COUNTING AND NUMBERS

The young of some animals have special names, and with many of these we are familiar. But there are other young creatures whose particular names are not so well known. In the pictures on this page we see the young of eighteen different creatures with their mothers, and the special names of these are given.

The young of some animals have special names, and with many of these we are familiar. But there are other young creatures whose particular names are not so well known. In the pictures on this page we see the young of eighteen different creatures with their mothers, and the special names of these are given.

On the garden wall a brownSpiderwas spinning herWeb. Backwards and forwards she went, making hundreds of little threads at once, twisting them into white ropes, arranging them with her feet and the little hooks on her jaws, and gluing them together where they crossed.

TheButterflystood on aLeafand watched.

“Is that to put your eggs in?” she asked at last. “Or do you put them on a cabbage?”

“On a cabbage! No, indeed!” said theSpider, staring with all her eight eyes at once. “I make a soft nest of silken threads to put them in.”

“That would not do formybabies.” And theButterflynodded her head and looked very wise. “They would get their wings fast in the threads.”

“Their what?” gasped theSpider, standing suddenly still in the middle of herWeb.

“Their wings,” repeated the innocentButterfly. “I don’t think I dare let my children come to play with yours if you always hangNetsabout.”

“But your children won’t have wings!” gasped theSpideragain. “They won’t be babyButterflies!”

TheButterflylaughed gaily.

“What a funny idea!” she said. “Your eggs hatch into babySpiders, don’t they? and they don’t have wings. And the hen’sEggshatch into little babyChickens, and they do have wings, like the hen. I saw them this morning running after her, with all their wings stretched out. I suppose they are not old enough to fly yet. When my babies can fly, I shall go back to the flower garden.”

She flew away, leaving the astonishedSpiderstill sitting in the middle of herWebtrying to understand it all.

“Well!” she exclaimed to herself at last. “That’s what comes of having no mother! I always did say that the family arrangements of theButterfliesare the most foolish I ever heard of.”

TheButterflywas very busy, gumming her eggs safely underneath a cabbage leaf. Each little jar hung by its narrow end, as close to the next as could be.

“What a funny oldSpider!” she thought at last, when she had finished. “I wonder if she has finished thatWeb.”

“Have you found a cabbage to please you?” called theSpider.

“Well, I suppose it’s all right,” answered theButterflya little doubtfully. “I don’t seem to be able to think of a better place to put my eggs, and I suppose the flowers will grow on the cabbage very soon. My babyButterflieswill not be able to fly far at first to find honey.”

“You mean your creepy, crawlyCaterpillars!”

“Don’t you meanSpiders?” asked theButterfly, trying to be sarcastic.

“Nothing so sensible! If you want to see——”

“Hush! hush! Don’t quarrel!” said the Breeze, shaking theSpider’sWeband puffing at theButterfly’s wings.

“She says that my babies will be creepy, crawly——”

“Come away! come away! Come and find some honey!” said the Breeze.

He shook theLeafand theButterflyfell off. Then the Breeze so hurried her across the garden that when they reached the flowers she was out of breath with laughing.

“I suppose that oldSpideris jealous because her children will not be so pretty as my babyButterflies” she said.

One summer Robert and his father and mother lived in a littleHousein the woods.

They saw aSquirrelrunning about in theTrees.

Robert put someNutson the ground, and hid behind aTree. Soon theSquirrelcame and carried them away.

The next day he put theNutsnearer theHouse. TheSquirrelcame again and carried them away.

So it went on for some time. Each day Robert put theNutsnearer theHouse.

They named theSquirrelLady Gray.

One day Robert’s mother sat down on aChairin the porch. She put someNutson the floor and kept very still.

After a while Lady Gray came up on the porch. She looked at Robert’s mother, then she took aNutand ran off as fast as she could.

By-and-by Lady Gray became so gentle that she would hunt forNutsin their pockets.

One morning father put aNuton his shoulder. Lady Gray jumped on father’s shoulder and ate theNut. How they all laughed!

Three littleKittenswere born in aHousewhere there were two livelyChildrenTheKittenswere at once named Tom, Dick, and Harry.

As soon as they were big enough to handle, theChildrenbegan to carry them round, indoors and out. Nancy, the mammaCat, did not like herKittensto be handled so much, for she knew it was not good for them. She mewed, but the children did not notice her distress.

