This student (above) looks like she is playing with a variety of triangles of different shapes, sizes, and colors which she is, but that is not all that is she is doing. She is building a strong foundation in Geometry and higher mathematics.
She is working with the Constructive Triangles, of which there are five different boxes, each containing triangles of different sizes, shapes, and colors. The boxes are presented one at a time in a series with the purpose of demonstrating that all plane geometric figures can be constructed from triangles.
In working with these boxes children discover that new shapes and figures, such as rectangles, parallelograms, rhombi, trapezoids, and hexagons, can all be formed using only triangles.
Working with the constructive triangles is an exploration in shape, relative arrangement of the parts, and relationships of points and lines. The Constructive Triangles provide a foundation for Geometry.
Later, in the Elementary years, the Constructive Triangles can be used to demonstrate the Pythagorean Theorem as a bridge to introducing the Theorem of Pythagoras material (below) and working with a squared + b squared = c squared.