Number names, numerals and zero

Why this exists

A number can show up in three forms: a word you say (“five”), a symbol you write (5, called a numeral), and an amount you can count (five shells). They are three names for one thing, and a child who moves easily between them can read a number on a page, say it, and know how many it means. Zero, written 0, is the number for none: it answers “how many?” when there is nothing there.

A child should already know that the last word said while counting tells how many. Forming the digits with a pencil is its own lesson, writing the numerals; here the child reads numerals and matches them, and needs only to point to a card. Each day takes about ten to fifteen minutes.

Day 1: Three ways to say one number

You need: index cards with one numeral each, 1 to 5, written large in marker; a small handful of dry pasta shells; three small paper bags.

Before the lesson, put 2 shells in one bag, 4 in another and 5 in the third. Lay the numeral cards face up. Hand the child a bag and say, “Pour them out and count them.” When the count is done, ask, “How many shells?” and then, “Which card says that number?” The child sets the card beside the shells.

Now point to three things in turn: the shells, the card, and your mouth as you say the word. “These shells are four. This card says four. And we say four. All three mean the same number.” Ask the child to do the pointing and saying for the next bag.

Turn it around once: hold up the card 3 and ask, “What is this number called? Show me that many fingers.”

Practice. For each picture, the child counts, says the number word, and points to the card.

1. Picture A. Answer: 3, “three”. The child points to the card 3.
2. Picture B. Answer: 5, “five”.
3. Picture C. Answer: 2, “two”.
4. Picture D. Answer: 4, “four”.
5. Hold up the card 5. What is it called? Show that many fingers. Answer: “five”, and one whole hand.

Day 2: Numerals from six to ten

You need: numeral cards 6 to 10, some clothespins, a strip of cardboard about a foot long.

Clip 6 clothespins along the cardboard strip. The child counts them, says the number, and finds the card. Unclip them and clip a new amount, up to 10, and repeat. Point out that 10 is the first card with two digits in it: ten is written with two symbols side by side, and later the child will learn why (Tens and ones).

Then go on a numeral hunt. Numerals are everywhere: a calendar page, a clock face, a house number, the buttons in an elevator. Each time the child spots one, ask, “What is that number called?”

Practice. For each picture, the child counts, says the number word, and points to the card.

1. Picture A. Answer: 7, “seven”.
2. Picture B. Answer: 9, “nine”.
3. Picture C. Answer: 6, “six”.
4. Picture D. Answer: 10, “ten”. The card has two digits.
5. Find the numeral 9 on a calendar page and say its name. Answer: the child points to 9 and says “nine”.

Day 3: Zero, the number for none

You need: four small boxes or cups, a few pasta shells, numeral cards 0 to 5, and a few toy animals.

Show a box with 3 shells. “How many?” Take the shells out and show the empty box. “How many now?” The child may say “none” or “nothing”, which is exactly right. Tell the child, “When there are none, the number is zero. We write it like this,” and show the card 0. Zero is a real answer to “how many?”, not a missing answer, so it gets a card like every other number.

Put a few toy animals on the table and ask silly questions: “How many cows are on the table? How many elephants?” There are zero elephants, and the child can hold up the card 0 to say so.

Then put shells in some boxes, leave others empty, and ask the child to set the right card beside each box.

Practice. For each box, the child says how many and names the card that goes with it.

1. Box A. Answer: 2, “two”.
2. Box B. Answer: 0, “zero”. The box is empty.
3. Box C. Answer: 4, “four”.
4. Box D. Answer: 0, “zero”.
5. How many of the four boxes are empty? Answer: 2 boxes hold zero shells.

Day 4: Say it, find it, show it

You need: numeral cards 0 to 10, with a short line drawn under the 6 and under the 9.

Lay all eleven cards out in a jumble. Play in both directions. First, you say a number word, the child finds its card and claps that many times. Then you hold up a card, and the child says its name and shows that many fingers. Mix in zero now and then: its claps are no claps at all.

Two cards can trick the eye. Turn the 6 upside down and it looks like a 9. That is why the line goes under each one: the line always sits at the bottom, and it tells which way up the card goes.

Practice.

1. You say “seven”. Answer: the child picks the card 7 and claps 7 times.
2. Hold up card B from the picture. Answer: “nine”, and nine fingers.
3. Turn card A upside down. What happens? Answer: it looks like a 9, but the line is now on top, so the card is upside down and still says 6.
4. Hold up the card 0. Answer: “zero”, and the hands stay still.
5. Hold up the card 10. Answer: “ten”, and all ten fingers.

Exercises

1. How many rings are in the picture? Point to the numeral card that names the amount, and say its name.
2. Close your hand, then open it to show it is empty. Ask, “How many marbles are in my hand? Point to the card for that number.”

Where this goes next

Reading a numeral and making that many things is counting out a given number, and forming each numeral with a pencil is writing the numerals. Once each number has a name and a symbol, two numerals can be put side by side in comparing numbers to ten, and moving one step along the names is one more and one less. Number words also describe place in a line, “first”, “second”, “third”, which is the work of Ordinal numbers. Ten, the first numeral with two digits, opens up Tens and ones and later reading and writing numbers to 120. Zero and the counting numbers 1, 2, 3 and so on together make up the whole numbers.