Numerals and Number Words

Numbers are all around you — a big 5 on a birthday cake, everyone singing "five!", and five candles to blow out. Written, spoken, or counted on your fingers, it is the same number each time.

A number is an idea: how many. That one idea wears three different outfits, and they all mean exactly the same thing:

the numeral — the digit we write: 5
the number word — the name we say: “five”
the quantity — that many real things: ●●●●●

Once you can count a group of things, you can give that group a spoken name and a written symbol. The numeral 5, the word “five”, and five apples are not three different numbers — they are three ways of pointing at the same amount. Learning numbers means learning to slide smoothly between the three: see a group and know its word, hear a word and write its numeral, read a numeral and picture the pile.

One amount, three names — together

Here is the number five, shown all three ways at once. Count the apples, look at the digit, and read the word. They line up perfectly:

apple apple apple apple apple

\underbrace{5}_{\text{numeral}} \;=\; \underbrace{\text{“five”}}_{\text{word}} \;=\; \underbrace{\text{five apples}}_{\text{quantity}}

If you swapped the apples for ducks, the picture would change but the number would not — five ducks is still five. The numeral and the word don't care what you counted, only how many there were.

Imagine a farmer with this many sheep: goat goat goat goat . To remember the flock tomorrow, the farmer could draw four sheep again — slow! — or just write the tidy little mark 4. A numeral is a shorthand for a quantity, so we can store and compare numbers without dragging the real things around. That is the whole reason humans invented digits.

Watch them line up. Each time you press play we pick a new number, count out that many dots, write its numeral, and say its word aloud — so you can see all three match.

See it: count, then name

Count the cartoons, and the diagram shows you the matching numeral and number word underneath. Press Refresh for a fresh group — a different amount and a different thing to count, but always the same three-ways-of-one-number idea.

The tricky teen words

Most number words are friendly, but the “teens” — the numbers from eleven to nineteen — try to trip you up. Two of them barely sound like numbers at all: eleven (11) and twelve (12). You simply have to learn those by heart.

From thirteen onward there is a pattern, but it runs backwards from how you write it. The word says the ones first and the “ten” second:

13 = thir-teen (three and ten)
14 = four-teen (four and ten)
15 = fif-teen (five and ten)
16 = six-teen, and so on up to nineteen.

So “-teen” is just a sleepy way of saying “and ten”. Fourteen means four plus ten, which is fourteen things in total.

We say “thirteen”, never “ten-three” — the ones part comes first and “three” gets squashed into “thir”. Same with “fifteen”, not “five-teen”.
The numeral, the word, and the count are three names for one amount. 14, “fourteen”, and fourteen apples are equal — pick whichever is handy, and you can always swap to another.

Worked examples

1. Numeral → word → quantity. You see the digit 8. Its word is “eight”, and it stands for this many things:

duck duck duck duck duck duck duck duck

2. Quantity → word → numeral. Count these stars: one, two, three… there are six. The word is “six”, so we write the numeral 6.

3. A teen. You hear the word “fourteen”. Take it apart: four and teen (ten), so it is four-and-ten. We write the numeral 14.

What if there is nothing to count? That amount also gets a numeral and a word: the numeral is 0 and the word is “zero”. An empty plate with no cookies on it — — has zero cookies. Zero is a real number word, meaning “none”, and it becomes a hard worker later when you learn place value.

Khan Academy shows how to write numbers in words here: