100 Fun Facts About 4th Grade Math

Which of these numbers is a prime number?

7 is prime: nothing divides it but 1 and 7, and huge primes keep data safe online, because multiplying two of them is easy while working out which two were multiplied is very hard.

What do we call a whole number with more than two factors, like 8 or 15?

Composite — every such number is made by multiplying primes together, as 8 is 2 × 2 × 2, which is why primes get called the building blocks of all numbers.

What do we call the distance all the way around the outside of a shape?

Perimeter is found by adding up the length of every side, which is how you would work out how much fence a garden needs.

What is the area of a rectangle 6 cm long and 4 cm wide?

24 cm²: picture 4 rows of 6 one-centimetre squares, which is why area is counted in square units.

What is the distance all the way around a rectangle 5 m long and 3 m wide?

16 m: add the length and the width, then double the total, because a rectangle's opposite sides always match.

In the fraction 3/4, what is the number on top called?

The numerator: a fraction is also a division waiting to happen, so 3/4 means 3 divided by 4, which comes to 0.75.

Which fraction is greater than 1?

7/4: a top number bigger than the bottom earns the name improper fraction, though nothing is wrong with one, and this is just 1 3/4 in disguise.

How many degrees are in a right angle?

90: to mark one without any tool, measure out a triangle with sides of 3, 4 and 5, a trick surveyors still use.

An angle bigger than a right angle but smaller than a straight angle is called what?

Obtuse: the word comes from the Latin for blunt, which is also why a person slow to catch on gets called obtuse.

How many degrees make a full turn all the way around a point?

360: the number splits evenly by every whole number from 1 to 10 except 7, which makes a circle easy to cut into equal parts.

Which tool measures the size of an angle?

A protractor: most carry two rows of numbers running in opposite directions, so an angle can be read whichever way it opens.

What do the three angles inside a flat triangle add up to?

180°: that only holds on a flat surface, because a triangle drawn on a globe has angles that add up to more.

A triangle with three sides all the same length is called what?

Equilateral: it is the very first shape Euclid's geometry book builds, from two overlapping circles whose crossing point becomes the third corner.

A triangle with exactly two sides the same length is called what?

Isosceles: the angles facing its two equal sides always match too, a proof nicknamed the bridge of asses, perhaps because weaker students could not get past it.

What is any shape with four straight sides called?

Quadrilateral: the family takes in squares, rectangles and kites, and every square also counts as a rectangle, though not the other way round.

What shape are the cells in a honeycomb?

Hexagon: six-sided cells fit together with no gaps using the least wall for the space they hold, a hunch about bees that was only proved in 1999.

What shape is a standard stop sign?

Octagon: in the 1920s American road engineers gave each kind of sign its own outline, so a driver could tell a stop from any other warning by shape alone.

A five-sided shape is called what?

A pentagon: the Pentagon near Washington got its outline from the roads around the first plot picked for it, and the five-sided plan stuck even after the site moved.

A closed flat shape made only of straight sides is called what?

A polygon: Archimedes pinned down the value of pi by trapping a circle between two 96-sided ones, one drawn just inside it and one just outside.

The distance from the centre of a circle to its edge is called what?

The radius: it is the gap a compass holds fixed between its spike and its pencil, which is why the curve it draws comes out perfectly round.

If a circle's radius is 5 cm, how wide is it all the way across through the middle?

10 cm: that is two radii end to end, and a string wrapped once around the edge would stretch just over three of those widths, the number called pi.

Two lines that stay the same distance apart and never cross are called what?

Parallel: railway rails are the classic pair, yet they seem to meet far away, a trick of the eye that artists copy with a vanishing point.

Two lines that cross to make right angles are called what?

Perpendicular: builders check that a wall stands perpendicular to level ground with a plumb line, a weight on a string that gravity pulls straight down.

A straight path that stops at two endpoints is called what?

A line segment: in geometry a true line never ends in either direction, so everything anyone actually draws with a ruler is only a segment of one.

A fold that makes both halves of a shape match exactly is called what?

A line of symmetry: stand a small mirror along it and the reflection rebuilds the whole shape, which is why it is also called a mirror line.

Which solid has six square faces?

Cube: that sameness is why dice are cubes, since six matching faces give every number an equal chance of landing on top.

What is the answer to a multiplication problem called?

The product: swap the two numbers and it stays the same, so 3 × 8 and 8 × 3 both come to 24, while 8 ÷ 2 and 2 ÷ 8 give different answers.

