# Binomial Cubes and Trinomial Cubes

The Binomial and Trinomial cubes are a Montessori sensorial material that teaches early math skills. The Binomial Cube represents the equation (a+b) while the Trinomial Cube represents (a+b+c). The purpose is not for the child to know of the equation or how to solve it, but the cubes develop the predisposition to understand math. They create all those wonderful connections in the absorbent mind that will lead to easier understanding of math concepts later.

Montessori Materials are the cornerstone of the Montessori Method of teaching. These materials provide children with a tangible, engaging, and interactive educational experience that not only focuses on cognitive development but also facilitates sensorial as well as physical development. Montessori Materials are a chief aspect of the Montessori Prepared Environment. There is a diverse range of Montessori materials that cover all aspects of the Montessori curriculum and Montessori programs.

From Sensorial materials, practical life materials, language materials to mathematical materials, through this unique characteristic of the Montessori method, education is effectively facilitated to achieve higher levels of attainments. Amongst the diverse range of Montessori Materials is the Binomial and Trinomial Cube. These Montessori materials are accommodated in the Montessori Mathematical curriculum.

Montessori materials incorporate a diverse range of materials and apparatus that facilitate the education of abstract and complex concepts in a concrete form to developing minds. It can be bewildering for most beginners to comprehend the basic function of this unique and exciting Montessori material. Here is everything one should know about Montessori Binomial and Trinomial Cubes.

## What are the Montessori Binomial and Trinomial Cube Exactly?

The Binomial and Trinomial cubes in Montessori when first introduced to children might seem like a confusing puzzle integrating several different colored blocks. These intimidating wooden cubes are accommodated in the Montessori Sensorial Materials and facilitate the education of mathematical curriculum.

The Montessori Binomial and Trinomial cubes are fascinating materials that are introduced to children between 3 to 6 years of age or Montessori cycle one classroom.

Both Binomial and Trinomial cubes represent the Mathematical algebraic formulas and their key purpose is to child comprehend and discriminate between spatial relationships with help of this tangible and concrete material.

## Montessori Binomial Cubes

The Binomial Cube is Montessori sensorial material that consists of a number of colored blocks that have to be arranged in a specific order. Unlike the Montessori Pink Tower that only varies in size, The Montessori Binomial cube incorporates blocks of different sizes, shapes, and colors. This Montessori Sensorial Material helps in the development of skills that are required for future mathematical concepts. The Montessori Binomial cubes are presented to children 4 years of age.

## What does the Montessori Binomial Represent?

The Montessori Binomial cube represents the mathematical binomial algebraic equation- (a+b)^{3} in a tangible concrete form. The Montessori Binomial cube consists of a total of 8 blocks where each block represents the equation- a^{3}+ 3a^{2}b+ 3b^{2}a+b^{3}.

## What does the Montessori Binomial Cube Incorporate?

The binomial cube consists of:

- 1 red-colored cube
- 3 black and red prisms
- 3 black and blue prisms
- 1 blue cube

These pieces are stored in a wooden box with a colored pattern painted on it.

The pattern of the lid of the box matches the patterns of the blocks inside the box.

## What is the aim of the Montessori Binomial Cube?

- The main aim of the Montessori binomial cube is to help the child understand the spatial relationship.
- The child will be able to visually discriminate between colors, patterns, and shapes.
- The child will be familiarized with the concept of the Montessori Binomial cube.
- The Montessori Binomial cube has manufactured control of error that helps the child understand the concept independently.

## How to Present the Montessori Binomial Cube to the child?

It is mandatory to introduce the name of the activity or material before inviting the child to participate in the activity.

