The top tray shown in the picture above is called the Presentation Tray. All of the figures in the cabinet are dominated entirely, or at least partly, by ten. 10cm side(s) or diameters.
Order of the Presentation Tray for Elementary School -
Presentation Tray: Triangle, square, circle
Rationale: The triangle is the first possible polygon, the square is its successor, and the circle is the limit of an infinite series of regular polygons. A polygon is closed figure made by joining line segments, where each line segment intersects exactly two others. Here is a nice website that explains and shows you what is and what is not a polygon. Figures and Polygons
Organization of the Geometry Cabinet for Elementary School
Drawer 1 - Triangles
Drawer 2 - Quadrilaterals
Drawer 3 - Regular Polygons
Drawer 4 - Curved Figures
Drawer 5 - Rectangles
Drawer 6 - Circles
First Year Presentations
The first-year student learns to name all of the Geometric Solids and the shapes of the Geometry Cabinet. The student also works with Constructive Triangles to see how geometric forms are made. Basic geometric nomenclature is introduced.
Presentations - Polygons, Quadrilaterals, Curved Figures, Triangles, Seven Triangles of Reality
Constructive Triangles - Rectangle Box: Series 1, Blue Rectangle Box: Series 1, Blue Right Scalene Triangles: Series 1, Drawings of Stars, Drawings of Diaphragms
Second Year Presentations
The second-year student works through the geometric nomenclature learning the name, etymology and definition of the following basic concepts: lines, angles, figures, triangles and quadrilaterals. More important than the nomenclature is the opportunity to construct and explore these principles using the Geometry Stick Box.
Presentations - There are many presentations, to many to list, so if you download the table of content of the manual found here, Montessori Research and Development Website, you will be able to see them in detail. Pages 60-218 are the presentations for this level.
Third Year Presentations
The third-year student continues his/her work with nomenclature with the study of polygons and circles. Once again the emphasis is on the child's exploration. The child who discovers the significance of pi when working with circles will remember it much longer than the one who has memorized it from a book.
Nomenclature Organization and When to Present the Lessons
1. She has a specific day and time that she introduces new Geometry Lessons. Since you are working with three different levels, there are three different times.
2. She has a different colored folder/envelop for each Nomenclature section. For Example: Basic Concepts Nomenclature would be in a green Folder. All Geometry Nomenclature Folders are in a File Box accessible to the students and the only thing on the shelf is what they are currently working on.