f hni ^fiiAt. *vva m Ni; ?|I1.11 \J1\JLA A liiS-Iilii \r\ CH$0&J#B P. CUT&BSJ, __• LIBRARY OF CONGRESS. >>*$* S|ap..k*e. inpgrigp fix.. Sh.elf.X-SL UNITED STATES OF AMERICA. PRIMARY MANUAL TRAINING, METHODS IN FORM STUDY, CLAY, PAPER AND COLOR WORK. BY CAROLINE F. CUTLER, Lucretia Crocker School, Boston. Special Instructor in Manual Training to the Primary Teachers of Boston. % f BOSTON AND CHICAGO- EDUCATIONAL PUBLISHING COMPANY. 1891. COPYRIGHT BY EDUCATIONAL PULISHING COMPANY 1891. pUBLI£HER$' J^OTE. The author presents, in plain language, practical methods of teaching Manual Training in primary schools. In fact, this book is but a transcript of the regular work done by the author in her own school, and no plans have been suggested that cannot be readily accomplished by the average pupil. After the school committee of Boston had added to the course of study for the primary schools, a course in Manual Training, the author was summoned by the committee to give instruction to the primary teachers in the methods to be employed in teaching Modeling in Clay, Paper-cutting and Folding, Stick-laying, etc. The line of instruction was in strict harmony with the course of study, and this book, which is the epitome of her instruction, is issued in response to the demands of many teachers. CONTENTS. Page General Suggestions, V. Plan of Development of each Type-Solid, VII. The Sphere, 5 The Cube, 13 Paper-Folding, Series I 22 Paper-Folding — Forms of Life, 32 Paper-Folding — Cutting and Pasting, ........ 35 The Cylinder, . 38 Review of First Three Solids, 45 Color, 46 Paper-Cutting — Color Work, 53 The Hemisphere, 57 The Square Prism, 62 The Right-Angled Triangular Prism, G6 Equilateral Triangular Prism, 69 Paper-Folding, Series II, 75 Dimensions, 89 The Ellipsoid, 93 The Oblate Spheroid, 99 The Ovoid, 100 The Cone, 107 The Square Pyramid, 113 The Equilateral Triangular Pyramid, 120 Suggestions for connecting Manual Training with other Studies, ... 122 Constructive Work in Card-board 124 Suggestions for Stick-Laying, 128 {^ENERAL J3uQQE£TI0N£. Clay. — Modeling clay may be obtained at the Pottery Works, or of a plaster image-maker, at a cost not exceeding three cents per pound. Buy the moist clay, and by keeping it in a covered earthen jar, with a damp cloth over the clay, it will be ready for instant use. After each lesson, preserve the best specimens, and always moisten the clay before returning it to the jar. Clay is generally so dry and hard, after the children have used it, that " simple moistening " may not be enough. It is best then to put it in a dish, and cover it with water. After it has thus stood a few hours, or until thoroughly softened, pour off the water, and wrap the clay in a large cloth. Place the clay thus wrapped upon a plane surface, as a slate or a board, and knead, turning it in different directions, till the water is thoroughly pressed out and a compact mass formed, when it will be in condi- tion to be returned to the jar for future use. Clay may be cut by means of a knife, w T ire or strong thread. Thread is better for children's use than wire, as the latter is apt to v vr GENERAL SUGGESTIONS. twist and become uneven. Thin, stiff cards can be used to cut small pieces of clay. Clay may be modeled by rolling between the palms of the hands or upon a plane surface, and by striking it gently upon a plane surface. A sharp-pointed stick — (A wooden tooth-pick, for instance), may be used to draw lines upon the clay. A stick with a rough end may be used to puncture the clay, to give a rough surface to the background. Paper,— Manilla paper in sheets, measuring 24x36 and weigh- ing thirty pounds to the ream, is "about right " for paper-folding, as it will be found thin enough to fold readily. This paper may be bought by the single pound, and the dealer will cut it into squares of any desired size. Four-inch squares are com- monly used, though large squares will be needed for certain forms. Thin card-board or development paper, should be used in the representation of solids in the higher classes. Development paper 24 X 36, weighs about eighty pounds to the ream. Manilla paper may be used for drawing in primary schools, but it should be of heavier quality than the folding paper. Paper should be furnished liberally to the children that they may become accus- tomed to using it freely in preference to the slate. Colored paper cut in four-inch squares, may be purchased by the package, or, it may be bought by the sheet, and cut to order. GENERAL SUGGESTIONS. vil Tablets. — Tablets of various sizes and shapes for use in form study, may be purchased, but if they are too expensive, satisfactory tablets can be made of card or stiff paper. The children can make them by tracing around the edge of a pattern and then cutting out the forms. Stick-laying. — Colored sticks are sold for this purpose, but splints, or even wooden tooth picks may be used. Scissors. — Short blunt-pointed scissors are the best for young children to use. Pasting. — Each child should have a little plate containing a small quantity of paste. A few children may be taught to fill the plates, and distribute them quickly. A wooden tooth-pick is better than a brush for applying paste. Card-Pricking. — Pricking cushions and pins are prepared for Kindergarten use. Draw any desired pattern upon paper and place the paper over the card to be sewed. At suitable intervals along the outline of the pattern prick holes through paper and card. Re- move the paper and the card is ready for sewing. If the cushions and pins cannot readily be obtained, place the card upon a piece of thick flannel and prick with a large shawl pin. Each subject of form study may be systematically developed by following the plan here suggested. 1. The study of the facts of the type-solid. 2. Modeling type-solid of clay. 3. Modeling objects based upon the type-solid. viii GENERAL SUGGESTIONS. 4. Half solid, and objects based upon it. 5. Study of views of type-solid, with the tablet exercises. 6. Tracing on clay tablets. 7. Sewing-cards. 8. Plane of the type-solid. 9. Paper-folding and cutting. 10. Stick-laying (where there are straight edges.) 11. Arm and pencil-movements. 12. Drawing of objects based upon the type-solid. PLAN FOR DEVELOPINQ THE SPHERE 1. Study the facts of the type-solid. 2. Model a sphere of clay. 3. Model clay objects based upon the sphere. 4. Cut the clay sphere. Hemispheres. 5. Place tablets. 6. Sewing-cards. ..... 7. Arm and pencil-movements. . 8. Draw free-hand circle. .... 9. Draw outline of objects based upon the sphere. . See page 5 6 6 7 8 ' 9, 10 1 11, 12 12 12 GENERAL SUGGESTIONS. PLAN FOR DEVEJLOPINQ THE CUBE. 1 . Compare with the sphere and study the facts of type-solid. .... 2. Model cube of clay. 3. Model objects based upon the cube. 4. Make a paper cube. 5. Faces of cube from the type-solid. 6. Tablet exercises. .... 7. Plane of the cube and objects based upon it. 8. Edges from study of the type-solid. 9. Corners from study of the type-solid. 10. Exercises with sticks and peas. 11. Sewing-cards. .... 12. Tablets laid in borders and groups. 13. Stick-laying. .... 14. Arm and pencil-movements. . 15. Draw the square. .... 16. Paper- foldings with sewing, stick-laying and drawing. First series, (omitting triangles.) 17. Draw outlines of one view of cubical objects. 18. Paper-folding and cutting, — basket, sled, etc. 19. Paper-folding and pasting. (Designs.) . 20. Clay plaques. ...... See page 13 14 14 14 16 16 18 17 17 18 18 19 19 20 20-21 22 36 32 35 37 THE SPHERE. Each child should hold in his hand a small sphere — while the teacher holds a large one before the class. The teacher should lead the children to perceive and state that the "ball " is round and smooth, and that it will stand and roll. Give the name — sphere. (Care should be taken that the children do not call this word, spear). Talk about the outside of the sphere, and of other objects, and give the name — surface. Let the children move their lingers over the surface of the sphere, and roll the sphere in their hands, and so call forth the expression — round surface. 