Thursday, September 13, 2012

Joint Ventures / Spinning Stars

I've been over in weaving land for a while (young children and grids here, inverse operations and multiples here, and Fibonacci here), but recently came back around to our star adventure.  As with most things, my seven year old learns best in an environment of exploration and self-directed learning, so I've been careful to present this star inquiry primarily as just that...exploration.  What's amazing to me is that although she and I are exploring different things about stars, we seem to be on parallel tracks, moving forward together.

A few weeks ago I built the skeletons for the "spiders who spin fancy webs" out of plywood and copper brads, but things were left there for a while.  Yesterday I decided I was ready to pull out all the beautiful embroidery floss we acquired for this project and try spinning some star webs. 

Below are some of my experiments with six, seven and eight pointed stars.  I do love how the different colors look but it was way too futzy for me to get the effect I wanted; mostly it was hard to keep the tension steady between posts.  I quickly determined that rubber bands work best in this activity, and that is now my official recommendation for when you try this at your house or classroom.

The best part of trying to 'spin' these webs was that I saw the six pointed star next to the seven and eight pointed stars. That got me wondering: What it would look like if I drew the stars using the same color for each variety of star within the same circle?  Would I see anything new in the stars, especially compared to each other?

When you read about how to draw stars you often see the words "over two points" or "over three points."  If the number of points = n that means that for me (n, 1) was red, (n, 2) was purple, (n, 3) was green, etc. And, all that means is that you use the starting point as 0, and if you go directly to the next point, that's (n, 1).  If you skip the 1 and go directly to the second point, that's (n, 2), etc.

Here are the six and seven pointed stars (three colors, green is 'over three' points).  I loved the different flavors of even-ness, balance and symmetry between the even and odd numbered stars. 

The eight and nine pointed stars (four colors, blue is 'over four' points):

 And the ten and eleven pointed stars (five colors, yellow is 'over five' points):


What thrilled me was that my daughter had a similar but completely separate line of inquiry happening around the same time.  She started her 'spinning' when she saw me doing it, but her drawings (which she made the day after the spinning) actually happened before I had a chance to explore the ideas I shared above:

If math is about asking questions and exploring different ways to answer and understand the questions you pose, then I'd say we've been doing some math.

The absolutely fascinating thing for me is that through this kind of visual inquiry I am not only learning a lot about stars, I also appear to be finding my way to thinking and reasoning numerically.  As I figured how to divide the circle into fifths, sixths, sevenths, etc. with my compass and protractor, I started wondering if there was some kind of pattern that would emerge if I compared those measurements.  In a 5-pointed star, for example, the points are 72 degrees apart and a 6-pointed star is comprised of points that are 60 degrees apart.  I kept an informal chart and didn't come up with anything that seemed newsworthy, but it was very interesting to observe myself open up to this line of questioning.  As someone who is slowly but surely remediating herself in math, I am thrilled that this visual design approach is helping me begin to see numbers as interesting, useful and, perhaps, even friendly!

p.s. As always, a huge thank you to Paul Salomon of Lost in Recursion and the Math Munch blog.  He teaches math at St. Anne's school in Brooklyn but I was lucky enough to benefit from his help and feedback over the summer months via the magic of the inter-webs.

p.p.s. Check out my new Math in Your Feet Facebook page!  I'd love to see you there!

1 comment:

Thanks for reading. I would love to hear your thoughts and comments!


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