- Ask the child to carry the Binomial Cube Material with both hands and place it on the table.
- Place the Binomial cube box on the upper left side of the table with the pattern side facing towards you.
- Take the lid from the box and lace the side that fashions the pattern towards the child.
- Show the child the matching patterns presented on the lid and the cube.
- Take the lid off from the box and one by one take out the blocks from the box.
- Starting from the blue cube begin to create the first layer of the cube in front of the child.
- Then show the matching pattern of the bottom layer on the lid of the box.
- Like the top layer of the cube, rebuild the bottom layer in front of the child.
- Then form a new column with blocks forming the bottom layer, starting with a red block and keeping the other blocks in their orientation.
- Put the blocks in the left column moving from left to right and then from the top to bottom, starting with the red blocks. Make sure the pattern matches the lid.
- Once you are done with this activity, place each cube one by one back into the Montessori Binomial Cube box.
- Then indicate the pattern of the cube imprinted on the box and on the lid is the same.
- Repeat the activity with the top layer, forming a column making a matching pattern on the lid.
- Then transfer the new column to the finished binomial cube.
- Indicate that the cube and the lid have the same pattern.
- Fold the sides of the box and invite the child to participate in the Montessori Binomial Cube activity.

## Montessori Trinomial Cubes

The Montessori Trinomial cube is introduced after the Binomial cube. The Montessori Trinomial Cube is similar to the Binomial Cube but represents the trinomial algebraic equation- (a+b+c)^{3}. It is a unique Montessori Sensorial Material that represents complex mathematical equations to elementary children in a concrete and tangible form. This material is introduced to children in the second year of the Montessori Primary program. With the help of the Montessori Trinomial Cube, the child is able to visually discriminate between different shapes, sizes, and colors.

## What does the Montessori Trinomial Cube Represent?

The Montessori Trinomial Cube represents the mathematical trinomial equation- (a+b+c)^{3 }in a tangible form. With the help of the Montessori Trinomial cube, the child is able to explore the expanded mathematical equation- (a+b+c)^{3 }= a^{3 }+ 3a^{2}b + 3a^{2}b + 6abc + 3c^{2}a + b^{3} + 3b^{2}c + 3c^{2}b + c^{3}.

## What does the Montessori Trinomial Incorporate?

The Montessori Trinomial cube is made of 27 colored blocks, 3 cubes, and 24 colored prism blocks.

The Montessori trinomial cube is a sensorial material consisting of the following components:

- 1 red cube
- 6 black and red prisms
- 1 blue cube
- 6 black and blue prisms
- 1 yellow cube
- 6 black and yellow prisms
- 6 black prisms all of which vary in size
- A wooden hinged box to keep all the components.

## What is the aim of the Montessori Trinomial Cube?

- The main aim of the Montessori trinomial cube is to help the child understand the spatial relationship.
- The child will be able to visually discriminate between colors, patterns, and shapes.
- The child will be familiarized with the concept of the Montessori Trinomial cube.
- The Montessori Trinomial cube has manufactured control of error that helps the child understand the concept independently.
- The Montessori Trinomial has the pattern imprinted on the lid of the box.
- Helps children prepare for future mathematical concepts.

## How to properly present the Montessori Trinomial cube to the child?

It is a prerequisite to introduce the name of the activity to the child and prepare the Montessori Trinomial cube properly constructed prior to use.

- Invite the child and instruct them to carry the Trinomial box with both hands to the workstation.
- Put the box on the upper left side of the workspace table.
- Put the lid that has the pattern imprinted on in front of the child to help the child comprehend the pattern.
- Gently open each side of the box to show the pre-constructed trinomial cube to the child.
- Starting with the yellow cube, begin to form the top layer of the cube in front of the child. Then follow up with other blocks moving from left to right, top to bottom.
- Move the completed trinomial cube towards the top of the table.
- Repeat the same steps for the middle and bottom layers of the trinomial cube.
- Starting for the red cube from the bottom layer, create a column withdrawing each block in its orientation from the previous blocks.
- After the proper column has been formed, start to move the box in the same pattern inside the box.
- Repeat the pattern with the other two layers, following the pattern on the lid.
- Invite the child to participate in the Montessori Trinomial Cube activity.