TEACHERS' MANUAL 
 
 BOARD OF EDUCATION 
 CITYOF NEW YORK 
 
 GRAMMAR GRADES 
 
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 Southern Branch 
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 University of California 
 
 Los Angeles 
 
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 STATE HORMAl SCHOOL. 
 
 Lm Angeles, C»t
 
 STATE NORMAL SCHOOL, /^^^ 
 
 Los Anfetcs, Cal. 
 
 A MANUAL 
 
 Discipline and Instruction 
 
 USE OF THE TEACHERS 
 
 GRAMMAR SCHOOLS 
 
 UNDEK THE CHARGE OF THE 
 
 Board of Education of the City of New York 
 
 PUBLISHED BY 
 
 J. S. BABCOCK 
 55 Cedar Street, N. Y. 
 
 ^■3 2.
 
 Copyright, 1884 
 
 By LAWRENCE D. KIERNAN 
 
 Clerk of the Board of Education of the City of New I 'ork 
 
 TROWS 
 TING AND BOOKBINDING COMPANV. 
 NEW YORK.
 
 LB 
 TEACHERS' MANUAL. 
 
 The following brief extracts from the Records of the 
 Board of Education show the circumstances and authority 
 ■under which this Manual of Instruction was prepared : 
 
 Journal of the Board of Education for 1882, page 693 : 
 " Resolved, That the Teachers' Manual be referred to the Committee on 
 Course of Study and School Books, for such revision as may be neces- 
 sary, and report thereon to this Board." 
 
 Journal op the Board of Education for 1882, pages 790 and 845: 
 " First, That the Teachers' Manual be revised, and its provisions be 
 made to conform to the present Course of Study. That the methods 
 of instruction recommended in said Manual shall be suggestive only, 
 but that in respect to other matter, when so stated therein, said Manual 
 shall have the same force and effect as a by-law of the Board." 
 
 By the authority of the Board and the Committee on 
 Coui-se of Study and School Books, John Jasper, City 
 Superintendent of Schools, and his Assistants, have pre- 
 pared the Manual herewith presented. 
 
 William Wood, ") 
 
 Gilbert H. Crawford, | Committee on Course 
 
 Ferdinand Traud, V of Study and School 
 
 J. Edward Simmons, | Books. 
 Edward Patterson, J 
 
 STEPHEN A. WALKER, 
 Law. D. Kiernan, President. 
 
 Clerk.
 
 TEACHERS' MANUAL 
 
 FOR THE 
 
 GRAMMAR SCHOOLS 
 
 OF 
 
 NE^\^ YORK CITY. 
 
 INTRODUCTION. 
 
 Object of this Manual. — The object of this manual 
 is to furnish teachers with tlie Course of Instruction pre- 
 scribed for the Grammar Schools, and with instructions 
 and suggestions to aid in cari-jing out this course in all its 
 requirements ; also, with the by-laws, rules, and regulations 
 which relate to the duties of teachers. 
 
 1!^ The Course of Studies and the by-laws and regula- 
 tions contained herein are valid requirements for the gov- 
 ernment of teachers in the discharge of their duties. As to 
 the suggestions in relation to methods of teaching given 
 herewith, although they embody the results of the long 
 and wide experience of many successful teachers, and al- 
 though their proper use has uniformly led to desired ends 
 in instruction, the teacher will be at liberty to receive and 
 to use them as the counsel of a trusted friend, and to make 
 the modifications necessary to meet the particular condi-
 
 INTRODUCTION. 
 
 tions of the pupils under instruction ; but she will be held 
 responsible for the use of such methods as will lead pupils 
 to the attainment of proper results in their education. The 
 true education of children is not dependent upon the use 
 of any particular method. Methods of education are val- 
 uable only when they harmonize with the conditions under 
 which the mind attains knowledge. 
 
 S!2^ Teachers are counselled to study carefully the sug- 
 gestions given in relation to each subject of instruction, 
 and to consider the principles that underlie and direct the 
 methods, in order wisely to modify these methods when 
 circumstances render it desirable to do so. In education 
 jprinciples are like fixed laws : true methods of teaching 
 are only ivays of obeying and carrying otd those laics. 
 
 Duties of the Teachek. — IS^o task can be more respon- 
 sible or require the exercise of greater care than that of 
 educating the young. To perform it properly, special 
 preparation and study are indispensably necessary, not 
 only in relation to the branches of knowledge which may 
 have been selected as a basis for the instruction, but in 
 regard to the proper methods and appliances to be em- 
 ployed, in order to render the instruction truly effective. 
 These methods must be determined by a consideration of 
 the faculties to be trained and educated, as well as the 
 nature of the subject taught. 
 
 To a great extent, experience must be our guide in 
 enabling us to judge of the character of the minds to be 
 educated, as well as to determine the means to be em- 
 ployed for cai-rying on the work. 
 
 The teacher's task is one of great magnitude, responsi- 
 bility, and labor. Great issues depend upon its right per- 
 formance. The future welfare of the community depends 
 upon her efforts. Neglect on her part — nay, conscious in-
 
 INTRODUCTION. 7 
 
 efficiency — is a crime. The impressions whicli are made 
 by her are ineffaceable. Hence it is of supreme impor- 
 tance that her work receive all the guidance that careful 
 study and mature experience can afford. 
 
 The natural education of each child is begun before he 
 enters school, by means of his personal experience with 
 the objects and phenomena that surround him. Knowl- 
 edge is the result of experience. Every teacher should 
 aim to continue the natural processes of education by ex- 
 tending the personal experience of the pupils, so that the 
 range of objects and phenomena observed by them shall 
 be daily increased. To produce this result the teacher 
 must select suitable materials for a proper exercise of the 
 child's senses ; then stimulate the pupil's mind to work 
 upon them. 
 
 It is the teacher's duty to adjust the conditions between 
 the child's mind and the objects, so that the natural exer- 
 cise of the senses shall develop mental power and pro- 
 duce intellectual growth. The teachers work should cause 
 the child to notice more and more carefully his personal 
 experiences with surrounding objects, and thereby lead to 
 the formation of habits of observation. It is the teacher's 
 duty to arrange the materials to which the pupils should 
 give special attention, so as to guide their observations in 
 a manner that will lead to a proper association of their 
 experiences. 
 
 Knowledge consists in ideas and facts gained and prop- 
 erly classitied by the learner. Words memorized and re- 
 cited about an object, even though their arrangement be 
 faultless, do not by themselves constitute knowledge. The 
 child cannot be a real learner while only a passive recip- 
 ient of words. Real education comes from what the child 
 does. To effect mental development, there must be activ-
 
 8 INTRODUCTION. 
 
 itj of the mind in connection with the object just as truly 
 as there must be activity of the body to promote physical 
 development. The teacher should act in accordance with 
 these facts in the application of all methods of instruction. 
 
 In no other period of education does the importance of 
 a proper attention to the laws of mental development rest 
 so heavily npon the teacher as it does during the first 
 three years of the child's school life. During this period, 
 especially, should instruction commence with perceptions 
 — perceptions of form, color, sounds, number, size, quali- 
 ties ; of right and wrong actions, obedience, etc. ; and the 
 appropriate words and language should be taught to enable 
 the child to express the ideas obtained l)y means of these 
 different perceptions. 
 
 Ideas are obtained in different ways. Some can be 
 gained only through the sense of sight, as color ; some 
 only through the sense of touch, as rough, smooth, soft, 
 hard, hot, cold ' some only through the sense of smell, as 
 odo7'S / some only through the sense of taste, as sweet, sour, 
 hitter, pungent, astringent ; some only through the sense 
 of hearing, as spoken words, music. Of some objects ideas 
 may be gained through several of the senses, as the shape 
 of an orange by the sense of sight and of touch ; its color 
 by sight ; its odor by smell ; and other properties by taste. 
 The ease and accuracy with which ideas ma}^ be obtained 
 in these different ways depend upon the degree of devel- 
 opment which these several senses have attained. The 
 senses are the gateways through which the mind holds 
 intercourse with the world around it ; and if these be but 
 partly opened, or if freedom of communication be ob- 
 structed by neglecting the use of the proper means for 
 such intercourse, the ideas obtained must be correspond- 
 ingly dwarfed and imperfect.
 
 INTRODUCTION. 9 
 
 It is a well-known fact that tlie proper exercise of any 
 power, whether physical or mental, increases that power. 
 Exercise of the several senses is therefore the true means 
 by which the power of gaining ideas may be strengthened, 
 and the ability to acquire knowledge increased. 
 
 It is also a well-known fact to all observing teachers 
 that a large proportion of young children, when they first 
 enter school, have not learned to use their senses in such a 
 manner as to enable them to gain accurate ideas. It there- 
 fore becomes a matter of great importance that teachers 
 of young children should give special attention to provid- 
 ing suitable exercises for this purpose. 
 1*
 
 GOVERiNMENT AND DISCIPLINE. 
 
 INSTRUCTIONS FOR ALL THE GRADES. 
 
 Tetje Objects of Discipline. — The training of pnpils 
 so that they &hal\ Jbrm right habits and leai'n self-control, 
 is the true object of discipline. In all the rales and 
 methods of discipline employed, this purpose should be 
 kept steadily in view. Discipline, in its relation to order, 
 exists for the sake of the pupils and the school. It pre- 
 pares the way for the work of instruction, and makes it 
 eflFective. Obedience is the first condition in discipline. 
 It includes conformity to requirements as to time, place, 
 and manner, such as punctuality, regularity, orderly habits, 
 and so forth. 
 
 " Like Begets Like." — " As is the teacher, so will be 
 the school." It is, therefore, requisite that teachers should 
 possess fixed habits of neatness, cleanliness, and order ; 
 gentleness of manner, a watchful self-control, and a cheer- 
 ful spirit. In speaking let pleasant tones of voice prevail ; 
 then the words of reproof will be more impressive and 
 effectual. 
 
 Teachers should never forget that their pupils are con- 
 stantly and closely watching their conduct, and are prone 
 to imitate whatever they observe. Scholars should, there- 
 fore, see and hear nothing that they may not safely imi- 
 tate. There is an " unconscious tuition," the silent influ- 
 ence of which produces the most permanent effects. 
 
 Sympathy fok Childken. — Teachers should seek to ob-
 
 12 GOVERNMENT AND DISCIPLINE. 
 
 tain the sympathetic regard of the children by giving a 
 due attention to their wants and requests. These should 
 be fulfilled as far as it is proper and reasonable. Children 
 are quick to perceive and to resent injury or injustice. 
 The child who asks for the privilege of a drink of water, 
 for instance, may be suffering acutely ; and, if not ac- 
 corded relief when this seems to be perfectly practicable 
 on the part of the teacher, may feel a sense of outrage 
 which, for a time, if not permanently, would impair its 
 respect and regard for the teacher. The cultivation of a 
 due feeling of sympathy for the children will wholly pre- 
 vent this. The possession of this feeling in its fulness is 
 the best foundation of success in both discipline and in- 
 struction. Kindness is the practical basis of sympathy. 
 It seeks the good of the pupil and endeavors to remove all 
 imperfections of the individual without injury to him. Its 
 influence for good is exceedingly strong, and its power 
 with children nearly irresistible. 
 
 Encourage Pupils. — Encouragement inspires confi- 
 dence. Children, more than others, need encouragement. 
 It is a strong incentive to effort. Let it be given in all 
 cases where this can be honestly done. To a want of this, 
 in the discipline of classes, are to be ascribed the timidity 
 and reserve often manifested among pupils by a hesitating 
 manner and a low voice. A proper degree of encourage- 
 ment will render them confident and spirited, eager to tell 
 what they know, and in an audible tone of voice. En- 
 couragement has a peculiar infiuence in promoting mental 
 and moral improvement. Letting a boy know that you 
 believe there is good in him is the best way for putting it 
 there. 
 
 Develop Right Opinions. — Aim to govern the class by 
 a development of public opinion among the pupils in favor
 
 GOVERNMENT AND DISCIPLINE. 13 
 
 of the right and against the wrong, and thus govern indi- 
 vidual members through the class. Give proper attention 
 to those cases of disorder by single pupils which cannot 
 be overcome through influence upon the class. Success in 
 discipline does not lie in telling individual pupils their 
 faults before the class. Attempts to detect and correct 
 each individual misdeed in detail will not develop the 
 right public opinion nor lead the pupils to a willing com- 
 pliance M'ith the wishes of the teacher. Judicious com- 
 mendation when pupils make efforts to overcome faults 
 is more effective toward accomplishing the desired results. 
 
 Avoid Scolding. — Harsh tones are unnecessary and 
 improper. Words of disapprobation may be nttered by the 
 teacher in a tone of decision, without the use of any sever- 
 ity that would imply resentment, anger, or antipathy on 
 the part of the teacher. On the contrary, the language 
 used and the tones of the voice should always express a 
 feeling of symimthy with the child. This is the way to 
 win the youthful mind, and to bend the will through the 
 affections ; a different course will antagonize it and pre- 
 vent all real submission, securing only a temporary sem- 
 blance of obedience. Nei^er threaten. Harsh words, 
 rough means, and appeals to corporal punishment, when 
 employed to secure school order and certain results of 
 study, break down the sense of honor and destroy in the 
 pupil the proper respect for his teacher. 
 
 Attention the Basis of Good Order. — Good order 
 does not require pupils to occupy, for a long time, a fixed 
 position ; nor to assume a constrained posture ; nor to fix 
 their eyes upon a given point ; nor to be as motionless as 
 statues. All this is unnatural, and much of it positively 
 injurious, and whatever is unnatural is not good order. 
 The postures of the pupil should be graceful, easy, and
 
 14 GOVERNMENT AND DISCIPLINE. 
 
 uniform, and should be frequently changed. The move- 
 ments, Avhile as simultaneous as perfect attention would 
 necessarily produce, should also be easy and natural. 
 
 1^^ Intelligent attention, j}7'omj>t and willing obedi- 
 ence, toith quiet, orderly movennents, a/re the chief requisites 
 of good order. 
 
 Physical, Education. — Xo system of education and 
 school management is complete which neglects to provide 
 for due attention to physical training. Children should 
 be taught how to sit, to stand, to move, to walk ; to ab- 
 stain from the use of those things, and to avoid the doing 
 of those acts which are injurious to health. Eegulations 
 and instructions in relation to this matter should be simple, 
 and due attention should be given to them at every ap- 
 propriate opportunity during the daily exercises of the 
 school. 
 
 Cleanliness of person and of clothing ; the importance 
 of breathing pure air, of eating proper food, of caring 
 properl}^ for the eyes, the teeth, and the ears ; and the 
 necessity for daily phj-sical exercise, should receive special 
 attention, and be made subjects of instruction and admoni- 
 tion. 
 
 In the matter of proper postures, movements, etc., it is 
 quite easy to enforce all necessary regulations, provided 
 they are not capriciously applied. Children must first be 
 taught them, and then never permitted to violate them 
 without admonition or correction. 
 
 Due attention should be given daily to calisthenics and 
 such other exercises as will aid the physical organs to per- 
 form their functions properly, and thereby to prepare the 
 mind for elSicient activity. 
 
 Xeatness, Regularity. — Neatness, method, and regu- 
 larity are among the necessary elements of popular educa-
 
 GOVERNMENT AND DISCIPLINE. 15 
 
 tion. The character of cliildren is greatly affected by 
 their surroundings. These should, therefore, be neat and 
 orderly. The rooms in which they assemble should be 
 clean, the desks and other furniture, as far as possible, 
 free from injury or defacement, everything giving evidence 
 of constant attention. Children thus unconsciously acquire 
 habits of order, neatness, and regularity, which have an 
 important bearing upon their usefulness and happiness in 
 after life. 
 
 To impart or maintain these habits, every proper means 
 should be employed, and every requisite rule should be 
 carefully and regularly enforced. 
 
 Moral Education. — No teacher who neglects the moral 
 training of the pupils in the essential elements of good 
 character does the whole duty of the instructor. The 
 main object in moral training, as in physical and intel- 
 lectual education, is to give a right direction to the action 
 of those powers that relate to this department of our 
 nature. Such training, to be effective, must provide suit- 
 able means for the exercise of the moral powers. It con- 
 sists, largely, in leading the children to understand their 
 duties to themselves and their duties toward others. 
 Among their duties to themselves are : self-control in all 
 matters relating to conduct — of the temper, the appetite, 
 and the desires ; speaking the truth ; and self -culture in 
 all things that aid in forming a good character. Among 
 their duties to others are : obedience to parents and teach- 
 ers ; kindness to brothers, sisters, and playmates ; and the 
 practical observance of the Golden Rule. That teacher 
 who kindly respects the rights of the pupils, and daily 
 illustrates the great virtue — kindness — in the management 
 of pupils, and in personal conduct elsewhere, will ac- 
 complish practical results in moral education which cannot
 
 16 GOVERNMENT AND DISCIPLINE. 
 
 be attained by rules or lectures. A spirit of true kind- 
 ness pervading a school will become a fountain of virtues. 
 
 Children do not comprehend virtue in the abstract ; but 
 they soon learn to understand it when they see it in the 
 actions of their teachers and parents and of others around 
 them. Let the teacher utilize the reading and other les- 
 sons, as well as school incidents, in leading the children to 
 admire honesty, truth-speaking, unselfishness, true courage, 
 and all right-doing, and thus sift in and mingle the moral 
 with the mental, as I^ature does in her teaching. 
 
 Lead children to discuss the character of actions de- 
 scribed in stories, reading lessons, etc., and thus aim to 
 develop in them the ability to discriminate justly between 
 the right and the wrong in their own conduct. 
 
 Social relations, the dependence of each individual upon 
 his neighbor, the necessity of labor, the benefits of society 
 and government, should be illustrated and taught by 
 means of easy and familiar lessons suited to the age and 
 capacity of the children. As the development of the 
 moral nature is of greater importance to the welfare of 
 the individual and the community than any other part of 
 education, no opportunity should be omitted for training 
 children in such habits as will cause them to grow up 
 truthful, honest, self-governing, and law-abiding citizens. 
 
 Modes of Punishivient. — Every punishment should be 
 adapted to the offence. As a general principle, if pupils 
 abuse a privilege, punish by depriving them of that 
 privilege for a while. If injury be done to that which 
 belongs to another, require a satisfactory reparation. 
 School loorh should never he given as a punishment. 
 
 Firmness, vigilance, and uniformity in dealing with 
 children are of the first importance. The teacher should 
 never resort to violent means, such as pushing, pulling, or
 
 GOVERNMENT AND DISCIPLINE. 17 
 
 shaking the cliildren, in order to obtain their attention. 
 All such practices constitute a kind of corporal punish- 
 ment which, in all its forms, is specially prohibited by the 
 Board. 
 
 Modes of punishment painful to the corporeal system, 
 such as the sustaining of wearisome burdens, unnatural 
 and long-continued attitudes of restraint, standing, kneel- 
 ing, etc., are wrongful and injurious. Equally so is the 
 confining of delinquents by tying them or by shutting 
 them in closets. These are all a resort to mere physical 
 force, instead of moral incentives, and involve no appeal 
 to a sense of honor or duty in the child. They do not 
 properly assert the authority of the teacher, nor do they 
 really produce obedience on the part of the pupil. 
 
 In directing the various movements required of the 
 pupils, care should be taken never to touch them. The 
 teacher should take such a position before the class as will 
 command the eye of eveiy pupil, and thence direct by the 
 voice, or by a signal. Pupils must be habituated to the 
 impression that the teacher will give the commands but 
 once^ and that they must be obeyed instantly. 
 
 Puhlic exjwsures and hadges of disgrace belong to a 
 class of punishments which, if ever resorted to, should be 
 employed under careful limitations, and with great circum- 
 spection and prudence ; for it requires a skilful, discreet, 
 and conscientious teacher to use them safely and with 
 advantage. In the discipline of girls such methods should 
 be avoided altogether, as destructive of that nice sense of 
 shame and that delicate sensibility to reputation which 
 should be carefully fostered in the female character. 
 Avoid the use of ridicule ; it is a dangerous remedy, and 
 tends to the loss of self-respect in the pupil. 
 
 SuM^iAEY OF Impoktant FoiNTs. — The following is a
 
 18 GOVEENMENT AND DISCIPLUSTE. 
 
 brief summary of the practically important points in moral 
 education, and in the training in morals and manners: 
 
 That intellectual training, however excellent, is not 
 enough : 
 
 That public schools are instituted to make not only 
 intelligent but good citizens : 
 
 That morals and manners are best taught incidentally, 
 not formally ; by personal example and anecdote, not by 
 mere lecture : 
 
 That " unconscious tuition " by the force of the teach- 
 er's example, is a most powerful influence for good or for 
 evil ; and that this includes habits of personal cleanliness, 
 tidiness, the avoidance of lounging in sitting or standing, 
 etc. ; punctuality, promptness, earnestness in the right, 
 respect for the rights and feelings of pupils and others ; 
 the use of kind tones, and a kind manner; private ad- 
 monition of the erring ; the avoidance of all coarse and 
 low expressions and of every form of petty tyranny. 
 
 Among the many points upon which opportunity for 
 incidental instruction should be sought, are the following : 
 
 Respect for parents and teachers, and for the aged ; kind- 
 ness to the infii-m ; the avoidance of crnelty ; abhorrence of 
 brutality, including pugilism ; courtesy and politeness; true, 
 and false courage ; bravery and foolhardiness ; moral cour- 
 age and decision as indispensable to a noble character ; 
 truthfulness, and the meanness of lying ; the degradation 
 involved in habits of profanity, indecency, and intemper- 
 ance ; the avoidance of bad books, bad papers, and bad 
 companions ; the indispensable virtue of patriotism ; and, 
 generally, to do and to be right because it is right, and 
 not for fear of punishment, discovery, or disgrace.
 
 COURSE OF INSTRUCTION 
 
 PRESCKIBED FOR 
 
 GRAMMAR SCHOOLS, 
 
 WITH 
 
 DIRECTIONS AND SUGGESTIONS TO TEACHERS. 
 
 EIGHTH GRADE. 
 
 Outline Course. 
 
 1. Language Lessons. — Beading ot the grade of a Third Reader: 
 oral lessons on the qualities and uses of familiar objects, such as articles 
 of clothing, food, materials for building, and so forth : compositions upon 
 subjects connected with the oral lessons of the grade : spelling, meaning, 
 and use of words, chiefly from the lessons of the reading book, and from 
 the oral lessons of the grade ; also selected miscellaneous words in gen- 
 eral use, at least 150 in number, to be taught chiefly by writing them 
 separately, and in short sentences from dictation. 
 
 2. AiiniUiKTic—Wiitfen and Mental. — Through the simple rules and 
 Federal money, with practical examples. Tables of weights and meas- 
 ures to be taught, with simple practical applications. 
 
 3. Geography (without text- book). —The World: from globes and 
 outline maps. 
 
 4. Penmanship. — Words of various length, presented in the order of 
 their difficulty. Practice in capitals continued. 
 
 5. Drawing.— Oil paper, illustrated on blackboard, from dictation 
 and from chart. 
 
 Draw semicircles on vertical and horizontal diameters of four inches. 
 Bi-symmetrical arrangements of simple and compound curves on verti- 
 cal axis, two of each. Two simple historic borders, illustrating horizon- 
 tal repetition of a unit. Two conventional cordate leaves ; symmetrical 
 arrangement of these leaves in the ecjuilateral triangle and the octagon.
 
 INSTRUCTIONS AND SUGGESTIONS. 
 
 LANGUAGE. 
 
 READING. 
 
 General Suggestions for all Grades. 
 
 1. The number of reading lessons should bear a reason- 
 able relation to the time the pupils have been in the 
 grade. Xo selection, other than the best English poetry, 
 should be so long dwelt upon and so frequently repeated 
 as to render the exercise a mere recitation. 
 
 2. Should a large number of consecutive lessons ia the 
 Reader be of the same general character, a part should be 
 omitted, so as to give variety of style and subject. 
 
 3. Where two or more classes are in different parts of 
 the same grade, and use the same Reader, care should be 
 taken to have a corresponding difference in their reading 
 lessons. 
 
 4. Distinctness of articulation and the avoidance of all 
 improper clipping of terminations, and of the omission or 
 slurring of syllables, should receive careful and constant 
 attention. 
 
 5. New and difficult words should be carefully pro- 
 nounced and explained before the piece or paragraph is 
 read by the pupils. 
 
 6. Where diacritical marks are used in the Reading 
 Book the pupils should be taught to understand and apply 
 them.
 
 LANGUAGE. 21 
 
 7. Lists of common words liable to be mispronounced, 
 such as length and strength, should be made bj the teacher, 
 and the class be exercised upon them. The elementaiy 
 sounds, and their more difficult combinations in words and 
 phrases which require great mobilitj of the vocal organs 
 (especially Jinal consonants), should receive frequent at- 
 tention. Particular attention should be given to pupils of 
 foreign birth or parentage, so as to insure their mastery of 
 the principal difficulties of English pronunciation. 
 
 8. Pupils should read only such selections as are within 
 their ready comprehension, and should be accustomed to 
 state, in their own language, the important facts, prin- 
 ciples, and moral lessons therein taught. Words, phrases, 
 or allusions should be briefly explained whenever neces- 
 sary for the proper understanding of the piece read. 
 
 9. The voice and manner of the pupil should accord 
 with the character and sentiment of the selection. All 
 drawling, sing-song tones should be prevented. This is 
 easily done when the pupils are led to understand and 
 enter into the spirit of the piece. 
 
 10. At least once a week it is expedient to require all 
 the pupils, except the one reading, to close their books. 
 In this way the class will be better able to criticise, and 
 the criticism will be more just and valuable. Besides, 
 while the other pupils will all be kept on the alert to 
 listen, the pupil reading will unavoidably endeavor to pro- 
 nounce correctly, enunciate distinctly, and emphasize nat- 
 urally. Additional effect will be given to these exercises 
 by requiring the pupils to reproduce, in their own lan- 
 guage, the substance of what has been read to them. The 
 principal application of this most important exercise is in 
 the use of supplementary Readers. 
 
 11. As silent reading constitutes nearly all the reading
 
 22 EIGHTH GRADE. 
 
 that is of practical use and value to us, this method of 
 reading should be commenced and tested in school. It is, 
 therefore, desirable that exercises in which the class read 
 silently should be given with proper frequency. The 
 teacher can determine the results of the pupils' efforts by 
 appropriate questioning and by calling upon the pupils to 
 tell the whole or a part of the matter thus read. 
 
 ORAL LESSONS. 
 
 General Suggestions fok all Grades. 
 
 1. The leading objects in this branch of instruction are, 
 first, to cultivate habits of observation and reflection,, and 
 second, to ^ive facility in descrij)tion, both oral and writ- 
 ten. Avoid everj'thing tending to convert these lessons 
 into recitations of set forms of words, however these forms 
 may have been obtained, however well they may be un- 
 derstood by the pupils, and however important the facts 
 thus stated. 
 
 2. In the selection of topics, ^''familiar objects,'''' and 
 familiar animals, plants, and minerals take precedence of 
 all others. 
 
 It is neither possible nor desirable to attempt to teach 
 all, or even the greater part of the topics that might be 
 classified with the requirements of any grade. ]^o topic 
 should be treated exhaustively, nor shotdd the topics se- 
 lected be so FEW or so frequently reviewed as to narrow 
 down or suspend the discipline of the observing faculty. 
 Too many reviews of a topic extinguish the pupil's interest 
 in it, and are worse than a mere waste of time ; they are 
 positively injurious. The selection and limitation are left 
 to the good sense of the teacher. 
 
 3. The objective method of teaching presents two dis-
 
 LANGUAGE. 23 
 
 tinct tliough intimately related departments: 2)et'Geptwe 
 teaching, in which the object, as an acorn or an egg, is 
 directly presented to the pupil's senses ; and conceptive 
 teacliing, in which impressions previously received are re- 
 called, arranged, and utilized, the objects themselves not 
 being presented to the senses during the lesson. An oak, 
 an elephant, or a thunder-storm, would fall under the 
 latter department. 
 
 The use of 2>ictwres, models, or other sensible represen- 
 tations of objects, is an important combination and 
 modification of the two principal methods, and should be 
 often employed. 
 
 4. Definitions should be very sparingly introduced, and 
 never in the first stages of a subject. If given at all, they 
 should sum up knowledge already attained. The terms 
 organic, inorganic, animal, vegetable, and inineral, are 
 prominent among the very few terms requiring definition. 
 Such definitions should be prepared for by a process at 
 once inductive and objective. 
 
 5. Ko fact which the teacher can readili/ lead the pupil 
 to discover or ascertain for himself should be imparted 
 by the teacher. Important facts not readily derived from 
 the pupil's own observation must of course be supplied by 
 the teacher. Avoid overloading a topic with details, es- 
 pecially those of technology. As far as the character of 
 the general subject of the grade will allow, no topic should 
 be selected in which the number oi facts to he told bears a 
 large proportion to those which the pupil may be led to 
 
 find Old for himself. 
 
 6. The language used hy the yu/pil must he entirely his 
 oion, excepting, of course, the few indispensable definitions. 
 Even these definitions should form no part of any continu- 
 ous oral or written statement.
 
 24 EIGHTH GRADE. 
 
 Note. — The following exemplifies the pupil's only use of definitions : 
 Teacher — You said coal is a mineral. What do you mean by meneraL? 
 You said it is a fossil substance. \Yhat do you mean \>y fosdl? 
 
 7. The^ocess employed will present two distinct stages : 
 Firsts the analytical or preparatory, in which the teacher 
 leads the pnpil to discover or to rememher the properties 
 or peculiarities of an object, or to state any other impor- 
 tant facts associated with it. The statements by the pnpil 
 will be, of course, in his own words ; and the additional 
 statements wdiich the teacher himself may find it necessary 
 to make, will be given in the form of familiar conversation. 
 This stage gives the principal discipline of the powers of 
 observation and reflection. 
 
 The points thus considered and the facts thus stated 
 should be written upon the black-board in the briefest 
 possible synoptical form, each one after it has been con- 
 sidered. While some such synopsis is indisyensdble to 
 the teacher as the first step of ]jrei)aration for giving the 
 lesson, it should never be presented to \hQ jpujpil except by 
 the gradual process above indicated. (See Note-hooTxS^ 
 paragraph 9.) 
 
 8. The second or review stooge of the process is based 
 upon the results of the firsts and furnishes the principal 
 discipline of the powers of oral and written statement. 
 The facts already considered should be rearranged, if 
 necessary, into an orderly synopsis upon the black-board, 
 the pupils being called upon to assist in this arrangement. 
 This furnishes a valuable and appropriate discipline of 
 logical faculty. Pupils should then be required, in turn, 
 to state what they can recall of eacli item of the synopsis, 
 then of each group of items, and, lastly, of the whole sub- 
 ject. Then the synopsis may be wholly or in part removed 
 or hidden, and the oral process of review repeated. As a
 
 LANGUAGE. 26 
 
 final stage, and before dismissing the subject, an extempoi-e 
 composition, first with and then without the aid of the 
 synopsis upon the board, sliould be written upon the slate 
 bv each pupih (See Coi7iposition.) 
 
 9. Note-looks. — No one can give an " oral language 
 lesson " properly without special and careful jpreparation 
 for teaching that lesson. To attempt to do otherwise is 
 to fail. A synoptical outline or syllabus of the chief points 
 or items in each lesson should therefore be carefully made 
 ready beforehand ; and, in order to economize the time 
 and labor of the teacher, to facilitate the few necessary 
 reviews, and to furnish a proper record of the work that 
 has been done or attempted during the term, these synop- 
 ses sliould be recorded in a note-bool; together M'itli such 
 additional memoranda of authorities, illustrations, etc., as 
 the teacher may think expedient. But it is particulai-ly 
 enjoined that these synopses and memoranda shall, as far 
 as possible, consist of words and brief phrases only, merely 
 full enough for their proper use, namely, to assist the 
 memory of the teacher^ to remind, not to inform. 
 
 If, on the other hand, the proposed lesson is written out 
 in sentences instead 'of separate words and phrases, the 
 teacher can scarcely avoid using these sentences, word for 
 word, over and over again in the exercises, and the note- 
 liooh becomes virtually a text-book, and a verj- crude and 
 imperfect one. In such case, no " oral language lesson " is 
 really given; the oral responses of the pupils are merely 
 7'ecitations of " set forms of words," and the final exercise 
 in writing, instead of being a comjwsition l>ij the pupil, is 
 only a memorized composition which has been written and 
 dictated hy the teacher. In this connection, see particularly 
 t\\Q first paragraph of these general suggestions.
 
 28 EIGHTH GKADE. 
 
 OKAL LESSONS OF THE EIGHTH GRADE. 
 
 The teacher is particularly referred to the preceding 
 general suggestions and to the directions and suggestions 
 given under the First Primary Grade, It is important 
 that special care be taken that the class in the Grammar 
 School Grade does not go over the topics taught before 
 the promotion from the Primary, To this end the record 
 of the promotions from the Primary should contain a list 
 of those topics that were used in the Primary " object les- 
 sons." The teacher of the Eighth Grade should have a 
 copy of this list in her note-book. 
 
 List of Topics suitable for Eighth Grade. — This 
 list is only suggestive,' no one vfill have time to take up 
 even half of these topics : make selections. With the 
 consent of the Principal the teacher may substitute any 
 other topic or topics that may properly be included under 
 " food, clothing, or building materials." Avoid all inhiute 
 details of technology. Do not "review" a topic so often 
 as to destroy the pupil's interest. Avoid frequent repeti- 
 tion of definitions: correct all crudit^ies of language — do 
 oiot here dwell upon them, but note the most important, 
 that they may form a part of the class exercises in correc- 
 tion of errors in speech. 
 
 Vegetable Food — Bread Grains. — Wheat, rye, oats, barley, maize, 
 buckwheat, rice. All of them seeds. Relation of some to straw. 
 Planted every year. Trace from sowing to bread, but not too minutely. 
 In geographical references use map of the world. Kinds of bread. 
 Flour, grits, cracked wheat ; meal, hominy, samp, green corn, corn 
 starch (other starches) ; misuses of grain in preparing various intoxicat- 
 ing drinks. 
 
 Common Esculent VegetaUes. — Select chief one.s in the general order 
 of their annual production. Tell where city children may see them 
 growing.
 
 LANGUAGE. 27 
 
 Berries, Melons, and Fruits. — Domestic ones first; foreign — oranges, 
 lemons, bananas, pineapples, figs, prunes, raisins, etc. Wine, cider, 
 vinegar. 
 
 Sugar. — Cane, beet, maple, sorghum, molasses ; other kinds and 
 sources of sugar, in honey, milk, fruits, licorice ; glucose or corn sugar. 
 
 Beverages. — Tea, coffee, chocolate. 
 
 Spices. — Black pepper, white pepper, red pepper, cloves, nutmegs, 
 mace, allspice, cinnamon, ginger ; other condiments — mustard, horse- 
 radish, salt, vinegar, catsup, etc. 
 
 Anim.yl, Food. — Flesh of domestic animals — beef, mutton, pork, 
 poultry; of other animals — game, fish, oysters, etc., etc. 
 
 Butter, cheese, lard, milk. — Trades and occupations connected with 
 food. 
 
 Clothing — Vegetable (h-igin. — Muslin, calico, linen. India-rubber, etc. 
 Animal Origin. — Woolens, silks, leather, furs, etc. 
 How fiirs and woolen clothes keep us warm. Trades and occupations 
 connected with clothing. 
 
 BurLDiNG Materials. — Common building stones — kinds of fine 
 building stones — mortar, glass, paints, lumber — metals. Trades and oc- 
 cupations connected with building and building materials. 
 
 Miscellaneous. — Matches, paper, soap, charcoal, coal, fire, feathers, 
 glue, ivory, plaster, putty, ink. 
 
 Objects — easily procurable. — Small bunches of heads of wheat, rye, 
 barley, ear of corn, sprigs of rice, small bottles or boxes containing va- 
 rious graiias, hulled and unhuUed rice, bran, unbolted and bolted flour ; 
 piece of sugar-cane or of corn-stalk, little boxes of sugar in three or four 
 kinds or forms ; coffee, raw and roasted ; tea, green and black ; cocoa- 
 nuts, almonds, peach-pits, apples, oranges, etc. , each in its season ; 
 wool, cotLon, hemp, flax, silk, and pieces of their fabrics ; bits of leather, 
 and of furs of various kinds ; pieces of common woods, smoothed to 
 show the grain, etc., etc.; pictures of objects. 
 
 These and many others are frequently found in schools. The skil- 
 ful teacher finds them indispensable. 
 
 Reference Books.— Sheldon's Object Lessons ; Sheldon's Elemen- 
 tary Instruction ; Parker's Talks on Teaching ; and, especiall}', articles 
 in Appleton's, Chambers', Johnson's, and other cyclopajdias.
 
 28 EIGHTH GRADE. 
 
 COMPOSITIOK 
 
 General Suggestions for all Grades. 
 
 1. Compositions on the subjects of the oral lessons are 
 specially prescribed for all grades excepting the first. 
 
 2. When any topic, such as sugar, nickel, the circulation 
 of the blood, or the indestructibility of matter, has been 
 as fully treated in the conversational lesson and review 
 as may be thought expedient, the exercise in composition 
 should immediately follow. This should be a class exer- 
 cise on slates. Care should be taken that the pupils do 
 not make them so long as to prevent proper correction. 
 
 3. A fevv^ pupils should be called upon in turn to read 
 what they have written, and should be led by judicious 
 questioning to detect any important errors in the language 
 ■used, or in the statement of facts. Under proper restric- 
 tion, mutual criticism by the members of the class can be 
 made a very profitable exercise. 
 
 4. To insure a proper variety of thought and expression 
 it is necessary that the oral lesson which forms the basis of 
 the composition should be so selected as to give a consider- 
 able number of interesting points or items. If injuriously 
 frequent repetition and review are avoided, the several 
 pupils will recall different groups of items, and all undue 
 sameness will be prevented. "When identical phrases or 
 sentences are frequently found in the exercises of the pu- 
 pils, they are unquestionable evidence of bad methods both 
 in the oral lessons and in the teaching of composition, Ko 
 definitions should be found in a composition. Their only 
 proper use is distinctly stated on page 133. 
 
 5. Some of the compositions written upon the slates
 
 SPELLING. 29 
 
 should be copied by the pupils upon paper. This should 
 be done at least once a month in grades eight to three, and 
 twice a month in the higher grades. As these are to be 
 separately corrected by the teacher and returned to the 
 pupils for rewriting, it is expected that the teacher will so 
 adjust the length of the compositions that their correction 
 will make no excessive demand upon his time. On the 
 other hand, they should not be so brief as to fail to fur- 
 nish the pupils with sufficient exercise. 
 
 6. The pupil should write his name and the date upon 
 each composition. All those of the same date should be 
 fastened together, so that the sequence of packets may 
 show the frequency of the lessons and the general progress 
 of the class. A list of all the subjects that have been used 
 during the term for compositions on the slate should also 
 be kept. 
 
 7. Written reviews of the lessons in geography and his- 
 tory are perhaps the very best method of permanently 
 fixing in the memory the facts taught by those studies, 
 and, therefore, should not be omitted : such written re- 
 views, however, should not be classed as compositions. 
 
 SPELLING. 
 
 General Suggestions for all Grades. 
 
 1. The exercises should be both oral and written, but 
 principally written. 
 
 2. Two lists of words that are to be studied by the pu- 
 pils should be kept by the teacher of each class. The first 
 should include only the words selected, as prescribed, from 
 the reading and oral lessons. Care should be taken to 
 avoid the repetition of words that have already been thor-
 
 30 EIGHTH GRADE. 
 
 onghly fixed in the pupil's memory by exercises in previous 
 grades. Words needing review on account of their diffi- 
 culty should form a part of the second prescribed, or mis- 
 cellaneous, list kept by the teacher. Both the miscella- 
 neous words selected and those taken from the Reader 
 should be suitable to the age and mental development of 
 the pupils. 
 
 3. " Miscellaneous words " will include the ordinary 
 proper names of persons (not the surnames), and common 
 words of the daily life of the household, the shop, and the 
 street. 
 
 In the selection of proper names, geographical and 
 personal, special care should be taken to include only such 
 as the pupils may have occasion to use in writing ; as 
 Chicago, Brooklyn, and Aaron, and not Tapajos, Pyrrhus, 
 and Richelieu. 
 
 4. In writing short sentences from dictation, special at- 
 tention should be given to words which are similar in 
 sound but are spelled differently. Iftstances will present 
 themselves, both in the selections from the reading lessons 
 and in the miscellaneous words. Thus piece will require 
 to be compared and contrasted with j?eace ; principle with 
 jprincipal, etc. 
 
 5, The written exercises should be as neat as possible, 
 care being taken to train pupils in habits of orderlj" ar- 
 rangement of their work on the slate and on paper. 
 
 6, When sentences are given, particular attention should 
 be paid to the ordinary troublesome monosyllables, the 
 proper use of capitals, the sign of the possessive case, the 
 period, the interrogation mark, and the use of the hyphen 
 in a word divided at the end of a line.
 
 MEANING AND USE OF WORDS. 31 
 
 MEANING AND USE OF WORDS. 
 
 General Suggestions for all Grades. 
 
 1. In selecting words for these exercises, two leading 
 purposes shonld be specially kept in view : (1) To impress 
 or illustrate the particular meaning of the word as used in 
 the lesson ; (2) to enlarge and correct the pupil's own vo- 
 cabulary. 
 
 2. Where a word has, in common use, two or more 
 meanings quite diverse, a separate illustration should be 
 required for each ; and where several words differently 
 spelled have the same or a similar pronunciation, a sepa- 
 rate construction should be required for each in the writ- 
 ten exercises. 
 
 3. A pupil's vocabulary should be understood to consist 
 of the words that he will use in speaking and writing, and 
 of those words only. Words that are found chiefly in 
 books, and in reference to which an appeal to the dic- 
 tionary must be made, are of little or no importance so far 
 as the pupils in our schools are concerned. Such words 
 as " through," " chimney," and " apron," which the schol- 
 ars habitually use correctly in speech, should be spelled ; 
 to require a special sentence for their use is a waste of 
 time. "Valetudinarian," '' argosy," "asphyxia," "proto- 
 plasm," and others, which the pupil may never use in con- 
 struction, the teacher should carefully avoid. When such 
 words do occur in the reading lesson or elsewhere, for the 
 illustration of the passage the meaning should be given by 
 the teacher, no special memorizing on the part of the pu- 
 pils being required. The context and the dictionary will 
 do what little remains to be done. To spell such words, 
 or to use them in sentences, is worse than idle.
 
 32 EIGHTH GEADE. 
 
 4. Do not attempt too mnch. Four or five words a day 
 are enough, if thoroughly taught and carefully reviewed. 
 Of these words the teachers should keep special lists, and 
 class lists should be compared, in oi-der that useless dupli- 
 cation may be avoided. The intelligent use of a word in 
 a sentence constructed by the pnpiL is the best test of his 
 knowledge of the meaning of the word. Home exercises 
 in the construction of sentences to illustrate the proper 
 uses of words should never be given. ISTo other exercise 
 is so dependent upon the prompt criticisra of the teacher. 
 
