[squeakland] Etoys Challenge #1: Help 6th graders figure out for themselves how to derive the value of Pi

[Steve Thomas]

*Why I think this is possible*: I created a project in Etoys (Circle
Explorer <http://www.squeakland.org/showcase/project.jsp?id=10212>) which
allows kids to inscribe and circumscribe a circle with a regular polygon of
N sides.  When I have shown this to kids (as young as 8) they comment (in a
number of cases without prompting)  "hey its filling up the circle".  The
regular polygon is made up of triangles.  I have seen kids can figure out
how to determine the area of triangle using GeoBoards (Here is a
sample GeoBoard
project <http://www.squeakland.org/showcase/project.jsp?id=7744> in Etoys
that uses squares, you can add a triangle by opening the object catalog,
 click on find and type triangle, place it on the GeoBoard and move around
the vertices to create different triangles.).

*My initial thoughts on how to do this**:*

   1. First ask the question:  How can we figure out the area of a Circle?
   2. Let them play with the Polygon in a circle tool
   3. Have them record in a table the "# of sides" and "area of the Polygon"
    This can be done with both inscribed and circumscribed polygons (the
   diameter of the circle can be set by them or they can inspect it by looking
   in the viewer for the circle object.
   4. They could try this for different size circles
   5. Then ask the question: What is the ratio of the area of the Polygon to
   the Radius squared (how to lead them to this I haven't figured out,
   suggestions welcome)
   6. Have them plot their results on graph.

The other possibility is to have them determine the circumference of the
circle and then the ratio of that to the Diameter of the circle.  They could
figure out the Circumference using the Ruler Object within Etoys.

*
*
*Ways in which you can help:*


   1. Provide a set of suggestion on how to use the Circle Explorer and a
   GeoBoard (to help kids figure out how to derive Pi
   2. Provide other activities within Etoys (or other similar tools) and
   hands on activities that can help facilitate understanding.
   3. Provide sample lessons and/or a set of lesson plans for these
   concepts.
   4. Point me to already created lessons (that I can use as is or use to
   derive lessons that can be freely distributed under a Creative Commons or
   similar license).
   5. Provide a set of "Head Games" they can play in the car to help them
   become more facile in playing with and manipulating the ideas in their
   heads.  An example of a simple "Head Game" you can play in the car is "Guess
   My Function" where you ask the kids to give you a number and you can make
   funny "machine" noises then spit out the answer.  Once the kids catch on
   they will come up with "trick" functions like "YourNumber + 2 * 20 / 20".
   This can lead to a discussion on equivalent functions, or in kid terms ("Hey
   you cheated its the same thing!!!")



*Screenshots*:
Here is a screenshot of the inscribed circles:


<http://3.bp.blogspot.com/_VzolrwmoPkw/TFYOBY1FUmI/AAAAAAAAABM/g3ByCCeuFSQ/s1600/Inscribed.png>


Here is a graph showing the results the kids would collect:
<http://4.bp.blogspot.com/_VzolrwmoPkw/TFYO_E4XykI/AAAAAAAAABU/sqUmCXyI3r8/s1600/graph.gif>


*Why Etoys?*
Etoys is a free educational software tool for teaching children powerful
ideas in compelling ways. It works on almost all personal computers and OLPC
laptops.  Projects created within Etoys can be easily modified by people
around the world (for translation into local languages and cultural
symbols).  Any kid can create their own work.  It allows kids (young and
old) to make their own models, stories and games.

This challenge is posted
here<http://etoys4teachers.blogspot.com/2010/08/etoys-challenge-1-help-6th-graders.html>
as
well.

Thanks to Carlos Rabassa for his initial Mathematical Challenge which
spawned this idea.

Stephen
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.squeakland.org/pipermail/squeakland/attachments/20100801/b985c931/attachment.html>