STUDY.-The pupil should add mentally as follows: 3, 5, 9, 10, 14, 18, &c., alternating backward and forward, until able to obtain the same result five times in succession.

RECITATION.-Ex. 1. Require each pupil in the class to read aloud one or all of these exercises in the same manner as they are to be studied.

Ex. 2. Require the pupils to add mentally, while the teacher dictates the numbers. Each scholar, after he has completed the addition, may raise his right hand. Let the teacher then call upon some pupil to give a result. Those who have not the same answer, should keep their hands up, until a result like their own is given, &c. Finally let the teacher give the correct answer.

FORM *-80 and 60 are 140; 140 and 7 are 147.

2. Rule.-II. To the sum of the tens annex the unit figure: thus; 14, 7, 147; 11, 4, 114; 6, 5, 65 ; &c. STUDY AND RECITATION.-(See Notes to Lesson I.)

PROBLEMS.

1. Ellen has 80 cherries on one tree, and 36 on another; how many cherries on both?

FORM.-(See Lesson I.)

N. B.*-The formulas should be omitted as soon as the operation is understood

2. George bought 5 books for 90 cents, and a slate for 47 cents; how much did both cost him?

3. If you give 80 cents for a pair of gloves, and 86 cents for a neck-tie, how much will both cost?

4. A bookseller sold 5 arithmetics for 99 cents, and 2 readers for 50 cents; how much did he receive for both?

5. For 7 sheep a farmer received $70, and for a cow $68; how much did he get for both?

6. A farmer sold 60 sheep, and kept 49; how many had he at first?

7. A farmer sold 80 bushels of oats, and had 85 left; how many bushels had he at first?

8. Charles is 43 years older than James; James is 20 years old; how old is Charles?

9. John was 20 years older than Richard; Richard died when he was 55 years old; how old was John at that time?

10. A boy spent 90 cents, and had 88 cents left; how many cents had he at first?

EXERCISES IN ADDITION.

What are the sums of the following series of numbers ?

1.--3, 4, 5, 6, 7, 1, 3, 4, 2, 5, 7, 1, 3, 4, 7, 5, &c. 2.-2, 4, 6, 7, 5, 3, 2, 6, 5, 4, 2, 7, 1, 3, 6, 5, &c. 3.-7, 5, 6, 4, 3, 1, 2, 3, 2, 4, 7, 3, 5, 4, 1, 3, &c. 4.—5, 6, 5, 7, 5, 2, 3, 2, 1, 2, 3, 4, 7, 5, 6, 5, &c. 5.—4, 3, 7, 6, 4, 2, 1, 4, 4, 7, 6, 3, 5, 4, 1, 2, &c. STUDY AND RECITATION.-(See Lesson I. Note.)

135.

FORM.-70 and 60 are 130; 2 and 3 are 5; 130 and 5 are

3. Rule.-III. To the sum of the tens annex the sum of the units: thus; 13, 5, 135; 10, 8, 108; 15, 5, 155, &c.

PROBLEMS.

1. If I pay $19 for a saddle, and $30 for a horse ; how much do I pay for both?

2. Andrew paid 36 cents for 8 quarts of nuts, and 83 cents for a loaf cake; how much did both cost?

3. James sold 8 melons for 93 cents, and his brother Henry sold 11 melons for 25 cents more; how much did Henry receive for melons?

4. Nine pens are worth 11 cents, and 20 are worth 56 cents, how much are all worth?

5. A farmer sold 2 pounds of butter for 93 cents, and 3 pounds for 94 cents; how much did he get?

6. A man bought 25 pounds of cheese for $2 at one time; and at another time 83 pounds for $12; how many pounds of cheese did he buy?

7. A miller sold 27 bushels of corn, and had 42 bushels left; how many bushels had he at first?

8. Bought a carriage for 60 dollars, and a harness for 35 dollars; how much did both cost?

PREPARATION AND RECITATION.-Exercise.-1. The above, and the following exercises are to be copied and completed on slates or paper at the seats, (see Ex. 1,) and then read with the answers at recitation.

Ex. 2. Let the class complete the exercises from the book, giving the answers aloud.

Ex. 3. Let the class be thoroughly questioned, and let the answers be given without the book.

Ex. 4. Should the above and the following exercises be insufficient to make the pupils skilful in combining numbers mentally, or at sight, let the teacher dictate combinations, to be completed at the seats and recited in the usual manner.

LESSON IV.

BLACKBOARD EXERCISES.

In which the sums of the columns of units exceed nine.

FORM.-70 and 30 are 100; 8 and 7 are 15; 100 and 15 are 115.

4. Rule.-IV. Write the sums of the tens and units separately; add the tens of each sum to the units of the preceding sum; thus: 10, 15; 1 (0+1)5; 115: 10, 11; 1 (0+1) 1; 111: 16, 10; 1 (6+1) 0; 170, &c.

STUDY AND RECITATION. (See Lesson I. Note.)

PROBLEMS.

1. Charles has two notes due him, one for $48, and the other for $78; how much is due him in all?

2. If I pay $57 for sugar, and $27 for salt; how much do I pay for both?

3. John gave 20 cents for 38 sheets of paper, and 94 cents for a slate; how much did both cost? 4. A merchant paid $37 for some sugar, and $46 for some molasses; how much did both cost? 5. There are 94 pens in one box, and 86 pens in another; how many have both?