 5. In the higher grades a few common synonyms, such 
 as divide and sejyarate, reflect and consider^ etc., if made 
 to form a part of these exercises, will add to their variety 
 and profit. 
 
 ARITHMETIC. 
 
 Mental Arithmetic. — 1. The mental arithmetic should 
 both precede and accompany the written arithmetic. The 
 principal distinction between these two divisions of the 
 subject is, that when the numbers involved are too great 
 or too many to be readily retained in the memory, the 
 slate should be employed as an assistant. 
 
 2. The exercises in mental arithmetic should, as far as 
 possible, be of the most practical character. As a rule, 
 examples given should be silently wrought by the class 
 simultaneously, and the results obtained be written upon 
 the slates promptly, and at a given signal. The analysis 
 may then be required of the pupils. 
 
 3. The explanatory or analytic statements made by the 
 pupil should be of the simplest and most direct character 
 consistent with clearness, and all unnecessary repetition of
 
 ARITHMETIC. 33 
 
 formulae should be carefully avoided. Where this is not 
 done, the principal effort of the pupil is to recall in due 
 order the set form of words, rather than to form the 
 arithmetical combinations necessary to the solution. 
 
 4. Besides simple examples in the four fundamental 
 rules and federal money, very simple operations involv- 
 ing practical applications of the selected tables of money, 
 ■weight, and measure, should constitute a portion of the 
 exercises in mental arithmetic. 
 
 5. In the explanation or analysis of examples, in mental 
 as well as in written arithmetic, the pupils should occa- 
 sionally be called upon, before solving, to state the ques- 
 tion. 
 
 6. Mental exercises in arithmetic should be conducted 
 in a spirited manner. They should always have the char- 
 acter of extemporized exercises. 
 
 ^Vf'itten Arithmetic. — 1. The slates should be kept in 
 the best condition as to cleanness ; the figures should be 
 distinctly and neatly made, and be written in lines parallel 
 to the upper edge of the slate. A reasonable allowance 
 should be made for imperfections in the forms of figures 
 in exercises in which rapidity is required ; yet, eveiy effort 
 should be made to fix in the pupils habits of care, neatness, 
 and system in all that pertains to the written exercises. 
 
 2. Exercises in adding columns of figures should be 
 given with such frequency as may be found necessary to 
 produce and retain accuracy and rapidity. 
 
 3. Every form of counting, whether by fingers, dots, 
 marks, or other devices, should be strictly prohibited, and 
 the class should be frequently tested for this special pur- 
 pose. 
 
 4. The pupil should name only the results arising fi-om 
 the additions of the successive figures, avoiding all that
 
 34 EIGHTH GRADE. 
 
 oral or mental repetition of the tables which is known 
 as the " spelling process," and all other unnecessary for- 
 mulae. 
 
 5. The above remark, in regard to the oi*al or mental 
 repetition of the tables, applies to all the fundamental 
 rules and their applications. The processes should be re- 
 duced to the most concise form practicable. 
 
 6. When pupils show an ability to add two or more 
 figures at a time, they should be encouraged to do so in 
 exercises that are wrought out silently. 
 
 7. When the divisor is less than 13, the long division 
 process is not to be employed or allowed. Examples with 
 such divisors as 60, 1,200, etc., should be solved by short 
 division. 
 
 8. Short practical examples, involving two or more of 
 the rules, should frequently be given, and in such a way 
 as to cultivate the intelligence of the pupil. 
 
 9. Examples requiring a very large number of figures 
 for their solution should be avoided, except as far as they 
 may be necessary in order to give practical expertness. 
 
 10. Examples should be given to test the pupils' accu- 
 racy in writing numbers requiring Os, and their knowledge 
 of the proper methods when the multiplier or divisor 
 contains Os. 
 
 11. Analogous exercises in federal money ^ould be 
 substituted for those in the simple rules referred to in the 
 preceding sections, as soon as may be found expedient. 
 
 12. Exercises should be given to insure facility in read- 
 ing and writing federal money, and in reducing, by inspec- 
 tio?i, and without analysis^ dollars, etc., to cents or to 
 mills, and conversely. 
 
 13. In all practical examples, instead of telling pupils to 
 add, subtract, multiply, or divide, give the question in such
 
 ARITHMETIC. 35 
 
 a manner as to oblige them to determine for themselves 
 the method and principle to be employed. 
 
 14. Xo detailed analysis is necessary in addition or sub- 
 traction. 
 
 15. Give examples of bills of purchase or sale involving 
 several items, and similar to those required in daily life. 
 
 16. Exercises in arithmetic are not to be assigned for 
 home study except in the First Grade. (See § 155 of the 
 By-Laws, 1883.) 
 
 FORMS OF ARITHMETICAL ANALYSIS. 
 
 A. {Fundamental) — Multiplkation. 
 
 Question. — If 1 yard cost $3, what will 4 yards cost ? 
 Analym. — If 1 yard cost $3, 4 yards will cost 4 times $3, or $12. 
 KoTE 1. — Avoid the too concise form " will cost 4 times 3, or 12." 
 Note 2. — Question. — If $1 will buy 3 yards, what will $4 buy ? 
 Analysis. — Similar to A. 
 
 B. {Derived) — Division. (1. ) 
 
 Question. — If 1 yard cost $3, how many yards may be bought for $12 ? 
 Analysis. — If 1 yard cost ,^3, $12 will buy as many yards as $3 are con- 
 tained times in $12, or 4 yards. 
 Note. — Avoid the too concise form " as many as 3 are contained in 12." 
 
 C. {Derived) — Division. (2. ) 
 
 Question. — If 4 yards cost $12, what will 1 yard cost ? 
 Analysis.— U 4 yards cost $12, 1 yard will cost i of $12, or $3. 
 Note. — Avoid the very faulty forms " as much as 4 is contained in 
 $12," or " times in 12," or " 4 is contained in 12." 
 
 D. {Derived) — Division. (3.) 
 
 Qu^Mion. — If $4 buy 12 yards, what will $1 buy ? 
 
 Analysis. — If $4 buy 12 yards, $1 Mill buy i of 12 yards, or 3 yards. 
 
 COMBIXATIONS OF A, B, C, D. 
 
 C and A. Division and Multiplication. 
 
 Question. — If 4 yards cost $12, what will 9 yards cost ? 
 
 Analysis. — First by C for price of 1 yard, then by A for price of 9 yards. 
 
 C and B. Division. {2) and (\). 
 
 Qnestton. — If 4 yards cost $12, how many yards may be bought for $27 ?
 
 36 EIGHTH GRADE. 
 
 Analysis. — First by G for price of 1 yard, then by B for number of 
 yards. 
 
 D and A. Division and Multiplication. 
 
 Question.— It $4 buy 12 yards, what will $11 buy ? 
 
 Analysis. —First by D for what $1 will buy, then by A, Note 2, for what 
 $11 will buy. 
 
 Note. — Avoid set forms of giving questions. — Vary the order of statement 
 as far as is consistent with perfect clearness. For instance, 
 the " C and B" question might have been put thus: 
 Spent $27 for cloth. How many yards did I buy, if $12 
 bought 8 yards V or, how many yards for $27, if 4 yards 
 cost $3 ? etc., etc. 
 
 TABLES OF MONEY, WEIGHT, ETC. 
 
 The teacliing of the Tables of Money., Weight, Measure, 
 etc., should be restricted to the following : 
 
 1. Federal Money. — The usual table, its notation, and halves, 
 quarters, and eighths of the dollar. The difference between the full 
 table and money of accounts. Adversely to the use of the terms sMl- 
 limj and penny. 
 
 2. Length.— 12 in. = 1 ft., 3 ft. = 1 yd., 5^ yds. = 1 rod, 220 yds. = 
 1 furlong, 8 furlongs, or 1,760 yds., or 5,280 ft. = 1 mile. 
 
 3. Surface. — 144 sq. in. ^ 1 sq. ft, 9 sq. ft. = 1 sq. yd., 30J sq. yds. 
 = 1 sq. rod. 
 
 4. Solidity.— 1,72S cu. in. = 1 cu. ft., 27 cu. ft. = 1 cu. yd., 128 cu. 
 ft. = 1 cord of wood. 
 
 5. Dry Capacity. — 2 pts. = 1 qt. , 8 qts. = 1 peck, 4 pecks, or 2,150 
 cu. in. = 1 bu., 36 bu. = 1 chaldron. 
 
 6. Liquid Capacity. — 4 gills = 1 pt. , 2 pts. = 1 qt., 4 qts., or 231 cu. 
 in. = 1 gal. 
 
 Note. — The dry quart is about one-sixth greater than the liquid 
 quart. 
 
 7. Awirdupois Weight.— IQ oz. = 1 lb., 100 lbs. = 1 cwt., 2,000 lbs., 
 or 20 cwt. = 1 ton, 2,240 lbs. = 1 long ton, or old ton. 
 
 Note. — The pound avoirdupois = 7,000 grains troy; the ounce = 437^ 
 grains. 
 
 8. Troy Weight— 24: grs. = 1 dwt., 20 dwt. = 1 oz., 12 oz. = 1 lb.
 
 GEOGKAPIIY. 87 
 
 Note. — The pound troy contains 5,760 grains ; the ounce, 480 grains. 
 The pound troy is the standard unit of weight. 
 
 Time-tahle and Calendar. — Explain leap year. Tell time by the clock. 
 
 Miscellaneous Table. — Teach dozen, r/ross, scoi'e, quire, ream. 
 
 General Note. — Pupils should be carefully taught the meanings, 
 uses, and simple practical applications of these tables. 
 
 GEOGEAPHY. 
 
 General Suggestions for all Grades. 
 
 1. It is of the first importance that geography should be 
 so taught and reviewed, as not to leave in the mind of the 
 pupil a mere collection of facts, without mutual relation 
 or dependence. On the contrary, the pupil should, from 
 the first, be taught to consider the earth as man's dwelling- 
 place — its motions as bringing him the alternation of day 
 and night, and the changes of the seasons — its laiul- surface 
 as the chief theatre of animal and vegetable life — the 
 ocean as the world's broad highway, and the exhaustless 
 source of clouds and rains, so necessary to every form of 
 life on the land-surface ; its currents as modifying the 
 climate of continents and islands — the great permanent 
 air-currents as carrying to the land the moisture from the 
 sea — the mountains as its condensers, as well as the chief 
 source of mineral wealth — the springs and rivers, with 
 their branches, as carrying back again the ever-circulating 
 water of the ocean — and its cities and toic/is, not as black 
 dots on a map, in colored patches which he has learned to 
 call countries, perhaps near some crooked black streaks, 
 which he has learned to call rivers, but as the centres of 
 social life and development, the seats of government, and 
 the crowded, busy hives of human industry and intelli- 
 gence.
 
 38 EIGHTH GRADE. 
 
 When geography is thus taught, it is one of the most 
 interesting, important, and practical of studies ; but, if it 
 is taught chiefly as a description, by unvarying formulae, 
 of rivers, capes, peninsulas, boundaries, etc., supplemented, 
 perhaps, by a precise, verbatim repetition of the descrip- 
 tive geography, as contained in even the very best text- 
 book, it is one of the dullest and most unprofitable. 
 
 2. Globes and maps are indispensable auxiliaries. There 
 is no more common and pernicious error than that of sub- 
 stituting the text-hook for the teacher, who thus is degraded 
 into a mechanical hearer of lessons. 
 
 The pupil should be taught to have distinctly before his 
 mind's eye the contour of the country which he may be 
 studying, and its leading physical and political features ; 
 to this end, rough sketching of maps (from memory) will 
 be of great assistance. 
 
 In all grades there should be exercises in latitude and 
 longitude, and in imaginary travels by land and by sea. 
 
 The teacher of geography will find in the daily newspa- 
 per a valuable auxiliary, giving information of important 
 events transpiring in countries under consideration. 
 
 GEOGRAPHY (EIGHTH GEADE). 
 
 In teaching the hemispheres, only such topics should be 
 included as may readily be taught by means of a hlack- 
 hoard, a globe, and an outline map of the hemispheres. 
 It is of the greatest importance that the pupil's first im- 
 pressions be formed from the globe, rather than from the 
 flat and distorted representation of the map. 
 
 The following are the principal points in the require-
 
 GEOGRAPHY. 30 
 
 ments of tliis grade. Tlie work done should be tested in 
 review, by placing the pointer in the hand of the pupil. 
 
 Theybrm of the earthy its magnitude, the continents and 
 grand divisions, their relative positions, their connecting 
 isthmuses, and a few of their most important projections 
 — the oceans, their positions, and principal arras and 
 islands — five or six of the mountain sj/stems of Amer- 
 ica, and a dozen in the rest of the world ; three or four 
 well-known volcanoes — about a dozen each of the chief 
 rhers and straits, and about half as many great lakes — 
 in a very general way, the location of the most important 
 countries, such as the United States, Great Britain, Ger- 
 tnany, China, Jajyan, etc., and of a dozen of the most 
 important cities of the world. With each of these cities 
 and countries some interesting or important fact should 
 be at once associated. 
 
 A general notion of climate, as affected by distance from 
 the equator, by elevation, and by the great ocean currents 
 — the motions of the earth, and the inclination of its axis 
 — the seasons — latitude and longitude — the zones, their 
 limits, and a very few of their well-known and character- 
 istic plants and animals — and, in a very general way, the 
 location of the chief races of mankind. Only such defini- 
 tions should be included as are strictly elementary.
 
 SEVENTH GRADE. 
 
 Outline Course, 
 
 1. Language Lessons. — Reading of the grade of a Third Reader (a 
 different hook from that used in the Eighth Grade) : oral lessons on ani- 
 mals : compositions as before : spelling, meaning, and use of words as be- 
 fore — at least one hundred and fifty additional words, and a review of 
 those previously taught. 
 
 3. Arithmetic — Written and mental. — Through subtraction of com- 
 mon fractions, including practical applications ; weights and measures 
 — as before — completed. 
 
 3. Geography — (without text-book) — The United States. 
 
 4. Penmanship. — Single words, each to commence with a capital ; 
 short phrases. 
 
 5. Drawing. — On paper, illustrated on blackboard, from dictation 
 and from chart. 
 
 Draw two circles of not less than four inches in diameter. Two bor- 
 ders illustrating the principle of horizontal repetition— two different 
 units to be used in each border. Two conventional hastate leaves. 
 Symmetrical arrangement of the cordate leaves of the previous grade 
 in trefoil and quatrefoil One example of surface covering, consisting 
 of the repetition of a geometric unit.
 
 STATE NORMAL SCHOOL. 
 
 L^ Angeles, Cal. 
 
 IXSTKUCTIONS AND SUGGESTIONS. 
 
 Lx\XGUAGE. 
 
 The general instructions and suggestions for 
 Reading, found on page 20 ; those for 
 Spelling, on page 29 ; those for the 
 Meaning and use of words, on page 31 ; and thosj for 
 CoiLPosiTioN, on page 28, are to be taken as belonging 
 to this grade also. 
 
 ORAL LESSONS. 
 On Animals. 
 
 It is particularly important that the teachers should bear 
 in mind the chief purposes of these lessons, as already 
 explained on pages 22-25 ; that they should carefully 
 conform to the suggestions there given, and more espe- 
 cially those relating to " the second or review stage of the 
 process." 
 
 Collections of objects for use in the class-room are indis- 
 pensable. They need cost nothing except a little effort in 
 procuring and care in preserving them : a properly man- 
 aged class will gladly assist to supply tliem. An appeal 
 to the pupils just before the summer vacation, with a few 
 suggestions as to what things to look for and how to pre- 
 serve them, will produce an abundance of material. Teeth,
 
 42 SEVENTH GEADE. 
 
 shells, bones, skins, fur, eggs, large insects, pieces of coral, 
 star-tislies ; the harder parts of small animals, such as the 
 feet, bills, wings, and feathers of birds ; and a thousand 
 other common things, are very serviceable and readilj pro- 
 curable. Some small and familiar pet animal, loaned to 
 the class for a few hours, can be made to awaken an in- 
 terest and to fix indeliblj" facts that are important. Pic- 
 ture charts and large wood engravings from illustrated 
 papers are among the desirable things that are easily ob- 
 tained. 
 
 In relation to the special work of the grade, the follow- 
 ing suggestions are made : 
 
 1. Zoology being a science of classification, it is evi- 
 dently necessary, even in the following simple introduction 
 to it, to teach the most obvious distinctions upon which the 
 classification depends. 
 
 2. Only the simjjlest outline need be taught, with such 
 facts and details as seem most appropriate to illustrate 
 the subject. 
 
 3. The process of classification being naturally ohjective 
 — that is, animals being classified by their obvious pecu- 
 liarities — the pupil should be led, by exercise of the ob- 
 serving faculties, to discover the peculiarities himself, '^o 
 part of this subject is a more profitable exercise, and none 
 furnishes so great a pleasure to the pupil. 
 
 4. Well-known typical animals should be taken as the 
 objective basis of the classification ; such as man, monkey, 
 hat, cat, rat, horse, deer, cow, and whale y — eagle, parrot, 
 canary, hen, ostrich, snipe, and duch • — turtle, alligator, 
 rattlesnake, 2^\A frog ^— perch, cod, shark, q\.c.', — hee, but- 
 terfly, beetle, earthworm, etc. ; — spider and crab / — squid, 
 snail, and oyster ; — star-fish, jelly-fish, and corals. 
 
 5. The simplest names should be used, where possi-
 
 LANGUAGE. 43 
 
 ble, in preference to the more scientific, or, at least, as 
 preparatory thereto ; tlnis, it is better to use the term 
 four-hamled t\ia.n quadiumayia I gnawers than roclentia / 
 scixitchers than rasores ^ two-winged than d'ljptera j etc. 
 A few scientific terms, sucli as moUiish and hivalve, are in 
 such common use that they may be readily and profitably 
 explained and applied. 
 
 6. Associated facts not strictly scientific — such as the 
 uses of animals, anecdotes concerning them, peculiarities 
 and habits which the pupils have themselves observed or 
 have learned by reading or otherwise — should form an 
 important part of these exercises. 
 
 7. Tlie pupils should be encouraged to acquire as many 
 facts as possible, by their own observation and reflection. 
 For this purpose the collection of animals in the Central 
 Park, and others tliat are occasionally exhibited in the 
 city, may be employed. 
 
 8. The exei'cises should be conversational^ the reviews 
 only frequent enough to assure the teacher that the class, 
 as a whole, has understood the instruction given ; the 
 instruction should also embrace exercises in classifying 
 well-known animals from a miscellaneous list, giving the 
 reasons in each case. Too much, however, should not 
 be attempted. 
 
 9. Some system of diagrams^ roughly sketched in chalk, 
 will be found of great service in assisting the pupils to 
 remember the classification. The best and simplest is, 
 probably, that used in the ordinary "genealogical tree." 
 The diagram should be gradually developed, item by item, 
 as the lesson proceeds — the whole of it should not be 
 given in the preliminary stages. 
 
 10. The indispensable classified " outline " can be readily 
 prepared from any of the school manuals on the rudiments
 
 44 SEVENTH GKADE. 
 
 of natural history. Some of them are mentioned below. 
 See also " General Suggestions," pages 22-25. 
 
 11. It is not expected that the classification should ex- 
 tend to species and varieties, sometimes not even to genera. 
 It is desirable that pupils sliould have some definite ideas 
 as to the relations of the following terms used in zoology : 
 kingdom, hranch or type, class, order, family, genus, spe- 
 cies, variety, individual. These can be best exhibited by 
 a diagram, but should in no case be presented by formal 
 definition. All but the last four should be mentioned in 
 describing any given animal. 
 
 12. The exercises should include poi'tions of the topics 
 suggested in the following synopsis, which is here pre- 
 sented for the guidance of the teacher. Ifo teacher or class 
 can find time to take up all the topics presented in this 
 synopsis. It is to he expressly understood that the teacher 
 will use only such part or parts of these outlines (or of 
 their equivalents from other sources) as the Princijxd of 
 the department may direct. This synopsis comprehends 
 three successive outlines, each complete in itself or with 
 that preceding it. 
 
 First General Outline. 
 
 Distinction between organic and inorganic objects taught objectively. 
 The principal differences between animals and plants. What is an 
 m'gan? An animal ? Four great types of animals (Cuvier's, omitting 
 the protozoa). Exercises in classifying, by types only, such animals as the 
 docj^ lobster, dam, coi'al, shad, wasp, goose, sUir-fish, garter fnuike, shrimp, 
 toad, tortoise, oyster, etc. : the reasons of the classification should be 
 given by the pupil in each case. Each type to be then briefly defined. 
 Why vertebrates are placed first, articulates next, etc. 
 
 Include, also, such of the following que.:tious as may be appropriate : 
 Where does it live ? How breathe ? Color of blood ? Blood warm or 
 cold ? What covered with ? How many limbs, and for what use ? 
 Upon what does it feed ? Term vertebrate and invertebrate.
 
 LANGUAGE. 45 
 
 Second General Outline. 
 
 Classes of Vertebrates. — (Tenney's arrangement is brief and simple.) 
 Illustrate as in cases of the types, by mentioning animals belonging to 
 the several classes, mammals (those which feed their young with milk), 
 birds, reptiles, batrachians (frog kind), fishes; brief description of each 
 class to be given. Why mammals ^/'si and fishes last? Vse questions 
 of first outline. Name common vertebrates to be classified, occasionally 
 mentioning an animal not a vertebrate, in order to test the attention 
 and accuracy of the pupils ; for example, alli{jator, robin, mouse, worm, 
 lierring, toad, lion, jelly-fish, rattlesnake, elephint, flea, hatck, turtle, etc. 
 The pupil should give the reason for the classification. 
 
 Classes of articulates to be treated very briefly, but in the same man- 
 ner as the vertebrates. Simplest division (as insects, Crustacea, and 
 uorms) to be employed. 
 
 Classes of moUusks — treat also briefl}', by referring to their genei-al 
 characteristics only. Teach the meaning of the terms uniralie and At'- 
 ralce. Specimens of shells will be useful for illustration ; but it must 
 be remembered that the structure of the animal itself is far more in- 
 teresting and important than that of the shell which incloses it. 
 
 Classes of radiates, probably treated with sufficient fulness in connec- 
 tion with types. Review, if necessary. 
 
 Here it would be well to teach very briefly the classification of ani- 
 mals as herbivorous, carnivorous, and omnivorous ; also, the general re- 
 lations of the teeth of animals to their other peculiarities, such as their 
 feet, forms, food, di()estice apparatus, and habits ; for instance, the rela- 
 tion of the talons of the eagle to its beak. Also, as far as may be readily 
 done, show that animals are useful in various ways ; the carnivora, for 
 instance, in preventing over-crowding ; and, if some animals are re- 
 ferred to as quadrupeds, do not omit to mention also that others are 
 bipeds, hexapods, octopods, decapods, centipedes, myriapods, and apods. 
 Better say two-footed, four-footed, etc. Name an animal with two feet; 
 four feet ; six ; eight ; ten ; twelve ; with many feet ; no feet. 
 
 Third General Outline. 
 
 In this outline many orders should be omitted by the teacher, or 
 merely referred to, because not readily treated objectively. The fol- 
 lowing embraces all that may be tauglit. Of course, the whole cannot 
 be taught to any one class. Make such selections as may seem expe- 
 dient.
 
 46 SEVENTH GEADE. 
 
 Mammals. 
 
 Order 1. — Two-handed {Bimana). — To be treated briefly. The five 
 races of men, with their characteristic peculiarities. The geographical 
 distribution of these races to be also briefly referred to. Use outline 
 map in geographical references. 
 
 Order 2. — Four-handed {Quadrummia). — A few examples only, ac- 
 cording to the experience of the pupils. Refer to the geographical dis- 
 tribution. 
 
 Order 3. — Hand-winged (Cheiroptera). — Use a drawing or a dried 
 specimen, if one can be procured. Any interesting facts about bats, and 
 their nocturnal habits. 
 
 Order 4. — Insect-eaters (Insectidora). — Omit altogether, except to name 
 the mole as such, and refer to its small, hidden eyes, etc. 
 
 Order 5. — Flesh-eaters {Carnuora). — To be treated somewhat more 
 fully. Refer to general structure of teeth, feet, and digestive organs. 
 Refer to cat family, using common cat as type ; dog family, using dog as 
 type; weasel family, their form, habits, etc., naming sable, marten, er- 
 mine, and mink, and referring to the value of their furs ; bear family ; 
 also, briefly to seal family ; name the most common carnivora found in 
 the United States. 
 
 Order 6. — (Marsupials). — Refer to the geographical distribution. The 
 exception of the opossum, very briefly. 
 
 Order 7. — Q-naicers (Rodents). — Use the rat or squirrel as a type. Re- 
 fer to peculiarity of teeth, and the provision for their continued growth. 
 Teach about the rat, mouse, squirrel, beaver, rabbit. Refer to the icood- 
 chuck, porcupine, and guinea-pig. 
 
 Order 8. — Tliick-skinned (Pachyderms). — Treat briefly of the eUphant, 
 the rhinoceros, and sinine families; more fully of the horse family, in- 
 cluding 7iorse, ass, and zsbra. Geographical origin of the horse, its dis- 
 persion, and its influence in human affairs. 
 
 Order 9. — Cud-chewcrs (Ruminants). — Relations of food to teeth, stom- 
 ach, feet, etc. Teach three families : 1, deer family, horns solid, de- 
 ciduous; 2, hollow-horned family (horns permanent); Z, camel family 
 (hornless). Refer to Uama and vicuna. 
 
 Order 10. — Whale-like (Cetacea). — Refer to fish-like character of 
 whale; how dissimilar ; its uses. T\xq porp&ise di.Ta.di dolphin. 
 
 Birds. 
 
 1. Birds of Prey (Raptores). — Vulture, falcon, owl, condor, hawk, 
 eagle. Soaring birds. 
 
 2. Climbers (Scansores). — Parrot, woodpecker, etc. Tree birds.
 
 LANGUAGE. , 47 
 
 3. Perchers (Tnsessorea). — Give a few well-known birds as examples. 
 Tree birds. 
 
 4. Scratchers (i?rtSO/"fs). — Gallinaceous birds and dove family. Ground 
 birds. 
 
 5. 'Runners (Cursores). — Ostricli; its habits. Ground bird. 
 
 6. Waders (Grallatores). — Crane, stork, snipe, etc. Shore birds. 
 
 7. Swimmers {Natatores). — Duck family, swan, petrel, penguin, alba- 
 tross, etc. Water "birds. Refer to nests oi birds; to their migrations, 
 instinct, etc. 
 
 Review in connection appropriate parts of first and second outlines. 
 
 Reptiles and Frog-kind. 
 
 Treat very briefly, teaching something of turtles, crocodiles, alligators, 
 and lizards ; snakes and their fangs ; the frog and its transformations ; 
 why called amphibious. 
 
 Fishes. 
 
 Treat classification very briefly. Show the two groups; first, the 
 group of hony fishes, including the order Spinefinned; perch, porgy, 
 blackfish, bluefish, weakfish, etc. ; and the order Sofffinjied; herring, 
 shad, trout, salmon, whitefish, smelt, goldfish, cod, flounders, halibut, 
 eel ; and second, the group of cartilaginous fishes, including the stur- 
 geon, the shark, the ray, etc. Interesting facts in regard to fisheries. 
 
 Articulates. 
 
 Tliese present many advantages for jthe school-room. They are small 
 and easily procured for perceptive teaching. A simple microscope is a 
 great assistant in awakening an interest. Of insects, collections of 
 type specimens can easily be made. Only tJte sijnplest and inostintfreMincj 
 fctcts, fiotrever, need be taught. The general characteristics of this class 
 of animals should be explained — their structure and the functions of 
 their chief organs. Their wonderful transformations should be ex- 
 ])lained and exemplified; difference between insects proper, spiders, 
 and many-footed articulates {myriajwds). The important influence of 
 many insects upon mankind; destructive insects. 
 
 The following orders may be taught and exemplified: 
 
 1. Membra ne-7cinged {Hymenaptera). — Including the be^ family, the 
 ant family, the icasp family; the ichneumon family. Their peculiari- 
 ties, habits, and instinct. 
 
 3. Scale-icinged {Lepid<^ptera). — Moths and butterflies, caterpillars, 
 etc., clothes moth, geometer.
 
 48 SEVENTH GRADE. 
 
 3. Ttco-%dnged {Diptera). — Mosquito family, wheat-fly, house-fly, etc. 
 
 4. Case-winged {Coleopiera). —Beetle, fire-fly, weevil, etc. 
 
 5. Ilalf-icinged (Ilemiptem), or bugs; cicadas or harvest-flies, tree- 
 hopper, cochineal, boat-fly, etc. 
 
 6. Straifjht-winged {Orthoptera). — Cricket, katydid, locust, grasshop- 
 per. 
 
 7. Net-icinged{NeuropUra). — Dragon-fly, May-fly. Refer to the white 
 ants. 
 
 Spiders. (AracJinida). 
 
 Many-footed insects {Myriapoda). — Centipedes. 
 
 Crustacea. — Crab, lobster, shrimp. 
 
 Worms. — Earthworm. (See Darwin's Vegetable Mould for inter- 
 esting and useful information.) 
 
 Note. —It is important to distinguish carefully the three terms, in- 
 sect {i.e., six-footed [hexapod], or true insects), arachnids, or eight-footed 
 spiders and scorpions, and myriapods, or many-footed millipedes and 
 centipedes. In using a representative of one of these groups it should 
 be the primary aim to establish firmly in the pupils' minds the ob- 
 vious characteristics by which it is distinguished. Thus, in the 
 insect proper, the body is divided into three divisions — the head, 
 the body (or thorax), and the hind-body (or abdomen). The head is 
 furnished with feelers {antenna); the body supports three pairs of legs, 
 and generally one or two pairs of wings ; the abdomen shows more or less 
 clearly a number (seven) of rings or joints. In the arachnids, the head 
 and body are consolidated into one division, which has no antennae, sup- 
 ports four pairs of legs, but no wings. In the myriapods, the entire 
 body consists of a series of very similar joints — not grouped into divis- 
 ions separated (insected) from one another — of which the first serves 
 as a head, whilst each of the others, however numerous, supports either 
 one or two pairs of more or less imperfect legs. 
 
 Reference Books. — Among the many books in which the teacher 
 may find an unlimited supply of interesting material suitable to this 
 grade, only a few of the most easily procurable can here be mentioned. 
 Any of the ordinary text-books on zoology ; Hooker's Child's Book of 
 Nature ; Wood's Homes Without Hands ; Wood's Natural History ; 
 Wood's Man and Beast; Stevenson's Boys and Girls in Biology; T. R. 
 Jones' Animal Creation ; Kirby and Spence's Entomology ; Lubbock's 
 Ants, Bees, and Wasps ; A. B. Buckley's Progress of Science, Fairy 
 Laud of Science, Life and Her Children, and Winners in Life's Race ; 
 numerous articles in Appleton's, Johnson's, and Chambers' Cyclopaedias.
 
 ARITHMETIC. 49 
 
 ARITHMETIC. 
 
 Wr{Ue7i and Mental. — For suggestions see pages 32-35 
 and the following : 
 
 1. A remeio of Federal Money should form a part of 
 every grade up to iliQ^ifth, inclusive, after which it blends 
 with nearly all the other arithmetical exercises. It should 
 form a part of the regular class-work each week, and at 
 the monthly reviews. 
 
 2. " Practical applications " will include such questions 
 as may be readily given in connection with the commonly 
 used tables of money, weight, measure, etc.; as, " In f lb. 
 of sugar, how many oz. ? '' " Eighteen quarts are what 
 part of a bushel ? " etc. 
 
 3. In the written exercises pupils should use the signs 
 of operation, +, — , x, -h, and the sign of equality, to 
 indicate the work performed and the result. 
 
 4. At the outset the subject of fractions should, as far 
 as possible, be made to coincide with the acquired experi- 
 ence and simple notions of a child. 
 
 SYLLABUS OF TOPICS FOR ARITHMETIC. 
 
 (With Suggestions and Examples.) 
 
 I. — The idea of a fraction developed ohjectively. 
 The equality of the parts to be very carefully illustrated. 
 The relatire value of various fractional parts, as (jreater or less. 
 The definition of a fraction. 
 
 The terms of a fraction defined, and the order of statement. 
 The notation of fractions and location of terms, or order of icriting. 
 Exercises in writing and explaining fractions. 
 What part one integer is of another ; as, 3 is what part of 7 ? 
 Show objectively that f = :J- of 3. 
 
 Fractional expressions Less than a unit — proper fractions. 
 Proper fractions defined, and examples. 
 3
 
 50 SEVENTH GRADE. 
 
 Fractional expressions equal to or (jreater than a unit — improper frac- 
 tions. 
 
 Improper fractions defined and illustrated. 
 
 Exercises in writing proper and improper fractions. 
 
 Note. — The consideration of compound and complex fractions is re- 
 served for the Sixth Grade. 
 
 II.— Fundamental Axiom, 1 = -; or, ^ = 1- 
 
 Reduction of units to improper fractions. — Analysis A. (Page 52.) 
 
 Definition of mixed numbers. 
 
 Heduction of mixed numbers to improper fractions. — Analysis A. 
 (Page 52.) 
 
 liednetion of improper fractions to wJiole or mixed numbers. — Analysis 
 B. (Page 52.) 
 
 III. — Reduction of fractions to higher terms. [What may halves, 
 thirds, etc., be changed into ? J ? etc.] To be illustrated objectively. 
 
 Examples to be solved by inspection ; also, those that cannot be 
 solved by inspection. — Analysis C. (Page 52.) 
 
 Term Divisor or Factor, with exercises in finding, by inspection, a 
 Common Divisor or Common Factor. Definition to be given. 
 
 Note. — Too great importance can hardly be given to this exercise of 
 inspection. The application of the principle is indispensable in many 
 of the arithmetical exercises in every succeeding grade. With proper 
 training, it will become, within reasonable limits, a fixed naental habit 
 requiring no conscious effort. 
 
 Greatest Common Dirisor. Definition. Examples to be solved by in- 
 spection ; also by special method. 
 
 Reduction of Fractions to Loicer Terms. Exercises, etc. — see above. 
 
 Definition of " Lowest Terms." — Exami^les in finding what part one 
 whole number is of another : corresponding examples in tables of 
 weights and measures. 
 
 Examples to be solved by inspection ; as ilo ui ff ni etc. 
 
 Examples involving the special method of finding the greatest com- 
 mon divisor ; as f |^, ^f ^, etc. Examples not to be too long. 
 
 IV. — Multiple — term illustrated and defined. Multiple identical with 
 product. 
 
 Common Multiple — term illustrated and defined ; also least common 
 multiple. 
 
 Exercises, to be solved by inspection, and otherwise. 
 
 Reduction to Common Denominator — use two fractions at first. 
 
 Application of common multiple to reducing to common denominator. 
 
 Distinction between common multiple and common denominator.
 
 ARITHMETIC. 51 
 
 Definition of common denominator. 
 
 Definition of least common denominator. 
 
 Examples in reducing to least common denominator. — Analysis 0. 
 (Page 52.) 
 
 Examples involving preliminary reduction to lowest terms. 
 
 V. — Impossibility of adding quantities with unlike names, illustrated ; 
 add 3 dogs and 4 cats ; 3 animals -I- 4 animals = 7 animals. 
 
 Adding things of like names. 
 
 Adding fractions of the same denominator — Examples. 
 
 Use of common denominator as the indispensable basis for the work- 
 ing and explanation of Addition and Subtraction of Fractions. 
 
 Addition of Fractions of different denominators — Examples — Analysis 
 a (Page 52.) 
 
 Importance of reducing to least common denominator. 
 
 Note. — Say " Reduce to least common denominator,^^ rather than 
 " Find the least common multiple of the denominators.^* Of course, the 
 latter forms a part of the process of the former. 
 
 Only the numerators added. Why ? 
 
 Note. — At the outset give not more than two fractions, but advance 
 beyond this limit as soon as practicable. Give examples involving re- 
 duction to lowest terms. 
 
 Addition of mixed numbers. Examples. — Analysis C. (Page 52.) 
 
 Note. — See that the sign of operation and the sign of equality are not 
 omitted. Avoid reducing mixed numbers to improper fractions. 
 
 Subtraction of Fractions of different denominators. Examples. — An- 
 alysis C. (Page 52.) 
 
 Subtraction of Mixed Numhers. Examples. — Analysis C. (Page 52.) 
 
 Note 1. — All suggestions with reference to addition of fractions apply 
 with equal force to subtraction of fractions. Say " Find the difference 
 of their numerators ;" avoid saying "Subtract their numerators." 
 
 Note 2. — Questions should occasionally be varied by asking "Which 
 is the greater ? " or " What is the difference ? " etc. 
 
 Note 3. — Give practical examples involving both addition and sub- 
 traction. 
 
 General Note. — Teachers should remember that arithmetic is not 
 only a science, but also a practical art ; that this art involves important 
 devices, many of which have already been taught, and the principles of 
 which have been explained. These devices, such as reducing to lowest 
 terms, rejecting terminal Os of a divisor, etc , should not at any time be 
 lost sight of. Examples of such character as to require those devices 
 should be given occasionally in the special subjects of each grade. The
 
 52 SEVENTH GRADE. 
 
 omission or neglect of these important matters will be a serious defect 
 in the character of the instruction given. 
 
 FORMS OF ANALYSIS FOR THE SEVENTH GRADE. 
 
 Analysis A. — Example — Reduce 5^ to halves, or to an improper frac- 
 tion : 1 = 1; 5 = 5 times f = ^i ; \^ + i = V. 
 
 Analysis B. — Examples. — Reduce ^.^ to units, or to a whole or mixed 
 number : | = 1 ; -'^^ = -i/- -f- 1 = 7^. This may be expressed, also, as 
 follows : Since | = 1 unit, -^2^ will equal as manj units as f are con- 
 tained times in ^^ ; or will equal 7^. 
 
 Analysis C. — Example. — Reduce f to ninths: 1 = | ; i = 9 ; f = 
 2 X t = t. 
 
 Note 1. — In teaching this analysis, attention should be carefully 
 called to the fact that, if both terms of a fraction be multiplied by the 
 same number, the value of the fraction will remain unchanged. Exam- 
 ple : Reduce f- to twenty -eighths : multiplying denominator and numer- 
 ator by 4 we have f = ^|. 
 
 Note 2. — By Analysis Cit is shown that f = f . From this it is evi- 
 dent that, conversely, f = f ; or, if both terms be divided by the same 
 factor, the value of the fraction will not be changed. Or, again, if the 
 question be asked, "6 is what part of 9 ? " the immediate answer will 
 be f. If the same question be modified into " two 3's are what part of 
 three 3's," the answer becomes f . Hence, it will be sufficient to say 
 that a fraction is reduced to its lowest terms by dividing both terms by 
 their greatest common divisor, because this does not change its value. 
 
 TABLES OF MONEY, WEIGHT, ETC. 
 
 1. Review thoroughly the tables of the Eighth Grade. 
 
 2. Add the following to Long Measure : 4 in. =1 hand, 3 feet = 1 
 pace, 6 feet = 1 fathom, 1^ miles = 1 knot. 
 
 3. Surveyors^ Long Measure. — 66 feet, or 4 rods, or 100 links = 1 
 chain, 80 chains = 1 mile. 
 
 4. Surveyors^ Square Measure. — 16 sq. rods = 1 sq. chain, 10 sq. 
 chains = 1 acre, 640 acres = 1 sq. mile or section^ 36 sq. miles = 1 town- 
 ship. 
 
 Explain the use of section and township in measuring land surveyed 
 by the United States. 
 
 5. Miscellaneous Avoirdupois Weight. — 60 lbs. = 1 bush, wheat, 196 
 lbs. = 1 bbl. flour, 200 lbs. = 1 bbl. beef or pork, 100 lbs. = 1 quintal 
 of fish, 62^ lbs. or 1,000 oz. = 1 cu. foot of water.
 
 GEOGRAPHY. 53 
 
 6. Apothecarifs' Weight. — Teach the table and its use. Show that its 
 lb., oz., and grain are identical with those of troy weight ; that the only 
 difference consists in the subdivision of the ounce. Teach the fluid 
 ounce and its divisions. 
 
 7. English Money, etc. — The usual table ; the value of a pound ster- 
 ling — $4.87; of the franc — 19 cents 3 mills ; of the German mark — 23 
 cents 8 mills. 
 
 If any foreign dollar is taught, let it be the doUar of North Germany 
 — 71 cents 4 mills. 
 
 8. Angular Measure. — Teach the following terms: Ctrde, circumfer- 
 ence, quadrant, radius, diameter. Teach the notation. Give examples 
 in reading : as, 16° 17' 45'. 
 
 60' =1', 60' = 1°, 90' r= 1 quadrant, 360' = 1 circle, 69i miles = 1 
 degree of latitude. Circumference of a circle = 3| times the diameter 
 (very nearly). 
 
 General Note. — Pupils should be carefully taught the meanings, 
 uses, and simple practical applications of the above. 
 
 GEOGRAPHY. 
 
 United States. — A simple outline will embrace the fol- 
 lowing : 
 
 1. Local Geography. — The boundaries of the country 
 as a whole, its dimensions and population in round num- 
 bers, the location of the great mountain systems, the west- 
 ern plateaux (a '"'■section'''' of the country roughly drawn in 
 chalk upon the blackboard will be found efficient), the 
 high western plain, the low central plain, the eastern slope, 
 and the California basin ; about a dozen of the chief rivers, 
 including their great branches ; about five or six each of 
 the great lakes, bays, and capes ; about twenty-five of the 
 principal cities, and the names of the several States and 
 Territories, individually and in groups. 
 
 The capitals and a few other important details of the 
 States should also be taught. 
 
 All local geography to be taught with the assistance of 
 the outline map and the pointer, and to be i-eviewed with
 
 54 SEVET^TH GRADE. 
 
 and without the map. Pupils should be required to sketch 
 rapidly on slate or blackboard outlines of maps. 
 
 2. Descriptive Geography will include a very brief de- 
 scription of the highlands, lowlands, and drainage system 
 already pointed out ; a general idea of the climate and its 
 gradual modifications by latitude, elevation, and distance 
 from the sea ; and a general statement of the leading 
 agricultural staples in the order of their latitude — rice, 
 sugar, cotton, tobacco, corn, and wheat ; also the chief 
 minerals, and the principal animals, wild as well as do- 
 mestic. 
 
 Special care is to be taken that this outline shall be 
 such that it can readily be completed and thoroughly re- 
 viewed before the promotion of the class to the next higher 
 grade. The descriptive geography, though very brief, is 
 of the highest importance. It is necessarily based upon 
 the map exercises. These are indispensable, but must not 
 be permitted practically to exclude the descriptive.
 
 SIXTH GRADE. 
 
 Outline Course. 
 
 1. Language Lessons. — Reading of the grade of an easy Fourth 
 Reader : aral lessons on plants : compositioiis as before : spelling, meaning, 
 and me of words, as before — at least 150 additional words, and review 
 of all previously taught : easy exercises in suffixes. 
 
