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A Look At The Binomial Cube

I giggle when I look back at my first visit to a Montessori Classroom. A small child had tripped and dropped the Trinomial Cube, and I had no idea how to help get it back together.  Without experience with materials, it would be a little tough to figure them out and see their purpose.  Luckily for me, I had a 4 year old show me during my tour.  Afterall, she did not need my help, I needed hers.

The Binomial Cube can be used in the child’s first year at Montessori.  At my house it happened as soon as mouthing was no longer a concern, around age two.  It provides a wonderful foundation for later math skills, by working the child’s skills in visual discrimination of form, size, and color.

There are several cubes for visual discrimination of form in the sensorial area, each physically representing mathematical equations.  Although the child may not be initially aware, the Binomial Cube’s equation is ( a + b)3  

When presenting this material, open the box carefully and sort the colors in rows.  Place the lid in this orientation.



Build one layer on the lid, outside the box.  Always start with red.  My daughter checks her work by putting her hand on top to see if it’s all one level.

layer one

two layers

Next, build the cube inside the box.  Starting with red, one layer at a time.  Red only touches red, blue only touches blue.  The child will know if it was put together correctly, otherwise the box will not properly close.  In Montessori, that self-correcting part of the lesson is called Control of Error.

Give it a try!

Jessie is a Primary Montessori Teacher and Mom to twin three year olds and a five year old.  Jessie has a Montessori blog at The Education Of Ours, and can be found on Twitter.  See her other Mommy Moment posts here.


Matt Bronsil

Friday 14th of March 2014

Heard about a teacher who would put the trinomial cube (the bigger one) on her coffee table and enjoy watching adults trying to put it back together.

Casa de los NiƱos Las Terrenas, material » » Montessori Monday: Colors, Cursive & Magnets

Saturday 14th of January 2012

[...] Peanut does this work every day.  She loves that binomial cube!  For a view of the lesson, check this older post-  A Look At The Binomial Cube [...]


Thursday 18th of August 2011

I love the binomial cube. The math materials is one of the reasons I fell in love with Montessori to begin with. I struggled so much in school with math, but if I had materials like these it probably would have been a different story.

Shabnum Butt

Wednesday 17th of August 2011

Though I have worked with it but when ever I see this exercise I do get panic. The control of error find my way out ............:) the exercise is presented clearly . Thanks for sharing your experiences with us.

Sarah Guildea

Wednesday 17th of August 2011

I had a similar experience on my first time entering a Montessori classroom! I hadn't a clue, I first thought it was a colour puzzle cube of some sort until the directress explained it to me. I was amazed at the thought of algebra being introduced at such a young age. The children in my class are enjoying working with the trinomial cube at the moment.