The Constructive Triangles

First Two Boxes: Rectangular

                                  Box 1

Material Box 1

  • 2 yellow isosceles right angled triangles, having a black line on one of the two sides containing the right angle.
  • 2 green isosceles right angled triangles, with the black line along the hypotenuse.
  • 2 yellow scalene right angled triangles, with the black line along the shortest side.
  • 2 green scalene right angled triangles, with the black line along the longest side containing the right angle.
  • 2 grey scalene right angled triangles, with the black line along the longest side containing the right angle.
  • 2 grey scalene right angled triangles with the black line along the hypotenuse.
  • 1 smaller red scalene right angled triangle with the black line along the side opposite the obtuse angle.

All the colours are pairs except for the red triangle.

                                       Box 2

Material Box 2 The blue triangles–four pairs of triangles in blue. These triangles do not have any black lines.

  • 1 pair of equilateral triangles.
  • 1 pair of right angled scalene triangles.
  • 1 pair of right angled isosceles triangles.
  • 1 pair of acute angled isosceles triangles.

Presentation

  1. On a mat on the floor. 
  2. Use box 1. 
  3. Take any three pairs of triangles. Lay them on the mat, taking one of the triangles, feel the black line carefully.
  4. Take its pair, and feel that line.
  5. Place the two together on the mat, matching the black lines, and making sure that the points match. This is very important.
  6. If the child has got the idea he may work on his own with the three pairs.
  7. When you feel he is ready for the rest of the box, just lay them out and ask him if he would like to try them.
  8. Later, when you notice the child starting to experiment with the material you will know that he is ready for the blue triangles. Show him that the points must match. He must find out the combinations for himself. After a while he will work with the two boxes together.

 

Third Box: Triangular

Box 3

Material

  • 1 large gray equilateral triangle.
  • 2 green right angled triangles, with black line along the longest side of the right angle.
  • 3 yellow obtuse angled triangles, with black line along the two sides containing the obtuse angle.
  • 4 red quadrilateral triangles. One has a black line on all sides, the other 3 have a black line on only one side.

Presentation

  1. Make sure that there is plenty of floor space, show the child the gray triangle. All the other triangles may be scattered on the mat.
  2. Take the green triangles, feel the lines and put the triangles together.
  3. Take the yellow triangles. Feel the lines and put them together.
  4. The child may complete the others if he wishes. They may be turned in any direction.
  5. Leave the child to work on his own.
  6. He must be shown how to put away all the triangles. They have to be put away very carefully to fit into their boxes.

Exercise

The child has to match together the lines. In this way he forms new designs and shapes.

Language (Later)

Height, base, center, vertex and apex. Teach the child the names corresponding to the lines, that is: Height, bisector, base, matrices. Later on more language may be given such as vertex, etc. N.B. Look these terms up in a dictionary if you are not sure of the meanings. Remember the language is not given until the end unless the child asks.  He should be doing it visually at first.

 

Fourth Box: Small Hexagonal

Box 4

Material

  • 6 gray equilateral triangles, the black line on one side.
  • 2 red equilateral triangles, the black line on one side.
  • 3 green equilateral triangles: (a) 2 with black line on one side; and (b) one with black lines on two sides.
  • 1 large yellow equilateral triangle.
  • 6 red obtuse angled triangles with black lines opposite the obtuse angle.

(These last two are not presented until later.)

Presentation

The child already has the experience, so we need only show him a couple of pairs.

Direct aim

  1. Is the development of appreciation of line and form
  2. The understanding of the make-up of geometrical shapes with triangles.

Further games

With the constructive triangles for further development; a number of the blue triangles–each of which is half the equilaterial triangle–are used to form other figures which resemble stars and other shapes. For instance, taking a triangle and placing 3 others in such a way that the vertices of the right angle coincide, one has a star with four points. If one joins instead the triangles of the vertices of the 60° angle, one would have to put 6 triangles another star would be formed with 6 points. On the other hand, making the vertices of 30° angles coincide, one would need 12 triangles to complete a circular saw shape.

Star Game

Building a star with many points.

  1. With the child, identify the 3 angles of any one of the triangles according to the following: a) the biggest angle, b) the smallest angle, c) the medium sized angle (Right angle, 30°, 60°).
  2. Invite the child to superimpose all the triangles colored side up to see that all of them are equal.
  3. With the child, display the triangles in such a way that the smallest angles are close to one another.
  4. Point out that we have constructed a big star. “Have we used all the triangles?”“Yes” “How many triangles are there?” “Twelve”. With the 12 triangles at our disposal we can build one star with 12 points.

For other games leave the children to experiment together or one child to experiment alone.

Age of great interest

From 3 years of age. The last box is not given until about 4 years.The child should be encouraged to work with the triangles up to the age of 6 years.

[Still need to add the Large Hexagonal Box]