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.
- 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.
- 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.
- 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.
- 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.
- 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
- 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.
- Thus, the cabinet contains all the regular plane figures and
- enables the child to classify every plane shape he sees in the
- environment.
- 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
- 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.
- The child uses the material as demonstrated.
- 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.
- 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.
- 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.
- 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.
MATERIAL II - THE CABINET
Drawer 1 - Six Circles
Drawer 2 - Six Rectangles
Drawer 3 - Six Triangles
Drawer 4 - Six Polygons
Drawer 5 - Four Quadrilaterals and the Ellipse and Oval
PURPOSE:
PRESENTATION:
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