This is a great activity that covers several objectives. Rational Numbers, Irrational Numbers, Geometry, and Pythagorean Theorem.
The activity starts with creating a unit of length. Once I have the unit I cut a unit by unit square out of the corner of a note card. This tool will act as a ruler for the students throughout the activity. Using the "ruler" start in the middle of a large piece of paper and make a right isosceles triangle that has legs one unit long and then connect the legs creating the hypotenuse. The next step is repeated as many times as you like. Make the previous hypotenuse the base of the new triangle and use the ruler to add a leg that is one unit long and is perpendicular to the base. Then connect the unit length leg back to the middle. Repeat, Repeat, Repeat.... I have my students use the Pythagorean Theorem to find the length of the hypotenuse for the first ten triangles. They see a pattern quickly and could give you the first ten hypotenuses without the work, but I make them show the work.
I only require that the students draw about 15 triangles, but many of them go much further than this. Several of them will make 50 to 60 triangles attaching extra papers everywhere to make it work. When the students finish drawing all of the triangles and the math, they spend some time decorating or adding on to the triangles.
See links below for examples
http://www.ldlewis.com/Teaching-Mathematics-with-Art/images/Wheels-of-Theo/Kyles-turkey.jpg
http://www.chatham-nj.org/156620131125737203/lib/156620131125737203/IMG_0198.jpg
This year I have thought of two different extensions.
a) Using GSP. I figured it would be pretty cool to make on GSP and it was :) I will post the file on the discussion board if you would like to see it.
b) The second activity has yet to be completed. I would like to take my class to the gym and use yarn and water bottles to build a large scale version of the Wheel of Theodorus. If I am successful, I will let you know.
I originally got this idea from an article in the Mathematics Teacher.
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I love this one! If you have a handout for this I would appreciate a copy to share with my students.
ReplyDeleteThis activity looks pretty neat. I had a hard time visualizing it at first, so the attachments were helpful. It looks like your students were very creative!
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