The Constructive Triangles: Triangular Box

Materials:

• A triangular box

• 1 large gray equilateral triangle without black lines

• 2 green right-angled scalene triangles – each is ½ the size of the gray triangle with black lines along the longer side of the right angle

• 3 yellow obtuse-angled isosceles triangles – each is 1/3  the size of the gray triangle with black lines along the equal sides

• 4 red equilateral triangles – each is ¼ the size of the gray triangle with black lines as follows: 

  • One triangle has black lines along all sides

  • Three triangles have a black line along one side only

• A rug

Purposes:

• To realize that the equilateral triangle can be subdivided into other types of triangles.

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

Note: This is the only box of constructive triangles in which we do have language

Age: 4 – 5

Preparation: The child has worked with the box of Blue Triangles.

Presentation: 

• Invite the child for a lesson on the Constructive Triangles the Triangular 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.    

• Open the box, remove all the triangles, and arrange them at random on the right side of the rug.

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

• Place a green triangle in front of the child and ask to find the match and put them together (the black lines should be united).

• Ask the child to name the triangle (equilateral triangle).

• Superimpose the gray triangle over the top to verify that they are the same.

• Repeat these steps for the yellow and then the red triangles (For the red, place the triangle outlined with black on three sides in front of the child). 

• Slide over one of the sides and match it at the black line and turn it over to the child.  

• With the help of the child, mix up all the triangles on the right side of the rug and invite the child to do it on their own.

• Fade and observe.

• Return to show the child how to return them to the box. First place the red triangles in the box, followed by yellow, then green, and gray on the top.

Control of Error:

• The child’s own judgment/visual discrimination of the matching of the black lines and match of the gray triangle. 

Language: Language is offered after the child has spent a good while working with the triangles.  For the lesson, invite the child to construct all the triangles and use them to introduce the language.

• The Gray Triangle: Vertex, Side, Angle, Base

• The Green Triangle: Height/Altitude

• The Yellow Triangle: Bisector of Angle, Center

• The Red Triangle: Midpoint of the Side

Following Exercises:  

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

Memory Games: None.

Pedagogical Notes: 

• The top triangle can be challenging to remove. Loop a small length of yarn around the vertex of the gray triangle.  This will make lifting the triangle smooth. 

Parts of the Triangle