# Plane Insets

## Contents

### Age

6-9.

### Materials

Geometry cabinet

- Additional insets, including pictures of the figures
- 2 of the 3 boxes of pictures of the figures: entire figure "surface" shaded; the fine "contour" margin of the figure
- Reading labels
- Box of command cards

### Preparation

Description of Materials:

Geometry cabinet- The presentation of this material follows the order in which the drawers are arranged. Since the presentations differ from Children's House to the elementary school, so the order of the drawers and the arrangement of the contents of each drawer differs from Children's House to the Elementary school.

### Presentation

__ Order:__Presentation tray - 0 comes first at both levels.

The names of the drawers in the Children's House and their order is:

1- circles; 2 - rectangles; 3 - triangles; 4 - polygons; and 5 - different figures.

At the elementary level the names and order are:

1 - triangles; 2 - rectangles; 3 - regular polygons; 4 - circles; and 5 - other figures.

At the Children's House level, the children worked directly for the education of the visual sense, and only indirectly to learn the geometric figures. In the elementary school what was a sensorial exploration becomes a linguistic exploration via etymology. What was an indirect approach to geometry becomes an actual study of geometry.

Therefore in elementary the drawer of triangles comes first because the triangle is the first polygon we can construct in reality, having the least number of sides. The second drawer logically follows as the quadrilaterals, specifically rectangles. Regular polygons follow beginning with the five-sided figure progressing to ten sides. circles follow, because a circle is the limit of a regular polygon having an infinite number of sides.

From Children's House to elementary the order has changed: from easiest to most difficult, to: from threes sides to an infinite number of sides. This correlates with the change from seeing, touching, and naming to a focus on etymology and reasoning.

__ Arrangement: __The presentation tray contains the three fundamental figures of geometry, that is the only regular figures. The equilateral triangle is the only regular triangle. The square is the only regular quadrilateral. The circle is the limit of all regular polygons having an infinite number of sides. the triangle is "the constructor of reality". For every plane figure can be decomposed into triangles, just as all solids can be decomposed into tetrahedrons. The square is the "measurer of surfaces" just as the cube is the measurer of solids. The circle is the measurer of angles. In Children's House. In the Children's House the arrangement is square (left), circle (top), triangle (right). In elementary the arrangement is triangle (left), square (top), circle (right).

The triangle tray examines triangles according to their sides on top; the bottom three examine triangles according to their angles, at both levels. In the Children's House the order is (top - from left to right): equilateral, isosceles, scalene (bottom - from left to right), acute-angled, right-angled, obtuse-angled. In elementary (top - from left to right): scalene, isosceles, equilateral (bottom - from left to right), right-angled, obtuse-angled, acute- angled.

In the rectangle tray, the base of the smallest figure is 5 cm. which is 1/2 the base of the largest which is a square. In Children's House the order is largest to smallest, elementary the reverse.

The regular polygon tray is ordered identically at both levels, progressing from five to ten sides. It is understood that these are the regular polygons having more than four sides, since the equilateral triangle and the square (first tray) are also regular polygons.

In the circle tray, the diameter of the smallest is 5 cm.; the diameter of the largest is 10 cm. It is ordered from largest to smallest in the Children's House and the reverse in elementary.

The arrangement in the other figure drawer is the same for both levels: trapezoid, rhombus, quatrefoil, oval, ellipse, and curvilinear triangle (Reuleaux triangle).

**Additional insets for the geometry cabinet:**

Two triangles: acute-angled scalene triangle, obtuse-angled scalene triangle

Eight quadrilaterals:

common quadrilateral (four different sides and four different angles)

common parallelogram (opposite sides are parallel and equal)

four trapezoids

equilateral trapezoid

(constructed from three equilateral triangles)

scalene trapezoid

right-angled trapezoid

obtuse-angle trapezoid (two obtuse angles opposite)

Two deltoids or kites: one with unequal diagonals

one with equal diagonals

Two quatrefoils: quadrilobed

epi-cycloid

Including surface cards for each.

**Note**: Ten dominates all of the plane insets:

Presentation tray: triangle sides - 10cm.; square sides - 10 cm.; circle diameter - 10 cm.

Triangles: Hypotenuse of the obtuse-angled triangle - 10 cm.

Rectangles: Height of each - 10 cm.

Regular polygons: All can be inscribed in a 10 cm. diameter circle

Circles: Diameter of largest - 10 cm.

Other figures: Trapezoid base, short diagonal in rhombus, distance between opposite lobes in quatrefoil, distance between two opposite cusps in oval and ellipse, base of triangle used to construct curvilinear triangle, all - 10 cm.

Extra figures: Triangles, diagonal of parallelogram, equilateral trapezoid base all 10 cm.

Distance between points on adjacent lobes of quadrilobed quatrefoil, and between opposite lobes of epi-cycloid - 10 cm.

No 10 cm. exists in the common quadrilateral, deltoids and the last three trapezoids.

### Control Of Error

### Points Of Interest

### Purpose

### Variation

### Links

### Handouts/Attachments