6 THE SPHERE. The children may next model a sphere of clay. Give to each child a piece of clay, a little larger than a cubic inch, and tell him to place it in the palm of his left hand. Then place the palm of his right hand upon the clay, and roll it and mould it, till a sphere has been formed. The teacher should model one at the same time, that the children may observe the process. Next, place before the class objects based upon the sphere — as, an apple, a round melon, and a round basket. (Figs. 1 — 3). Let the children model a sphere, and then change the form of its surface to resemble the object selected. This attempt to imitate in clay, trains both the eye and hand, and will lead the children to notice the spherical form of other objects. To make an apple, the sphere must be indented by pressing slightly with the thumb upon the surface, and then inserting a stem, which may be made of clay, though a real apple stem would prove more THE SPHERE. 7 effective. On the side opposite the stem make a few scratches on the clay, to imitate the blossom. (Fig. 1). A melon is made by flattening the upper and lower surface a trifle, and marking the stripes. For this, use a sharp slate pencil, a wooden tooth-pick, or a thin strip of wood shaped like a knife-blade. The basket should have a line marked around it, to represent the edge of the cover. Roll a small piece of clay between the hands, until a long thin strip is made, which may be fastened to the basket for a handle. A sphere may be cut in halves, and the hemisphere described — but it is best to make the study of the hemisphere a separate subject. (Fig. 4). Tablets. — Work with tablets should follow clay modelling. Place square and circular tablets, (thin card-board) of the same diameter as the type-solids, upon a table where the children can see them. Tell the children to hold the sphere in front of the eye, and then ask a child to select a tablet that looks like a picture of the sphere . THE SPHERE. Give the name of the tablet — circle. Let the children place the tablets upon the desk in a position to imitate spherical objects — as a string of beads, or a bunch of grapes. (Fig 4 *. 5 and 6). With colored circles of various sizes very pleasing pictures of objects can be easily made, and the children should be taught to paste the tablets upon gray, or other neutral-tinted paper. THE SPHERE. The spherical outline may also be taught by sewing cards having circles or circular objects pricked upon them. Let the children sew with appropriate colored worsteds or threads. ^~~ ^% s \ / / \ \ / -^ """ - -^ \ \ 1 / V 1 / \ \ 1 \ \ 1 1 l 1 1 \ \ i \ \ \ \ \ / 1 1 \ K / \ ^ tmm ^ ^,* / \ / \ / \ / v ... . s SAMPLE OF SEWING CARD. 10 THE SPHERE. // 1/ \\ SUBJECTS FOR SEWING CARDS. ARM AND PENCIL-MOVEMENT. H ARM AND PENCIL-MOVEMENT. The children should next be taught arm and pencil-move- ments, preparatory to drawing the circle. Let the children extend the right arm horizontally, and describe the form of the circle in the air, by moving the hand toward the left side, then up — then down toward the right side, and back to point of starting. Let them practice the same movement at the black-board, using the chalk, until a smooth, free circular movement of the arm is obtained, without regard to the size of the circle, except that it be a large one. The chalk should be held with the pointed end at an 12 ARM AND PENCIL-MOVEMENT. angle of about forty-five degrees to the surface of the board, always pointing toward the left, and the circle drawn as indicated by figure. Let the children practise upon slate or paper, (paper is preferable) holding the pencil in the same manner as the chalk. Children should draw simple spherical forms from the object. Their attention should be called to the prominent features of the object selected. If it is not perfectly round, ask them where the surface is flat or elevated ; whether it is longer ' ' one way than the other," also what additions are made to the spherical form to complete the object? Train the child to see the form — and afterward, orally, and by drawing, to give descriptive explanations. Suppose the object selected to be drawn was a spherical tea-kettle. The children will find, by measuring, that the body of the kettle is longer horizontally than vertically. That the distance from the top of the kettle to the highest curve of the handle is equal to one- half the diameter of the circle. They will also discover that the bottom of the kettle and the edge of the cover look straight, and that the spout is placed nearer the lower, than the upper part of the right side of the kettle. (Fig. 9) . THE CUBE. 13 THE CUBE. In the study of the cube, use type solids as with the sphere. Compare the cube with the sphere. Observe that the cube is not round, that it has edges and cor- ners, that it will stand and slide, but will not roll. Observe also that its surface is flat or plane. There are six parts to the outside of the "block ," all parts of the same size and shape. Give the name — cube. When the children have become familiar with the facts of the type solid, they should be taught to mould the cube of clay. 14 THE CUBE. Give a piece of clay to each child , and have them all model a sphere. Then holding the sphere in the right hand, between the thumb and fingers, tap it gently upon the slate three times (the teacher counting aloud for this movement, that the action may be uniform ) . Turn the clay and tap three times upon the opposite side, con- tinuing to turn the clay until the six sides have been flattened, and the clay has assumed the form of the cube. Direct the children to be careful to make all the faces of the same size, with sharp edges and square corners. Objects like the cube, as a square basket, a safe, dice, lump of sugar, may also be modeled in clay. (Figs. 1 and 2). The cube should also be formed of paper. Give each child a square of paper. The teacher holds a large square before the class, and folds and dictates ; while the children follow her directions. Fold front edge to meet back edge. Open paper. Fold front edge to meet centre fold. Open paper. Fold back edge to meet centre fold. Open. Fold left edge to meet right edge. Open. Fold left edge to meet centre fold. Open. Fold right edge to meet centre. Open. Result, — sixteen small squares. THE CUBE. 15 Cut off one entire row of squares from the lower side of paper. From the larger piece cut off each corner square. The paper now is like Fig. 1. .Fig l. Fig. 2. Now, cut off one of the two upper squares and also the one opposite on the low^er row. (Fig. 2). Fold this paper till the edges meet in the form of a cube — join the edges by sewing or pasting. Many objects, based upon the cube, may be made of paper. By joining (as for the cube) all the faces, except one, a box is formed. The face left open serves for the cover. Instead of sewing the edges, tie each corner with colored worsted. (Fig. 3). 18 FACE OF THE CU3E. FACE OF THE CUBE. Let the children find and count the different parts of the surface of the cube. There are six parts — all of the same size. Each part is called a face. Find the front face — - top face — and the other faces. Give exercises that will illustrate the terms — level and up- right. Let the children find surfaces, upon which objects will rest evenly. Give term — horizontal. Find the horizontal faces of the cube. Let the children place object in upright position. Find the faces of cube that are upright. Give term — vertical. Find a tablet like one face of the cube. Give name — square. Find horizontal and vertical faces. Interesting and valuable exercises with tablets may be given. FACE OF THE CUBE. 17 Place six tablets to form a cube, like the paper model of the cube. Edges. — Direct the children to find the places on the cube, and on different objects about the room, where the faces meet. Give term — edge. Find horizontal and vertical edges. Find any two edges of the cube that extend in the same direc- tion — for example, those from left to right, also those from front to back, and again those from top to bottom. And give the term — parallel. Corners. Have the children find the points where the edges meet, and give the name — corner. Have them find also, the outside comers of the cube — and of other objects. Also find the inside corners of the room, and of boxes — find face corners of the cube, of the floor and of the slates. A skeleton cube can also be formed of sticks and peas by 18 FACE OF THE CUBE. placing the sticks to represent the edges of the cube, and joining the corners with peas. Cut a plane from a clay cube and from it model a square cracker, or a card of buttons. O O o AFTERNOON TEA. O O Square objects may be outlined on sewing cards, and given the children to sew. FACE OF THE CUBE. 19 Make borders of tablets using both squares and circles — edge to edge. Next, place them with their edges near, but not touching. ODO Edges overlapping. In groups. Lay sticks for edges to the borders. Tablets of colored paper pasted on coarse paper make pretty borders. Stick Layixg. — Lay sticks to represent the edges and corners of a square . 