The situations of life are often complicated by many elements of little or even of no relevance to the correct solution. The offerer of A may belong to your church; your dearest friend may urge you to accept offer B; you may dislike to talk with the dealer who makes offer C; you may have a prejudice against owing money to a relative; that prejudice may be wise or foolish; you may have a suspicion that the B piano is shopworn; that suspicion may be well-founded or groundless; the salesman for C says, "You don't want your friends to say that you bought on the installment plan. Only low-class persons do that," etc. The statement of arithmetical problems in school usually assists the pupil to the extent of ruling out all save definitely quantitative elements, and of ruling out all quantitative elements except those which should be considered. The first of the two simplifications is very beneficial, on the whole, since otherwise there might be different correct solutions to a problem according to the nature and circumstances of the persons involved. The second simplification is often desirable, since it will often produce greater improvement in the pupils, per hour of time spent, than would be produced by the problems requiring more selection. It should not, however, be a universal custom; for in that case the pupils are tempted to think that in every problem they must use all the quantities given, as one must use all the pieces in a puzzle picture. It is obvious that the elements selected must not only be right but also be in the right relations to one another. For example, in the problems below, the 6 must be thought of in relation to a dozen and as being half of a dozen, and also as being 6 times 1. 1 must be mentally tied to "each." The 6 as half of a dozen must be related to the $1.00, $1.60, etc. The 6 as 6 times 1 must be related to the $.09, $.14, etc. Buying in Quantity These are a grocer's prices for certain things by the dozen and for a single one. He sells a half dozen at half the price of a dozen. Find out how much you save by buying 6 all at one time instead of buying them one at a time. Doz. Each 1. Evaporated Milk $1.00 $.09 2. Puffed Rice 1.60 .14 3. Puffed Wheat 1.10 .10 4. Canned Soup 1.90 .17 5. Sardines 1.80 .16 6. Beans (No. 2 cans) 1.50 .13 7. Pork and Beans 1.70 .15 8. Peas (No. 2 cans) 1.40 .12 9. Tomatoes (extra cans) 3.20 .28 10. Ripe olives (qt. cans) 7.20 .65 It is obvious also that in such arithmetical work as we have been describing, the pupil, to be successful, must 'think things together.' Many bonds must coöperate to determine his final response.