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Montessori in a Minute: Binomial and Trinomial Cubes

At first glance, many assume the Binomial and Trinomial Cubes are math materials. These tools represent binomial and trinomial algebraic equations, but in the Primary classroom they are used primarily as a sensorial element and are viewed by the children as puzzles. To put the puzzle together, red touches red, black touches black and blue touches blue. The lid of the box has a template for children to see the relationship of the pieces to create each layer of the cube. This wonderful tool familiarizes younger students with abstract mathematical concepts in a concrete way. Teachers introduce the Binomial Cube first, and once mastered, the Trinomial Cube comes next.


The Binomial and Trinomial Cubes consist of wooden blocks, varying in size and color, presented as a three-dimensional puzzle. When fit together correctly, these color blocks form the cube pictured on the lid of the wooden container box. Through exploring the ways these blocks fit together, children begin to recognize dimensional relationships and patterns.


Students are shown how to deconstruct and reconstruct the cube and then arrange and rearrange on their own. Over time, they learn to form cubes and rectangular prisms through trial and error until they succeed in creating the desired cube. Throughout the entire process, students are gaining invaluable fine motor skills practice and spatial awareness.


The Binomial Cube is reintroduced in Elementary classrooms to demonstrate the algebraic equation (a+b)3 = a3 + 3a2b + 3b2a + b3. Once that’s mastered, the Trinomial Cube is used to explore the trinomial equation: (a+b+c)3 = a3 + 3a2b + 3a2b + 6abc + 3c2a + b3 + 3b2c + 3c2b + c3.


Montessori schools like Hudson Montessori School utilize specially designed tools like the Binomial and Trinomial Cubes to promote experiential and sensorial learning that students can repeatedly practice at each age level. Often, these tools are self-correcting, allowing the child to check their work and adjust accordingly. This Montessori In A Minute series regularly explores the unique benefits of these fundamental materials.

To learn more about Hudson Montessori School’s interdisciplinary, theme-based learning approach to education, the Montessori philosophy and methodology, or how the school fosters the love of learning for children age 2 to sixth grade, sign up for an open house tour most Tuesdays at 9 a.m.




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“Fostering a Love of Learning” for students is the central, guiding theme of Hudson Montessori School. It is the school’s mission to create lifelong learners, independent thinkers, and problem solvers. Serving children from age 2 through 6th grade, the school’s small class sizes are supervised by qualified staff experienced in the Montessori Method, who are specialized to focus on the individual interests and needs of each child entrusted in their care.

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