The Constructive Triangles: Small Hexagonal Box

Materials:

• A small hexagonal box

• 2 red equilateral triangles with a black line along one side

• 3 green equilateral triangles with black lines as follows: 

  • one has black lines along two sides

  • two have black lines along one side

• 6 gray equilateral triangles, with black lines along two sides

• A rug

  *Remove the following from the box. They are used for later geometry work with theorems at the elementary level.

  *1 large yellow equilateral triangle, without black lines.

  *6 red obtuse-angled triangles, with a black line along the longer side.

Purposes:

• To further the child’s exploration of equilateral triangles

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

Age: 4 – 5

Preparation: The child has worked with the Large Hexagonal Box

Presentation:

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

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

• With the help of the child, place the triangles at random on the right side of the rug.

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

• Slide a red triangle in front of the child, prompt them to find the match and to name the shape.  

• Repeat for the green triangles.

• Slide a gray triangle in front of the child. Invite them to help you put the remaining gray triangles together uniting the black lines. 

• Mix them all on the right and invite the child to build them.

• Slide over the rhombus and ask the child if they can see that shape in the hexagon. 

• Slide apart the rhombus and superimpose. Repeat for the others allowing the child to superimpose.

• Reunite the gray triangles and slide the rhombus back to the left.

• Slide over the trapezoid. And repeat

• Place all the triangles at random on the right side of the rug.

• Invite the child to work with the triangles

• Fade and observe.

• Return to demonstrate clean-up.  

Control of Error: 

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

Language: None.

Following Exercises: 

• Explore Combinations: The child may now work with two boxes at a time, exploring combinations without the use of the black lines.

  • Gradually add more boxes until the child is working with all of the boxes together.

Memory Games: None.

Pedagogical Notes: 

• You may find colored dots on the backs of the triangles to help the child in getting the triangles back into their correct boxes after exploration.

• This box is used in the proof of the theorem of Pythagoras.