100 Fun Facts About Elementary School Math

Which symbol did Welshman Robert Recorde invent in 1557 to avoid 'the tedious repetition' of a three-word phrase?

The equals sign replaced the words 'is equal to', which Recorde was tired of writing out, and he chose two lines 'because no two things can be more equal'.

Which number name was coined, mathematician Edward Kasner said, by his nine-year-old nephew?

Googol, a 1 followed by a hundred zeros, was the boy's suggestion, and a respelling of it later gave the search engine Google its name.

What is 7 times 8?

56: a classroom trick is to count 5, 6, 7, 8, because the digits of the answer and the two numbers multiplied line up as 56 = 7 × 8.

How many squares does a standard chessboard have, laid out as eight rows of eight with the colours alternating?

64: in a famous legend a grain of wheat is doubled on every square, and the heap that results comes to more than 18 quintillion grains.

What shape is a standard red stop sign?

Octagon: the shape was settled in the 1920s but the colour was not, and American stop signs stayed yellow until the 1950s.

How many loaves make a baker's dozen?

13: the extra loaf is said to have been insurance, because medieval English bakers who sold short weight could be fined or flogged.

What do the three inside angles of any triangle on flat paper add up to, the same as a straight line?

180° holds only on a flat surface: a triangle drawn on a globe from the North Pole down to two points on the equator can have three right angles.

Which date is Pi Day, chosen because of the way the United States writes the month before the day?

March 14 is 3/14, pi's first three digits: physicist Larry Shaw started the party at San Francisco's Exploratorium in 1988, on what is also Albert Einstein's birthday.

Which shape do honeybees give the wax cells of a honeycomb, the most economical way to divide a flat surface?

Hexagon: people had guessed since antiquity that no pattern walls off equal cells with less material, but it took until 1999 for Thomas Hales to prove it.

Which name, from a Latin word meaning 'namer', does the bottom number of a fraction go by?

The denominator 'names' the kind of part, such as halves, thirds or quarters, while the top number, the numerator, from the Latin for 'counter', counts how many of them there are.

Which number does the Roman numeral L stand for, the letter that sits between X and C in value?

50: a smaller numeral written before a larger one is subtracted, which is why 40 is XL, ten short of fifty, and 90 is XC.

How many items are in a gross, the old trade count that means a dozen dozens?

144 is 12 × 12; the word comes from the Old French grosse douzaine, a 'large dozen', and a dozen gross makes a great gross of 1,728.

How many years is 'four score and seven', the span Abraham Lincoln counted back to 1776 at Gettysburg?

87: a score is 20, and Lincoln, speaking in November 1863, was counting back to the Declaration of Independence, perhaps echoing the 'threescore years and ten' of Psalm 90.

Which US coin is the smallest and thinnest in circulation, despite being worth more than a penny or a nickel?

The dime is 17.91 mm across and 1.35 mm thick, smaller than a penny worth a tenth as much, and its name comes from the Old French disme, a 'tenth part'.

Which name, from the Greek for a sharpened stick, does the ÷ division sign go by?

The obelus was first printed as a division sign by Swiss mathematician Johann Rahn in 1659; ancient scholars had used the same mark to flag suspect passages in manuscripts.

When 47 balloons are shared equally among 6 children, how many balloons are left over?

5 are left over: each child gets 7 balloons, which uses up 42, and the 5 that cannot be shared out fairly are what mathematicians call the remainder.

Which clear plastic half-circle, marked in degrees along its curved edge, do pupils use to measure angles?

A protractor usually carries two scales running in opposite directions, so that an angle can be read off whether it opens to the left or to the right.

How many full weeks are in a year, leaving one spare day, or two in a leap year?

52 weeks and one day make a year, which is why a date's day of the week moves on by one each year, or by two once a leap day has passed.

At how many degrees Fahrenheit does water freeze, on the scale used in United States weather forecasts?

32 °F is 0 on the Celsius scale; the two scales disagree at every temperature but one, 40 below zero, where they read exactly the same.

Which drawing of overlapping circles, named after a Victorian English logician, shows what two groups have in common?