 2. Arithmetic. — Written and mental. — Common fractions completed. 
 
 3. Geography — (without text-book). — General Outlines of South 
 America and Europe. 
 
 4. Penmanship. — Single words continued ; also short phrases and 
 easy sentences. 
 
 5. Drawing. — On paper, illustrated on blackboard, from dictation 
 and from chart. 
 
 Draw two ellipses, one on vertical jtnajor axis of 4 inches, one on 
 horizontal major axis of 4 inches. Draw two ovals of different propor- 
 tions. Compound curves on vertical axis. Two examples of vases of 
 different styles. Draw one conventional leaf and one flower, two views 
 of each ; the same in an original design. Draw a vertical border, 
 using the hastate leaves of the Seventh Grade.
 
 INSTRUCTIONS AND SUGGESTIONS. 
 
 LANGUAGE. 
 
 The general instructions and suggestions for 
 Reading, found on page 20 ; those for 
 Spelling, on page 29 ; those for 
 
 Meaning and Use of Words, on page 31 ; and those for 
 Composition, on page 28, are to be taken as belong- 
 ing to this grade also. 
 
 OEAL LESSONS. 
 On Plants. 
 
 1. The general suggestions given in connection with the 
 subject of animals in the preceding grade, in relation to 
 the extent of classification, the terras employed, the col- 
 lection of objects, etc., are equally applicable to the subject 
 of plants. As a field for cultivating the observing facul- 
 ties, the study of plants has a decided advantage over the 
 study of animals, especially for educational purposes, inas- 
 much as the objects of which it treats may be exhibited 
 more conveniently in the class-room, and may be examined, 
 dissected, and analyzed with greater facility. 
 
 2. The classijication of plants into orders and families 
 being based upon distinctions often very minute, must, for 
 the purposes to be accomplished in these simple lessons, be 
 carefully limited. Only a few common plants need be
 
 LANGUAGE. 57 
 
 classified. Suggestions as to the nature and limitations of 
 the classification are indicated below. 
 
 3. The first lessons should train pnpils to notice how 
 plants grow from the seed ; should show the structure of 
 plants and the general functions of each of their organs 
 of vegetaiion — the root^ the stem^ and the leaf. Make se- 
 lections from the followins: : 
 
 A few large beans and other seeds may be conveniently examined in 
 the class-room. Soak them and show the (jerm or embryo, the Sieed 
 leaves, the coat. Show that the coat protects the germ, as the shell does 
 the egg ; that the seed leaves contain and supply the first food for the 
 infant plant, before it can obtain food for itself from the ground and from 
 the air. Plant a few such seeds in boxes a few weeks or days before 
 wanted for study. Show the development of the root and the stem, the 
 latter always toward the light. Warmth and moisture needed first, then 
 light, soil, and air. 
 
 liooU^ kinds of ; fibrous, branching, etc., parts of the root — the little 
 sponges ; iises of the root to the plant ; air roots of certain vines. 
 
 Stcfyis, varieties of ; solid and hollow, simple and branching ; varieties 
 of size, from trees to the smallest ; some increase from inside, therefore 
 called inside growers (endogens), (corn, sugar-cane, palm tree, grasses, 
 etc.), and have no bark. Some have a bark and increase by layers of 
 wood just under the bark ; therefore called outside groirers (exogens), 
 (oak, apple, flax, sunflower, etc.). Illustrate both kinds by specimens. 
 
 8ttp. — Vegetable blood — flows up and down through the bark, and 
 the young wood under it. Uses of the bark in circulation, respiration, 
 growth, and protection. 
 
 Leaver. — Parts; blade, foot-stalk, stipules: kinds of; mostly flat 
 blades and needle-shaped ; examples. Simple leaves ; compound 
 leaves ; examples. Forms of flat leaves {very briefly) from objects ; use 
 simple terms, round, heart-shaped, etc., instead of orbicular, cordate, 
 hastate, etc. Marcfins {very briefly), entire, toothed, wavy, jagged. Vein- 
 ing ; ribs, veins, veinlets ; net-veined, parallel-veined. Green jmlp of 
 leaf — all inclosed in transparent skin. Seed-leaves — of embryo— division 
 of plants into those having one seed-leaf, two seed-leaves, many seed- 
 leaves ; examples of each. 
 
 Show the important connection of the character of the veining and the 
 number of the seed-leaves, with the method of growth of stem, as inside 
 3*
 
 58 SIXTH GRADE. 
 
 growers and outwJe groiners. Which of these two classes of plants is 
 more directly important to lis ? 
 
 Uses of the leaves to the plant.. The countless little mouths ; the ac- 
 tion of air and sunshine on the sap in the green leaf. The food of 
 plants. How we know that the greater part, even of a great tree, was 
 taken from the air by the leaves. How the leaf-stalk, the irregular 
 form of the leaf, and the blowing of the wind, all help to feed the trees. 
 Opposite effects of the Respiration of plants and of animals upon air. 
 
 Plants as herbs, shrubs, and trees — examples of each. As annuals, bi- 
 en7iials, and perennials — examples of each ; perennial herbs (dahlia, 
 sweet potato, artichoke, potato). Tubers and bulbs; what they are 
 — examples. 
 
 4. A few lessons on the reproductive organs of plants 
 sliould then follow ; the Jhive)', fruity and seeds. Selec- 
 tions and limitations to be made bj or under the direction 
 of the Principal, or equivalent exercises on plants substi- 
 tuted by him. Flowers, common fruits, and engravings 
 should be shown, and the blackboard should be frequently 
 used. The flowers and their several parts form the chief 
 basis of classification. 
 
 5. First show the parts of a blossom, taking a regular 
 one to begin with — as a lily^ a iiiornirig -glory., or a hutter- 
 ciip. Use also the blackboard for drawing and spelling. 
 Analyze so that the pupils can see the parts, showing the 
 calyx and sejyals., the corolla and jpetals., the stamens with 
 the anthers a,nd pollen, and the pistil with its ovary. Give 
 a sufficient number of exercises to make this familiar, and 
 let the pupils analyze for themselves. The principal forms 
 of flowers, as hell-shaped, wheel-shaped, salver-shaped, cross- 
 shaped, hutteiip I -shaped, etc., may then be shown. The 
 arrangement of the blossoms on the stem (inflorescence), 
 as far as it can be exemplified by actual specimens, as head, 
 racetne, spike, umbel, etc., may also be learned : incident- 
 ally, the importance of insects, especially bees, in carrying
 
 LANGUAGE. 59 
 
 pollen to the pistil, and the importance of the sweet fluid 
 in the blossoms as a bait, and of the colors of the petals 
 as a guide to the insects. 
 
 GENERAL OUTLEN'E OF CLASSIFICATION BY BLOSSOMS. 
 
 A. (Series.) Flowering (pTuBnogamous) plants. Examples — rose, lily, 
 geranium. 
 
 B. (Series.) JF^lowerless (^cryptogamous) ■pla.nts. Examples— /^r/?, wo.ss, 
 mushroom. 
 
 Use only the familiar terms. Give other examples of plants in each 
 series. 
 
 Flmcering plants, two classes. 
 
 Outside-growing {exogeiwus) plants. 
 
 Inside-growing {endogenous) plants. 
 
 Familiar examples to be found by the pupils ; such as rose, buttercup, 
 geranium, pea, potato, grapevine, etc., and lily, Indian corn, common 
 grass, etc. 
 
 Illustrate by stems, showing the rings or annual layers of growth in 
 the former, with bark, mood, and pith, and their absence in the latter 
 class. Review the coincident peculiarities of the leaves, as net-reined 
 and parallel-veined, which afford a ready method (approximate) of dis- 
 tinguishing these plants, thus giving opportunity for useful exercises ; 
 also those of the seeds, as of two-seed leaves, or only one. 
 
 Outside-groicing. — Including, 1, orders or families of plants, with 
 blossoms of many petals {polypetalous) ; and, 2, orders or families of 
 those with blossoms of one petal {monopetalous). The xuipils will readily 
 find specimens of each, the popular names of which they have already 
 learned. 
 
 Tnside-grmnng . — The orders should not be taught. Nor need any 
 instruction be given in relation to the classification of cryptogamous 
 plants, /fr7i«, mosses, etc., this being too difficult, and depending upon 
 distinctions not sufficiently obvious for the purpose of these lessons. 
 Attention, however, may, if occasion ofifers, be called to the fntctifica- 
 tion of ferns. 
 
 Such of the orders, or families, should be taught as are very familiar 
 and depend upon quite obvious distinctions, familiar names being ex- 
 clusively used. Thus the mustard family, the pidM family, the crowfoot 
 family, the rose family, the lily family, etc., may be taught as far as the 
 collection and presentation of specimens render it desirable ; that is, 
 not the mere fact that there are such families, but in connection with an
 
 60 SIXTH GRADE, 
 
 actual objeci, and in answer to an inquiry about fhe family to which the ob- 
 ject belongs. If the season permits, and there is an opportunity for the 
 pupils to seek for specimens, this part of the instruction may be extended. 
 Here the judgment of tlie teacher (never to be superseded) must be 
 carefully exercised, it being constantly kept in view that the object of 
 these lessons is not to make tJie pupils botanists, but to create a basis for 
 the study of natural objects, to develop the faculties of perception and 
 reflection, and to cultivate facility of statement. Species need not bo 
 taught at all, although the pu-pils may, as occasion offers, be made to 
 perceive the diversity presented by different individuals of the same 
 family, so as to learn what is meant by species. 
 
 G. The common uses of jjlctnts may be taught to some 
 extent incidentally with some of the above instructions, 
 but more fully at this stage. This will embrace their uses 
 ioY food^ dotfiing, medicine., etc. Take our own plants 
 first. Show that the 7'oots of some plants are useful ; of 
 others, the seeds ; others, the leaves / others, the fruit / 
 others, the hcvrlx., etc. Some few plants of other climates 
 and countries may then be referred to, as cotton., rice., tea., 
 sugar., coffee., etc. The relationship of these plants to our 
 own may then be shown ; that is, the families to which 
 they belong. Do not let these exercises become a mere 
 repetition of a part of those of the Eighth Grade, 
 
 7. Objects. — The things necessary for the indispensable 
 objective presentation of this subject have been already 
 sufficiently indicated in the text. Good drawings may be 
 used when the natural objects are not procurable. 
 
 8. Reference. — All that any teacher can possibly need 
 for any part, or for the whole of these outlines, may be 
 found in Gray's How Plants Grow, Hooker's Child's Eook 
 of Nature, and Buckley's Fairy Land of Science (articles 
 on Bees and Flowers, and on Sunbeams and their Work). 
 There are, besides, many other excellent popular works on 
 botany.
 
 SUFFIXES AND PKEFIXES^ — ARITHMETIC. 61 
 
 SUFFIXES ANB PEEFIXES. 
 
 For the Sixth Grade, exercises in suffixes only are pre- 
 scribed. For the liigher grades both prefixes and suffixes 
 are required. These exercises involv^e certain important 
 changes in spelling as well as modifications of meaning. 
 They should include only such words as the pupil may 
 readily be trained to use in oral and written expression. 
 
 In order to insure systematic progress, lists of these 
 words should be kept by the teacher. 
 
 The following groups of words are submitted as sug- 
 gestive illustrations : Pity, pitied, wvpitied, jpitying, piti- 
 fully, piteous, piteously. Sweet, sioeets, srceeten, siveeten- 
 ing, sioeetly, sioeetness. Just, unjust, unjustly, justice, in- 
 justice, justify, justif cation. 
 
 AEITHMETIC. 
 
 Written and Mental. — For suggestions see pages 32-35, 
 and the following: 
 
 1. Particular care should be taken in the selection of 
 examples that no one of them be so intricate and prolix 
 as to consume a large amount of time, without affording 
 proper exercise of thought in the application of arithmet- 
 ical principles. 
 
 2. Too much importance, nevertheless, can scarcely be 
 given to the requirement of rapid calculation in the simple 
 rules of arithmetic. No part of the arithmetical disci- 
 pline has a higher utilitarian value, whether for the pur- 
 poses of practical life or for progress in the more advanced 
 portions of the study ; for nothing is more discouraging to 
 the pupil than to find that, in any exercise involving other
 
 62 SIXTH GRADE. 
 
 than a few figures, his results are almost always incorrect, 
 from a want of habitual accuracy in performing the simple 
 combinations involved in the elementary rules. Teachers 
 are, therefore, especially advised to employ every variety 
 of proper stimulus to make the exercises for this purpose 
 thorough and effective. 
 
 SYLLABUS OF TOPICS. 
 
 Principle of Cancdlation. 
 
 Its identity with dividing by common factors, and with reducing to loio- 
 est terms. Show this by examples in fractions. 
 
 Examples of simple applications of cancellation to whole numbers. 
 Compound fractions defined and illustrated. 
 
 Multiplication of Fractions. 
 
 Multiplication of fraction by integer. 
 
 Multiplication of mixed number by integer. Teach both methods. 
 
 Converse of these two cases. 
 
 Multiplication of fraction by fraction. 
 
 Compound fraction same as this case. 
 
 Multiplication of mixed numbers and fractions. Generally reduce 
 the mixed numbers to improper fractious ; also, cancel before multiply- 
 ing. 
 
 Note. — In this last case it is sometimes more convenient not to reduce 
 the mixed number ; as, 125f x i, 12| x §•. 
 
 Examples to be given in a practical form at as early a stage as can be 
 made expedient. 
 
 Find how many cents, or cents and mills, in a given fraction of a dol- 
 lar. 
 
 Examples involving preliminary reduction to lowest terms. 
 
 Note. — It must not be forgotten by the teacher that, from the nature 
 and definition of a fraction, every example in fractions must involve or 
 relate to division in some way. 
 
 The following explanations and suggestions will be found useful : 
 
 Multiply f by 12 ; 12 times f = 2.£ _ 51., 
 
 Multiply f by 12 ; 12 times | = 3-fi = 4| = 4^. Tliis result would be 
 more readily reached by the cancellation of the common factor 4, in 
 the multiplier 12, and the divisor 8. Whenever possible, cancellation 
 should be used.
 
 ARITHMETIC. 63 
 
 Find i of 12 ; i of 12 = 3 ; I of 12 = 3 x 3 = 9. 
 
 Find ^ of 12 ; f of 12 = i of 3 times 12 = \ of 36 = Sj. 
 
 Find |§ of 12. Use cancellation. 
 
 Find f of -.'^r ; i of A = -ft- ; S of A = 3 x -^ = A. 
 
 Find f of fr ; i of -,V = -h ; i of ,\ = f,^ ; f of -,\ = 3 x -/,- =r f i. 
 
 Find it of 1^,-. Use cancellation. 
 
 Division of Fractions. 
 
 Division of fraction by integer. Solve as compound fractions. 
 
 Division of mixed number bj integer. Solve as compound fractions. 
 
 Converse of these two cases. (See below.) 
 
 Division of fraction by fraction. (See below.) 
 
 Quotients of mixed numbers and fractions. (See below.) 
 
 Examples in finding what part one fractional quantity is of another. 
 
 Complex fractions — best considered as cases of division of fractions. 
 
 The form of putting the questions should be varied as much as possi- 
 sible, so as to train the pupils to select and apply the right principle and 
 method. 
 
 Introduce practical examples as soon as possible. The teacher should 
 always keep in mind, and should impress on the piipils, that the an- 
 alyses of such examples correspond exactly with those of similar exam- 
 ples in the Eighth Grade, the essential difference being that fractional 
 numbers now take the place of integers. 
 
 Note. — The question : " If 4 of a yard cost $1, what will a yard 
 cost ? " involves the finding of the cost of |^ of a yard. 
 
 •' If $1 buy f of a yard, how much will a dollar buy ? " involves $|. 
 
 Give examples involving simple combinations of the multiplication 
 and division of fractions ; also addition or subtraction, with multiplica- 
 tion or division, like the following : 
 
 Bought 7| yards and 3^ yards at -flf a yard ; cost of the whole ? 
 
 Bought 36 yards, kept 9+ yards, sold the remainder at $.j a yard ; 
 how much did I get for it ? 
 
 If I had sold it for $7^, how much a yard would that be ? 
 
 If I yard cost $r, what will -i*", yard cost ? 
 
 If f yard cost $5? how much can be bought for |l5| ? 
 
 The following explanations and suggestions will be found useful : 
 
 Divide 9 by ^ (first method), 9 = ^^^ ; e/ -h ^ = ^5^= 12^. 
 
 Divide 9 by ^ (second method), 9-=-i = 7x9 = 63; 9-J-^ = iof 
 63 = 12|. From this method it is seen that the dividend has been mul- 
 tiplied by 7, and the product divided by 5 ; or, in other words, the 
 dividend has been multiplied by the dicmr inverted . The method of
 
 64 SIXTH GRADE. 
 
 division by inverting the divisor is preferable, as it more frequently 
 permits cancellation and thus shortens processes. 
 
 Divide 9 by 3^, Reduce the divisor to an improper fraction. 
 
 Divide -i^i- by ^ : 1 -f- ^-=i ; therefore, -?t of 1 -J- t=-A- of i = U- 
 
 Divide 7-i^r by Aj. Reduce to improper fraction. 
 
 Note. — Teachers should remember that arithmetic is not only a sci- 
 ence, but also a practical art ; that this art involves important devices, 
 many of which have been already taught, and their principles explained. 
 These devices, such as reducing to lowest terms, cancellation, rejecting 
 terminal Os of a divisor, etc., should not be at any time lost sight of. 
 Examples in the special subject of the grade should be occasionally 
 given of such a character as to require these devices. The omission or 
 neglect of these important matters will be a serious defect in the charac- 
 ter of the instruction given. 
 
 It will be readily perceived that solutions which follow the steps of a 
 logical analysis are much more tedious than those which follow a rule 
 derived from the result of the analysis. The methods by analysis are 
 essential to the proper teaching of the principles of arithmetical compu- 
 tation, but they should be employed in written arithmetic no longer 
 than is absolutely required for the accomplishment of such a purpose. 
 
 GEOGEAPHY. 
 
 South Ai7ierica. — The geograpliy of South America is 
 to be studied only in outline. Great care must be taken 
 from the outset that no part of the work be made so full 
 as to prevent the ready com/pletion and thorough review 
 of the whole requirement of the grade before the promo- 
 tion of the class to the ne.xt grade. The following are the 
 essential points : The boundaries of South America ; area 
 and population in round numbers ; simplest physical di- 
 visions, as in the United States ; the names and relative 
 positions of the several countries ; brief statements of 
 general facts relating to the climates and productions of 
 the countries ; the names and locations of their capitals, 
 and of those islands, mountains, seas, gulfs, bays, rivers,
 
 GEOGRAPHY. 65 
 
 lakes, straits, and otlier physical features that have already 
 been included in teaching the Western Hemisphere. 
 
 EurojK. — The local and descriptive geography of Eu- 
 rope for this grade will include the following : 
 
 General boundaries of Europe ; area and population in 
 round numbers ; simplest physical divisions, as in the 
 United States; names of all its countries. 
 
 In relation to each country the following will be re- 
 quired : Relative position ; large rivers, not more than one 
 or two ; large islands, and prominent capes and mountain 
 chains (if there are any) ; one or two leading exports ; the 
 capital.
 
 FIFTH GRADE. 
 
 Outline Cotikse. 
 
 1. Language Lessons. — Beading ot the grade of a Fourth Eeader : 
 <M'al lesso)}s on the human body : comjyositions as before : sjyelling, mean- 
 ing, and use of words, as before — at least 150 additional words, and re- 
 view of all previously taught : exercises in prefixes and svffixes. 
 
 2. Akithmetic. — Written and mental. — Decimals, and practical ap- 
 plications of common and decimal fractions ; also, reduction, ascending 
 and descending, of integral denominate numbers. 
 
 3. Geogkaphy. — North America in outline, and the United States in 
 detail. 
 
 4. History of the United States (without a text-book). — A brief gen- 
 eral outline. 
 
 5. Penmanship. — Phrases and sentences varying in length and de- 
 gree of difficulty. 
 
 6. Drawing. — On paper, illustrated on blackboard, from dictation 
 and from chart. 
 
 Draw a regular pentagon. Draw two varieties of trilobate conven- 
 tional leaves and two conventional flowers. One Greek vase without 
 perspective effect or ornament, not less than five inches in height. Two 
 examples of historic ornament (borders), Egyptian and Greek. One 
 original border, composed of the leaves and flowers used in this or the 
 Sixth Grade. One original combination of the above leaves and flowers 
 in a square ; repeat the square for wall-paper or oil-cloth design.
 
 INSTRUCTIONS AND SUGGESTIONS. 
 
 LANGUAGE. 
 
 The general instructions and suggestions for 
 Reading, found on page 20 ; those for 
 SpELLESfG, on page 29 ; tliose for the 
 Meaning and Use of "Words, on page 31 ; those for 
 Composition, oh page 28 ; and those for 
 Prefixes and Suffixes, on page 91, are to be taken as 
 belonging to this grade also. 
 
 ORAL LESSONS. 
 On the Human Body. 
 
 1. The chief purpose of this study in the Grammar 
 Schools is to give \\&ein\ practical hnoioledge of the laws of 
 health. As this subject receives, at most, but a small part 
 of the time of a single grade, it is the more important that 
 only those parts of it should be considered that are essen- 
 tial to the main purpose. 
 
 2. The teacher will observe that Anatomy, which occu- 
 pies so much space in many text-books, is not called for in 
 this grade, except as far as it is necessary to teach what is 
 specially prescribed. It is a matter of little consequence 
 to the pupil to know exactly the number of bones, or ver- 
 tebree, or of pairs of muscles in his body, or to repeat their
 
 68 FIFTH GKADE. 
 
 scientific names. Only those anatomical terms and facts 
 should be introduced that are inseparable from the main 
 subject {physiology and hygiene). 
 
 3. Oral descrvption of structure or function should take 
 the place of definitions. These should be omitted alto- 
 gether. 
 
 4. The appliances necessary for teaching this branch 
 are the blackboard and charts. The teacher should care- 
 fully consider, at every step, to what extent the subject 
 can be treated objectively. This can, in part, be done by 
 drawing the pupil's attention to his own body, as in case 
 of the joints, the pulse, the veins, arteries, respiration, etc. 
 For several very important parts of the subject, there is 
 no better apparatus than that which can be procured with- 
 out expense at any butcher's stall — such as the lungs and 
 windpipe of a sheep ; the diaphragm ; the heart and part 
 of the great tubes leading to and from it ; the brain and 
 the bony cavity which contains it ; the eye ; portions of 
 the spinal cord and nerves ; small glands ; and portions of 
 limbs showing the relations of muscles, tendons, ligaments, 
 and joints. Kone of these need present anything offensive 
 or disgusting. Add to these a small knife and proper 
 preparation on the part of the teacher, and the instruction 
 given will be both interesting and profitable. 
 
 5. A syllahus of leading points is subjoined. It is not 
 required that all these should be taught in one class, though 
 all are important. Neither is it expected that any point 
 shall be treated exhaustively, nor is the teacher obliged to 
 follow exactly the order laid down. Any order (so that it 
 be an order) which presents the parts of the general sub- 
 ject in their natural relations will be satisfactory.
 
 LANGUAGE. C9 
 
 SYLLABUS OF TOPICS. 
 
 The pupil should be led to look upon the body as a complex appara- 
 tus for the use of the mind. To know that it consists primarily of — 
 
 First, a bony framework (tlie skeleton) ; Second, a motor apparatus 
 attached to the frame (the muscular system) ; Third, a directing appara- 
 tus by which the mind controls the body (brain and nervous system 
 and sensory organs) ; Fourth, a general envelope protecting the preced- 
 ing, as well as serving other purposes (the skin). 
 
 He should then be led to see that every motion of the body or of its 
 minutest part, however slight, and whether voluntary or involuntary, 
 requires the destruction of a minute part of the organism and the re- 
 moval of the destroyed part from the system — that this constant destruc- 
 tion and removal make necessary a corresponding reconstruction and 
 renewal, by means of new material, and that for these purposes there 
 are provided — 
 
 Fifth, a circulatory apparatus — (the blood-vessels) — to carry away old 
 material and to distribute the new ; Sixth, an aerating apparatus (the 
 respiratory system), to purify, warm, and enliven the circulating fluid ; 
 Seventh, a system of drainage (the skin and kidneys), to take from the 
 blood a large part of the worn-out material ; and Eighth, an apparatus 
 to prepare and supply the new material (the digestive and assimilative 
 organs). 
 
 Under each of these heads a few points are noted : 
 
 1. Bones — their composition and various uses; the covering mem- 
 brane; joints, their various uses and lubrication— important peculiari- 
 ties of the spinal column, cautions as to injuring the large bones of an 
 infant ; the repairs of broken bones. Compare briefly with correspond- 
 ing arrangements in cow, fowl, turtle, fish. See charts. 
 
 2. Muscles and Tendo7is — their appearance and uses — arrangement of 
 the muscles in pairs, and why ; how attached, how able to contract ; ef- 
 fects of exercise ; use of calisthenics. 
 
 3. Nervous System — means of becoming conscious of the external 
 world — spinal cord — its importance and protection — its many pairs of 
 branches— effects of severing or injuring the spinal cord ; care of in- 
 fants in this respect. The sympathetic system, the nerves (as tele- 
 graphic wires), the brain and its principal functions ; uses of pain — uses 
 of sleep — excitement, caution against— late hours, stimixlants, etc. 
 
 Special Senses — touch, papillw — taste — smell — the ear, its mechanism, 
 hearing — the eye. its mechanism, sight — injury of the eye by misuse. 
 
 4. Skin — its structure and uses. Perspiratory glands and tubes — uses
 
 70 FIFTH GRADE. 
 
 of perspiration — importance of bathing, misuse of bathing ; importance 
 of proper clothing — sympathy of skin witli lungs — with digestive or- 
 gans — caution against exposure of limbs, arms, or chests of little chil- 
 dren ; the skin as an absorbent — danger of cosmetics and hair-dyes ; 
 treatment of burns and scalds, etc. 
 
 5. Circulation — general relations of heart, arteries, veins, and capil- 
 laries — valves, where and use — pulse— its rate — rapidity of circulation. 
 Effects of fresh air and exercise on the circulation ; limits of exercise — 
 dangers of excessive rope-]'umping, etc. Effects of sleep ; cautions nec- 
 essary — effects of tight garments — of scanty garments — of insufficient or 
 improper food. Wounds — how to know when an artery is wounded, 
 and what to do. 
 
 6. Respiration. — Practically the most important department of hy- 
 gienic knowledge. The apparatus — how protected — arrangement of ribs 
 for flexibility and the expansion of the lungs — muscles of chest and dia- 
 phragm concerned in respiration ; importance of the diaphragm ; show 
 its positions at beginning and end of inspiration ; the trachea ; the or- 
 gan of the voice — minute structure of lungs — the cells and their mem- 
 brane — exosmosis and endosmosis simply stated without using the terms ; 
 intimate relations of capillaries and air-vessels ; frequent full inspira- 
 tion a means of increasing the capacity of the lungs ; exercises that will 
 ensure this ; pernicious effects of tight lacing on the capacity and ac- 
 tion of the lungs. The air — its composition — relations of oxygen to car- 
 bon and hydrogen introduced with food — products of respiration all in- 
 visible except water— poisonous nature of carbonic acid when inhaled — 
 in wells — in vats— effects of smaller quantities; other poisonous sub- 
 stances thrown off by lungs and skin — effects of tobacco, onions, liquor, 
 teeth, etc., etc. Rapid diffusion of gases and vapors — ventilation of 
 class-rooms — of sleei^ing-rooms — simple devices for ventilation of small 
 sleeping-rooms in winter — why called "vital air" — careful inspection of 
 premises to remove all decomposing substances, etc.; foul air from 
 cellars, sewers, sinks, water-pipes, garbage, gas-lights, stoves, etc.;. brief 
 but distinct statement of the germ tJieory of disease, as in diphtheria, 
 scarlet fever, cholera, yellow fever, etc.; simple and cheap disinfectants 
 — chloride of lime — chlorine — sulphate of iron — carbolic acid — sulphur, 
 whitewash, etc. Respiration as affected by position in standing — in sit- 
 ting — especially in sitting to write or to draw ; importance of proper 
 habits in this. Popular errors in regard to condition of drowned per- 
 sons — proper treatment for their resuscitation. 
 
 7. The digestive apparatus — the teeth, their uses, structure, and hy- 
 giene — brief notice of salivary glands, their position and uses— of the
 
 ARITHMETIC. 71 
 
 gullet — structure and function of the stomach — brief notice of the duo- 
 denum, the intestines, lacteals, etc. — importance of the liver — tlie link 
 between the digestive and circulating systems. Dyspepsia, its prevent- 
 able causes and serious consequences — importance of chewing the food — . 
 of regular hours in eating — of light suppers — of good cooking — the art 
 of preparing wholesome food the most important of household arts — 
 common errors to be avoided in the preparation of food. Common 
 poisons and their antidotes. 
 
 Reperekce Books. — Any of the numerous excellent manuals on 
 Physiology ; History of a Mouthful of Bread, and The Servants of the 
 Stomach, by Jean Mace ; Appleton's Health Primers ; Hooker's Child's 
 Book of Nature ; articles Digestion, Respiration, etc., etc., in Appletons' 
 American Cyclopaedia. 
 
 ARITHMETIC. 
 
 Suggestions for mental and written arithmetic, as in 
 preceding grades. Also 
 
 1. Definitions pertaining to fractions should be retained 
 and occasionally rev^iewed. 
 
 2. The exact nature of decimal fractions should be ex- 
 plained and illustrated ; also the meaning of the word 
 decimal. Show that decimal fractions may be used like 
 common fractions by writing the denominator. Illustrate 
 by the decimal notation, showing that whole numbers 
 greater than 9 are also expressed decimally. 
 
 3. The illustrations may embrace the following: 1. 
 How to write decimals, as 7-tentlis, 7-hundredtlis, 7 thou- 
 sandths, T-ten-thousandths, etc. 2. Show that the n^i- 
 m-erator., as in common fractions, is written first. 3. 
 Show that the "decimal point" and the ciphers, M'hen 
 used, are only required to indicate the denominator. 4. 
 In reading decimal fractions the pupils should be cau- 
 tioned to avoid such expressions as " tens of thousands" 
 for ten-thousandths^ "hundreds of thousands" for hun-
 
 72 FIFTH GEADE. 
 
 dred-thousandths, etc., etc. In connection with the read- 
 ing of such fractions, pupils should be trained to recognize 
 readily the comparative value of different fractions ; as, 
 that .3 is greater than .0987, or .01 than .009596, etc. 
 They may also be made to perceive readily the wpproxi- 
 inate value of decimals as compared with simple common 
 fractions ; as that .7634 is a little more than f ; that .8741 
 is somewhat less than f, etc. Previous to this, however, 
 it is well to teach the exact value of certain decinaal ex- 
 pressions; as, .75 = f, .125 = \^ .375 = f, etc. These 
 exercises will seiwe to render the subsequent work of the 
 pupil intelligible. 
 
 SYLLABUS OF TOPICS. 
 
 Reading decimal fractions. 
 
 Exercises in telling how many places are necessary for a given de- 
 nominator, and vice versa. 
 
 Writing decimal fractions. 
 
 Reduction of decimal fractions : 
 
 1st. By inspection., with analysis as in common fractions. 
 
 Examples, mental and written. 
 
 .3 to .GO'S, to .OOO's, etc. .15 to .OOOOO's. 
 
 .3 to .O's, to .GO'S, to .OGG's, etc. 7.3 to .G's, to .OGO's, etc. 
 
 Reduce .700 to lowest decimal tei'ms. 
 
 Reduction of common fractions to decimal fractions. Give analysis. 
 
 Use principle — f of 1 = J of 3. 
 
 Reduce^! to .O's— | of 1 = i of 3 = i of 30 tenths = .7^. 
 
 Similarly, 3 is how many tenths of 7 ? 
 
 Note. — Pupils should be accustomed to read decimal fractions, es- 
 pecially hundredths (in subsequent grades applied to per cent.), so as to 
 include outstanding fractional parts, where there are any. 
 
 Example. — Reduce -^ to .OG's. 
 
 -A- = -jL of 4 = tV of 4. GO (four hundred hundredths) = .36 t^. 
 
 Reduce MS to a decimal : §^1} = §| = | = ^ of 3 = i of 3.00 = .75. 
 
 Note. — Give example to show that common fractions in their lowest 
 terms can be made entirely decimal only when every prime factor of 
 their denominators is either 2 or 5. In the general work of the class,
 
 ARITHMETIC. 73 
 
 pupils should rarely be required to continue the division beyond three 
 or four places. 
 
 Uedacing Decimal Fractions to Common Fractions in tlceir Loirent 
 Terms. 
 
 Rule. — Write the fraction as a common fraction and reduce to lowest 
 terms. 
 
 Examples: .025, .4125, .87500, 14.125. 
 
 Examples: .07t, .3i, .66|, 5.11^, .87i. 
 
 Examples of this class may be solved very simpl}' as follows : 
 
 .V*7 — • 7 ■"^ IdJI — 7 ■*■ 100 — 14- 
 
 Note. — Pupils should be made thoroughly familiai- by rapid mental 
 exercise, usually without analysis, with the decimal expressions for 
 halves, 3ds, 4ths, 5ths, 6ths, 7ths, Sths, 9ths, llths, 12ths, and vice 
 rersa, using preliminary reduction to lowest terms whenever possible, 
 
 SiS 111 ~\~2 1 Hj 6XC< 
 
 Addition of Decimal Fractions. 
 
 Examples: Add .2, .05, .008, .7283. Add .0005, .97, .0101, etc. 
 
 Examples : Give mixed numbers. 
 
 Note. — Explain, as in common fractions, b\- principle of least com- 
 mon denominator; the necessary additional ciphers may be "under- 
 stood " in the solution. 
 
 Sahtraction of Decimal Fractions. 
 
 Examples : .1 - .075 ; 1.001 - .01009, etc. 
 
 Explain as in common fractions, with the same analysis. 
 
 Multiplication of Decimal Fractions. 
 
 Note. — Do not give large denominators ; use tJie brief rule of common 
 fractions. Cases as in common fractions : 
 
 1. When a fraction or a mixed number is to be mtdtiplied ; as, 
 4 times .75, 17 times 8.047, 100 times 9.625, 1,000 times 1.3, 
 Value of 13 barrels at $8,375 a barrel ? 
 
 2. When a, fractional part is to be taken ; as, 
 .4 of .83, .4 of 75, .4 of 8.75. 
 
 How much is .7 of $38.45 ? .079 of $120 ? .OOJ of $160.48 ? 
 Value .179 of ton @ $92 a ton V at $92.87i a ton ? 
 
 3. Combinations of the 1st and 2d cases; as, 
 3.4 lbs. at 79 cts. a lb. V $.79 x 3.4 ; 
 
 8 cwt., 75 lbs. @ $2.47 a cwt. ? $2.47 x 8.75. 
 Note. — As preliminary to 2d and 3d cases, give mental exercises in 
 finding the product of two decimal denominators, as lOths by lOths, how 
 many decimal places ? lOOOths by lUOths, how many decimal places ? 
 etc. 
 
 4
 
 74 FIFTH GRADE. 
 
 Examples of cases involving reduction : 
 
 .024 X .15= ? Product of numerators, 24 x 15 = 360, the new- 
 numerator ; 1000 X 100 = 100,000, the new denominator. Ans. .00360 
 = in loweist decimal terms, .0036. Why cross off the last ? To di- 
 vide both terms by 10. 
 
 Note. — Many questions are as well solved by the application of a 
 principle in common fractions, as follows : 
 
 0.79 of $14.83 = .001 of 79 times $14.83, etc. 
 
 Use or not, as may be judged expedient. 
 
 Division of Decimal Fractions. 
 
 There are two cases : 
 
 1. When the divisor is an integer— 
 
 7h-8, 8-1-7, 6h-5, 6-^-120, 7.2 -r- 6, 3.6-^-120, 3.6 -- 100, etc. 
 Put question in several ways : 1st. Divide 7.2 by 6. 2d. How much is 
 ^ of 7.2 ? 3d. How many times is 6 contained in 7.2 ? etc. 
 
 2. When the divisor is, or contains, a decimal fraction : 
 
 6 -^ .03, .8 ~ .005, .004 -r- .8, .0036 ^ .024, 7.2 -^ .009, 8 -^ 5.45, 
 3 ^ 7.203, .2 -=- 8.75, .3006 -h 7.4, 8.5 -r- 9.78, 8.638 -f- 9.5, 
 8.638 -T- 4.3, etc. 
 
 All examples under this head are reducible to the first case by multi- 
 plying divisor and dividend by the same number, or by moving the de- 
 cimal point of the divisor to the right until it becomes an integer, and 
 moving the decimal point of the dividend to the right a corresponding 
 number of places. 
 
 Note. — As a substitute for the above the following may be employed 
 if preferred : Show that, when the dividend contains a less number of 
 decimal figures than the divisor, the method of reducing to a common 
 denominator, or sa?ne denomination, may be applied. Also show that, 
 when the dividend contains more decimal figures than the divisor, the 
 number of decimal places in the quotient must be the excess of tliose in 
 dividend over those in divisor. 
 
 Applications. — The most important applications of decimal fractions 
 will be found in Federal money. Simple combinations with common 
 fractions should occasionally be made ; also simple combinations of two 
 or more of the rules of decimal fractions. 
 
 Use the principles of cancellation and redaction to common fractions 
 whenever they will simplify the operation. It would be a defect, in a 
 class that had completed multiplication of decimal fractions, to go 
 through the long process when finding .125 of a number. If properly 
 taught, they will know the value of that fraction to be \, and will pro- 
 ceed accordingly.
 
 ARITHMETIC. 75 
 
 Examples in finding what decimal fraction one number or quantity is 
 of anotlier ; especially l»ow many hundredths — use only small amounts 
 or very simple examples : 
 
 8c.-, liow many hundredths of 64c. ? $7.25, how many hundredths of 
 $9.75 ? 
 
 Solutions as follows : 
 
 1st. What common fraction : -/j = ^ = ? ^f f = §^ =r ? 
 
 2d. What decimal fraction : \ — .125 or .12^ ; %% = .74^. 
 
 The last case is the extreme limit of " applications " in this grade, in 
 which the example should never take the following involved form of 
 statement: "Bought for $9.75, sold at $7.25 profit, how many hun- 
 dredths did I gain ? " 
 
 General Remarks. — It must not be forgotten that the teaching of prin- 
 ciples and their most common and useful applications is the principal 
 matter in the study of common and decimal fractions. Therefore, 
 
 AVOID LONG EXAMPLES. 
 
 Reduction of Integral Denominate Numbers. 
 
 In the reduction of integral denominate numbers, only the most prac- 
 tical of the weights and measures should receive attention in this 
 grade. Teach in the following order : Avoirdupois weight, Troy weight. 
 Linear measure, Surface measure, Solid measure, Dry and Liquid meas- 
 ures. Time. See that the tables are not only memorized, but under- 
 stood. 
 
 Reduction Descending. — Why so called. — Denominations always writ- 
 ten. — Do not allow pupils to " add in " by a separate line ; it greatly 
 increases the work and the time, and indicates mental feebleness. Ex- 
 plain by any process which makes the multiplier an abstract number. 
 The "adding in" is identical with that in the reduction of mixed 
 numbers. When the question will allow it, insert frequently the find- 
 ing of the value at a given price. 
 
 Reduction Ascending. — Best taught and understood in immediate 
 connection with reduction descending ; at first by reviewing the same 
 example. Do not allow long division by divisors less than 13 ; nor if 
 cutting off Os will change to short division. 
 
 Explain by any process which will clearly account for the denomina- 
 tions of the successive quotients and remainders. 
 
 The necessary analyses have already been given in the preceding 
 grades. 
 
 Give examples in finding the quantity purchased for a given sum of 
 money at a given price for some small quantity, such as a pint, an 
 ounce, a foot, etc., etc.
 
 76 
 
 FIFTH GRADE. 
 
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 GEOGRAPHY. 
 
 GEOGEAPHT. 
 
 North America. — The outline of ISTorth America will 
 include its boundaries ; area and population in round num- 
 bers ; simplest physical divisions ; the names and bound- 
 aries of its countries ; a few facts in regard to Greenland 
 and Iceland ; Canada — the names and boundaries of its 
 Provinces and Territories, its chief rivers, lakes, and other 
 bodies of water, chief capes, mountains, and islands, its 
 climate, people, form of government, language, chief ex- 
 ports, its capitals, and other lai'ge or important cities and 
 towns. Corresponding points in regard to Mexico as a 
 whole, the States of Central America, and the islands of the 
 West Indies. In the simplest and most general waj, the 
 leading articles, if any, exported to the United States, and 
 the articles we send in exchange. 
 
 United States in Detail. — 1. In teaching the geography 
 of the United States, it is particularly important that the 
 time of the pnpil be not exclusively taken up by the study 
 of mere local details — by learning the several courses, etc., 
 of long lists of rivers, and the exact situation of still longer 
 lists of towns. A certain, but limited, amount of local 
 geography is indispensable as a basis for the more import- 
 ant descriptive geography. 
 
 2. The necessary local geography embraces the names of 
 the several States and Territories and their division into 
 several groups, as New England, Middle, etc., etc. ; their 
 boundaries or relative positions ; their important rivers, 
 lakes, bays, capes, islands, mountain ranges and peaks ; 
 the capital of each State, and a few of its other cities or 
 towns, if of any importance. All these should be care- 
 fully learned as a basis for the subsequent portions of the
 
 78 FIFTH GEADE. 
 
 study. For review of local geography, the rapid sketching 
 of maps from memory is the best general test. 
 
 3. The descrijttive geograjphy should include the sim- 
 plest physical outlines of the country as a whole ; the great 
 mountain ranges, plateaux, and plains ; the drainage on 
 the Atlantic slope by single rivers, and by extensive com- 
 plex systems in the remainder of the country ; the cli- 
 mate, with its modifications in the several sections, as 
 cold or hot, wet or dry ; the leading industries and the 
 staple agricultural, mineral, and manufactured productions, 
 and their dependence upon the physical conditions. 
 
 4. Add to this a simple and very brief outline of the gen- 
 eral and State governments, the population, its four races 
 and their distribution ; the great commercial routes, na- 
 tural or artificial, and the cities, as the centres of manu- 
 facturing and commercial industry. 
 
 5. The descriptive geography of individual States or 
 Territories may then, in great part at least, be deduced 
 from a consideration of these general facts. All tiresome 
 sameness and repetitions will thus be avoided, and the 
 pupil will be made to appreciate the real importance of 
 the study. 
 
 HISTORY OF THE UNITED STATES. 
 
 General Suggestions. — 1. The leading purpose of this 
 study is, that the pupil may understand the origin, char- 
 acter, and condition of the nation of which he is a part, 
 and that he may be fitted for an intelligent exercise of his 
 duties and responsibilities as a citizen. 
 
 2. It is obviously impossible to treat so comprehensive 
 a subject exhaustively : the immaturity of the pupil's mind 
 and the pressure of other studies alike forbid. Yet the
 
 HISTORY OF THE UNITED STATES. 79 
 
 leading facts and principles may be readily comprehended 
 and remembered, and the outline which he is to retain 
 may be made coherent and definite. 
 
