We mean by concrete objects actual things, events, and relations presented to sense, in contrast to words and numbers and symbols which mean or stand for these objects or for more abstract qualities and relations. Blocks, tooth-picks, coins, foot rules, squared paper, quart measures, bank books, and checks are such concrete things. A foot rule put successively along the three thirds of a yard rule, a bell rung five times, and a pound weight balancing sixteen ounce weights are such concrete events. A pint beside a quart, an inch beside a foot, an apple shown cut in halves display such concrete relations to a pupil who is attentive to the issue. Concrete presentations are obviously useful in arithmetic to teach meanings under the general law that a word or number or sign or symbol acquires meaning by being connected with actual things, events, qualities, and relations. We have also noted their usefulness as means to verifying the results of thinking and computing, as when a pupil, having solved, "How many badges each 5 inches long can be made from 3-1/3 yd. of ribbon?" by using 10 × 12/5, draws a line 3-1/3 yd. long and divides it into 5-inch lengths. Concrete experiences are useful whenever the meaning of a number, like 9 or 7/8 or .004, or of an operation, like multiplying or dividing or cubing, or of some term, like rectangle or hypothenuse or discount, or some procedure, like voting or insuring property against fire or borrowing money from a bank, is absent or incomplete or faulty. Concrete work thus is by no means confined to the primary grades but may be appropriate at all stages when new facts, relations, and procedures are to be taught.