The constructive
triangles are used to demonstrate that all plane geometric figures can be
constructed from triangles. There are five boxes: 2 rectangular, 1 triangular,
and 1 large and 1 small hexagonal. Each box contains triangles of different
sizes, shapes, and colors. With the exception of Rectangular Box 2, black
guidelines are painted in different positions on the triangles to help the
child to construct other figures. This should be encouraged as an exploratory
work that will provide a foundation for later concepts of equivalency, similarity,
and congruency.
Rectangular Box 1
three pairs
of large right angled scalene triangles in three different colors
a pair of
red triangles that form an isosceles trapezoid bisected diagonally
a pair of
equilateral yellow triangles
two different
colored pairs of large right angled isosceles triangles
Rectangular
Box 2
Two equilateral
triangles
Two right
angled isosceles triangles
Two right
angles scalene triangles
A trapezoid
divided diagonally to form an obtuse angled scalene triangle and an acute
angled scalene triangle
All of the
figures are blue and there are no longer any guidelines.
Triangular
Box
Large Hexagonal
Box
One large
yellow hexagon, the same size as the box, cut by joining the vertices of
every other angle to form one large equilateral triangle and three obtuse
angled isosceles triangles. There are black guidelines along the perimeter
of the equilateral triangle and the bases of the smaller triangles.
A second
large equilateral triangle divided along its intersecting angle bisectors
to form three obtuse angled isosceles triangles. There are black guidelines
along the two equal sides of each triangle.
Two equal
red obtuse angled isosceles triangles the same size as the yellow ones,
but with their guidelines along the base opposite the obtuse angle.
Two equal
gray obtuse angled isosceles triangles the same size as the others with
black lines along one of the equal sides.
Small Hexagonal
Box
6 gray equilateral
triangles with guidelines along two sides to form a hexagon, the same size
as the box
3 green equilateral
triangles (same size as above) which are put together to form an equilateral
trapezoid. One triangle has black guidelines along two sides, the other
two have a single guideline.
A large yellow
triangle which inscribes within the box, formed by joining every other vertex
of the hexagon
2 additional
red equilateral triangles (same size) each with a single black guideline
6 red obtuse
angled isosceles triangles with guidelines along the base opposite the obtuse
angle
PRESENTATION
Rectangular
Box 1
The teacher
opens the box and says to the child, "We call these the constructive
triangles. Why? Because we can construct other figures with them."
She asks
the child to remove them from the box and group them by similar shapes.
"Now can we group each set by color also?"
When the
child has done so, beginning with the equilateral triangles, the teacher
traces the black guide lines with her fingers and moves them together until
they touch. "Now what do we call this?"
If the child
does not know the name, the teacher should give it.
She might
take the isosceles triangles next, and ask the child to do the same. There
are two sets of isosceles triangles, one forms a square and the other forms
a parallelogram.
"Let's
try putting the scalene triangles together." The result is a rectangle,
and a parallelogram."
"Now
our last two red ones. Can you put those together on the guideline. What
is the figure you have made? A trapezoid."
Review with
the child the figures that have been made with the different kinds of triangles.
With the younger children the attention is on the black line and it is a
sensorial experience of shape, and vocabulary review of terms that have
already been learned in the geometric cabinet.
The children
can trace these new shapes and label them to put in their own geometry book.
Rectangular
Box 2
Here the
child can see how many shapes can be made using one shape. With this material
we have no guidelines to tell us what we must do. The child takes the equilateral
triangles and discovers that there is only one shape to be made, no matter
how he joins them. He takes the other triangles in turn and discovers how
many different shapes can be made with each pair. Here the teacher can check
the child's work orally to be sure that he knows the names of the figures
and that the child can write and spell them correctly, since this is a sensitive
period for reading and handwriting.
Use the same
procedure with each o the successive constructive triangle boxes, allowing
plenty of time for experimentation, practice and mastery before the child
is invited to go on to the next box.