20 ARM AND PENCIL-MOVEMENT. ARM AND PENCIL-MOVEMENT. The next step is to give arm and pencil-movements preparatory to drawing the square. Send as many children as possible to the board- — the others meanwhile working at their desks. Direct the children to turn slightly toward the left, and hold the point of the chalk toward the left also, at an angle of forty-five degrees to the surface of the board — draw downward in a vertical line. (Fig. 1). Now, direct the children at the board to turn slightly toward the right, and with the chalk pointing upward, place the point at the upper end of the vertical line, and draw from left to right, a line as long as the vertical line. (Fig. 2). ARM AND PENCIL-MOVEMENT. 21 Turn again toward the left — and draw downward from the right end of the horizontal line, to make the right vertical line. Resume position for the horizontal line, and draw the lower side of the square, from left to right. (Fig. 3). In drawing on the black-board the children may use a ruler to measure the lines but must not draw by it. 22 PAPER-FOLDING, PAPER-FOLDING. The following foldings form a systematic series, but some of them, for example, the angles and triangles, may be omitted until after the study of the solids illustrating those forms. These foldings may be used separately, but it is well to connect them with drawing and sewing lessons. Thus after folding No. 1, fold another just like it and let the child trace the crease with a lead pencil. Next with a ruler measure the line and draw one the same length on slate or paper, testing carefully with ruler. In this way the use of ruler is learned, and eye and hand trained to accuracy. Then draw the line again entirely free-hand. These four steps having been taken , a child will thoroughly under- stand and be able to draw a horizontal line. Proceed the same with No. 2, and all the figures, taking four steps with each before attempting the next figure. These same figures can be pricked on cards and sewed with colored thread or worsted, giving a series of sewing lessons. Sewing on canvas or scrim will do as well. If the papers are cut through the creases and the strips pasted on gray or neutral-tinted coarse paper, another development of manual training will result. Stick-laying in these forms should precede drawing, The papers used for these foldings are four inches square. In this first set of foldings each crease should be made sepa- rately that all may be accurate. Never allow the children to double the paper and make several creases at once. PAPER-FOLDING. 23 Number Oxe. — Fold front edge of square to meet back edge. Open paper. Result — a horizontal line. Number Two. — Fold front edge of square to meet back edge. Open paper. Fold front edge to meet horizontal line in centre. Fold back edge to meet centre line. Open square. Result — three parallel horizontal lines. Number Three. — Fold left edge to meet right edge. Open paper. Result — vertical line . Number Four. — Fold left edge to meet right edge. Open paper. Fold left edge to meet centre line. Fold right edge to meet centre line. Result — three parallel vertical lines. 24 PAPER-FOLDING. Number Five. — Fold front edge to meet back edge. Open paper. Fold left edge to meet right edge. Open paper. Result — two diameters of square. Number Six. — Fold lower left corner of square to meet upper right corner. Open paper. Result — oblique line — also diagonal of square. Number Seven. — Fold lower left corner to meet upper right corner. Open paper. Fold lower right corner to meet upper left coiner. Open paper. Result — two diagonals of square. PAPER-FOLDING. 25 Number Eight.— Fold lower left corner of square to meet upper right corner. Open paper. Fold lower left corner to meet centre of oblique line. Fold upper right corner to meet centre line. Open paper. Result — three parallel oblique lines. Number Nine. — Fold diameters of square (See No. 5). Result — four small squares. Cut out upper right square. Result — right angle . Number Ten. — Fold diameters of square. Open square. Fold lower left corner to meet upper right corner. Open paper. « (No. 10 a) . Cut out triangle in upper left square. Result — acute angle. (No. 10 b). 26 PAPER-FOLDING. r Number Elevex. — Fold diameters of square. Open paper. Fold lower right corner to meet upper left corner. Open paper. (No. 11 a). Cut out upper left square and adjoining triangle. Re- sult — obtuse angle. (No. 11 b). Number Twelve.— Fold diameters of square. Open paper. Fold each corner of square to centre of square. Open paper. Re- sult — inscribed square. PAPER-FOLDING. 27 Number Thirteen. — Hold right edge of square in right hand and left edge in left hand. Pass right hand under towards left, and left over towards right till upper side of square is divided into thirds. (See No. 13 a). When the upper edge is lapped so it is even at both ends press the creases down the whole length of paper. Open paper. Result — square divided vertically into thirds. (No. 13 b) . ^5511, Number Fourteen. — Fold square in three horizontal, parallel lines. (See No. 2). Open paper. Fold upper side into thirds. (See No. 13 a). Open paper. Result — three parallel horizontal lines divided into thirds. 28 PAPER-FOLDING. Number Fifteen. — Fold left side of square so it will be divided into thirds as No. 13 a. Press paper in two horizontal folds. Open paper. Result — square divided into thirds horizontally. Number Sixteen. — Fold square into three parallel vertical lines. (See No. 4.) Open paper. Divide into thirds. (See No. 15.) Open paper. Eesult — three parallel, vertical lines divided into thirds. 17. Number Seventeen. — Fold square into four small squares by folding front edge to meet back edge. Then left edge of oblong to meet right edge. Hold corner which forms the centre of the paper in left hand. Cut in a line curving outward from lower right corner of square to upper left corner. Open paper. Eesult — circle. PAPER-FOLDING. 29 Number Eighteen. — Cut a circle. (See No. 17). Cut through one diameter. Result — semi-circle. 19. 20. Number Nineteen. — Cut circle. (See No. 17). Cut from edge of circle through half of horizontal diameter — also from centre of circle through one half vertical diameter. Quarter circle. Number TwEXTr. — Cut circle. (See No. 17). Fold edge at end of one diameter to meet centre of same diameter. Open paper. Cut off small section. Result — curved edge or small section of circle. Number Twexty-oxe. — Fold lower left corner to meet upper- right corner. Cut through diagonal . Result — ri^ht-angled triangle . 30 PAPER-FOLDING. Number Twenty-two. — Fold front edge to meet back edge. Open paper. Fold front edge to meet centre fold. Open paper. Fold back edge to meet centre fold. Open. Fold left edge to meet 22 a. / / right edge. Open. Fold left edge to meet centre vertical fold. Open. Fold right edge to meet centre fold. Open. Result — sixteen small squares. (No. 22 a.) Cut off from entire upper side of square a strip equal to one-eighth the width of square or one-half- inch, (No. 22 b) . Fold back upper left corner of paper so that the PAPER-FOLDING. 31 crease will extend from upper end of vertical diameter to lower left corner of paper. (No. 22 c). Fold back upper right corner so the crease will extend from upper end of vertical diameter to lower right corner of paper. Cut through the last two folds. Result — equi- lateral triangle. (No. 22 d). Number Twenty-three. — Fold lower left corner so crease extends from upper left corner to middle of lower side of square. Cut through fold. Result — the smaller section is a scalene triangle. Number Twenty-four. — Fold square in four small squares. (See first part of No. 17). Fold again to get diagonals of small square. Open paper. Result — four squares with diagonals form- ing construction lines for various designs. 