Dick, a lovely grey, seemed to be her pet. She took the best care of him, and seemed most worried when the children picked him up.

One day little Dick could not be found. TheChildrenhunted for him, but in vain. They noticed that Nancy did not seem anxious, nor did she go looking for her lostKitten.

They did not notice, however, that she would often go up theStairs, and stay away awhile from Tom and Harry.

When washing day came, they found out all about it. In a low, darkCupboardupstairs, where the soiled clothes were kept, Nancy and Dick were found. Dick was snugly wrapped in the clothes, and purred contentedly. Mamma Nancy lay beside him. She had taken her favoriteKittenand hidden him, so that the children should not play with him.

Once upon a time a great many littleStarslived up in the sky.

Their father was theSun, and their mother was theMoon.

Usually theseStarswere good littleChildren. They liked to help brighten the sky and so make theEarthbrighter.

But one night when their mother called to them to come and light up the sky, they came very slowly. They looked very cross. They did not shine when she told them to do so.

MotherMoonfelt sad. She called up from theEarthsome good littleStars. They were onlyFlowersonEarth, but MotherMoonchanged them intoStarsin the sky.

The naughtyStarsfelt themselves falling. Faster and faster they fell, until they sank down into theEarth.

They cried and cried until they fell asleep for they were very sorry for what they had done.

In the morning FatherSunshone out so brightly that everything, even the babyStarsunder the grass, wakened. They began to cry again.

Their father felt sorry for them. He told them they might shine on theEarth.

So now the stars shine in the sky at night, and in the morning, when FatherSunshines for them, theFlowersopen their eyes and shine in the grass all day.

NATURE AS THE FIRST INVENTOR AND CRAFTSMAN

Panic

A timid hare was resting one day in a grove of palm-trees, and a strange thought came into his head.

“What should I do if an earthquake occurred?”

At that moment a gust of wind shook the palm-trees, and some ripe fruit pattered down.

“An earthquake is beginning!” cried the timorous hare. And, starting up, he fled without daring to look behind him. A deer met him as he was racing along.

“What is the matter?” said the deer, catching up with him and running by his side.

“An earthquake is destroying the forest!” the hare gasped out.

The terrible news quickly spread among the hares, deer and rabbits, and they scampered away in wild terror. As they went on, they were joined by elks, buffaloes, elephants, tigers, and rhinoceroses.

“What is the matter?” said each animal in turn, as he joined the fugitives.

“An earthquake is destroying the forest!” they panted, rushing on, and never stopping to see if it were so. At last the line of frightened animals extended across the country for a full mile. All the smaller beasts standing in the path of the army of fugitives were unable to ask any question; they had to race ahead to avoid being trampled down. But as the maddened host was sweeping blindly down to the bank of a great river, which looked like being choked up with dead bodies, a lion came up, and stopped the frightened beasts with a terrible roar.

“What is the matter?” he said to the tigers.

“The buffaloes told us that an earthquake is coming,” said the tigers.

“Who saw it coming?” said the lion.

“We don’t know,” said the tigers. “The elephants know.”

“The rhinoceroses told us,” said the elephants.

“And we heard it from the buffaloes,” said the rhinoceroses, panting for breath.

The buffaloes heard it from the elks; the elks heard it from the deer; and at last it got down to the timid hare.

“Do you mean to tell me,” roared the lion, “that you have all been frightened to death by a timid little hare? Let us go to the grove of palm-trees, and witness this terrible earthquake.”

When they arrived there, the fruit was still pattering to the ground.

“Now, you see,” said the lion, “what comes of following the lead of the most timorous creature on earth. He has made you all more cowardly than he is himself. You ran away without even hearing the noise that frightened him. Henceforward avoid the gossip of the crowd, and trust to your own judgment.”

When the little drop of rain fell, he didn’t know in the least what was going to happen. For a minute or two he felt quite frightened. Then he suddenly found himself rolling down a hill. He had just begun to think it great fun, when he noticed a lot of other drops beside him, all laughing together and all rolling down the hill.

One of them came close to him and touched him, and he found himself growing bigger. Then more and more came up, and presently he saw that he was quite a big fellow. He felt very proud of himself. “I’m getting bigger and bigger every minute,” he said.

