The Binomial and Trinomial Cube

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The binomial cube is a cube that has the following pieces: one red cube, three black and red prisms, three black and blue prisms, and one blue cube. A box with eight prisms represent the elements of (a+b)^3 or: a^3 + 3a^2b + 3ab^2 + b^3

The material is not designed as for math education until the elementary years of Montessori education. In the primary levels (ages 3–6), it is used as sensorial material.

The trinomial cube is similar to the binomial cube, but has the following pieces instead:

  • 1 red cube and 6 black and red prisms (varying in size)
  • 1 blue cube and 6 black and blue prisms (varying in size)
  • 1 yellow cube and 6 black and yellow prisms (varying in size)
  • 6 black prisms (same size)

This is similar to the binomial cube, but is a physical representation of this formula:

(a+b+c)^3 = a^3 + 3a^2b + 3a^2c + b^3 + 3ab^2 + 3b^2c + c^3 + 3ac^2 + 3bc^2 + 6abc



The Broad Stair



The brown stair helps to develop the child’s visual discrimination of differences in two dimensions. It indirectly prepares the child for later work in geometry and for the concept of numbers, in demonstrating the unit difference in height and width between the ten successively thicker prisms. The child will build the brown stair from the thickest to the thinnest.