The twenty centimeter ruler divided into millimeters they use constantly in design; and they love to calculate the area of the geometric figures they have designed or of the metal insets. Often they calculate the surface of the white background of an inset and that of the different pieces which exactly fit this opening, so as to verify the former. As they already have some preparation in decimals it is no task for them to recognize and to remember that the measures increase by tens and take on new names each time. The exercises in grammar have greatly facilitated the increase in their vocabulary.
They calculate the reciprocal relations between length, surface, and volume by going back to the three sets which first represented "long," "thick," and "large."
The objects which differ in length vary by 10's; those differing in areas vary by 100's; and those which differ in volume vary by 1000's.
The comparison between the bead material and the cubes of the pink tower (one of the first things they built) encourages a more profound study of the sensory objects which were once the subject of assiduous application.
By the aid of the double decimeter the children make the calculations for finding the volume of all the different objects graded by tens, such as the rods, the prisms of the broad stair, the cubes of the pink tower.
By taking the extremes in each case they learn the relations between objects which differ in one dimension, in two dimensions, and in three dimensions. Besides, they already know that the square of 10 is 100, and the cube of 10 is 1000.
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Designs formed by arranging sections of the insets within the frames.