From: Terry Trotter 
To: Teacher2Teacher Public Discussion
Date: 2001022620:44:12
Subject: Re: Re: Geometry project

But you know, using equilateral triangles is a great way to teach the
"concept" of area.

To the question "What is area?", too many older students answer like
parrots, saying "length times width!"  That's NOT what area is; that's
merely a convenient shortcut to find the area of a rectangle.  The
basis of area is how many times would a unit shape, whatever it may
be, cover a given space (of 2 dimensions). 

Here's what I did once with a 4th grade class...

I drew circles about the size of an ordinary paper plate on pieces of
construction paper.  Then each group of students were given a quantity
of the green equilateral triangles from the manipulative called
Pattern Blocks.  [Each side is 1 inch in length.] They were now asked,
"How many of these ET's would it take to cover your circle?"

Of course, things don't fit nicely.  And we got different answers, tho
they were usually close.  Discussion ensued as to "why".

We also brought in 3 more types of the Pattern Blocks: blue rhombus (=
2 ETs), red trapezoid (= 3 ETs), and yellow hexagon (= 6 ETs).  Using
those along with the green ETs made the task of covering the circular
space a little more efficient.

But, in summary, I think they learned a little more about the concept
of area, rather than how to just mechanically and mindlessly apply a
shortcut formula.

Try it.

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