Tuesday, February 7, 2012

Geometry - Table of Contents

Geometry is a very hands-on experience in Montessori. Nothing theoretical and everything practical here! 

There is no explicit geometry table of contents for primary. Geometric concepts are explored through the use of the following inexhaustible list of experiences: 

Golden beads (point, line, plane, 3D that becomes a point again)
Wooden Hierarchical Material
Bead Cabinet displayed and used

Environment Language Games
Card materials
Cutting and other art experiences
Metal Insets (design work - preparation for writing)

Exercises of Practical Life: 
visual layout of materials
design work on materials and in art pieces
variety of shapes available in the environment

Geometry Cabinet
Geometry Cards
Leaf Cabinet
Leaf Cards
Constructive Triangles
     Rectangular Box A
     Rectangular Box B
     Triangular Box
     Large Hexagonal Box
     Small Hexagonal Box
     12 Blue Triangles
Binomial Cube
Trinomial Cube
Graded Geometric Figures
Decanomial Square
Knobless Cylinders
Geometric Solids
Metal Insets (design work)

Elementary - 1st-6th grade: 

I. Introduction to Geometry
        Original Geometry Story
II. Congruency, Similarity, Equivalency I
        Iron Material
        Constructive Triangles/Blue Box
III. Polygons
IV. Angles I
        Parts of an Angle
        How to Measure an Angle
        Addition and Subtraction of Angles
        Regular Protractor (including bisecting an angle)
V. Lines
        Position of Two Lines
        Intersecting Lines
VI. Angles II
        Relationships Between Angles
        Rel Bet Angles Formed by Parallel Lines Cut by a Transversal
        Size Relationships of These Angles
VII. Equivalency II
        Pythagoras Plates I and II
        Pythagoras with the Constructive Triangles
VIII. Polygons II
        Nomenclature of Polygons
        Sum of the Angles in Plane Figures
IX. Equivalency III
        Equivalency with Iron Material
        Euclid’s Plate
X. Area
        Concept of Area
        Deriving Formulae with the Yellow Material
        Deriving Formulae with the Iron Material
XI. Circle I
        The Circle Nomenclature
        Relationship Between Lines and Circumferences
        Relationships Between Two Circumferences
XII. Circle II
        Area of a Circle:
                Circle as a Special Polygon
                Measuring the Circumference
                Formula for Area of a Circle
        Relationship Between the Apothem and Side of a Plane Figure
XIII. Solid Geometry
        Concept of Volume
        Equivalence as Related to Solid Figures
        Three Important Dimensions
        Equivalence Between Prisms with Various Bases
        Derivation of the Formula
        Solids of Rotation
        Volume of the Pyramid
        Volume of the Cylinder and Cone
        Lateral and Total Surface Area of Solids
XIV. Addendum
        Geometry Nomenclature Material
        Geometry Commands
        Geometry Summary
XV. Appendix
        Geometry Charts
        Geometry Stories

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