In 30 ÷ 2 = 15, which number is the quotient?

15: the quotient is the answer to a division, and multiplying it back checks the work, since 15 × 2 returns the 30 you started with.

When you divide 17 by 5, what is the remainder?

2: three fives make 15, leaving 2 over, and a remainder can never reach the number you divide by, or one more group would fit.

Which of these is a factor of 12?

6: twelve splits evenly among 2, 3, 4 or 6 people, a handiness that ten, with only 2 and 5, cannot match.

Which of these is a multiple of 7?

42: it is 7 × 6, whereas a number that merely ends in 7, such as 17 or 187, need not be in the seven times table at all.

What is the value of the 7 in 4,725?

700: each step to the left makes a digit worth ten times more, so the same 7 one place further over would count for 7,000.

9 is a square number because it equals what?

3 × 3: nine dots can be laid out as a grid three across and three down, which is exactly where square numbers get their name.

Which multiplication means the same as 5 + 5 + 5?

3 × 5: count by fives three times, 5, 10, 15, and you have done the multiplication, which is why skip counting is taught as the way into the times tables.

In Roman numerals, what number does IX stand for?

9: a smaller numeral placed before a larger one is subtracted, yet many clock faces ignore that rule and show four as IIII.

In Roman numerals, which letter stands for 100?

C: the sign probably did not begin as that letter at all, because an older symbol for a hundred seems to have been reshaped over time until it matched the Latin C.

How many millimetres are in a centimetre?

10: metric prefixes all step by powers of ten and attach to any unit, so the same steps work for litres and grams as for lengths.

Which unit of length equals 12 inches?

A foot: for decades the United States actually had two of them, because surveyors kept an older, very slightly different foot after the unit was redefined.

How many feet are in a yard?

3: but a square yard holds nine square feet, not three, because the three counts along the length and again along the width.

How many ounces are in a pound?

16: that is the everyday pound, but in the troy system used for gold and silver a pound holds only 12 ounces.

How many quarts are in a gallon?

4: a quart is a quarter of a gallon on both sides of the Atlantic, but the British gallon is about a fifth bigger than the American one.

How many seconds are in one hour?

3,600: 60 × 60, and the sixties go back to the base-60 counting of ancient Sumer and Babylon, which astronomers carried into the way we split time.

In a leap year, which month gets an extra day?

February: the extra day keeps the calendar in step with the seasons, yet century years such as 1900 skip it unless they divide by 400.

How many years are in a century?

100: counted strictly from AD 1, each century starts in a year ending in 01, so the 21st began on 1 January 2001, though popular usage started it a year sooner.

How many items are in a dozen?

12: a baker's dozen is 13, said to come from bakers slipping in a spare roll so that nobody could punish them for selling a batch that weighed light.

What is a 1 followed by six zeros called?

One million: three zeros further the names once disagreed, because a British billion long meant a million million rather than a thousand million.

Rounding means changing a number to what kind of value?

A close, simpler one: on an exact tie, Python and many other computer languages round to the even neighbour, so 0.5 becomes 0 while 1.5 becomes 2.

Which fraction is the same amount as one half?

2/4: multiplying the top and bottom of a fraction by the same number changes how it looks but not its size, so 1/2, 2/4 and 50/100 all match.

In a number like 25.97, what is the dot between the 5 and the 9 called?

A decimal point: much of Europe writes a comma in its place, and the world's measurement body officially accepts either mark.

How many grams are in one kilogram?

1,000 g: until 2019 the kilogram was not a formula but an object, one metal weight in a vault near Paris that every other kilogram was checked against.

About how much does one litre of water weigh?

1 kg: that is no accident, because the kilogram was originally defined as the mass of a litre of water, and the match still holds almost exactly.

How many years are in a millennium?

1,000: as the last one turned, programmers feared that computers storing years as two digits would take the new year for 1900, the Y2K bug.

What are the corners of a cube called?

Vertices: add them to the faces, subtract the edges, and any box, pyramid or prism gives exactly 2, a pattern named after Euler.

Which solid has two flat circular faces and one curved side?

Cylinder: unroll the curved side and it flattens into a plain rectangle, so the whole solid can be made from two circles and one rectangle of paper.

What do you call a triangle that has one square corner?

A right triangle: draw any triangle inside a half circle with the straight edge as one side, and the corner that touches the curve always comes out square.

