To show that by joining together different triangles, foursided figures are formed.
Preparation for geometry: to show that all plane figures constructed with straight lines are composed of triangles.
Extending the understanding for the concept of equivalence and its application for finding the area of plane figures.
The black lines.
4 – 5 years
Materials
 One large yellow equilateral triangle with a black line along all sides.
 Ten obtuseangled isosceles triangles:
A red pair, with a black line along the longer side
A gray pair, with a black line along one of the equal sides
Six yellow, of which:
Three have a black line along two of the equal sides
Three have a black line along the longer side
Invite the child by telling him you have something to show him. Bring him over to the correct shelves. Show the child clearly that you are choosing the large hexagonal box. Have him carry it to the table and have him place it near the top right corner of the table. Have the child sit to your left, and then you sit down.
 Remove the lid of the box using both hands.
 Place the lid directly in front of the box and place the box on top of the lid.
 Take out the pair of red triangles, and the pair of gray triangles.  Place them randomly to the left of the box.
 Move the box above the lid and then replace the lid on the box.
 Using the black lines as your guide, create a rhombus with the two red triangles.
 Slide the rhombus up to the top left corner of the table.
 Using the black lines as a guide, create a parallelogram with the two gray triangles.
 Slide the parallelogram up to the right of the rhombus.
 Mix up the triangle and allow the child to build the two shapes.
 Remove the lid of the box as before and remove all of the yellow triangles.
 Place them randomly on the table and close the box.
 Place the equilateral triangle in front of you.
 Choose the three triangles (one at a time) with the black line opposite the
obtuseangle and place accordingly around the equilateral triangle, thus creating a hexagon.
 Slowly and gently fold one of the three yellow triangles over onto the
equilateral triangle.
 Repeat for the other two until they are now creating an equilateral triangle
above the original equilateral triangle. This shows the child that they make the
same equilateral triangle.
 Unfold the three triangles to come back to the hexagonal shape.
 Build an equilateral triangle with the three remaining triangles.
 Then superimpose them over the large equilateral triangle or in the center of
the hexagon.
 Slide two triangles away from the hexagon to form a rhombus.
 Repeat to make two more rhombi.
 Place them under the red rhombus to show the similarity.
 Mix up the yellow triangles and allow the child to build the shapes.
 Once the child is done, show him how to put all of the triangles back into the
box: first put the large yellow equilateral triangles, then cover the space that is
left with the three yellow obtuseangled triangles (with the black line along the
longer side), then place the other three yellow obtuseangled triangles on top,
and then put in the gray and red triangles.
As the child has been taught the names with the geometry cabinet, there is no language lesson given with this material.
