[Confab] Circle-Square by Dy/Dan

Dan Meyer had posed a great problem on his blog

[Confab] Circle-Square

believe it originates from The Stanford Mathematics Problem Book, though I've seen it elsewhere in other forms.

Given an arbitrary point P on a line segment AB, let AP form the perimeter of a square and PB form the circumference of a circle. Find P such that the area of the square and circle are equal. 

 In it he posted one comment from Peter Boon (my emphasis added):

Off the ISDDE mailing list, Freudenthal Institute curriculum designer Peter Boon had some useful comments on the use of interactives and videos:

I would like to investigate the possibility of giving students tools that enable them to create those videos or something similar themselves. As a designer of technology-rich materials I often betray myself by keeping the nice math (necessary for constructing these interactive animations) for myself and leaving student with only the play button or sliders. I can imagine logo-like tools that enable students to create something like this and by doing so play with the concept variable as tools (and actually create a need for these tools).

Well for me Etoys is the tool of choice (not perfect, could be better, but a great choice).  Etoys is an educational tool for teaching children powerful ideas in compelling ways and a media-rich authoring environment and visual programming system for kids to create.  Besides logo like programming it hashas GeoGebra like functionality built in with DrGeo. But for this problem you don't even need Dr. Geo.

Below are the simple steps for kids to create a model of the problem.

1) Create a "Square" using the rectangle object. Below is a screen shot where I added one variable and a simple two line script.

2) Create a "Circle" using the Ellipse Object. Below is a screen shot again adding one variable and a simple two line script.

3) Now we need to create the line segment and showing the different segments.  Below is a screen shot of two Rectangle Objects and three simple scripts. Two to have the widths match the square's side and the circle's diameter and one to keep them aligned.

Plus kids can use Etoys to construct Multiplication Models, Explore Fractions and much much more. (See EtoysIllinois from the Office for Mathematics, Science, and Technology Education (MSTE) at the University of Illinois at Urbana-Champaign is a great resource)