32 PAPER-FOLD LN"G. PAPER-FOLDING ILLUSTRATING UPON SOLIDS. OBJECTS BASED As the square is the form from which the greatest variety of paper-folding and design can be obtained, it can be used throughout the course interspersed with studies from all the type-solids. Many of the Kindergarten forms can be used with advantage . Here is a simple one, a little basket. Number One. — Fold front edge of square to meet back edge. Open. Fold left edge to meet right edge. Open. (Fig. 1). Fold each corner to centre of square, (Fig. 2). Turn paper. Fold each PAPER-FOLDING. corner to centre, (Fig. 3). Turn paper. Fold back each of the corners that meet in the centre, (Fig. 4). Insert the fingers and thumb in the pockets thus made and press the four under corners together. Result — Fig. 5. Number Two. — Fold front edge of square to meet back edge. Open. Fold front edge to meet centre fold. Fold back edge to meet centre. Fig. 7. Turn paper — longest edges horizontal. Fold upper and lower left corners to meet on horizontal line. Fold right corners the same way. (Fig. 7). 34 PAPER-FOLDING. Fold upper edge to meet lower edge, boat. (Fig. 9). (Fig. 8). Result — a fig. 8. Fig. 9. Number Three. — Divide (by* folding) a square into thirds, both vertically and horizontally. (Fig. 10). Fig. 10. Fig. 11. Cut out the middle square on upper side. (Fig. 11). PAPER-FOLDING. 35 Fold upper right corner of upper right square to meet the lower left corner of same square. Fold upper left corner of upper left square to meet the opposite corner of the same square. (Fig. 12). Fold right edge of paper to meet the vertical crease next it. Fold left edge of square to meet vertical crease next it. (Fig. 13) . Turn paper. Result — a sled. (Fig. 14). Number Four. — Let the children cut Kindergarten designs from colored paper and paste upon gray square. The following is easily made. Fold front edge to meet back edge. Fold left edge to meet right edge. Fold lower left corner to meet upper right corner. Open. Fold lower left corner to meet centre of square. Fold upper right corner to meet centre of square. Cut off both corners through the folds last made. Open the large figure and paste on gray square. Open the corner cut from lower left corner of square. It is a little square. Paste diagonally across open centre of the octagonal figure. The other corners cut off are triangles. Paste them around four sides of large figure. (Fig. 15). During the lesson each child can have a little plate of paste, and wooden tooth-picks are better than brushes with which to apply the paste. 36 VIEWS OF CUBICAL OBJECTS. DRAWING THE VIEWS OF CUBICAL OBJECTS. Drawing from cubical objects should be practiced as with the sphere. The objects which have been modeled in clay, and also cubical object* in the room should be drawn. At first, it is best to draw views of each face separately, as young children are rarely able to draw correctly, when views involving persoective are attempted. Cubical boxes, and baskets, toy money-banks, toy trunks, (see illustration) and similar objects are suitable subjects. VIEWS OF CUBICAL OBJECTS. 37 Another step in clay work may follow the paper-folding and drawing. Cut from a large cube a plane about one-quarter inch in thick- ness or make a square tablet by placing bits of clay on a slate and moulding them into a flat smooth surface. With a sharp slate pencil, draw simple designs upon the clay. Clay can be added within the outline of the figure, building it up in bas-relief if desired, or if left in flat outline a pretty effect will be given by puncturing the surface of the clay around the design. i.i. ulll' '.■-Yi'.'r _l — LU — ' ' i i — i LL_ CLAY TABLET. Nearly all the figures used in the drawing course can be repeated upon clay. The youngest pupils can have various plane figures cut from card-board, and placing them on the clay, trace around the edo-es. 38 THE CYLINDER. THE CYLINDER. Use the type-solids as in the previous lessons. Direct the child- ren to compare the cylinder, with the sphere, and the cube. They will discover that it will roll, and stand, and that its surface is plane and curved. The plane faces are circles. Give the name — cylin- der. The children can model a cylinder of clay, by first making a sphere, and then rolling it on a slate, or, between the hands, until the desired length is obtained. Then flatten the ends by tapping them alternately upon the slate. THE CYLINDER. 39 Cylindrical objects can now be made of clay, as, a rolling-pin, muff, water-pot, drum, and bottle. Y. i For a rolling-pin, make a cylinder of the desired length. Then make small cylinders for handles ; instead of flattening the outer ends of the handles, curve them slightly. The rolling-pin and the handles may be joined together more firmly, by inserting in the joined ends a wooden tooth-pick. Join spouts to tea-kettles and watering pots in the same manner. A paper cylinder may next be made. Fold a square into sixteen small squares. Cut out each corner square, and all of the two lower squares, except a slight margin as in Fig. 1. o O Cut circles from the squares on left and right sides, leaving the circles attached to the paper. (Fig. 2). 40 THE CYLINDER Fasten the upper and lower edges of paper together by sewing or pasting, and join the circles to the ends of the hollow cylinder thus formed. Make another clay cylinder, and cut it in halves, through its longest diameter. Scoop out a portion of the clay from a half- cylinder, and a trough is made. By attaching the trough to an upright cylinder the principal parts of a pump are formed. To com- plete the pump, add the handle and spout. ica The half-cylinder, may also form a basket by the addition of a handle. THE CYLINDER. 41 Cut a thin slice from the end of a cylinder and mould it into a round cracker. From a thicker slice may be moulded a cheese, or a circular box. 42 THE CYLINDER. Let the children hold a cylinder in a vertical position, in front of the eye and study the outline. Then find a tablet like it. Give the name — oblong. Let the children find tablets like the upper and lower faces of the cylinders — (circles). All these tablets may be arranged in groups. THE CYLINDER. 43. Ask the children to cut an oblong plane and a circular plane, from the clay cylinder. Figures containing oblongs maybe traced on clay plaques, or sewed on cards. A great variety of forms, combining oblongs, squares and circles may now be introduced. c £X 3. *• Number Three. — Pink circles. Black square. Number Four. — Large square or two oblongs of dark red, small squares light pink. COLOR. 51 Number Five. — Dark violet square. Light violet triangles. Number Six. — Brown bronze square. Light, yellow semi- circles . Number Seven. — Three shades of one color. An almost inexhaustible field of color lessons can be found in coloring the clay forms made by children. Dry paint in the form of a powder may be found at the art stores. This powder comes in various shades and tints. If the correct shades of powder be rubbed with the finger upon the clay objects before they harden, the resemblance to the object repro- duced will be greatly increased. Treat a clay banana in this way. Cover the clay thoroughly with the correct shade of yellow, and add touches of green on the curves and near the end. A touch of brown on the stem will complete the coloring, and the resemblance to the natural fruit will be quite marked. The clay peach similarly treated acquires the beautiful velvety appearance characteristic of the fruit. Children are often perplexed in naming colors by their inability to distinguish a hue of color from a shade or tint of the standard. Thus carmine, scarlet and magenta are all known to them as red, but only the carmine can be assigned to the scale of standard red. To explain these differences resort to the colored liquids again. Assuming orange to be produced by mixing equal parts of red and yellow, add more red to the orange and a color is made that may be termed