Arithmetic Trinomial CubeAdvanced Mathematical Formula Exploration
The first photo is the maker's own. The other shots are illustrative.
Inv. no. NIE-018700
- Maker
- Nienhuis Montessori, since 1929
- Approval
- AMI
- Primary Material
- Solid wood
- Finish
- Paint in multiple colors
- EAN
- 8719924009816
Final price incl. VAT. Free delivery.
Advice, warranty and returns are handled by us.
Why it costs €230.90
Behind the price of the original are things you can check yourself.
AMI approval
The material is approved by the Association Montessori Internationale (AMI). Nienhuis has made Montessori materials since 1929.
A verifiable original
The EAN 8719924009816 is on the box. It is the maker's number, not ours.
Arithmetic Trinomial Cube in a child's hands
The trinomial cube built for arithmetic rather than pattern. It represents (a + b + c)³ in solid form, and unlike the plain trinomial cube its pieces are colour coded by hierarchical value, from one unit up to a million. That single change turns a puzzle into a calculation: a child can put a number on every cube and prism in the box and read the expansion off the pieces instead of memorising it. Sits naturally after the plain cube and before written algebra. Solid wood in a hinged box with lid, for ages 6 to 12.
Mathematical Abstraction
Prepares children for algebra by providing concrete representation of abstract mathematical concepts through sensorial exploration.
Spatial Intelligence
Develops three-dimensional thinking and spatial reasoning through manipulation of geometric forms and pattern recognition.
Concentration & Precision
Requires sustained focus and exact placement of blocks, refining fine motor control and attention to detail.
Pattern Recognition
Strengthens ability to identify and reproduce complex patterns, fundamental for advanced mathematical thinking.
How to present it
Place the Arithmetic Trinomial Cube box on a large work mat. Have paper and colored pencils available for recording observations. Ensure the child has mastered the Binomial Cube and understands basic algebraic notation.
- 1Open the box and carefully remove all 27 pieces, laying them out systematically on the mat
- 2Identify the three different edge lengths representing a, b, and c values through careful observation
- 3Begin reconstruction by placing the a³ cube in one corner, then systematically add pieces that share common faces
- 4Notice how each piece represents a term in the expansion: a³, 3a²b, 3a²c, 3ab², 6abc, etc.
- 5Complete the cube and verify all faces show the characteristic pattern of the trinomial square
- 6Record the completed cube pattern and write the algebraic expansion: (a+b+c)³
3 tips for parents
- This is an advanced material - support your child's pace without rushing toward algebraic notation
- Celebrate the process of building rather than focusing solely on completion speed
- Ask open-ended questions like 'What patterns do you notice?' rather than explaining the mathematics
If you are not sure it suits your child, we answer in person.
Norbert Kovalčín, founder of Faborino · write to him
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What's in the Box
- Wooden storage box: with hinged lid and pattern guide
- 27 colored wooden blocks: various sizes representing trinomial components
- 2D pattern guide: printed on inside of lid
Size and material
| Packaging | 15 × 15 × 12 cm |
| Primary Material | Solid wood |
| Finish | Paint in multiple colors |
| Storage | Natural wood with hinged lid |
| Recommended Age | 6-12 years |
Care
Wipe with slightly damp cloth, dry immediately
Frequently Asked Questions
What mathematical concepts does the Arithmetic Trinomial Cube teach?
The Arithmetic Trinomial Cube visually represents the algebraic formula (a+b+c)³, teaching cube expansion, algebraic expressions, spatial relationships, and advanced mathematical patterns. Children explore volume, surface area, and the relationship between 2D and 3D representations while developing abstract thinking skills.
How does this differ from the Sensorial Trinomial Cube?
While the Sensorial Trinomial Cube focuses on visual discrimination and pattern recognition for younger children, the Arithmetic version introduces mathematical notation, algebraic formulas, and numerical relationships. It includes labels and requires children to understand the mathematical significance of each piece's dimensions.
What skills should children have before using this material?
Children should have mastered the Binomial Cube, understand basic multiplication and exponents, and be comfortable with abstract thinking. Typically introduced around age 9-10, students should have experience with the sensorial version and be ready to connect concrete manipulation with algebraic concepts.
How do children progress from concrete to abstract with this material?
Children begin by physically building the cube, then match pieces to algebraic expressions, create 2D representations on paper, and eventually work with the formula abstractly. This progression allows them to internalize complex mathematical relationships through repeated hands-on experience before moving to purely symbolic work.
What extensions can be done with the Arithmetic Trinomial Cube?
Extensions include calculating the volume of individual pieces, exploring the expanded formula term by term, creating algebraic equations for each layer, connecting to Pascal's triangle, and preparing for polynomial multiplication. Children can also explore patterns in coefficients and prepare for advanced algebra.
Product safety
Manufacturer: Nienhuis Montessori, Anders Celsiusstraat 15, 7442 PB Nijverdal, Netherlands
Arithmetic Trinomial Cube