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Constructive Triangles, Triangular Box

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1 large gray equilateral triangle.
2 green right-angled scalene triangles with black lines on the longer of the two sides enclosing the right angle; each green triangle is equal to one-half of the large gray triangle.  
3 yellow obtuse-angled isosceles triangles; black lines on each of the sides enclosing the obtuse angle; each yellow triangle is equal to one-third of the large gray triangle.  
4 red equilateral triangles; three have the black lines on one of the sides and one has a black line drawn on all three sides, each red triangle is one-fourth the size of the large gray triangle. 


  1. Invite the child to the lesson. 
  2. Take out the large gray equilateral triangle.  
  3. Place the green triangles together by the black lines.  
  4. Place the gray triangle on top of the green triangles to show they are same size.  
  5. Take off the gray triangle. 
  6. Slide the green triangles to the top of the rug.  
  7. Repeat this process for the 3 yellow triangles. 
  8. Repeat this process for 4 red triangles.  
  9. Randomize the triangles.  
  10. Ask the child to explore. 
  11. Tell the child to get you when he is done so that you can show him how to put the triangles back in the box in a good way.


Child works independently.


None, however when the child is around 5 or 6 years old, you can talk about the height, bisector, midpoint, and base of the triangles.

Control of Error

The black lines on each triangle; the gray triangle also acts as a control of error.

Direct Purpose

To show that an equilateral triangle can be divided into different kinds of triangles. 

Indirect Purpose

Preparation for geometry.  
Show that straight line figures are made up of triangles. 
Preparation for understanding equivalence.  


4 to 4 1/2


A ribbon should be glued or taped to the bottom of the box to make removal of triangles easier.

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