orange-red. By mixing wdiite with orange-red, its tint, (which is salmon) is produced. By mixing black with orange-red, its shade (or scarlet) is produced. These tones are the yellow hues of red. 52 COLOR. Show orange again and add more yellow — giving buff or the red hues of yellow. Young children can describe carmine as standard red, — scarlet as a color having more red than yellow — and buff as a color having more yelloAV than red. There is one red which has not been mentioned in the scales, but which children are very apt to bring as a sample — viz. , magenta. This is a mixture of red and blue like the purple only in unequal quantities, nearly all red with but little blue. The greens can be divided into blue-greens and yellow-greens. For blue-green put more blue than yellow. For yellow-green put more yellow than blue. Violet can be divided the same way. More red than blue, giving red-violet — more blue than red, giving blue-violet. This chart will be found to illustrate the proper position of the hues of these colors. TINT, Pink. Salmon. Light Orange. Buff. Cream. Apple Green. STANDARD, . Red. Or ange- red. Orange. Orange- yellow. Yellow. Yellow- green. SHADE, . Garnet. Scarlet. Dark Orange. Dark O. Yellow. Corn. Dark Y. Green. TINT, Light Green. Light-hlue Green. Light Blue. Lavendar. Light Violet. Lilac. STANDARD, . Green. Blue- green. Blue. Blue Violet. Violet. Red Violet. SHADE, . Dark Green. Dark B. Green. Dark Blue. Dark B. Violet. Dark Violet. Dark R. Violet. PAPER-CUTTING. 53 PAPER CUTTING.— COLOR WORK. The following designs can be cut from paper and placed upon a suitable background allowing the under color to show through the openings. Cut the design from any bright color and place over black, or gray, or white paper. Another set can be made by cutting from a tint and placing over a shade of the same color. If the designs are cut from gold or silver paper and placed over proper colors the effect is agreeable. Fold the front edge of a square to meet back edge. Fold left edge of oblong to meet right edge. Fold lower right corner to meet upper left corner. Upon the triangle thus formed draw the figures indicated by dotted lines and cut through dotted lines, thus — Figure A. when opened gives Fig. 1. 54 PAPER-CUTTING. Figure B. when opened gives Fig. 2. Figure C. when opened gives Fig. 3. PAPER-CUTTING. Figure D. when opened gives Fig. 4. f)5 Figure E. when opened gives Fig. 5. 56 TERTIARY COLORS. TERTIARY COLORS. The Tertiary colors are citrine, olive, and russet. Citrine is a combination of orange and green. Russet — of orange and purple. Olive — of purple and green. Citrine is called the yellow tertiary, because yellow predominates — being in both the orange and green. Russet — is called the red tertiary, as red predominates. Olive — the blue tertiary, as blue predominates. CONTRAST AND HARMONY. Contrast must not be mistaken for harmony. Harmony may include contrast, but, contrast to be harmonious, must always be delicate, never coarse. Blue and Orange are complementary colors, because each increases the brilliancy of the other, but the violent con- trast offends good taste. Tints and shades of both colors arc often blended with harmonious effects, but children should use simpler combinations. THE HEMISPHERE, THE HEMISPHERE. The teacher will show to the children two hemispheres, so placed, as to form a sphere. Separate them, and ask the children to name them — the natural reply will be, rr half of a sphere." Give the proper name — hemisphere. Now, distribute hemispheres to the class, and ask the children to describe them. They will see that the hemisphere has one plane face and one curved face. The plane face is a circle. The day hemisphere is formed by cutting the clay sphere in halves. 58 THE HEMISISPHERE. Model clay objects resembling the hemisphere — as a hat, a half apple, or a fruit dish. Have the children find the tablet like the plane face of the hemis- phere (circle). Direct the children to hold the hemisphere on a level with the eye, the plane face downward and find tablet like this view. Give the name — semi-circle. These semi-circular tablets may be so placed as to form a border, THE HEMISPHERE. 59 Place semi-circles around the sides of a square, and of an oblong — to make a quatre-foil. r\ Clay Tracings. — The teacher may cut from cards, various forms, resembling the semi-circle, and let the children place the forms on clay tablets, and trace around the edges. Good subjects may be selected from the tablet forms already mentioned, to which may be added — the side view of an open umbrella, and mouse- trap and mouse. 60 . THE HEMISPHERE. These same clay and tablet forms may be pricked on cards, to be sewed by the children. / / / / 1/ i \ i i SEWING CARD. The children having now received these various impressions of semi-circles, in clay, card, and sewing, should give expression, by paper-folding, and drawing, to their knowledge of this form. Paper-folding. — Cut a circle (See page 28, Fig. 17) and then cut it in halves (semi-circle). Fold a four-inch paper square to mid the diameters, and upon them draw semi-circles. Repeat these semi-circles, by drawing free hand, both the diameters and curves. The children may now draw free hand, simple objects having the form of the hemisphere. Draw also upon clay tablet. Designs. — A practical application of the form study, may now be made by the children in making the following design. THE HEMISHHERE. 61 Upon a square of red paper draw the quatre-foil, as in Fig. 1. Cut out the quatre-foil. Upon a square of black paper (of same size as Figvi) draw Fig. 2. Cut out the central drawing and place it in the centre of thlf quatre-foil, mounting the figure thus formed, upon a black or neutral ground. (See Fig. 3). • 62 SQUARE PRISM. SQUARE PRISM. The teacher will hold up before the children, a cube composed of four square prism solids, and then separate the blocks, to demon- strate that the square prism is one-fourth of the cube. Then, direct the children to model the clay cube, which they are to cut vertically, into quarters and thus obtain the square prism. Distribute the type solid amongst the class and ask the children ♦to describe the faces and angles. (Four equal oblongs and two squares). The children may form a square prism from a clay cylinder by flattening the curved surface, into four oblongs of equal size. SQUARE PRISM. 63 Direct the children to make a paper square prism. First fold a square into sixteen squares, then cut off squares 1, 3, 4, 13, 15, 16. / J 4 /J /r /6 Edges to be joined by sewing or pasting. A skeleton square prism can be made with sticks and peas. 64 SQUARE PRISM. Have the children model in clay, objects based upon the square prism — as a carpenter's plane, chest, and oblong basket. Faces of the square prism. The children may find tablets like the faces (four oblongs — two squares). Let the children be reviewed by finding the vertical, horizontal, a,nd parallel edges and right angles of the square prism. SQUARE PEISM. 65 Paper Folding. — Cut a paper oblong — fold for diameters and diagonals — then make an oblong clay tablet of the same size, and mark on it the diameters and diagonals. Make another clay tablet of the same size, and draw the diameters upon it, place & point in the centre of each half -diameter , connect the points by lines (to form a Rhombus) add more clay to the rhombus, to build it up above the surface of the oblong. 66 RIGHT-ANGLED TRIANGULAR PRISM. THE RIGHT-ANGLED TRIANGULAR PRISM. Let the children mould a clay square prism and bisect it diag- onally to form a Right- Angled Triangular Prism. Give the type solid to the class to study, and compare with the clay. They will find Jive plane faces, three oblongs (one wider than RIGHT-ANGLED TRIANGULAR PRISM. 67 the others) and two triangles. Let the children describe the tri- angular face as to its sides and angles. With an open pen-knife, the teacher may illustrate the three angles of the triangle. Give the terms triangle and acute-angle. The right-angled triangular prism may also be modeled from the clay cylinder, by flattening the cylinder upon three sides, remembering to finish one face broader than the others. Have the children mould a clay square prism, and a clay right- angled triangular prism of the same length. The two prisms prop- erly joined resemble a house, — outline doors and windows on the square prism. 