The Constructive Triangles: Rectangular Box (Box A)

Materials:

• A rectangular box

• 2 yellow right-angled isosceles triangles with a black line along one of the equal sides

• 2 yellow right-angled scalene triangles with a black line along the shortest side

• 2 yellow equilateral triangles with a black line along one of the sides

• 2 green right-angled isosceles triangles with a black line along the hypotenuse (longest side)

• 2 green right-angled scalene triangles with a black line along the longer side that forms the right angle

• 2 gray right-angled scalene triangles with a black line along the longest side

• 1 red smaller right-angled scalene triangle with a black line along the longer side that forms the right angle

• 1 red obtuse-angled scalene triangle with a black line along the side opposite to the obtuse angle

• A rug

Purposes:

• To show that two triangles joined together form four-sided figures.

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

Age: 3 ½ - 5

Preparation: The child will have experience with the Geometric Cabinet and knows the names of all triangles and quadrilaterals

Presentation: 

• Invite the child for a lesson on the Constructive Triangles 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 two yellow equilateral triangles, the two gray right-angled scalene triangles, and the two green right-angled isosceles triangles and place them randomly on the right side of the rug.

• Close the box and move it to the top right corner of the rug.

• Place one of the green right-angled isosceles triangles in front of the child. Locate the other and slide them together matching up the black lines. 

• Ask the child to name the shape and slide it to the left.

• Repeat in this way for the other two pairs.

• Mix the triangles at random on the right side of the rug and invite the child to build the three shapes.

**If the child does not match the lines, stay with just these three shapes.  

• Remove the rest of the triangles, except the two red, from the box.  Close the box and return it to the top of the rug.

• Continue sliding the triangles together in front of the child and having the child name the shape they create. 

• Mix the second set at random on the right side of the rug and invite the child to build the three shapes.

• Once the child is done, remove the red triangles and close the box.

• Unite them at the black line and ask the child to name the shape (trapezoid).

• Place them at random on the right side of the rug and allow the child to build the trapezoid.

• Invite the child to help you mix up all the triangles on the right side of the rug.

• Invite the child to build them. Encourage repetition.

• Fade and observe.

• Return to demonstrate how to return them to the box.  Reverse the order they were removed from the box:

  • Place the red triangles on one side of the box. On top of the red triangles, place all the right-angled scalene triangles with the gray pair on the top.

  • On the other side of the box, place the large yellow right-angled isosceles triangles, then large green right-angled isosceles on the top.  The equilateral yellow triangles are placed on top of the green.

Control of Error:

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

Language: None

Following Exercises:

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

Memory Games: None.

Pedagogical Notes:

• The child is learning about the construction of shape through this work. This is a hands-on preparation for geometry. 

• A rug is preferable, but a large table may also be used.

• When we ask the child for the names of the shapes, often we see that they are surprised to see them emerge from the triangles.  This is the reason why the experience with the Geometry Cabinet is so vital. 

• The colors: Scalene triangles have three different sides, so it has three colors.  The isosceles has two different sides, so it gets two colors.  Equilateral all sides are the same so only one color.  The red is the only one made of two different triangles so it must stand out.