 3. To this end a hrief (jeneral outline should be carefully 
 fixed in the minds of the pupils of the Fifth Grade, and 
 be reverted to freqiiently in the remews in all the higJoer 
 grades. This outline can be given most expeditiously and 
 eificiently by means of oral instruction and the use of the 
 map : it should be very brief and simple, all detail being 
 reserved for subsequent study. 
 
 4. The following outline is presented as illustrative of 
 this suggestion. Its modification, or the substitution of an- 
 other in its place, is left entirely to the discretion of the 
 Principal. 
 
 Brief General Outline. 
 
 1. The people of the United States, excepting the Negroes, Indians, 
 and Chinese, are of European descent. 
 
 2. Four hundred years ago our ancestors knew nothing of the exist- 
 ence of this Continent. 
 
 3. Spain, guided by Italian genius, led the way to its discovery, ex- 
 ploration, and colonization. 
 
 4. The first permanent English settlement within our limits was not 
 effected until more than a century after the voyage of Columbus. In 
 the interval, Spain and Portugal had possessed themselves of the shores 
 and islands of the Mexican Gulf, and of nearly all South America. 
 
 5. For a century and a half the English colonies were confined to a 
 narrow strip east of the Alleghanies. 
 
 6. Spanish slavery exterminated the Indians of the West Indies. 
 This led directly to the opening of the African slave trade, and in- 
 directly to the introduction of slaves into our own country. 
 
 7. The colonists had wars with the Indians in whose country they had 
 settled, and with the neighboring French colonists. The English were 
 successful and took possession of the territories formerly controlled by 
 the French. 
 
 8. Less than a century ago all European settlements were yet de- 
 pendent colonies.
 
 80 FIFTH GKADE. 
 
 9. The necessities of distant colonial settlements gradually developed 
 in the English colonies a spirit of self-reliance and of political freedom, 
 and a system of local and elective self-government. 
 
 10. The expenses of the French wars left a heavy deht and led to un- 
 usual taxation. A tyrannical system of taxation led to the War of Inde- 
 pendence, which fixed the national boundary at the Mississippi. The 
 colonies became States. 
 
 11. The present form of government (the Constitution) was established 
 soon after the close of the war, nearly a century ago. 
 
 12. The number of States has been greatly increased by immigration 
 and emigration. The population and wealth have vastly increased. 
 
 13. By purchase, and otherwise, the national territory has been ex- 
 tended to the Gulf of Mexico, and to the Pacific and Arctic oceans. 
 
 14. Since the War of Independence there have been three important 
 wars: 1, a war with England, in defence of naturalized citizens, and 
 in vindication of the rights of neutrals ; 3, a loar toith Mexico, resulting 
 from our annexation of Texas ; 8, a great civil war, arising in part 
 from questions originating in our colonial history, and in part from 
 more recent causes. 
 
 5. The oral lessons in History given to the Fifth and 
 Fourth Grades should be familiar and conversational. 
 In the higher grades the lessons from text-books should 
 be assigned by topics and not by pages. 
 
 6. All verbatim recitations of sentences and paragraphs 
 should be strictly forbidden, and the pupils should be re- 
 quired to state the facts in their own language. 
 
 7. Only such dates should be committed to memory as 
 are indispensable as landmarks in history. The sequence 
 of events, rather than the precise date of each, is what is 
 usually necessary. 
 
 8. Maps should be used in all grades, whenever the 
 subject admits of their use. 
 
 9. Historic episodes, however interesting, should not 
 receive the careful study given to the essential narrative. 
 The stories of Juan Ponce de Leon, the conquest of Mex- 
 ico, De Soto's Expedition, John Smith, Pocahontas, the
 
 HISTORY OF THE UNITED STATES. 81 
 
 Salem "Witchcraft, etc., should indeed be carefully read, 
 and, as far as may be necessary, explained ; but, unless 
 great care is taken by the teacher, the pupils will be apt 
 to conceive that these are the most important portions of 
 the history. 
 
 10. Important incidental allusions to European history, 
 such as the rise of the English Puritans, the expulsion of 
 the Stuarts, the French Revolution, etc., should be care- 
 fully but briefly explained. Great care must be taken 
 throughout to state all facts in such a manner as not to 
 wound religious or political sensibilities. 
 
 11. Reviews of the portion already taught, with fre- 
 quent references to the hrief general outline^ are of the 
 highest importance. These reviews should take three 
 distinct forms : the Chronological, the method usually fol- 
 lowed in the text-book ; the Biograjpliical, requiring the 
 pupil to state all that has been learned in regard to par- 
 ticular individuals ; and the Geograjyhical, requiring a 
 statement of all important facts relating to the history of 
 a locality. Many of the topics treated by the second and 
 third of these methods necessarily become cumulative. 
 For instance, the facts relating directly to Washington 
 will be gathered from at least three distinct and important 
 periods in our history. A connected statement of the im- 
 portant events that have taken place in Philadelphia, or 
 in the valleys of the Hudson and Lake Champlain, or in 
 the State of Virginia, will necessarily cover a large part 
 of the general subject in the higher grades. Such state- 
 ments must of course be brief, and frequently will be 
 mere synopses. 
 
 Many of these i-eviews, and certain parts of the regular 
 recitations, may be made spirited general exercises for the 
 whole class by the use of the slate or paper. The writing
 
 82 FIFTH GRADE. 
 
 of the few essential dates, the sequence of important 
 events, the names of important individuals, etc., are in- 
 stances. The narrative reviews will necessarily be for the 
 most part oral. 
 
 It will be observed that the system of reviews above 
 suggested must, if faithfully carried out, result in a thor- 
 ough unifying of the general subject in the mind of the 
 pupil.
 
 FOURTH GRADE. 
 
 General Outline. 
 
 1. liANGtTAGE LESSONS. — Beading of the grade of a Fourth Reader 
 (a different book from that of the Fifth and the Sixth Grade) : oral 
 lessons on common minerals and metals : compositions as before : spell- 
 ing, meaning, and use of words as before — at least 150 additional 
 words, and review of all previously taught : exercises in prefixes and 
 suffixes continued : English grammar (without text-book)— the construc- 
 tion of sentences, with a view to develop a knowledge of the parts of 
 speech, and to illustrate the terms subject, predicate, and object. 
 
 2. Arithmetic. — Written and mental. — Denominate numbers com- 
 pleted, with practical applications. 
 
 3. Geography. — Review of the United States ; other parts of North 
 America in detail, and Asia and Africa in outline. 
 
 4. History of the United States (without text-book). — Outline with 
 greater detail. 
 
 5. Penmanship. — Writing in copy-books continued ; practice in large 
 and small writing. 
 
 6. Drawing. — On paper, illustrated on blackboard, from dictation 
 and from chart. 
 
 Draw the spiral. Two varieties of conventional lobed leaves and two 
 flowers. Combinations of the leaves and flowers of this grade in a 
 geometric form. Two examples of bi-symmetrical ornament, mediaeval 
 and moresque. Two original examples of surface covering, using the 
 leaves or flower forms of Fifth Grade. One vase, not less than five 
 inches, without perspective effect, ornamented, using the spiral.
 
 INSTRUCTIONS AND SUGGESTIONS. 
 
 LANGUAGE. 
 
 The general instructions and suggestions for 
 Eetuding, found on page 20 ; those for 
 Spelling, on page 29 ; those for the 
 Meaning and Use of Words, on page 31 ; those for 
 Composition, on page 28 ; those for 
 Prefixes and Suffixes, on page 61 ; and those for 
 History, on page 78, are to be taken as belonging 
 to this grade also. 
 
 ORAL LESSONS. 
 On Minerals. 
 
 1. The " General Suggestions " found on pages 22-25 
 are to be taken as indispensable to this grade also. 
 
 2. In no other department is it so completely within 
 the power of the teacher to present the subject to thepe?'- 
 ceptions of the pupils while in the class-room. Though the 
 objective method is peculiarly applicable to this branch of 
 oral lessons, no other branch requires so large a share of 
 imparted information. This, however, should not be 
 given by the teacher until nothing more can be drawn 
 from the pupils. Draw out first what they can readily be 
 led to discover or perceive, and then any other facts that 
 they may remember to have read or to have heard.
 
 LANGUAGE. 85 
 
 3. Points that should be specially looked np and prepared 
 
 for are suggested in the syllabus given below. A sufficient 
 amount of detailed and very valuable and interesting in- 
 formation may readily be culled from Dana's "Manual 
 of Mineralogy " and similar text-books, and particularly, 
 under their several heads, from articles in Appleton's and 
 other cyclopaedias. See, for instance. Salt, Sulphur, Mica, 
 etc. 
 
 Read also in Buckley's *' Fairy Land of Science " the very 
 interesting and instructive articles, "A Drop of Water on 
 its Travels ;" " The Two Great Sculptors, Water and Ice ; " 
 " Histoiy of a Piece of Coal," and Tyndall's " Matter and 
 Force." 
 
 4. What has been said in preceding grades, as to the 
 propriety or necessity of attempting only a part of the 
 subject, is equally applicable here. Make such selections 
 from the syllabus as may be thought advisable. W^hat is 
 done should be systematic. Do not attempt to treat any 
 topic exhaustively. A large part would not be understood 
 or remembered, and valuable time would be misapplied. 
 A properly prepared note- book (see page 25) is indispen- 
 sable. 
 
 5. Be particular to avoid reviewing a topic so often as 
 to destroy the pupil's interest. As these exercises are to 
 be simply lessons on minerals^ and not in systematic min- 
 eralogy, the terms form., structure, cleavage, hardness^ 
 weight, color, lustre, etc., need be used only occasionally, 
 and as the topic may make necessary. When any such 
 term is used it should be carefully illustrated and explained, 
 but not defined. 
 
 6. Begin with Minerals — rocks, as mineral aggregates, 
 to be considered afterward. A clear perception of the 
 general properties of minerals may readily be given by
 
 86 FOURTH GEADE. 
 
 commencing with ivater, as %oater — ice — steain. Air 
 should follow next, so as to lead the way to some idea of 
 the vast amount of gas locked up in the rocks. 
 
 7. As a preparatory step, lead the pupil to form some 
 idea of the variety of forms of crystals, by briefly com- 
 paring, objectively, of course, salt^ alum, 'borax, quartz, 
 mica, 7'ock candy, and other easily procurable crystals, all 
 of which should be carefully labelled. I tis not here nec- 
 essary to name any of the substances to the pupil. 
 
 8. In treating of ice, draw attention, not by telling, hut 
 hy jprojper questioning, to its transparency, color, lustre, 
 weight, solidity, hardness, fracture, and especially to the 
 needle-like crystals, which can be so readily shown in ice- 
 films when water is beginning to freeze, and in the frost 
 flowers on the window-panes. Lead him now to see that 
 a block of ice, or a snow-bank, must be made up entirely 
 of such crystals, even though their individual forms are 
 no longer perceptible. The application to other solid 
 masses is obvious. 
 
 9. Show that many fluid substances, as in the case 
 of water, upon losing their heat, crystallize into definite 
 solid forms under favorable conditions, as in melted sul- 
 phur, and in the beautiful zinc crystals which cover the 
 surface of so-called galvanized iron, a piece of which is 
 an easily procured and a desirable "object." A sheet of 
 common tinned iron (tin) after being heated and then 
 washed with nitro-muriatic acid, reveals even more brilliant 
 crystals. Dwell somewhat upon these easily shown phe- 
 nomena of crystallization, and draw special attention to the 
 mysterious and indestructible force which somehow re- 
 builds the molecules of water or of salt into the same 
 
 forms, no matter how often the ice may be melted or the 
 salt dissolved. Few topics are better fitted to awaken
 
 LANGUAGE. 87 
 
 thought and to develop in the young mind a permanent 
 desire to know. 
 
 10. It will also be profitable, as well as interesting, to 
 show that crystals are often formed from substances iji 
 solution. Alum, salt, or borax will furnish ready and 
 simple means of illustration. With sulphur, salt, zinc, 
 alum, etc., as with ice, the crystals may become so massed 
 as to be no longer individually distinguishable. 
 
 11. The jprincijpal jpoints to be fixed in such a lesson 
 on crystals are, that there are many Mnds of crystals, 
 some formed from liquids which have become solid by a 
 loss of heat, and others that were deposited from solidiori. 
 These simple facts will be found of great importance in 
 further treating the subject. They should not be im- 
 parted by telling, but by means of the pupil's own ob- 
 servation. 
 
 12. The pupil is then prepared to compare ice with a 
 quartz crystal, which should be presented, but not at jirst 
 named — compared first as to the resemblances, then the 
 differences. When the pupils can be made to furnish no 
 more ideas, the teacher should state where quartz is 
 found, its relative abundance, geological importance, eco- 
 nomic uses, etc. Be particular not to introduce an un- 
 explained term — such as the NA:yiE of any rock or mineral, 
 as gneiss, or gypsum. The name means nothing until 
 explained as quartz has been. A few other forms of 
 quartz may then follow, each treated in the same way, 
 and each in its turn briefly compared with those that have 
 preceded it. This will constitute an excellent review, and 
 will thoroughly fix what has been already taught. 
 
 13. That so many apparently different substances can 
 possibly be only different forms of one and the same sub- 
 stance, quartz, may be readily illustrated by referring to
 
 88 FOURTH GRADE. 
 
 sugar^ another crystallizing substance and well known to 
 the pnpil under many forms, solid and liquid. 
 
 l-i. Encourage the pupils to look for and bring in speci- 
 mens which they think to be of the same character as 
 those studied. Let them tell why they think they are the 
 same. Let others tell why they think they are not, 
 
 15. Having thus treated of quarts, next consider, in the 
 same way, feldspar and Tyiica. The pupils will now be 
 ready to consider a rock. Suppose it to be gneiss or 
 granite. Let the pupils look for the minerals in it [a 
 cheap single lens as a magnifier will often be of service]. 
 Then consider the texture, structure, where found, uses, 
 etc. The mineral hornblende and its important varieties 
 may then follow, and after that the rock syenite. 
 
 16. A list of the more important topics suitable to this 
 grade and taken mostly from Dana, is subjoined. From 
 this the teacher will make such selections as the Principal 
 may direct. A few of these are also given below, with 
 brief synoptical notes, for the purpose of illustrating a 
 proper form of note-book. 
 
 17. The qualities, sources, and uses of common minerals 
 and metals should form the chief substance of these les- 
 sons : 
 
 Minerals. 
 
 Water, air, carbon, diamond, coal (anthracite, bituminous), lignite, 
 jet, plumbago, amber, petroleum, asphalt, sulphur, saltpetre, salt, borax, 
 lime, gypsum, alabaster, chalk, stalagmites, lime-stones, crystalline and 
 compact marbles, quicklime, hydraulic lime, alum, talc, soapstone 
 (French chalk), meerschaum, hornblende, corundum and emery, feld- 
 spar, garnet, mica. 
 
 Metals. 
 
 Mineralized (ores) or Native — Ores of tin, iron, nickel, zinc, lead, 
 mercury, copper, gold, silver, platinum. Enter into no details of Metal-
 
 LANGUAGE. 89 
 
 lurgy— a few simple facts in regard to smelting, fluxes, etc., will not he 
 out of place. The economic uses of these metals and the poisonous prop- 
 erties of some of them should receive very careful attention. 
 
 Rocks. 
 
 As single Minerals. — Example, pure Limestone. As compounds — 
 granite or pudding stone. Rocks as crystalline and non-crystalline ; 
 stratified and unstratified ; aqueous, igneous, and metamorphic. 
 
 Characters and uses of important Rocks. — Granite, syenite ; gneiss, 
 mica — slate, talc, steatite, trap, basalt, lava, pumice ; slate ; quartz rock, 
 buhr-stone, sandstones, conglomerates ; limestones, marbles ; sand, and 
 clay. 
 
 Such of these rocks as are found on Manhattan Island, and in its vicin- 
 ity, or as have important uses in paving, flagging, building, etc., should 
 receive particular attention. 
 
 Synoptical Notes from Note-Book. 
 
 Water as a mineral. Solid, liquid, gas Csteam). Effects of heat and 
 of lo.<s of heat. Properties as a mineral ; transparent, tasteless, odor- 
 less. As a solvent ; uses to vegetable life ; to animal life ; to mankind ; 
 found in all rocks and soils ; small underground streams ; wells and 
 springs. Miscellaneous : droughts, floods, clouds, rain, rainbow ; bene- 
 ficial and destructive. 
 
 Nifkel. — A metal, silver white, tenacious, malleable, ductile, mag- 
 netic, similar to iron, but not easily rusted (oxidized), will 7rfW, can be 
 plated upon other metals as silver is, therefore very useful. Generally 
 found in certain ores of copper, iron, and arsenic. Principal supply 
 from New Caledonia. Found also in many parts of Europe and in 
 Pennsylvania. Uses : German silver, an alloy of nickel, copper, and 
 zinc ; nickel coins, five cent and three cent, are three-fourths copper 
 and one-fourth nickel ; nickel cent only one-eighth nickel ; nickel plat- 
 ing, by battery and otherwise— bright surface is pure nickel. (From 
 articles Coin and Nickel in Appletons' Amer. Cycl.). Objects, three 
 cent, five cent, and one cent nickels ; pieces of nickel, plated wai-e ; 
 German silver. Ore. 
 
 Clay. — Qualities: plastic (when moist), tough, tenacious — absorbent 
 when dry - colors of — peculiar smell and taste. Found in many places 
 and in most countries. Many kinds according to purity. Formed from 
 granite and other rocks by the pulverizing action of frost and water. 
 Fine particles of feldspar and quartz — settled down from water. Ordi- 
 nary clay is brick clay — red color of bricks and flower-pots from iron
 
 90 FOURTH GRADE. 
 
 rust in clay — Milwaukee bricks are straw colored, no iron. If lime is 
 in the clay a brick easily melts. Other kinds and uses. Fire clay for 
 fire bricks ; potter^ s clay for common crockery ; fuUer^s earth for dressing 
 cloth ; Kaolin or porcelain clay, mostly pure feldspar. Clay contains the 
 rust or oxide oi an exceedingly valuable and useful metal called alumin- 
 ium, white, brilliant, tougher, and stronger than steel, but much 
 lighter ; can be welded, soldered, and plated ; makes valuable alloys. 
 3Iiscellaneous. — Most New York bricks from Hudson River clay beds. 
 Tiles, earthenware, stoneware — alum obtained from clay — aluminium 
 from alum — clay used in clarifying sugar ; adobe houses. Most impor- 
 tant use — most valuable part of fertile soils. Antiquity, variety, and 
 importance of ceramic art. (From articles Ckiy and Pottery, Dana's 
 Mineralogy, and in Appletons' Amer. Cycl.) Objects — lump of clay, 
 pieces of various kinds of bricks, tiles, pottery, etc. 
 
 GRAMMAE. 
 
 Grammar is the science of the sentence • therefore, the 
 fundamental idea to be imparted is, what constitutes a sen- 
 tence. This information must be imparted bj means of 
 oral lessons. Ideas involved in definitions should be de- 
 veloped before the pupils are required to commit such 
 definitions to memory. 
 
 Let a short sentence be written on the slate or black- 
 board, and then let the pupils be made familiar vt^ith the 
 relations of the words used as subject, verb or predicate, 
 and adjuncts. The distinctions comprehended in the parts 
 of speech can all be successively taught in this way, and the 
 pupil be enabled readily to point them out before he is re- 
 quired to say what a noun or pronoun, or verb, and so forth, 
 is. The learning of the definitions will be easily accom^ 
 plished as he proceeds. Thus, when the teacher presents 
 the sentence, " Industrious pupils learn very rapidly," the 
 pupil is made to discover, first, the principal parts — stdjject 
 and verb, or simple predicate • next, that industrious is
 
 GRAMMAR, 91 
 
 added to pupils, rapidly to learn, and very to rapidly. 
 The pupil then knows that industrious being an adjunct 
 of a noun is an adjective; that rapidly being an adjunct 
 of a verb, is an adverb, and that very being an adjunct of 
 an adverb is also an adverb. This instruction can be sup- 
 plemented by requiring the pupils to construct sentences 
 of a similar kind ; as sentences containing a simple subject 
 and predicate — sentences containing a subject and adjuncts 
 with a simple predicate — sentences containing a subject 
 and predicate, with adjuncts of both. 
 
 The sentences presented should at first be carefully 
 classified, so that no difficulties may be presented which are 
 beyond the pupils' ability or actual attainments to solve. 
 In grammar especially should the instruction be systematic 
 and logical. 
 
 The sentences required to be studied in this grade in- 
 clude : 
 
 1. Sentences with a simple subject and a simple predi- 
 cate ; 2. Those with simple word adjuncts of either subject 
 or predicate or both ; 3. Those with simple phrase adjuncts 
 (so as to teach the preposition). 
 
 Of course, the study of grammar as prescribed in this 
 grade does not supersede the "exercises for correction," 
 required in all the grades. These exercises, however, by 
 degrees lose their empirical character and become scientific. 
 
 Outline. 
 
 Teach subject, predicate, ol^ect, noun, verb, adjective, advei'b, pronoun, 
 preposition, and conjunction ; the distinction between transitive and in- 
 transitive verhs ; case and number (best exemplified in the pronoun). 
 Make the sentence the basis of instruction. As a simple preliminary 
 step in the important matter of the arrangement of words in a sentence, 
 direct attention to the order in which the principal parts usually appear ; 
 namely, 1, subject ; 2, predicate ; 3, object. The simple sentence, 
 as a rule, does not admit the comma.
 
 92 FOURTH GRADE. 
 
 AKITHMETIC. 
 
 Written and Mental. — Suggestions as in preceding 
 grades, and also the following : 
 
 Mental. — 1. For the purpose of review, brief examples 
 in fractions, both common and decimal, should be em- 
 ployed, so as to test, and more thoroughly fix in the pupil's 
 mind a knowledge of the principles and applications of 
 fractions as taught in the preceding grades. The im- 
 provement made by the pupils in accuracy and rapidity, 
 as well as in the ready application of arithmetical princi- 
 ples to particular cases involving an exercise of the judg- 
 ment and reasoning powers, should be progressive from 
 grade to grade, and should be carefully tested in the 
 mental work. 
 
 2. The special province of this grade being Denominate 
 N'umbers, the exercises, both mental and written, should 
 deal largely with the applications of fractions to that class 
 of numbers, including Federal money, and should, of 
 course, combine practice in all the essential tables of 
 weight, measure, etc. 
 
 3. The review of the analyses previously taught should 
 be systematic and thorough, but should not consume a 
 large part of the time of the pupils. 
 
 Written. — 1. The arithmetic specially prescribed in 
 this grade is of a practical character, perhaps more geuer- 
 all}^ so than in any of the other grades of the course. All 
 that precedes has been, to a considerable extent, a pre- 
 paration for the work of this grade, and will be found 
 involved in it. In view of the great importance of the 
 subject, and in order to render the requirements as definite 
 as possible, the syllabus given below presents, first, certain
 
 ARITHMETIC. 93 
 
 preliminary considerations ; and, second, specific directions 
 as to the extent of the field comprehended in the grade. 
 
 2, The whole subject of conapoiind denominate numbers 
 is strictly utilitarian. Practical utility should, therefore, 
 be the controlling element in all the exercises employed. 
 The daily necessities of the house, the shop, the market, 
 etc., indicate the general character of the selections to be 
 made. These will furnish at least as good mental disci- 
 pline in calculation and analysis as those of a less severely 
 practical character. 
 
 3. The average time which pupils in this grade can yet 
 spend in school is short. Secure, therefore, the essentials 
 first. lieview and test thoroughly the indispensable basis 
 — the tables. (See Grades 8 and 7.) Train your pupils 
 to work with reasonable rapidity. Carefully avoid long 
 and complex examples. Avoid all things obsolete or 
 obsolescent. Keep a clear record of the points you have 
 covered; it will assist in the reviews and in the examina- 
 tions. Do not dwell so long on Eeduction as to omit 
 important practical points in other rules. AVith the tables 
 commence Keduction. See that the tables are not only 
 memorized but understood ; many of the tables have al- 
 ready been reviewed and applied to the reduction of in- 
 tegral denominate numbers in the Fifth Grade. 
 
 SYLLABUS. 
 
 Fractional Denominate Numhers. — Eeject all examples in addition, 
 subtraction, multiplication, and division of fractional denominate num- 
 bers. In reduction there are but tico cases, and the second of these is 
 simply the converse of the first. Each divides into two varieties, in 
 one of which the fraction is common and in the other decimal, but the 
 principle applied in working is the same. 
 
 Be careful to select only those denominate numbers in which such 
 fractional quantities are likely to need consideration, chiefly sterling 
 monev.
 
 94 FOURTH GRADE. 
 
 I A. f f of a bushel to pecks, quarts, etc. 
 B. .673 of a £, how many shillings, pence, etc., 
 or dollars and cents ? 
 
 f A. 7 cu. ft. 95 cu. in., what common fraction of 
 I a cubic yard ? 
 
 '• p q 1 ! B. 15 cwt. 38 lbs. are what decimal fraction of a 
 
 ~' ■ I ton V 
 
 I £8 14s. 9-id. are how many dollars and cents 
 L (at $4.87) ? 
 
 Addition and Subtraction of Denominate Numbers. — Subtraction best 
 taught in connection with addition. 
 
 Multiplication of Denominate Numbers. 
 
 Division of Denominate Numbers. — Note the distinction between the 
 different cases. 
 
 Note. — Suggestions for the application of these four rules, and of 
 reduction of integral denominate numbers, will be found below, in 
 connection with the " Weights and Measures." 
 
 Weights. — Teach briefly, by examples, the relations of Avoirdupois 
 and Troy weights, the essential identity of Troy and Apothecaries' 
 weights. Let most of the examples in Reduction be in the first of the 
 three. They should be few and very short in the last. 
 
 Remember that the quarter of a hundred weight and the avoirdupois 
 dram are seldom used now excepting in text-books. 
 
 In addition and subtraction give avoirdupois weight. Remember that 
 in things sold by the ton the ounce is not taken into account. 
 
 Linear Measure. — Beduction. — Employ the denominations most in 
 use — inch, foot, yard, rod, and mile. Give a few examples to show the 
 use of the chain and its subdivisions. 
 
 Omit addition, subtraction, multiplication, and division. 
 
 Surface Measure. — {Of very great practical importance.) — Treat briefly 
 in reduction. Be particular to avoid long examples. When 30i is used 
 as a divisor let it be in very short examples. Give examples in ad- 
 dition and subtraction. Give examples in finding areas of rectangular 
 figures. Give the feet, or the chains, in the sides of rectangles, to find 
 acres and value ; acres and hundredths the most usual form. Simple 
 questions, involving cost, may occasionally be given in plastering, pav- 
 ing, carpeting, dress linings, etc., etc. 
 
 Solid Measure. — Employ only the inch, the foot, the yard, and the 
 cord ; use the last but little. See that pupils understand the mutual 
 relations of linear, surface, and solid measures, and that these measures 
 are not convertible. Reduction — a few simple questions. Omit addi- 
 tion and subtraction. Give examples in finding cubic inches, feet, or
 
 GEOGPwAPHY. 95 
 
 yards, in boxes, bins, cellars, cylindrical cisterns, etc.; also contents in 
 bushels and gallons. 
 
 Dry and Liquid Measures. — Use no obsolete denom'nations. Omit 
 beer measure. Remember that the barrel and the hogshead are not 
 oTten measures in commerce. Simple examples in reduction, multipli- 
 cation, and division. 
 
 Circular Measure. — Treat briefly ; explain the terms and their use ; 
 omit signs. Reduction — Short examples of two or three terms. Addi- 
 tion and Subtraction — Questions in difference of latitude and longitude. 
 Geographical and statute miles on the meridian, on the equator, on 
 parallels of 60^. 
 
 Time. — (In part ver}' important.) Treat reductions very briefly. Do 
 not involve more than two or three denominations in one example. Ad- 
 dition and subtraction. Difference of dates by days, and by years, 
 months, and days. 
 
 Miscellaneous. — Practical examples in values, involving dozen, gross, 
 quire, ream, quintal, barrels of flour, fi.sh, etc., making out simple bills, 
 receipts, etc. 
 
 Money. — Give but few examples in each rule in sterling money. Re- 
 duction of sterling to Federal, and vice versa, omitting, of course, all 
 reference to the percentage of exchange. 
 
 Pupils should know something of the money of Canada, identical 
 with our own ; the value of the franc and of the German mark. 
 
 GEOGRAPHY. 
 
 United States reviewed. — See Fif tli Grade. 
 
 North Ainerica in Detail. — Follow general directions 
 for Fifth Grade in greater detail. 
 
 Asia and Africa. — The outline of these grand divisions 
 will include their boundaries ; area and population in 
 round numbers ; simplest physical divisions ; names and 
 relative positions of their several countries ; brief state- 
 ments of general facts relating to the climates and produc- 
 tions of the countries; the names and location of their 
 capitals, and of the moi-e important islands, mountains, 
 seas, gulfs, rivers, lakes, etc. 
 
 In Africa, only the Barbary States, Egj^t, and Cape 
 Colony, should be made at all prominent.
 
 96 FOURTH GRADE. 
 
 HISTORY OF THE UNITED STATES. 
 
 Suggestions. — Note carefully the general suggestions of 
 preceding grade. 
 
 The work of this grade is, " Outline with Greater De- 
 tail." The following Syllabus of Topics is indicative of 
 the amount of information the pupils may properly be ex- 
 pected to possess at the conclusion of this grade, 
 
 SYLLABUS OF TOPICS. 
 
 1. Discovei'ies. — Col iambus, 1492 — first voyage only — (refer in general 
 way to his subsequent voyages) — The naming of America — Spanish 
 claims — The Cabots — English claims— Discovery and occvipation of the 
 St. Lawrence — French claims. 
 
 2. Virginia. — Settlement of Jamestown, 1607 (omit unessential de- 
 tails) — Tobacco — Slavery— Refer briefly to Indian wars, but omit all 
 details — Refer briefly to other colonies once wliolly or partly within the 
 limits of Virginia. 
 
 B. New England. — Puritans in England — " Pilgrims" — Settlement of 
 Plymouth, 1620 — Salem— Boston — Refer very briefly to other colonies 
 wholly or partly settled from these three — also to Indian wars. 
 
 4. New Netherlands.— Henry Hudson, 1609 — Fort Orange — Manhat- 
 tan — Stuyvesant — English conquest — Refer briefly to extent of New 
 Netherlands and to other colonies afterward cut off. 
 
 5. New York.. — Changes in name, 1664 — Refer briefly to reconquest 
 by the Dutch, and subsequent restoration to the English. 
 
 6. French and Indian War. — 1753 — Causes — a few leading events — 
 results — It trains and prepares the colonists to become soldiers of the 
 Revolution. 
 
 7. Revolution. — 1775 — Chief causes — Declaration of Independence, 
 July 4, 1776 — a few other principal events — results — Refer briefly to 
 Articles of Confederation, and to the adoption of the 
 
 8. Constitution. — First President, 1789 — events— Jefferson and Louisi- 
 ana — its extent. 
 
 9. Madison and War of 1812— Its causes and results (briefly). 
 
 10. Mexican War — 1846 — Its causes and results. 
 
 11. Civil War — 1861 — Chief causes and general results (treat briefly 
 and carefully avoid making or allowing partisan statements). 
 
 Be careful so to lay out the work to be done, that it may readily be 
 completed before promotion.
 
 THIRD GRADE. 
 
 Outline Coukse. 
 
 1. Language Lessons. — Beading of the grade of an easy Fifth Reader 
 — at least one lesson per week in supplementary reading : oral lessons on 
 the simple facts of natural philosophy : compositions as before : spelling, 
 meaning, and use of words, as before : exercises in the formation of de- 
 rivative words : English grammar (without text-book) continued. 
 
 3. Arithmetic. — Written a.nd Menial — Through percentage, includ- 
 ing such rules as do not involve consideration of time, with their appli- 
 cations. Problems to be chiefly such as involve the ordinary business 
 transactions. 
 
 3. Geography. — South America and Europe in detail. 
 
 4. History of the United States. — To the Revolution. 
 
 5. Penmanship. — Writing in copy-books, with practice in different 
 styles ; short paragraphs to be written from dictation ; instruction in 
 letter-writing. 
 
 6. Drawing. — On paper, illustrated on blackboard, from dictation 
 and from chart. 
 
 Draw one historic vase, not less than six inches high, without 
 perspective effect, decorated. One original pottery form, without 
 perspective effect, decorated with any leaf, flower, form, or historic 
 ornament, used in previous grades. Two examples of bi-symmetrical 
 Ihistoric ornament of different styles, greatest dimension not less than 
 six inches. Two original examples of surface covering, using not less 
 than two different units for the repetition. One original circular bor- 
 der. An example of design for textile fabric.
 
 INSTRUCTIONS AND SUGGESTIONS. 
 
 LANGUAGE. 
 
 The general instructions and suggestions for 
 
 Reading, found on page 20 ; those for 
 
 Spelling, on page 29 ; those for the 
 
 Meajstings and Uses of Words, on page 31 ; and those 
 for 
 
 Composition, on page 28, are to be taken as belonging 
 to this grade also. 
 
 ORAL LESSONS. 
 Natural Philosophy. 
 
 1. As a means of appropriate mental discipline, no 
 other department of the Oral Lessons prescribed for the 
 several Grammar School grades is of equal importance 
 with these lessons on simple facts of natural philosophy. 
 It is needless here to dwell upon the practical and perma- 
 nent value of a knowledge of these facts. It will not be 
 inappropriate, however, for the teacher to impi-ess upon 
 the pupils the general relations of this knowledge to the 
 marvels of modern progress, and to direct their reading for 
 more extended information. 
 
 2. In the work assigned to this and to the next higher 
 grade, nothing beyond a simple introduction to and^r^a- 
 ration for scientific study is attempted. 
 
 3. Only a small part of the vast field can be covered,
 
 LANGUAGE. 99 
 
 jet whatever is done, should be done with system. To 
 this end, a carefulJj prepared note-book — not ^a?^-book — 
 is indispensable for the teacher. See page 25. 
 
 4, Begin every lesson with an experiment, or, if neces- 
 sary, with several experiments. The oixil work in the 
 teaching will consist chiefly in careful questioning upon 
 the phenomena as observed by the pnpils. Tell when you 
 must ; but tell as little as the nature of the special topic, 
 and a proper economy of time will allow. 
 
 5, It is of especial importance that the pupils should 
 be in every way encouraged to find instances of the appli- 
 cations of the principles they have been taught : these 
 they can themselves discover in the phenomena and inci- 
 dents of their daily life, at home, in the street, the shop, 
 and the school. Thus they will be led to form habits of 
 observation and reflection, 
 
 6, The teacher will find a wide difference in the readi- 
 ness with which pupils will conceive and apply scientific 
 principles. With a few, the bare statement of a principle 
 will often enable them to point out its simpler applica- 
 tions. The results of a certain order of experiments, and 
 the simpler deductions from them, will be promptly an- 
 ticipated by such minds. But it will not be so with all : 
 only after careful and repeated illustration will the prin- 
 ciples which interpret the facts represented be clearly 
 apprehended by some. In all experiments the pupils 
 themselves should be made, as far as possible, participants. 
 In reviews they should be called upon to repeat the ex- 
 periments or statements that have been made, and to give 
 the proper explanation. They should be encouraged to try 
 further experiments for themselves at home, and then to 
 furnish an account or repetition of them in the class-room, 
 if possible. The teacher will also particularly remember
 
 100 THIRD GRADE. 
 
 that it is not necessary to follow slavishly the exact order 
 or selection of topics given in the subjoined syllabus. For 
 instance, the consideration of the mechanical powers may 
 precede that of the properties of matter, or of the attrac- 
 tive and repellent forces. 
 
 7. When the scientific meaning of a common term 
 differs greatly from the popular one, great care should be 
 taken to point out clearly such difference, in order that the 
 pupil may not be misled by thinking that he knows that 
 of which he is really ignorant. Among the many cases in 
 which this will be found necessary, the terms j[)orosity, 
 porous, solid, and invpe7utrability may be talcen as in- 
 stances. It is by no means necessary that the pupil should 
 be able to give an exact and comprehensive scientific deji- 
 oiition of such terms ; a few analytical questions by the 
 teacher will readily show whether the subject is under- 
 stood. 
 
 8. As far as the subject will allow, the pupil should be 
 led through the medium of exjperiment to a knowledge of 
 \hQ facts. The facts once ascertained, the princijjles un- 
 derlying them may be deduced. A limit will, sooner or 
 later, be reached, where parts of the subject, so far as they 
 may be entered upon, must he taught empirically, in con- 
 sequence of the pupil's limited knowledge of other depart- 
 ments of science. 
 
 For instance, suppose that the teacher has already ex- 
 perimentally established in his pupil's mind a general idea 
 of the terms/brce and gravity, and that he now wishes to 
 lead him to' know that " the weight of a body is the Pleas- 
 ure of ikiQ. force of gravity " acting upon it, and after that 
 to establish the law of its variation. Let the teacher or 
 one of the pupils borrow a common spring scale — the 
 smaller and simpler the better ; let a pupil pull, and at
 
 LANGUAGE. 101 
 
 the same time notice that he is exerting deforce / that the 
 position of the index will vary with the degree or amount 
 of force ; that the tnotion is in the direction of the force, 
 however the instrument may be held : now place a succes- 
 sion of heavy bodies in the scale, and let him notice that 
 the effects are identical with those produced by his muscu- 
 lar force. He will no longer vaguely conceive that the 
 effect produced upon the scale is because the body is heavy 
 (which was to him a vague term), but because the earth 
 actually jyi^Z/s it as he did, though no connecting bond is 
 visible, as when he pulled. A knitting-needle suspended 
 and balanced upon a thread, and acted upon by a sim})lc 
 magnet, will clearly convince liim that a force may be 
 exerted by one body upon another without actual contact. 
 You have clearly defined for him the idea that " the 
 weight of a body is the measure of the earth's attraction 
 upon it." If now you wish to teach the law of the variation 
 of the weight of a body of invariable mass, as should indeed 
 be done, the next step must be evijpirical. The pupil's de- 
 ficiency in mathematics forbids any other course of proce- 
 dure. The " Law of Gravitation " must be stated to him, 
 together with the reason for stating without pi-oof . It will 
 develop in many a mind an earnest desire to supply that de- 
 ficiency. The law of the variation of weight may now be 
 readily deduced by first adding to the pupil's mathematical 
 knowledge the technical meaning of the term square, and 
 then giving a variety of simple arithmetical problems to 
 illustrate it. 
 
 9. There is, perhaps, no graver or more common error 
 in relation to this subject, among earnest teachers who are 
 called upon to teach it, than the notion that this requires 
 expensive or complicated apparatus. The very contrary 
 is indeed the case in the great majority of instances. Ex-
 
 102 THIRD GRADE. 
 
 pensive apparatus, with its show of brass and glass, has a 
 direct tendency to repress the most precious element and 
 evidence of a teacher's success — experimenting at home by 
 the pupils themselves. The principles of the lever may be 
 just as well developed by means of a pen-handle, a pointer, 
 or a window-pole, as by a polished brass or steel bar ; a 
 large spool makes an excellent wheel and axle j a ribbon- 
 block, a good single pulley, fixed or movable ; a slate, a 
 book, or a shingle, an inclined plane ; a pocket-knife will 
 soon furnish a good wedge from a little piece of board, 
 while the use of the blade itself is an excellent illustration 
 of the application of the principle ; and a large screw or a 
 discarded auger-bit, with a knitting-needle or a pen-holder 
 for a lever, makes an efficient single screw. And so through 
 every department of the subject. Nothing marks more 
 fully the ability of a teacher than fertility in such resources. 
 Strings, tops, balls, and marbles ; pop-guns, potato-mills, 
 bean-shooters, and putty-blowers, and the thousand and 
 one nameless articles to be found in pupils' pockets fur- 
 nish an exhaustless mine of apparatus, and good apparatus 
 too, for the skilful teacher. The immortal Dalton wrought 
 out his atomic chemical theory with apparatus which may 
 be excelled in many a junk or old-bottle shop, and the 
 teacher determined to succeed will find that " where there 
 J is a will there is a way." 
 
 SYLLABUS OF TOPICS. 
 
 (To be illustrated, as far as possible, objectively.) 
 
 Properties of Matter. — Body or mass, molecule, atom ; solid, fluid, 
 liquid, gas ; sensible or cellular pores, as in bread or sponge ; physical 
 or intermolecular pores, as in iron, water, air, etc.; porosity. Extension, 
 impenetrability, rarity and density, compressibility and expansibility, 
 inertia, mobility, molecular attraction and repulsion. Indestructibility 
 of matter briefly explained. Cobesive force ; properties dependent
 
 COMPOSITION. 103 
 
 upon cohesion; tenacity, flexibility; brittleness, hardness, ductility, 
 malleability. Properties dependent iipon cohesive attraction and mo- 
 lecular repulsion ; elasticity ; elasticity of flexure, of compression, of ex- 
 pansion, of torsion. Relations of tlie forms of matter, as solids, liquids, 
 and gases, to molecular attraction and rei^ulsion. Adhesive force ; prop- 
 erties dependent upon it ; capillary attraction and its important uses in 
 organic and inorganic nature. Divisibility of matter : into particles by 
 mechanical force ; into molecules by heat, solution, etc. ; what forces 
 are overcome in each case, and by what force. 
 
 Oravity. — Why called universal gravitation : its simplest phenom- 
 ena ; why bodies fall : mutual attraction of floating substances ; law of 
 gravitation ; weight a measure of gravity. Centre of gravity ; line of 
 direction ; plumb-line ; stable, unstable, and indifferent equilibrium. 
 Motion : simple and compound ; circular motion ; centripetal and cen- 
 trifugal force. 
 
 Mechanical Powers. — Lever, with simple problems in mental arith- 
 metic ; pulley, wheel and axle, inclined plane, wedge, screw. 
 
 Reference Books. — The usual text-books on physics ; numerous 
 articles in Appletons' and other cyclopaedias ; Faraday on Physical 
 Forces ; Tyndall's Matter and Forces. 
 
 COMPOSITION. 
 
 1. Letter- writing is specially prescribed as an exercise 
 in the Third, Second, and First Grades. From the dating of 
 the letter to the final direction upon the envelope, great 
 care should be taken to insist, as in all other written exer- 
 cises, upon neatness and legibility. A habit of scribbling 
 is easily formed but is very hard to break. 
 
 2. In these three grades a special exercise preliminary 
 to writing out the composition should occasionally be 
 given, in which, a suitable subject being announced, the 
 pupils should be required to write, without assistance, a 
 brief synoptical outline of the points and items to be in- 
 cluded in the composition, and then to number or arrange 
 them in some logical order, so that, when expanded into 
 a composition, a proper consecutiveness will be observed.
 
 104 THIRD GRADE. 
 
 The form already advised for the teacher's note-book of 
 subjects taught orally will be found simple and efficient 
 for this purpose. Some such plan is indispensable to the 
 best work, and to the development of that self-help and 
 self-reliance which every element of school training should 
 tend to establish as a permanent habit of the mind. 
 