68 RIGHT-ANGLED TRIANGULAR PRISM. Find tablets like the faces of the triangular prism and form designs. Let the children cut planes from the clay triangular prism, and also cut the the same forms from paper. A right-angled triangle can be cut from paper, by bisecting a square diagonally. The children should lay sticks for oblongs and triangles, and then draw the figures. EQUILATERAL TRIANGULAR PRISM. G ( J EQUILATERAL TRIANGULAR PRISM. The teacher will distribute to the class the type solid square, and equilateral triangular prisms. By comparison, the children will find that the oblongs are equal in size, in each prism. They will also find that the equilateral tri- angular prism has hut' three oblong faces, and that the triangular faces have three equal sides. Give the name — equilateral triangular prism. Have the children mould a clay equilateral triangular prism, from a clay cylinder, by flattening the curved surface to form three equal oblongs. Next, direct the children to make this prism from paper — in this manner — fold each side of a square into four equal parts, 70 EQUILATERAL TRIANGULAR PRISM. making sixteen small squares, cut off the lower row of squares, then cut off each corner square. (Fig. 1). Cut the left and right squares to form equilateral triangles. (Fig. 2). Fasten the edges to form an equilateral triangular prism. EQUILATERAL TRIANGULAR PRISM. 71 A skeleton prism may be made with sticks and peas and the children study the edges and corners. Have the children cut planes from the clay equilateral triangu- lar prism, and give new term — equilateral triangle. Find tablets like the faces of this prism, and arrange in designs. 72 EQUILATERAL TRIANGULAR PRISM. Trace the figures on clay, and sew on cards. Fold paper to form equilateral triangles. Fig. 22). Draw these figures : (See Series I. Draw objects based upon the equilateral-triangular prism. Place the square prism, and the right-angled triangular prism so that the ends form an obtuse angle. Illustrate with an open pen-knife, and let the children lay sticks to form the angle, and then draw it. EEYIEW. 73 REVIEW. At this point it should be ascertained if the children have a clear idea of the type-forms. Without showing the solids the chil- dren should be asked to state what they know about their surface — tfie kind, number, and shape of faces, the edges and corners. Let the children — from memory — model them of clay, and when practicable make them of paper. Have them draw the faces and views. Ask them to mould in clay familiar objects which they have not made in school. Much good will be derived from these review lessons, and pos- sibly marked latent talent will be shown. By this means, errors and misunderstandings will be quickly detected. The same test should be applied to drawing. An excellent test in drawing will be found in a dictation exer- cise — for example, tell the children to think of a square prism, four inches long, two inches wide, and two inches high, resting on the table, and on a level with the eye. Suppose the prism to be in a direct front view, with an oblong face, in a vertical position. Ash the children to draw the front view . Xext think of a cube, placed on that prism so that the edges and corners of the two solids meet. Add the drawing of the front view of the cube, to that of the prism. Tell the children to imagine the cube replaced by an apple, and draw that view. 74 KEVIEW. After the drawings have been made, show the groups of objects. Carefully place the objects, so that the views seen by the children, may exactly correspond with the dictation exercise. PAPER-FOLDING. 75 PAPER FOLDING. A series of foldings is here given, which may be developed in regular order, although it is better to use each figure after studying the solid from which it is derived. The same method should be followed, as in the first series of paper foldings, viz. : Fold and cut from dictation. Next fold and trace outline with lead pencil. Then draw same figure, — testing with ruler. Finally draw free hand upon paper. Papers used in folding are four inches square. Figure One. — Keep paper upon desk, not allowing it to be held in the air when folded. Fold front edge to meet back edge and left edge of oblong so formed to meet right edge. Fold upper left corner of square to meet lower right corner. Next fold so crease shall extend from centre of lower side to upper right corner. (Fig. A). Cut through last fold. Result, (Fig. 1). w PAPER-FOLDING. Now fold'another square just like first one, and instead of cutting, open the square, when the outline of star will be seen. Let children trace with pencil. Figure Two. — Fold and cut as in Fig. 1. Fold another square to obtain inscribed square. (See first series, Fig. 12). Cut out inscribed square and place over star. Fold another square upon its diameters and cut out one of the small squares. Place this upon the square on the star as in Fig. 2. 1 Figure Three. — Use oblong 4x2 inches, or one-half of four inch square. Place on desk, long edges vertical. Fold front edge to meet back edge. Left edge to meet right edge. PAPER-FOLDING. Cut from lower right corner to upper left corner. (Fig. B. Eesult, Fig. 3) . Figure Four. — Divide square into thirds vertically and hori- zontally. Cut out each corner square. Cut upper and lower squares into triangles. (See Fig. C). Fold to form envelope (Fig. 4). Figure Five. — Cut equilateral triangle. (Series 1, number 22). Place it with base horizontal on front of desk. Fold left angle to meet right angle. Fold lower right angle to meet upper angle. Fold left angle to meet right angle. Fig. D. Fig. 5. Cut from middle of lower edge to point equally distant from right corner on right edge. (Fig. D. Result, Fig. 5). .78 PAPER-FOLDING. Figure Six. — Fold triangle as in Fig. 5. Cut from middle of lower edge, in a vertical line to meet left edge. (Fig. E. Result. Fig. 6). Figure Seven. — Fold square into small right-angled-triangle like first part of Fig. 1. Then cut from middle of lower side to middle of light side. (Fig. F. Result, Fig. 7). PAPER-FOLDING. 79 Figure Eight. — Fold as for Fig. 7, but cut line curving inward. Fig. G. Result, Fig. 8). Figure Nine. — Fold front edge to meet back edge, and left ed^e to meet ri^ht edo-e. ^\" / Fold upper left, upper right and lower right corners to meet in centre of square. Fig. H. Cut oft* corners. Result, Fig. 9). 80 PAPER-FOLDING. Figure Ten. — Fold square into right-angled-triangle, and eut in line curving upward from lower right corner to a point on left edge. (Fig I. Result Fig. 10) . Figure Eleven. — Fold square into sixty-four small squares. Then into right-angled-triangle, and cut as indicated by dotted line. (Fig. J. Result, Fig. 11). PAPER-FOLDING. 81 *- — -^ V (Figure Twelve. — Fold as for Fig. 11. Cut curve as per dotted line. (Fig. K. Kesult, Fig. 12). Figure Thirteen. — Fold square so it will be divided into thirds. Cut out each corner square. Result, (Fig. 13 or Greek Cross). 82 PAPER-FOLDING. Figure Fourteen. — Divide square into thirds. Open square. Fold front edge of square to meet back edge. Fold left edge to meet right edge, (Fig. I.) Fold upper right corner, upper-left corner and lower-right corner as in Fig. II. corners. Open paper. (Result, Fig. 14). Cut off these Figure Fifteen. — Fold square as for Fig. 1. Cut in a line curving inward from lower-right corner to upper-left corner, (Fig. III). Open paper. (Result, Fig. 15) . PAPER-FOLDTXft. 83 Figure Sixteen. — Maltese Cross. Fold as in Fig. I. Then upper left corner to lower right corner, (Fig. IV.) Cut from middle of right edge to point on left edge which intersects, crease from first fold. Open paper. (Result, Fig. 16). Figure Seventeen. — Cut circle (See Series I. Fig. 17). Cut another square in halves. Place one of the oblongs on desk with short ed°*es horizontal. Fold front edge to meet back edge. PAPER-FOLDING. Fold left edge to meet right edge. Cut in line curving outward from lower right corner to upper left corner. Fig. V. Open paper, Kesult, (an ellipse). Place ellipse so diameters coincide with dia- meters of circle. (Kesult, Fig, 17). Figure Eighteen.