This guest post has been republished fromย Montessori East.
The Binomial Cube is one of those amazing Montessori materials.
It introduces abstract mathsย concept to children as young as four-years-old without them even knowing it.ย The early sensorial experience with theย cube inspires them again at age eightย or nineย when they use the cube for algebra.
The material provides the all important bridge between concrete and abstract thinking. ย And not so amazingly (because itโs logical) the child develops a much deeper understanding of the maths.
What is it?
The cube is composed of eightย wooden blocks which fit together in a binomial pattern, representing the cube of two numbers, (a + b), or tens plus units. ย All the blocks fit into a natural wood box.
Each box contains colour coded blocks;
One red cube aยณ, One blue cube bยณ
Three red and black blocks โaยฒbโ
Three blue and black blocks โabยฒโ
The algebraic expression represented is :
(a + b)ยณ = (a + b)(a + b)(a + b) = aยณ+3aยฒb+3abยฒ+bยณ
Purpose of the material
Cycle 1:ย ย
Introduced at around fourย years of age, the purpose of the material is not to teach maths, but instead, to provide a challenge for a child’s ability to find patterns and relationships. Therefore, the material is presented as a sensorial activity. It is presented like a 3D puzzle. People who are masters at puzzles will tell you that they take out, and organise, puzzle pieces very carefully. This is what is modelled for the child in this activity.
The child is not asked to understand the formula, but is using the cube in a mathematical way. The child will build up a predisposition to enjoy and understand mathematics later.
Cycles 2 & 3:ย ย
The Binomial is used in the primary years to understand and experience algebraic concepts. The numerical activities allow the children to cube numbers like 34 or 67 or 89, and the whole process is logical because the Binomialโs cubes and prisms are used as a literal representation of the numeric values. This work ultimately prepares them for high school mathematics.
Got it?
Donโt worry if the algebra above sends you starry eyed! Just remember that the purpose of this material is to progress the children towards an understanding of cubing and early algebra which then flows into high school maths.
