TO TEACHERS.

THE extent to which the book can be dispensed with by the class, in recitation, should be determined by the nature of the lesson and the attainment of the pupil.

When the book is not used, each question should be repeated by the pupil after the teacher, and the required solution should always be given promptly, and in every case should form a complete sentence.

A brief form of analysis only is given in the book, so as to allow the fullest scope for the exercise of ingenuity, judgment, and discrimination on the part of the pupil in the invention of others.

No form of solution, however, should be permitted to pass, unless it is neatly expressed, and is entirely

accurate.

Each example can be taken as a model for many original examples to be dictated by the teacher. In no other way than by giving a multiplicity of examples, can a teacher fix firmly in the minds of his pupils the principles which he is imparting.

Mental and written arithmetic should always be combined. Hence the wise teacher will always follow up what the pupil has learned, with suitable examples, illustrating the same principles, which will require the use of pencil or crayon.

1.

LESSON I.

1. Count ten. How many ones in ten? 2. Count twenty, or two tens. How many ones in two tens? In twenty?

3. Count thirty. How many tens have you counted? How many ones in three tens? In thirty?

4. Count forty. How many ones in four tens? In forty?

5. Count fifty. How many ones in five tens? In fifty?

6. How many ones in six tens? In seven tens? In eight tens? In nine tens? In ten tens?

7. How many tens in sixty? In seventy? In eighty? In ninety?

8. How many are ten and one? Ten and two? Ten and three? Ten and five? Ten and nine? 9. How many tens and ones are there in twelve? In fifteen ? In nineteen ?

10. How many are two tens and one? Two tens and two? Two tens and four? Two tens and six ? Two tens and eight?

11. How many tens and ones are there in twentyone? In twenty-two? In twenty-five? In twentynine?

12. How many are expressed by 1? By 2? By 3? By 4? By 5? By 6? By 7? By 8? By 9?

13. How many tens are expressed by 10? By 20? By 30? By 40? By 50? By 50? By 60? By 70? By 80? By 90?

14. How many ones are expressed by 11? By 15? By 19? By 21? By 23? By 42? By 42? By 57 ? 15. How many tens and ones are expressed by 18? By 28? By 63? By 75? By 98?

16. How many tens are expressed by 100? By 200? By 400? By 700? By 800?

17. How many hundreds and tens are expressed by 110? By 210? By 220? By 350? By 430? Bv 970?

18. How many hundreds, tens, and ones are expressed by 111? By 222? By 561? By 763? By 887 ?

DEFINITIONS.

2. What is a unit? A Unit is a single thing, or

one.

3. What is a number? A Number is a unit or a collection of units.

ADDITION.

LESSON II.

4. 1. John had 1 peach and his father gave him another; how many peaches did he then have ?

SOLUTION.-John had 1 peach and his father gave him another; he then had 1 peach and 1 peach, or 2 peaches.

2. Susan has 2 books, and Mary has 1 book; how many books have they both?

3. If you had 2 cherries, and I should give you 2, how many cherries would you then have?

4. Lucy found 2 pins, and Sarah found 3 pins ; how many did they both find?

5. If you should recite 2 lessons to-day, and 4 tomorrow, how many would you recite in all ?

6. A lemon cost 2 cents, and an orange cost 5 cents; how many cents did both cost?

7. Gave 2 cents for a pencil, and 6 cents for some paper; what was the cost of both?

8. On one bush there are 2 roses, and on another

there are 7 roses; how many on both bushes?

9. 2 boys and 8 boys are how many boys?

10. A farmer sold a lamb for 2 dollars, and a calf for 9 dollars; how many dollars did he get for both ?

11. Alfred caught 3 birds, and Jason caught 1 bird; how many birds did they both catch?

12. James has 3 marbles, and Charles has 2 marbles; how many marbles have they both?

13. A man sold a pig for 3 dollars, and a sheep for 3 dollars; how many dollars did he receive for both? 14. Mary has 3 books, and Margaret has 4 books; how many books have they both?

15. Edward gave 3 cents for a postage-stamp, and 5 cents for a box of wafers; how much did both cost?

16. Eliza is 3 years old; how old will she be in 6 years, if she lives?

17. A farmer has 3 cows in one field, and 7 in another; how many has he in both?

18. In a class there are 3 girls and 8 boys; how many pupils are there in the class?

19. A boy found under one apple-tree 3 apples, and under another 9 apples; how many did he find in all?

20. If you have 4 chestnuts in one hand, and 1 chestnut in the other, how many have you in both hands?

21. Susan had 4 merit marks, and obtained 2 more ; how many did she then have?

22. George found 4 eggs in one nest, and 3 eggs in another; how many did he find in both?