Children in the primary classrooms (ages 3-6) don’t know they are learning the foundations of multiplication, squaring, and cubing when they count the math chains. They do know that the math chains are aesthetically inviting, displayed in graduated rows with order and beautiful colors. They do know that working with the chains and counting them is fun work!
What the children don’t consciously know, however, is that these chains, like many materials in the Children’s House, are scientifically designed specifically for their age group, to lay a strong foundation and prepare their minds for more complex mathematical concepts later on.
The beauty and success of these Montessori materials lie in the way the materials are designed to be used. When counting the math chains, for example, the children don’t just start with numeral one and continue counting until they are done. There is a simultaneous process of counting AND labeling in a very specific way that reveals patterns and lays the foundation for multiplication, squaring, and cubing.
For example, the child above is counting the long six chain in a primary classroom (ages 3-6). The long six chain represents six cubed in linear form (6x6x6=216). This chain literally has 216 unit beads on it in groups of six.
When counting the chain, every bead is counted and every sixth bead is labeled (6, 12, 18…). This creates a visual pattern and subconsciously lays the foundation for the multiplication table of six. Repeated use of the chains helps to solidify the pattern in the brain.
Similarly, while counting, every thirty-sixth bead (6×6) is labeled with a wider label (36, 72, 108…). Additionally, the square of six in bead form (literally 36 beads laid out in a 6×6 square) is placed above the chain at these points. This square of six visually represents the 36 beads on the chain between this wide label and square and the previous wide label and square. This numeric pattern and concrete visual lays the foundation for squaring.
At the very end of the long six chain the 216th bead is labeled with the widest label of all. Then all six squares of six along the top of the chain are stacked on top of each other to create six cubed (literally, a cube of 216 beads made from stacking six squares of six, each with 36 beads). The linear chain is transposed into a cube and the foundation for cubing is laid.