7. Add 3 to all numbers from 3 to 30.

1, 11, and 21; 2, 12, and 22; 3, 13, and 23 should be

associated.

Use the drill cards.

8. Subtract 3 from all numbers from 3 to 12.

As the process of the addition of two numbers is a process by which the mind puts two numbers together and gets a new number, so subtraction is a process in which the mind sees complementary numbers. To develop this idea, let such questions as these be asked:

The child should derive his table from actual additions, since multiplication is simply a short process of adding equal numbers.

Figures should not be used until the numerical ideas which they express are clearly apprehended.

10. Find how many times 3 is contained in all numbers up to 30.

Give children a number of objects more than three and less than thirty. Let them count the objects and then separate them into groups of three. Then let them count the threes and tell how many threes and how many remain over. Separate 18 into groups of 3 each, viz.: 111 111 111 111 We find that there are 6 groups of 3 each. This may also be expressed in two ways:

111 111.

1836; or 3) 18

6

Now separate the 18 into three equal groups: 111111 111111 111111. Each group will consist of 6.

of 18 =

1. Separate the following numbers into groups of 3 each: 9, 15, 6, 18, 21, 30, 27, 24, 12.

2. Find one-third of each of the following groups: 12, 9, 27, 6, 15, 30, 18, 24, 21, 27.

3. Find two-thirds of 12, of 18, of 9, of 15, of 21, of 6.

Problems.

1. A boy spent 3 cents for an orange, 2 cents for taffy, 1 cent for an apple, 3 cents for nuts, 1 cent for candy and 3 cents for peaches; how much did he spend in all?

2. John has 9 marbles which number is 3 more than George has; how many marbles has George?

3. How much will nine tops cost at 3 cents each? at 2 cents each? at 1 cent each?

4. How many tops will 24 cents buy at 3 cents each? at 2 cents each?

5. If 27 apples are divided equally among three boys, how many apples will each boy receive?

Analysis.

Since there are three boys, each will receive

of 27 apples, or 9 apples.

6. If 18 oranges are divided among three girls, how many oranges will each receive?

7. Divide 21 dolls among three girls.

18. Slate and blackboard work.

Write a column of 3's, also of O's, 1's, 2's and 3's mixed, upon the blackboard and drill upon rapid addition. Also reverse the process by subtracting the numbers of the column successively. Also multiply the numbers of the column by the digits 1 to 9, reading as rapidly as possible. Also divide numbers below 30 by the numbers of the column, giving remainders. Find halves and thirds of all multiples of 2 and 3 below 30.

Note. The pupil ought by this time to be moderately accurate in writing units, tens and hundreds. Teach them that these three places constitute the units' period, and that the units' period is separated from the thousands' period by a

comma.

At first only dictate thousands and require the pupil to say the number indicating the thousands followed by a comma, and then wait for the dictation of the units' period. Thus:

dictating 3,205. Teacher says "three thousand", Pupil „3 comma Teacher, "two hundred five". Pupil "2-0--5.”

66

In like manner dictate the following:

1. Find the sum of 3,012; 313; 31; 2,123; 330; 32; 3,232; 301; 32; 3,203; 32.

2. From 71,025 subtract 21,031.

3. Multiply 31,323 by 1, 2, 3, 4, 5, 6, 7, 8, 9.

4. Divide 71,927 by 3, by 2, by 1.

5, Find the sum of 1,321; 232; 3,213; 2,331; 223; 1,303; 1,202; 2,013; 1,230; 323; 231; 323; and 232.

6. From 91,027 take 33,222.

7. Multiply 21,032 by 2, 3, 4, 5, 6, 7, 8, 9.

8. Divide 62,893 by 2, and by 3.

9. Find the sum of 2,013; 1,302; 2,131; 3,012; 2,013; 3,120; 231; 3,012; 2,012.

Example.-What is of 18.

Analysis. Since of 18 is 6, of 18 is two times 6,

which is 12.

Problems.

1. William bought a cow for $30.21, a sheep for $2.33, a plow for $22.30, harness for $33.21, a cart for $23.10, a harrow for $13.32, and five hogs for $13.30; how much did he pay for what he bought?

There is no good reason why children at this stage should not be taught how to write dollars and cents. They can thus deal with values within the limits indicated.

2. If a farmer still owes on his farm $2313.22 and has paid $926.49; how much did his farm cost him?

3. A's farm is worth $9173.61, which is $ 2023.23 more than B's farm is worth; what is the value of B's farm?

4. What is the value of 3230 acres of land at $8 an acre.?

5. How many barrels of apples at $3.00 a barrel can be bought for $6187.00?

6. Three partners gained $986. 37; what was each man's share of the gain?

7. How many barrels of flour can you buy for 12 dollars at 3 dollars a barrel?

8. A lady bought a hat for 3 dollars, a shawl for 2 dollars, and a pair of gloves for 2 dollars. How much did she pay

for all?

9. A man earns 18 dollars in 3 weeks; how much is that a week?

10. How many trees in my orchard, if there are 7 rows and 3 trees in each row?

11. There are 3 feet in one yard. How many in 6 yards?

feet are there

12. A boy caught 11 bass and sold 3; how many does he keep?