The Montessori Binomial Cube is a sensorial material.
The binomial cube, when first introduced to the child, is presented as a challenging, three-dimensional puzzle. The cube is made up of a number of colored blocks, which fit together in a specific way. Assembling it uses a child's fine-motor skills and requires the ability to discriminate between the blocks based on multiple characteristics.
The blocks are color coded, and different sizes, and fit together to create a binomial pattern, representing the cube of two numbers, (a + b). The Binomial Cube is introduced to children from around 3.5 years to 4 years old.
This material is a precursor for more complex mathematical concepts including fractions and algebra.
The indirect purpose of the binomial and trinomial cubes in the Primary Class becomes the direct purpose when the material is re-introduced in the elementary classrooms. Elementary-aged children use the cube to develop an understanding of the expanded equation (a+b)3 = a3 + 3a2b + 3b2a + b3.
Abstract understanding of concepts of numbers and formulas develops from a child’s interactions and experiences with real-life objects. By working with the sensorial materials, children learn to generalize and abstract from observed physical relationships, gradually progressing to greater levels of conceptual complexity. They build a solid, grounded foundation upon which they will build new knowledge. This mental process of forming concepts from abstractions is one that children will use continuously, and in every domain, for the rest of their lives.