Binomial Cube
The binomial cube is a hinged wooden box of eight painted blocks, a red cube, a blue cube and six black-sided prisms, used as a building puzzle from about 3.5 and for algebra years later. It costs $29.95 to $113.00 at the US sellers we checked on October 2, 2026. Buy it; the blocks need exact cuts.
The first lesson with it is Binomial Cube. Not sure your child is ready for it? Two minutes of questions place your child on the sequence.
| Area | Sensorial |
|---|---|
| Used in | |
| From age | 3.5 to 6 years |
| Make it | Better bought than made |
| Buy it | About $30 to $113 (noted ) |
What the binomial cube is for
The eight blocks are the parts of (a + b)³ cut apart: one cube of a, one cube of b, three prisms a by a by b and three prisms a by b by b. The paint makes the parts easy to tell apart: red for a squared, blue for b squared, black where a meets b.
In Montessori's 1917 book the cube is an elementary material for studying the powers of numbers, made from a 6 cm cube, a 4 cm cube and six prisms. Giving it to 3 to 6 year olds as a puzzle is the later tradition.
| Part | What it looks like |
|---|---|
| Red cube | One; a × a × a |
| Red and black prisms | Three; two red square ends and four black sides |
| Blue and black prisms | Three; two blue square ends and four black sides |
| Blue cube | One, the smallest block; b × b × b |
| Box | Wooden, with sides on hinges and the top layer's pattern on the lid. Alison's is 3.5 by 3.5 by 3 inches |
The lessons that use the binomial cube
Binomial Cube
3.5 to 6 yearsTaking apart and rebuilding a cube of eight colored blocks, matching faces by color and size, a puzzle that years later shows (a + b)³.
Buying one: 5 listings checked October 2, 2026
| Seller and set | Made of | Price |
|---|---|---|
| Montessori OutletBinomial Cube (510500510)Eight painted cubes in a hinged box with the pattern printed on the lid. Market price shown $110.80. In stock. | Wood | $29.95 |
| Alison's MontessoriBinomial Cube (M06)Sale price; regular $63.00. Box 3.5 by 3.5 by 3 inches, internal hinges, pattern on the lid. Made in Thailand. | Wood, painted red, blue and black | $56.70 |
| Alison's MontessoriBinomial Cube, Premium Quality (PM01)Made in Sri Lanka. | Wood, painted red, blue and black | $98.00 |
| NienhuisBinomial CubeUS store price. The page doesn't state the piece count. | Birch plywood, beech plywood, metal | $113.00 |
| The Montessori RoomBinomial CubeCanadian store. Sold as a budget version; eight prisms in a hinged box. | Beech and plywood | $44.99 CAD |
- Montessori Outlet's $29.95 set and Nienhuis's $113.00 set do the same job for a 4-year-old. Check that the lid closes with every block in place; that's the one thing a cheap set can get wrong.
- If an older child might use it for algebra later, any of these sets will do. The algebra needs the same eight blocks, not a better finish.
- Nienhuis's page shows the blocks but doesn't state how many; every other listing says eight.
- Montessori Services doesn't sell it, and Amazon's search page wouldn't load for us.
Keeping a full set on the shelf
- Count eight blocks back into the box after every turn. The blue cube is the smallest piece and the first to go missing.
- Wipe with a barely damp cloth. Chipped paint makes faces harder to match by color, so touch it up.
Questions parents ask about the binomial cube
What does the binomial cube teach?
At 3.5 to 4, it trains the eye to match blocks by size and color and to rebuild a whole from its parts. Years later the same blocks show (a + b)³ = a³ + 3a²b + 3ab² + b³.
Can I make a binomial cube?
We wouldn't. The eight blocks come in two sizes that must fit a box with no gaps, and the hinged box is fiddly. Sets start at $29.95 in our table.
Is the binomial cube in Montessori's own books?
Yes, in The Montessori Elementary Material (1917), as a 10 cm cube built from a 6 cm cube, a 4 cm cube and six prisms, for older children. The painted puzzle for the primary years came later.
Before the binomial cube, make sure the work before it is solid. The red rods (long rods) lesson lists the signs that a child is ready to move on.