Tuesday, March 31, 2009

Geometry Training: Constructive Triangles

After the elementary child has gone through the geometry cabinet lessons posted previously he is ready to begin the Constructive Triangles.

Rectangle Box Series 1
Control Chart of each quadrilateral formed with this material and labeled.
Labels: Constructive Triangles, parallelogram, rhombus, square, trapezoid, rectangle, rhomboid, rhomboid, rhomboid

Begin your lesson by saying:
Triangles have three sides, quadrilaterals have four sides. These triangles are called constructive triangles because we can use them to build quadrilaterals. How can we make one four sided shape with two three-sided shapes?
You will show the child how we can make parallelograms, rhomboids, squares, rectangles, and trapezoids. Elicit from the children the name of the shape you have formed.

This work is put on the shelf. You may add colored construction paper to match the triangles. The children at a later can trace the quadrilaterals they construct, paste and label in their geometry notebooks.

You can show the students how Engineers and Architects use triangles. Find pictures of different structures like bridges and buildings where you can see triangles.

Blue Rectangle Box - Series 1

Blue Rectangle Box - the triangles are all blue with no black lines.
Labels - Blue Constructive Triangles, rhombus, square, trapezoid, rectangle, parallelogram, rhomboid, rhomboid, rhomboid, concave, and quadrilateral.

This is a more advanced work. There are no longer guidelines (no black lines on the triangles), and the child is working to discover figures. This is a preparation for equivalences. Guide older children to observe the relation ship between the number of lengths in the triangles and the number of quadrilaterals it is possible to form. In the equilateral triangle (all 3 sides equal) it is possible to form only one quadrilateral figure. In the isosceles triangle, there are two lengths, and it is possible to form two quadrilateral figures. In the scalene triangle, there are three lengths, and it is possible to form three quadrilateral figures.

The Last Section on Constructive Triangles is the
Blue Right Scalene Triangles - Series 1

There are 12 scalene triangles in this box. All blue and all the same size. With these triangles you demonstrate to the student how to create different stars - twelve point, six point, four point
Diaphragm with twelve sides, six sides, and four sides.

Start by asking the child to analyze the triangles with respect to sides and angles. He or she will discover with your help that these are all right scalene triangles.

The child can trace this one and make a pinwheel!


Kathy said...

I am interested in how you make
controls for the geometry boxes.
Does anyone have a print out for
controls available?
PS please come visit kathysmontessorilife.blogspot.com

Gigi said...

Kathy, you would need to either draw or cut out of construction paper all shapes for each box and label it.
This can also be an example of how you want the children to record their work. So, if after exploring and making all of the shapes you want them to trace each one and label or cut out each one from construction paper/paste/label, you would have these already made as an example.

Kathy said...

Thank you for the info!

Kathy said...

Hi again
Do you have pictures of
the other boxes of triangles
that you can put up?
I am interested in how you'd
approach the other boxes...

Gigi said...

Kathy, which boxes of triangles are you referring to? What do they look like?

Kathy said...

Ok, I know I'm not nuts...
I may be confused with
the "Series One" title
does this include all the
boxes except the blue

Gigi said...

Kathy, The Series one is all of the blue triangles.
There is also a post I did with the Geometric cabinet which has blue triangles (some cabinets have red ones).

The triangles in the cabinets have the little handles and are not part of the series discussed in this post.

I hope this answers your question. I was not totally clear on the question.

Kathy said...

Ok, thanks for the info.
I was confused by the term
"series one". I found a
resource for a set of free
printable triangles at
No membership is required
for this download.
I ended up printing them
and making control charts
to match the triangles.
I came up with a few more
possible patterns by printing a few extra blue triangle sets.
Thanks again for your great
and detailed blog!