 FOEMATION OF DEEIYATIYE WORDS. 
 
 The exercises prescribed for the First, Second, and Third 
 Grades naturally include those prescribed for the lower 
 grades ; their further extension to the formation of deri- 
 vative words being understood to include wider and more 
 difficult groups, such as those given below. The uses of 
 these words in illustrative sentences will, of course, form 
 the best test that the instruction given has been practical 
 and efficient. The formal study of English etymology 
 from Latin and Greek roots is not prescribed for any 
 grade. 
 
 Sense : Ifonsense, sensation, sensational, senseless, sense- 
 lessly, sensory, sensitive, sensitively, sensitiveness, sensible, 
 sensibly, hisensihle, sensibility, sensual, sensually, sensuous, 
 sensuality, etc. 
 
 Scribe: Inscribe, etc., describe, etc., circumscribe, etc., 
 prescribe, etc., proscribe, etc., subsc7'ibe, etc., ascribe, etc. 
 ScT'ipt: Description, etc., scripture, etc., conscript, etc., 
 prescription, etc. 
 
 GRAMMAR. 
 
 The sentences, still simple, should be of a more difficult 
 character than in the previous grade. 
 
 The exercises in construction should be made to corre-
 
 GRAMMAR. 1()5 
 
 spond with the character of the grammatical work of the 
 grade ; and the pupils in their compositions should, as far 
 as possible, exemplify the grammatical instruction given. 
 Sentences which occur in these compositions should al- 
 ways constitute a portion of the subject-matter of the 
 grammar lesson for the day. In the character of the sen- 
 tences selected for this purpose, the good judgment of the 
 teacher will be displayed. 
 
 Etymological exercises should be interspersed, especially 
 in the use of the apostrophe as a sign of the possessive case 
 — in the proper plural termination of nouns — the proper 
 forms of the pronouns, etc. This is a point of considerable 
 importance. 
 
 The exercises for the special purpose of accustoming 
 the pupils to care and criticism in the use of language, 
 should be continued. 
 
 Outline, 
 
 All the parts of speech ; declension of nouns and pronouns ; compari- 
 son of adjectives and adverbs. 
 
 Introduce the attribute. Teach all the uses of the phrase. Make 
 the sentence the basis of instruction. Omit gender of nouns ; make 
 little or no reference to person of nouns. With the exception of the 
 possessive, the cases of nouns are of little practical importance. The 
 case of a pronoun is a matter of inflection. 
 
 Refer to the normal order, (1) Subject, (2) Predicate, (3) Object 
 or Attribute, By the simplest illustrations direct attention to the 
 changes in the sense that changes in 1 his order bring about. For ex- 
 ample, " Great is Diana of the Ephesians ! " (Emphatic) ; "Is John at 
 home?" (Interrogative); "Go ye and teach" (Imperative), etc. 
 Teach the general rule that qualifying words and phrases should be 
 placed as near as possible to what they qualify. Examples: " I only 
 spoke a few words," should be, " I spoke only a few words ; " "I saw 
 the city, sailing up the river," for " Sailing up the river, I saw the 
 city." Phrases, when they do not closely follow the words on which 
 they depend, are generally set ofif by the comma. 
 5*
 
 106 THIRD GRADE. 
 
 AKITHMETIC. 
 
 The teacher is enjoined to bear in mind that, in teaching 
 business arithmetic, it is especially important to insist 
 upon clearness, neatness, legibility, accuracy in results, 
 and reasonable rapidity. Mental exercises, corresponding 
 to the written, should form a large part of the work of 
 this grade. 
 
 1. The commercial arithmetic of this grade differs from 
 that taught in the preceding grades, chiefly in the intro- 
 duction of the various forms of Percentage. 
 
 2. The divisions of this subject should be presented 
 in the following order : First, Sinvple Percentage, in 
 four cases — one fundamental and three derived ; second, 
 the applications of Simple Percentage, technically known 
 as Profit and Loss, Commission, Brokerage, Insurance, 
 Taxes, etc., following the same order and with the same 
 analysis as in the four cases of Simple Percentage. 
 
 3. In treating this subject many skilful teachers prefer 
 to introduce algebraic formulae, in which the initial letters 
 of the several terms employed in Percentage are the ele- 
 ments. To this course there is no objection, provided 
 that the formulae be not employed in the mental arithme- 
 tic, and that they accompany the usual analysis and be 
 not used as a substitute for it. 
 
 4. The subject of arithmetic being necessarily and to a 
 great extent cumulative, the teacher of the Third Grade 
 is especially advised to read over the directions given in 
 all the preceding grades, and in particular the table on 
 page Y6. For the sake of brevity, the terms Base, Per- 
 centage, etc., are employed in the following Syllabus of 
 Topics, in the usual technical sense of the text-books.
 
 AEITHMETIC. 107 
 
 The teacher will so use them or not, as the Principal may 
 deem expedient. 
 
 SYLLABUS OF TOPICS. 
 
 The term percentage — Reading per cent. 
 
 Examples — Read the following decimal fractions as per cent. : .75, 
 .8, .605, .003, .08i, .00|, etc. 
 
 Change common fractions to per cent., and vice versa: 
 
 Emmpks-l, I, ^%%, It, 3|, l-,^, if, etc. 
 
 25 per cent., 75 per cent., 83^ per cent., 14?^ per cent., 88 1 per cent., 
 325 per cent., 137^ per cent., etc. 
 
 Note. — The common business fractions — halves, thirds, etc., to 
 twelfths, inclusive — should be reduced to per cent., and the pupils be 
 made thoroughly familiar with them. 
 
 First Case {Fundamental). 
 
 To find the percentage when the base and rate are given. 
 
 See table, page 76. — To find a given fractional part of a given num- 
 ber. 
 
 Examples — How much is 9 per cent, of 750 ? Had $750 in the bank ; 
 drew out 9 per cent. : how much was it ? 
 
 Analysis as in the multiplication of decimal fractions. 
 
 Note. — When this form of the case has been taught, its modifications 
 should immediately follow. 
 
 Examples — Had $750 ; paid out 9 per cent. How much had I left ? 
 
 Had $750 ; earned 9 per cent. more. How much had I then 'i 
 
 Second Case {Derived). 
 
 To find the rate when the percentage and base are given. 
 
 See table, page 76. — To find what fraction one number is of another 
 number. 
 
 Examples — 140 is what per cent, of 400 ? 
 
 Had 400 sheep ; sold 140. What per cent, did I sell ? 
 
 Analysis as in reducing a common fraction to a decimal fraction 
 whose denominator is hundredths. 
 
 Modifications of Case Second : 
 
 Examples — I had 400 sheep ; I now have 540. What is the per cent, 
 of increase ?
 
 108 THIED GRADE. 
 
 I had 400 sheep ; I now have only 260. What is the per cent, of de- 
 crease ? or what per cent, have I left ? 
 
 Third Case {Derived). 
 
 To find the lase when the iiercentage and raU are given. 
 
 See table, page 76. — To find the number of which another number is 
 a given fraction. 
 
 Examples — 140 is 35 per cent, of what number ? 
 
 Sold 140 sheep, which was 35 per cent, of my flock. How many had 
 I at first ? 
 
 Analysis as in simple fractions — 140 is i^JV of what number ? 
 
 Modifications of Case Third : 
 
 Examples — Sold 140 sheep, which was 35 per cent, of my flock. 
 How many had I left ? 
 
 Sold 140 sheep, and have 65 per cent, of my flock remaining. How 
 many had I at first ? 
 
 Fourth Case {Derived). 
 
 To find the base when the amount — or the difference — and rate are 
 given. 
 
 To find a number which differs by a given fractional part of itself 
 from a given number. 
 
 Examples — What number is by 8 per cent, of itself more than 351 ? 
 or 351 is 8 per cent, more than what number ? 
 
 My fiock of sheep increased 8 per cent. ; I then had 351. How many 
 had I at first ? 
 
 I lost 8 per cent, of my sheep, and had 299 remaining. How many 
 had I at first ? 
 
 ^ First, find the per cent, represented by the given number, 
 
 . , . J thus : 100 per cent. — 8 per cent = 92 per cent. 
 
 J Second, proceed as in Third Case : 299 is i^o^j of what 
 (_ number ? 
 
 As a part of the general review, give an example in the fundamental 
 case, and let the pupils derive the other three cases from it. 
 
 Commission and Brokerage, and Profit and Loss are but applications 
 of Simple Percentage. Each presents itself under all the four cases, 
 but requires no special additional teaching, except in regard to the 
 technical terms employed.
 
 GEOGRAPHY. 1(9 
 
 GEOGRAPHY. 
 
 South America m detail. — The continent, as a whole ; 
 its boundaries ; the names and boundaries of its political 
 divisions ; a few of the chief capes and islands ; the posi- 
 tion and direction of the great plateaux and mountain 
 ranges ; five or six of the most famous volcanoes. In the 
 drainage, only two or three lakes, the courses of the Ori- 
 noco, the Amazon, the San Francisco, and the Parana 
 described ; their great branches named and pointed out as 
 systems, but not described. 
 
 The local geography of the countries taken separately 
 will include a review of the matter previously considered 
 in the study of the continent — that is, the boundaries, the 
 positions of the mountains and plateaux, the principal 
 rivers, etc., together with the capitals of the several coun- 
 tries, and about thirty other principal seaports and interior 
 cities of the continent. 
 
 Teach the descriptive geography of the continent as a 
 whole. That of the several countries may thence be very 
 easily deduced. It should include the surface of the 
 country, as mountain, plateau, or plain ; the zones ; the 
 climate as modified by latitude, elevation, and the preva- 
 lent winds ; the leading characteristics of the great plains 
 and plateaux ; a brief notice of volcanoes and earthquakes ; 
 principal plants and animals ; the three races, their dis- 
 tribution and principal occupations; the European lan- 
 guages ; the chief productions and exports ; and the forms 
 of government. 
 
 Europe in detail. — The general plan to be pursued has 
 been sufficiently indicated in the suggestions made with 
 reference to other grand divisions. The greater our in-
 
 110 THIRD GRADE. 
 
 tercourse with any country, the greater is the necessity for 
 our study of its geography in more minute detail. 
 
 Our intimate relations with the various countries and 
 peoples of Europe, in race, language, religion, literature, 
 and commerce, and the prominence of its affairs in the 
 newspapers read by every class of the community, give 
 great importance to the careful and intelligent teaching of 
 its geography. 
 
 When classes are studying or reviewing the geography 
 of the several countries of this continent, these various re- 
 lations should receive brief but definite attention ; and, 
 when considering the prominent industries and exports of 
 each, our imports from that country and exports to it 
 should be briefly noticed. 
 
 HISTORY OF THE UNITED STATES. 
 
 Suggestions. — The teacher is particularly referred to 
 the General Suggestions on United States History in the 
 preceding grades. 
 
 The work of the Third Grade is comprised in the fol- 
 lowing : 
 
 SYLLABUS OF TOPICS. 
 
 Voyage of Columbus — the naming of America — the occupation by the 
 Spaniards of the West India Islands and all the neighboring portions of 
 the continent — their enslavement of tlie Indians and its results (the 
 last very briefly). 
 
 The discovery, exploration, and occupation of the St. Lawrence and 
 Nova Scotia by the French. 
 
 Virginia. — The settlement of Jamestown and the events directly lead- 
 ing to it. The cultivation of tobacco — the introduction of slavery — the 
 navigation acts and Bacon's rebellion. 
 
 Maryland. — The Calverts — religious freedom — Clayborne.
 
 HISTOKY OF THE UNITED STATES. Ill 
 
 New England. — The Plymoutli Company and the settlements nnder 
 their patent. The Puritans — their previous history — why called Pil- 
 grims. Settlement of Plymouth ^of Boston — of Dover — Massachusetts 
 Bay Colony. Settlement of Connecticut — of Rhode Island — provisions 
 for religious freedom. The Union — Indian Wars (read) -Andros— King 
 William's War, its causes and results — Salem witchcraft (read) — Queen 
 Anne's War, its causes and results — King George's War, its causes and 
 results. 
 
 Neio Netherlands. — Hudson — settlement on the Delaware — at Fort 
 Orange — at Manhattan Island — tlie Dutch Governors — Kieft's conduct 
 — Stuyvesant — existing evidences of the Dutch occupation. 
 
 New York. — Changes of name — reconquest by the Dutch and restor- 
 ation to England. Andros — the extent of his rule. Dongan — Leisler — 
 Schenectady — the Negro plot — existing evidences of English rule. 
 
 New Jersey. — Its name — its division — union with New York — separ- 
 ation. 
 
 Delaware. — Settlement by Swedes — conquest by Stuyvesant. 
 
 Pennsylvania. — William Penn — his grant — his objects. Settlement 
 of Philadelphia — relations to Delaware. 
 
 North Carolina. — The grant of Charles II. — its limits — John Locke. 
 
 South Carolina. — Charleston settled — Carolina divided into two sep- 
 arate governments. 
 
 Georgia. — Savannah settled — character of Oglethorpe. 
 
 General condition of the English colonics in 1752. Their population 
 — their national derivation — their industries, social condition, planters, 
 patroons, proprietors — the causes which were developing a love of lib- 
 erty. 
 
 Review chronologically under the heads of sovereigns of England — 
 Elizabeth — James I. — Charles I. — Cromwell — Charles II. — James II. — 
 William and Mary — Anne — George I. — George II. 
 
 Review biographicaJly — Columbus, Bacon, Williams, Penn, etc. 
 
 The French and Indian War. — This should be taught in outline, tlie 
 principal points being: The gradual extension of the English and 
 French settlements, leading to conflicting claims — the explorations and 
 posts of the French in the valleys of the Mississippi, the St. Lawrence, 
 and the Lakes — Marquette and La Salle— the debatable land on the 
 upper Ohio — relatively small population of Canada — the building of Fort 
 du Quesne, 1754 — Colonial Congress at Albany, 1754 — Braddock's and 
 Johnson's expeditions, and their results, 1755 — Monckton's exjiedition, 
 1755 — cruel expulsion of the Acadians— capture of Oswego, 1756 — Fort 
 William Henry, 1757 — siege and capture of Louisburg, 1758 — repulse
 
 112 THIRD GRADE. 
 
 at Ticonderoga, 1758 — concentration of French forces at Quebec, by- 
 abandoning nearly all other posts— battle of Quebec, 1759, and results 
 — Treaty of Paris, 1763 — its conditions. 
 
 In teaching the French and Indian War, let the ten dates marked be 
 studied by the years only. Bead, but do not memorize, the details of 
 military movements and events — fix the sequence of events — use tlie 
 map. 
 
 In the review, let the pupil tell very briefly of Washington, Brad- 
 dock, Johnson, Monckton, Amherst, Abercrombie, Howe, Wolfe, 
 Dieskau, and Montcalm.
 
 SECOND GRADE. 
 
 Outline Cotjrse. 
 
 1. Language Lessons. — Reading oi the grade of a Fifth Reader- 
 supplementary reading continued : oral lessons on the simple facts re- 
 lating to air, water, light, heat, and sound : compositions as before : 
 spelling, meaning, and use of words, as before : exercises in the forma- 
 tion of derivative words, continued : English grammar — the construction 
 of compound and complex sentences, with the view of teaching pro- 
 priety of expression. 
 
 2. Arithmetic — written and mental. — Interest, simple and com- 
 pound, including partial payments ; discount, bank and true ; propor- 
 tion, simple and compound. 
 
 3. Geography. — The review of Europe; Asia, Africa, and Oceanica 
 in detail. 
 
 4. History of the United States. — Completed. 
 
 5. Penmanship. — Writing in copy-books; also of paragraphs and 
 business forms, such as bills, receipts, and drafts ; letter-writing con- 
 tinued. 
 
 6. Drawing. — On paper, illustrated on blackboard, from dictation 
 and from chart. 
 
 Draw one natural lobed leaf and flower — conventionalize them and 
 with them draw two designs for industrial purposes. Draw from the 
 model or round the following : cube, square prism, cone, cylinder, and 
 square pyramid. Draw {free hand) concentric squares, hexagon, octa- 
 gon, circle, concentric circles, ellipse, oval. 
 
 Perspective Drawing {permissible). — Draw in linear perspective, 
 from drawings made on hlackboard only, the following : picture plane, 
 horizon, points of sight, points of distance, points at different distances 
 within the picture plane ; horizontal and vertical lines of different 
 lengths and distances, within the picture plane ; vertical and horizontal 
 squares, cubes, square prism, and square pyramid in parallel perspec- 
 tive ; in angular perspective, horizontal cubes and square pyramids.
 
 OSTKUCTIONS AND SUGGESTIONS. 
 
 la:nguage. 
 
 The general instructions and suggestions for Reading 
 found on page 20 ; those for 
 
 Spelling on page 29 ; those for the 
 
 Meaning and Use of Words on page 31 ; those for the 
 
 Formation of Derivative Words on page 104; and 
 those for 
 
 CoMPosrrioN on page 28, are to be taken as belonging to 
 this grade also. 
 
 ORAL LESSONS. 
 Water, Air, etc. 
 For general suggestions, see page 98. 
 
 SYLLABUS OF TOPICS. 
 (To be illustrated, as far as possible, objectively.) 
 
 Water. — Mobility of liquids — its cause ; their small compressibility ; 
 pressure in every direction ; gravity the primary cause ; how down- 
 ward pressure is converted into side and upward pressures. Equality 
 of pressure at a given point ; variation with the depth ; the term level; 
 why water has a level surface ; why the hydrant water flows from the 
 open tap ; at what height it ceases to flow, and why ; other illustra- 
 tions of the same principle ; what that principle is ; the hydrostatic 
 paradox ; the hydraulic press ; specific gravity ; floating bodies ; why 
 iron ships float ; the quantity of water displaced by any floating body. 
 
 Air. — Its mobility, compressibility, expansibility, and elasticity ; 
 chief mechanical difference from liquids ; its weight ; its pressure in
 
 NATURAL PHILOSOPHY. 115 
 
 all directions ; how shown ; the common lift-pump ; the mercurial 
 barometer ; its construction ; principle and uses ; Torricelli's experi- 
 ment ; Pascal's experiment ; the aneroid barometer ; height of atmos- 
 phere and gradual diminution of its density. 
 
 Sound. — Preliminary. A general idea of the transmission of vibra- 
 tions, illustrated. The nature of sound, its objective and subjective 
 elements. Sonorous bodies highly elastic. A medium necessary. The 
 air as a medium. Other media. Limits of audibility of vibrations. 
 Velocity in air and other media. Loudness does not alter the velocity. 
 Reflection of sound. Echo, its causes and limits. Physical distinction 
 between mere noise and a musical sound. Pitch in music. Influence 
 of sound-boards. Tuning-forks, speaking-trumpets, speaking-tubes. 
 Resonance — murmur of shell. The ear, its construction and action — 
 the wonderful physical condition of the tympanum when listening to a 
 full orchestra. Trace the successive transmissions of vibrations from 
 a street organ to the brain, through closed windows. 
 
 Note. — Many important experimental illustrations may be given by 
 the aid of a simple tuning-fork. 
 
 Heat. — Known only by its effects. Effect on the nerves — effect upon 
 the constitution of bodies. Transmission of heat — three ways illus- 
 trated — air a bad conductor and worse radiator — important relation of 
 this to clothing, to vegetation, etc. Heat as a sensation — relation pf 
 terms hot and cold. Sources of heat — quantity and effects of solar 
 heat — its relations to physical geography. Source of the heat devel- 
 oped by friction — motion of mass converted into molecular motion. 
 Heat only a mode of vibratory motion. Force as indestructible as mat- 
 ter. Source of heat in combustion. The common thermometer — 
 principles employed in its construction — zero, what it is and how ob- 
 tained. Evaporation — its causes — effects on temperature of bodies. 
 Phenomena of boiling — temperature of boiling water— why invariable 
 at a given elevation — economic applications — why the boiling-point 
 varies with elevation — boiling in a closed vessel. The steam-engine — 
 its essential elements and general principles — high-pressure and low- 
 pressure engines. 
 
 Light. — Moves in straight lines. Shadows. Sources of light. Vi- 
 bratory nature of light (only refer to it). Velocity of light — how 
 known. Law of intensity illustrated. Photometry by shadows. Non- 
 luminous bodies — how seen. Reflection — its law — mirrors, and their 
 uses (treat more fully of the plane mirror than of the others). Refrac- 
 tion — its simplest phenomena — its law. Lenses — uses of, especially the 
 convex lens. Color — the prism and the solar spectrum — the order of
 
 116 SECOND GRADE. 
 
 the colors, and their dependence upon wave-length (refer very briefly to 
 thermic and actinic rays). Phenomena of the rainbow — the colors of 
 objects — primary colors. The eye and vision. 
 
 Reference Books. — The ordinary manuals on Natural Philosophy ; arti- 
 cles in Appletons' and other cyclopaedias ; 'I'yndall's Forms of Water ; 
 Tyndall's Heat as a Mode of Motion ; Tyudall on Sound ; Tyndall 
 on Light ; Youman's Correlation and Conservation of Forces ; Rood's 
 Modern Chromatics ; Le Conte on Light ; Lommel on the Nature of 
 Light ; Cooke's New Chemistry (introductory chapters) ; Buckley's 
 Fairy Land of Science (articles, The Aerial Ocean in which we Live, 
 The Voices of Nature). 
 
 GEAMMAK. 
 
 In this grade the pupil should learn the construction 
 and use of complex and compound sentences. The gen- 
 eral structure of such sentences, and the relation of their 
 clauses and members should be clearly seen by the pupil. 
 Such insight is essential to a correct and definite under- 
 standing of the meaning of what we read and hear, as well 
 as to facility and variety of expression. All subtle and 
 practically useless distinctions must be avoided. What 
 follows will illustrate the requirements and instruction in 
 this grade : 
 
 " Pay the debts which thou owest ; for he who gave 
 thee credit relied upon thy honor, and to withhold from 
 him his due is both mean and unjust." 
 
 This sentence consists of two members : (1) " Pay the 
 debts," etc., to " owest ; " (2) " He who gave thee," etc., 
 to " unjust." These members are connected by " for." 
 
 The first member contains the clause " which thou 
 owest," used as an adjunct of " debts." 
 
 The second member consists of two clauses : " He who 
 gave thee," etc., to " honor," and " To withhold," etc., to 
 " unjust."
 
 GRAMMAR — ARITHMETIC. 117 
 
 The structure of the sentences constructed by the pupil 
 sliould be made the subject of criticism, with reference to 
 their clearness in expressing the meaning intended to be 
 conveyed — their j)roj)'riety, unity, etc. The thouglit itself 
 may be, to some extent, subjected to critical remark. 
 
 Exercises in the correction of false syntax should be 
 abundantly used in this grade. The construction of sen- 
 tences should assume the character of extended compo- 
 sition, the themes being selected by the pupils them- 
 selves, or assigned by the teacher. Of course, care should 
 be taken that the themes are of a simple character, ap- 
 propriate to the youthful mind, and calculated to awaken 
 thought, not to repress it, as is too often the case, when 
 subjects of an abstract or comprehensive character are 
 chosen for the exercise. 
 
 Outline. 
 
 Compound and complex sentences ; mood and tense ; declension and 
 comparison reviewed ; exercises in changing simple sentences to com- 
 plex, complex to simple, etc. Teach the general rule, that qualifying 
 clauses should be placed as near as possible to what they qualify : for 
 example, "The book that belongs to me is lying upon the table," not 
 " The book is lying upon the table that belongs to me." Show that each 
 sentence should have only one principal subject of thought. Sliow that 
 the agreement of the verb with its subject is true only so far as the 
 verb has inflection : that in the imperative mood, for instance, the rule 
 of agreement in person and number does not apply. The clauses 
 of compound and of complex sentences are generally separated by a 
 comma. 
 
 ARITHMETIC. 
 
 1. In this grade, the teaching consists in large part of a 
 review of what has gone before, with exercises sufficient 
 in number and difficulty to familiarize the pupils with the 
 principles, and render them expert and accurate in their
 
 118 SECOND GRADE. 
 
 application. For suggestions in regard to this part of the 
 work, the teacher is referred to the preceding grades. 
 
 2. The advanced work comprises the following: In- 
 terest — Simple and Convpound — including Partial Pay- 
 ments^ Bank Discount and True Discount ; Simple and 
 Compound Proportion. The exercises employed to teach 
 these departments of arithmetic should be of as practi- 
 cal a character as possible ; and all the processes should 
 be specially analyzed, the rules given being in all cases 
 deduced from this analysis. A knowledge of the husi- 
 ness transactions involved and of the terms employed in 
 any of the rules or their applications, should always be 
 imparted to the pupils before they are required to solve 
 the problems. Failure more frequently arises from a want 
 of this knowledge than from a deficiency in arithmetical 
 attainment. 
 
 3. The following syllabus contains a brief summary of 
 what is suggested to be taught in this grade : 
 
 Interest. — Teach the definitions of the terms — the distinction of 
 simple from compound interest — the legal rate of United States and of 
 the State of New York. 
 
 In classes of an average character, one good method will be found 
 to give better results than two or more. Whatever method be em- 
 ployed, the pupils should, from the first, be carefully guarded against 
 considering and calling the multiplier a concrete number. 
 
 If the six per cent, method be employed, it should be carefully 
 analyzed, and the pupil should not be allowed to sacrifice sense to con- 
 ciseness by such statements as " the half of 7 months is 3 cents and a 
 half" — " one-sixth of 24 days is 3 mills," etc. As a preliminary to ap- 
 plying this method, the class should have a thorough training on such 
 questions as the following : In 2 years, 3 months, and 20 days, at 6 per 
 cent, per annum, wJuit decimal fraction of tlie principal is equal to the 
 interest ? At 7 per cent. ? at 5 ? at 8 ? at 7 J ? etc. 
 
 Note. — In finding interest, at any given rate, by the six per cent, 
 method, the interest on the pi-indpal should first be found at six per
 
 GEOGliAPIIY. 119 
 
 cent., and afterward increased or decreased, as may be required ; by so 
 doing, diflBcult fractional multipliers will be avoided. 
 
 Give examples involving the various forms of tlie difference of dates. 
 Example : Find the interest of $340 from January 5tb to July 2d, at 6 
 per cent. 
 
 Examples involving the method, when the year is estimated to con- 
 sist of 365 days, should also be given. This is one of the most important 
 of the business methods. 
 
 Example. — Find the exact interest of $340 from December 1, 1883, 
 to January 27, 1884, at 4^ per cent. 
 
 Give examples in Bank Discount ; also in True Discount, distinguish- 
 ing carefully its differences in principle and method from hank and 
 from commercial discount. 
 
 Note. — (On the derived cases of simple interest.) — In teaching the 
 four derived cases of simple interest, begin with an easy example in the 
 fundamental case, and from that derive the others in their order, being 
 particularly careful to teach that, being derived, they all require 
 division ; that, to find the rate, the given interest is to be divided by 
 the interest at 1 per cent. ; to find the tinu, by the interest for 1 year ; 
 to find the principal, by the interest of a principal of $1 ; and that, in 
 the fifth case, the given amount is to be divided by the amount of %\. 
 
 Partial Payments and Compotind Interest shonldi be very briefly treated, 
 and with very simple examples. 
 
 The form and nature of a promissory note, and the meaning of the 
 several terms applicable to it, and the forms of bills and receipts, are 
 included in the work qf this grade. 
 
 PuopoRTiON. — Ratio ; proportion defined ; relation of antecedents 
 and consequents ; ratio of 4 to 12, 4 : 12, = iV; method of finding the 
 missing term ; simple and compound proportion distinguished ; prob- 
 lems involving each (these problems should be only such as are re- 
 quired to illustrate the principle, since they are ordinarily to be solved 
 by analysis previously given). 
 
 GEOGKAPHY. 
 
 Europe reviewed. — See Third Grade. 
 Asia, Africa., and Oceanica in detail. — For the plan to 
 be pursued, see preceding grades. 
 
 Complete the local and descriptive geography uf one
 
 120 SECOND GRADE. 
 
 continent, or grand division, before beginning that of 
 another. 
 
 As in the preceding grades, it is of great importance 
 that the entire field covered by the grade be completed and 
 reviewed before the promotion of the class to the next 
 grade. 
 
 HISTOEY OF THE UNITED STATES. 
 For general suggestions, see preceding grades. 
 
 SYLLABUS. 
 
 Review, and teach as follows : 
 
 The Outlines of the Revolutionary War. — (Teach as in the French and 
 Indian War.) 
 
 Causes of the Revolution. — Navigation Acts — restriction of colonial 
 manufactures — effects of war on the national debt of England — taxa- 
 tion without representation — the Stamp Act, 1765 — its nature — causes 
 which led to its repeal — the Tea Tax — riot in Boston, 1770 — the Boston 
 •' Tea Party " — its immediate causes, and its consequences — Nature of 
 the Port Bill, 1774 — first Congress at Philadelphia, its measures — Lex- 
 ington, April 19, 1775 — its effects upon the country — Bunker Hill — 
 siege of Boston — Washington appointed Commander-in-Chief — evacua- 
 tion of Boston, and subsequent general drift of military events to- 
 ward the West and South — Declaration of Independence, July 4, 1776 
 — battle of Long Island — its purposes and results — retreat to the Dela- 
 ware—capture of the Hessians at Trenton — Princeton — La Fayette — 
 British move on Philadelphia, 1777 — Chad's Ford — its consequences — 
 Burgoyne's invasion, its route and purpose, 1777 — Schuyler — Bur- 
 goyne's disasters — Gates — the two battles of Stillwater — Clinton's 
 movements — Burgoyne's Surrender .^ October, 1777 — its far-reaching 
 consequences — the French alliance and assistance — British retreat 
 from Philadelphia— battle of Monmouth, 1778 — New York the base of 
 the British — destruction along the coasts of Connecticut and Virginia 
 — Wyoming — battle of the Chemung, 1779 — it breaks forever the 
 power of the Iroquois — Paul Jones — Charleston captured, 1780 — Large 
 numbers of Tories in the South — consequent years of guerilla warfare 
 — Sumter — Marion — Gates at Camden — destruction of his army, and 
 of Sumter's force — Arnold's treason — the mutiny at Morristown, 1781 —
 
 HISTORY OF THE UXITED STATES. 121 
 
 its causes — condition of the Army — Robert Morris — Arnold's ravages — 
 Greene's retreat — battles in Carolina aud their consequences— Corn- 
 wallis at Yorktown— combination of the French and American forces — 
 Surrender of CormcalUs, October, 1781 — its effects in America aud 
 England — Treaty of Paris, 1783 — its terms — condition of the country. 
 
 Articles of Confederation, 177o, 1777, 1781 — the Government before 
 1781 — after 1781 — Shays' rebellion, 1780 — lead* to a convention to re- 
 vise the Articles^a new Constilution devised instead, 1787 — adopted 
 by the States — goes into operation, 1789 — ordinance of 1787. 
 
 1789-1797 — Washington' s Adininistration. — Domestic History. — Cabi- 
 net — leading measures — States admitted — their former relations. 
 
 1797-180 1 — Adams' Administration . — Foreign relations. — Continued 
 troubles with France. Domestic History. — Unpopular measures — the 
 death of Washiugtoa — removal of the Capital. 
 
 1801-1809 — Jefferson's Administration. — Domestic History. — Admis- 
 sion of Ohio— its previous relations. The Louisiana purchase, its im- 
 mediate and subsequent importance. Hamilton and Burr, 1804 — a 
 sketch of the history of each. Fulton's first steamboat, 1807. Foreign 
 relations. — Tripolitan war, 1801-1805, its causes aud results. {Read 
 the detail, if given.) 
 
 The state of Europe, and the importance of our carrying trade. Ex- 
 traordinary measures of France and England in relation to the rights 
 of neutrals. English claims of right of search and impressment — bear- 
 ing of the impressment claim upon our naturalized citizens, and our 
 national honor. ''Once a subject, always a subject." Affair of the 
 Leopard and Chesapeake, 1807. Orders in Council and tlie Milan De- 
 cree, 1807. Embargo, 1807-1809. Non-iutercourse Act, 1809. 
 
 1809-1817 — Madison's Administration. — The entire interest centres 
 in the Foreign relations — they control the Domestic history. Berlin De- 
 cree abolished, 1810. (Bead the affair cf the Little Belt — Indian war.) 
 
 War declared June 19, 1813 — its two chief causes. 
 
 Note. — Bead the detail of the military and naval operations ; show 
 briefly in outline, first, the aggressive expeditious into Canada, from 
 Detroit to the St. Lawrence ; their general failure ; second the small- 
 ness of the navy— its brilliant success, but little direct influence on the 
 fortunes of the war, excepting on the Lakes — utter destruction of 
 American commerce ; third, the aggressive expeditions of the British, 
 the Americans being chiefly on the defensive after 1812. Indian war 
 in the West and Southwest. Invasions from Canada. Blockade of all 
 important ports. Naval and militarj' expedition against Washington 
 and Baltimore. Invasion by the way of Lake Chtimpl.iin. Expedition
 
 122 SECOND GRADE. 
 
 against New Orleans, and its purposes — final repulse of all these at- 
 tempts, and similar fate of renewed aggressions of the Americans 
 against Canada. Destruction of the Indian power. 
 
 Give the sequence of leading events, omitting the dates, excepting 
 as to years. 
 
 The Hartford Convention — its alleged purposes— its effects. Treaty 
 of Peace, December, 1814. A part of the general pacification of 
 Europe upon the fall of Napoleon. The causes of the war not even 
 alluded to in the treaty. Have these questions ever been settled ? If 
 so, when and how? 
 
 Note. — Read the second Barbary war, 1813-1815 — its causes and 
 results. 
 
 181 7-1 825— Monroe's Administration, — Domestic History. — Missouri 
 Compromise, 1830 — formation of new parties on questions of com- 
 merce and finance. Whigs and Democrats. The leading que-tiona 
 until 1845. Foreign relations. ^ — Purchase of Florida. The Monroe 
 Doctrine, 1823, its origin and importance. 
 
 1825-1829— Jtf/i/i Quincy Adams' Administration. — Tariff of 1838, 
 and its consequences. 
 
 1 839-1837 — Jackson's Administration. — Domestic History. — United 
 States Bank. Nullification, 1832. Clay's Compromise. 
 
 1837-1841 — Van Buren's Administration. — Panic of 1837. Sub- 
 Treasury Bill, 1840- Political revolution. 
 
 1841-1845 — Harrison and Tz/ler's Administration. — Domestic History. 
 — Bankrupt Law. Dorr's Rebellion. Foreign relations. — The Maine 
 boundary. Annexation of Texas. 
 
 1845-1849 — Fo!k's Administration. — Domestic relations now give di- 
 rection to Foreign policy. Oregon boundary. . Chain of ca".ses leading 
 to the Mexican war. Boundary claimed by Texas. Mexican war, 
 May, 1846, to February, 1848. 
 
 Note. — Head the details ; give the leading military events in se- 
 quence, omitting all dates excepting years. Teach with the following 
 grouping : Northern operations — Taylor east of the Rio Grande — west 
 (if it. Wool — Kearney — Doniphan — Fremont. Southern operations : 
 Scoti's campaign. 
 
 Treaty of Guadaloupe Hidalgo — its terms. Discovery of California 
 gold in 1848 — its important subsequent influence upon the national 
 development. 
 
 1849-1853 — Taylor and Fillmore's Administration. — Slavery question 
 the leading element in subsequent history. California question, 1850 
 — its alleged relation to the Missouri Compromise. Death of Taylor 
 Clay's Compromise Bill, 1850.
 
 HISTORY OF THE UNITED STATES. 123 
 
 1853-1857 — Pierce's Administration. — Effects of the Fugitive Slave 
 Bill. Kansas-Nebraska Bill, 1854 — it abrogates the Missouri Compro- 
 mise. Rise of a new party, " Free soil" or Republican. Civil war in 
 Kansas, its causes ; flow of immigrants into the Territory. 
 
 1857-1861 — Buchaiinn's Administration. — Kansas troubles. John 
 Brown's afEair — ^its effects. Split of the great Democratic party. Four 
 Presidential candidates. Election of Lincoln. Extreme doctrine of 
 State Rights. Secession of South Carolina, December, 1860. Fort 
 Sumter. More States secede. Confederate Government formed, 
 February, 1861. 
 
 1861-1865 — Lijicolrt's Administration. — Civil "War. Fort Sumter, 
 April 12, 1861. Effects upon the North. President's proclamation. 
 More States secede, making eleven in all. 
 
 Note. — Read the details of the war ; show the importance of foreign 
 intervention, and the efforts on both sides in regard to it. 
 
 lu the review show that the operations of the Confederates were 
 mainly defensive, except in the great sorties of Lee at Antietam and 
 Gettysburg, of Hood at Nashville, and of Early at Chambersburg — all 
 of which were repelled. That the main objects of the aggressive 
 movements of the Union troops were, 1st, the destruction of Lee's 
 army ; 2d, the opening of the Mississippi. That after the opening of 
 that river by the fall of Forts Henry and Donelson, and the subse- 
 quent capture of New Orleans and Vicksburg, the lines were con- 
 tracted by a movement from the northwest to the southeast, ending in 
 Sherman's march from Atlanta to Savannah and Goldsboro'. The 
 leading incidents will then readily fall into place. Show the im- 
 portance of the blockade, the chief function of the fleet ; also, but very 
 briefly, the enormous expenditure of men and money on both bides, 
 and the measures by which they .were obtained. 
 
 1865-1869 — Johnson's Administration. — Death of Lincoln. The two 
 subjects of leading importance— 1st, providing for the public debt; 
 2d, reconstruction. The Thirteenth Amendment. The President and 
 Congress quarrel. Impeachment. The French in Mexico and the de- 
 mand of the United States Government. Purchase of Alaska. Laying 
 of the Atlantic cable. 
 
 1860-1877 — GranVs Administration. — Pacific Railway. Fourteenth 
 and Fifteenth Amendments. Alabama question. Leading provisions 
 of the Treaty of Washington. The Geneva arbitration. 
 
 1877-1881 — Ilayei Administration. — Dispute about election of 
 Tilden. 
 
 1881 — Garfield's Admirmtration. — Death of Garfield. Successor, 
 Vice-President Chester A. Arthur.
 
 FIRST GRADE. 
 
 Outline Course. 
 
 1. Language Lessons. — Reading, spelling, meaning, and use of 
 words, continued ; supplementary reading as before ; English Gram- 
 mar, continued ; composition, continued ; a review of the previous 
 grades in t^e formation of woi'ds. 
 
 2. Arithmetic. — Written and mental: a review of the business 
 arithmetic of the preceding grades ; also, exchange, equation of pay- 
 ments, averaging accounts, custom-house business, partnership, and me?i- 
 suration. 
 
 3. Geography. — A general review. 
 
 4. History of the United States. — A general review, and the principal 
 features of the Federal, State, and Municipal Governments. 
 
 5. Penmanship. — Exercises in copy-books, and in writing selected 
 paragraphs from dictation ; business forms ; letter- writing, continued. 
 
 6. Drawing. — On paper, from illustration on blackboard only. 
 Draw from the round (free hand), hexagonal and octagonal prisms. 
 Groups of the following models : cube, cone, cylinder, plinths, pyra- 
 mid, antique vase. Original designs for industrial purposes. 
 
 The oval, ellipse, hexagon, octagon, pentagon, concentric circles, 
 concentric squares, spiral, equilateral triangle, and trefoil. 
 Two examples of bi-symmetrical historic ornament. 
 
 Perspective Drawing {permissible). — Draw in parallel perspective 
 the cube, square prism, pyramid, hexagonal prism, the circle, cone, 
 and cylinder. 
 
 Draw in angular perspective the cube, square prism, and pyramid.
 
 INSTRUCTIONS AND SUGGESTIONS. 
 
 LANGUAGE. 
 
 The general instructions and suggestions for 
 
 Reading, found on page 20 ; those for 
 
 Spelling, on page 29 ; those for the 
 
 Meaning and Uses of "Words, on page 31 ; and those 
 for 
 
 Composition, on page 28, are to be taken as belonging 
 to this Grade. 
 
 GEAJVJGVIAR. 
 
 1. Sentences of an irregular or idiomatic construction 
 should be presented to the pupil, with the view to show 
 how far they can be made to harmonize with the ordinary 
 methods of construction, and to teach the just limits of 
 their use. 
 
 2. The exercises in grammar should embrace the care- 
 ful and critical study of select passages from some of 
 the best English and American writers ; as Shakspeare, 
 Milton, Pope, Cowper, Young, Bryant, Longfellow, etc. 
 Prose writers, such as Addison, Johnson, etc., should also be 
 drawn upon for exercises, always, however, with a critical 
 end in view, to discover and correct errors, as well as to 
 find exceUences and beauties. 
 
 3. Such exercises, to however limited an extent it is 
 possible to carry them, will always exert an important in-
 
 126 FIRST GRADE. 
 
 fluence upon the pupils' style of composition, if not of 
 daily speech. They will serve, moreover, to cultivate the 
 taste of the pupils, and to awaken an interest in their 
 minds in the study of English and American literature. 
 A good reading- book will be found an important auxiliary 
 in carrying on the instruction here suggested. 
 
 Outline. 
 
 Idiomatic expressions and sentences of irregular construction ; sim- 
 ple, complex, and compound sentences continued ; conjugations ; para- 
 phrases exercising the pupils in the interchange of words and their 
 equivalent phrases, and of phrases and their equivalent clauses. Gen- 
 eral review. 
 
 AEITHMETIC. 
 
 Every topic to be treated in this grade should be intro- 
 duced by mental exercises, the slate being used only when 
 the numbers involved are too large to be readily retained 
 in the mind without being written. The pupils should be 
 constantly practised in this mental work. The text-hook in 
 mental arithmetic should be sparingly used, if used at all; 
 and great care should be exercised in assigning lessons for 
 home-study in this branch. 
 
 SYLLABUS OF TOPICS. 
 
 1. Exchange. — Its nature ; bills of exchange ; par of exchange ; 
 acceptance; domestic exchange — to include two cases. 1. To find 
 the cost of a draft when its face and the rate are given. 2. To find the 
 face, the cost and rate being given ; foreign exchange, including the 
 consideration of bills on England, France, and Germany (cases as in 
 domestic exchange) ; analysis as in percentage. 
 
 2. Equation op Payments. — Cases : 1. To find average time of 
 payment, when the items have the same date^ but different credits. 2. 
 When the items have different dates. 3. To find the average time for 
 paying balance of account, having both debits and credits. Analysis, 
 on the principle of interest ; reduction of each principal involved to $1 
 preferable.
 
 GEOGRAPPIY. 127 
 
 3. CusTOM-HouSE Business. — Meaning and practical applications 
 of the following terms : Customs, Custom-house, Port of Entry, Collec- 
 tor of Port, Tariff, Duties — Specific and Ad Valorem, Invoice, Tare, 
 Tret, or Draft, Gross, Net, etc. 
 
