Counting Numbers

Note to parents: Babies that can barely speak can learn how to count. As a parent, I encourage you to count with your child as often as possible. Count beans, count hands, count toes, etc...

Counting is a convention. That means that everyone does it the same way.

The counting series is simply:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11...

To count really high, you need to know what to do beyond 10.

..., 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20...

Do you see how that works? We simply put a '1' in front of the numbers.

With 20, the pattern should now be obvious. Let's count to 100:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10,

11, 12, 13, 14, 15, 16, 17, 18, 19, 20,

21, 22, 23, 24, 25, 26, 27, 28, 29, 30,

31, 32, 33, 34, 35, 36, 37, 38, 39, 40,

41, 42, 43, 44, 45, 46, 47, 48, 49, 50,

51, 52, 53, 54, 55, 56, 57, 58, 59, 60,

61, 62, 63, 64, 65, 66, 67, 68, 69, 70,

71, 72, 73, 74, 75, 76, 77, 78, 79, 80,

81, 82, 83, 84, 85, 86, 87, 88, 89, 90,

91, 92, 93, 94, 95, 96, 97, 98, 99, 100, ...

And if you are really smart, you'll see how the pattern continues beyond 100.

101, 102, 103, 104, 105, 106, 107, 108, 109, 110,

111, 112, 113, 114, 115, 116, 117, 118, 119, 120,

121, 122, 123, 124, 125, 126, 127, 128, 129, 130,

131, 132, 133, 134, 135, 136, 137, 138, 139, 140,

141, 142, 143, 144, 145, 146, 147, 148, 149, 150,

151, 152, 153, 154, 155, 156, 157, 158, 159, 160,

161, 162, 163, 164, 165, 166, 167, 168, 169, 170,

171, 172, 173, 174, 175, 176, 177, 178, 179, 180,

181, 182, 183, 184, 185, 186, 187, 188, 189, 190,

191, 192, 193, 194, 195, 196, 197, 198, 199, 200, ...

And you can continue all the way up to 1,000:

201, 202, ... , 299, 300,

301, 302, ... , 399, 400,

401, 402, ... , 499, 500,

501, 502, ... , 599, 600,

601, 602, ... , 699, 700,

701, 702, ... , 799, 800,

801, 802, ... , 899, 900,

901, 902, ... , 999, 1,000,

And then to a 1,000,000:

1,000, 1,001, ... , 1,999, 2,000

2,000, 2,001, ... , 2,999, 3,000

3,000, 3,001, ... , 3,999, 4,000

4,000, 4,001, ... , 4,999, 5,000

5,000, 5,001, ... , 5,999, 6,000

6,000, 6,001, ... , 6,999, 7,000

7,000, 7,001, ... , 7,999, 8,000

8,000, 8,001, ... , 8,999, 9,000

9,000, 9,001, ... , 9,999, 10,000

10,000, 10,001, ... , 19,999, 20,000

20,000, 20,001, ... , 29,999, 30,000

30,000, 30,001, ... , 39,999, 40,000

40,000, 40,001, ... , 49,999, 50,000

50,000, 50,001, ... , 59,999, 60,000

60,000, 60,001, ... , 69,999, 70,000

70,000, 70,001, ... , 79,999, 80,000

80,000, 80,001, ... , 89,999, 90,000

90,000, 90,001, ... , 99,999, 100,000

100,000, 100,001, ... , 199,999, 200,000

200,000, 200,001, ... , 299,999, 300,000

300,000, 300,001, ... , 399,999, 400,000

400,000, 400,001, ... , 499,999, 500,000

500,000, 500,001, ... , 599,999, 600,000

600,000, 600,001, ... , 699,999, 700,000

700,000, 700,001, ... , 799,999, 800,000

800,000, 800,001, ... , 899,999, 900,000

900,000, 900,001, ... , 999,999, 1,000,000

Hopefully, you see the pattern and can count now to infinity. There really is no end to these numbers.

More or Less?

When you want to know what is more, you can look at the number. Bigger numbers are more, and smaller numbers are less.

You have to be careful and compare numbers by their value, not digit! 100 is much more than 9.

Your First Algorithm

Counting beyond 10 is an exercise in applying algorithms. For counting, the algorithm is simply:

something, something-1, something-2, ... something-9, something else.

The something else depends on what something was. The rules are rather simple and children can figure them out on their own.

Sets and Set Theory

Now we can talk about sets. Group some items together. Count how many there are. As long as no one adds or removes items (and the items don't change themselves), then that number won't change. Getting children to understand this takes some time. A good way is to emphasize the final count over the counting process. After a while, they'll do the counting in their head, and just announce the final count.

You can group things arbitrarily: count the things that are red, on the table, wearing a hat, that are girls, that are jumping rope, that are in the tree, etc... If you change the rules of the group, even though the things haven't changed, the count might change.

We'll talk about what happens when you take two groups later. For now, just talk about forming group.

Problem Solving

Solving problems at this stage are simply applying the rules of grouping. Teach the children to listen for cues, and see if they can apply those cues to each object in turn. If they get an object in the wrong group, explain why it is in the wrong group: "No, he doesn't count, because he is wearing a hat and we want people who don't have hats this time. Let's skip him and count again."