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are presented in the 24th, 25th, 26th, and 27th lessons. These operations are so closely connected with each other that it must certainly be more philosophical to thus present them together, than to entirely dissever them, as is usually done in works on primary arithmetic. What, for instance, are “3+2=5,” “3 from 5 = 2,” and “5 = 3 more than 2,” but different forms of expressing the idea that 5 is made up of 3 and 2? Again, what are the questions, “How many are 4 times 3 ?” “12 = how many times 3 ?” and “12 = 4 times what number?” but different forms of expressing the fact that 4 times 3
are 12 ?
The lessons from the 28th to the 32d, inclusive, illustrate the nature of fractions and of some of the more simple operations involving them, and are followed by tables of moneys, weights, and measures.
Such is an outline of the plan of this work. The materials for it have been drawn chiefly from the First Steps in Numbers, published in 1849 by George A. Walton, of Lawrence, Mass., and myself, and from the First Book of Arithmetic, prepared by me in 1856.
With these explanations the Child's Book of Arithmetic is commended to the favor of those interested in primary instruction.
BRISTOL, R. I., July 15, 1859.
TO THE TEACHER.
Young children commencing the study of Arithmetic need much oral instruction. At first each number and each operation should be illustrated to the eye by familiar exercises, similar in character to those indicated in the following
The Teacher, taking a book, asks, “ What have I in my hand ?" Ans.—“A book.” “How many books?" Ans.—“One book.” “How many pencils do I show you?” Ans. One pencil.” 6. How many chairs do I point at ?" Ans.—- One chair.” “ How many desks?"
desks?” Ans. One desk.” Let the pupils now point to one boy, to one girl, to one window, &c.
Make the figure 1 on the blackboard, and tell the class that it means one, as 1 dog, 1 book. Show them also the script figure, as 1 dog, 1 book.
The questions of Lesson I. may now properly be asked, the pupil having his book open before him. This will prepare the way for the
SECOND ORAL LESSON.
“ How many pencils have I in my right hand ?” 1*
6 How many
Ans.—“. One pencil.” “ How many in my left hand ?" Ans.-« One pencil.” “How many in both ?" Ans.-“ Two pencils." pieces of chalk have I in my right hand ?” Ans.66 One." • In my left ?” Ans.—66 One."
- In both ?” Ans.-6. Two." “ How many fingers do I hold up?" Ans.-“ Two." Taking up one pen and then another, ask, “One pen and one pen are how many pens?” “If I lay down one pen, how many shall I have left ?” Lay down one pen, and show the remaining one.
Then ask, “How many more must I get to have two ?” Taking two pens in the right hand and one in the left, ask, “How many pens have I in my right hand ?” “How many in my left hand ?"
How many more in my right hand than in my left ?" less in my left hand than in my right hand ?” 6 If I should pass one from my right hand to my left hand, how many would there be in my right hand?" “How many would there be in my left ?”
The transition from these exercises to those of Lesson II. will be very easy. In reciting the subsequent lessons the pupil may or may not read the questions and problems from the book, at the discretion of the teacher.
If each of the first four or five lessons of this book are thus introduced by familiar oral exercises, the pupil will not be likely to find any serious difficulty with those which follow.
« How many
1. How many pictures are there on this page ? 2. How many boys do you see in the picture ? 3. How many girls do you see in the picture ? 4. How many balls do you see in the picture ? 5. How many thumbs have you on your right hand ? 6. How many thumbs have you on your left hand ?
Two soap-bubbles. 2 soap-bubbles.
The mark 2, or 2, is called the figure two.
How many boys do you see in the picture ?
A. TO THE TEACHER.—The following questions should first be asked by substituting concrete in place of the abstract numbers. Thus: “How many apples are 1 apple and 1 apple? 1 pear and how many pears are two pears ?” &c. The pupils should be taught to make such changes for themselves. The work is not, however, completed till the abstract numbers and operations are mastered.
1. How many are 1 and 1 ? 2. 1 and how many are 2?