Cabinet of Geometrical Plane Figures
MATERIAL I  THE PRESENTATION TRAY:
 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.

MATERIAL II  THE CABINET
 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 cutout 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
 Obtuseangled Scalene Triangle
 Rightangled Scalene Triangle
 Acuteangled Scalene Triangle
 Obtuseangled Isosceles Triangle
 Rightangled Isosceles Triangle
 Acuteangled 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)
 Obtuseangled Triangle  One angle greater than 90 degrees
 Acuteangled Triangle  Three angles less than 90 degrees
 Rightangled 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 (rightangled 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.
PRESENTATION:
 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.



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