## Stars for Second Graders (maybe)

### November 30, 2016

I will be working with about 75 second graders later on in the school year, doing what I do, which is to make books that are artful, and that relate to curriculum. The teachers haven’t settled on exactly what that curriculum link will be, so I’m trying to develop a two-prong math/design based project to pitch to them. The first prong is about numbers, which I will write about at a later date. The second part will be about how to use math to make beautiful designs.

I’ve been inspired by a number or educators to work with stars, including Alan Parr, who has prodded and poked the possibilities of this kind of math/design artivity, I mean activity, with a very young crowd. I won’t have nearly the amount of time with the students to go into the details that Alan explored in his star posts, but I do think I can expose these kids to a way of making interesting images with math.

I want to keep this simple, but still spectacular. I’ll be giving the students circles that are divided into 12 parts, as this is more like a unit circle than a pizza circle. What else, I will ask them, is circular or cyclical that is divided into 12 parts? Clock. Calendar. My original thought was that I would have the students use a ruler to connect the dots according to a rule, but I abandoned that strategy for one main reason…

…which was I didn’t like that hole in the middle of many of the stars.

I did try out some ways of filling that hole…

…but it just didn’t seem right. What I came up with, then, was the idea of providing the students with shapes that they could rotate around the circle, which I may or may not mention is called rotational symmetry. Students can use a square or a triangle and rotate and trace it within the circle, touching the corners to the 12 dots on the perimeter of the circle, then they can cut out a shape and line the corners of that shape up to just the black dots around the circle, always rotating around the point in the center of the circle.

The shapes above are the ones that students can use.

The designs above are some of the ones that can be made with the shapes, which…

…I will encourage students to color in. Notice the use of Sharpies. I think that the black Sharpies really make these designs pop. I will be buying lots of Sharpies.

I also hope to have some time to have students try to draw some circle on their own, divide them up just as best they can, then play around with using their freehand circles to make a different kind of drawing.

So that’s my plan. I hope I get to do this project with the second graders that I will be working with!

Here are some links to what people who’ve gotten me thinking about this way of working:

Malke Rosenfeld: Stars, Factoring, and Patterns,

John Golden: Stars made While I should have been sleeping, and once again

and, finally, an interactive star by Dan Anderson (hover your cursor over the image, and move it around! )

My thanks to my son, his girlfriend and my daughter who helped me trouble-shoot this project by letting me do a math project with them on Thanksgiving Day.

November 30, 2016 at 6:45 pm

Oh, this is lovely!

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November 30, 2016 at 8:49 pm

We’re on the same star wavelength! I do another making math at the library in a couple weeks and have planned on an exploration of mathematical stars. I want to have a number of ways for kids & parents to create a skip counting star and I love the idea of having some pre-designed stars for coloring so they can explore the structure another way. I’d like to use the unit circles you created to ease them into making the star polygons by numbering the dots. (I may also have an option for turning them into ornaments.) I also want to repeat the hexagon star project…but maybe that’s too many things?

I have a neighbor boy who is super interested in the star polygon skip notation I promised him I’d print out odd and even unit circles through the number 20 so he can think closely about the patterns.

Also, I just want to say I love the center of the 12 star. You can see the dodecagon clearly there and how it relates to the star portion. 🙂

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November 30, 2016 at 8:57 pm

Do you have odd and even unit circles through the number 20? let me know if you what me to make any…did you notice I alternated black and white filled circles around the perimeter? this was my son’s suggestion, to help things stay more manageable as the patterns get more complicated.

I know what you mean about having some pre-designed stars for coloring. Having these on hand has worked really well for me with other groups (of all ages) that I’ve worked with: it assures that everyone, regardless of dexterity, ambition or energy level, has a good experience.

Looking forward to seeing results of your workshop!

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