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How many balls are 2 balls and 5 balls?
How many balls are 2 balls and 6 balls?
How many are 2 and 7; 2 and 8; 2 and 9; 2 and 10?

When the children cannot give the answer, they , should be required to count them.

Lesson V.

Repeat without the frame, keeping time by striking the fists upon the lap:

2 and 1 are 3; 2 and 2 are 4; 2 and 3 are 5; 2 and 4 are 6; 2 and 5 are 7; 2 and 6 are 8; 2 and 7 are 9; 2 and 8 are 10; 2 and 9 are 11; 2 and 10 are 12.

Thus proceed through the addition, taking care that a lesson is well learned before a new one is given.

Subtraction.

Move out 2 balls with the pointer.

Here are 2 balls; if I take one away, how many will there be left? .

Move out 3 balls, take 1 away, how many?
Move out 4 balls, take 1 away, how many?
Move out 5 balls, take 1 away,

how

many?

Repeat, while the teacher moves the balls

2 less 1 are 1; 3 less 1 are 2; 4 less 1 are 3; 5 less 1 are 4.

Multiplication.

Point out two wires on the numerical frame.

Here are two wires; I will move out one ball on each wire;-how many balls are there? 2. Now you see how twice 1 are 2. I will move out 2 balls on each wire;-how many are there?. 4. Now you see how twice 2 are 4. Repeat as the balls are moved out Twice 1 are 2;

Twice 4 are 8;
Twice 2 are 4;

Twice 5 are 10;
Twice 3 are 6;

Twice 6 are 12;

Twice 7 are 14;
Twice 8 are 16;

Twice 9 are 18;.
Twice 10 are 20;

The number of wires on which the balls are moved form the multiplier.

Proceed with the same care through the multiplication table.

This method of teaching the multiplication table, has the same advantage, as that of teaching to count on the frame.

Division.

Numerical frame,

Move out 2 balls. If I move one ball at a time, how many times must I move, to move them back?

Move out 4 balls. If I move 2 balls at a time, how many times shall I move, to place them back?

6 balls, 2 at once, how many?
8 balls, 2 at one time, how many?
10 balls, 2 at a time, how many?

Then while the balls are presented, ask, How many times 2 in 4; 2 in 6; 2 in 8?

By this method many simple lessons may be taught, which will be both pleasing and useful.

Numeration.

Merely teaching children to name the several places of figures in this rule is easily accomplished; but it requires no small degree of care, to make it intelligible to them.

The child should be led by degrees to understand the nature of classification in general. A grove, a flock, a class of children may be explained to them.

There are in school, first, second, and third classes. Present them the numerical frame, held so that the balls may stand in perpendicular columns. Here I will call these classes, and teach you names for them. We must begin at the right hand, this is the lowest class. Then teach them the names of the classes, all speaking together: units, tens, hundreds, thousands, tens of thousands, hundreds of thousands, millions, tens of millions, hundreds of millions, thousands of millions, tens of thousands of millions, hundreds of thousands of millions, billions.

When these námes have become familiar, they may be explained in the following manner.

Teacher. Now, dear children, I wish you to tell me what these classes mean, and what is the difference between them; pointing to the right hand class, What is this class called? Units.

What are units? Ones. If I write 4 in this class, what is it? - 4 ones.

Pointing to the next class, what is this? Tens. If I write four in this 2d place, what is it? 4 tens. What is 4 tens? 40.

Pointing to the next class, what are these? Hundreds. If I write 4 in this 3d place what will it be? 4 hundreds. Pointing to the next class, what is this? Thousands.

If I write 4 in this place what will it be? 4 thousands.

When by this method of teaching the children have learned that the difference in the value of figures depends upon the place they stand in, they may next be taught what their difference is in the following manner.

How many does it take of one class to make one of the next highest? Ten.

Why does it take ten units to make one ten? Because one ten is ten units.

Why does it take ten tens to make one hundred? Because one hundred is ten tens.

Why does it take ten 'hundreds to make one thousand? Because one thousand is ten hundreds.

Why does it take ten thousand to make one of the next class? Because the next class is tens of thousands.

Why does it take ten tens of thousands to make one of the next? Because one hundred thousand is ten tens of thousands.

Why does it take ten hundred thousand to make one million ? Because one million are ten hundred thousands.

If you must have a figure for every number, how many figures would you have to read to make one hundred? We should have to read 100 figures.

By classing the figures by the rule of numeration how many figures must you read to make one hundred? Three figures.

How many to make one thousand? Four figures. Where do you begin to numerate? At the right hand.

Next they may be taught to read figures upon the black board.

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A very important use of geography is, to bring to view, the beauty and grandeur, the vast variety and wise arrangement of the works of God, and to evince the Holding up the hand, and counting the fingers.

almighty power, and immediate presence of Him who is the life of all, and for whose pleasure they are and were created.

That children may derive such benefits from the study of this science, the following lessons are prepared with frequent allusions to the providence and attributes of God, displayed in his works.

The teacher must be furnished with a globe. One made to turn on an axis held in the hand is preferable, because the children can thus see it, detached from its cumbrous standard.

The globe must be held in view of the children, while the questions which are to be explained by it, are asked.

Lesson I.

What is the ground on which we walk, and on which our houses are built, and from which grow the beautiful plants and high trees? It is land.

How far' does this land extend? Thousands of miles. It is a part of the great earth.

Did you ever walk one mile?

The people whom you usually see at meeting are those which live within a few miles, and inhabit the same township of land. How far does one town usually extend? About six miles each way.

When we have passed through this town what is next? There are other towns on every side of this, and beyond them are other towns, and beyond them other towns.

Is the land all level, like this floor? In some places the land is level, and in some places it rises into hills, and in some places are lofty mountains, higher than the clouds.

We can see but a small part of the earth as we stand in one place, how would the land appear if we could see all over it at once? Very beautiful.

What are some of the things you would see on the earth? Fields covered with grass, plants and flowers, hills and forests of trees, large rocks and lofty mountains, water ever flowing in many deep long rivers and small streams.

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