The Constructive Triangles: Blue Triangles Box (Box B)

Materials:

• A box or tray

• 2 isosceles right-angled triangles

• 3 right-angled scalene triangles

• 2 equilateral triangles

• 1 scalene obtuse-angled triangle

• A rug

Purposes:

• To show the “constructive power” (or analyzing power) of the triangle by exploring all possible shapes using only two triangles.

• Preparation for geometry: to show that all plane geometric figures constructed with straight lines are composed of triangles.

Age: 4 – 5

Preparation: The child has already worked with the Rectangular Box 1

Presentation: 

• Invite the child for a lesson on the Constructive Triangles- the second Rectangular Box and ask them to unroll a rug.  Show them how to carry the box, return it to the shelf, and have them take it to the rug.    

• Sit to the child’s right and open the box.

• Remove the triangles and place them at random on the right side of the rug.  

• Close the box and place it at the top right corner of the rug.

• In front of the child, take the two equilateral triangles and slide them together to make a rhombus.

• Prompt the child to name the shape.

• Using the left fingers to keep one triangle still, use the right fingers to slide the other triangle upward until the angles touch.

• Lift the hands from the triangles and pause. 

• Replace the hands as they were and with the right fingers, slide down the triangle until the edges are flush.

• Lift the hands and pause again.  Prompt the child to name the shape (rhombus).

• Repeat to slide the triangles until the angles touch, pause removing the hands, and slide down the third side.

• Prompt the child to name the shape (rhombus).

• Invite the child to slide the equilateral triangles in the same.  

• Select a different pair of the same triangles and repeat for all. The trapezoid should be left until last.

• Place all the triangles at random on the right side of the rug and invite the child to repeat. 

• Fade and observe.

• Return to demonstrate how to return the triangles into the box in the same manner as Rectangular Box 1. 

**On another day, show the child to turn over one or each of the pairs (to the brown side) and go through the same process.  The child will discover that the triangles will make new shapes.

Control of Error: None.

Language: None, it was given with the Geometry Cabinet.

Following Exercise:

• These are done after the child has worked with all boxes of Constructive Triangles individually.

Memory Games: None

Pedagogical Notes: 

• The child had foundational knowledge of each of the triangles from their work with Rectangular Box 1.  We have an additional level of difficulty in there being no black lines to guide the child.

• The genius of this box is that through the manipulation of the triangle, the child can see how the shapes change.