Geometry (Upper Elementary 9-12)

The advanced Montessori Geometry materials seamlessly blend concrete experiences with mathematical precision. In her book "Psychogeometry" P.55, Dr. Montessori describes these materials as "a gymnasium for the mind". Now everything makes sense and concepts that were once learnt unconsciously or at a sensorial level in casa and lower elementary, are now introduced with the mathematical terms and formulas paving the way towards abstraction.

This course is for educators, parents, or anyone who is passionate about learning how to empower children age (9-12) to internalize advanced Geometry concepts through step-by-step Montessori video lessons.

Module 1: The Study of Lines and Angles

In this module we will dive into the fundamental building blocks of geometry with the study of lines and angles. We will explore diagonals and the angles created by the transversal line and much more!

Module 2: The Study of Triangles

When children are introduced to the triangle, they are told that we call the triangle constructor because it is the smallest possible geometric plane figure (there cannot be other closed figures with fewer than three sides) and it is the constructor of all other figures. In one way or another, all straight-sided figures are a multiplication of the triangle. learners will manipulate geometric shapes to discover the relationships within triangles.

Module 3: The Study of Quadrilaterals

In this module, we will explore quadrilaterals and their properties. The videos include how to calculate the area of quadrilaterals and how to prove the formulas of the sum of angles at a concrete level.

Module 4: The Study of Circles

In this module, we will explore circles and their radii, diameters, and circumferences. Through Montessori-influenced exercises, learners will construct circles and explore geometric principles such as pi. Enhance the learning experience with art projects like creating mandala designs or arabesque designs usually inspire our students with the study of circles!

Module 5: Area with the yellow materials (Note: Can be introduced at the beginning of upper elementary before the previous modules)

Students will learn to calculate the space enclosed by geometric shapes using square units. This material is used as an introduction to the study of area. Through exercises with these triangles, the child discovers how the area of a triangle is derived.

Module 6: Equivalency

In this module, we will use the constructive triangles to demonstrate that all plane geometric figures can be constructed from triangles. By putting triangles together, equivalent figures are formed.

Module 7: Pythagoras Theorem

In this module, we will investigate the relationship between the sides of a right triangle using the Montessori metal plates.

Module 8: Volume

In this module, we will explore the concept of volume and its application to three-dimensional shapes. Montessori Metal Volume Containers are used to understand the formulas in an impressionistic concrete way rather than memorization.