Venn diagram: John Venn was handy with machines too, and in 1909 his cricket-bowling contraption clean bowled one of Australia's star batsmen.

Which graph, first published by William Playfair in 1801, shows how a whole splits into parts?

Pie chart: Florence Nightingale later reworked the idea into her 'coxcomb' diagrams, which showed that far more soldiers in the Crimea were dying of disease than of wounds.

Which Chinese puzzle cuts a square into five triangles, a square and a parallelogram to rearrange into pictures?

Tangram pieces are called tans, yet the name is a Western coinage of uncertain origin; in Chinese the puzzle is simply the 'seven boards of skill'.

Which word, one that also means 'blunt', describes an angle between a right angle and a straight line in size?

Obtuse comes from the Latin for 'blunted', which is also why a person who is slow to take a hint gets called obtuse.

Which triangle, named from Greek words for 'equal' and 'leg', has exactly two sides of the same length?

Isosceles triangles also have two equal angles, a proof so early in Euclid that it was nicknamed the 'bridge of asses', perhaps because weaker students could not get across it.

Which solid shape has every point of its surface the same distance from its centre?

A sphere wraps a given volume in the smallest possible surface, which is why a soap bubble settles into one; the name comes from the Greek sphaira, 'ball'.

Which family name covers squares, rectangles, kites and trapeziums alike?

Quadrilateral is built from the Latin for four and side, which makes it an oddity: pentagons, decagons and most other many-sided shapes take their names from Greek.

Which word describes the total every time two odd numbers are added, as in 3 + 5 or 7 + 9?

Even is the only possibility, because each odd number is an even one plus 1 and the two spare 1s pair up; odd times odd, by contrast, stays odd.

Which bead-and-rod counting frame is taught in Japan as a way to speed up mental arithmetic?

Abacus did not always mean beads: when the word entered English it meant a sand table, a board dusted with sand on which sums could be traced and wiped away.

Which kind of number word, such as 'third' or 'tenth', tells you position in a line rather than how many?

Ordinal numbers rank where cardinal ones count, and English has an impostor among them: 'second' was borrowed from French and Latin to replace the native word 'other'.

How many degrees are in a right angle, the corner carpenters check with the 3-4-5 rule?

90° is the angle a triangle with sides of 3, 4 and 5 units always contains, so a builder with a tape measure can square a corner with no other tool.

How many degrees make a full turn?

360° may echo ancient calendars: the old Persian year ran to 360 days, and the Babylonians counted in sixties, which divide 360 neatly.

How many equal parts make up the whole when a share is written as a percentage?

100: per centum is Latin for 'by the hundred', which is why a 100 percent discount makes something free, while a rise can run past 100 percent.

How many days are in four years in a row when one of them is a leap year?

1,461: three years of 365 days and one of 366, the extra day mopping up the roughly six hours by which each 365-day year falls short of the seasons.

How many feet are in a mile, a unit the Romans defined by counting a marching soldier's paces?

5,280 feet became the legal mile under Elizabeth I, when a statute set it at 8 furlongs of 660 feet each in place of the Romans' 5,000 Roman feet.

How many seconds are in a day, the product of 24 hours, 60 minutes and 60 seconds?

86,400 is 24 × 60 × 60, though some days run a second longer: 27 leap seconds were added between 1972 and 2016 to keep clocks in step with Earth's uneven spin.

How many five-cent nickels add up to one dollar, coins that are mostly copper despite their name?

20 nickels make a dollar, but the nickname is older than the coin: it first belonged to a one-cent piece of 1857, nine years before the five-cent nickel appeared.

How many pins stand in a bowling triangle of four rows, with one pin at the front and four at the back?

10 is a triangular number, 1 + 2 + 3 + 4; add a fifth row and you get 15, exactly the triangle of balls racked up to start a game of pool.

What is the name for the seven-sided shape of Britain's 50p coin?

Heptagon: the 50p's seven sides are gently curved so that the coin is the same width whichever way it is measured, which lets it roll through vending machines.

How many ounces are in a pound, the unit whose odd abbreviation lb comes from the Roman libra?

16 ounces make a pound, a word cut down from the Latin libra pondo, 'a pound by weight'; the other half of that phrase survives in the abbreviation lb.

