The smooth, shiny, vibrant geometric solids beckon from the shelves of any Children’s House or Montessori Elementary classroom. The shade of blue unites them and calls attention to their differences.
Children are introduced to them early in their Children’s House experience. They feel the weight of the solid and glide their hands across their sleek surfaces. They begin to develop a sense of dimension and identify similar forms in the outside world. The guide introduces the child to the name of the figure and an association emerges: cube, sphere, cone, cylinder, pyramid, rectangular prism. Later, the children learn to identify the solid without looking — by feel alone. Eventually, the children will match the base of the solid to a card with an outline of its two-dimensional counterpart.
In elementary, their knowledge becomes more refined. The guide presents the children with even more specific vocabulary: face, edge, vertex, base, altitude, slant height, lateral face, lateral area, total area, etc. Many children delight in rolling the solids out on paper, tracing their edges, cutting them out and folding them to create their own three-dimensional models.
Building Understanding and Facility
In a child’s earliest years of Montessori, she will be able to identify the cylinder by sight and touch and find objects in her home and in her daily travels that meet the conditions of being a cylinder.
Throughout elementary, she will develop familiarity and comfort with the parts of the circle, area of a rectangle, area of a circle, and foundations of algebra. Before the end of the of her time in elementary, she will be able to both deduce and apply the formula for the total surface area of a cylinder by rolling out the solid on paper and showing relationships between the parts:
The child doesn’t memorize a formula to achieve this. The layers of understanding have been building toward this pinnacle moment all along!