pupils' use, as well as with the Teachers' Edition for teachers' use.

The object of having the double book, the Teachers' Edition and the Pupils Edition, is that while the pupil is to prepare his lesson from the Pupils' Edition, the teacher has, in the Teachers' Edition, additional examples which the pupil has not seen, which are intended to be assigned for solution during recitation as a test of his knowledge of the subject in hand.

The first 96 pages of the Teachers' Edition, together with the parallel work of the Pupils' Edition to p. 44, are bound separately for the use of teachers in the oral instruction of pupils during their first two or three years in graded schools. It is intended wholly for oral work and is called "First Steps Among Figures, Oral Edition."

Much care has been taken in each edition to proceed from the easiest examples to those that are more difficult, in order to avoid discouraging the pupil.

The author is indebted to his assistant teachers for aid in the preparation of the very large number of examples in the book.

For a more extended notice of the scope and plan of this work see the preface to the Teachers' Edition, and also the Special Notice which precedes it.

LEVI N. BEEBE.

SPECIAL NOTICE.

Persons who may examine this book are asked to notice especially the following: Examples for rapid solving on pp. 17, 20, 25, 29, 38, 41, 45, 51, etc., as well as the foot notes, pp. 16 and 17; the drill in reading and writing numbers on pp. 39, 47, 53, 60, 69, 83, III to 116, etc.; the series of division with remainders, which is to prepare the pupil for short division, pp. 107, 128, 129, 145, and 157. In the examples in long division, on p. 136, Teachers' Edition, and on p. 82 of the Pupils' Edition, since the second figure from the left in the divisor is a cipher, while the figures of the quotient are small, the divisor is contained in each partial dividend just as many times as it appears to be. For instance, the first divisor in the Pupils' Edition, p. 81, is 201; and if the reader doubts that the path is thus made easy for the beginner, let him give his pupils an example with 19, 29, or 291 for a divisor, and then one with 201 as a divisor. There are no ciphers in the quotients on those pages, so that every difficulty is postponed to a later time that can be so put off. The examples were made

by assuming such a divisor and quotient as were desirable, multiplying them, and adding an assumed remainder to the product, which gave the dividend found in the book.

After the practice on the twelve examples on p. 136 in the Teachers' Edition, and on the twenty-nine examples on p. 82 of the Pupils' Edition, there are a number of pages of other work, after which long division, with the same sort of easy examples, recurs on p. 146, Teachers' Edition, and p. 97, Pupils' Edition. After a few examples the cipher occurs in the quotient, of which the teacher is warned at the bottom of p. 146, Teachers' Edition. Additional difficulties are treated on pp. 147 and 148, followed by examples in illustration, and still others on pp. 114, 115, and 116, Pupils' Edition.

The continuous form commonly used for tables of addition, subtraction, multiplication, and division, (as 2 and 2 are 4, 3 and 2 are 5, 4 and 2 are 6, etc.), has been forsaken for the form found on pp. 33, 37, 43, 48, 56, 63, etc., Teachers' Edition, and on pp. 6, 9, 18, 24, 29, etc., Pupils' Edition.

If the teacher copies the series on the blackboard, he may write the answers underneath, or require the pupils to find the answers, as he prefers.

For instructions see pp. 42 and 43, Teachers' Edition, and pp. 5, 6, and 19, Pupils' Edition.

The teacher will see that at p. 63 he should

though the pupil has not yet obtained his book. The number at the bottom of that page refers to the page of the Pupils' Edition that has the same kind of work. The numbers at the bottom of the following pages in the Teachers' Edition refer in the same way, while those in the Pupils' Edition refer back to the Teachers' Edition. The work of the two editions after reaching these parallel pages should be carried along together carefully.

The operations of addition, subtraction, multiplication, and division being taught together throughout the whole book, beginning with the easiest examples and progressing gradually to more difficult ones, work in each rule is constantly recurring. This necessitates a peculiar arrangement of the work, but it constitutes one of its chief excellencies.

The Pupils' Edition is bound separately for pupils' use.

The key containing answers will be found on pp. 171-183, Teachers' Edition.

For a still further description of the plan of the book please read the preface of each edition

1

by assuming such a divisor and quotient as were desirable, multiplying them, and adding an assumed remainder to the product, which gave the dividend found in the book.

After the practice on the twelve examples on p. 136 in the Teachers' Edition, and on the twenty-nine examples on p. 82 of the Pupils' Edition, there are a number of pages of other work, after which long division, with the same sort of easy examples, recurs on p. 146, Teachers' Edition, and p. 97, Pupils' Edition. After a few examples the cipher occurs in the quotient, of which the teacher is warned at the bottom of p. 146, Teachers' Edition. Additional difficulties are treated on pp. 147 and 148, followed by examples in illustration, and still others on pp. 114, 115, and 116, Pupils' Edition.

The continuous form commonly used for tables of addition, subtraction, multiplication, and division, (as 2 and 2 are 4, 3 and 2 are 5, 4 and 2 are 6, etc.), has been forsaken for the form found on pp. 33, 37, 43, 48, 56, 63, etc., Teachers' Edition, and on pp. 6, 9, 18, 24, 29, etc., Pupils' Edition.

If the teacher copies the series on the blackboard, he may write the answers underneath, or require the pupils to find the answers, as he prefers.

For instructions see pp. 42 and 43, Teachers' Edition, and pp. 5, 6, and 19, Pupils' Edition.

The teacher will see that at p. 63 he should