 4. Stocks and Bonds. 
 
 5. Partnership. — Terms defined. Cases: 1. To find each partner'.^ 
 Bhare when the profit or loss is divided according to capital only, in- 
 cluding simple cases of gener<il average. 2. To find it when time is con- 
 sidered. Analysis, fractional, or by means of proportion. 
 
 6. Mensuration. — Include at least the following cases : 1. To find 
 the area of a parallelogram when the base and altitude are given. 2. 
 To find the area of quadrilaterals, with sufficient data. 3. To find the 
 area of triangles. 4. To find the area of a circle. 5. To find the diame- 
 ter or circumference of a circle. 6. To find the solid contents of a 
 cube, parallelepiped, prism, pyramid, cylinder, cone, and sphere. 7. 
 To find the contents of a cask or other vessel. 
 
 GEOGRAPHY. 
 
 General Review, — This review slioiild include and gen- 
 eralize so much of the simple facts of the Physical Geog- 
 raphy already taught in the preceding grades as will enable 
 the pupil to understand and illustrate the great principle 
 of geography as a science, namely, that the resources and 
 development of a country depend intimately upon its sit- 
 uation, latitude, elevation, winds, rain-fall, temperature, 
 soil, minerals, waterways, and the gcnei-al character of its 
 surface. The review of Industrial and Commercial Ge- 
 ography, with which the preceding should be blended, 
 should include a brief outline of the leading agricultural, 
 mineral, and manufactured ])roducts, and the chief exports 
 of the various countries of the world, their principal ports, 
 and especially those that have an important trade with the 
 United States. The review of Political Geography should 
 comprise a brief resume of the names and location of the 
 capitals and large cities of the several countries, and their 
 forms of eovernment.
 
 128 FIKST GRADE. 
 
 HISTOEY OF THE UNITED STATES. 
 
 For general suggestions and syllabus of topics, see pre- 
 ceding grades. The general review should be in all the 
 three forms described on page 81. 
 
 It should also include a brief but definite outline state- 
 ment of the rapid development of the country since 1815, 
 and of the leading elements in that development. Emi- 
 gration and Immigration. Ei-ie Canal and the Great Lakes 
 as the great waterway. Steam — steamboats — railways- 
 telegraphs. In the review include a notice of prominent 
 men, such as Calhoun, Clay, Webster, Seward, Greeley, 
 Fulton, Morse, etc. 
 
 The study of the History of the United States is to in- 
 clude a very brief consideration of the principal features 
 of the Federal, State, and Municipal Governments, but 
 not as a separate study. Only the leading features are to 
 be taught, and most of these as incidental to the current 
 study or review of the lessons in history. For instance, 
 the preamble of the Constitution is intimately comiected 
 with certain historic events, and the real significance both 
 of the events and of the preamble can be perceived only 
 by studying them in combination. Firsts the adoption of 
 the Constitution — see 1787-89 ; Second^ the term ^'^ peo- 
 ple " — not peoples ; Third, States already " united " — see 
 1860 ; Fourth, " more perfect union " — see Articles of Con- 
 federation and the imperfect union then existing ; Fifth, 
 " insure domestic tranquillity " — see Shay's Rebellion, the 
 dangerous boundary disputes of New York, New Hamp- 
 shire, Vermont, and other States, etc. Again, the im- 
 peachment of Burr, or of Johnson, the succession of Tyler 
 and other Yice-Presidents to the presidency, etc., will give
 
 HISTORY OF THE UNITED STATES. 129 
 
 proper occasion to consider tlie functions of these officers 
 and of the Supreme Court. The Whiskey Rebellion and 
 the Nullification dispute will give significance to the phrase 
 " power to lay and collect taxes, duties, excise," etc. ; 1812 
 and 1846 will illustrate "power to declare war" — and so 
 on with scores of points of interest and importance to 
 every intelligent citizen. A brief and convenient syllabus 
 is subjoined. 
 
 SYLLABUS OF TOPICS. 
 
 Constitution. — Meaning of the term ; supreme law ; when, why, how, 
 and by whom established ; how amended. 
 
 Branches of Government. — General function of each ; what and who 
 are citizens ; some of their most important rights ; rights of accused 
 persons ; fugitives from justice. Census ; when and why taken. 
 
 Congress. — Branches ; principal powers of Congress ; powers denied ; 
 on holding other offices ; time and place of meeting. 
 
 Senate. — Ntimber of Senators ; qualifications ; by whom chosen ; they 
 represent the States as States ; term ; chief special powers and duties ; 
 presiding officer. 
 
 House of Representatives. — Number from each State ; qualifications ; 
 by whom chosen; direct representatives of the "people" — not of a 
 State, but of the United States. Principal special powers and duties ; 
 presiding officer. 
 
 Laws. — The several stages by which a " bill " becomes a law. 
 
 Executive. — President and Vice-President ; qualifications ; how chosen ; 
 chief powers and duties ; veto. 
 
 Judiciary (very briefly). — Courts ; judges ; how appointed ; general 
 duties ; impeachment. 
 
 State Governments. — Officials ; Legislature ; branches ; law-making 
 power ; where meet ; municipal government ; cities ; officials ; their 
 powers and duties. 
 
 Im,portant Terms and Phrases. — Trial by jury ; habeas corpus act ; ex 
 post facto law ; treason ; attainder ; quorum ; elector ; presidential 
 elector. 
 
 6*
 
 130 PENMANSHIP. 
 
 PEOIANSHIP. 
 
 Penma/nship is prescribed to be taught in each grade of 
 the Grammar School Course : in addition to this constant 
 practice is also required in slate-writiiuj,. By means of the 
 latter much can be accomplished in insuring to the pupil 
 readiness and fluency in the exercise of penmanship. 
 
 The exercises in written spelling, composition, etc., 
 sliould be performed with accuracy, even if some sacrifice 
 of rapidity be at first required. Of course, there should 
 be a constant effort to improve both in rapidity and ac- 
 curacy — quantity as well as quality being made a criterion 
 of merit and success. 
 
 The slate-writing should, as far as it is practicable, ex- 
 emplify the principles and methods formally taught in the 
 lessons in penmanship. Pupils should not be permitted 
 to violate in one class of exercises the rules and precepts 
 taught and practised in another. This is especially ap- 
 plicable to the holding of the pencil, which should be 
 sufficiently long to be held as a,_pen. 
 
 The lessons on penmanship should be methodical and 
 progressive, whatever system may be employed. In the 
 lower grades the exercises should be rudimentary, but the 
 pupil should not be retained in them too long. He should 
 be permitted to write as much as possible : making strol:es 
 and curves is not writing, although it may be valuable as 
 leading to it. 
 
 The use of trial 2)apers should not be carried to the ex- 
 treme of withholding the pupil for a considerable tin)e 
 from the use of his copy-book. The pupil should be 
 taught the necessity of doing everj-thing as well as he can 
 do it ; but perfection in details should not be expected in
 
 PENMANSHIP. . 131 
 
 the radimental stages. It should, J'ro?n the first, be deeincd 
 essential (at least meritorious) to execute the prescribed 
 work with despatch, provided there is no want of care or 
 attention. 
 
 A proper distinction should be made between the les- 
 sons given to show the pupils how to write and the exer- 
 cises designed to practise them on what they have thus 
 learned. In the former, the whole class should invariably 
 be occupied in the same work, the teacher explaining, and 
 illustrating from the blackboard, the principles and 
 methods which form the subject of the lesson : in the lat- 
 ter, practice being the object in view, it is not so essential 
 that all the pupils should be doing the same thing at the 
 same time, although even here it is a convenience to the 
 teacher, since it facilitates supervision. 
 
 It should be carefully kept in view that the hand and 
 the eye as well as the ?nindoi the pupil are to be trained in 
 this branch of instruction — the hand to execute, the eye 
 to discern, the mind to judge. These are not to be edu- 
 cated separately and successively, but simultaneously. 
 
 A correct method of holding the pen, a proper position 
 of the body while sitting at the writing-desk, and a suit- 
 able placing of the book or paper, are highly conducive to 
 the acquisition of a good handwriting. Ev^ery lesson 
 should, for some time, be introduced by distinct directions 
 as to the proper method of holding the pen, and these 
 the pupils should not be peruntted to violate. AVith re- 
 gard to the position of body and position of book, a 
 few simple directions will be all that are requisite. The 
 teacher should see that the pupils sit in such a position as 
 to allow perfect freedom of motion of the right hand and 
 arm, ease of respiration, and as much physical ease other- 
 wise as the seat and desk will permit.
 
 132 DRAWING. 
 
 The books should, if possible, be provided with covers 
 and blotters ; the pens should be carefully cleaned at the 
 end of each lesson, and should be changed as often as 
 necessary ; and the ink should be kept in the best condi- 
 tion. Each page of the book should end with the name 
 of the pupil and with the date. 
 
 In the higher grades — the Ji?'st at least — the writing of 
 copies consisting each of a single line, should be discon- 
 tinued ; and paragraphs, verses, business forms, notes, 
 superscriptions, etc., should take their place. The exer- 
 cises in book-keeping should be made subservient to the 
 instruction in penmanship, writing up the usual blank- 
 books being made, to some extent at least, a substitute for 
 the use of copy-books. Yarious styles of writing should 
 be taught, as far as time and opportunity may permit — 
 as the business style, epistolatory style, engrossing style, 
 etc. This has reference to the Female as well as the Male 
 Grammar Schools. 
 
 DRAWING. 
 
 Instructions and Suggestions. 
 
 The course in drawing for the primary classes has been 
 designed to familiarize the pupils with the use of the 
 pencil in drawing (free hand) straight and simple curved 
 lines in different positions ; to teach them to draw lines of 
 given lengths, and to divide lines into equal parts ; to 
 cause them to make applications of this elementary work 
 in drawing various plane figures ; and to give them some 
 idea of symmetry as shown by simple arrangements of 
 straight and curved lines in plane figures. With this prep- 
 aration the pupils of the Grammar Grades should be able,
 
 DRAWING. 133 
 
 without any great difficult}', to accomplish the work laid 
 down for them. In what follows, work of the same 
 character, extending through several grades, is considered 
 under one general head, and not in detail in the separate 
 grades : notes are also made under each grade when found 
 necessary. 
 
 Lead Pencils. — A very soft pencil should not be used 
 for sketching, as it interferes with the neatness of the 
 drawing : a hard pencil should not be used for strengthen- 
 ing lines, as it makes depressions in the paper. If but one 
 pencil be used, let it be of a medium grade. 
 
 In sketching the pencil should be held lightly, at least 
 an inch from the point ; in strengthening a line the pencil 
 may be held nearer the point. Use the point of the lead 
 for fine lines, the side of the lead for stronger ones. 
 
 Eraser's. — In general the eraser is necessary, but it 
 should be used as seldom as possible. To impress upon 
 pupils the necessity of carefulness, have them draw a 
 figure occasionally without the eraser. 
 
 Mechanical Aids. — Mechanical aids, such as rulers, 
 measures, and compasses, may be used with advantage in 
 the following cases : a plane figure which is to inclose a 
 svmmetrical arrano-ement or a desisrn : construction lines of 
 such arrangement or design ; lines that contain a border 
 or that separate its units. 
 
 The construction lines of vases and of conventionalized 
 leaves and flowers are sufiiciently simple to be made with- 
 out mechanical aids. 
 
 Bla^hhoards. — In each grade the blackboard should be 
 used by the teacher to illustrate the method of drawing 
 the figure or of forming the design under consideration : 
 the slate or paper may be used by the pupils to follow 
 rapidly the successive steps of the teacher.
 
 134 DRAWING. 
 
 While it is preferable that the teacher's blackboard 
 sketching should be neat and accurate, it is not essential 
 for this point of the instruction : it is essential, however, 
 that drawings which are to be copied^ whether from chart 
 or blackboard, should be as accurate as it is possible to 
 make them. 
 
 Plane Figures. — All the plane figures are suflSciently 
 simple to be drawn M^ithout mechanical aids. 
 
 Symmetry. — In forming a bi-sym metrical figure the 
 principal axis should be drawn first, the transverse auxili- 
 aries next, and then the outline. If the principal axis be 
 vertical the left-hand portion of the figure should be 
 drawn first ; if horizontal, the upper portion first. These 
 suggestions are often applicable in drawing vases and con- 
 ventionalized leaves. 
 
 Borders. — In drawing horizontal borders it will be well, 
 after the construction lines have been made, to complete 
 tlie left-hand unit before beginning the next: in drawing 
 vertical borders begin at the top. 
 
 Le(mes and Flowers. — Encourage pupils to gather leaves 
 and flowers appropriate to the grade, and teach them to 
 conventionalize them : by this means the pupils will be 
 led to seek originality in design, a most important point 
 in the instruction in drawing. 
 
 Yases. — As it is almost impossible to have a sufficient 
 variety of vases in any school, ask the children to note 
 carefully the forms of such as they may see elsewhere. 
 Have them sketch these rapidly, as they may remember 
 them : from these sketches make selections for general 
 class-work. By preserving the best forms thus gathered, 
 each teacher may, in the course of a few terms, become 
 possessed of a great variety. 
 
 Ornjinal Designs. — In designs for wall-paper, etc.,, in
 
 DEAWING. 135 
 
 wliich a unit is to be repeated, the first unit slionld be 
 drawn with great accuracy ; the remaining units may 
 be " transferred ; " few repetitions of the unit need be 
 made. 
 
 Dravnncj from the Model. — In teaching drawing from 
 the model it is necessary that instruction first be given on 
 such essential points as the following : the apparent con- 
 vergence of receding parallel lines ; the representation of 
 a circle, viewed obliquely, by an ellipse ; tangential lines 
 in a drawing of a cone. After this preliminarj' instruc- 
 tion, tlie model should be so placed that each pupil will 
 liave a good view of its characteristic features : each pupil 
 should then draw it on paper as he sees it. Tlie drawing 
 of the object as it actually appears to each pupil — not the 
 copying of what may appear to some one pupil in a par- 
 ticular position — is the work designed for the Second and 
 First Grades. 
 
 Home Work. — Home work may be given to pupils in 
 the First and Second Grades. 
 
 Seventh Grade. — In the example of surface covering 
 it may be found desirable to arrange the design by actual 
 measurements : the lines, however, should be drawn free- 
 hand. 
 
 Sixth Grade. — It will be well to show the pupils how 
 to make ellipses by means of their foci: afterward teach 
 them to draw, with the aid of the axes, the ellipses speci- 
 fied for this grade. 
 
 The two views of the conventional leaf and flower may 
 be a front and a side view. 
 
 Fifth Grade. — The method of constructing the penta- 
 gon ma}^ be taught the pupils first by mechanical aids : af- 
 terward the same principles of construction should be i\\>- 
 plied in drawing it free-hand.
 
 136 INSTRUCTION IN VOCAL MUSIC. 
 
 Fourth Grade. — Three convolutions of the spiral will 
 be sufficient. 
 
 Third Grade. — In the circular border the ornamenta- 
 tion should not be so minute as to cause many repetitions 
 of a unit. 
 
 COUESE OF IXSTEUCTION IN VOCAL MUSIC. 
 
 Eighth Grade. — Songs and exercises in key of C. 
 Whole, half, and quarter notes and rests. Dotted halves 
 and quarters. Double, triple, and quadruple time. Ex- 
 pression marks J9, f, mf. Common chord in three posi- 
 tions. 
 
 Seventh Grade. — Songs and exercises in key of C. 
 Scale extended upward to F, downward to G. Sixteenth 
 notes and rests. Dotted eighths. Expression marks ;ff 
 and 2)p. Common chord in three positions. Common 
 intervals. Formation of major scale. Tetrachords. 
 J^otes of common chord in accord. 
 
 Sixth Grade. — Songs and exercises in key of C con- 
 tinued. Formation of G scale and coinparison with that 
 of C. Easy exercises and songs in key of G. Common 
 chord of each key in three positions. Sextuple time. 
 
 Fifth Grade. — Two-part singing in keys of C, G, and 
 F, Use of sign <> . 
 
 Fourth Grade. — Two-part singing in keys of C, G, 
 F and D. 
 
 Third Grade. — Two-part singing in keys of C, G, F, 
 D and A. 
 
 Second Grade. — Two-part singing in keys of C, G, D, 
 A, F, B flat and E flat. Triads. 
 
 First Grade. — Three-part singing. Major and minor 
 thirds. Chord of the seventh. Minor keys.
 
 INSTRUCTION IN VOCAL MUSIC. 137 
 
 Rules Relating to the Posture of the Body and the 
 Position of the Mouth. 
 
 The singer should stand upright, letting the body rest 
 upon both feet, the heels just touching each other. 
 Tlirowing the weight upon one foot is to be avoided, be- 
 cause it forces the body into a curved and inelegant posi- 
 tion, and causes tones produced to be wanting in precision. 
 The arms should neither be fixed rigidly by the side nor 
 be folded across the chest. 
 
 The head should be held easily erect. 
 
 The shoulders should be thrown back, the chest inflated, 
 and the abdomen somewhat drawn in so as to allow the 
 lungs fully to expand. 
 
 The mouth should be opened wide enough to admit the 
 passage of the thumb in its breadth between the front 
 teeth. The jaws should be held one exactly above the 
 other, and the tonirue be allowed to lie flat in the mouth, 
 before any attempt to sing is made. This position of the 
 organs in question should be assumed, lest the nasal 
 sound of n become audible ; and it must not be altered 
 during the continuance of a tone, for by every such 
 change the tone is modified. 
 
 Beware especially of any distortion of the countenance. 
 
 The Breathing. 
 
 The management of the breath in singing is of the 
 greatest importance ; for upon the manner and regularity 
 of the singer's breathing depend the formation of the 
 tone and the successful rendering of the nuisical phrases 
 and of the text. 
 
 The breathing should be done in audibly. The pupil
 
 138 INSTRUCTION IN VOCAL MUSIC. 
 
 sliould be especially instructed in the art of producing 
 prolonged tones at as little expense of breath as possible ; 
 at first with soft tones, with loud tones afterward. 
 
 Breath may be taken at any point wdiere the meaning 
 of the text and the connection of the melody will not be 
 interrupted ; therefore, after pauses or punctuation marks ; 
 at the completion of a musical group ; before long notes ; 
 before the last or after the first beat of a measure ; or, in 
 other words, after the accented beats. The latter direction 
 is given, because at snch points a better conclusion of the 
 melody is possible. It is a rule of the first importance 
 that breath be not taken at a bar ; that is, after an un- 
 accented beat. An exception to this rule is made only 
 when the rhythmic structure of the melody, or the punc- 
 tuation, demands it. 
 
 The time that is needed for breathing never is to be 
 taken from the tone hefore, but from the tone after which 
 breath is drawn. For instance, if the tone after which 
 one breathes is represented by a quarter note, it is sung 
 as an eighth note, the other half of its value in time being 
 used for breathing. 
 
 As the singer should always have a good supply of 
 breath on hand, prudence demands that he should not 
 only use his breath economically, but that he always 
 should take breath wherever, according to the foregoing 
 rules, he is permitted to do so ; for if he do not, he may 
 be forced to breathe Mdien the rules forbid it. Neglect of 
 this wise precautioTi is apt to force the singer to " press " 
 the tone, whereby it receives a languid, thin, uneasy 
 coloring. 
 
 After one long, full breath has been taken, it is well 
 that the subsequent breathings be short or medium in 
 length ; otherwise the lungs may become fatigued. It is,
 
 INSTRUCTION IN VOCAL MUSIC. 139 
 
 perhaps, needless to add that the physical constitution 
 and the age of the singer must always be taken into con- 
 sideration. 
 
 Peonunciation. 
 
 The pronunciation of the words of the text must be 
 clear and correct. A distinct enunciation is of great im- 
 portance in singing ; for upon a clear utterance of the 
 vowel sounds depends the beauty of the tones, and upon 
 a distinct pronunciation of the consonants depends the 
 hearer's understanding of the words of the text. 
 
 Musical accent or rhythm is simple or compound. 
 Double time and triple time are forms of simple rhythm, 
 in each of which the first beat is accented. Double time 
 gives origin to quadruple time ; triple time to sextuple, 
 9-8, and 12-8 time. 
 
 Ex])ressioii depends npon the choice of the right tempo 
 and pitch, the proper degree of loudness, and upon cor- 
 rect declamation. 
 
 In singing, beware of dragging and shouting. The 
 initial tone mnst be given precisely, even in piano pas- 
 sages. The sliding of the voice in search of the right 
 tone is not to be tolerated. The singing must pour foith 
 as from a single mouth. 
 
 Gloomy weather causes the spirit to flag, and makes 
 every exertion a burden ; the judicious teacher will take 
 this into consideration in determining tlie possibilities 
 regarding correctness.
 
 140 PERMISSIBLE SUBJECTS. 
 
 PERMISSIBLE SUBJECTS. 
 
 Elements of plane geometry, algebra, perspective draw- 
 ing, book-keeping, and outlines of astronomy are per- 
 missible subjects. Any or all of these subjects may be 
 taught in any school if permitted by the Committee on 
 Course of Study upon application by the Board of Trus- 
 tees, 
 
 ALGEBRA. 
 
 1. This subject is to be taught as a peculiar mathemati- 
 cal language^ by means of which the relations of quantities 
 and the results of their combinations may be expressed, 
 and reasoning in regard to them may be facilitated. The 
 symbols of quantity, relation, and operation, should at first 
 be carefully taught and illustrated. 
 
 2. The simple operations of addition, subtraction, mul- 
 tiplication, and division, should not be exhaustively treated, 
 as is usually done, before the pupil is made acquainted 
 with the nature and use of equations. The equation is to 
 Algebra what the proposition is to ordinary language. It 
 is the means of definitely expressing a mathematical truth, 
 either particular or general. Inequations (technically so 
 called) express truths, but not exactly. When we say 
 X + y > T5, we do not indicate Tiow much the sum of x 
 and y exceeds 75 ; but when we say x+y = 6, we express 
 a pi'ecise fact. It is suggested, therefore, that equations 
 be presented very soon after the preliminary explanation 
 of the symbols employed. The examples of equations 
 first presented should be of the simplest character ; and 
 their use in the solution of problems should be objectively 
 shown. This can be done by employing a few very easy 
 questions ; as, What number is that, to tJie half of which if
 
 PERMISSIBLE SUBJECTS. 141 
 
 5 he added the sum will Jt? 11 ? The pupil can be easily 
 made to perceive the use of so expressing the condition 
 that it can be kept clearly in view ; as {x representing the 
 unknown number) f + 5 = 11. 
 
 } In solving such a problem, the successive steps or jpro- 
 cesscs of reasoning should be kept in view. Thus, sub- 
 tracting 5 from each member, the result (expressed by a 
 second equation) is, f = 6 ; and, multiplying by 2, the re- 
 sult (expressed by a third equation) is x = 12, which gives 
 the solution. (Applied axiom to be referred to.) 
 
 Such an exercise, properly performed, will develop more 
 intelligence than will whole months of mechanically work- 
 ing out by blind rules, long sums in addition, subtraction, 
 multiplication, and division. These exercises are proper 
 in their place, but of themselves they have little, if any, 
 educational or practical value. 
 
 Syllabus op Topics. 
 
 1. Preliminary eyplanation of symbols — letters, as representatives of 
 quantity signs ; signs of relation or operation, as, +, — , x , -j-, =, etc.; 
 exercises to familiarize the pupil with their significance and the mode of 
 reading them. 
 
 Note. — It will be of great service to accustom the pupil to read alge- 
 braic expressions in such a way as at once to indicate their meaning ; 
 as, a -h 6, the sum of a and b ; a—h, the difference between a and h ; 
 a X hy the product of n and h, etc. Exercises in finding the numerical 
 value of expressions, when particular values are attributed to the repre- 
 sentative letters, will greatly aid in accomplishing this result. Thus, 
 
 find the value of — — 6", when a = 3, b = 2, c = l, etc. 
 c 
 
 2. Easy problems in arithmetic, the solutions of which may be facil- 
 itated by the use of equations, the latter to be of the simplest form, and 
 involving only an application of the pupils' acquired knowledge of 
 symbols. This will at once show the pupils the value of the algebraic 
 notation, and will interest them in the study of the subject, as being of 
 practical value.
 
 142 PERMISSIBLE SUBJECTS. 
 
 3. Mental practice in solving such problems, by means of equations. 
 Most of the text-books in use will afford a sufficient variety. 
 
 4. Practice in solving equations of this character ; each equation to 
 
 X X 
 
 be read previously in the form of a problem ; as — = 10, which 
 
 3 8 
 may be read : What number is that one-third of which exceeds one- 
 eighth of it by 10 ? 
 
 The method of clearing equations of fractions and of transposition 
 should be taught, not by applying mechanical rules, but as processes of 
 analytical reasoning. Thus, in the equation above given, the pupil 
 will easily be made to perceive, that the multiplication of both members 
 by 24 will produce an equation without fractions. 
 
 5. After the pupils have acquired a clear idea of the nature and use 
 of equations, and some expertness in operating with those of a simple 
 character, those of a more difficult or complex form should be pre- 
 sented — giving occasion for the use of the operations of addition, sub- 
 traction, multiplication, and division, which can then be more exhaus- 
 tively treated. 
 
 6. The nature of literal equations or general expressions should then 
 be taught, and examjiles be given, some of which may be made to in- 
 volve an application of all these processes. Such as the following are 
 suggested : 
 
 X 4- a X — a 
 
 (1.) =d 
 
 b c 
 
 X — a X — b 
 
 (3.) + = 2 
 
 b a 
 
 X — a- X — b^ 
 
 (3.) = 
 
 b a 
 
 (4.) =1 
 
 a — b a + b 
 (a + b) X (a — b) X 
 
 a — b a + b 
 
 Such equations as the above involve much useful practice, not only 
 in adding, subtracting, multiplying, and dividing, but also in fractions 
 and in factoring. The latter should receive careful attention. 
 
 6. The method of solving equations containing more than one un- 
 known quantity — involving the various methods of elimination— should
 
 PERMISSIBLE SUBJECTS. 143 
 
 follow this, and sufficient practice in the sohition of problems should also 
 be afforded. The latter, with the preparation herein indicated, may bo 
 made a most important aid in training the mind to careful and exact 
 analysis, and logical reasoning — perhaps the most important object, 
 generally, of the study of this subject. 
 
 Note. — This syllabus is not designed to be entirely exhaustive, but 
 to afford hints as to the order and method of presenting the most im- 
 portant topics. 
 
 ELEMENTS OF PLANE-GEOMETRY. 
 
 The study of geometry, properly pursued, is of great 
 advantage in several respects: it trains the pupil in habits 
 of careful observations and of accurate e.xpression ; devel- 
 ops methods of close and critical reasoning, and furnishes 
 the scholar with many principles essential to the study of 
 mensuration, and of great practical value in the various 
 departments of drawing. 
 
 In presenting this subject to the pupil the teacher 
 should be very careful not to confine the attention to or 
 dwell unduly upon any one of the purposes indicated 
 above, but should, by variety of method, combine all the 
 advantages to be gained from the study of geometry. 
 
 As the course in geometry is intended to be of a strictly 
 elementary character, it is essential that there be made a 
 careful selection of those propositions that are of a funda- 
 mental character, or of general practical application, and 
 such selection should be the basis of the instruction. The 
 proper selection having been made it will be found that, 
 with accurately drawn figures, many of the propositions 
 will be discovered by the pupils, and, after a little prac- 
 tice, will be accurately stated ; the drawing should, as far 
 as practicable, be done by the pupils themselves. Simi- 
 larly, simple geometrical constructions can be made in ac- 
 cordance with the propositions thus discovered. Finally, 
 some of the simpler demonstrations may be elicited.
 
 144 PERMISSIBLE SUBJECTS. 
 
 To encourage the slower pupils, and to keep the body 
 of the class from depending upon the few more precocious 
 minds, it will at times be found advisable to have each 
 scholar draw the figure upon a slate, and write whatever 
 geometrical fact he may see ; for instance, if isosceles trian- 
 gles be drawn, many of the scholars will readily perceive 
 the equality of certain angles. Similar practice may be 
 given in constructions and demonstrations. 
 
 The selected propositions that have been found too 
 difficult for consideration in the preliminary discussion of 
 the subject may be taught with the aid of an elementary 
 text-book. In using this it is essential that the theorem 
 be carefully analyzed ; the diagram be drawn in obedience 
 to the conditions of the theorem— not in imitation of the 
 figure in the text-book ; and that the demonstration be a 
 conclusion from things clearly seen and correctly stated by 
 the pupil reciting — not a mere repetition of words, how- 
 ever well committed to memory. 
 
 BOOK-KEEPING. 
 
 1. After the forms required in single-entry book-keeping 
 liave been briefly taught, the nature of double-entry book- 
 keeping should be explained, by showing the relation of 
 dehit and credit, by means of which one set of entries may 
 be made to verify the accuracy of another. 
 
 2. The classification of accounts should be followed by 
 an explanation of the three books — Day-Book, Journal, 
 and Ledger. Journalizing simple entries in the Day-Book 
 should then be taught ; and sufficient exercises be given to 
 impart readiness and accuracy in the process. Then by 
 keeping a simple and brief set of accounts, the pupils will 
 understand the whole theory and process, and will also be- 
 come sufficiently expert in their application.
 
 PERMISSIBLE SUBJECTS. 145 
 
 3. All the common husiiuss foimis should be taught ; as 
 the form of bills, receipts, bank checks, promissory notes, 
 bills of exchange, invoices, etc. Business correspondence 
 should also receive attention ; that pupils should become 
 expert in writing a good business letter is of great impoi-t- 
 ance. In every exercise fluency, legibility, and grace in 
 penmanship should be carefully attended to. Both quantity 
 and quality should be insisted on, 
 
 ASTRONOMY. 
 
 1. Astronomy, like the other permissible subjects, when 
 selected and taken as one of the studies of a class, is to be 
 examined and reported upon by the Principal, as in the 
 case of studies regularly prescribed for all schools. 
 
 2. It is to be borne in mind that the chief purpose of 
 this study in the Grammar Schools is, to teach the pupil 
 to look intelligently upon the heavens; not with the min- 
 ute and profound knowledge of the astronomer, bnt with 
 such knowledge as is readily attainable even by the young 
 mind, when its inspection of the common phenomena of 
 the heavens is properlj^ supervised and directed. 
 
 3. Nor should the teacher fail, in connection with this 
 instruction, incidentally to impress upon the pupil, that, 
 in studying the laws and facts of the universe, he is con- 
 templating the works of a beneficent Creator, infinite in 
 wisdom and power. No subject is so well qualified as as- 
 tronomj' to give just ideas in this respect, and, while pei-- 
 forming a peculiar and most important otHce in the train- 
 ing and development of the intellectual powers, to exalt 
 the understanding and give elevation and tone to the 
 whole character. 
 
 4. A syllabus of leading points is subjoined. It will be 
 
 7
 
 146 PERMISSIBLE SUBJECTS. 
 
 seen that nearly all of these may be readily taught without 
 astronomical instruments or apparatus other than a globe 
 and a blackboard. The highly interesting results of in- 
 strumental observation should be read in connection with 
 the pupils' own observations, but no time should be spent 
 in the endeavor to commit to memory the precise mathe- 
 matical and other results. Just ideas of the magnitude 
 of the heavenly bodies and of the interplanetary and 
 interstellar spaces may readily be retained from careful 
 reading. 
 
 5. As in the oral lessons of the lower grades, it is to be 
 expressly understood that it is not expected that the whole 
 of the subjoined syllabus will be taught, but that the Prin- 
 cipal will make such selection of topics and parts of topics 
 as he may think expedient. The only special conditions 
 2a'e, first, that as far as time and opportunity will allow, the 
 pupils shall be led to observe for themselves the most 
 simple and obvious phenomena of the heavens ; and, second^ 
 that a record of topics considered be kept to show progress. 
 
 Syllabits. 
 
 The Heavens. — Apparent shape of (an illusion). — Things we see there 
 — clouds, sun, moon, stars, comets, meteors, aurora. Horizon, the circu- 
 lar hase of the visible heavens — where they seem to rest upon the earth. 
 Apparent daily motion of the whole heavens — easily seen by different 
 positions of stars and moon at early and late hours of a winter's evening. 
 Notice the circular and oblique character of these motions. Some stars 
 move very slowly and make very small circles — this easily leads to dis- 
 covery of the nearly motionless Pole star ; it never sets (to us). A very 
 few conspicuous and neighboring constellations (Great Bear, Little 
 Bear, Swan). How to recognize the Pole star. How to know which 
 way north is. Show that the sun from its rising to its setting has similar 
 motions. Highest daily point of sun — noon — meridian (through this 
 point and noi'th and south). 
 
 The Earth. — Shape, how known — ships, mountainous islands, shadow 
 on moon in lunar eclipse (all these known to the learned among
 
 PERMISSIBLE SUBJECTS. 147 
 
 the ancients). Size, motion around sun, a year, meaning of orbit. 
 Motion on axis, known from apparent daily motions of stars, etc. 
 "What a day is. Inclination of axis to plane of orbit (indispensable for ex- 
 plaining the seasons), 23^". Tropics, polar circles, parallels, zones, lati- 
 tude, longitude. 
 
 The Sun. — Varying points and times of rising and setting — correspond- 
 ing variation of length of day and night — its connection with the seasons. 
 AVhen it is noon. Variation of clock time with difference of longitude — 
 examples given. What a clock is. A good clock more regular than the 
 sun. Why. Cses of a noon-mark and the table Equation of Time in 
 almanac (useful and easily shown in class-room). 
 
 Solar influences — brief reference to animal and vegetable life, and to 
 currents in atmosphere and oceans, etc. 
 
 Distance of the sun — magnitude. 
 
 What the telescope tells us of the sun — (briefly) read. 
 
 Solar System. — Brief general outline of its composition and arrange- 
 ment. Use a diagram. 
 
 77ie Moon. — Phases. Why. New moon, where first seen. Eastward 
 motion in orbit — the word month. The "old moon in the new moon's 
 arms" — why the dark side is then visible (effect of "earth-shine"). 
 Eclipses lunar and solar (briefly). Lunar influences — tides — pseudo- 
 scientific and superstitious notions about the moon's influences. Distance 
 and size of the moon. What the telescope tells about the moon (read). 
 
 The Planets. — How known — why so called. Fixed stars -why so 
 called. Names of chief planets — make use of almanac to identify them. 
 How they severally look to the naked eye. Morning star, evening 
 star. What the telescope tells us of the chief planets (read). 
 
 Fixed Stars. — A few general ideas in regard to their enormous dis- 
 tances — magnitude — how known to be suns. What the telescope tells 
 of their number. 
 
 The following should from time to time receive brief attention and 
 explanation, so much at least as to insure the pupil's having some in- 
 telligent ideas concerning them. Comets, Meteors, Milky Way, Aurora, 
 Zodiacal Constellations, Zodiacal Light. Importance of Astronomy to 
 Commerce.
 
 A48 INSTRUCTION IN GERMAN AND FRENCH. 
 
 COURSE OF INSTRUCTION IN THE GERMAN 
 AND FRENCH LANGUAGES. 
 
 COURSE OF INSTRUCTION IN THE GERMAN LANGUAGE. 
 FOURTH GRADE. 
 
 1. The Alphahet. — Both printed and script, with exer- 
 cises in reading and writing. 
 
 2. Graimnar. — Declension of tlie Definite and Indefinite 
 Articles and the Noun ; the present and imperfect tenses 
 of sein and haben. The cardinal numbers from one to one 
 hundred. 
 
 3. Translaiions. — Both oral and written, of simple sen- 
 tences, including examples under the rules learned in the 
 grammatical lessons of this grade, as well as subject, pre- 
 dicate, object, and simple adjuncts. 
 
 4. Colloquial Eicercises. 
 
 THIRD GRADE. 
 
 1. Exercises in Reading and Writing, continued. 
 
 2. Grammar. — Declension of Adjectives and Pronouns. 
 The active voice of the weak conjugation. 
 
 3. Translations. — Oral and written, including examples 
 under the rules of the grammar lessons of this grade, as 
 well as of prepositions ; also easy compound sentences. 
 
 4. Colloquial Exercises. 
 
 SECOND GRADE. 
 
 1. Exercises in Reading and "Writing, continued. 
 
 2. Grammar. — The passive voice of the weak conjuga- 
 tion. The principal parts of strong and irregular verbs.
 
 INSTRUCTION IN GERMAN AND FRENCH. 149 
 
 3. Translations. — Oral and written, of sentences afford- 
 ing practice in tlie application of the several tenses of the 
 verb, and in compound sentences. 
 
 4. Readiwj. — From a German Reader, with translations 
 into English, and exercise in etymology. 
 
 COURSE OF INSTRUCTION IN THE FRENCH LANGUAGE. 
 FOURTH GRADE. 
 
 1. Reading. — Rnles of Pronunciation and the accents, 
 
 2. Grammar. — The Definite and Indefinite xirticles ; 
 Xouns, formation of the plural ; Adjectives, formation of 
 the feminine gender and comparisons ; Auxiliary verbs 
 avoir and etre. First conjugation of regular verbs. 
 
 3. Translations. — Oral and written, including exercises 
 on the grammatical rules taught in the grade ; also the use 
 of nouns in a partitive sense, the place of nouns in a ques- 
 tion, and the form of negative sentences. 
 
 4. Colloquial Exercises adapted to the grade. 
 
 THIRD GRADE. 
 
 1. Reading and Pronunciation, continued. 
 
 2. G-rammar. — Pronouns ; the second, third, and fourth 
 conjugations of the regular verbs ; some of the principal 
 irregular verbs; adverbs. 
 
 3. Translations. — Oral and written, on the grammatical 
 rules taught in this grade. 
 
 4. Colloquial Exercises adapted to the grade. 
 
 SECOND GRADE. 
 
 1. Reading and Pronunciation, continued. 
 
 2. Grammar. — Regular verbs reviewed ; irregular verbs
 
 150 INSTRUCTION IN GERMAN AND FRENCH. 
 
 continued ; the principal rules on the use of moods and 
 tenses. 
 
 3. Translations from a French Reader ; also oral and 
 written translations in the grammatical rules of the grade. 
 
 4. Colloquial Exercises adapted to the grade. 
 
 5. Easy Comjpositions. 
 
 INSTRUCTIONS AND SUGGESTIONS. 
 
 1. The course of instruction in German and French has 
 been framed with a view to impart to the pupils of the 
 liigher grades of the Grammar Schools a rudimentary 
 knowledge of these two languages, as well as to enable the 
 pupils to acquire, by comparison, a better insight into the 
 structure of the English language. 
 
 2. Pronunciation and Reading. — As the rules of pro- 
 nunciation in these languages differ very widely from 
 those that prevail in English, it is of importance, from 
 the beginning, to direct the pupils' attention to these dif- 
 ferences. They should be required to practise as soon as 
 possible all the peculiar sounds of the foreign language ; 
 and this practice should be continued in every recitation 
 until they are able to pronounce these sounds with consid- 
 erable facility. 
 
 3. It is much better to practise the sounds as they 
 occur in words, than to practise separately as phonic exer- 
 cises. The pupils will more easily acquire the sounds of 
 the German u and eh by pronouncing the word Biicher than 
 by a continuous repetition of these as separate sounds. 
 
 4. It should always be borne in mind by the teacher 
 that the method of learning a foreign language should 
 approximate as nearly as possible to that by which the
 
 INSTRUCTIONS IN GERMAN AND FRENCH. 151 
 
 mother tongue is acquired ; and tiiat the acquisition of a 
 correct pronunciation will be sooner made by imitating the 
 sound, as pronounced by the teacher, than by memorizing 
 any set rules. 
 
 5. Grammai'. — Care should be taken not to waste time 
 in the needless memorizing of grammatical rules. A fa- 
 miliarity with the principal inflections in the different 
 parts of speech will suffice to enable the scholars to un- 
 derstand the reading lessons, and to practise easy colloquial 
 exercises. 
 
 6. Translation. — The translation of simple sentences 
 into English should be commenced as soon as possible, as 
 this exercise affords valuable practice in the application 
 of the grammatical knowledge acquired. The translation 
 should at first be entirely literal, to be followed by a com- 
 parison of the idiomatic expressions of the two languages, 
 as far as they occur in the lesson. This practice becomes 
 especially im}>ortant in the Second Grade, in which a Read- 
 er is to be employed, and in which the pieces to be trans- 
 lated are longer and more difficult. Written translations 
 should be frequently required, as this promotes care and 
 precision in rendering the meaning, and besides is particu- 
 larly valuable for the training which it affords in English 
 composition. 
 
 7. Colloquial Exercises. — These are of the greatest im- 
 portance in the acquisition of a foreign language. The 
 teacher, almost from the first, by a simple series of object 
 lessons, can familiarize the pupils with many of the com- 
 mon colloquial forms of expression ; and this practice can 
 be continued in the use of graded exercises so that in a short 
 time the ear and the tongue of the pupils will become fa- 
 miliarized with the words of the foreign language and a 
 large number of their most necessary combinations.
 
 152 INSTEUCTIONS IN GERMAN AND FRENCH. 
 
 8. Etymology. — As the German language is nearly akin 
 to the Anglo-Saxon, and the French language to the Latin 
 element of English, there is for almost every word, both 
 of the German and the French language, some word in 
 English that may be traced to the same root, though its 
 meaning may be considerably modified. In most cases 
 this affinity is so striking that a simple reference to it 
 will be all that the pupil needs to perceive it. In other 
 cases more care is required to enable the pupil fully to 
 understand the relationship of the words and their mean- 
 ings, especially when the latter have become changed. 
 All such exercises will be found very valuable and inter- 
 esting, as the pupil will recognize in German and French 
 roots and afiixes old etymological acquaintances, made in 
 the study of English in preceding grades. The study of 
 the relationship of English with the foreign language will 
 aid very greatlj' in giving to the English-speaking pupil 
 a knowledge of his mother tongue.
 
 GENERAL REGULATIONS 
 
 EELATIYE TO GKAMMAK SCHOOLS. 
 
 Size of Class. — No class shall contain more than sixty 
 pupils ; this is a very important restriction, and should 
 be strictly observed by every Principal. (See " Seating 
 Capacity," on a subsequent page.) 
 
 Progress of Classes. — Whenever it is found that a class 
 has advanced further in one or two subjects of its grade 
 than it has in others, the Principal of the school may di- 
 rect the teacher to devote less time to the subjects in 
 which the class has thus advanced, and to give more time 
 to the subjects in which the class has made the least prog- 
 ress : provided, however, that the law prescribing the 
 minimum time per week be strictly complied with. By 
 this means the grade of the class may be equalized in all 
 its studies. 
 
 The Course of Study for one grade must be completed 
 and thoroughly reviewed, and the fp\\^\\& promoted, before 
 they can enter upon any part of the Course of Study of 
 the next higher grade. 
 
 In each grade, certain subjects, such as Arithmetic, Ge- 
 ography, Drawing, and Oral Lessons, may be profitably 
 divided into four parts, to be assigned to as many suc- 
 cessive months ; the work of the fifth month to include a 
 careful reconsideration of the essential points. This plan,
 
 154 GENERAL REGULATIONS. 
 
 if adopted, will be understood not to supersede the " brief 
 monthly reviews " specifically called for by the Course of 
 Study. 
 
