number — it is the fact that counting never has to stop. Infinitely many fractions fit between 0 and 1, with room to spare.
Let’s go →The catalogue is not the shelf
How Does a Library Find One Book?
Shelves cannot be sorted by subject and by author at once, so a library keeps a small separate list of pointers that sends you to one exact spot.
Let’s go →Everything divided by the same number
How Does a Map Fit a Country on a Page?
Halve a map's scale and it takes a quarter of the paper, not half — and the wording runs backwards: a small-scale map is the one covering a country.
Let’s go →Everyone agreeing
Why Do We Measure With Units?
Measuring is counting agreed, equal-sized steps. The agreement is the whole point: without it, the number you end up with tells nobody anything.
Let’s go →One giant number spoils it
Why Is the Average Sometimes a Lie?
One extreme value drags an average a long way and leaves the middle value untouched. Which of the two is honest depends on the question being asked.
Let’s go →Making any amount
Why Do Coins Have Different Values?
Coin values follow a 1-2-5 pattern so that a handful can build any price out of very few coins. Their worth comes entirely from agreement.
Let’s go →Many equal groups
What Does Multiplying Do?
Multiplication is adding the same number over and over, compressed into a single move — which is exactly why the times tables are worth knowing by heart.
Let’s go →The line carries on
How Can a Number Be Less Than Nothing?
Negative numbers are just the number line carrying on past zero instead of stopping there. The minus sign says which side of zero you are standing on.
Let’s go →Numbers as places
What Is a Number Line?
Lay the numbers out in order and arithmetic turns into walking. Adding steps right, subtracting steps left, and suddenly negatives have somewhere to live.
Let’s go →Can everyone find a partner?
Odd and Even Numbers
Pairing is the whole test: what pairs up is even, what strands one is odd. It is also why odd plus odd is even — the two lonely ones find each other.
Let’s go →Something that repeats
What Is a Pattern?
A pattern is a rule that keeps going. Name the rule and you can say what comes next without doing any of the work of getting there.
Let’s go →Out of a hundred, always
What Does Per Cent Actually Mean?
Half a class of eight and half a school of eight hundred are the same share and wildly different numbers of children. The hundred is just a yardstick.
Let’s go →Every circle's hidden number
What Is Pi and Why Does It Never End?
Fifteen decimal places would size a circle as wide as the solar system to within a finger's width, which is rather more than anyone has ever needed.
Let’s go →Position carries meaning
Why Does 25 Mean Twenty-Five?
A digit's worth depends on where it sits, not on what it looks like. That one idea is why ten symbols are enough to write any number at all.
Let’s go →No rectangle but a line
Which Numbers Refuse to Split?
Twelve always breaks down to two, two and three, however you start. Primes thin out as numbers grow but never stop — proved two thousand years ago.
Let’s go →One of four
What Is a Quarter?
A quarter is one of four equal shares, which makes it half of a half. Four unequal pieces contain no quarter at all, whatever anyone calls them.
Let’s go →You are usually in the slow one
Why Is the Other Queue Always Faster?
With three tills, two queues are beating yours most of the time. One shared queue feeding every till makes the wait both fairer and shorter.
Let’s go →Two out of a million is still nearly none
Why Does Buying Two Tickets Barely Help?
Doubling a tiny chance leaves you with a tiny chance, twice over. And somebody winning is an entirely different claim from you winning.
Let’s go →Position is not distance
Why Do Rankings Change When Nothing Does?
A ranking keeps the order and throws the gaps away, so a hair's difference can flip two positions while an enormous gap disappears without trace.
Let’s go →The bit left over
What Is a Remainder?
Make as many equal groups as you can and the bit that will not fit is the remainder. It is not a mistake — it is the honest answer to an uneven split.
Let’s go →Balance beat arithmetic
Why Do Clocks Sometimes Say IIII?
Clock faces often use IIII rather than the correct IV, because four heavy strokes balance the VIII sitting opposite. On a dial, looks beat the rule.
Let’s go →Close enough, on purpose
Why Do We Round Numbers?
Rounding deliberately gives up a little accuracy to get a number you can actually hold in your head. Do it at the end of a sum, never at the start.
Let’s go →Length halves, weight drops by eight
Why Is a Model Never Quite Right?
Halving a length quarters the area and cuts the volume to an eighth, which is why a model never quite behaves like the thing it copies.
Let’s go →Faster than one at a time
Counting in Jumps
Counting in twos, fives or tens moves in equal jumps instead of single steps. It gets you there faster, and it quietly builds the times tables.
Let’s go →A third direction
What Makes a Shape 3D?
Depth is what lets a shape hold space rather than merely cover it, and with that third direction come faces, edges and corners.
Let’s go →Order makes finding easy
Why Do We Sort Things?
Unsorted, finding one thing among a thousand costs 500 checks on average. Sorted, halving the problem at every look gets you there in ten.
Let’s go →Sharing, with an awkward remainder
How Do You Split a Bill Fairly?
Splitting a bill is straightforward division until the remainder appears. At that point it stops being arithmetic and becomes a question about people.
Let’s go →What is left
What Does Taking Away Do?
Subtraction does two jobs with one operation. It finds what is left after some is taken away, and it measures the gap between two numbers.
Let’s go →Counting without losing your place
Why Count in Groups of Five?
Tally marks bundle counts into fives so that you record one event at a time and add up groups at the end, instead of recounting from the beginning.