Half-way down the hill he looked back, and saw himself stretched out like a line of silver, glittering and shining between the trees and stones and bushes.

“I’m a stream now,” he murmured proudly as he hurried over sand and gravel and clay, “and I’m getting bigger and bigger still.”

Suddenly he found himself falling over a big black rock. Down, down he fell, thirty feet or more. But he was so big and strong now that he didn’t care a bit.

At the bottom of the hill there were a great many rocks and stones right in front of him. “Get out of my way!” he roared. “I’m a river now! Get out of my way!” And he dashed and splashed and flew right over them.

A little farther on he came to a lovely meadow, with beautiful trees hanging down, and birds singing, and great sleepy red cattle standing knee-deep in the long, sweet grass, and the big blue sky shimmering overhead. It was so very, very pretty that he thought he would stay here a while. So he twisted and wound round and round, just to get another look at the trees, and to watch the birds flying from branch and bush.

He laughed merrily to a little boy who was standing on the bank with a fishing-rod in his hand, and hurried on again.

As he turned a corner quickly he saw a great blue plain stretching for miles and miles, with ships and boats and birds dotted here and there on its broad, heaving, shining surface.

“Hello! There is the sea at last!” he cried joyfully, and rushed forward eagerly to meet it. And as he joined the great ocean he shouted out as if he meant that all the world should hear, “Here I am; I’m a sea now!” (See full page illustration onpage 68.)

The spider was in a rare temper as she hurried back to the dark corner where she had her home.

“Upon my word,” she muttered, “it is too bad! This is the third time that wretched housemaid has swept my web away. The ignorant creature calls me an insect. I am not an insect. My body is in two parts instead of three; my head is part of my chest; and I have eight legs instead of six.”

The spider sat in her dark corner thinking very hard. Presently a buzzing sound caught her ears, which happened to be placed at the end of her feet. Her six pairs of eyes glistened with anger.

“There’s that old bluebottle again,” she murmured. “His noise makes my head ache. If I make haste and spin another web, perhaps I can catch him before the maid comes with her broom.”

Having made up her mind, the spider began. On the underpart of her body were four tiny tubes, each with about a thousand still tinier holes. From each tube came a thousand delicate threads made of a gummy fluid. The spider’s hind feet combed and twisted them into one fine thread.

The thread gradually increased in length until a draught caught it and carried it to the edge of the window-curtain, to which it clung.

Several other threads were then stretched from point to point.

“Now,” said the spider, “I can go on building my web.”

Line after line appeared as if by magic. The lines crossed and recrossed, and at every point where they touched a tiny drop of sticky fluid held them firmly together.

The spider viewed her work with satisfaction.

Lastly, she ran a more delicate thread round and round in spiral fashion. Atthe end of an hour the web was complete.

“Now I will test it,” said the spider; and she tried her work here and there, and found it quite good.

Only a short time passed before the big fly buzzed into the elastic strands. The more he struggled, the more he became entangled.

The spider was hungry and very impatient. She darted from her lair and seized the fly with her terrible claws.

At the end of the feelers were tubes from which she poured poison into the body of her prisoner, while with her fore feet she entangled still further the fly’s legs and wings.

In a few moments the bluebottle was quite still. Securely bound up in the sticky strands, bitten and poisoned, it was clear that he would never again buzz about in the sunshine. Then the spider enjoyed a better meal than she had had for a long time.

An hour later the housemaid came along, and, catching sight of the web, she flicked it with her duster.

“That miserable insect has been at its tricks again,” she said.

The spider was just settling down to a quiet nap after her hearty meal. She did not like being disturbed, but it did not matter so much now. She simply smiled to herself. (See articles onSpiders;FliesandInsects in generalinBook of the Animal Kingdom.)

Every child in the world grows up to be a woman or a man. The only one who doesn’t grow up, and won’t, is Peter Pan. He always stays a little boy, which is very jolly indeed, and he’s friends with all little boys and girls,—as you’ll understand if you read.

The Darlings,—Wendy, John, and Michael,—lived with their father and mother. They were rather poor, but it didn’t matter, they were all so fond of each other. They’d a little maid called ’Liza, and, because they hadn’t the money for a proper nurse, they’d a dog instead, named Nana,—wasn’t it funny?

