Area of Rectangles, Square Measure, Solid Contents, Cubic Measure, Surfaces of Rectangular Solids, Angles, Triangles, Quadrilaterals. REVIEW OF SIMPLE NUMBERS AND FRACTIONS Special Drills, Sight Approximations, Fundamental Finding Percentage, Base, Rate; Commission, Insur- ance, Duties, Taxes, Profit and Loss, Commercial Special Drills, Review of Fractions, Review of De- nominate Numbers, Review of Commercial Discount, ALGEBRAIC EQUATIONS OF ONE UNKNOWN QUANTITY : 415 to 440 Coefficients, Clearing of Fractions, Positive and Nega- SUGGESTIONS TO TEACHERS. Additions and Omissions. — The teacher should freely supplement the work of the text-book when she finds it necessary to do so; and she should not hesitate to leave a topic that her pupils fully understand, even though they may not have worked all the examples given in connection therewith. Oral and Written Work. - The heading "Written Problems" is merely a general direction, and it should be disregarded by the teacher when the pupils are able to do the work "mentally." The use of the pencil should be required only so far as it may be necessary. It is a pedagogical mistake to insist that the brighter pupils of a class should set down a number of figures that they do not need. As an occasional exercise, the pupils may be directed to give all the work required to solve a problem, and to make a written explanation of each step in the solution; but it should be the teacher's aim to have the majority of the examples done with as great rapidity as is consistent with absolute correctness. It will be found that, as a rule, the quickest workers are the most accurate. Conduct of the Recitation. It is often advisable, for some purposes, to divide an arithmetic class into two sections, even where its members are nearly equal in attainments. The members of one section may work examples from their books while the others write the answers to oral problems given by the teacher, etc. Where a class is thus taught in two divisions, the members of each should sit in alternate rows, extending from the front of the room to the rear. Seated in this way each pupil is doing a different kind of work from those on the right and the left, and he does not have the temptation of a neighbor's work to lead him to compare answers. To save time, explanations of new subjects may be given to the whole class; but much of the arithmetic work should be done in " sections," one of which is under the immediate direction of the teacher, while the other is employed in "seat" work. The "seat" work of pupils of the more advanced classes should consist largely of problems solved without assistance. Especial pains have been taken to grade the X Suggestions to Teachers. problems so as to have none beyond the capacity of the average pupil. It is not necessary that all the members of a division should work the same problems at a given time, or the same number of problems, or that a new topic should be postponed until all of the previous problems have been solved. Whenever it is possible, each of the members of the division working under the teacher's immediate direction should take part in all the work done. In mental arithmetic, for instance, while only a few may be called upon for explanations, all of the pupils should write the answers to each question. The same is true of much of the sight work, the approximations, some of the special drills, etc. Drills and Sight Work. To secure reasonable rapidity, it is necessary to have regular and systematic drills. These should be employed frequently, but should not last longer than five or ten minutes. A page of special sight drills is given in each chapter. These may also be used in oral problems. It often happens that as pupils go forward in school they lose much of the readiness in oral and written work that they possessed in the lower grades, owing to the neglect of their teachers to continue to require quick, accurate review work in the operations previously taught. In this book these special drills follow the plan of the combinations of the earlier book, but gradually grow more difficult. They should first be used as sight exercises, either from the books or from the blackboard. To secure valuable results from drill exercises, the utmost promptness in answers should be required. Language. While the use of correct language should be insisted upon in all lessons, children should not be required in arithmetic to give all answers in "complete sentences." Especially in the drills, it is important that the results be expressed in the fewest possible words. The teacher should be careful always to employ exact arithmetical language and to require it from the pupils. Objective Illustrations. The chief reason for the use of objects in the study of arithmetic is to enable pupils to work without them. While counters, weights and measures, diagrams, or the like are necessary at the beginning of some topics, it is important to discontinue their use as soon as the pupil is able to proceed without their aid. Approximate Answers. An important drill is furnished in the "approximations" (see Arts. 104, 180, 233, etc.). Pupils should be required in much of their written work to estimate the result before beginning to so ve a problem with the pencil. Besides preventing an |