Binomial Cube

A detailed guide to understanding the Binomial Cube material and how it is used within the Early Years curriculum.

How does it work?

The Binomial Cube—an iconic Montessori material—is a concrete representation of the algebraic formula (a + b)^3. The factors of the equation are represented by the cubes and prisms. The lid shows the pattern in plane dimension.

With this material, the child explores how the pieces relate to one another in terms of their dimensions, shapes, and colors. It is a puzzle that the child can tackle in stages of increasing challenge; for example, by matching pieces to the box lid, building one layer at a time, or building it outside the box.

Practice with the Binomial Cube provides the child with a concrete experience of a foundational mathematical term, one that they will relate back to repeatedly in mathematical explorations later in the Montessori Elementary program. This hands-on experience helps to ground the child’s understanding of early algebraic concepts because they know how the terms relate to one another.

Prerequisite Skills - As with all Sensorial materials, the Binomial Cube's benefits are best enjoyed by the child who has developed their ability to work logically through multi-step tasks. The exercises of Practical Life are the ideal training ground for this. Extensive work with Practical Life activities or other real, everyday tasks is the best way to prepare a child for this and other Sensorial activities.

Introducing the Binomial Cube

sample lesson.

Start by watching this sample lesson from our Guidepost Homeschool platform that will familiarize you to the Binomial Cube and its use.

If you are already subscribed to Guidepost Homeschool, scroll down to see all the corresponding lessons where this material is used in our curriculum. To unlock more than 2,000+ lessons subscribe to Guidepost Homeschool today.

how to set up.

Setup - Carefully remove all packaging material. Note that some Montessori parts are very small – be mindful not to inadvertently discard anything. The Binomial Cube comes with pieces of tissue paper separating the layers of the cube; if you aren’t yet confident in building the cube yourself, be mindful to keep the pieces in order while you remove the paper (the lid can be a useful guide).

With the box positioned so that the two hinged sides fold down to the front and right of the box, orient the prism pieces inside of it with the red square in the top left corner of each layer.

Usage Tips - The Binomial Cube is best used at a child-height table (rather than on the floor). When not in use, store the Binomial Cube on the shelf to the right of other beginning Sensorial materials.

  • The photo shown depicts one way you might work with the Binomial Cube, using the lid as a guide and the box as a frame for the cube.
  • A more advanced version of this would be to close the box and put the lid out of sight, then build the cube freestanding on the table.

For Guidepost Homeschool subscribers

If you are already subscribed to Guidepost Homeschool, start in the order below to navigate to the corresponding lesson plans using the Binomial Cube in our Altitude learning platform.

Wondering about supplies used in particular lessons? Detailed materials lists can be found at the beginning of each lesson in Guidepost’s Altitude system, as well as on the materials cards at the beginning of each unit.

  • Corresponding Altitude lessons

    Lessons where the Binomial Cube is used

    Sensorial: (3-6) No Isolated Sense

    • Introducing the Binomial Cube
    • Follow Up: Building Outside the Box
    • Follow Up: Building by Horizontal Layers
    • Follow Up: Building by Vertical Layers
    • Follow Up: Building by Colors

    Mathematics: (11-12) Cubing

    • The Algebraic Cube - Binomial Starting from the Square
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