Peter Pan came every night; the window blew open wide, and in he hopped, without a sound, and hurried to Wendy’s side. And a curious little dancing light came in with Peter as well; this was a fairy lady, and her name was Tinker Bell. Peter was dressed in skeleton leaves; he had pipes on which he played—a delightful person. Wendy was not the least little bit afraid. He talked to her of the Never-Land, where she’d always wanted to go. And he said, “If I only teach you to fly, you can get there now, you know!” So John and Michael were taught to fly, and Wendy too, and they found it’s as easy, when you get used to it, as walking on the ground. And at last, when both their father and mother were out, one Friday night, the Darling children and Peter Pan and Tinker Bell took flight. Away in their little nightgowns they flew, as fast as they could go, till they came to the island, the Never-Land, where all the adventures grow.

Now in this island, I must tell you, were wonderful things to find: unknown birds, and curious beasts, and Redskins, fierce but kind. Fairies were there, and Mermaids, and Wolves,—some wild, some tame; and a Crocodile that had swallowed a clock, and ticked wherever it came. But—hush, let us whisper!—the “Jolly Roger,” a rascally pirate craft, with raking masts, and swelling sails, and guns both fore and aft, was anchored there, and the hideous crew were lying in wait, each man, and the captain, Hook, in particular, to kill little Peter Pan. Hook was not his real name; Peter, some while ago, in open fight, had cut off his hand, so now he’d a hook, you know. And as, with a stern and gloomy air, he paced, on his quarterdeck, he was thinking all the time, “I’d like to wring that Peter’s neck!” And the rest of the horrible band of Pirates were always prowling about, to see if they couldn’t capture Peter, and kill him, without a doubt. They crept along, singing “Yeo-ho-ho”—as stealthily as could be, they, and the bo’sum, who, indeed, was the best of them—one Smee. But the Redskins, with the tomahawks, were on the Pirates’ track, and followed them quite noiselessly,—not a singlerustle or crack. For they thought the world of Peter Pan; in fact, they all were rather inclined to kneel at his little feet. And they called him “Great White Father.”

PETER PAN, WHO COULD NEVER GROW UP TO BE A MAN

PETER PAN, WHO COULD NEVER GROW UP TO BE A MAN

Upon the island there were also some boys—well, counting rightly, there were six: Nibs, Tootles, Curly, and the Twins (no names), and Slightly. And Tootles, by a silly mistake, when he saw the Darlings near, hastily aimed his swiftest arrow, and drew his bow to his ear, and shot poor Wendy. Just at first she was thought to be dead, by her friends. But, finding she wasn’t, they built her a house, in the hope of making amends. They built it right, round her, with branches, leaves, and moss, and lovely make-believe roses clambering quite across. And when it was completed(and it looked remarkably fine), “Oh, Wendy, do be our mother!” they cried, and they hadn’t to ask her twice. “Come in at once, you naughty children!” Wendy delightedly cried; and they all squeezed in, except Peter Pan, who stayed upon guard outside.

There was also a beautiful house under-ground, where elegant mushrooms grew, and a Never-tree also (but every morning they sawed the trunk right through). You entered the house by hollow trees, going up and down quite fast, which was hard at first, but the children did it exceedingly well at last. And here, in the charming underground house, the eight boys slept alone in a great big bed,—for Wendy lived in that dear little house of her own. But every evening she told them stories, and when the stories were done, they’d have a dance in their night-clothes, and a pillow fight,—Oh, such fun! Peter Pan wasn’t always there, because, as you understand, he was busy strolling about the island, or watching with sword in hand. But in the day-time he would come, and take them, not very far, to the blue lagoon, where the weedy rocks and the hundreds of Mermaids are.

And here, one day, both Peter and Wendy received a bit of a shock; for Hook pursued them, and so they climbed on a rock—the Marooners’ Rock. Wendy fainted, and so did Peter. A Mermaid came to see whoever those two little dripping folks on the slippery rock could be. Then Peter perceived the tide was rising, and he tied up Wendy tight to the tail of a kite which was drifting near, and sent her away with the kite. And there he stayed on the rock alone, and he thought he’d be drowned each minute. But the Never-Bird, in her floating nest, came up, and Peter got in it, while the Never-Bird took to a Pirate’s hat, which was luckily close at hand. So Peter went gaily sailing off, and arrived quite safe at land.

