Re: tessellations and angles

[Kathy Boyle <boyle@xxxxxxxxxxx>]

I know this may be a little too late, but there is a wonderful book -- 
Mathematics and Logo, A Turtle Trip Through Geometry, by Kathleen  
Martin and Donna Bearden.  I've used it for years.  It has a chapter  
on Tessellations.  The authors suggest starting out with paper cut  
outs or shape blocks and letting the students experiment hands on for  
while.  I've also had my students create polygons of their choosing  
with the turtle, turn them into turtle shapes and experiment.   
Usually, I do this after I have covered drawing radiating lines and  
coming up with the following algorithm:  repeat :lines[fd :size  
bk :size rt 360 / :lines].  Then we create polygons by removing the  
"bk :size".  Then we experiment with stars and lots of other  
triangles.  I have done this successfully with many different  
students 3rd grade and up for years.  We do spent lots of time  
experimenting with the turtle and angles and the whole idea the turns  
adding up to 360 or a multiple of 360.  I've also had students use  
hinged mirrors and paper folding as hands on activities. I think it  
is nice for my students to begin to see the different angles in a  
shape - the outside, the internal and the central ones.  I'm lucky,  
because all the students in my school learn and play with LOGO from  
Kindergarten on, so they are very fluent by 3rd or 4th grade.  It has  
also been my experience that most elementary students are not wedded  
to the internal angle and in fact understand turning 360 already from  
their personal experiences with bikes and skateboards and dancing  
etc.  If not this is a wonderful opportunity to expand their  
knowledge base.
Kathy Boyle
Computer Teacher
Londonderry School
1800 Bamberger Rd
Harrisburg, PA 17110

School ph# 717 540 0543
Home ph# 717 245 0030
Cell ph# 717 448 2416

email: boyle@xxxxxxxxxxx



On Mar 2, 2008, at 3:15 PM, Tamara Weinstein wrote:

> I have a question about a project I will be starting shortly with  
> 5th graders using MW EX to create a tessellation using simple  
> polygons.  It is a question regarding teaching about angles.  When  
> programming a turtle to create a triangle (for example) the  
> relevant angle is the amount the turtle has to turn to create the  
> triangle (the outside angle).  However when math is taught, usually  
> the focus is on the internal angle.  As well one way to determine  
> whether a shape can tessellate is to measure whether the place  
> where the tessellated shapes meet equals 360 degrees.  If anyone  
> can help me think this through that would be great.  If it is not  
> clear what it is that I am asking,  please let me know.
> thanks
> tamara
>
>
> Tamara Weinstein
> Educational Technology Specialist
> The Children's School
> 404-835-4602