 1. Order of Exercises, etc. — In the several grades the 
 minimum time for Language Lessons, per week, shall be 
 5 houi's ; Arithmetic, 3 hours ; Penmanship, 2 hours ; Ge- 
 ography, 1 hour ; Drawing, 40 minutes ; History (Grades 
 1, 2, 3, 4, and 5), 40 minutes. 
 
 The remaining time per week to be distributed at the 
 discretion of the Principal. 
 
 2. Opening Exercises, 15 minutes; noon intermission, 
 60 minutes. 
 
 Opening Exercises to commence punctually at 9 o'clock 
 A.M., and dismissal at 3 o'clock p.m. 
 
 Ko class exercise shall take place before 9 o'clock a.m., 
 or after 3 o'clock p.m. 
 
 3. Reading. — In the reading lessons of each grade the 
 pupils shall be required to state in their own language the 
 subject-matter of the lesson. Prose and verse recitations 
 by the pupils in the school shall be selected from books 
 upon the supply list of the Board of Education. 
 
 4. Use of Pencils and Pens. — The pupils not to be al- 
 lowed to write with short pencils ; in all the grades par- 
 ticular attention to be given to the proper manner of 
 holding the pen, and the position at the desk. The exer- 
 cises in each grade to be such as are required to give ease 
 and rapidity, as well as accuracy in style. Blackboard in- 
 struction to be given in each grade. Pupils of the first 
 five grades to be supplied with blank books for dictation 
 exercises, which should be given at least once a week. 
 
 5. Composition. — Compositions shall be written once a 
 week in all grammar classes, in presence of the teachers, 
 upon subjects connected with the oral lessons of the grades,
 
 GENERAL REGULATIONS. 155 
 
 or upon subjects read and explained in the class-room ; 
 and these compositions shall be criticised and rewritten. 
 Home work shall be limited to the First Grade. 
 
 6. Dictation and Connection of Language. — Exercises 
 in writing sentences and paragraphs, from dictation, shall 
 be given in each grade, and the pupils in all the grades 
 shall be trained in the correction of language, and taught 
 to avoid common errors of speech. 
 
 7. Arithmetic. — Eapid calculation in the simple rules 
 of Arithmetic should be practised by all the pupils from 
 the lowest to the highest grade. 
 
 8. Yocal Music. — Instruction in singing shall be given 
 to the pupils in every grade, except the first grade of bovs. 
 The music used shall be such as is found in the books 
 contained in the supply list of the Board of Education. 
 
 9. Sewioig. — Instruction in sewing may be given to the 
 pupils in the Female Grammar Schools. (By-Laws, § 151, 
 page 255, Manual ISStt.) 
 
 Lessons and Recitations. — Xo lesson shall be given to a 
 pupil to be learned out of school until it shall have been 
 sufficiently explained and illustrated by the teacher to the 
 class ; nor shall the lessons be such as to require a period 
 of study each day, in the case of a child of ordinary ca- 
 pacity, longer than two hours. Exercises in grammatical 
 analysis and parsing, and written and mental arithmetic, 
 shall not be assigned for home-study, except to pupils of 
 the First Grade. (By-Laws, § 155, page 262, Manual 1884.) 
 
 In every class, however well graded, the pupils will dif- 
 fer much in age, health, mental capacity, and home advan- 
 tages. A correct and judicious classification by the Prin- 
 cipal will reduce this inequality to a minimum ; but there 
 will still remain a wide field for the exercise of discrimi- 
 nation, care, and caution on the part of the class teacher.
 
 166 GENERAL REGULATIONS. 
 
 The lessons should, in all respects, be adapted to the aver- 
 age ability of the pupils of the class ; but, even beyond 
 this, some allowance will often have to be made in the 
 case of pupils of inferior mental capacity or inferior op- 
 portunities for home-study. Teachers must bear in mind 
 that the one great object of home-study is to train the pu- 
 pils to self- exertion — to give them the ability to depend 
 upon their own efforts as students, and by degrees to dis- 
 pense with the aid of a teacher. It is, therefore, of su- 
 preme importance to avoid everything that will discourage, 
 or deprive of self-reliance ; and nothing has a stronger ten- 
 dency in this direction than the imposition of excessive 
 tasks. 
 
 Teachers are especially admonished to be considerate 
 toward pupils of a delicate constitution, an over-excitable 
 brain and nervous system, or in temporary ill-health. 
 Many children of this class are precocious in mental 
 activity and exceedingly ambitious to excel ; and the 
 gi'eatest care is required to prevent them from injuring 
 themselves by an inordinate devotion to books and study. 
 
 The length of the tasks imposed should be most care- 
 fully scrutinized and adjusted. The practice of assigning 
 a jixed number of words, lines, paragraphs, pages, or ex- 
 amples, without a minute inspection of their nature or 
 contents, is often accompanied with disastrous results. 
 The pupils are wearied and discouraged ; and the parents, 
 finding the work of the school-room transferred to the 
 home-circle, lose all confidence in the judgment and ability 
 of the teacher. 
 
 The teacher should ascertain the methods which pupils 
 employ in home-study. Verbatim study is to be dis- 
 couraged. While making the necessary preliminary ex- 
 planations, a brief abstract of the leading points should be
 
 GENERAL REGULATIONS. 157 
 
 written upon the blackboard, and made the basis of the 
 i-ecitation. This will do much to induce a rational method 
 in study, and prevent a slavish adherence to the text. 
 
 Unless thoroughly familiar with the details of the text- 
 book, the teacher needs special and renewed preparation 
 quite as much as the pupils. Without this he will not 
 succeed. The recitations should be spirited exercises. 
 The questions should be as definite as possible. The 
 teacher should carefully avoid stating in the question any 
 of those facts or principles that should be given by the 
 pupil. The habit of repeating the pupil's answer should 
 be avoided. Pupils should be invariably required to use 
 natural and proper tones in recitation, to enunciate dis- 
 tinctly, and to avoid errors in speech. If this be not 
 done, the special lessons of the reading-book or the gram- 
 mar will be of little avail to break up the pernicious 
 habits of speech which the teacher has himself, by his 
 neglect, assisted to fix. 
 
 The teacher should advise with his pupils as to their 
 hours and opportunities for home-study. Household du- 
 ties, cramped and noisy homes, and bad light, no doubt 
 greatly interfere in many cases. These should be as far 
 as possible ascertained and allowed for. On account of 
 the tendency to myopia caused by studying by artificial 
 light, very small print should be entirely excluded from 
 home-lessons. The many hours of confinement in the 
 crowded class-room, and tlie long-continued and close at- 
 tention required there, make mental rest and relaxation, 
 with some kind of physical exercise, indispensable to 
 growing boys and girls. The teacher should advise that 
 these come before home-study. 
 
 Reviews. — In connection with each new lesson, such a 
 review of previous lessons in the same subject should be
 
 158 GENERAL REGULATIONS. 
 
 had as will cause the pupils properly to associate the facts 
 previously learned and those of the new lesson. 
 
 Brief reviews of the lessons on each subject should be 
 had on Friday of each week. 
 
 On the last Friday of each month there shall be, in 
 every class, a general review of all the studies of the pre- 
 vious month, at which review all text-books shall be laid 
 aside by teachers and pupils. (By-Laws, § 156, page 262, 
 Manual 1884.) 
 
 Physical Training. — The pupils should be exercised 
 daily, in such a manner as to expand the lungs, develop 
 the muscles, and impart an easy and graceful carriage to 
 the body. Calisthenic exercises, to the utmost practicable 
 extent, should be employed for the attainment of these 
 objects. Let the windows be opened, both at the top and 
 at the bottom, for two or three minutes, while the pupils 
 stand and sit several times in succession, and also while 
 they engage in other physical exercises. Due attention 
 should be given to securing a good ventilation of the 
 class room, but all improper use of the windows and ex- 
 posure of pupils to drafts while sitting must be carefully 
 avoided. (See " Physical Education.") 
 
 Discipline. — The children should never he compelled to 
 sit without employment J or the mind, the hands, or the hody. 
 As a means of preserving good order in the class, attract 
 the attention of the pupils by introducing new subjects, by 
 changing the manner of giving the lesson, or by allowing 
 individual pupils to take a special part in the lesson exer- 
 cises. 
 
 They should be taught cleanliness by being led to ob- 
 serve what it is to be cleanly ; and to be truthful and obe- 
 dient, by perceiving examples of these virtues ; and to 
 avoid all bad habits, by being led to look upon them with
 
 GENERAL REGULATIONS. 1.59 
 
 dislike. They should be led to do right by encouragement 
 rather than driven to do so by fear. Judicious praise is 
 more efficient than scolding. (See "Government and 
 Discipline " for instructions.) 
 
 Manners and Morals. — Such instruction should be 
 given daily to the pupils of all the grades as will foster a 
 spirit of kindness and courtesy toward one another, a feel- 
 ing of respect toward parent and teacher, and a love of 
 cleanliness, order, law, and truth. (See " Moral Educa- 
 tion," page 15 ; also " Government and Discipline," page 
 11, for instructions.) 
 
 School Sessions. — The several schools shall be opened at 
 nine o'clock a.m., and the sessions shall be continued until 
 three o'clock p.m., with an intermission of one hour at 
 noon, when the pupils may leave school. An intermis- 
 sion, not to exceed twenty minutes, may also be given 
 during the morning sessions. 
 
 Ko school shall be dismissed, except by special authority 
 of the Trustees, sooner than three o'clock p.m., except that 
 in case of very wet or stormy weather the Principal may 
 detain the pupils in school between the hours of twelve 
 and one o'clock ; but in such cases the school shall be dis- 
 missed for the day at two o'clock p.m. 
 
 Meritorious pupils, as a reward, may be permitted to 
 leave school one hour earlier on Friday of each week. In 
 no case shall any school be dismissed before three o'clock 
 P.M., except as provided in Section 6-i. (By-Laws, § 63, 
 page 147, Manual 1884.) 
 
 Vacatio7is and Holidays. — The vacations and holidays 
 allowed in the schools in the several wards shall be as 
 follows : 
 
 Every Saturday throughout the year ; the day commonly 
 known as Good Friday ; the twenty-second day of Febru-
 
 160 GENERAL REGULATIONS. 
 
 ary; the fourth day of July; any day appointed by the Pres- 
 ident of the United States or the Governor of the State for 
 a public fast or thanksgiving, and the day thereafter ; the 
 twenty -fifth day of December, the second day of January, 
 and the intermediate days ; the thirtieth day of May ; elec- 
 tion day ; the day next following any day above specified, 
 when such latter day shall be Sunday, and the interval 
 between the third of July and the second Monday in Sep- 
 tember. (By-Laws, part of § 63, page 148, Manual 1884.) 
 
 Reading the Bible. — All the schools of this city under 
 the jurisdiction of the Board of Education shall be opened 
 with reading a portion of the Holy Scriptures, without note 
 or comment. (By-Laws, § 134, page 208, Manual 1884.) 
 
 Doors to he Unfastened. — And all modes of egress, 
 including the visitors' doors, shall be left unfastened dur- 
 ing school hours. (By-Laws, § 61, part of subdivision 2, 
 page 140, Manual 1884.) 
 
 Pupils Micst he Residents of the City. — No person other 
 than an actual resident of the city of New York shall be 
 allowed to attend the Normal College or any school under 
 the control of this Board. A boarding and lodging, by a 
 minor, within the city, who leaves the house of his or her 
 parents in another State or county, merely to gain an op- 
 portunity to attend the Public Schools, does not constitute 
 such minor a resident within the meaning of the statute. 
 
 Where a parent, residing in another State or in another 
 county, sends his minor child to the city of New York for 
 the temporary purpose of enabling that child to attend 
 and receive the benefits of the Public Schools, in nowise 
 parting with his control over such child, and intending 
 that the child shall return to him as soon as that tempo- 
 rary process is accomplished, such child, although not i-e- 
 turning to his parents, except at considerable intervals of
 
 GENERAL REGULATIONS. 161 
 
 time, is not a resident in tlie city of New York within the 
 meaning of Section 35 of the Act organizing and regulating 
 the free school system within the city of New York. 
 
 Cases will occur to which this rule may not be applica- 
 ble to the facts ; in such case, if the teacher has any dif- 
 ficulty in determining whether the child be a resident, it 
 shall be referred to the Board. (By-Laws, § 127, page 
 201, Manual 1884.) 
 
 Affes of Pupils. — All children between the ages of five 
 and twenty-one years, residing in the city and county, shall 
 be entitled to attend any of the common schools therein. 
 (Statute Laws, § 1051, page 36, Manual 1884.) 
 
 Vaccination. — No pupil shall be allowed to attend any 
 school, nor shall any teacher be employed in the sauie, 
 unless such pupil or teacher has been vaccinated. 
 
 Every Principal of a school shall require satisfactory 
 evidence of such vaccination as a requisite for the admis- 
 sion, employment, or continuance of a pupil or teacher, and 
 the Principal shall also enter in the register of tlie school 
 the dates, as near as possible, of the respective vaccina- 
 tions of the pupils and teachers, and shall co-operate with 
 such agents of the Board of Health as may be authorized 
 to visit the schools for the purpose of examining and vac- 
 cinating the pupils, and shall require a revaccination of all 
 pupils ascertained by said agents of the Board of Health 
 not to be fully protected by a former vaccination, and no 
 pupil refusing to be so revaccinated, either by the agent 
 of the Board of Health, or by the physician of the family 
 to which he or she may belong, shall be permitted to at- 
 tend any Public School until such requirement is fully 
 complied with. 
 
 A certificate of any physician in good standing in his 
 profession, stating that the pupil does not require revac-
 
 163 GENERAL REGULATIONS. 
 
 cination, shall be accepted by the agents of the Board of 
 Health in lieu of a personal examination. (By-Laws, § 
 130, page 206, Manual 1884.) 
 
 Contagious Diseases. — Whenever it becomes known to 
 the Principal or teacher in charge of a school that a con- 
 tagious disease prevails in a house other than a tenement 
 in which a child or children attending the school lives or 
 live, such child or children shall be immediately excluded 
 from the school, and shall not be readmitted except as 
 elsewhere in this article provided. 
 
 AVhenever the Principal or teacher in charge ascertains 
 that a contagious disease other than small pox or typhus 
 fever exists in a tenement-house, but on one floor only, 
 a child or children living on another floor of the same 
 house need not be for this reason excluded, but children 
 thus situated must be questioned daily about their health 
 and that of their respective families ; and must be sent 
 home at the first symptom of illness, or the first intelli- 
 gence of contagion in their families. 
 
 But if a contagious disease of any description exists on 
 more than one floor of a tenement-house, or if the disease 
 existing on only one floor be small-pox or typhus fever, 
 all children living in the house must be promptly excluded 
 from school. 
 
 Children excluded pursuant to the above rules shall not 
 be again permitted to attend school — 
 
 In case of scarlet fever^ until three weeks after the 
 heginning of the last case, on the floor or in the house, 
 according to whether the exclusion has applied to a floor 
 or an entire house under the above rules. 
 
 In case of measles^ until two weeks after the heginning 
 of the last case, on the floor or in the house, according to 
 the extent of the exclusion.
 
 GENERAL REGULATIONS. 163 
 
 In case of di2>htheria, until one week after tlie termina- 
 tion of the last case, on the floor or in the house, accord- 
 ing to the exclusion. 
 
 In any case of scarlet fever, measles, or diphtheria, until 
 a certificate of the Board of Health is produced, stating 
 that the apartments, bedding, and clothing affected by the 
 contagion have been properly disinfected. 
 
 If the disease be small-jyox or typhus fever, children 
 who have been in such a case excluded must not resume 
 their attendance without producing a certificate from the 
 Board of Health stating that it is safe for them to do so. 
 
 New scholars applying for admission, and living in 
 houses or on floors where a contagious disease prevails, 
 must be admitted or excluded in compliance with the 
 above rules. 
 
 Principals and teachers in charge are required to com- 
 municate to the Clerk of the Board of Education any 
 information received by them relative to this subject and 
 not known to be in his possession. (By-Laws, § 166, page 
 283, Manual 1884.) 
 
 Seating Capacity. — It shall be the duty of every Prin- 
 cipal to reject all applications for the admission of pupils 
 into any school or class whenever the room occupied by 
 the same is filled to the extent of its seating capacity. In 
 fixing the seating capacity of rooms, the following shall 
 be a minimum allowance of floor surface and air space 
 per pupil : 
 
 In the three lower classes of Primary Schools and De- 
 partments, five square feet and seventy cubic feet. 
 
 In the three higher grades, six square feet and eighty 
 cubic feet. 
 
 In the four lower grades of Grammar Schools, seven 
 square feet and ninety cubic feet.
 
 164 GENERAL EEGULATIONS. 
 
 In the four higher grades, nine square feet and one hun- 
 dred cubic feet. 
 
 In the admission of pupils, those residing nearest to any 
 school shall in all cases have the preference. All rejected 
 applicants shall be sent to the nearest school having ac- 
 commodations for thejn. 
 
 The seating capacity of each room in each school build- 
 ing (estimated in accordance with the provisions of this 
 by-law) shall be conspicuously posted in each room. (By- 
 Laws, § 33, subdivision 14, page 103, Manual 1884.) 
 
 See " Size of Class," page 151. 
 
 License Necessary. — No person shall be permitted to 
 perform service in any position as a teacher until licensed. 
 * * * (By-Laws, § 25, part of subdivision 2, page 
 T9, Manual 1884.) 
 
 Teachers to Report their Absence. — Any teacher absent 
 from duty shall report promptly, in writing, to the Princi- 
 pal of the school, the cause of such absence, and state its 
 probable duration, and anj^ teacher wilfully making a false 
 report shall thereby forfeit his or her position. * * * 
 
 !No subordinate teacher, absent from duty, who fails to 
 communicate promptly with the Principal, shall be excused 
 for such absence, nor shall any teachei-s absent be excused 
 except upon a report thereon by the Principal to the Board 
 of Trustees of the "Ward. (By-Laws, § 33, part of sub- 
 division 8, page 100, Manual 1884.) 
 
 Female Teachers to Report Marriage. — Any female 
 teacher marrying, shall report in writing her married name 
 and address to the Clerk of this Board and Chairman of 
 the Board of Trustees of the "Ward in which she is em- 
 ployed ; and any teacher failing to comply with this by- 
 law within thirty days after her marriage, shall thereby 
 forfeit her position as teacher, and all salary that may be
 
 GENERAL REGULATIONS. 165 
 
 due her from the time of lier marriage. (By-Laws, § 33, 
 subdivision 8, page 100, Manual 1884.) 
 
 Time Occxijpied in Teaching. — It shall be the duty of 
 every teacher to occupy the whole of each school session, 
 or time for which the teacher is employed, in the purposes 
 of instruction, or the making of entries necessary to be 
 made at the time; and no assistant teacher shall draw a 
 salary or receive compensation as a special teacher, if em- 
 ployed as such during the regular school hours. (By-Laws, 
 § 33, subdivision 12, page 103, Manual 1884.) 
 
 Frnfeiture of Position. — The situation of a teacher or 
 janitor shall be forfeited for disgraceful or immoral con- 
 duct, incompetency, or wilful violation of any rule or 
 regulation of this Board ; and no teacher or janitor so re- 
 moved shall thereafter be employed in any school, unless 
 the forfeiture be remitted by this Board. (By-Laws, § 
 135, page 209, Manual 1884.) 
 
 See, also. Violation of the By-Laio relative to corporal 
 punishment. 
 
 Corjpoi^al Punishment Prohibited. — Xo corporal pun- 
 ishment of any description shall hereafter be inflicted in 
 any of the common schools. (By-Laws, § 44, page 122, 
 Manual 1884.) 
 
 Violation of this By-Law. — It shall be the duty of every 
 Principal, Trustee, Inspector, or Superintendent, when cog- 
 nizant of the fact, to report to the Board of Education the 
 name of any teacher who may liave resoi-ted to unusual 
 punishments tending to inflict physical injury, or to 
 evade the by-law abolishing corporal punishment in the 
 schools under the control of the Board. 
 
 Any teacher found guilty of a violation of the by-laws 
 of this Board, in regard to corporal punishment, shall be 
 liable to a penalty of forfeiture from his or her salary of
 
 166 GENERAL REGULATIONS. 
 
 not less than five nor more than thirty days' pay, or dis- 
 missal from school, as in the discretion of the Committee 
 on Teachers may be deemed just and proper; provided the 
 action of the Committee be approved by the Board of 
 Education. (By-Laws, § 44, page 122, Manual 1884.) 
 
 Review of Studies to Precede Promotions. — Every ex- 
 amination for promotion to a higher grade shall be preceded 
 by a thorough review of all the studies pursued in the 
 grade from which said promotion is to be made. (By- 
 Laws, § 154, page 262, Manual 1884.) 
 
 Credit Marks. — 1. In every class of the Primary and 
 Grammar Schools the daily record of credit marks awarded 
 to the pupils for regular and punctual attendance, and for 
 excellence in deportment and in the several studies and 
 exercises, shall be kept in the book known as " School Rec- 
 ord Ko. 7." 
 
 2. In all of the Grammar Grades, and in the Primary 
 Grades 1, 2, and 3, the daily maxinmm of credit marks for 
 conduct shall be 10 ; for regular and punctual attendance, 
 10 ; and for each recitation or other exercise, 10. In 
 awarding the credit marks, the various degrees of merit 
 shall be indicated by 10 for " perfect," 8 to 5 for " imper- 
 fect," and for "failure." 
 
 3. At the close of each calendar month, the product 
 obtained by multiplying the whole number of recitations 
 and other class exercises during the month by 10, added 
 to the product of the whole number of school-days of 
 the month by 20, shall constitute the standard number 
 for that month. This number shall form the basis of all 
 merit rolls, certificates of merit, and monthly reports to 
 parents. 
 
 4. In the Primary Grades 4, 5, and 6, the daily maxi- 
 mum of credit marks for conduct shall be 10 ; for regular
 
 GENERAL REGULATIONS. 167 
 
 and punctual attendance, 10 ; and for all of the class exer- 
 cises taken together, 10 ; the maximuui of forfeiture for 
 or during any one exercise being 2. The standard number 
 for the month shall be obtained by multiplying the number 
 of school-days by 30. 
 
 5. If extra credit marks are awarded for superior merit, 
 they shall in no case be allowed to exceed ten per cent, of 
 the standard number. 
 
 6. In no case shall credit marks earned for attendance, 
 or for recitations or other exercises, be forfeited for mis- 
 conduct. 
 
 7. In the column headed " attendance," each half day's 
 attendance shall be marked separately. 
 
 8. When diaries are used, they shall be marked to cor- 
 respond with the general class record kept as above directed. 
 
 9. "Whenever it shall be satisfactorily shown by the cer- 
 tificate of the parent or guardian that pupils have been 
 prevented from attending school in consequence of sickness 
 or religious observances, their absence shall be excused 
 without a forfeiture of the usual certificate of merit, and 
 as far as possible without loss of class standing thereby. 
 Such pupils are nevertheless to be considered as absentees. 
 (By-Laws, § 128, page 203, Manual 1884.) 
 
 Incorrigible Pupils. — Any pupil found to be incorrigible, 
 or persistently disobedient to and regardless of the rules 
 and regulations prescribed for the government of the 
 school or class, or of resisting the authority of the Princi- 
 pal or class teacher, or who, by a reckless depravity, may 
 injure or demoralize the school or class, may be suspended 
 by the Principal from the school. 
 
 It shall be the duty of the Principal of every school 
 thus suspending a pupil, to give immediate notice thereof 
 to the parent or guardian of such pupil, and also to re-
 
 168 GENERAL REGULATIONS. 
 
 port the same to the City Superintendent and the Chair- 
 man of the Board of Trustees of the Ward. 
 
 The parent or guardian of such pupil may, within ten 
 days thereafter, appeal from the action of the Principal 
 to the said Trustees, who shall thereupon investigate 
 the matter, and report their action to the City Superin- 
 tendent. 
 
 If no such appeal be taken, or if such appeal be dis- 
 missed by the Trustees, it shall be the duty of the City 
 Superintendent to notify the Principal of every other 
 school for the same sex, of the name of such suspended 
 pupil, and he or she shall not be admitted into the same 
 or any other school until satisfactory proof of amendment 
 on the part of such pupil shall have been furnished to the 
 City Superintendent, whose certificate of the removal of 
 the disability shall entitle any suspended pupil to read- 
 mission in the same or any other school. 
 
 The Trustees may require the transfer of any pupil sus- 
 pended from one school to any other school under their 
 management, if, in their judgment, they shall deem it 
 beneficial or advantageous to such pupil. (By-Laws, § 
 44, page 120, Manual 1884.) 
 
 Pupils not to he Sent from School. — Pupils shall not be 
 sent from the school premises, upon errands, during the 
 school hours, except in cases of necessity or emergency, 
 and with the consent of the pupil, and in such cases only 
 by the authority of the Principal or Acting Principal, who 
 only shall be autiiorized to send a pupil of suitable age and 
 discretion, and shall record in a suitable book the name of 
 the pupil so sent, with the date, the occasion, and the du- 
 ration of absence. (By-Laws, § 65, subdivision 4, page 
 151, Manual 1884.) 
 
 Exhibitions. — No public exhibition requiring special
 
 GENERAL UEGULATIOXS. 1G9 
 
 preparation shall be given in any school or department, if 
 at all, oftener than once dnring each year, except by per- 
 mission of the Board of Trustees, and no public exhibition 
 or entertainment shall be given outside the school build- 
 ing without the consent of the Board of Education.- (By- 
 Laws, § 156, page 263, jNIannal 1884.) 
 
 Gifts ProJiihited. — I^o teacher shall make or contribute 
 any gift to a school officer or superhitendent, nor shall 
 money or other things be in any case collected or taken 
 from a pupil or teacher, for the purpose of presenting a 
 gift or testimonial to a teacher, school officer, or superin- 
 tendent, or for any other purpose, unless previously sanc- 
 tioned by this Board. (By-Laws, § 133, page 207, Manual 
 1884.) 
 
 Extra Coinpensation. to Teachers.— ^o compensation 
 shall be received by any teacher for instruction given in 
 any school building, except the salaries paid by this Board. 
 (By-Laws, § 133, part of subdivision 1, page 208, Manual 
 188L) 
 
 See also "Time Occupied in Teaching," page 167. 
 
 Conditions Requisite to Engagement. — Xo teacher shall 
 be appointed in any school to whom any school officer en- 
 titled to act upon the question of the appointment or 
 payment of such teacher is related, by either blood or mar- 
 riage, as husband, father, son, brother, nncle, nephew, or 
 first cousin ; but the provisions aforesaid shall not apply 
 to the appointment or promotion of teachers employed in 
 the schools previous to the election or appointment of a 
 school officer who may be related to said teacher. (By- 
 Laws, § 33, subdivision 1, page 93, Manual 1884.) 
 
 Additional Teachers — Hoio Granted.— l^o teacher shall 
 be appointed by the Board of Trustees in any Ward un- 
 less the average attendance of pupils shall be equal to at
 
 170 GENERAL REGULATIONS. 
 
 least thirty-five to each teacher in a Grammar School, and 
 at least fifty to each teacher in a Primary School (exclu- 
 sive of the Principals and teachers of special subjects), 
 based upon the sworn returns, made by the Principal, for 
 the year ending December 31st, next preceding. In mixed 
 schools and departments, for every thirty -five pupils of a 
 Grammar grade, and for every fifty pupils of a Primary 
 grade, one teacher shall be allowed. 
 
 But if the Committee on Teachers shall deem it neces- 
 sary for the proper instruction of the pupils of any school, 
 that additional teachers should be employed therein, it 
 shall be their duty to investigate the same, and if found 
 necessary, to authorize the Trustees of any Ward to em- 
 ploy such additional teachers. When such teachers are 
 authorized to be employed, said committee shall designate 
 the time from which the said employment shall commence 
 and at which it shall terminate, and the amount of salary 
 to be paid, subject to the general regulations prescribed for 
 teachers' salaries ; and no additional teacher so authorized 
 shall be paid except for the time and at the rate so stated. 
 (By-Laws, § 33, subdivision 2, page 93, Manual 1884.) 
 
 Vice-Princijpals and Male Assistants. — Iso Yice-Prin- 
 cipal shall hereafter be appointed in any Grammar or 
 Primary School or Department. Xo more than two 
 male assistants shall be appointed in any Male Grammar 
 School, unless the average attendance of scholars for the 
 year ending on the preceding 31st day of December, shall 
 have exceeded two hundred and fifty pupils of a Gram- 
 mar grade ; nor moi*e than three male assistants, unless 
 the average attendance shall have exceeded five hundred. 
 ^o more than five male assistants in any Male Grammar 
 School shall be allowed. (By-Laws, § 33, subdivision 3, 
 page 95, Manual 1884.)
 
 GENERAL REGULATIONS. 171 
 
 W/ien Teax;hers may he Envployed rcithout Clcuises. — In 
 no Grammar School, the average attendance of which is 
 less than five huDclred, and in no Primary School or De- 
 partment the average attendance of which is less than 
 seven hundred, shall any teacher, except the Principal, 
 he employed for any other purpose than regular class in- 
 struction ; nor should more than one teacher, in addition 
 to the Principal, be employed, except as a class teacher, in 
 any Primary or Grammar School, except that in Gram- 
 mar Schools in which the average attendance exceeds 
 eight hundred, and in Primary Schools or Departments 
 having an average attendance exceeding twelve hundred, 
 two teachers, iu addition to the Principal, may be em- 
 ployed, besides those engaged in the regular instruction 
 of classes ; and whenever, by reason of the closing of a 
 school, any teachers are without employment, though 
 drawing the salaries of their respective positions, it shall 
 be competent for the Committee on Teachers to direct 
 their employment in positions in which their services may 
 be needed in any ward, according to arrangements to be 
 adjusted with the Trustees of said ward. Provided that 
 nothing in this by-law shall be construed to conflict with 
 section 33, subdivision 2, of the By-Laws, so far as said 
 section gives the Committee on Teachers the power to 
 grant additional teachers. (By-Laws, § 33, subdivision 6, 
 page 98, Manual 1884.) 
 
 Absences of Teachers — Hoio Excused. — Ko teacher 
 shall be excused by any Board of Trustees for absence 
 from duty, unless such absence has been caused by the 
 teacher's illness, or by death in the family of which the 
 teacher is a member. No leave or excuse of absence on 
 pay, for a longer period than two school days in any one 
 month, shall be valid, unless conlii-med by the Board of
 
 172 GENERAL REGULATIONS. 
 
 Education. (By-Laws, § 33, part of subdivision 7, page 
 99, Manual 1884.) 
 
 ]S[o leave of absence shall be given to any teacher with- 
 out the appointment by the Trustees of a licensed teacher, 
 as substitute to take the place of the absentee, when neces- 
 sary to provide that no class shall be left without instruc- 
 tion ; and such substitute shall be paid out of the salary 
 forfeited by the absent teacher ; except when the absence 
 of a regular teacher has been excused with pay by the 
 Board of Education, on the recommendation of the Com- 
 mittee on Teachers. The absence of a rpgular teacher 
 may be excused by the Board, with full pay, on the appli- 
 cation of a Board of Trustees, certifying that the absence 
 is necessary for the restoration to health of the teacher. 
 No such application shall be entertained or granted unless 
 in the case of a teacher whose record shall show a meri- 
 torious service for five years. Such application shall be 
 referred to the Committee on Teachers, who shall examine 
 the case and report thereon to the Board. No such ab- 
 sence shall be granted or excused for a longer period than 
 three months in the aggregate, and no other application 
 in the same case shall be entertained. 
 
 The absence of any regular teacher may be excused by 
 the Committee on Teachers, with full pay, on application 
 of the Trustees, when such absence is caused by or on ac- 
 count of contagious disease. (By-laws, § 33, part of sub- 
 division 9, page 101, Manual 1884.) 
 
 Salary of Substitute Teacher. — 1S.0 salary paid to a sub- 
 stitute teacher shall exceed three-fourths of the regular 
 salary of the position in which the substitute teacher is 
 emploj^ed. (By-laws, § 33, part of subdivision 9, page 
 102, Manual 1884.) 
 
 Salaries of Assistant Teachers. — The salaries of assist-
 
 GEISTERAL REGULATIONS. 173 
 
 ant teachers sliall be graded by the Trustees of the respec- 
 tive AVards in applying the average sums allowed for the 
 respective schools and departments, so that in no case the 
 difference between the salaries of any two successive 
 grades shall exceed the sum of one hundred dollars, as to 
 female teachers, and the sum of three hundred dollars as 
 to male teachers. (By-laws, § 35, subdivision 6, page 111, 
 Manual 1884.) 
 
 1. The minimum salary paid to any assistant teacher 
 employed in the schools under the control of the Board 
 shall be five hundred dollars. 
 
 2. The salaries of teachers shall commence at the times 
 they respectively enter upon their duties, when legally 
 appointed. 
 
 3. No retrospeeti\-e increase of salary shall in any way 
 be allowed. (By-laws, § 36, page 111, Manual 1884.) 
 
 Reducing Salaries of Teachers hy Trustees — when Pro- 
 hibited. — Xo reduction of salary shall be made in the case 
 of any Principal or Yice-Principal or assistant teacher 
 whose appeal from the action of the Board of Trustees 
 shall have been sustained by the Board of Education, ex- 
 cept upon the approval of the said last-mentioned Board ; 
 and no reduction shall be made in the salary of any teacher 
 whose removal by a Board of Trustees has not been ap- 
 proved by the Inspectors of a school district, or a majority 
 of them, unless the decision of the latter is overruled by 
 the action of this Board. (By-Laws, § 38, page 113, Man- 
 ual 1884.) 
 
 French and German. — Whenever the parents or guar- 
 dians of at least thirty pupils attending a Grammar 
 Department shall desire the introduction of French or 
 German, the Trustees of the Ward shall introduce the 
 study of such language in said department, but no child
 
 174 GEXERAL REGULATIOIVS. 
 
 shall be compelled to study German or French contrary to 
 the wishes of its parents or guardians, expressed either 
 personal!}^ or in writing;; and whenever the average at 
 tendance of pupils engaged in the study of French ( 
 German, in any class, shall fall below fifteen for the periot 
 of three months, such study shall thereafter be discon- 
 tinued in said class. (§ 158, page 263, Manual 1884.) 
 
 Salaries of Special Teachers of Music, French, Ger- 
 man, and Draicing. — Teachers of Yocal Music, Drawing, 
 French, and German shall be classified as special teachers. 
 Ko salary paid to a teacher of Yocal Music in a Gram- 
 mar or Primary School, or to a teacher of French or Ger- 
 man in a Grammar School, shall exceed the rate of one 
 dollar and fifty cents per hour for the time actually em- 
 ployed in instruction. Ko salary paid to a teacher of 
 Drawing in a Grammar School shall exceed the sum of 
 two dollars per hour for the time actually employed in in- 
 struction. 
 
 The time occupied in the teaching of said studies re- 
 spectively shall not exceed the following, viz. : 
 
 Music. — One hour and twenty minutes per week in 
 Primary Schools and Departments. 
 
 Music. — One hour and forty minutes per week in Gram- 
 mar Schools. 
 
 Draioing. — Three hours and twenty minutes per week 
 in Grammar Schools. 
 
 French. — One hour and fort}' minutes per week for 
 each class where such study is authorized to be taught in 
 Grammar Schools. 
 
 German. — One hour and forty minutes per week for 
 each class where such study is authorized to be taught in 
 Grammar Schools. 
 
 No person shall be employed to teach in any school any
 
 GENERAL EEGULATIONS. 175 
 
 study not authorized by the Course of Studies specified by 
 the By-Laws of tliis Board. Teachers of special subjects 
 shall obtain licenses from the City Superintendent for the 
 subjects which they are required to teach, in the same 
 manner as provided by the rules of the Board for teachers 
 of general subjects. Special teachers of the German and 
 French languages shall not be hereafter employed, except 
 in the manner provided by Sections 158, 159, and 160 of 
 these by-laws as amended. 
 
 "Whenever a vacancy in the position of a special teacher 
 shall occur, the Committee on Teachers shall determine 
 whether the duties of such position, in any school, shall 
 be performed by a special teacher or by a regular teacher 
 in said school. 
 
 In schools where no special teacher of Music is em- 
 ployed, the teacher having charge of the Music shall re- 
 ceive fifty dollars salary in addition to the amount allowed 
 as a regular assistant teacher, provided the usual instruc- 
 tion in Music is given ; but no Principal or Yice-Principal 
 of a school shall be appointed to such position. (§ 39, 
 page 114, Manual 1S84.) 
 
 Duties of Principals. 
 
 Shall Keep Register of Daily Attendance of Teachers. — 
 It shall be the duty of every Principal to keep a register 
 of the attendance of teachers, in which shall be entered 
 daily the time of the arrival and departure of each teacher, 
 and any absence from duty, with the reason of such ab- 
 sence. (By-Laws, § 33, subdivision 10, page 102, Manual 
 1884.) 
 
 Shall Report Ahsences of Teachers. — It shall be the
 
 176 GENEEAL EEGULATIOISrS. 
 
 duty of the Principal to report, without delay, all ab- 
 sences of teachers in his or her school, to the Board of 
 Trustees, with a statement of the cause of each absence as 
 far as known. (By-Laws, § 33, part of subdivision 8, 
 page 100, Manual 1S84.) 
 
 Shall Report other Facts. — The Principals of the several 
 schools shall report to the City Superintendent, each 
 month, such facts as he may require in relation to the at- 
 tendance of teachers and pupils. (By-Laws, § 25, subdivi- 
 sion 5, page 80, Manual IS 84.) 
 
 Suspensioji of Pupils. — It shall be the duty of the Prin- 
 cipal of every school thus suspending a pupil to give im- 
 mediate notice thereof to the parent or guardian of such 
 pupil, and also to report the same to the City Superintend- 
 ent and the Chairman of the Board of Trustees of the 
 Ward. (By-Laws, § 44, part of subdivision 1, page 120, 
 Manual 1884.) 
 
 School Sessions Omitted. — A special report from the 
 Principal of each school shall accompany each paj^-roll, 
 stating whether or not the whole or a part of any session 
 of such school has been omitted previous to the date of 
 such report, and subsequently to the last preceding report, 
 other than such vacations and holidays as are specially 
 allowed by the By-Laws of the Board of Education ; and 
 if the whole or a part of any session has been so omitted, 
 for what reason, and by what authority the same was 
 omitted. (By-Laws, § 65, page 149, Manual 1884.) 
 
 Principals may Visit other Schools. — The Board of 
 Trustees of any ward may, however, permit any Princi- 
 pal therein, who may apply therefor, to absent himself or 
 herself from his or her department or school, without loss 
 of pay, for a period not exceeding three days in any one 
 year, for the purpose of visiting other schools in the city,
 
 GEJs^EEAL REGULATIONS. 177 
 
 but sncli absence shall be reported, as required by the 
 succeeding subdivision. (By-Laws, § 33, subdivision 7, 
 page 99, Manual 1884.) 
 
 Provide Statement for Examiner. — Whenever any 
 school is visited for examination by the City Superintend- 
 ent, or his assistants, it shall be the duty of the Principal 
 of said school to provide the examiner with a statement 
 showing the number of pupils on record in the class, the 
 length of time in it, their age, the studies pursued, the 
 progress of the pupils therein, and such other facts as he 
 may deem requisite to enable him to form a correct esti- 
 mate of the efficiency of the instruction imparted. (By- 
 Laws, § 162, page 265, Manual 1884.) 
 
 Promotions from Primary Schools. — Promotions shall 
 be made from the Primary to the Grammar Schools semi- 
 annually, and not oftener, except by the Avritten permis- 
 sion of the City Superintendent ; and no pupil shall be 
 promoted from any Primary School iinless examined in 
 all the studies jirescrihed for the First Grade of the Course 
 of Instruction for Primary Schools, ?ii\^ found qualified 
 by the Principal of the Department into which the pro- 
 motion is to be made ; and when found qualified, such 
 pupils shall be promoted without delay. 
 
 Pupils may be transferred from the Primary to the 
 Grammar Schools before completing the First Primary 
 School Grade, with the consent of the Committee on 
 (^ourse of Study and School Books, and on the recommen- 
 dation of the City Superintendent, to whom application 
 may be made by the Trustees in any ward, showing that 
 said ti-ansfer is necessary in order to relieve the crowded 
 condition of any Primary School, and to fill vacancies in 
 the classes of the Grammar School. Pupils thus trans- 
 ferred to any Grammar SchtJol shall, hOwevcr, be taught in
 
 178 GENERAL REGULATIO]!^S. 
 
 the Primary Grade until regularly promoted from the same, 
 but may be counted as a part of the regular attendance of 
 the Grammar School. (By-Laws, § 149. page 242, Manual 
 1884.) 
 
 Pupils Leaving School hetween the Ages of Eight and 
 Fourteen. — The Principal of every school shall transmit 
 to the City Superintendent, hereinafter mentioned, at the 
 close of each week, a list of children between the ages of 
 eight and fourteen years, who, such Principal shall have 
 reason to believe, have left the school for the purpose 
 of engaging in any employment. 
 
 It shall be the duty of the Principal of every school to 
 report to the Agent of Truancy, for the district in which 
 such school is situated, the names of all children between 
 the ages of eight and fourteen years, and those only, 
 whose non-attendance at school, such Principal has reason 
 to believe, is the result of a truant disposition. (By-Laws, 
 § 144, subdivisions 3 and 5, pages 221 and 222, Manual 
 1884.) 
 
 Keejp Record of Truants hetween Ages of Eight arid 
 Fourteen. — It shall be the duty of the Principal of every 
 school to keep a record, in a register especially provided 
 for that purpose, of all children between the ages of eight 
 and fourteen years, who have been reported to the Agents 
 of Truancy hereinafter mentioned, for a violation of the 
 said Act of May 11, 1874, as amended May 28, 1876, to- 
 gether with an accurate record of the disposition made 
 of each case by said Agent of Truancy, when reported by 
 them to said Principal. 
 
 It shall also be the duty of said Principal, when an 
 Agent of Truancy shall bring to a school any child, be- 
 tween the ages of eight and fourteen years, not registered 
 as a pupil of said school, to enter his or her name upon
 
 GENERAL REGULATIONS. 179 
 
 said special register, and to note upon said register any 
 facts relating to said child that may have been communi- 
 cated to said Pi-incipal by said Agent of Truancy. (By- 
 Laws, § 144, subdivision 1, page 220, Manual 1884.) 
 
 Keep Register of Residence of Parents^ etc. — It shall 
 be the duty of every Principal, on the reopening of the 
 schools in September of each year, to ascertain and regis- 
 ter the residences of the parents or guardians of each 
 and every pupil attending or applying for admission to 
 the school. (By-Laws, § ^i)., subdivision 2, page 150, 
 Manual 1884.) 
 
 Keep Record of Children Refused Admission. — The 
 Principal of each school and department under the juris- 
 diction of the Board of Education shall be required to keep 
 a record of all children who are refused admission, and the 
 names, ages, and residences of the same shall be inserted 
 in the monthly report made to the City Superintendent. 
 (By-Laws, § %h, subdivision 3, page 150, Manual 1884.) 
 