Now every night the Redskins were camped above the underground house. And every night the Pirates were creeping, each as still as a mouse (with the terrible Crocodile after them, showing its crunching teeth), while Wendy was cheerfully telling tales to the children down beneath. But, oh dear me! there came a night when that treacherous pirate Hook contrived to surprise the Redskins, and the children; and he took the whole nine children prisoners, exceedingly sad to tell. The only ones who made their escape were Peter and Tinker Bell. And while the unhappy children were roughly carried on board, Peter was off to rescue them, with his trusty dagger and sword. And, just in the nick of time, he arrived. He armed the boys, and they slew, after a most tremendous fight, fifteen of the Pirate crew. And after a thrilling duel, which lasted a very short while, between Hook and Peter, the wicked Hook was thrown to the Crocodile.

So Peter took command of the ship, and they all sailed home, and then, how glad their father and mother were, to have them back again! They all were dressed in the Pirates’ clothes (cut short), and exceedingly grand; and oh, what tales they had to tell of the wonderful Never-Land! Peter, who didn’t like houses at all,—brick ones, and that sort of thing, returned to the Never-Land by himself. But he comes back every spring, and fetches Wendy to help him do spring-cleaning, and Wendy stops and tidies up the little house, which is now in the high tree-tops. As for the boys, they’ve all grown up, so the Pirates’ clothes won’t fit. And as for the great adventures they had, they’ve forgotten them every bit. Only Wendy and Peter Pan can still do just as they please. How happy they are, as they talk up there in the dear little house in the trees!

In numbers, as in other primary subjects, a child should betaughtandpermittedto do things himself. Rousseau said, “What the childdoes, it easily remembers”; and we shall soon find that time spent in this way is far from being wasted.

Children who have been taught numbers gradually, in this easy, interesting fashion, develop an astonishing aptitude for dealing with figures as they grow older.

Learning to count 1, 2, 3, 4, etc., parrotlike, does very little good. Rather let the child countobjectsand point out 5 marbles, 6 blocks, etc., in order that you may determine if he knows exactly what 5 or 6 of anything means.

Take a number of blocks or marbles and ask the child to take 3, 5, 7, or any number of them.

Hold up 3, 5, or 6 of them and ask him to tell how many you have. When you are told thenumberyou have, write thefigurewhich tells the number on paper, or the blackboard. Have the child copy the figure, making a large character.

Then reverse the work by writing afigureon paper and asking the child to take thenumber of blocksthe writing asks for.

Spend a few minutes every day in asking him to show you 2 pins, 3 houses, 5 stripes, etc.

Teach the child to count 50 as soon as he has started in his number work at school and later on to 100.Objectsshould be counted at first and then counters substituted, such as pennies, marbles, blocks, beads, etc.

Recognition of Numbers.—The purpose ofcounting objectsis to give the children a clear idea ofnumber. They should be able to recognize 2, 3, 4 and 5,i.e., be able to tell four objects when they see four, without counting them, also 3, 5, etc. Stories and games with objects should be repeated again and again, until the children can do this easily.

Analysis of Numbers.—When the numbers can be recognized without difficulty, the children should be encouraged to analyze them,i.e., tell what they are made up of, but objects should be put in front of the class to represent the numbers until they can do this readily.

Suppose the numberfiveto be the lesson, each child would take five shells out of its box, and lay them on the desk, thus:—5 dotsor5 dotsor5 dotsetc. The child should always be able todescribewhat it has done: thus, the first child would say—four shellsandone shellarefive; the second,three shellsandtwo shellsarefive, and so on.

Higher Numbers.—The analysis of six, seven, eight and nine may be taught in the same way, each number being taken separately and thoroughly mastered, before proceeding to the next. The children should learn all the different combinations of numbers that make six—threeandthree,fiveandone,fourandtwo,three twos, etc.—but always with the objects, and when they have seen the number analyzed by the Teacher, they should do it for themselves with shells, bricks or other objects.

Number Ten.—This is the most important number of all, and it should be thoroughly well taught. The Teacher should show on the table the different analyses that can be made of ten, and the children should lay these with shells or other objects again and again. It is necessary to learn these perfectly, for however well any or all of the numbers may be learned, they are comparatively useless without ten.

