## Cabinet of Geometrical Plane Figures

### This is a strong wooden tray containing three square of plain
wood, and three wooden frames with insets of a square (sides 10 cm),
a circle (diameter 10 cm), and an equilateral triangle (sides
10 cm). Each inset and the bottom of the tray are painted blue.
The rest of the wood is finished with a clear, colorless varnish.

### The cabinet has five drawers. Some cabinets have six drawers.  All the insets of the cabinet are
either light gray or blue, and the bottom of each drawer is light grey or blue to match the insets.
All the rest of the wood is lightly varnished. Each figure in the
presentation tray and the cabinet has a small knob in the center
to hold it by.

Drawer 1 - Six Circles There are six circles, each inset in a square wooden frame and arranged in
order of size. They have diameters of 10 cm, 9 cm, 8 cm, 7 cm, 6
cm, 5 cm, respectively. Thus, they vary in size in a regular way
with 1 cm difference in diameter between any two in succession.

Drawer 2 - Six Rectangles There are six cut-out rectangles kept in order of size, each in a square
wooden frame. The rectangles are 10x10 cm., 9 x 10 cm., 8 x 10 cm.,
7 x 10 cm., 6 x 10 cm., and 5 x 10 cm., respectively. Thus, they also
vary in a regular way with 1 cm. difference on one side between
each in succession.

Drawer 3 - Six Triangles • Obtuse-angled Scalene Triangle
• Right-angled Scalene Triangle
• Acute-angled Scalene Triangle
• Obtuse-angled Isosceles Triangle
• Right-angled Isosceles Triangle
• Acute-angled Isosceles Triangle
There are six different triangles inset in square frames. Three scalene
triangles (no equal sides) in one row, and three isosceles triangles
(two equal sides) in the other row. Triangles are classified by their
sides and their angles. All triangles have at least two acute angles.
They are named by the third angle.

• Equilateral Triangle - All angles and sides equal (presentation tray)
• Obtuse-angled Triangle - One angle greater than 90 degrees
• Acute-angled Triangle - Three angles less than 90 degrees
• Right-angled Triangle - One angle is 90 degrees
Counting the equilateral triangle in presentation tray, there are
seven triangles in all.

Drawer 4 - Six Polygons • Pentagon
• Hexagon
• Heptagon
• Octagon
• Nonagon
• Decagon
The six polygons all inscribe within the10 cm. diameter circle.
A Pentagon (5 sides and 5 angles)
A Hexagon (6 sides and 6 angles)
A Heptagon (7 sides and 7 angles)
An Octagon (8 sides and 8 angles)
A Nonagon (9 sides and 9 angles)
A Decagon (10 sides and 10 angles)

Polygon means many angles

Drawer 5 - Four Quadrilaterals and the Ellipse and Oval • Parallelogram
• Rhombus
• Ellipse
• Trapezoid
• Trapezium  (right-angled trapezoid pictured above)
• Oval
This drawer contains the other four quadrilaterals - the
parallelogram, the rhombus, the trapezoid, and the trapezium. (The
square and the rectangle are in drawer 2.) It also contains two curved
figures - the ellipse and oval.

With this drawer all the possible regular quadrilaterals are in
the cabinet.

• Square - all sides are equal and all angles are right angles.
• Rectangle - opposite sides are equal and parallel, angles are right angles.
• Parallelogram - opposite sides are equal and parallel (the square, rectangle, and rhombus are all parallelograms).
• Rhombus - all four sides are equal (equilateral parallelogram) but the angles are not right angles.
• Trapezoid - two sides parallel. (In countries other than the U.S. this is called trapezium.)
• Trapezium - no two sides are parallel (not in the Neinhuis cabinet).
• Oval - egg shaped (from ovum meaning an egg).
• Ellipse - A symmetrical plane figure bounded by a single curved line every point of which is not equally distant from the point at the center when viewing 1/2 of the symmetrical plane.
•
Thus, the cabinet contains all the regular plane figures and
enables the child to classify every plane shape he sees in the
environment.

### PURPOSE:

1) A visual and tactile study of the full classification of the
regular plane shapes as a foundation for the later study of
geometry
2) To learn the words which will be needed and which will allow the
child to express himself
3) To make the child aware of shapes in the environment and to get him
to observe the environment with intelligence
4) Perfection of movement of the hands
5) Indirect preparation for writing as the child is feeling the
curves and straight lines similar to the ones which compose the
letters of the alphabet and his hand is being trained

### PRESENTATION:

The Presentation Tray The presentation tray is placed in front of the child on a table.
The teacher sits beside the child. The teacher removes each inset
in turn and places it on the blank square above or below the space
from which is was taken out. The teacher pauses after removing the
inset to let the child observe the fact that the space left by a
figure is the same shape as the figure itself. The fact that the
bottom of the drawer is the same color as the figures helps make
this more apparent.

The teacher takes one figure, holding it by its knob, and with the
tips of the first two fingers of her dominant hand she traces
exactly around the circumference of the figure. Then, she also
traces around the circumference of the space left by the figure.
She then replaces the figure in its socket. The teacher repeats
this with each figure in turn.

At any point in the demonstration, the child may join in using the
material as demonstrated, or the child may be invited to use the material
him or herself when the demonstration is over.

The exact feeling of the contours is difficult and most children
need to be given exact demonstrations several times. The teacher
does not interrupt the child when he or she is working but, instead,
gives the child a lesson another day before he or she begins to use the
material, stressing the handling of the material at that time. The
figure is held still and the fingers move around it.

Before giving a lesson the teacher must herself practice with the
material until her own movements are perfect.

### PRACTICE:

The child uses the material as demonstrated.

### EXTENSION:

When the children have had the material to work with for some time
the teacher may, after school, prepare the tray for the next day
by varying the figures with three other contrasting figures from
the cabinet. For example, the teacher might remove the circle,
square, and equilateral triangle and put an ellipse, a rectangle,
and a polygon in the tray. Over a period of time the children
become familiar with all the figures in the cabinet because the
teacher changes the figures in the tray from time to time. The
cabinet is kept in a stock cupboard outside the classroom during
the period that the figures are being introduced in the
presentation tray.

### LANGUAGE:

When a child knows any figures well, their names may be taught
using the three period lesson.

The Cabinet

### Place the cabinet in the room. Once the cabinet has been brought
into the classroom all the figures must be kept in their right places
in the cabinet. It is no longer possible to vary the figures in the tray. The teacher takes a drawer (e.g. of circles) from the cabinet and
places it on the table in front of the child. She removes the
insets, placing them in a mixed order on the table to one side of
the drawer. She picks up a figure, feels around it, then feels
around the sockets until she has decided where the circle fits;
she then replaces it and takes another. The child joins in as soon
as he or she understands the exercise; then the teacher can leave the child to
work alone.

When one tray has been introduced to a child, the child may help him or herself
to any tray and do the exercise in this way.

### OBSERVATION:

The teacher must be aware that the child may use the cabinet in a
free way. She must watch before deciding to interrupt him or her.
Children may spin the circle around, they may discover that a
square will fit into its socket in four positions, that the
rectangle must be rotated through 180 degrees, etc. They are
gaining valuable knowledge when they experiment in this way.

The figures may be compared and some geometrical deductions made.
For example, the polygons may be inscribed in the largest circle.
It can be clearly seen when doing this that the more sides a
figure has the nearer it is to the area of a circle.

### CONTROL OF ERROR:

Many figures will not fit into the wrong sockets. In the case of
the circles or the rectangles, if a mistake is made, there will
always be one figure at the end which will not fit into the last
socket.