Montessori Binomial Cube Lesson Details

What is the Montessori Binomial Cube?

The Montessori binomial cube is composed of 8 wooden blocks designed to fit within the box and form a bigger cube. Among these 8 wooden blocks, there is a single red cube, three matching red and black prisms, a blue cube, and three blue and black prisms. This introduces essential algebraic concepts and provides a tangible representation of the (a + b)^3 formula, thus preparing them for more advanced mathematical understanding.

Construction of the binomial cube follows this formula:
(a+b)^3 = a^3 + 3a^b + 3ab^2 + b^3


  • Show the child how to remove and rebuild the binomial cube.
  • Use visual discrimination to choose and place a^3 in the corner.
  • Look at and point to the red side. Locate and place the red and black prisms (a^2 b) on each side of the red cube.
  • Build the rest of the layer from the inside out.
  • Build the second layer from the inside out as well.
  • Close the box and invite the child to repeat.

Extension Activities

  1. Building outside the box and showing the patterns on the sides and top horizontally and vertically
  2. Building one layer next to each other
  3. Building stereognostically.

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