Figures.—When the figures are introduced they should invariably be shown with the concrete numbers which each figure represents. They say, “Here are four balls”4 dots“I will show you a figure that means those four balls,4, and I will put the four balls beside it, thus:”—44 dots.

Number on Paper or Slates.—If the children have learned how to use a pencil, they may transfer the number-pictures made with shells to their slates, using dots for “shells,” thus:—6 dots.

Then another “picture” may be made with the shells6 dotsand this be copied on the paper at some distance from the other. Then another is made and copied, and so on until the child sees on his paper all the combinations of numbers that go to make six. He should be able to read them all out, and because a child rememberswhat he has done himself, it will be found that numbers taught in this way are seldom forgotten.

As the children become more proficient, the two signs + and = may be taught, + meansand, = meansare. Then they may put on their slates2 dots+2 dots=4 dotsand use these signs in the analysis of other numbers.

When the children know numbers up to ten, they might play little “shopping” games with coins. Show them actual coins in teaching money. Lessons on money should be given frequently after the first year of school life.

Begin by teaching the value of thecentand thenickel, then thedime, then thequarter, then thehalf-dollar, and then thedollar.

Make little problems involving change. Develop the ability to make change rapidly. The child may have some money of his own and he should be taught the comparative values of the coins.

Simple Table of Money

10 cents make 1 dime.

2 five-cent pieces make 1 dime.

100 cents make 1 dollar.

A quarter of a dollar = 25 cents.

A half-dollar = 50 cents.

$ means dollars and c means cents.

A 5-cent piece is called a nickel, because it is made of nickel.

A cent piece is made of copper.

The other coins named are made of silver.

(SeeUnited States Moneyfor more advanced instruction.)

We now come to the method of teaching the combinations in Addition and Subtraction.

We can count books, tables, and houses and say that we have counted so manythingsbut we do notaddbooks, tables, and houses. Weaddbooks and books, tables and tables, houses and houses.

We count byones. When we add three beads and two beads we are counting by ones, for it means that we are adding three ones of beads and two ones of beads, making five beads in all.

From1to9we use only one figure to tell how many we mean. When we wish to say in writing that we have ten of anything we write a0after the1and have10, ten.

1. Add 1 to every number up to 10; later to 20.

2. Subtract 1 from every number up to 10; later to 20.

3. Add:

+2+3+4+5+6+7+8+9+10+2+3+4+5+6+7+8+9+10

Here the addends are equal and easily added. The figures should be placed as above and not 2 + 2, 3 + 3, etc., because the vertical form is the natural one which the child will use all through life. It does not look so formal and represents better what he really does with the objects.

4. Add:

+1+2+3+4+5+6+7+8+19+2+3+4+5+6+7+8+9+10

Here one addend exceeds the other by 1.

5. Subtract:

-2-3-4-5-6-7-8-9-10-1-2-3-4-5-6-7-81-9

Here the minuend is one greater in each case.

6. Teach the parts of 10.

+5+2+3+4+9+5+8+7+6+1

7. In adding 9 to numbers have the child think of 9 as 10,

thus9+6=10+5and9+8=10+7

8. Teach the corresponding subtractions.

9. Add 8 to each number up to 10.

10. Teach the corresponding subtractions.

11. Add 7, 6, and 5 to each number up to 10.

12. Teach the corresponding subtractions.

13. Review and give combinations not taught above.

Objects should be grouped by tens and units, in showing numbers aboveten. Ten should be the basis of all our reckoning, and if the children know ten, and the numbers which precede it, they can soon be taught the rest. Little children should not have “sums” given them to do on their slates, for “sums” are made up ofabstractfigures, and children of tender years cannot grasp the abstract.

Number to One Hundred.—When the children are conversant with numbers up to ten, it is very easy to teach them one hundred.

In teaching the two ideas of division—division bymeasurement(division proper) and thefractionalidea of division (partition)—proceed very slowly and see that each step is thoroughly understood.

The following suggestions may be useful:—

Use blocks or any other counters in illustrating the process.

Example:

412

The teacher should ask the child, “How would you count this story?”

Facts Given by Child

12 = whole number of blocks.

4 = number in each part.

We want to know the number of parts.

We place the blocks so, 4 in each part:—


Back to IndexNext