Geometry Cabinet & Cards
Materials:
A demonstration tray containing a square, circle, and triangle. These are the basic geometric figures. The square is the measurer of areas. The triangle is the constructor of all other figures. The circle is the calculator of angles.
A wooden cabinet with six drawers.
Each drawer contains six square divisions. In most of the divisions, there is a wooden inset with a knob. The inset and the bottom of the drawer are painted the same color. The square frames around the insets are a contrasting color and are also removable. In the demonstration tray and in some drawers where there are not six insets, the remaining square divisions are whole.
There is no rule for the order of the drawers nor is there a rule for how the contents of the drawer are arranged within each drawer. You may follow the order given here or devise your own, only classification remains the same as given:
Demonstration tray: 1 circle, 1 square, and 1 equilateral triangle
First drawer: 6 circles that vary in diameter
Second drawer: 6 rectangles with the same height but varying in width up to the square.
Third drawer: 6 different triangles: right-angled isosceles, acute-angled isosceles, obtuse-angled isosceles, right-angled scalene, acute-angled scalene, obtuse-angled scalene
Fourth drawer: 6 regular polygons: pentagon, hexagon, heptagon, octagon, nonagon, decagon
Fifth drawer: 4 quadrilaterals: rhombus, parallelogram, isosceles trapezoid, right-angled trapezoid
Sixth drawer: 4 curved figures: oval, ellipse, quatrefoil, curvilinear triangle
Three sets of cards for each geometric shape in the cabinet.
In the first set, the figure is filled in. In the second set, each figure has a 1cm wide outline. In the third set, each figure has a 1mm wide outline.
A wooden cabinet with three compartments to hold the cards
A rug
A blindfold
Purposes:
Visual discrimination of form (shape)
Muscular memory by repetition
Absorption of the plane geometric figures
Preparation for mathematics: geometry
Indirect preparation for writing: Three-fingered grip; following a contour, firmness of touch
Age:
Cabinet: 3 – 4
Cards: 4 – 4 ½
Preparation: None
Presentation:
Presentation 1: Demonstration Tray
Invite the child for a lesson on the Geometry Cabinet.
Show the child how to carry the tray, return it to the shelf and have the child carry it to the table.
Start with the shape on the left. Remove by the knob with the left fingers.
Starting at the point closest to your body, trace around the edge with pads of the index and middle finger a few times.
Set the shape in the empty space above or below and repeat for the other two.
Select a frame and starting at the point furthest from yourself, trace around the aperture with pads of the first two fingers several times.
Pick up the shape by the knob with the left fingers, hold vertically, and trace the edge with the left first two finger pads several times.
Replace the shape.
Repeat for the rest.
Invite the child and encourage repetition
Fade and observe.
Extension: Subsequent Presentation with the Demonstration Tray
When the child is confident in tracing the first three figures, show them how to lift the lattice and change the shapes with contrasting shapes from the other drawers.
Note: If the child can easily trace three shapes in the demonstration tray, move on to lesson 2
Presentation 2: Tracing a Single Drawer
Invite the child and show them how to remove the drawer and how to slide it back in.
Have the child bring it to the table.
With the child’s help, remove all the shapes and place them at random on the right side of the table
Select a shape, trace it several times, and set it down.
Look for the match in the drawer and trace the aperture a time or two.
Place the shape in the frame.
Invite the child.
Fade and observe. Return to encourage the child to try other drawers.
Control of Error:
Mechanical: the shape will only fit accurately into one frame.
Language:
Is to be given in a three-period lesson after the child can remove, trace and replace all the shapes in an individual drawer.
Quadrilaterals: rectangle, square, rhombus, parallelogram, isosceles trapezoid, right-angled trapezoid
Curvilinear figures: circle, oval, ellipse, quatrefoil, curvilinear triangle
Triangles: equilateral, right-angled isosceles, acute-angled isosceles, obtuse-angled isosceles, right-angled scalene, acute-angled scalene, obtuse-angled scalene
Polygons: pentagon, hexagon, heptagon, octagon, nonagon, decagon
Following Exercises:
Tracing and Matching-the child can work with 2 drawers together. Gradually more drawers are added until the child can work with the entire cabinet
Tracing and Matching with a Blindfold
Presentation of the Geometry Cabinet with Cards
Presentation 1: Find the Shape
Invite the child to unroll a rug.
Start with the shapes from the demonstration tray or three contrasting shapes.
Give the child the solid cards (the first set) of the shapes you selected
Place them on the rug.
Invite the child to carry the demonstration tray to a table.
Back at the rug, point at a shape and ask the child to bring the shape that matches.
When the child returns with the shape, place it on the card to check the match.
Repeat for the rest.
Invite the child to try another drawer
On subsequent days, the child can work directly from the cabinet. The child will examine the solid card and go to the cabinet to find the corresponding shape. Over time you give more cards until they are working with all the solid cards.
Presentation 2: Find the Card
The opposite of Presentation 1
Sit at the table with the tray and the child.
Cards to match the shapes are laid on the rug.
Indicate a shape from the tray for the child to find on the rug.
The child goes to the rug, finds the shape, and brings it back to the table.
Following Exercises
Matching the Insets to the Second Series of Cards
Matching the Insets to the Third Series of Cards
Matching the Insets to all Series of Cards: bring all three sets of cards to the rug. Bring one drawer to the rug and pick a shape from the drawer.
First, find the shape from the pile of solid cards. Turn cards over as you are looking one at a time through the stack. Once found, match the inset to the card by superimposing then, place the card at the upper left corner of the rug.
Do the same for the thick-lined card. Once found, set it to the right of the solid card.
Do the same for the thin-lined card and place it to the right of the thick-lined card. Place the inset at the right of the line.
Repeat for the rest of the shapes in the drawer.
Which One is Missing? Take out all the cards and mix up the three sets. (You may need a couple of rugs) Have the child close their eyes and you will take one card and hide it. The child must go through and organize the cards to find the one that is missing. Let the child discover their strategy.
Control of Error: The child’s own judgment/visual discrimination of the shapes
Memory Games:
Distance Games: Pairing
with insets and frames
with insets and cards.
Material to the Environment: Isolating a shape that the child can find a match for in the environment.
Pedagogical Notes:
Keep the child working at the table in the early stages. Tracing comes more naturally at the table and allows for proper body posture for writing.
This is an important material and should be introduced very early. The Sensitive periods make the tracing enticing and the more a child traces, the better they come to know and understand shape.
The Demonstration Tray offers the most contrasting shapes: the circle, square, and triangle. The triangle is the constructor of other shapes. The square measures area. The circle is the calculator of angles.
The child passes gradually from working in a very concrete manner to an abstract manner. The material gradually becomes more abstract- passing from solid figures to thin lines.
Around the age of 4, the child loses interest in tracing because Sensitive Periods are fading. The cards can keep interest alive in this material.