Fractals, Triangles, and Kites Oh My!

Mandel_zoom_08_satellite_antennaAhhh, the STAAR test is complete for another year.  Sadly, some topics such as these are put on the back burner…   But now that burner is on!  The last two months of school we’ll be digging deeper into some concepts that we skimmed over while covering the curriculum, while also covering topics to prepare them for 9th grade.

Next week, we’ll be designing and constructing Tetrahedral Kites.  We’ve been building these kites since the mid 90’s in the classroom.  Students  (ok not all but I’d say most) enjoy the time spent working together, creating the kites and then going to a nearby park to fly them later in May. And every year, I’ve got a few students who will fly kites for the first time!

 

To introduce the unit, we usually start with the Sierpinski Triangle.   However, this year180px-Britain-fractal-coastline-50km, I jumped into the concept of Fractals.  These are figures that are considered self-similar when there can be found a point in the figure that contains a copy of the entire figure.  There are many websites out there.  Of course, there is no need at an 8th grade level to share too much of the equations behind the design of the fractals.  But we can discuss the fractional relationships and the correlation with measurements (Mandelbrot fractal), the history of fractals (Cantor’s Dust) and the associations between fractals and the mathematics and sciences of the world, such as with the Coastline dilemma of Great Brittain.

 

While viewing a PowerPoint and parts of the video – The Mandelbrot Set ( a video including a segment from @profkeithdevlin ) of different examples, the students use whiteboards and markers to create Cantor’s Ternary Set.  Then we design Koch’s snowflake.  The whiteboards make it easy to erase and add to the line segments.   Another day we discover how easy to make Heighway Dragons out of strips of paper.

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Then, onto Sierpinski’s triangle.

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The YouTube videos can be eerie, but fascinating, and so those played on the screen as we designed our triangles.   And as we finish, we build our own Sierpinski triangle along the hallway

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And now, this week, the building of 3-d tetrahedron kites will commence this week. Looking forward to it!  We’ll discuss volume, surface area, fractions, the relation between the kites and Sierpinski’s Triangle…  and of course the history and science of kites and flying.

 

I’ll add photos here later in the week.  😉

 

 

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