I've been playing with Zack's spiral design which I mentioned in the previous post. It's fun to have it in a tool like
Geometer's Sketchpad where it's a real mathematical object and you can play with it and change it and color it in different ways. I was surprised to think somehow this design was not like Zack's because this had four spirals and it seemed Zack's had only two. However, re-visiting Zack's design I see he used each color twice: a simple difference but it seemed quite different to my brain.
I keep thinking about this in terms of an assessment I saw at a conference where they gave students a square and asked them to shade it to show four equal parts, and to do this in several different ways. The four color version would be a good solution. Zack's two color version would be a good solution to shading the square to show two equal areas. Of course in each case there's a little empty square in the middle that would have to be divided as well.
I've been playing with Zack's spiral design which I mentioned in the previous post. It's fun to have it in a tool like Geometer's Sketchpad where it's a real mathematical object and you can play with it and change it and color it in different ways. I was surprised to think somehow this design was not like Zack's because this had four spirals and it seemed Zack's had only two. However, re-visiting Zack's design I see he used each color twice: a simple difference but it seemed quite different to my brain. 
I keep thinking about this in terms of an assessment I saw at a conference where they gave students a square and asked them to shade it to show four equal parts, and to do this in several different ways. The four color version would be a good solution. Zack's two color version would be a good solution to shading the square to show two equal areas. Of course in each case there's a little empty square in the middle that would have to be divided as well.
