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3. 1 from two leaves how many 7?

4. How many must be taken from 2 to leave 1? 5. How many more are 2 than 1?

B. 1. George blew 1 soap-bubble, and Joseph blew 1. How many did both blow?

SOLUTION.-If George blew one soap-bubble, and Joseph blew one, both blew one soap-bubble and one soap-bubble, which are two soap-bubbles.

NOTE.-If such full forms of solution are at first too difficult for the pupils, less complete ones may for a time be substituted. Thus, instead of the above, the answer may be, "Two, because one and one are two." The full forms should, however, be introduced as soon as practicable; for they will not only teach pupils how to trace the connection between the problems and the numerical operations, and thus how to reason, but they will also prepare the way for the solution of more complicated problems. Attention to them early in the course will save much labor, both to teacher and to pupil, in the more advanced parts of Arithmetic, and even in the higher departments of Mathematics.

2. George has 1 bowl, and William has 1. How many bowls do both the boys have?

3. There were two soap-bubbles in the air, but of them burst. How many remained?

4. Sarah has 2 dolls, and Mary has 1. How many more has Sarah than Mary?

5. A STORY ABOUT JAMES.-James was a little boy who lived in the country, and studied the First Book of Arithmetic. On his way to school one day, he found 2 apples. At recess, he gave 1 of them to his Teacher, and ate 1; but just before recess was over, he received a present of 1 from a

schoolmate.

After school, he found 1 under a tree, and gave 1 to a little boy whom he met. When he reached home, he roasted all he had left. How many did he roast?

NOTE.-Probably it will at first be desirable for the teacher to simplify such long problems as the one just given, by asking intermediate questions. For instance, after reading as far as "He gave one of them to his Teacher," ask "How many did he have left?" "He ate one, how many did he have then?" &c. The pupil will soon learn to perform the problems without such aids.

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The mark 3, or, is called the figure three.

A. 1. How many are 2 and 1?
2. How many are 1 and 2?
3. How many are 1 and 1 and 1?

4. 2 and how many are 3?
5. 1 and how many are 3?
6. 2 from 3 leaves how many?
7. 1 from 3 leaves how many?

8. How many more are 3 than 2?
9. How many more are 3 than 1 ?

B. 1. Edward had 2 tame rabbits, and his cousin gave him 1 more. How many had he then? 2. A cross dog afterwards killed 2 of Edward's rabbits. How many had he left?

3. Emma had 3 rabbits, 1 of them was black, and the rest were white. How many were white? 4. Lucy's father gave her 1 rabbit, her mother gave her 1, and her uncle gave her enough to make 3. How many did her uncle give her?

5. Henry's father gave him 2 cents, and his mother gave him 1, and then he spent 1 cent. How many cents did he have left?

6. A STORY ABOUT CARRIE.-Carrie was a brighteyed little girl who lived in a village. One day she cut out 2 paper dolls, and the next day she cut out 1 more. She then gave 1 to her playmate, Martha, and 1 to Maria. She afterwards cut out 2 more, but through carelessness, let 1 fall into the fire, when her mother cut out 1 very nice one, and gave it to her. How many had she then?

TO THE TEACHER.—Make additional problems, and encourage · the pupils to do it for themselves, arranging them somewhat in the form of stories, to increase their interest. Problems proposed by the pupil will usually be more interesting to a class than those proposed by a teacher or author.

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The mark 4, or 4, is called the figure four.

NOTE. It should be made a part of the lesson for the pupil to write out the exercises in abstract numbers. He will thus learn to use figures and mathematical signs, and to write out arithmetical work neatly and correctly.

EXPLANATION. -A cross made thus, +, is sometimes used in place of "and" in such questions as, how many are 1 and 2? In like manner, "2+2 are 4" means the same as "2 and 2 are 4." This sign is also called plus, and sometimes the sign of addition.

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4. 1+2+1?

5. 1+1+2? 6. 2+1+1?

2. 1+3? EXPLANATION.-Read and perform the following questions, and similar ones throughout the book, as though the words "how many" were put in the place of the star. Thus, the question "2+*= 4?" means the same as "2+ how many = 4?"

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E. 1. George has 2 apples, and Rufus has 1.

How many have both?

George than Rufus?

How many more has

2. Edward had 2 marbles, and his father gave him a cent, with which he bought 2 more. many had he then?

How

3. Edward afterwards lost 1 marble, and gave
2. How
How many had he left?

away 2.

4. Henry has money enough to buy an orange for 2 cents, an apple for 1 cent, and still have 1 cent left. How many cents has he?

5. Jane had 1 picture-book, and on her birthday her father gave her 1 more, her mother gave her 1, and her uncle Henry sent her 1, which was very pretty. How many had she then?

6. Susan cut 2 pictures out of one newspaper, and 2 out of another; she then gave 1 of the pictures to her little brother Henry, and 2 to her sister Fanny. After cutting out 3 more pictures, she sent what she had to her cousin Abby. How many pictures did she send to her cousin Abby?

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