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. DSC_0349 (1)

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?”…DSC_0343

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.DSC_0356 (1)

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:

Learning Through Sensory Discovery

Our HBMH friends have been enjoying this week’s Summer Camp theme, “Learning through Sensory Discovery”. With so many options to choose from, they are invited each day to pick and choose which sensorial materials they would like to work with, then given the opportunity to create and manipulate a masterpiece of their own. It is truly amazing to see their creativity unfold as they put their minds (and hands) to work.

Our camp themes were designed to feature creative hands-on activities that build skills, bodies, and excitement. We offer an environment that fits the needs and interests of all our children, incorporating Montessori principles that foster independence and freedom with responsibility. I’m hoping to update our blog all summer long to show the children as they progress through the different themes.

Children use their senses to learn. At a very young age, they have a natural desire to discriminate objects by their similarities and differences, using their visual, auditory, tasting, olfactory (smelling) and tactile abilities. Each sensorial material in the Montessori classroom was designed to better define these abilities, not to mention all of the abstract lessons the child is learning from the same work such as introduction to language, reading, writing, math, and so forth. Children are given the opportunity to exercise their senses through working with different textures, colors, shapes, dimensions, masses, tastes, smells, temperatures, pitches and intensity of sounds. Not only do these works advocate creative expression, but they also promote abstract thinking.

Knobless Cylinders

I chose to work with the knobless cylinders. Using a guide, I created a beautiful design, displaying each group of cylinders by their relationships in height and diameter.

Pink Tower

By diminishing my vision, I’m able to utilize my tactile senses to feel the lengths and heights of each cube as I build my tower in decreasing size.

Pink Tower_Yellow Cylinders

The bright colors of the yellow cylinders and pink tower stimulate my visual senses. Each cube and cylinder is graded by decreasing size and diameter, and placed in order to create a tower taller than my body! This work is also indirectly preparing me for counting, geometry, and other mathematical lessons by giving me an in depth understanding of varying dimensions.

Color Tablets_1

I’ve chosen to work with the Color Box III, which allows me to grade the tablets by intensity of color (darkest to lightest).

Apple Sound Test_1

Our Apple friends participated in a group activity to test their auditory senses. Using different musical instruments and a blindfold, Ms. Patti tests our ability to identify and distinguish between each sound.

Resources: The Namta Journal, Volume 37, Number 1, Winter 2012