— Cut ellipse as in Fig. 17. and cut circle from one-fourth of large square. Place the circle upon the ellipse as in Fig. 18. PAPER-FOLDING. 85 Figure Nineteen. — Cut circle four inches in diameter. Fold edges together till circle is divided into eighths, (Fig. VI). Fold curved edges as in line a, b. Open last fold. Cut from point b to centre of line a, b. Then cut in line curving upward to point c. (Fig. VI). Open paper. (Result, Fig. 19). 1 1 -- 1- 1 i \ i \ 1 — 1- y A- i Figure Twenty. — Oval. Divide square into thirds. Open paper. Fold left edge to meet right edge. Cut in a curved line from lower left corner to upper left corner, (Fig. VII). Open paper. (Result, Fig. 20). 86 PAPER-FOLDING. Figure Twenty-one. — Axis of symmetry. Fold an oblong as in Fig. V. Cut from centre of lower edge to centre of right edge, then to upper left corner. Fig. VIII. Open paper. (Re- sult, Fig. 21). Figure Twenty-two. — Fold squares into fourths both ways. Open paper. Fold left edge to meet right edge. Cut as indicated by curved lines Fig. IX. Open paper. (Result, Fig. 22). PAPER-FOLDING. Figure Twenty-three. — ■ Fold square so it is divided into thirds. Open paper. Fold left edge to right edge, and cut as in Fig. X. Open paper. (Result, Fig 23). Figure Twenty-four.— Fold as for Fig. X. and cut as in Fig. XI. Open paper. (Result, Fig. 24). 88 PAPER-FOLDING. During these paper-foldings, the children have learned to divide the squares into halves, thirds and fourths ; and now, the dictation may be assisted, by using the terms — bisect, trisect, and quadrisect. The facts of proportion, and symmetry, should be presented; for example, give the children an oblong ^aper, four inches long, and two inches wide. Let them describe the sides and angles. The short sides are one-half 'the length of the long sides. The long sides are twice the length of the short sides. Fold for the diameter, by bisecting the sides. The divisions must be equal, and the proportions even. Bisect each half diameter, thus quadrisecting the entire diameter. Connect these points, and see that the different portions of the figure, balance each other. i Many dictation lessons should be given upon the forms already studied, as well as upon new figures, containing the same principles. Not only for the purpose of furnishing variety, in the methods of impressing facts, but also to ascertain the ability of the children to express what they have learned. DIMENSIONS. 89 DIMENSIONS. The children have studied solids, as wholes, their faces, and edges — also representations of them, by foldings and drawings. The paper used thus far, has been of uniform size (4 inches) and the children should have, by this time, a clear idea of a four- inch square, and of its proportions in halves, quarters and thirds. Attention should now be given to the study of the inch. Paper- folding is one of the best methods to use in teaching it, and the figures may be repeated by drawing from dictation — as for example, fold a four-inch square, so that it will be divided into sixteen small squares. (See Fig. 1). Open paper. Each square measures one inch. Cut the squares apart, and study the length and width. Draw the same square from dictation. 90 DIMENSIONS. Fold another paper, as described in Fig. 1, and then, fold the front edge to meet the back edge, and the left edge, to meet the right edge. (See Fig. 2). From this folding, an almost endless variety of foldings may be formed. When dictating for drawing, sometimes give a portion of the figure, covering only one-fourth of the surface, and direct the chil- dren to complete the figure, by drawing the other parts. Symmetry will thus be taught, and also one of the fundamental principles of design, viz. : the repetition of a unit. Having folded paper as described in Fig. 2. Cut from the centre of the right side, to the centre of the square — also cut from the centre of the square, to the centre of the upper side, as indicated by the heavy lines in Fig. 3, and the result will be as developed in Fig. 4. Dictate this figure — first, by giving directions for each corner. Afterward, give directions for one corner, and let the children complete the figure. DIMENSIONS. This Fi£. 5, when developed, gives Fig. 6. 91 Another dictation — Fig. 7, developes into Fig. 8. 92 DIMENSIONS. Another example (Fig. 9) results in Fig. 10. Again, Fig. 11 develops into Fig. 12. L > Many interesting figures may also be made by dividing tri- angles and circles in like manner. THE ELLIPSOID. 93 THE ELLIPSOID. Compare the sphere with the ellipsoid. The ellipsoid has a curved surface, but is longer one way than the other. Both ends are alike. Model a clay ellipsoid , by first mak- ing a sphere, then gradually elongate it, keeping the ends equal, and the entire surface curved. (Fig. 1). Clay forms of objects based upon the ellipsoid, as for example, melon, lemon, potato, banana and cucumber, should also be mod- eled. (Figs. 2, 3). Next cut the clay ellipsoid in halves 04 THE ELLIPSOID. Objects based upon the half ellipsoid should be modeled as vegetable-dish, turtle, and pods of peas half open. (Figs. 5 and 6). Tablets. — Let the children find tablets that represent the views of the ellipsoid. (Figs. 7, 8, 9). Have each child hold the ellipsoid in a horizontal position, from left to right. Also in a vertical position. The views are represented by the ellipse. Give name — the ellipse. THE ELLIPSOID. Then direct the class to look at the ends of the ellipsoid. These views are represented by the circle. Tablets may be arranged to represent groups of elliptical solids, as plums and barberries. Let the children cut a plane from the centre of the clay ellip- soid, showing the ellipse. Let them paste paper ellipses in simple designs. (Figs. 10 and ii)- 96 THE ELLIPSOID. m^ -VJ" Mi / \ //// / v / / J U L ^ i y-*"\ I A—' ^/ THE ELLIPSOID. 97 \ i i ' / x. i i y 98 THE ELLIPSOID. Let the children trace the outline of objects upon clay, as leaves, lemon, or plum and branch. (Figs. 12 and 13). These figures may also be sewed on cards. (Figs. 14 and 15). They are now ready to cut the ellipse from paper (See page 84, Fig. V). Follow the four steps as given in directions (See page 75) . The drawing of the ellipse should now be practiced. In draw- ing a verticle ellipse, hold the pencil as in drawing a circle. In drawing a horizontal ellipse, hold the pencil with the point upward. Objects of elliptical form should now be drawn by the children, as the lemon, potato, leaf, cup ; a cylinder, tipped so that the upper end appears to be elliptical, and other similar objects. (Figs. 16, 17, 18). Leaves and flowers of elliptical forms, should be studied and drawn. Also simple conventionalized forms. Plaques of clay should be made, and ellipses drawn upon them. A border drawn accurately, and cut out of colored paper, is a pleasing application of these forms-. THE OBLATE SPHEROID. 99 THE OBLATE SPHEROID. The study of the oblate spheroid should follow the ellipsoid — as many objects which are familiar to the children, are based upon it. Let the children make a clay sphere — and press it lightly between the hands, to increase the horizontal circumference, and diminish the vertical circumference, while carefully preserving the curved surface. Objects based upon this solid — are the turnip, tomato, door- knob, balls of twine and certain dishes, as above. 100 THE OVOID. THE OVOID. Ask the children to compare the ovoid with the ellipsoid. They will notice that one end is smaller than the other. Direct the class to mould a day sphere and to roll it between the palms of their hands until the sphere has been gradually lengthened, and one portion of it has become somewhat pointed. Then shape and smooth the clay, till a perfect ovoid is formed. Objects based upon the ovoid are pears, acorns, strawberries, a duck, clover blossom, or the body of the stork. THE OYOID. 101 Children should now make clay plaques and upon them build up bas-relief designs. Let them begin this line of work by moulding three acorns, 102 THE OVOID. place them in a graceful cluster upon the plaque and complete the design by adding the stem and leaves. Make another clay plaque, and draw the outline of the acorns on its surface, and gradually build up with little pieces of clay, within the outline, until the acorn is formed. Complete the design. On another plaque, build up the body of the stork, in the same manner. THE OVOID. 