The children in the geography class had a contest in estimating the areas of different surfaces. Each child wrote his estimates for each of these maps, A, B, C, D, and E. (Only C and D are shown here.) In the arithmetic class they learned how to find the exact areas. Then they compared their estimates with the exact areas to find who came nearest. [Illustration] Write your estimates for A, B, C, D, and E. Then study the next 6 pages and learn how to find the exact areas. (The next 6 pages comprise training in the mensuration of parallelograms and triangles.) In some cases the affairs of individual pupils include problems which may be used to guide the individual in question to a zealous study of arithmetic as a means of achieving his purpose--of making a canoe, surveying an island, keeping the accounts of a Girls' Canning Club, or the like. It requires much time and very great skill to direct the work of thirty or more pupils each busy with a special type of his own, so as to make the work instructive for each, but in some cases the expense of time and skill is justified. GENERAL PRINCIPLES In general what should be meant when one says that it is desirable to have pupils in the problem-attitude when they are studying arithmetic is substantially as follows:-- _First._--Information that comes as an answer to questions is better attended to, understood, and remembered than information that just comes. _Second._--Similarly, movements that come as a step toward achieving an end that the pupil has in view are better connected with their appropriate situations, and such connections are longer retained, than is the case with movements that just happen. _Third._--The more the pupil is set toward getting the question answered or getting the end achieved, the greater is the satisfyingness attached to the bonds of knowledge or skill which mean progress thereto.