Moth. 3 times 1 more once 1 (adding a fourth cube) are 4 times 1. 4 times 1 more once 1 (adding a fifth) are 5 times 1. Thus she contiuued, till 9 times 1 more once 1 are 10 times 1. The children always repeating after her. In order to convince herself whether the children thoroughly understood the numbers from 1 to 10, she threw a certain number of cubes upon the table, for instance 5, and asked, How many lie now upon the table? Childr. 5 are lying upon the table. Moth. If I add to these 5 one more (adding another to them,) how many will there be? Childr. If you add to those five cubes one more, there will be 6. Moth. Why? Childr. 5 times 1 more once 1 are 6 times 1. Moth. (Taking away the sixth.) Here are 5 again; but (taking up one) if I take away 1 from these five cubes, how many will remain? Childr. If you take 1 from five, there will remain 4. After the children have gone through these exercises (which may be varied and extended, but very gradually, and always with patience and good humour,) and the elder children practising the younger as far as they know, the Mother may make them count as far as 20 in the same manner, proposing to them similar questions; for instance: Moth. (Throwing at random a number of cubes, exceeding however ten, upon the table.) How many cubes are here? Childr. (After having counted them.) There are 13. Moth. 13 times 1 more once 1, how many times 1? Childr. 13 times 1 more once 1, are 14 times 1. Moth. But 13 times 1 less once 1, how many times 1? Childr. 13 times 1 less once 1, are twelve times 1. Moth. If you add to 16 times 1, 3 times 1, how many times 1 does it give? Childr. By adding to 16 times 1, 3 times 1, it will give 19 times 1. Moth. But if you take from 16 times 1, 4 times 1, how many times 1 will remain? Childr. By taking from 16 times 1, 4 times 1, 12 times 1 will remain, &c. As soon as the children were able, with facility, to return correct answers to such questions, with and without the aid of visible objects, the Mother was convinced that they had perfectly acquired the first elements of combining numbers, and she proceeded to the combined unity 2. Moth. (Placing two cubes together.) Twice 1 are once 2. Childr. Twice 1 are once 2. Moth. (Separating them again, and lifting one of them up) 1 is the half of 2. Childr. 1 is the half of 2. Moth. (Placing again the second next to the first.) Twice 1 are once 2. Childr. Twice 1 are once 2. Moth. (Adding to the two cubes a third, which she placed below them, thus :) 3 times 1 are once 2, and the half of 2. Childr. 3 times 1 are once 2, and the half of 2. Moth. (Adding to the third a fourth cube, so as to form two pair.) 4 times 1 are twice 2. Childr. 4 times 1 are twice 2. Moth. 5 times 1 are twice 2 and the half of 2. Childr. 5 times 1 are twice 2 and the half of 2. Moth. 6 times 1 are 3 times 2. 888 Childr. 6 times 1 are 3 times 2. Moth. 7 times 1 are 3 times 2 and the half of 2. 888 Childr. 7 times 1 are 3 times 2 and the half of 2. Moth. 8 times 1 are 4 times 2. Childr. 8 times 1 are 4 times 2. This exercise is carried on to 20 times 1 and 10 times 2, so that twenty cubes are placed by pairs upon the table. This first step in composing, or combining, will require much time and patience. When the children are quite firm in it, and understand perfectly the nature of the operation, the mother may give the exercise inversely, by decomposing the combined number 2. Thus : (Placing 2 cubes upon the table.) Once 2 are twice 1. Childr. Once 2 are twice 1. Moth. (Taking one of the cubes up.) The half of 2 is 1. Childr. The half of 2 is 1. Moth. (Replacing the cube next to the first.) Once 2 are twice 1. Childr. Once 2 are twice 1. Moth. (Adding a third.) Once 2 and the half of 2 are 3 times 1. Childr. (Always looking at the cubes.) Once 2 and the half of 2 are 3 times 1. Moth. Twice 2 are 4 times 1. Childr. Twice 2 are 4 times 1. Moth. Twice 2 and the half of 2 are 5 times 1. Childr. Twice 2 and the half of 2 are 5 times 1. Moth. 3 times 2 are 6 times 1. Childr. 3 times 2 are 6 times 1. Moth. 3 times 2 and the half of 2 are 7 times 1. |