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Child. 4 times 1 are twice 2; once 1 is the half of 2; 4 times 1 and once 1 are 5 times 1.

Similar questions are applicable to all ordinary objects of life; for instance:

Moth. Two sixpences make 1 shilling, how many shillings do 7 sixpences make? Child. 7 sixpences make 3 shillings and the half of a shilling.

Moth. Why?

Child. 2 sixpences make 1 shilling; 4 sixpences make 2 shillings; 6 sixpences make 3 shillings; 1 sixpence is the half of a shilling; 7 sixpences are 3 times 2, and the half of 2 sixpences; 7 sixpences, therefore, are 3 shillings, and the half of a shilling,

Moth. 2 pair of shoes and half a pair, how many single shoes?

Child. 2 pair of shoes and half a pair are 5 single shoes.

Moth. Why?

Child. 1 pair of shoes consists of 2 single shoes; twice 2 single shoes are 4 shoes; the half of a pair is 1 single shoe; 4 shoes and 1 shoe make 5 shoes.

After several questions of this nature, the mother may proceed to the combined unity

of 3 and of 4, continuing the use of cubes, or of other objects.

Moth. (Placing 3 cubes in a straight line at equal distances.) How many times 1 are here?

Child. 3 times 1..

Moth. (Lifts up 1 of the 3 cubes, shews it to them, and places it at some distance from the two others.)

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Once 1 is the third part of 3.

Child. Once 1 is the third part of 3. Moth. (Removing one of the two cubes. which lie close together, and placing it next to the single one.)

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Twice 1 are twice the third part of 3. Child. Twice 1 are twice the third part of 3.

Moth. (Moving the third cube nearer to the two first, so that all 3 are lying in the same line and at equal distance.)

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3 times 1 are (moving all 3 close together, so as to form a rectangle) once 3.

Child. 3 times 1 are once 3.

Moth. (Placing a fourth cube below the first of the 3 former, so that with the fourth a new row begins, as represented here.)

4 times 1 are once 3 and the third part of 3. Child. 4 times 1 are once 3 and the third part of 3.

Moth. 5 times 1 are once 3, and twice the third part of 3.

Child. Repeat.

Moth. 6 times 1 are twice 3.

Child. 6 times 1 are twice 3.

Moth. 7 times 1 are twice 3, and the third

of 3.

Child. 7 times 1 are twice 3 and the third of 3.

Moth. 8 times 1 are twice 3, and twice the third part of 3.

Child. 8 times 1, &c.

Moth. 9 times 1 are 3 times 3.

Child. 9 times 1 are 3 times 3.

The various exercises which the Mother has given to the children relative to the combined unity of 2, may be repeated with the combined unity of 3, the Mother continuing to form rows of 3 cubes one after another, till she has placed 10 times 3 cubes before them.

As soon as the children have advanced so far as to answer, and to prove without the aid of cubes or other objects, to the mother's question: 26 times 1, how many times 3? 26 times 1 are 8 times 3, and twice the third part of 3; and inversely, to the question: 7 times 3 and the third part of 3, how many times 1? 7 times 3 and the third part of three are 22 times 1; she then proceeds to the combined unity of 4, 5, &c. in the same mauner.

Those who are neither theoretically nor practically versed in methods of development, who have been accustomed to mistake mere instruction for education, will probably inquire: To what purpose all the preliminary steps, the exercises, the questions, the descriptions, the minute observations recommended in former numbers, and the many preparations for arithmetic in this? Can we do better than have our children taught to read as early as possible, in order not only to furnish them with an independent amusement, (which we find extremely convenient,) but one also which will enable them to learn much by themselves in a short period? To such inquiries, it may be briefly answered, that the Pestalozzian system, taking nature for its guide, professes gradually to unfold, patiently yet vigilantly to watch, tenderly to support and assist; not prematurely to force, far less to stifle which it may be feared will be the effect of an eager and rapid perusal of the books now so unsparingly provided for youthful instruction. These, it is admitted, are infinitely superior to the mere stories and fairy tales formerly composing the juvenile library; and being often upon useful and

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