The Constructive Triangles: Large Hexagonal Box
Materials:
A large hexagonal box
2 red obtuse-angled isosceles triangles, with a black line along the longer side
2 gray obtuse-angled isosceles triangles, with a black line along one of the equal sides
6 yellow obtuse-angled isosceles triangles, with black lines as follows:
three have a black line along each of the equal sides
three have a black line along the longer side
1 large yellow equilateral triangle, with a black line along all sides
A rug
Purposes:
To show what figures can be built with an obtuse-angled isosceles triangle that is 1/3 the size of an equilateral triangle
Preparation for Geometry
Age: 4 – 5
Preparation: The child has worked with the Triangular Box
Presentation:
Invite the child for a lesson on the Constructive Triangles Large Hexagonal 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.
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.
Prompt the child to match the red triangles and to name the shape.
Prompt the child to match the gray triangles and to name the shape.
Slide the yellow obtuse-angled isosceles triangle, with the black line on two sides, in front of the child, have them match the other two, and name the shape.
Move the equilateral triangle in front of the child.
Slide a yellow obtuse-angled isosceles triangle, with one black line, to the base of the equilateral triangle, ask the child to find the rest and place them, and then to name the shape.
Mix all the triangles to the right and invite the child to construct them all.
Suggest to the child what might happen if we flipped the triangles up onto the equilateral triangle. Let the child flip them brown side up.
Flip them back to their original position.
Remove the large yellow equilateral triangle in the center of the hexagon and ask the child if he sees anything on the rug that will fit in that space.
Let the child place the three double black-lined obtuse-angled isosceles triangles in the center of the hexagon.
Move the red rhombus beside the hexagon and ask the child if they see that shape in the hexagon.
Slightly slide away from the ones that are indicated and superimpose. Repeat for other two.
Place the triangles at random on the right side of the rug and invite the child to work with them for as long as he likes.
Fade and observe.
Return to show the child how to put the triangles back into the box.
Control of Error:
The child’s own judgment/visual discrimination of the matching of the black lines.
Language: None
Following Exercises:
Only done after the child has worked with all boxes of Constructive Triangles individually.
Memory Games: None.
Pedagogical Notes:
The gray parallelogram is an exploration of what can be made with this specific triangle. They make another shape but one that will not fit in the hexagon, so they stay above the other on the rug.
“By studying figures which we can see and handle we begin to discover the secrets of geometry.” (Montessori, 1998, Creative Development in the Child Volume 1, p. 130)