ELEMENTARY ARITHMETIC

CHAPTER I

PRELIMINARY LESSONS

TO THE TEACHER. The lessons of this chapter are designed to indicate the nature of the work that should be done by the class before the text is placed in the hands of the pupils. Space does not permit of the introduction of sufficient material to furnish all of the exercises which the pupils will need. The lessons in this chapter should, therefore, be regarded as type lessons which the teacher is to expand and to supplement to meet the needs of the class. It is not expected that all of the work suggested in any one of the lessons will be given at any one time. Several parallel lines of work are suggested in the various lessons, and these should be carried on together, the work gradually increasing in difficulty until the pupils have finally mastered all of the work indicated in each of the lessons.

No abstract number work, aside from counting and the reading and writing of numbers, is provided, and none should be given. The pupils should deal with number in its relation to things, and not with abstract number facts. In the exercises suggested in this chapter, the pupils themselves play an important part. They are required to do, as well as attend to what is done by others. They are led to discover number relations in the quantities that are

handled by them, and to express these relations in correct language.

These lessons are presented in the form of questions and directions given by the teachers, as serving best to illustrate the methods to be followed in presenting them to the class. No exercise should be continued so long that the pupils will begin to lose interest in it. The teacher is expected to use whatever objects may be at hand, and to vary the objects frequently. A box of 1-inch cubes will be found very useful in this as well as in subsequent number work. They are easily handled, and may be conveniently arranged to show relative quantities, etc.

The pupils should be encouraged to express themselves freely, but at the same time correctly. Sufficient time should be taken to acquaint the pupils with the language forms involved in these lessons. If properly presented, the work suggested in this chapter should not only give the pupils familiarity with simple number facts, and an insight into the common operations with number, but should also establish habits that will be found extremely valuable in all subsequent number work. Some of the number facts developed in these lessons are designated as facts to be learned. These should be perfectly memorized.

LESSON I-MAGNITUDE

The primary purpose of Lesson I is to train the pupils to hear and interpret simple directions. The secondary purpose is to acquaint the pupil with the language forms used to denote relative position, direction, magnitude, etc. After giving a direction, allow sufficient time for all the pupils to interpret the direction, and to image its execution. Should the pupil called upon fail to execute correctly the

direction given, do not call upon a second pupil for it, but give a new direction. This will be found more effective in keeping the attention of the whole class than the more common procedure, namely, that of permitting the brighter pupils to do most of the work. Later, return to the direction upon which a failure was made, and call upon some other child to carry it out, unless you have reason to think that the pupil who once failed can now execute it correctly.

Simple directions are to be executed, showing the meaning of the following and similar terms: in your right hand, in your left hand, to the right of, to the left of, above, below, nearer, farther from, beside, between, in front of, larger than, taller than, tallest, shorter than, shortest, smallest, twice as long as, one half as long as, twice as far from, one half as far from, the same distance from, a line, at the end of, in the middle of, etc.

ILLUSTRATION. Have two boys from the class, say John and James, stand in line in front of the class, John several feet to the right of James. Problems: 1. I want some one to stand in line with John and James. 2. Stand in line with the two boys, to the right of John. 3. Stand in line, to the left of James. 4. Stand in line, so John is to your right and James is to your left. 5. Stand in line, the same distance from the boys. 6. Stand in line, nearer John than James. 7. Stand in line, farther from James than from John. 8. Stand in line, one half as far from John as from James. 9. Stand in line, to the right of John, one half as far from John as from James. 10. Stand out of line, but the same distance from each of the two boys.

ILLUSTRATION. With colored crayon draw on the board lines of different lengths, for comparison. Problems: 1. Alice, tell me a story about the yellow line and the

blue line. Story: The yellow line is longer than the blue line. 2. Walter, tell me a story about the red line and the blue line. Story: The red line is shorter than the blue line. 3. Mary, tell me a story about the green line and the red line. Story: The green line is as long as the red line. 4. Who can tell me a story about the orange line and the blue line? Story: The orange line is one half as long as the blue line. 5. Who can tell me a story about the yellow line and the red line? Story: The yellow line is two times (or twice) as long as the red line. 6. Ethel, tell me a story about the red line, the blue line, and the yellow line. Story: The red line and the blue line together are as long as the yellow line.

Substitute lines drawn with white crayon and lettered a, b, c, etc., in place of the colored lines, and treat in a similar manner. Have the pupils point to the lines as they name them in giving their answers. Later, make written statements regarding these lines, leaving blanks for the pupils to fill in, thus: The red line is than the blue line. The line is shorter than the red line. Compare the length of the board with its width, the height of the room with its width and length, etc.

LESSON II-COUNTING

In the preparation of this lesson, it is presumed that the pupils have acquired some number knowledge before entering school. The teacher should ascertain as soon as possible what knowledge the pupils have, and should adapt the lessons to the needs of the class.

ILLUSTRATION. Problems: 1. Harry, bring me one book from the table. 2. Jane, bring me two books. 3. How can I show on the board the number of books