In this way we have made a cube measuring 8 cm. on a side. From this we see that:
23, 26 have the form of a cube.
22, 25 have the form of a square.
2, 24 have a linear form.
The Cube of a Binomial: (a + b)3 = a3 + b3 + 3a2b + 3ba.
Material: A cube with a 6 cm. edge, a cube with a 4 cm. edge; three prisms with a square base of 4 cm. on a side and 6 cm. high; three prisms with a square base of 6 cm. to a side and 4 cm. high. The 10 cm. cube can be made with these.
These two combinations are in special cube-shaped boxes into which the 10 cm. cube fits exactly.
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Weights and Measures: All that refers to weights and measures is merely an application of similar operations and reasonings.
The children have at their disposal and learn to handle many of the objects which are used for measuring both in commerce and in every-day life. In the "Children's House" days they had the long stair rods which contain the meter and its decimeter subdivisions. Here they have a tape-measure with which they measure floors, etc., and find the area. They have the meter in many forms: in the anthropometer, in the ruler. Then, too, they use the metal tape, the dressmaker's tape measure, and the meterstick used by merchants.
Hollow geometric solids, used for determining equivalence by measuring sand, sugar, etc.