THE TEACHING OF NUMERATION 335 The first exercise consists in trying to group together the piece shorter than ten, in such a manner as to make up ten. The simplest way of doing this is to take in succession the shortest rods, from one upwards, and place them at the top of the rods successively shorter from nine downwards. This work can be guided with orders; take one and add it to nine, take two and add it to eight, take three and add it to seven, take four and add it to six. Thus there are made up four sticks all equal to ten. There remains only the five, but when this is used twice lengthwise, it reaches from one extremity to the other-of the ten; let us measure and we will see that 10 results from twice five. Such an exercise is repeated many times, and little by little, a more technical language is taught to the child. Nine plus one equals ten; eight plus two equals ten; seven plus three equals ten; six plus four equals ten; and finally five multiplied by two equals ten. The next step is to learn to write the signs which stand for * plus/ ' equal to,' and * multiplied by'. Here is the result, written in the nice little exercise-books of our little ones: 9+1=10 8+2=10 7+3-10 8+2=10 5X2=10 When all this is thoroughly learnt and fixed on paper to the great satisfaction of the children, the attention is drawn to the work necessary to be done in putting back into their places all the pieces which have been grouped together to form tens. From the last piece of ten there is taken away the four and there remains alone the six; from another ten three is taken away, leaving the seven; from the other the two is removed, leaving the eight. We say more briefly: ten minus four equals six, ten minus three equals seven, ten minus two equals eight, ten minus one equals nine.