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H          A           P          T           E          R          XIX


THE first material which is used for numbers is the series of ten
rods used for lengths, a1 ready part of the education of the senses;
the rods are graduated in length from one to ten. The shortest
rod is 10 cms long, the second 20 cms, and so on, up to the tenth
which is 10 cms, or one metre. When they are to be used in teach-
ing number, the rods are no longer all of the same colour, as when
they are used as sense-material intended to make the eye estimate
graduated lengths. Here, the various segments of 10 cms are
coloured alternately in red and blue, and can therefore be
distinguished and counted on every rod. If the first of them
represents the quantity 1, the others represent successively the
quantities 2, 3, 4, 5, 6, 7, 8, 9, 10. The advantage of this material
is that it is possible to present united together, though distinct
and countable, the units composing each of the numbers which
they represent. The stick of 5, for instance, is a whole piece which
corresponds to the number 5, but by means of the colours the five
units are distinguished. By this means one overcomes a very great
difficulty, that involved in the numbering which is done in adding
separately one unit after the other. If they are used for counting
any small objects, such as small equal cubes, why, in setting up