What is any four-sided shape with four equal sides called, whatever its angles?

A rhombus: every square is one, since a square is simply a rhombus with square corners, and the leaning diamond on a playing card is another.

At what temperature does water boil on the Fahrenheit scale?

212 °F: only at sea level, though, because the boiling point falls as air pressure drops, so water on a high mountain boils at a lower temperature.

In Roman numerals, what number does MM stand for?

2,000: the earliest Romans would not have recognised it, because they wrote a thousand with a different symbol and the letter M only took over later.

Multiplying any number by 1 gives what?

The same value: adding has a do-nothing number too, which is zero, yet multiply by zero and any number is wiped out instead of kept.

Which digit of a whole number tells you whether it is even?

The last digit: if it is 0, 2, 4, 6 or 8 the number is even, and the list starts at 0 because zero itself is an even number, however odd that sounds.

Which name for a 1 followed by one hundred zeros was coined in 1920 by a nine-year-old boy?

Googol was the invention of Milton Sirotta, nephew of mathematician Edward Kasner, and the search engine Google took its name from a misspelling of the word.

Which maths symbol did Welshman Robert Recorde invent in 1557 to save writing the same words again and again?

The equals sign first appeared in Recorde's book The Whetstone of Witte, where he reasoned that no two things can be more alike than twin lines of one length.

A spider has eight legs: how many legs are there altogether on nine spiders?

That makes 72 legs, and every one of them is built from seven separate parts, which a spider straightens by pumping up its blood pressure.

Super Bowl 50 dropped Roman numerals for a year: which single letter would have stood for its number?

L stands for fifty, but designers found a lone L hard to build a logo around, so the NFL used ordinary digits for one year and went back to Roman numerals for Super Bowl LI.

Sunlight reaches Earth after about 500 seconds: how many whole minutes is that, with 20 seconds left over?

The trip takes 8 minutes and 20 seconds, so the Sun seen in the sky is always the Sun as it was that long ago.

A chessboard has 64 squares, half of them light and half dark: how many dark squares are there?

There are 32 dark squares, and the board is always turned so that each player has a light square in the near right-hand corner.

Which seven-sided shape is Britain's 50p piece, the first coin of that shape in the world?

The heptagon coin has gently curved sides that keep it the same width at any angle, so it still rolls through vending machines.

A score is twenty: how many years did Abraham Lincoln mean by four score and seven at Gettysburg?

It comes to 87 years, which Lincoln counted back from 1863 to reach 1776, the year of the Declaration of Independence.

The Titanic sank in 1912 and its wreck was found in 1985: how many years lay between the two?

The gap was 73 years, and the wreck was finally spotted by a French and American team led by Jean-Louis Michel and Robert Ballard.

Which solid shape, with no flat faces, edges or corners, does a soap bubble form as it floats?

A sphere wraps a given amount of air in the smallest possible surface, which is why a floating bubble pulls itself round.

A standard deck of 52 playing cards is dealt out equally to four players: how many cards does each get?

Each player gets 13 cards, which is also how many cards the deck holds in each of its four suits, from ace to king.

The Eiffel Tower in Paris is 330 metres tall: what is that height rounded to the nearest hundred metres?

It rounds down to 300 m, and for 41 years no structure on Earth stood taller, until New York's Chrysler Building passed it.

Which of these numbers means the same as one quarter, the share of a dollar that a quarter coin is worth?

0.25 is one quarter, which is why a quarter coin is worth 25 cents and it takes exactly four of them to make a whole dollar.

Which ancient counting frame of sliding beads is used to teach arithmetic to children in Japan and China?

An abacus was still the everyday calculator in shops and markets across the Soviet Union, where most schools taught it until the 1990s.

Which word for a period of ten years, such as the 1980s, comes from the Greek for a group of ten?

A decade lasts ten years, and the same Greek root names the decathlon, an athletics contest made up of ten events.

A classic sudoku grid has nine rows of nine squares: how many squares are there in the whole grid?

The grid has 81 squares, and although the puzzle is known by a Japanese name, its modern form first appeared in American puzzle books in 1979 as Number Place.

Which number is both the smallest prime with two digits and the number of players on a soccer side?

11 can only be divided evenly by 1 and by itself, and its English name, eleven, is the smallest number name with three syllables.

Which picture of overlapping circles, introduced by an English logician in 1880, shows what groups have in common?

