Think of a fraction as a part of a whole. When the fraction becomes a whole, or more than a whole, it is Improper. It needs to be changed to make it a unit, or a Mixed fraction, a unit and a part. The Multiplication Tables These are a problem which every one has to work with and because the use of them requires speed to be most valuable there must be a certain amount of repetition in learning them. The Multiplication Game The aim is to teach children their multiplication tables by visual repetition and at the same time to introduce the game spirit, thus to increase the interest and to prolong the period of effort without fatigue. The child can work with these cards himself and thus by self instruction can learn this most difficult lesson of Arithmetic, and without any possibility of error, accuracy is insured. The equipment consists of a series of eleven pieces of cardboard about 2×6 inches on which are printed in large black numbers the tables without the answers. A series of ten odd shaped cards is then made and the digits printed on them in bright red. The following are the suggested shapes for the ten digit cards. [Illustration] (Digit cards should not exceed one and one half inches in height.) The digit cards which are the correct answer to the table printed on the larger cards are then laid in the correct position and the shapes marked out. With a sharp knife cut out the shapes a trifle larger than the marked size of the digit card. The result is a card as illustrated, with the table and two holes of irregular shape into which the digit cards with the correct answer in bright red will fit. No other card but the correct one can be put into this opening, there is never any danger of the child seeing a wrong answer to the table. [Illustration] The only cards which can be fitted into this table are the two and the cipher making the correct answer 20. This card with the black 4×5= and the bright red answer 20 will make a strong impression upon the brain of the child, and by use of the strongest sense, that of sight. At the same time he can repeat the table audibly and gain the added advantage of the ear impression. Give the child only one set at a time so that he learns one table thoroughly. When he has learned it, mix the cards and place them one at a time in front of the child and see how many correct answers he can give without fitting the cards. In cases where there is hesitation have him fit the digit cards and make sure. See to it that he is accurate and certain. After one table is well mastered make a similar set of cards for the next table. If you do not wish to take time to cut out the irregular shaped holes for the digit cards, the place can be blackened and the digit cards laid carefully on. The cut outs are far better and well worth the little effort necessary to make them.