The first problem not only presents a situation that would rarely or never occur, but also takes a way to find the answer that would not, in that situation, be taken since the price set by another would determine the amount.
Much thought and ingenuity should in the future be expended in eliminating problems whose solution does not improve the real function to be improved by applied arithmetic, or improves it at too great cost, and in devising problems which prepare directly for life's demands and still can fit into a curriculum that can be administered by one teacher in charge of thirty or forty pupils, under the limitations of school life.
The following illustrations will to some extent show concretely what the ability to apply the knowledge and power represented by abstract or pure arithmetic—the so-called fundamentals—in solving problems should mean and what it should not mean.
Samples of Desirable Applications of Arithmetic in Problems where the Situation is Actually Present to Sense in Whole or in Part
Keeping the scores and deciding which side beat and by how much in appropriate classroom games, spelling matches, and the like.
Computing costs, making and inspecting change, taking inventories, and the like with a real or play store.
Mapping the school garden, dividing it into allotments, planning for the purchase of seeds, and the like.
Measuring one's own achievement and progress in tests of word-knowledge, spelling, addition, subtraction, speed of writing, and the like. Measuring the rate of improvement per hour of practice or per week of school life, and the like.
Estimating costs of food cooked in the school kitchen, articles made in the school shops, and the like.