Tags:
Interesting points: Perimeter is approaching infinity. Area is approaching zero. Randomly generated points generate a fixed picture. Fractals/Chaos is a new and emerging field of Mathematics.
Materials:
* Dice (#number of students/3), random number genarator on calculator.
* Overhead projector transparencies.
* Overhead projector.
* transparency writing markers.
* ruler
** Web 2.0 alert .. maybe you could replace this stuff with google docs, or draw.
Prep:
* Draw an Equilateral Trinangle on (#students/3) transparencies.
* Label the vertices on the triangle 1 and 4, 2 and 5, 3 and 6 clockwise starting at the top vertex.
1, 4
/\
/ \
/ \
3, 6 _____ 2, 5
Activity:
* Break students into groups (three per group works well, but size of class may require modification)
* Give each group an overhead transparency. (predrawn equalateral triangle, and lableled vertices)
* each group should:
-- roll die
-- measrure half way from top vertex: 1, 4; to point rolled.
-- put a dot at the half way point on the transparency.
~ then roll die again and measure half way from the current point to the
rolled vertex and put another dot.
-- do this twenty times (for each group)
* call the students to attention.
* overlay the transparencies one at a time on the overhead.
* ask for observations about patterns.
* prompt about
area?
perimeter?
random?
does this happen every time?
Extensions:
research
Sierpinski
Triangle
Square
Sponge
Fractals
Mandelbrot
Julia
Randomness
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