SUGGESTIONS TO TEACHERS. IN the belief that written explanations are as likely to be a stumbling-block as an aid to the pupils for whom the Elementary Arithmetic is intended, many points have been left without explanation. In such cases it is expected that the teacher will introduce the explanation at such points in the pupil's progress, and to such an extent, as the teacher may deem best. Accurate work is what practical life requires; but accurate work (except, perhaps, when such work is merely mechanical) is most surely attained by a thorough understanding of the principles and the processes involved. The explanations that are given are designed as a guide to the teacher fully as much as to the pupil, and at the discretion of the teacher may be omitted by the pupil, or deferred to a later point. The method given of casting interest is the one used by business men, and is the simplest as well as the most expeditious. Facility in its application can best be gained by actual practice. To this end the teacher should introduce as many additional examples as time will allow. A large number of examples have been added at the end of the book. These will be valuable for additional work and for review. ELEMENTARY ARITHMETIC. NOTATION AND NUMERATION. 1. A Unit is a single thing of any kind; as, one apple, one book. 2. A Number is a unit, or a collection of units; as, six apples, ten books. 3. Notation is the writing of numbers. 4. Numeration is the reading of numbers. 5. To express numbers ten figures are used, viz.: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Zero, One, Two, Three, Four, Five, Six, Seven, Eight, Nine. The first figure is called zero, a cipher, or naught; standing alone, it signifies nothing. The remaining nine figures represent in order the numbers one, two, three, four, five, six, seven, eight, nine. 1. How many units are there in five? in seven? in nine? 2. Write in figures, three; five; eight; nine. |