A Venn diagram is named after John Venn, and the region where two of its circles overlap holds whatever belongs to both groups at once.

An ordinary year has 365 days: how many days are left over after 52 full weeks are counted?

Just 1 day is left over, which is why the year after an ordinary one starts on the next day of the week instead of the same one.

Many clock faces with Roman numerals show four o'clock as IIII: how is that number usually written instead?

IV is the usual form, yet clockmakers have favoured IIII since at least the Wells Cathedral clock of the late 14th century.

A standard guitar has six strings: how many strings are there altogether on nine standard guitars?

Nine guitars carry 54 strings, though a twelve-string guitar doubles each one up into pairs, like a mandolin or a lute.

Kilimanjaro, Africa's highest mountain, is 5,895 metres tall: what is that to the nearest thousand metres?

It rounds up to 6,000 m, and Kilimanjaro is also the highest mountain in the world that stands alone instead of in a range.

A United States dime is worth ten cents: which fraction of a whole dollar is one dime?

A dime is 1/10 of a dollar, and its name comes from an Old French word meaning a tenth part.

Which name, from the Latin for sharp, is given to any angle narrower than the square corner of a page?

Acute angles are the pointed ones, and the word goes back to acus, the Latin name for a needle.

Which simple counting strokes, usually bundled in fives, go back to notches cut in bones over 25,000 years ago?

Tally marks are bundled in fives to keep a long count easy to read, and the style with a fifth stroke slashed across four is nicknamed a five-bar gate.

A 10K fun run covers a distance of ten kilometres: how many metres do the runners travel?

Ten kilometres is 10,000 m, which on a standard 400-metre running track means going round 25 times.

On the 24-hour clock, which counts the hours since midnight, how is half past nine in the evening written?

It is 21:30, because the 24-hour clock keeps counting past noon instead of starting again, so no am or pm is needed.

Which name is given to an amount such as 2½, with a whole part written beside a part smaller than one?

A mixed number can always be rewritten as a single top-heavy fraction, so 2½ is the same amount as five halves.

A fridge is kept at about 4 °C and a freezer at −18 °C: how many degrees colder is the freezer?

The gap is 22 degrees: 4 down to zero, then 18 more below it. Food kept that far below freezing stays safe to eat indefinitely.

An ice hockey match is split into three equal periods: which fraction of playing time remains after the first?

2/3 of the match is still to come, which is 40 minutes of play, because each period lasts 20 minutes on the clock.

A day has 24 hours of 60 minutes each: how many minutes are there in one whole day?

A day holds 1,440 minutes, and because each of those lasts 60 seconds, it also holds 86,400 seconds from one midnight to the next.

Which number of items, known as a gross, do you get by counting out a dozen dozens?

A gross is 144 items, and a dozen of those bundles makes a great gross of 1,728.

Mount Everest is 8,849 metres high and K2 is 8,611 metres: how much taller is Everest?

Everest is taller by 238 m, though K2, the second-highest mountain on Earth, is the one climbers nicknamed the Savage Mountain.

Which name is given to the point on a coordinate grid, written (0, 0), where the two axes cross?

The origin is usually labelled with the letter O, and every other point on the grid is found by counting along and up from it.

Which way of showing data, credited to Scotsman William Playfair in the 1780s, uses columns of different heights?

A bar chart was one of several graphs pioneered by Playfair, an engineer who argued that pictures of numbers communicate better than tables of them.

Which word, from the Latin for by the hundred, describes a test score such as 80 out of every hundred?

Percent means out of every hundred, and its sign, %, grew over centuries from scribes' shorthand for the Italian words per cento.

Which word for the answer to an addition comes from the Latin for highest, as Romans wrote totals on top?

Sum comes from summa, and the old Latin phrase summa linea, the top line, was where the total of a column of figures was written.

Usain Bolt won the 2009 world sprint title in 9.58 seconds: which digit is in the tenths place?

The 5 stands for five tenths of a second, and Bolt's run that day was the biggest improvement on the record since electronic timing began.

June has 30 days, while July and August have 31 each: how many days is that altogether?

The three months add up to 92 days, and counting the months across the knuckles of a fist is an old trick for recalling which ones are long.

In Europe a standard drink can holds 330 ml: how many millilitres do three of those cans hold?

Three cans hold 990 ml, a little less than a litre, while the standard can in North America is slightly bigger at 355 ml.