Mathematics for Common Schools: A Manual for Teachers, Including Definitions, Principles, and Rules and Solutions of the More Difficult Problems - Softcover

This historic book may have numerous typos, missing text or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1900. Not illustrated. Excerpt: ... VII NOTES ON CHAPTER FOUR 253-258. In the last chapter, pupils were required to add only fractions containing the same denominator; in this chapter, an addition or a subtraction example may contain fractions whose denominators are different. For the present, however, it will not be necessary to call attention to the need of reducing fractions to a common denominator. The average scholar can solve these examples without assistance, if he has been able to work out those found in Chapter III. 259. While these problems are becoming more difficult, they are still well within the powers of a pupil that is really anxious to solve them. When, however, they are found to be beyond the capacity of many members of the class, the teacher may first use them as "sight" problems, with some slight changes in the figures. If, for instance, after a pupil that reads the first from his book declares that he is unable to obtain the answer mentally, the teacher may give it as follows: A sailor has 10 yards of cloth. He uses 4 yards for a coat and 2 yards for a vest. How many yards has he left? In the second, 1^ pounds may be substituted for 1 pounds; in the third, 3 packages instead of 4; 20 dozen in the fourth, instead of dozen. Slate work on these problems should not be permitted until so many have been solved in this way that the pupil has had time to forget what operations have been used in each. This will 32 require him to study the conditions of the different problems, instead of relying upon his memory. 266. When the formal analysis of oral problems is made a feature of the work, it is important that the statements be not so long as to be tedious. In the first, for example, the following would be sufficient, after the pupil has stated the problem: "If 8 ounces of tea cost 40 ce...