To realize that the equilateral triangle can be subdivided into other types of triangles.
Preparation for geometry: to show that all plane figures constructed with straight lines are composed of triangles.
Preparation for understanding the concept of equivalence and its application for finding the area of plane figures.
The black lines and the gray triangle.
4 to 5 years
 1 large gray equilateral triangle without black lines.
 2 green rightangled scalene triangles. Each is a half of the gray triangle, with the black lines along the equal sides.
 3 yellow obtuseangled isosceles triangles. Each is a third of the gray triangle with the black lines along the equal sides.
 4 red equilateral triangles. Each is one fourth of the gray triangle with black lines on: one triangle along all the sides, three triangles along one side only.
Invite the child by telling him you have something to show him. Bring him over to the correct shelves. Show the child how to carry the 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 palace the box on top of the lid.
 Take out all of the different triangles and lay them randomly to the left of the box.
 Replace the lid on the box.
 Choose the one gray triangle and using both hands to hold the triangle around the edges, place the gray triangle near you but a little to the side.
 Pick up one of the green triangles and place it in front of you with the black line vertical.
 Pick up the other green triangle and place it so it makes one triangle with the other green piece.

Pick up the gray triangle and gently place it on top of the green triangle to show that these two green triangles make the same shape and size as the gray triangle.
 Remove and replace the gray triangle slightly off to the side and gently move the green triangles, as a whole, up to the top left corner of the table.
 Create one large triangle using the three yellow triangles in a similar fashion by following the black lines.
 Once put together, check with the gray triangle as you had done for the green triangles.
 Gently slide the yellow triangle to the top of the table to the right of the green triangles.
 Create one large triangle in a similar fashion for the red triangles, always using the black lines as your guide.
 Check with the gray triangle.
 Gently slide the red triangles up next to the yellow triangles.
 Mix up the triangles and allow the child to make the large triangle out of the smaller triangles.
 Once the child has created all three triangles out of the other triangles, show the child how to replace them back into the box in the correct order: the red triangles, then the yellow triangles, then the green triangles, and then the gray triangle.
Later on, give the terms of side, base, vertex, etc….