Which number is the smallest prime, and the only prime in the two times table?

2 is the only prime that is not odd, since any larger non-odd number is 2 times something smaller; 1 is left out of the primes by definition.

In modern English usage, which number is written as a 1 followed by nine zeros?

One billion today means a thousand millions, but older British usage made a billion a million millions, with 12 zeros, and called this number a milliard.

How many inches are in a foot, in the old English system where three feet make a yard?

12 inches make a foot, and since 1959 the inch has been defined through the metric system, as exactly 2.54 cm, so every American ruler is a metric one in disguise.

How many cells does a standard Sudoku grid hold, nine rows of nine that are also split into nine 3×3 boxes?

81 cells, 9 × 9: the modern puzzle first appeared in an American magazine in 1979 as 'Number Place', and took off only after a Japanese publisher picked it up in 1984.

In the number 3,512, what is the digit 3 worth, sitting in the place furthest to the left?

3,000: each place to the left multiplies a digit by another ten, so 3,512 is 3 thousands, 5 hundreds, 1 ten and 2 ones.

How much fence goes all the way round a rectangular garden 9 m long and 4 m wide?

26 m is twice 9 plus twice 4, the perimeter, a word built from the Greek for 'measure around'; the 36 square metres of the area answer a different question.

What fraction of a pizza is left after three of its eight equal slices are eaten?

5/8 of the pizza is left, because 8/8 − 3/8 = 5/8 when the bottom numbers match, and that works out at 0.625, or 62.5%.

What fraction of an hour is 20 minutes, an hour being 60 minutes long?

1/3: 20 goes into 60 three times, and 60 suits the job because it also splits cleanly into halves, quarters, fifths, sixths, tenths and twelfths.

A film starts at 6:40 pm and runs for 95 minutes; at what time does it end?

8:15 pm: 95 minutes is 1 hour 35 minutes, so 6:40 plus an hour is 7:40, and 35 more minutes reaches 8:15.

Which mark separates whole numbers from tenths in the United States and Britain, where much of Europe uses a comma?

A dot: it caught on in English after John Napier, the inventor of logarithms, used one to mark decimals in the tables he published in the 1610s.

How many grams are in a kilogram, a unit originally based on the mass of a litre of water?

1,000 grams make a kilogram, and since 2019 the unit has been defined through the Planck constant instead of the platinum-iridium cylinder that had been the standard since 1889.

On a standard die the 1 sits opposite the 6: what do any two opposite faces always add up to?

Opposite faces add up to 7, and the rule is old: one terracotta die dug up at Mohenjo-daro, about 4,000 years old, already follows it, which is unusual for an Indus die.

Which five-sided shape gives its name to the headquarters of the United States Department of Defense?

The Pentagon has five sides, five floors above ground and five rings of corridors on every floor, with 17.5 miles of corridor in all.

A Connect Four grid has seven columns and six rows: how many discs does it take to fill every space?

It takes 42 discs to fill the grid. Connect Four is a solved game: the player who moves first can always win by making the right moves.

Most modern pianos have 88 keys, and 52 of them are white: how many of the keys are black?

The 36 black keys were traditionally made of ebony, while the white keys were covered with thin strips of ivory.

A haiku is taught as three lines of five, seven and five syllables: how many syllables altogether?

The 17 units of a Japanese haiku traditionally include a kigo, a word or phrase that points to the season of the year.

In Harry Potter the Hogwarts Express leaves from Platform 9¾: which two platforms does that number lie between?

The magical platform is reached through a barrier between platforms 9 and 10. At the real King's Cross, those two platforms stand in a separate building from the main station.

The classic Lego brick has two rows of four studs on top: how many studs is that altogether?

That makes 8 studs, and a few bricks go a long way: just six bricks of that size can be combined in 915,103,765 different ways.

A soccer match starts with two teams of eleven players: how many players are on the pitch in all?

There are 22 players, and only two of them, the goalkeepers, may handle the ball, and then only inside their own penalty areas.

Disney's One Hundred and One Dalmatians ends with two parents, their 15 puppies and how many adopted puppies?