103 Sprays of flowers, and leaves, also, are suitable subjects for bas-reliefs. The four oval petals of the syringa can be easily moulded by the children. From the half-ovoid, we obtain the model for a s poon, a mouse or a boat. The plane cut from the ovoid is an oval. Tablets representing views of the ovoid are the oval and circle. 104 THE OVOID. Following the clay work, tablet designs based on the ovals may be made. These designs may also be sewed on cards. Next, have the children fold, and cut, a paper oval. (See pages 83 — 85). Drawing from objects that are oval in form, may now follow. THE OVOID. 105 An egg, a pear, a duck, and the tablet designs previously used are suitable subjects. Groups of objects may be drawn- — for example, a lemon and a pear, or a pear, apple and plum. 106 THE OVOID. Many vase forms contain the oval, but before attempting to draw them, the children should be taught the necessity of finishing both sides of the object alike — that the value of the axis of sym- metry may be recognized. The oval may be introduced into designs for covering a surface, and also in borders. >W, THE CONE. 107 THE CONE Let the children name the solid having a base similar to the cone — the cylinder. Ask them to roll the two solids (cone and cylinder) on their desks, that they may observe the difference of action. Give the terms — base and vertex . Let the children mould a clay cone — by making first a sphere — then roll it slightly, as for a cylinder, but gradually tapering it at one end. Have the children roll the type solid on their desks, and that action will show them how to roll the clay. Objects based upon the cone should also be moulded in clay, as a top, a pine- 108 THE CONE. apple,— tapering roots such as a parsnip or carrot— and certain kinds of shells. The children may also make & paper cone. Divide a square into thirds, by foldings. In the middle square of the lower row, cut a circle having the same diameter as the square, and leave the THE CONE. 109 circle attached to the middle square. Fold back the paper in a line from the middle of the right side of the large square, to the middle of the upper side of the large square. Also fold back from the middle of the left side, to the middle of the upper side. Cut the paper in a curved line from the middle of the right side of i \ I \ the square, — and also from the left side of the square, to the upper part of the circle. Then cut off the upper left and right corners that were folded back. (See Fig.) Join the edges by sewing — first the slanting edges — then bend up the circle, and join to the hollow cone. Tablets. — In finding the tablet resembling the cone, the chil- 110 THE CONE. dren will discover a new triangle. Let them describe it and give the name — isosceles triangle. Direct the children to mould a clay cone, and then cut it verti- cally. Let them describe the plane faces. They will recognize the semi-circle. The triangular face may be cut from an oblong, whose width equals the diameter of the base of the cone, and whose length equals the height of the cone. Fold the oblong vertically, left edge to meet the right edge, and cut a slanting line from the lower right cor- ner to the upper left corner. THE CONE. Ill Let the children study the views of a cone and draw them. The plane face, or bottom view, is a circle. The top view is a circle with a point in the centre for a vertex. In the front view, be sure the vertex of the triangle is over the centre of the base. THE TRUNCATED CONE. Let the children mould a clay cone, and cut through it parallel to the base. Teach the name — truncated cone. A flower pot, tumbler or basket may be moulded from this cone. 112 THE TRUNCATED CONE. Let the children draw the top view of the truncated cone, pro- ducing the concentric circles — THE SQUARE PYRAMID. 113 THE SQUARE PYRAMID. The cone and the square pyramid should be compared by the children. Let each child handle the type-solids, and they will dis- cover that both solids have a base and a vertex, and that a portion of the surface of the cone is curved, and the surface of the square pyramid is all plane. Also, that the base of the cone is a circle, and that of the square pyramid is a square. The sides of the square pyramid are isosceles triangles. Direct the children to mould a square pyramid from a clay cone 114 THE SQUARE PYRAMID. in this manner : Tap the curved surface of the cone, until four equal triangular faces are made, and the base becomes a square. Be careful to finish the faces with sharp edges. On one side of a clay pyramid, let the children mark lines and figures to imitate a thermometer — on another insert pegs, imitating a rack. The children should next make a paper pyramid. Divide a square into thirds by folding. Then, using the sides of the centre square for bases, cut triangles, as in Fig. 1, page 115. THE SQUARE PYRAMID. 115 / \l i Fold the paper so that all the triangles can be cut at once. The faces of the pyramid should next be studied. Find tablets like the base and front faces of the pyramid. Describe the square and isosceles triangle. 116 THE SQUARE PYRAMID. Direct the children to place the tablets to represent the pyramid and borders. Let the children make a skeleton pyramid of sticks and peas, by making a square base. Then insert a stick in each corner THE SQUARE PYRAMID. 117 in an upright position and join the four uprights with a pea, at the vertex. Let the children bisect, vertically, a clay pyramid, and study its faces (triangles and oblong.) Views of the Pyramid. — Let the children draw the bottom view of the pyramid (a square), and then draw the front and side views (isosceles triangles.) Then direct them to hold the pyramid, with its vertex directly in front of the eye, and draw the top view. (See Fig., next page). 118 THE SQUARE PYRAMID. In this drawing, care must be taken to represent the vertex by a point — and also to represent the edges of the faces. The children may now truncate a clay pyramid, as they did the cone, and also model objects based upon it. Draw the top view. (See Fig. 1, page 119). Designs may be made with tablets and drawn. (Figs. 2, 3, 4.) THE SQUARE PYRAMID. 119 120 EQUILATERAL TRIANGULAR PYRAMID. I EQUILATERAL TRIANGULAR PYRAMID. Give to the children for comparison — the square pyramid and the equilateral triangular pyramid. They will find that the triangles in the one, are isosceles triangles, and equilateral triangles in the other — that one has a square base, the other has a triangular base, that the faces on the triangular pyramid are all alike. Direct the class to model a clay equilateral triangular pyramid. They can readily do so from a sphere. First, shape one portion of the sphere into an equilateral tri- angular face, and use it as the base of the pyramid. Then, shape another triangular face with its vertex over the centre of the base of the pyramid. The other two faces can be formed by shaping and pressing with the fingers, more easily than by tapping the clay on the slate as was done in moulding other models. EQUILATERAL TRIANGULAR PYRAMID. 121 A paper pyramid may be made in this manner. Cut an equilat- eral triangle. (See page 30.) Then fold each corner, to meet the centre of the opposite side ; this gives a central triangle, which forms a base. Fold the thr.ee sides of the large triangle, that the corners may meet in a point and join the edges. Let the children find tablets like the faces, and arrange in de- signs and draw them. 122 SUGGESTIONS. SUGGESTIONS. When possible to do so, use clay modeling to illustrate each subject of study. In the study of birds and animals the distinguishing character- istics of form may thus be taught in a very interesting manner. The roots, leaves, and blossoms of plants may be modeled on plaques. Language lessons may be illustrated by the children in free- hand sketches, after this method : — The teacher may tell the class a story, and while she talks the children should draw, in outline, various objects mentioned by her. These objects should be the same as those previously modeled or drawn. _^M.