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

[karl ramberg]

You should take a look at DrGeo in the new Etoys image. It's just the right
tool for your challenge. It's a fantastic extention to Etoys for geometrical
work. It is a litte confusing to begin with.
Open a new DrGeo. You can click and get a tool menu to pin down. Or get a
button menu from the halo menu to build a interface for your challenge.

Karl




On Mon, Aug 2, 2010 at 5:52 AM, Steve Thomas <sthomas1 at gosargon.com> wrote:

> *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
>
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>
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