# Montessori Geometry Moment

For a week or so we’ve been working with constructive triangles (yes, those lovely puzzles from Casa). It has been interesting trying to do this work with paper representations rather than wooden shapes.  We’ve found the blue painter’s tape works well at holding shapes together as we work with them and removes easily afterward.  Yesterday we proved the 4,3, 1 ratio which extrapolates to the Pythagorean theorem in Hexagons.  I completely forgot to photograph the work.

Today we dug into the insets of equivalent figures.

We began with figure 1 – demonstrating the equivalence of triangle to rectangle.

Our rough "proof" with our triangle to rectangle attempts

The general aim is to make the child aware of the reason why certain figures are equivalent.  Up til now, we have been learning that figures are equivalent because they are constructed with the same number of equivalent figures. Working through through relationships into a written “proof” shows that the child has comprehended the lesson.

The proof for this work is written this way:

A triangle will be equivalent to a rectangle if: 1) the base of the triangle equals the base of the rectangle and 2) the height of the rectangle is half the altitude of the triangle.

AV's rule of equivalence

It was frustrating for JV who is spatially really good. In the presentation I gave everyone a different shaped triangle and asked them to make a rectangle out of it.

Then we took out triangles and make a proof paper. (We used the triangle as a mathematical conclusion too.) This was amazingly difficult to get to come out correctly.