Let’s go →Sharing between three
What Is a Third?
A third is one of three exactly equal shares: bigger than a quarter, and the first fraction most people meet that cannot be written exactly as a decimal.
Let’s go →Shortcuts, not memory
What Patterns Hide in the Times Tables?
Four times six is a rectangle of counters, not a phrase to recite — and every answer in the nine row has digits that add up to nine.
Let’s go →Ten per cent, then adjust
How Do People Work Out a Tip in Their Head?
Nobody calculates a tip exactly. You move the decimal point one place to get ten per cent, build the rest from that, and round to something friendly.
Let’s go →The number under the price
Which Packet Is Actually Cheaper?
Divide the price by the amount and two packets become comparable at last. The catch is that the cheaper unit price only counts if you actually use it all.
Let’s go →Size and heaviness are separate
Why Is a Big Thing Not Always Heavy?
Big does not mean heavy. Weight depends on how tightly matter is packed into a space, not on how much space the thing happens to take up.
Let’s go →A number your eye reads first
Why Does Everything Cost £4.99?
People read the leftmost digit first and round the rest away, so a price of 4.99 gets quietly filed in memory as four. Shops have known this for a century.
Let’s go →A number for nothing
What Is Zero?
Zero counts what is not there, and it also holds an empty place in a written number. Without that second job, 105 and 15 would look exactly the same.
Let’s go →How things work
Everyday machines, taken apart — 6 stories.
All how things work →A compass painted on the ground
Why Are Runways Numbered?
A runway's number is its compass heading divided by ten, so a pilot lining up can check the direction against the instruments.
Let’s go →And that is the boring half
Your Phone Beats the Computer That Flew to the Moon
The computer that landed Apollo 11 had less memory than one photo, and it was enough — because it did one job perfectly rather than everything adequately.
Let’s go →Millions of tiny corrections
How Does a Computer Learn?
Nobody writes the rules for recognising a cat. The computer guesses, is told how wrong it was, and nudges its own numbers a million times.
Let’s go →Rows and columns, checked constantly
How Does a Keyboard Know Which Key You Pressed?
No wire runs from every key. They are wired as a grid and scanned hundreds of times a second, so twenty wires find one key among a hundred.
Let’s go →Guessing is done by machine
Why Do Passwords Have to Be Long?
Nobody sits typing guesses. A computer tries billions a second and every human trick first, so length beats cleverness every single time.
Let’s go →Mostly by not being sent
How Does a Picture Get to Your Television?
A moving picture is far too much to send, so almost all of it is thrown away: only what changed, and only what your eye would notice, makes the trip.
Let’s go →Space
Crashy night-sky stories — 3 stories.
All space →Neptune, 1846
The Planet Found With a Pencil
Neptune was found by arithmetic: Uranus was being pulled off its predicted path, and the calculation said exactly where the puller must be.
Let’s go →Further than you think
How Far Away Is the Moon?
The Moon sits about 384,000 km away — a gap wide enough to line up every other planet in the solar system, side by side, with room to spare.
Let’s go →Bigger than your brain wants
How Big Is the Sun?
109 Earths would span the Sun's face and 1.3 million would fill it. It holds 99.8% of everything in the solar system, and among stars it is ordinary.
Let’s go →Earth & sky
Weather, light, and the air around us — 3 stories.
All earth & sky →An argument about very large numbers
Every Breath You Take Has Been Breathed Before
A single breath holds more molecules than the atmosphere holds breaths — so an old one, well mixed, is almost certainly inside the breath you just took.
Let’s go →One-ninth showing
Why Do Icebergs Float So Low?
Ice is only slightly less dense than seawater, so an iceberg floats with roughly eight-ninths of itself hidden below the surface and out of sight.
Let’s go →Two numbers for anywhere on Earth
How Do You Say Exactly Where You Are?
Any point on the planet can be named with two angles, and longitude was far harder than latitude: it had to wait for an accurate clock.
Let’s go →Life & body
Seeds, hearts, senses, and growing things — 3 stories.
All life & body →And a short list of exceptions
You Are Not Made of What You Were Made Of
Tissues replace themselves at wildly different speeds — days for gut lining, a decade for skeleton — and a few things are made once and never renewed.
Let’s go →Roughly one bacterium per human cell
About Half of You Is Not You
Your body is roughly half bacteria by cell count, mostly living in your gut, and the famous ten-to-one version of that figure turned out to be wrong.
Let’s go →Harvey, 1628
How We Found Out Blood Goes Round
William Harvey proved blood circulates by multiplying: the heart pumps far more blood in an hour than the body could possibly make.
Let’s go →Animals
Creatures on land, in the sea, and in the air — 2 stories.
All animals →Counting down
What Does Endangered Mean?
Endangered is about the trend and the risks, not just the number: a shrinking, scattered population is in danger long before it is small.
Let’s go →Drawing a line that nature blurs
What Makes Two Animals the Same Kind?
A great dane and a chihuahua are one species; two identical birds can be two. The test is whether the young can have young of their own.
Let’s go →Physics
Invisible forces you can play with — 1 story.
All physics →What things are made of
Atoms, metal, glass, plastic, and every kind of stuff — 1 story.
All what things are made of →Everyday wonders
Kitchen, bubbles, echoes, and odd little magic — 1 story.
All everyday wonders →