Algebra without Arithmetic

So this problem was suggested by Don Cohen ("The Math Man") who suggested we look at Take a look at Prelude to Mathematics by W.W. Sawyer p.98+ Algebra without Arithmetic, The Group of the Rectangle on the Natural Math mailing list.

You could easily add a Triangle or any other shape to this project in Etoys (you would need to use a graphic object as those are the only objects that you can currently "flip" in Etoys 4.1)

One idea I had was to color the rectangle (based upon position of the inner square) and add an arrow to help kids visually compare and identify equality.

As always suggestions welcome, post a comment below.