Explanation.- Begin on the left. 2 is contained in 7 three times and 1 over which makes ten units of the next lower order. Ten added to 1 makes 11. 2 is contained in 11 five times and 1 over. Proceed in this manner until the units are reached and then write the 1 which remains over the divisor 2.

When numbers are dictated for subtraction, multiplication, or division, spell them by giving a figure at a time to be written in line.

9. Teach the half of multiples of two.

Any number of times a number is called its Multiple. Thus the multiples of 2 are 4, 6, 8, 10, 12, and so on.

Exercises.

1. How much is two and the half of two?

2. How much is eight and the half of eight?

3. How much is twelve and the half of twelve?

4. How much is six and the half of six?

5. If a dot increases the value of a musical note one half, what is the value of a dotted half-note? whole-note? quarternote?

16. Teach the form of a written examination.

Take the slate with its longer side toward you. Do not write too near the edges nor crowd your work on the slate. Give five examples and mark any one of them 0, if there is even one figure wrong. Secure neat work.

Make similar examinations and drill on this work until at least 90% of accuracy is obtained.

Problems.

1. A farmer pastured thirteen droves of sheep during the season, containing respectively 212, 121, 202, 111, 221, 200, 211, 222, 122, 101, 220, 110, 221 sheep; how many sheep did he pasture in all?

2. Mr. A owns 70,221 acres of land, which is 2,112 acres more than Mr. B owns; how many acres does Mr. B own? 3. How much would 212,212 barrels of flour be worth at $7 a barrel?

4. A grocer received $7,194 for apples at $2 a barrel; how many barrels of apples did he sell?

5. A man bequeathed to his two sons $9,462; how much was each to receive?

6. There are 7 birds in one cage and 2 in another; how many birds in both cages?

7. John had 12 marbles and lost 2; how many had he left? 8. What will 9 turkeys cost at 2 dollars a piece?

9. If a man spends 20 dollars for books, at 2 dollars a piece; how many does he get?

10. If 2 trees yield 18 bushels of apples, how many bushels does one tree yield?

11. From a piece of cloth containing 13 yards, 2 yards were cut off; how many yards remained?

12. If a boy earns 2 dollars in one week, in how many weeks can he earn 16 dollars?

13. John has 6 apples and his brother gave him 2 more; how many had he then?

14. There are 2 pints in a quart. How many pints are there in 8 quarts?

15. If 2 sacks of flour are worth 8 dollars, what is one sack worth?

16. How many pieces each, when 2 children get 20 pieces of candy?

17. There are 2 boys in a seat and 6 seats in a division; how many boys in the division?

18. If a man can travel 7 miles in one day and 2 miles the next day, how far does he travel in both days?

19. A grocer bought 9 bushels of apples and sold 2 bushels; how many bushels had he left?

20. If one barrel of apples is worth 2 dollars, how many barrels can be bought for 24 dollars?

21. Willie has 6 rabbits and Henry has 2; how many have both?

22. If there are 2 peaches on a dish, how many would there be on 7 dishes?

23. If 2 sheep were sold for 20 dollars, what was the price of each?

24. John has 8 marbles and his brother has 2 more, how many has his brother?

25. William has 2 marbles and his brother has 6 times as many, how many has his brother?

26. A man earns $2 per day, how much will he earn in a week?

27. James gives each of his six brothers 2 apples, how many does he give them all?

28. In a class there are 9 boys and two more girls than boys; how many girls in the class?

29. If Mary has 2 rings on each finger of her right hand, how many rings has she?

30. If I divide 18 apples among 2 girls, how many apples will each girl receive?

31. If a man divided $16 between his 2 children, how many dollars will he give to each?

32. If 2 children sit at each desk, how many children sit at 8 desks.

33. If 1 yard of ribbon cost $2, how much will 9 yards cost? 34. How many balls at 2 cents each can be bought for 10 cents?

17. Teach all the processes with THREE. 1. Count by threes from 0 to 30.

2. Count by threes from 1 to 28.

3. Count by threes from 2 to 29.

4. Count by threes backward from 28, from 29, and from 30.

By using small objects or the numeral frame and separating the THREES, these processes can be sensibly illustrated. Since number is a property of things, conscious ideas of number are primarily obtained from the objects themselves.

5. Give some number and let pupils tell what other number is three less or three more than the given number. Nine is three less than 12 and three more than 6.

Thus:

Given numbers: 4, 21, 8, 13, 6, 15, 7, 25, 27, or 19.