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. Computing the cost of telegrams, postage, expressage, for a real message or package, from the published tariffs. Computing costs from mail order catalogues and the like. _Samples of Desirable Applications of Arithmetic where the Situation is Not Present to Sense_ The samples given here all concern the subtraction of fractions. Samples concerning any other arithmetical principle may be found in the appropriate pages of any text which contains problem-material selected with consideration of life's needs. A 1. Dora is making jelly. The recipe calls for 24 cups of sugar and she has only 21-1/2. She has no time to go to the store so she has to borrow the sugar from a neighbor. How much must she get? _Subtract_ 24 _Think "1/2 and 1/2 = 1." Write 1/2._ 21-1/2 _Think "2 and 2 = 4." Write the 2._ -------- 2-1/2 2. A box full of soap weighs 29-1/2 lb. The empty box weighs 3-1/2 lb. How much does the soap alone weigh? 3. On July 1, Mr. Lewis bought a 50-lb. bag of ice-cream salt. On July 15 there were just 11-1/2 lb. left. How much had he used in the two weeks? 4. Grace promised to pick 30 qt. blueberries for her mother. So far she has picked 18-1/2 qt. How many more quarts must she pick? B