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many? 7 and 6 how many? 9 and 8 many? The object in the second questioning, when the numbers are reversed, is to make the child understand that 4 and 3 are equal to 3 and 4, and that 7 and 2 are equal to 2 and 7. A child being constantly told that 2 and 7 are 9 is sometimes surprised when you tell it that 7 and 2 are 9 also, but leading him to perceive this at the first, he adds to his mechanical memory, which may be called the first steps of thought.
The teacher will, in addition to this, question the pupils of every combination of the figures in the table up to 10 and 10 are 20, until he is satisfied that every part of it is understood, and he will then be able to apply the table and its combinations after the following manner:
We have hitherto supposed the pupils to be ignorant of the Arabic signs of the numbers, and it will now be necessary to show how numbers are written. He will therefore do this by means of the black board and chalk, and here it will be quite proper to let the pupils see the great advantage of these arbitrary signs. Having his class around him, he will proceed by saying, "Now let us see what can be done with this piece of chalk and the black board. Let us put down 7. Seven what ?" "Seven sheep," says one. "Seven dogs," says another. "Seven hats," says a third. "Well, I can't draw dogs, hats, or sheep, but we will put a mark for a sheep, and we will put the flock down thus in a row:
We will call these seven marks seven sheep. There are 1 and 1 make 2, and 1 are 3, and 1 are 4, and 1 are 5, and 1 are 6, and 1 are 7. But
instead of putting them all in a row we put them thus:
How many would there then be? Seven. Why? Because 2 and 2 are 4, and 3 are 7. But supposing we had fifty sheep, how should we Here they are in a row—
put them down?
But sheep do not always run in a row like this; and if we had to count them they would run by threes, and fours, and sixes, and sevens, thus :—
Now let us count them. There is first 1, and then
3, and then 5, and then 5, and then 7, and then 4, and then 5, and then, 9, and then 7, and then 4, and all these together make 50, the same as they do when they are in one row.
But let us see if we cannot put these sheep down in another way, as it will save us a good deal of trouble. I will make this mark (1) for one sheep, but instead of making || marks for two sheep, I will
make this mark, which is always to stand for two-2; and this for three
-3; this for four-4; this for five-5; this for six-6; this for seven |||||||
-7; this for eight-8; this for nine-9; and now you must tell me what the numbers stand for when you see them without the marks.
1 2 3 4 5 6 7 8 9
Which stands for 2? which for 4? which for 6? which for 8? which for 7? which for 9? which for 3? &c.
Now then, instead of putting the marks for the sheep as they go over the hedge, we will put the numbers thus
So here you see I have made only ten marks instead of a fifty. Hence you see it is worth your while to learn these figures, which are always to stand for numbers. Not only for numbers of sheep, but for the numbers of any thing you can think of.
Of course it may be expected that the pupils will be some few days in learning the arbitrary signs of numbers, but they must be taught the use and value of them after this method. When they are pretty ready in a knowledge of them, the teacher may proceed as follows, having the black board and chalk in use as before:
had 3 apples. How many had he?
Similar questions may be used to prove that the pupils thoroughly understand the Arabic signs for number, that is, the figures; and when this is accomplished, the next step will be to apply them in a practical
The following will be proper examples, usually called sums, to be given to the pupils to work on their slates, if they can succeed in making the figures, or on the black board if they should be instructed orally:
These examples must be gone over by the pupil with the aid of the teacher, after which he may be allowed to do them by himself; and when he becomes pretty conversant with the addition of simple numbers, questions similar to the following may be proposed, to be answered vivá voce.
1. James had 1 apple, Robert had 2, William had 3, and Richard had 4. How many apples?
2. A boy had 8 buttons on his coat, 6 on his waistcoat, 4 on his trousers, and 6 on his boots. How many buttons?
3. A girl had a row of beads; she put 6 off the string into her pocket, 4 into a box, 8 she placed round her doll's neck, and 4 on each of the doll's hands. How many beads?
4. A lady bought a comb for 4 pence, a knife for 6 pence, some pins for 5 pence, some needles for 7 pence, and some thread for 3 pence. How many pence did she spend?
5. A drover bought some sheep as follows-of a farmer he bought 6, of a shepherd, he bought 3, of a butcher he bought 9, of a grazier How many did he buy?
he bought 8, and of a salesman he bought 10.
6. Mary is 3 years old, Jane is 4 years old, Lucy is 5 years old,
Martha is six years old, Ann is 8, and Emily is 9. How many years in the whole ?
7. A company of children went to a confectioner's; one eat 2 tarts, another eat 3, another eat 4, another eat 5, another eat 6. How many tarts were eaten ?
8. A man walked 6 miles on Monday, 7 on Tuesday, 8 on Wednesday, 9 on Thursday, 10 on Friday, and 1 on Saturday. How many miles did he walk during the week?
By Mrs. PULLAN.
A KNOWLEDGE of needlework is so essential to every governess, and so many of our friends have expressed a wish that we should give a few observations on this very useful as well as fashionable occupation, that we do not hesitate to devote a portion of our pages to such hints and observations as we trust may be useful.
Perhaps, the most fashionable kinds of work at the present day are muslin embroidery, and braid work. The former, at least, every one attempts to do, and, as there is an obvious utility in being able to make, at a very trifling cost, collars, sleeves, &c.—the part of a lady's dress at once the most expensive, and the most essential for an elegant appearance —it is well to be able to cultivate the power of doing such work quickly and easily.
It is always better to buy the designs worked on the material, than to work them yourself; for as of late years, apparatus has been invented for printing these designs, they are done with an accuracy and a neatness with which no amateur can hope to vie.
But the choice of a pattern, and the mode of working it, are worthy of all attention. Some patterns are more effective with far less work than others. Always choose good muslins, whether of a close or a soft texture, for nothing can be more mortifying than to expend a good deal of time on work which will not bear more than one or two washings.
All the over-cast or button-hole stitch that is done should be considerably raised, in order to make it look well; and in the simple sewing over of many parts of Broderie Anglaise a thread should be held in, which gives firmness to the edges, and prevents them from being so easily torn.
At our instigation an embroidery cotton has been made in England, superior in every respect to the French, as well as very much cheaper. It is known as Evans's Royal Embroidery Cotton. It varies
in size from No. 8, which is suitable for very coarse work only, to No. 120, adapted to the most delicate designs on the finest cambric.
Braiding is another extremely simple work. The pattern is marked. on cloth, velvet, or any other material, and then a round, flat, or fancy braid is sewed on it.
For sofa cushions, such as the one of which we give a design, the Albert braid is the richest and most appropriate; for slippers, we prefer the star, Eugenie, or Russian. For children's frocks, the twist looks very well, par