9. "I have an odd picture frame that I wish to use for this landscape which came from a magazine illustration. The picture is the right width, but it is too long for the frame. How do you suggest cutting it so that it can be used in this frame and still retain its pleasing proportions?"
(Such a landscape will obviously have a division of space in it by the line of the horizon. The problem will be one of retaining pleasing space divisions in the picture, as well as retaining pleasing proportions of the whole, while fitting it to the frame.)
Possible assignment
10. "Choose a plain card most pleasing in proportion, which may be used as a place card for the home economics luncheon that the class is giving to the mothers. Plan the placing of the names on these cards. Justify your choice of card and the place you have chosen for the name."
Problem 10 may well be given as an assignment. It may be given at any desired time in the problem series as a judgment problem following the establishment of the principle. A definite attempt has been made to arrange problems 1 to 8 in order of degree of difficulty. It is evident that those which necessitate creative planning and manipulation call for greater ability than the problems of selection.
Although problems 9 and 10 are given last they may be introduced at any point. They are given last here because they require the use of two principles of proportion, i. e., relation of length to width in objects and division of a space into two parts. Problems 1 to 8 make use of only one, i. e., the principle concerned with the division of a space into two parts.
Further Suggestions for Problems, Illustrative Materials, and Assignments
There are various possibilities of introducing this lesson on proportion other than through the arranging of curtains. The curtain problem is used here because it involves a school situation. Such a problem sometimes has as great an appeal for girls as some of the most personal ones. However, any one of a number of problems, such as the placing of a belt on a dress, the depth of a flounce or yoke on a dress, the relative lengths of jacket and skirt in a suit, or the length of candles for candlesticks may be used for the introductory one. Choice will be determined upon class needs and school possibilities. The important factor will be to see that the problem is so stated that it stimulates a desire on the part of the pupil for adequate solution.
If the school windows and real curtains are not available for this problem, some window and curtain models may be borrowed from drapery departments of local stores for class use. If it is not practicable to use curtains or to borrow store models, the teacher might prepare in advance of the class meeting miniature windows for this problem. These may be made of heavy construction paper, cardboard, or beaver board, and should be of a size and scale that will permit accuracy in the conclusions drawn from their use. The use of miniatures should be confined to emergency situations, when the real things are not obtainable.
With some classes it may be necessary to use additional illustrative materials in which there are no other factors than those of space division. The teacher may prepare rectangles of neutral paper, representing any given space to be divided, in which the division is made by a contrasting line in each of the following ways: