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and more rational modes of discussion, based upon the central underlying principle of the relations of quantities.

Arithmetic is but the science of the relation of quantities as expressed by number. To know, for instance, that 3 apples and 4 apples equal 7 apples is to know that 7 apples less 4 apples equals 3 apples; and to know that A's money equals 1 of B’s money is to know that other relation that B’s money equals twice as much as A's; and further to know that C's equals of D's is to know that D's equals of C's.

This, it is believed, will be found to be the distinguishing feature of the work, and upon this feature its claim for indorsement is submitted. It is the outgrowth of years of study and trial in the class-room, -the crucial test of every work of this kind, — and is sent forth to seek favor in other class-rooms.

SECOND GRADE.

SECOND GRADE.

LESSON 1.

1. A boy spent 2 cents for paper and 2 cents for pens. How much did he spend for both ?

2. A girl paid 4 cents for a ball and 2 cents less for needles. How much did she pay for the needles ?

3. A pupil gave 3 cents for a pencil and 2 cents for a top. How much did he give for both ?

4. Mary paid 5 cents for a bottle of ink and 2 cents less for a postage stamp. How much did the postage stamp cost ?

5. A ton of coal cost four dollars ($ 4), and a load of wood two dollars ($ 2). What was the cost of both ?

6. A quart of milk costs 6 cents, and a pound of sugar 2 cents less. What is the cost of the sugar ?

7. A man traveled 5 miles by rail and 2 miles afoot. How far did he travel ?

8. A yard of lace costs $ 7, and a yard of velvet $ 2 less. What is the cost of the velvet?

9. A dealer sold 3 barrels of flour to one man, and 3 barrels to another. How many barrels were sold to both ?

10. James read 6 pages of history, and John read 3 pages less. How many pages did John read ?

11. A wagon has 4 wheels, and a tricycle has 3 wheels. How many wheels have both ?

12. A girl is 7 years of age, and her brother is 3 years younger. How old is the brother?

13. A boy had 5 marbles left after losing 3 marbles. How many marbles had he at first?

7

LESSON II.

acres.

1. A man earned $ 8, and a boy in the same time earned $ 4 less. How much did the boy earn ?

2. A farmer has one field of 5 acres, and another field of

How many acres are there in both fields ? 3. A man paid $ 9 for a pair of shoes, and $ 4 less for a hat. How much did he pay for the hat ?

4. Five dollars was paid for a vest, and $5 for a boy's sled. How much was paid for both ?

5. One man bought 10 pounds of tea, and another man bought 5 pounds less. How many pounds did the second man buy ?

6. A table was sold for $ 6, and a rocking chair for $2. How much was received for both ?

7. A dealer sold 8 tons of coal to one man, and 2 tons less to another. How many tons did he sell to the second man?

8. A farmer planted 6 acres of land in wheat and 3 acres in corn. How many acres were planted in both grains ?

9. A field is 9 rods in length and 3 rods less in width. How wide is the field ?

10. A barrel of apples is worth $ 6, and a barrel of flour worth $ 4. How much are they both worth?

11. Mr. A. has built a house of 10 rooms, and Mr. B. one of 4 rooms less. How many rooms are there in Mr. B.'s house? 12. Albert is 6 years of age, and Robert is 5 years

older. How old is Robert ?

13. John gathered 11 roses and gave 5 of them to his sister Helen. How many roses did he keep ?

14. How many oranges has a man, if he can give 2 to his daughter and keep 7 ?

15. John bought a slate for 9 cents and sold it at a loss of 2 cents. How much did he get for the slate ?

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