Part 7

(=g=) On what train did he come on (54)?

(=h=) Neither the boy or his mother are here (55, 4).

(=i=) You cannot write like the teacher does (56).

(=j=) Carthage and Rome were rival powers; the one on the northern coast of the Mediterranean, the other on the southern (51, 57).

(=k=) The weight of the sun is 300,000 times heavier than that of the earth (58).

(=l=) Mary sent her sister back for her shawl which she had forgotten to bring (59).

(=m=) A boy who studies and that improves his spare moments will become eminent (60).

(=n=) Nearly every one of the applicants were from this county (4).

(=o=) Neither of the workmen have brought their tools (4, 7).

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INSTITUTE LESSONS. Primary Arithmetic.

1. Use each of the numbers (1, 2, 3, 4, &c.) one at a time, and devise many different ways of illustrating and using each objectively. First, the perception of the number as a whole—then, the analysis of the number. Part of the work should involve subtraction.

2. Each number may be illustrated in many ways by large dots variously grouped on cards. With these cards drill the perception in quickness. Let each pupil arrange a certain number of “counters” in several ways of regular form.

3. On each number, ask every possible variety of question. Let the pupils make problems. Let some be made that are to have a certain given answer.

4. As each number is used, let its script form be learned and made by the pupils. After progressing in this way as far as 4 or 5 (some say to 9) teach the figures. Practice counting objects as far as 20.

5. The exercises for slate work should progress very gradually. A higher number should be introduced only after the pupils can use, with readiness, those below it, in their many and varied combinations. Let there be oral work consisting of easy objective problems illustrative of the slate work.

6. In the black-board work the teacher should use a pointer and call for ready and correct mental recitations, as he points to the various problems.

7. The exercises for slate work may be of several different kinds: as,

(a) 1 and 1 are . 2 and 3 are . &c.

(b) 5 less 1 are . 6 less 4 are . &c.

(c) 2 and are 6. and 1 are 5.

(d) 6 less are 5. less 2 are 2.

(e) 1 1 1 2 2 1 1 2 2 2 1 2 3 2 3 _

The columns of (e) may contain from three to nine figures. The teacher must not lengthen them at any time beyond the ability of the pupils.

(f) 1 1 1 1 1 1 1 1 1 2 1 3 9 4 5 6 8 7 _

The upper figure is the same in each: the lower figures are different and are arranged miscellaneously. In the advancement, increase the upper row a unit at a time, as far as 11.

8. Teach the use of the signs ×, -, and =, and let the pupils have slate work similar to the following:—

8 × 5 = . 9 - 6 = . &c.