Pongo and Perdita adopt 84 puppies, bought from shops for their fur, after finding them held alongside their own stolen litter.

Each of a Rubik's Cube's six faces shows nine coloured squares: how many squares is that altogether?

The 54 squares were stickers on the original puzzle, invented in 1974 by Ernő Rubik, a Hungarian professor of architecture.

A standard American bingo card has five rows and five columns: how many squares is that altogether?

The card has 25 squares, though the one in the centre is usually marked free and counts as filled before a single number is called.

How many days are in a fortnight, the two-week stretch whose name comes from Old English?

A fortnight is 14 days, and the word is a squashed form of the Old English for 'fourteen nights', because the Anglo-Saxons counted by nights.

A day has 24 hours: how many hours are there in a whole week of seven days?

A week lasts 168 hours, or 10,080 minutes. Someone who sleeps nine hours a night spends 63 of those hours asleep.

Tic-tac-toe, or noughts and crosses, is played on a grid of three rows of three: how many spaces is that?

The grid has 9 spaces, and with best play from both sides the game always ends in a draw, as most players soon discover.

In Monopoly a player collects $200 for passing Go: how much is collected for passing it four times?

Four trips past Go bring in $800. Every player also starts the standard game with $1,500 from the bank.

An octopus has three hearts: how many hearts are beating inside a group of six octopuses?

Six octopuses share 18 hearts: each animal has one main heart for the body and two smaller ones that pump blood through the gills.

The seven-spot ladybird is named for the spots on its back: how many spots do three of them have?

Three ladybirds carry 21 spots: each has three on either wing case and one more where the two wing cases meet.

On the 24-hour clock, which counts the hours since midnight, which afternoon time is written as 15:00?

15:00 is 3 pm, because 15 hours have passed since midnight. In the United States the 24-hour clock is often called military time.

Which solid shape, with two flat circular ends and one curved side, is a typical tin can of soup?

A cylinder is the usual shape of a food can, and its name comes from an ancient Greek word for a roller.

How many days does February have in a leap year, one more than in an ordinary year?

February has 29 days in a leap year. With only 28 in other years, it is the one month that can pass without a single full moon.

In Quidditch a goal scores 10 points and catching the Golden Snitch 150: what do four goals plus the Snitch total?

That comes to 190 points. Catching the Snitch also ends the match at once, yet Viktor Krum's Bulgaria still lost a World Cup final after he caught it.

An Olympic swimming pool is 50 metres long: how many lengths do swimmers cover in the 1,500 metres freestyle?

The race is 30 lengths of a 50-metre pool. In the 25-metre pools used for 'short course' events, the same race takes twice as many.

The first Pokémon games introduced 151 species: how many are left to catch after a player has caught 90?

That leaves 61 to catch. The original list runs from Bulbasaur, at number 1, to Mew, the last of the 151.

How many lines of symmetry does a square have, counting every fold that makes the two halves match?

A square has 4 lines of symmetry: two run through the middles of opposite sides and two run from corner to corner.

Which idea, written as a figure eight lying on its side, means going on for ever without any end?

Infinity got its sideways-eight symbol from the English mathematician John Wallis, who introduced it in 1655 and never explained why he chose it.

Triceratops had three horns on its skull: how many horns would a herd of eight Triceratops have between them?

The herd would carry 24 horns. The name Triceratops comes from ancient Greek words meaning 'three-horned face'.

Each baseball team bats until three outs are made, in each of nine innings: how many outs is that per team?

Three outs in each of nine innings make 27 outs for a side, though a home team that is already ahead skips its last turn at bat. A game tied after nine innings goes to extra innings.

Most starfish have five arms: how many arms would seven of these five-armed starfish have between them?

Seven starfish share 35 arms, and a lost arm is rarely a disaster, because most starfish can grow back damaged or missing arms.

A century in cricket is a score of 100 runs: how many more does a batter on 62 need?

The batter needs 38 more runs. A century is also known as a ton, and is rated about as highly as a bowler taking five wickets in an innings.

How many wheels are there altogether on one unicycle, one bicycle and one tricycle parked side by side?

