Geometry 6-12
In the early years of their education, Montessori learners are exposed to an abundance of materials that indirectly refine the mathematical mind formation. Perhaps the most impactful material is the set of Constructive Triangles. They consist of five boxes with various shapes filled with colorful shapes. Out of small parts, children explore different ways to build new shapes such as rhombi, hexagons, trapezoids, and parallelograms. They are implicitly exposed to concepts in geometry such as congruence, similarities, and equivalence.
In the elementary level, children are invited to a series of presentations that aim to demonstrate these latter mentioned concepts. At Alison’s Montessori, we designed an economical wooden version of our Metal Squares and Rectangles with Stands. Our Wooden Squares and Rectangles material consists of 9 square frames containing variously shaped pieces. Below, you will find more about the ways this material is used in the Montessori Geometry curriculum.
Study of Congruence
In geometry, children come to the conclusion that some materials contain geometric figures of the same size and same shape. These characteristics helps them build creative new shapes. Two geometric figures with the same size, and same shape are said to be congruent. Their corresponding angles and sides are equal. With congruent properties, children are able to construct amazing repetitive or symmetrical patterns (stars, wheels, etc…) Using the materials below, it is possible to demonstrate how two shapes that match perfectly are congruent. We can also demonstrate that we can build a congruent shape using two smaller shapes. For instance, in the example below, we used two small squares to form a rectangle. The 2 squares combined are congruent to the rectangular shape. The same is true for the triangles in the example below.
Study of Similarities
Children may encounter geometric figures with the same shapes, but with different sizes. These figures still have the same properties in terms of sides and angles, but have a different area. These geometric figures are said to be similar, and they are not congruent. Using our material, you can demonstrate this concept. In our example below, we used 3 squares to show how similar figures have the same proportions in terms of sides and angles, but have a different area. The same is true when using other shapes such as the triangles shown below.
Study of Equivalence
Finally, children learn about equivalence, geometric figures with the same area, but different shapes and sizes are not congruent, nor similar. They are said to be equivalent. Using our material, you can create a visual statement. In the example below, we used a rectangle, half of a square, and a triangle, half of a square as well. This alone proves that the rectangle is equivalent in area to the triangle. You can reinforce this evidence by breaking down the triangle into pieces and using these pieces to reconstitute the rectangle.
Try this for a fun activity. Have 2 square pieces of chocolate. Split one in half to obtain 2 congruent rectangles, and one in half to obtain 2 congruent triangles. Present the children one rectangle piece and one triangle piece. Ask them which piece would they choose if they were to eat one. Obviously, they will wonder which one is the biggest! By overlapping the rectangle over the triangle, you can cut part of the triangle to separate a part that can be reconnected to form a rectangle. Children will see that both the rectangle and the triangle are equivalent!
Our Wooden Squares and Rectangles are extremely versatile and can be used to demonstrate fractions in shapes other than a circle. We hope this post was informational to you. Please note that the insets do not have a backing. They are therefore more affordable and easy to store. Please check out our website for more Geometry materials.
