ΝΟΤΑΤΙΟΝ.

1. What is a single thing called?

Ans. A unit or one.

2. What are one and one more called?

"Two."

5. What are the terms, one, two, three, four, etc.? Ans. The Names of numbers, and are often taken for numbers themselves.

6. What is number?

Ans. Number is a unit, or a collection of units.

7. How are numbers commonly expressed? Ans. By figures and letters.

8. What is the method of expressing numbers by figures called?

Ans. The Arabic Notation.

9. How many figures does the Arabic Notation employ ?

Ans. The following ten, viz.:

1, 2, 3, 4, 5, 6, 7, 8, 9, O. One, two, three, four, five, six, seven, eight, nine, naught. 10. What is the greatest number that can be expressed by one figure?

Ans. Nine.

11. How is ten expressed? (p. 11.)

12. What is the greatest number that can be cxpressed by two figures?

Ans. Ninety-nine.

13. How is a hundred expressed? (p. 15.)

14. What is the greatest number that can be expressed by three figures.

Ans. Nine hundred and ninety-nine. 15. How is a thousand expressed? (p. 16.)

Write the following numbers in figures:

1. One hundred and one.
2. One hundred and seven.
3. One hundred and ten.
4. One hundred and twelve.
5. One hundred and twenty.
6. Four hundred and fifty.
7. Five hundred and ninety-nine.
8. Two thousand and ten.

9. Three thousand two hundred and one.

10. Four thousand three hundred and twenty.
11. Five thousand two hundred and three.

12. Six thousand six hundred and ten.

13. Eight thousand and five hundred.

14. Nine thousand nine hundred and ninety-nine.

1. What is the method of expressing numbers by letters called?

Ans. The Roman Notation.

2. What letters does it employ?

Ans. The following seven: I, V, X, L, C, D, M.

MDCCCLXXVI, eighteen hundred and seventy-six.

Express the following numbers by letters:

1. Four. Six. Eight. Nine. Eleven. Twelve. 2. Fourteen. Eighteen. Sixteen. Thirteen. Nineteen. 3. Twenty. Twenty-one. Twenty-two. Twenty-nine. 4. Forty. Forty-four. Fifty-six. Sixty-nine. Eighty. 5. One hundred. Ninety. One hundred and ten. 6. Five hundred. Five hundred and twenty. 7. Six hundred and ten. One thousand and ten. 8. Fifteen hundred. Sixteen hundred and five. 9. One thousand eight hundred and seventy-two.

NUMERATION.

1. What is the method of reading numbers expressed by figures called?

3. What orders occupy the first three places?

4. The second three? The third? The fourth?

5. How many figures in a period ?

6. What is the first period on the right called? The second? The third? The fourth?

Copy and read the following, naming the orders.

FRACTIONS.

LESSON I.

TO TEACHERS.-The object of this and the next two Lessons is to. develop the idea of Fractions, and the meaning of the terms by which they are expressed. It is advisable to have a variety of objects at hand, as upples, pears, paper, etc., which can easily be separated in two, three, or more equal parts, and, as far as practicable, let the pupils separate these objects into different fractional parts for themselves.

1. If you cut an apple into two equal parts, what is one of the parts called?

Ans. One half.

2. If you put these parts together again, to what will they be equal?

3.

Ans. A whole apple.

How many halves make a whole one?

Ans. Two.

4. If you break a pencil into three equal parts, what are the parts called?

Ans. Thirds.

5. If you put these three parts together again, to what will they be equal?

Ans. A whole pencil.

6. How many thirds make a whole one?

Ans. Three.

7. If you divide a sheet of paper into four equal parts, what are the parts called?

Ans. Fourths, or quarters.

8. How many fourths make a whole one?

Ans. Four.