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d. 1 and 2 give 3 3 from 3, 0 remains.

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Moth. Deducting 1 from 4 and 3, how many remain?

Child. Deducting 1 from 4 and 3, 6 remain.

Moth. How did you find that?

Child. 4 and 3 are 7; 1 taken from 7, 6 remain; consequently, deducting 1 from 4 and 3, 6 remain.

Moth. Taking 2 from 6 and 3, what will remain?

Child. Taking 2 from, &c. 7 will remain.

Moth. How do you account for that?

Child. 6 and 3 are 9, 2 taken from 9, 7 remain; consequently, 2 taken from 6 and 3 leave 7.

MtfA. Deducting 3 from 7 and 1, how many remain?

Child. Deducting, &c. 5 remain, &c.

In the same manner the Mother may increase the numbers from J—6 by 4, from ]—5 by 5, and likewise diminish them by I, 2, 3, &c.

Of the Equality of Numbers.

The Mother places the cubes in two columns, from 1 to 10; so that the number of cubes in the different partitions of the first column correspond with that in the partitions of the second column opposite. She enunciates, and the pupils repeat after her.

The cubes are to remain as they have been arranged without separating them; and each number is to be compared with itself, as:

1 is equal to 1

2 are - 2

3 - - 3

4 . - 4

5 - - 5

6 - - 6, &c.

till 10.

Here the cubes of the second column are separated; but those of the first remain untouched. The cubes of the second column are to be formed into 2 partitions, as:

2 are equal to I and f

8 - -1-2

.. - -2-1

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ikfotft. Which 2 numbers are equal to 5?

C/«'W. 1 and 4 are equal to 5; 2 and 3 are equal to 5; 4 and 1 are equal to 5.

Moth. Prove that 1 and 4 are equal to 5.

CTii/c?. 1 and 4 are 5 times 1 ; 5 times 1 are equal to 5; consequently 1 and 4 are equal to 5. application.

Moth. Suppose I give you 4 nuts at 2 different times, how many can I give you each time?

Child. 1 and 3; or 2 and 2; or 3 and 1, &c.

2. The cubes of the second column are to be formed into 3 partitions, as:

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Questions.

Moth. In how many ways can you arrange 3 numbers so as to form 5?

Child. 1 and 1 and 3; 1 and 2 and 2; 1 and 4; 2 and, 1 and 2; 2 and 2 and 1; 3 and 1 and 1.

Moth. Prove that each set of numbers are equal to 5.

Child. 1 and 1 and 3 times 1 are 5 times 1; 5 times 1 are once 5, &c.; consequently each set of numbers I have mentioned are equal to 5.

Application.

Moth. At 4 different times you are to receive 6 shillings, how many can you receive each time?

Child. 1 and 1 and 4; 1 and 2 and 3; 1 and 3 and 2; 1 and 4 and 1, &c.

This exercise may be continued.

Comparison of Numbers by more.

The cubes are arranged as represented below in the two columns.

Nothing is to be mentioned but that 2, 3, 4, &c. are more than 1, 2, 3, &c. without stating by how much.

D

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