 Drills for Rapid Dismission. — The Principals of the 
 several schools and departments shall, under the direction 
 of the City Superintendent, instruct and train the pupils 
 by means of drills, so that they may, on a sudden emer- 
 gency, be able to leave the building in the shortest possi- 
 ble time and without confusion or panic. (By-Laws, § 25, 
 Bubdinsion 6, page 80, Manual 1884.) 
 
 Shall Examine Classes and Report. — The Principals of 
 the schools shall examine all their classes in the prescribed 
 bi'anches of study at least twice a year, namely, imme- 
 diately before each regular promotion, and record the re- 
 sults of the same in a book kept for that purpose. A re- 
 port of all such examinations shall be sent to the (.^ity 
 Superintendent, who sliall have it recorded in a book kept 
 for that purpose. The adjectives to be used by the Prin-
 
 180 GENERAL EEGULATIONS. 
 
 cipals in such examination shall be the same as those 
 made use of by the Superintendent under these by-laws. 
 (By-Laws, § 161, page 265, Manual 1884.) 
 
 Ascertain that Teacher has License. — It shall be the 
 duty of the Principal of each school to ascertain that every 
 subordinate teacher has received a proper license before 
 such teacher shall be assigned to any duty. (By-Laws, 
 § 25, part of subdivision 2, page 79, Manual 1884.) 
 
 Eini)loy Medical Service in Case of Accident. — The 
 Clerk of the Board shall furnish the Piincipals of the 
 Public Schools in the several wards with a correct list of 
 the names and residences of the Police Surgeons and 
 Health Inspectors living nearest to such schools respec- 
 tively, with instructions that in case of accidents said 
 Principals shall send for and ask the medical officers herein 
 named for such aid as the necessities of the case may re- 
 quire, and in case of the absence of such officers, the 
 Principal of the school where the accident happens is 
 empowered to employ the services of the first available 
 medical practitioner at the expense of this Board. (By- 
 Laws, § 129, page 205, Manual 1884.) 
 
 Pupils not to PuTchase Suvplies. — The Principal of 
 the school shall procure from the depository, and furnish 
 each pupil with the books, slate, and other supplies re- 
 quired to be used by such pupil ; and no pupil shall be 
 requested or required to purchase any book or other article 
 of supply. 
 
 School Suipjplies — Inventory. — When supplies of any kind 
 are needed for any school, they shall be plainly entered in 
 the pass-book provided by the Committee, and the list 
 shall be dated and attested by the signature of the Prin- 
 cipal, and countersigned by the proper officer or committee 
 of the Board of Trustees authorized for the purpW^.
 
 GENERAL KEGULATIOXS. 181 
 
 An accurate inventor}^ shall be made, during the last 
 week in each year, of the books, slates, maps, and all other 
 articles usually embraced under the name of supplies, in 
 every school within the jurisdiction of the Board of Edu- 
 cation — blank forms of inventory being furnished by the 
 Clerk for the purpose — the same, when completed, to be 
 forwarded to and filed in the Clerk's office. 
 
 The inventory shall designate the three conditions of 
 supplies on hand, in separate columns, viz., Good, Half- 
 worn, and Old. In estimating the stock on hand, the whole 
 of the class '' Good " shall be entered on the list, one-half of 
 the class " Half-worn," and one-fourth of the class " Old," 
 the total being the quantity on hand of each item. (By- 
 Laws, §§ 122 and 123, pages 194 and 195, Manual 1884.) 
 
 Admission of Pupils to School Building, and their 
 Supervision. — It shall be the duty of the Principal of the 
 school to make provision for the admission of pupils into 
 the building at 8.40 a.m., and on stormy mornings at 8.20 ; 
 and also to provide suitable supervision of the play- 
 grounds, by one or more teachers, while the pupils remain 
 in the yard. 
 
 It shall be the duty of the Principal to make the neces- 
 sary inspection to ascertain that tire school-rooms, yards, 
 etc., are kept in a cleanly condition, and to report in 
 writing to the Board of Trustees any neglect on the part 
 of the janitor, and to report in writing repeated subse- 
 quent neglect to the City Superintendent. 
 
 Principals to Prepare Pay-Bolls. — The Principal of the 
 male school having the largest attendance in any school 
 building, for his own school, for the other schools in the 
 same building, and for such primary and female schools as 
 shall be assigned to his charge for that purpose by the 
 Board of Trustees fdr the "Ward, shall prepare monthly pay-
 
 182 GENERAL REGULATIOTs^S. 
 
 rolls for the teachers and janitors employed therein. Each 
 pay-roll shall embrace the names of the persons included 
 therein, the number of days for which they are entitled 
 to pay, and the rates ; the amounts to be paid to them 
 severally, with blanks for their signatures, in acknowledg- 
 ment of the receipt thereof, and the total amount of the 
 payments. It shall be delivered to the chairman of the 
 appropriate Board or Committee on or before the first 
 day of the next ensuing month, and shall be certified and 
 audited by the proper ofiicers and filed with the Clerk of 
 this Board within five days thereafter. (By-Laws, § 40, 
 page 116, Manual 18S4.) 
 
 Declaration of Independence or Washington's Farewell 
 Address to he Read. — On the school days immediately pre- 
 ceding the fourth day of July and the twenty-second day 
 of February, in each and every year, the Principals of all 
 the common schools of this city shall assemble the pupils 
 of their respective schools and read, or cause to be read 
 to them, either the " Declaration of Independence " or 
 " Washington's Farewell Address to the People of the 
 United States," combining therewith such other patriotic 
 exercises as may be advisable. (By-Laws, § 65, subdi- 
 vision 5, page 151, Manual 1884.) 
 
 To Re;port Violations of the Rules and Regulations of 
 the Board. — Every Principal shall report to the proper 
 Board of Trustees, and to this Board, all violations of the 
 rules and regulations of this Boai-d, by any teacher or 
 janitor of which the Principal may be cognizant ; and each 
 pay-roll shall contain an allegation that the Principal has 
 duly reported every case of such violation by a teacher 
 or janitor included therein. (By-Laws, § 135, page 209, 
 Manual 1884.)
 
 GEISTEEAL REGULATIONS. 183 
 
 Duties of Janitors. 
 
 Diiring School Hours. — It shall be tlie duty of the 
 janitors to remain in the school buildings, or adjacent 
 grounds, during the ■whole time the schools are in session, 
 and be at all times ready to render personal assistance in 
 case of any emergency. 
 
 Heport to Principal. — They shall also report in person 
 to the Principal of each school at each and every daily 
 school session ; and they shall also ascertain, on the first 
 day of every month, by the index of the gas-meters in 
 their respective schools, the amount of gas consumed 
 during the preceding month, and report tlie same in writ- 
 ing to the Clerk of the Board of Education, who shall 
 keep a record of the same. 
 
 It shall be the duty of all janitors who reside on the 
 premises to leave some responsible person in charge dur- 
 ing their occasional absence. 
 
 Janitors who do not reside on the premises must visit 
 the school building for a sufficient time on each day when 
 tlie schools are not in session ; but in no case should their 
 place of residence be further than five hundred yards from 
 the school premises, unless permission be given by the en- 
 gineer to the contrary, and all such permissions given by 
 him to be reported to the Board for its approval. 
 
 Responsible for Security of Buildings. — All janitors will 
 be held responsible for the security of the school buildings, 
 by locking or otherwise securing all doors, gates, windows, 
 and other means of access. They must also report immedi- 
 ately, to the Trustees or Principlal, any damage that may
 
 184 GENERAL REGULATIONS. 
 
 happen to any part of the school property. (By-laws, § 
 61, subdivisions 2 and 3, page 139, Manual 1884.) 
 
 Teachers' Manual. 
 
 If adopted by said Board, it {The Teachers' Manual) 
 shall become valid as a rule for the government of teachers 
 in the discharge of their duties, except so far as its provis- 
 ions are inconsistent with the By-Laws of the Board. (By- 
 Laws, §28, subdivision 5, page 88, Manual 1884.)
 
 JUNIOR EVENING SCHOOLS. 185 
 
 COURSE OF IXSTRUCTIOX FOR JUXIOR 
 EYEKING SCPIOOLS. 
 
 EIGHTH GRADE. 
 
 Reading from a First or Second Reader. 
 
 Sw fPsHons. — 1st, it sliould lie borne in mind that the pupils of this 
 grade have a mental developmi^nt as well as a practical use of words far 
 beyond the young children for whom a Reader of this grade is chiefly 
 designed; 2d, that tiierefore the principal efforts in this grade should 
 be to develop a facility in pronouncing all the words of the Reader 
 promptly at sight ; 3d, great care should be taken to make the exer- 
 cises as spirited as the subject will permit ; and 4th, considerable atten- 
 tion should be given to distinctness of articulation and correctness of 
 pronunciation. 
 
 Spelling and Definitions of the words of the reading 
 lessons. 
 
 Suggestions. — 1st, the spelling in this grade should be chiefly oral, in 
 order to cover as much ground as possible in each lesson ; 2d, before 
 closing the lesson a selection of from five to ten of the most difficult 
 words should be tested by having the whole class write them on the 
 slate ; 3d, the difficult words of preceding lessons should be rapidly re- 
 viewed at least twice a month ; 4th, the sijelling and meaning of words 
 of like sound with those in the lessons should be carefully taught ; 5th, 
 only those words the meaning of which the pupil is likely to mistake 
 or not to know, should be dwelt upon in the definition exercises ; 6th, 
 ability to use words properly in a brief sentence or phrase is the best 
 test of the knowledge of their meaning in the lower grades. 
 
 Arithmetic, through multiplication. 
 
 Suggestions. — 1st, the lesson in arithmetic should consist of three 
 parts : first, a few minutes' rapid class drill with the blackboard to se- 
 cure facility and precision in the tables of addition, subtraction, and 
 multiplication ; second, a few minutes in short practical exercises in
 
 186 JT'NIOR EVENING SCHOOLS. 
 
 mental arithmetic, chiefly for rapid calculation without analysis ; third, 
 the remainder of the time should be given to exercises wrought upon 
 the slate ; 2d, all the examples given should be short ; 3d, if any 
 analysis is required, it should only be in multiplication, and should then 
 be as concise as clearness will permit ; 4th, neat work and legible figure?^ 
 should invariably be insisted upon. 
 
 Penmanshvp. — Elenientarj'-exercises in small letters and 
 capitals ; also in short words. 
 
 Snggestions. — 1st, each lesson should first be briefly illustrated upon 
 the blackboard ; 2d, the lesson should not always be from printed cop- 
 ies ; 3d, the letters should be presented in the order of their difficulty, 
 and short words should be introduced as soon as a few letters have been 
 taught. 
 
 SEVENTH GRADE. 
 
 Reading from a Third Reader. 
 
 Suggestions as in Eighth Grade as far as apposite. Care should be 
 taken to select interesting and instructive pieces. 
 
 Sjpelling and Dcfimtions of the words of the reading 
 lessons ; also of miscellaneous words bv dictation. 
 
 Suggestions as in Eighth Grade, excepting that the exercises in written 
 spelling should occupy at least half the time given to the subject. 
 
 Arithmetic. — Short and Long Division, and Federal 
 Money. 
 
 Suggestions as in Eighth Grade, except that the words and Division 
 are to be added after the word Multiplication. 
 
 Penmaiislii]). — Words and short sentences. 
 Suggestions — see 1 and 2 of Eighth Grade. 
 
 SIXTH GRADE. 
 
 Heading of the gi'ade of a Third Reader continued. 
 SuggeMions as in Eighth and Seventh Grades.
 
 JUNIOR EVENING SCHOOLS, 187 
 
 Spelling and Definitions of the words of tlie reading 
 lessons ; also of miscellaneous words from dictation. 
 Suggestions as in Eighth and Seventh Grades. 
 
 Arithmetic through Common Fractions and their appli- 
 cations to Federal Money, 
 
 Suffffestions. — 1st, thoseof Eighthand Seventh Grades, as far as apposite; 
 2d, the examples selected should be short and practic-al as possible ; 8d, 
 Common Divisor and Least Common Multiple should be chiefly from 
 inspection and only in immediate connection with their applications to 
 the reduction and combination of fractions , 4th, Addition, Subtraction, 
 and Division may be advantageously taught together on their common 
 basis of Least Common Denominator ; 5th, the chief analyses to be 
 taught are those of Common Denominator, Multiplication, and the two 
 cases in Division; 6tli, the applications of Fractions to Federal Money 
 should constitute a prominent element of the exercises. 
 
 Penmanshijp. — AVords and short sentences, continued. 
 Suggestions as in Seventh Grade. 
 
 FIFTH GRADE, 
 
 Reading — a book of the grade of a Fourth Header, -u-ith 
 continuous text, on Familiar Science. 
 
 Suggestions. — 1st, every lesson should be accompanied with a brief 
 review of the subject-matter ; 2d, an occasional general review of the 
 subject-matter will give one of the brief advantages of a continuous 
 text ; 8d, difficult words and those requiriug explanation should be 
 carefully attended to ; 4th, distinctness of articiilation and naturalness 
 of tone should have a proper share of attention. 
 
 Spelling and Definitions from the Reader, and miscel- 
 laneous words. 
 
 Suggestions as in Eighth and Seventh Grades. 
 
 Arithmetic. — Decimal Fractions and Common Fractions 
 reviewed, with simple business applications of both.
 
 188 JUNIOK EVENING SCHOOLS. 
 
 Suggestions. — 1st, after teaching the principles of decimal notations, 
 the reduction, addition, subtraction, multiplication, and division of 
 decimal fractions should be taught and explained on the same princi- 
 ples as similar operations in common fractions ; 2d, facility in convert- 
 ing simple common fractions to decimals and decimals to common frac- 
 tions is very important in the business applications of fractions. 
 
 Peiimanshvp. — Copies and longer sentences. 
 
 Suggestions. — 1st, double-lined books, that is, those having both base- 
 line and head-line for the small letters, should not be used ; 2d, all 
 members of the class should write the same lesson ; 3d, the special 
 difficulties of each lesson should be carefully taught by means of the 
 blackboard. 
 
 FOUKTH GRADE. 
 
 Heading. — From the same Reader as in Fifth Grade. 
 Suggestions as in Fifth Grade. 
 
 Spelling and Definitions as in Fifth Grade. 
 Suggestions as in Fifth Grade. 
 
 Arithmetic. — Compound ISTumbers, including Federal 
 Money, Tables of Weights and Measures. 
 
 Suggestions. — 1st, great care should be taken to select those tables 
 which are of most practical importance in daily life ; 2d, no long ex- 
 amples should be given ; 3d, the analysis, when required, should be 
 brief and simple ; 4th, the different values of the pound, ounce, ton, 
 and gallon should be carefully taught ; 5th, areas of rectangles and 
 circles, and short examples in finding the contents of boxes, bins, and 
 cylinders, in feet, inches, gallons, or bushels, should constitute a part of 
 the basis of instruction. 
 
 Pentnanship. — Copies ; writing short paragraphs from 
 dictation, or from the Reader or some other book. 
 
 Suggestions. — 1st, the latter element is by far the more important ; 
 2d, draw attention to the correct use of capitals and points, and to the 
 use of the hyphen at the end of the line ; 3d, insist upon the proper
 
 JUNIOR EVENING SCHOOLS. 189 
 
 legible medium between a compact and a sprawling hand ; 4th, do not 
 allow either vertical or backliand to be used ; 5th, insist upon a plain 
 style without flourishes ; 6th, permit only such rapidity as is thoroughly 
 consistent with neatness and legibility. 
 
 Geography. — An outline of the world ; to be taught 
 orally aud with the use of the globe aud outline map. 
 
 Suggestions. — 1st, the lessons should be short and spirited; 2d, they 
 should not be allowed to degenerate into mere lectures. The pupils 
 should take a leading and active part in pointing out and describing ; 
 3d, the lessons should include the shape of the earth, its size, zones, 
 seasons, day and night, divisions into land and water, and the principal 
 subdivisions of each. Ideas of latitude and longitude, their necessity 
 and importance. The distinctions of mountain systems, plains, and the 
 location of the most important of each ; the most important rivers and 
 lakes ; a few of the leading countries, and of the chief commercial and 
 manufacturing cities ; 4th, before commencing the lesson the teacher 
 should have as definite ideas as to its plans, limits, and details as in the 
 lessons in arithmetic or penmanship ; 5th, frequent and rapid reviews 
 of five minutes each are indispensable. 
 
 THIRD GRADE. 
 
 Reading. — History of the United States. 
 Suggestions as in Fifth Grade. 
 
 Spelling and Definitions from the reading lessons. 
 
 Suggestions as in Eighth and Seventh Grades, excepting that the spelling 
 should be tested only by writing selected words and sentences on slates. 
 
 Ai'ithmetic. — Percentage vydhoid Time ; a review of 
 those parts of the compound numbers which are of the* 
 most practical importance. 
 
 Suggestions as in Fifth and Fourth Grades. 
 
 Penmanshi/p. — Copies and paragraphs as in Fourth Grade 
 Suggestions as in Fourth Grade.
 
 190 JUNIOR EVENING SCHOOLS. 
 
 Geography. — A brief outline of the Western Hemi- 
 sphere, with the use of the globe and outline maps. 
 
 Suggestions as in Fourth Grade, except as to suggestion 3d. Tlie lesson 
 should include, first, very simple outlines of the physical geography of 
 each continent, its form, dimensions, chief mountain systems, plateaus, 
 and plains; its drainage, general climates, and leading vegetable and 
 animal products. The separate countries of the continent should then 
 be considered, great care being taken not to present too many topo- 
 graphical details. The leading cities, resources, commerce, and com- 
 mercial routes should receive careful attention. 
 
 SECOND GRADE. 
 
 Reading. — History of the United States continued. 
 Sttggestioxs as in Fifth Grade. 
 
 Spelling and Definitions from the reading lessons. 
 Suggestions as in Third Grade. 
 
 Arithmetic. — Review of simple percentage ; interest, 
 and the business rules dependent upon both. 
 
 Suggestions. — 1st, no subordinate topic should be treated exhaustively 
 before proceeding to the next ; 2d, frequent reviews with brief ex- 
 amples will insure correctness, rapidity, and thoroughness ; 3d, clear 
 explanations should be required ; 4th, before completing the subject 
 of interest, a few exercises should be given in finding interest by tables, 
 and the tables should be explained. 
 
 Penmanship. — Copies and paragraphs as in Third Grade. 
 Suggestions as in Fourth Grade. 
 
 Geograj^hy . — The Eastern Hemisphere, with the use of 
 the globe and outline maps. 
 
 Suggestions as in Third Grad«.
 
 JUNIOR EVENING SCHOOLS. 191 
 
 FIRST GRADE. 
 
 Reading. — General History. 
 Suggestions as in Tliird and Second Grades. 
 
 Spelling and Definitions from the reading lessons. 
 Suggestions as in Third Grade 
 
 Arithmetic. — General review and completion of busi 
 ness arithmetic. 
 
 Suggestions as in Second Grade. 
 
 Penmanship. — Paragraphs and business forms and busi- 
 ness letters. 
 
 Suggestions. — The points of each business letter should be briefly writ- 
 ten \ipon the blackboard, and each pupil then be required to construct 
 the letter himself. 
 
 Book-keeping. 
 
 Suggestions. — The time given to this subject should not be allowed to 
 interfere with the other subjects required to be taught in this grade. 
 
 Geography. — General review, with outline maps. 
 
 Suggestions. — Special attention should be given to such important cur- 
 rent events as have geographical relations. The daily paper will furnish 
 an abtiudance of valuable and useful illustrations,
 
 102 CLASSES FOR FOREIGNERS. 
 
 COURSE OF INSTRUCTION IN THE ENGLISH 
 LANGUAGE FOR CLASSES OF FOREIGN- 
 ERS IN EVENING SCHOOLS. 
 
 THIRD GRADE. 
 
 1. Heading. — Second or Third English Reader ; special 
 attention to be called to idiouiatic phrases occurring in the 
 lessons. 
 
 2. Penmanshij). — Writing from dictation. The use of 
 capitals to be taught. 
 
 3. English Grammar. — Special attention to be given to 
 the peculiar sounds of the language ; the comparison of 
 adjectives ; the formation of the plural ; the simple tenses 
 of auxiliary verbs ; the principal parts of a few of the 
 most common irregular verbs. 
 
 4. Translations. — Translations from English into the 
 native language of the pupils, and vice versa. 
 
 5. Colloquial Exeixises. — Among the first topics to be 
 selected for colloquial exercises should be the following : 
 (a) easy exercises in addition, subtraction, multiplication, 
 and division ; (J) the human body ; (c) house and home, 
 garden and field ; (r?) family relations and friends ; {e) the 
 city we live in ; other subjects at the discretion of the 
 teacher, who should keep a list of the exercises. 
 
 The teacher should give the usual directions as soon as 
 jpossible in the. English language. 
 
 SECOND GRADE. 
 
 1. Reading. — Fourth English Reader. 
 
 2. Penmanship. — Writing from dictation, including 
 words and sentences.
 
 CLASSES FOR FOREIGNERS. 193 
 
 3. English Grammo/r. — Special attention to he given to 
 the principal parts of irregular verhs occurring in the 
 Reader, to the passive voice, and to the principal adverhs 
 and conjunctions. 
 
 4. Translations. — Continued. 
 
 5. Colloquial Exercises. — The following subjects should 
 be treated of : {a) the weather ; (J) mechanical arts ; (c) 
 the grocery ; [d) social amusements ; {e) the United States 
 and its government ; other subjects at the discretion of the 
 teacher, who should keep a list of them. 
 
 The medium of instruction should he^ as miich asprac- 
 ticdblej tlie English language. 
 
 FIRST GRADE. 
 
 1. Reading. — Fifth English Reader, History of the 
 United States, or Constitution of the United States. 
 
 2. Penmanship. — Writing from dictation. 
 
 8. English Grammar. — The chief peculiarities of syn- 
 tax, attention to be called to points of difference between 
 the English and the native language of the pupils. Les- 
 sons in composition, with instruction in letter-writing. 
 
 4. Translations. — Continued. 
 
 5. Colloquial Exercises. — Review of the exercises of the 
 two preceding grades ; otlier subjects to be selected by 
 the teacher ; discussions on the contents of the reading les- 
 
 jsons; debates. 
 
 Teachers should keep a list of the subjects selected by 
 them for colloquial exercises and debates. 
 
 Tlie English language should he exclusively the medium 
 of instruction in this grade. 
 9
 
 194 EVENING SCHOOLS FOR SENIORS. 
 
 EVENmG SCHOOLS FOR SENIOES. 
 
 i. Reading. — Including Spelling, Definitions, and His- 
 torical Readings. 
 
 2. Arithmetic. 
 
 3. Pemnanshijp. 
 
 4. Book-Tieejping. 
 
 5. Conyposition. 
 
 Any pupil upon his admission may, at his option, select 
 not more than two of the said branches of study which he 
 desires to pursue during the term. 
 
 It shall be the duty of the Principal of each School for 
 Seniors, by and with the advice and consent of the City 
 Superintendent, to arrange an order of exercises for each 
 evening during the term.
 
 APPENDIX. 
 
 FIRST PRIMARY GRADE, 
 
 Outline Coukse. 
 
 Langttage Lessons. — Reading— oi the grade of an easy Third 
 Reader : the meaning of words and phrases read : elementary sounds in 
 the pronunciation of words : punctuation marks : spelling, as in the 
 previous grade : lessons on objects, as in the previous grades, with more 
 complete descriptions of objects ; special attention to be given to those 
 properties which fit the objects for their particular uses: geography, 
 without text-books — points of the compass ; location and direction of 
 familiar places ; elementary definitions ; shape of the earth, and situa- 
 tion of the principal countries and bodies of water. 
 
 Arithmetic. — Written and Mental. — Addition, and subtraction con- 
 tinued ; midtiplication — multiplicand not exceeding six fgures, multi- 
 plier not exceeding four figures ; division — divisors not exceeding 25 ; 
 practical examples in the several rules : tables of Long Measure and 
 Avoirdupois Weight, with review of previous grade ; simple practical 
 questions. 
 
 Slate-Writing and Penmanship. — On slates — brief descriptions of 
 familiar objects : on paper — words with capitals ; during the last half 
 of this grade one lesson each week to be written from dictation. 
 
 Drawing. — On slate and paper, illustrated on blackboard, from dic- 
 tation and from chart : quadrants with radius of two inches ; design 
 composed of straght and simple curved lines symmetrically arranged 
 in the square, equilateral triangle, hexagon, and octagon ; two ovate 
 conventional leaves on axis of three inches. 
 
 Sewing. — (In girls' classes.) 
 
 Vocal Music. — Instruction continued as in Second Grade ; teach the 
 singing of simple tunes in the natural scale by numerals, syllables, let- 
 ters, la, la, la, and by appropriate words 
 
 Physical Training. — As in previous grades. 
 
 Manners and Morals. — Due attention to be given in each grade to 
 training pupils in right habits.
 
 INSTRUCTIONS AND SUGGESTIONS. 
 
 LANGUAGE. 
 
 Reading. — The instructions for teaching reading in tho 
 two preceding grades, are appropriate as suggestions for 
 this grade. While chief attention should be given to 
 Buch reading as will enable the pupils to gain the thoughts 
 readily from the printed page, due attention should also 
 be given to such elocutionary exercises as will increase the 
 pupils' ability to speak those thoughts in such a manner 
 that those who listen may understand them. 
 
 For the purpose of tmining pupils to gain knowledge 
 by silent reading^ require them to read a paragraph si- 
 lently^ and then to state the substance of what it con- 
 tains. 
 
 As an exercise in language, allow the pupils to choose a 
 familiar reading lesson, and to write from memory the 
 substance of the lesson, chiefly in their own language. 
 Require different pupils to read what they hav^e written, 
 and other members of the class to notice how their own 
 statements differ from those read. Then the pupils may 
 be allowed to correct their own statements, and to write 
 the lesson again. An exercise of this kind may be given 
 once a week, in place of the reading and slate- luriting ex- 
 ercises. It would be profitable, also, for the teacher to 
 vary this language exercise by reading a short, interesting 
 story and requiring the pupils to write about it.
 
 APPENDIX. 197 
 
 Meaning of Words. — Read carefully the suggestions 
 given in the Third and Second Grades. 
 
 Ele7nentary Sounds and Punctuation. — The suggestions 
 already given for the preceding grades will indicate what 
 ought to he done in these matters. 
 
 Such additional attention should be given to diacritical 
 marks as will enable the pupils to ascertain by their aid 
 how the given words in the Readers should be pronounced, 
 and will prepare them for using dictionaries for this pur- 
 pose. 
 
 Sj-'elling. — More attention should be given to written 
 than to oral spelling. Words may be dictated for the pu- 
 pils to write on their slates ; short sentences may be given 
 for the same purpose ; the pupils may be required to write 
 in groups the names of kinds of food, of articles of cloth- 
 ing, of furniture, of tools, of occupations, of animals, 
 of trees, of fruits, of things that may be purchased at 
 a grocery, etc., etc. These exercises will enable pupils 
 to learn the spelling of a large class of words in common 
 use. 
 
 Object Lessons. — Through the instruction of the preced- 
 ing grades the pupils will have become familiar with tho 
 forms, colors, qualities, materials, and uses of common ob- 
 jects, have learned the terms necessary to an intelligent 
 description of them, and have been provided with suitable 
 facts, to prepare them for practical lessons in language. 
 It is intended that the pupils shall be taught in this grade 
 how to use these facts in gaining a more complete knowl- 
 edge of the materials, qualities, and uses of articles of food 
 and clothing ; also, how to gain appropriate information 
 in relation to occupations, trades, productions, and arti- 
 cles of manufacture. To this end it is desirable that the 
 classification of substances as animal^ vegetable^ and inineraZ
 
 198 APPENDIX. 
 
 should now be tanglit. Lead the pupil to observe that 
 animals have animal life, take food, grow, h'eathe, move 
 froin jplace to jplace hy their own jpower, have feelirig, 
 and die ', that vegetables have vegetable life, take food, 
 grow, and die y that minerals have no Ife, take no food, 
 do not grow, breathe, move, nor die. 
 
 Animals and vegetables have organized parts — that is, 
 parts adapted to separate and particular purposes ; as, 
 ejes, ears, hands, hair, nails, bones, muscles, blood ; roots, 
 trunks, limbs, wood, sap, bark, leaves, buds, blossoms, 
 fruit, etc. Minerals have no such organized parts. 
 
 The pupils may also be taught that substances such 
 as wool, hair, bone, and skin, which once formed parts of 
 animals, etc., are called animal substances ^ that wood, 
 bark, gum, and sugar, which once formed parts of vegeta- 
 bles, are called vegetable sidjstances. 
 
 Objects are to be used, as previously, whenever they 
 may be necessary to proper instruction : select chiefly 
 those objects with which the pupils have some acquaint- 
 ance by personal observation. In giving a lesson the fol- 
 lowing steps should be taken : 
 
 First. Find what tlie pupils already know about the ob- 
 ject ; notice and correct their wrong impressions. 
 
 Second. Teach them to examine the object systemat- 
 ically in learning its properties, uses, etc. 
 
 Third. Train the pupils to describe the object intelli- 
 gently (stating its chief property, and its most important 
 qualities and uses), and to give other interesting facts con- 
 cerning it. 
 
 Topics for the Lessons. — The following list will indicate 
 topics appropriate for lessons in this gi-ade: 
 
 Apple, banana, fig, lemon, orange, peach, raisin ; coffee, corn, ginger, 
 uuts, ijejiper, potato, peanut, rice, salt, sugar, corn-starcli, tapioca.
 
 APPENDIX. 199 
 
 wheat ; brick, cotton, calico, flax, glass, earthen-ware, India-rubber, 
 leather, paper, silk, soap, wool ; roots, buds, leaves, blossoms, fruit ; 
 camphor, chalk, coal, cork, copper, iron, lead, whalebone ; baker, 
 blacksmith, carpenter, dressmaker, farmer, grocer, hatter, mason, mil- 
 liner, painter, printer, shoemaker, tailor ; cat, cow, dog, duck, fish, goat, 
 goose, hen, horse, sheep, etc. 
 
 It is not supposed that lessons will be given on all the 
 above topics, nor that the teacher will confine the lessons 
 to those in this list ; but it is desired that the number of 
 lessons shall be sufficient to teach the pupils such modes 
 of observation as will prepare them for obtaining useful 
 knowledge from surrounding objects. If right methods 
 of conducting the lessons be employed, eight or ten sub- 
 jects, embracing a suitable variety, will be sufficient to ac- 
 complish the pui-pose. 
 
 The general plan of proceeding with the lessons may be 
 understood from the following points in the examination 
 of the 9bject : 
 
 "What is it, animal^ vegetable^ or mineral ? 
 
 Is it a natural jproduction or a manufacture ? 
 
 Where and hoio is it obtained f 
 
 "What are the chief occujpatioas or trades required to 
 obtain or to produce it f 
 
 Which are its most useful qualities f 
 
 AVhat are its chief uses? 
 
 What is its general shape ? — its color ? 
 
 Give a brief description of the object. 
 
 "What is produced by the occupation of ? 
 
 What does the do ? 
 
 In view of the great practical importance of the sub- 
 ject, the condition of the pupils, especially the l)oys, in 
 relation to color-blindness and other defects of visual per- 
 ception, should be carefully ascertained. Fur this pur-
 
 200 APPENDIX. 
 
 pose, test the pupils' ability to distinguish and match red^^ 
 greens^ and jc>urj)les. Harmony of colors should receive 
 attention, especially from the girls. 
 
 Geography. — The instruction of the Primary Course in 
 geography is to be given without text-books. It is impor- 
 tant that the first lesson commence with things known by 
 the pupils through their personal experience. Attention 
 may be directed — 
 
 First. — To the location, direction, and comparative dis- 
 tance from the school, of the streets in the immediate vi- 
 cinity, and of a few important ones farther away ; also, 
 of familiar parks, depots, ferries, and of a few prominent 
 public buildings and places, such as City Hall, churches, 
 libraries, post-office stations, etc. 
 
 Second. — To the relative location and direction of places 
 in the vicinity of the city. As far as possible the location 
 of these places should be shown by an outline map of 
 !New York and vicinity, or by sketches on the blackboard. 
 
 During these lessons the terms river, ^ciy, island, ocean, 
 strait, etc., will be employed, and the meaning of these 
 terms should be taught, with the aid of chart, map, black- 
 board, or other available objects. 
 
 The names and location of islands, rivers, oceans, etc., 
 need not be taught at this stage of the lessons. 
 
 Third. — Extend the lessons about places, villages, etc., 
 by means of the personal experience of members of the 
 class, as obtained by their visits, excursions, and vacation 
 travels. Let the places so mentioned be pointed out on 
 maps. These lessons will prepare the pupils for under- 
 standing more clearly subsequent lessons about distant 
 places. 
 
 Fourth. — In giving the pupils ideas of the shape of the 
 earth, use marbles, balls, oranges, and the terrestrial globe.
 
 APPENDIX. 201 
 
 Teach the location of difterent countries, islands, etc., on 
 the globe first. 
 
 Fifth. — To assist the pupils in remembering the names 
 and locations of the grand divisions, associate with the 
 places, as they are pointed out on the globe and on the 
 map, familiar people, animals, and productions, somewhat 
 as follows : Korth America, tlie country in which we live ; 
 South America, the home of the monkey, and the place 
 where Brazil nuts, cocoanuts, and India-rubber are ob- 
 tained ; Africa, the home of the Negro, the camel, ostrich, 
 lion, and zebra ; Asia, the home of the Chinese, of the 
 elephant, the tiger, and the place where tea, pepper, cloves, 
 and cinnamon grow ; Australia, the land of the kangaroo ; 
 Europe, the home of the English, Irish, German, French, 
 Italians, etc. 
 
 In a similar manner the names and locations of countries 
 and other places may be learned ; as, Greenland, the home 
 of the white bear, and the waters around it, the home of 
 the whale from the mouth of which whalebone is ob- 
 tained ; West Indies, the place whence we obtain oranges, 
 bananas, etc. ; Spain, the country where cork and raisins 
 are produced. 
 
 The most important groups of islands, two or three of 
 the largest rivers and prominent ranges of mountains, and 
 a few of the largest cities of the world may be included in 
 these lessons ; also the cold and warm countries may be 
 pointed out: the houndaries and capitals of countries 
 shoicld not he taught. 
 
 Care should be taken that the pupils do not obtain the 
 false impression that, to travel from a place represented 
 at or near the bottom of a map toward a place represented 
 at or near the top of the map, one must go vjy. In lead- 
 ing the pupils to avoid this common error, point out the
 
 202 APPENDIX. 
 
 course of the St. Lawrence River, and ca,use them to 
 understand that its waters flow down toward the north- 
 east, and not wpioard. 
 
 The relative direction and location of places may be 
 easily illustrated by simple dots on the blackboard, and on 
 slates. 
 
 ARITHMETIC. 
 
 Addition and Subtraction. — Continued and special at- 
 tention should be given to teaching the uses of these rules 
 by means of practical examples. It is expected that the 
 pupils will have been taught so thoroughly before they are 
 placed in this grade that each one will be able to add and 
 subtract with facility, and with a good degree of accuracy; 
 yet reviews of these rules should be had, with examples as 
 above stated, at least twice each week. 
 
 Multijjlication. — The simple processes of multiplication 
 having been taught in the previous grade, the exercises 
 given for this grade should be presented in steps, some- 
 what as follows : 
 
 First Step. — Use multipliers similar to the following: 
 120, 3-18, 5,630 ; multiplicands not to contain more than 
 four figures. 
 
 Second Step. — Use multipliers similar to the following : 
 406, 9,030, 8,007 ; multiplicands not to contain more than 
 fi.ve figures. 
 
 Pupils should be carefully trained to write the first 
 figure of each 'partial product under the figure used as a 
 niulti])lier. 
 
 1^^ Revieuy each step loith j^^'fJ^ctical examples enihraG- 
 ing transactions that come 'within the ohservation of the 
 pupils.
 
 APPENDIX. 203 
 
 Division. — The idea of separating groups of objects and 
 numbers into several equal parts having been illustrated 
 with objects, etc., as an introductory step to division, the 
 teacher should now proceed to show the different ways hy 
 which division may he represented vnth figures. 
 
 First Step. — Place upon the blackboard the following 
 forms of division : 
 
 2)8( 2)8 8-^2= 
 
 Tell the pupils that each of these forms of writing 
 numbers means that they are to find how many twos there 
 are in eight ; or, that the number 8 is to be divided into 
 tioo equal j'CiJ'ts. Let the pupils tell how many each part 
 will contain ; then write the number in connection with 
 each example, as follows : 
 
 2)8(4 2)8_ 8-^2=4. 8=4 
 
 8 4 2 
 
 After repeating the four modes of representing division, 
 with otlier numbers, require the pupils to copy each form 
 on the slate, and to perform the division. 
 
 N. B. — Do not allow the pupils to say " divide two into 
 eight." Eight is divided hy two. 
 
 Second Step. — Proceed to illustrate the process of 
 division by the lo7ig division form, using small numbers 
 for the divisor. Use examples first in which each figure 
 of the dividend wiU contain the divisor without a re- 
 mainder, thus :
 
 204 APPENDIX. 
 
 2)48(24 3)96(32 4)84(21 
 
 4 9 8 
 
 08 06 04 
 
 8 6 4 
 
 
 
 Third Step. — Give examples, with the divisor of one 
 figure, in which remainders occur during the partial 
 divisions, thus : 
 
 4)976(244 8)952ril9 T)861(123 
 
 8 8 ' 7 
 
 17 15 16 
 
 16 8 14 
 
 16 72 21 
 
 16 72 21 
 
 
 
 Fourth Step. — Teach ^^ short dwulon,^^ first by working 
 t^^ same example hy both the long and the short forrn^ 
 thus leading the children to see that one form is much 
 shorter than the other, therefore may be called short 
 division^ and that the other, as appropriately, may be 
 called long division. 
 
 The illustrations for any one of these steps need not 
 occupy the time given to division for more than one week / 
 and the time devoted to the four steps should not exceed 
 that assigned to this portion of arithmetic for one month. 
 When the divisor is less than 13, do not allow the long 
 division form to he used after the pupils understand the 
 diference between the two processes.
 
 APPENDIX. 205 
 
 Fifth Step — Give examples with divisors from 13 to 25, 
 to be worked by long division, the dividends varying from 
 four to six figures, including the use of nawjlds. 
 
 Examples should be given with a naught in the divisor, 
 and also (at the right hand) in the dividend ; as, 30)4560 : 
 the pnpils should be required to work such examples by 
 short division. 
 
 Aim first to make the pupils imderstand the process of 
 the rule ; then train them to he accurate / and finally, drill 
 in rapidity. Never attempt to gain rapidity to the neg- 
 lect of accuracy. 
 
 As soon as the pupils understand the manner of doing 
 the work in any rule, give practical examples : do not wait 
 for either accuracy or rapidity before giving such ques- 
 tions. 
 
 1^^ The ability ofpujnls to work practical examples in 
 tliefour simple rules^ is the real test of their Jcnoicledye of 
 this subject. 
 
 Mental Arithmetic. — The forms for answering ques- 
 tions in addition, subtraction, and multiplication, in this 
 grade, may be the same as in the Second Grade. (Ques- 
 tions may also be introduced which may require both ad- 
 dition and subtraction for their solution, as : 
 
 Henry had 18 cents; he gave 2 cents for pencils, and 
 C cents for a sponge ; how many cents had he left i 
 Ans. 10. Henry spent the sum of 2 cents and cents, 
 which was 8 cents. He then had left the difference be- 
 tween 8 cents and 18 cents, which is 10 cents. 
 
 The same example might be performed by the subtrac- 
 tion of 2 cents, and then of G cents. 
 
 Division. — The two following examples will illustrate 
 forms of solutiuu ap})rupriate for mental questions in di- 
 vision :
 
 206 
 
 APPENDIX. 
 
 How many tops at 3 cents each can be bought for 13 
 cents ? Ans. 4. As many tops as 3 cents, the price of 1 
 top, is contained times in 12 cents, which is 4 times. 
 
 If 2 apples cost 4 cents, what will 1 apple cost ? Ans. 
 2 cents. If 2 apples cost 4 cents, 1 apple will cost one- 
 half of 4 cents, which is 2 cents. 
 
 Oral Drills for rapid combinations of numbers may 
 embrace combinations with multiplication, addition, di- 
 vision, and subtraction. See also suggestions for oral 
 drills in the previous grades. 
 
 Multiplication Tahle, reviewed as a Division Table. — 
 In making this review the teacher may ask. How many 
 fours in 20 ? How many j/jves in 30 ? How many twelves 
 in 48 ? etc. The form of the questions may be changed 
 to, In 40, how many eights ? How many nities in 72 ? 
 The teacher can easily change the form of this review so 
 as to make it both practical and interesting. 
 
 Tables of Weights aiul Measures. — Review the tables of 
 the Second Grade, and teach the following : 
 
 Common, or Avoirdupois Weight. 
 
 Miscellaneous Tables, 
 
 16 ounces make 1 pound. 
 
 12 things make 1 dozen. 
 
 8 " "1 half pound. 
 
 144 " " 1 gross. 
 
 4 " " 1 quarter of a pound. 
 
 12 dozen " 1 " 
 
 100 pounds " 1 hundred weight. 
 
 13 gross " 1 great gross. 
 
 20 hundred weight make 1 ton. 
 
 20 things " 1 score. 
 
 2,000 pounds make 1 ton. 
 
 24 sheets " 1 quire of paper. 
 
 
 20 quires " 1 ream. 
 
 "Renews. — After these tables have been thoroughly learned in order, 
 the teacher should conduct brief reviews of the tables of both the First 
 and Second Grades, by questions somewhat like the following : 
 
 How many inches in three-quarters of a yard ? How many yards in 
 one rod ? How many rods in a mile ? How many pounds in a half 
 ton ? How many pecks in twelve bushels ? How many quarts in nine 
 gallons ? How many days in a year ? How many months in half a 
 year ? Which is the longer, six feet or two yards ? How many buttons
 
 APPENDIX. 207 
 
 in a gross ? How many sheets of paper in a quire ? How many in half 
 a quire ? 
 
 Simple questions in mental arithmetic may be given, 
 with a view to a practical application of the foregoing 
 tables. 
 
 WRITING. 
 
 Slats- Writing. — Continue instruction in the use of capi- 
 tals, the period, the interrogation mark, and the hyphen ; 
 the pupils should be taught that a syllable can never be 
 divided. Exercises should be had in writing brief de- 
 scriptions of familiar objects, and the substance of some 
 previous lesson. The pupils of this grade should be 
 trained in writing exercises from dictation. 
 
 Penmanship. — In addition to the exercises in the writ- 
 ing-book, occasional lessons should be given in copying 
 sentences from the blackboard. During the last half of 
 this grade, exercises should be given in writing from dic- 
 tation.
 
 UCLA-Young Researi-h Libinry 
 
 LB1563.N4 N4 
 
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 L 009 572 962
 
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