Together they have 6 wheels, and the names do the counting: uni-, bi- and tri- are prefixes meaning one, two and three.

In the Fibonacci sequence each number is the sum of the two before it: which number follows 8, 13, 21?

Next comes 34. Leonardo of Pisa, known as Fibonacci, brought the sequence to Europe in a book of 1202, where it counts a growing family of rabbits.

April, June, September and November each have exactly 30 days: how many days is that in total?

The four months add up to 120 days. In the knuckle trick for remembering month lengths, they land in the dips between the knuckles, as does February.

A rugby union match is played in two halves of 40 minutes each: how many minutes is that in total?

The match lasts 80 minutes of play, though the clock stops for injuries, so the time that actually passes is usually longer.

Which decimal number means exactly the same as the fraction one half, or 1 ÷ 2 on a calculator?

One half is 0.5, because the digit after the whole number counts tenths, and five tenths make a half.

Which word describes a number such as 121 or 3,443 that reads the same forwards and backwards?

A palindrome can be a number, a date or a word: racecar, rotor and madam all read the same in both directions.

Which word names a straight line across a circle through its centre, twice as long as the radius?

The diameter takes its name from Greek words meaning 'across' and 'measure', and no straight line drawn inside a circle can be longer.

Which name is given to the ten digits 0 to 9, a system that Fibonacci helped to spread through Europe?

Arabic numerals became known in Europe partly through Fibonacci, who met them in the Algerian city of Béjaïa; the place-value idea behind them began in India.

On the clock face of Big Ben the hours are written in Roman numerals: which hour does XI mark?

XI marks 11: an X for ten with an I added for one more. Big Ben writes four as IV, although many clock faces with Roman numerals use IIII instead.

Which name do mathematicians give the diamond shape on a playing card, a slanted figure with four equal sides?

A rhombus is also called a diamond or a lozenge, and a square is simply a rhombus whose four corners are all right angles.

Which chart uses rows of small icons to stand for numbers, such as one smiley face for every ten pupils?

A pictogram turns numbers into rows of icons, which makes the figures more interesting to look at and easier to understand.

In a famous story, which total did schoolboy Carl Gauss find in moments by adding every number from 1 to 100?

The answer is 5,050. Gauss is said to have paired the numbers off, 1 with 100, 2 with 99 and so on, making 50 pairs that each add up to 101.

In the ancient Chinese Lo Shu magic square of the numbers 1 to 9, every row adds up to what?

Every row, column and diagonal adds up to 15. In Chinese legend the pattern first appeared on the shell of a magical turtle that emerged from the water.

The word 'calculate' comes from the Latin name for which small object, once used as a counter?

A pebble was a calculus in Latin, and Romans did their sums by pushing pebbles around a counting board; doctors still call a kidney stone a calculus.

What do the twelve hour numbers printed around an ordinary clock face, from 1 to 12, add up to?

The total is 78. A quick way to find it is to pair 1 with 12, 2 with 11 and so on, then add up the six equal pairs.

Which ancient people's habit of counting in sixties is the reason an hour still has 60 minutes?

The Babylonians counted in sixties, a system they inherited from the Sumerians, and it survives today in minutes, seconds and the measuring of angles.

How many minutes are there in three quarters of an hour, the length of one half of a soccer match?

Three quarters of an hour is 45 minutes. The referee then adds stoppage time to each half to make up for injuries and substitutions.

A volleyball court is 18 m long and 9 m wide: what is the area of the whole court?

The court covers 162 square metres, and the net splits it into two halves that are each a perfect square, nine metres along every side.

Folding a sheet of paper in half doubles its layers every time: how many layers are there after seven folds?

Seven folds make 128 layers, which is why paper soon becomes too thick to bend. In 2002 Britney Gallivan, a Californian student, managed twelve folds with a very long strip.

Chess players count a queen as nine points and a rook as five: what are a queen and two rooks worth?

Together they are worth 19 points. On the same scale a pawn counts as one point, and a knight or a bishop as three.

A football league awards three points for a win and one for a draw: what do seven wins and two draws earn?

The team earns 23 points. Leagues used to give only two points for a win, and the switch to three was meant to encourage more attacking play.