# The Mysterious Trinomial Cube

Today, we’re going to highlight on one of our students’ favorite works; the trinomial cube. There’s real beauty behind the intricate details of this mathematical work, details that are hard to notice at first glance.

The direct aim of this work is rather obvious; to build a puzzle in a box. The indirect aim, an introduction to algebra and preparation for the formula a+b+c³.

The child approaches the box with curiosity. It’s elegant details can spark the interest of anyone. Children are inherently captivated by mathematical materials. The colors, the difference is sizes and heights…”Why these specific colors?”, “Why do they fit together like that?”…

While there are many hidden lessons in this puzzle, the child is actively working towards building a concrete foundation for the abstract nature of the formulation, which they will later expand upon. The puzzle helps the child grasp the concept of a+b+c³ at such a young age, rather than simply memorizing the formula.

Through the child’s discovery, they come to unlock the intricate layers of the trinomial cube.

To begin, the guide carefully opens the box, and lays out all of the pieces, organizing them in different manners. With little, to no words, she places the cubes upon the lid, pairing the colors to one another. Each layer is placed in the box upon completion. The child is then invited to do the work on their own. There are many variations of the trinomial cube that call upon the child’s creativity, imagination and critical thinking.

“These small objects fascinate a child. He must first of all group them according to their color, then arrange them in various ways, making up a kind of little story, in which the three cubes are three kings, each one having a retinue identical to that of the other two, the guards being dressed in black. Many effects can be obtained through the use of this material…when playing with this material, a child forms a visual image of the arrangement of the objects and can thus remember their quantity and order. The sense impressions received from these objects furnish material for the mind. No object is so attractive for four-year-old children. Later on, by calling the kinds a, b, c, and writing the names of the separate pieces according to their dependence upon their own king, five-year-old children, and certainly six-year-olds, can store up in their minds the algebraic formula for the cube of a trinomial without looking at the material, since they have fixed in their visual memory the disposition of the various objects. This gives some idea of the possibilities that can be attained in practice.” (Montessori, The Discovery of the Child)

To see the lesson in full, click on the link below: