# Rotational Symmetry project with 5-9 year olds and Moms

I got to spend some time with a group of kids and moms this past Sunday. They had asked me to plan a math/art project for them. Last time we did this we played with shapes scaled according to the golden ratio. This time I wanted to help them make images that are made by rotating a graphic around a circle. We used a circle that was divided into twelve equal sections, and we got to talk about how rich the number 12 is, in that it comes up often in measurement of time (hours, months), quantities (dozen), distance (Inches) and so much more.

Images were made in two ways. One was to connect the dots around the circle according to a rule, such as connect the first dot to the fifth, connect the fifth dot to the tenth, connect the tenth dot to the dot that is plus+5 further around the circle, then continue until you are back where you started from. A star emerges!

We started the afternoon by sitting in a circle of eight people, and doing the skip-counting activities that I described above. This was actually a thrill to me, as it’s something I’ve wanted to try out for a long time. As the star shape grew within the circle of people, who were the “points”, everyone was thrilled. They had no idea a star would emerged. I knew, but I was thrilled too.

I had PDF printout of circles and shapes.People cut out shapes that they wanted to rotate around the center, then colored them in if they wanted to.

The moms seemed to like this activity at least as much as the kids.

I never know how these projects will go. A couple of the boys didn’t want to be coloring any more after a while. One boy in particular really liked cutting paper, so I got him started with another kind of rotational symmetry: making snowflakes!

I hadn’t thought about snowflakes beforehand, but liked the way I was able to link to something that was already familiar to this group.

After awhile one of the girls was finished with coloring, I showed her how to make an origami pockets that were sized for the drawings to slip into.

She really liked making the pockets, and made them for everyone. This also let me segue into showing her how to make a square from a sheet of paper.

In the end, we had made lots of images, pockets, snowflakes and our work area was delightfully messy. Everyone helped with the cleanup, especially with the tiny pieces of paper on the floor.

At the end we put our tiles out on display.

A couple of hours later one of the mom’s texted me saying that, on the way home, her kids were asking to do more of these. YAY!

# 5th Graders’ Kaleidocycles of the Bill of Rights

They did it! This group of fifth grades did this hand-lettering kaleidocycle class project! I described the details of this project a few posts back so check out that post for more details. Here’s the general gist: After introducing the project, which is a 3D paper construction with rotating faces that will be graced with references to the Bill of Rights, students were given pages of letter fonts to choose from.

Using the windows of the library as light boxes, students traced out letters to created one phrase eachÂ that described one of the first ten constitutional amendments, aka The Bill of Rights.

Every single student was highly engaged. Really.

Within two class sessions theÂ students produced something that I could take home and scan into my computer . I won’t lie..scanning and cleaning up their work took time. Above you can compare what they gave me, on the left, to what I ended up with on the right. Some pages required much more work than others. The middle example above was so easy to work with that next time I will encourage students to just give me outlines. The most time-consumingÂ letters to work with were those that were colored in and touching other letters. I moved things around a bit, like in the top example you can see I centered the word “OF.”

I brought home their work, scanned them into my graphics program, cleaned them up and laid them into a kaleidocylce template. Brought them back for students to cut around the perimeter and score.

Students made score lines so that the paper would fold easily and accurately. Scoring is generally done with bone folders but we used glitter pens to score the lines. They worked great, and kids were excited to be using the gel pens.

Then came the folding and gluing. I didn’t take many pictures of this process as I was, like, really really occupied helping move this process along.

This project turned out so well. Not everyone had a chance to finish up and decorate, but the wonderful school librarian will be able to help with the few than still need finishing.

Students enjoyed individualizing their own kaleidocycles.

I tried to get them to use completely different color schemes on each face, so that the differences between the four rotation of faces were dramatic. Students didn’t much listen to my suggestions.

Here’s one of their kaleidocycles in action:

I consider this project a great success. I got to talk to the students about design, about hand lettering, and they got to work with some cool geometry. I’d even go so far as to say that they are also much more familiar with the Bill of Rights , as they were constantly asking each other, which one do you have, which one is yours, and talking about their own. Â I have to say that at first the students were confused about what I was asking them to do, after which the librarian told me that doing a group project was pretty much out of their experience, so the concept was hard to grasp at first.

One thing that made this possible was that this was a small class, just 12 students. I often work with 60 to 70 students in a grade level: I wouldn’t do this project with a big group. OH, but it was so delightful doing this with a small group.

Do I get to pick a favorite project of my teaching season? Yes? This is it.

For more about all this take a look at these posts:

https://bookzoompa.wordpress.com/2017/02/19/kaleidocycles-and-tetrahedrons/

and

https://bookzoompa.wordpress.com/2017/03/19/designing-a-seriously-fun-project/

group project

# Gathering Stars

I’ve been working on putting together the colored paper tiles people have sent me for my gathering of stars (see Invitation to My Sandbox). Â This will be a short post to let those of you are participating to let you Â know that I am in the assembly stage, and that it’s going well, and to say thank you again to all the people who are participating.

Also, I wanted to publicly answer a question my friend Rowan Jai asked as he handed me his tile, just before heading back to college in NYC. He asked if I would be doing any more of these stars? I am assembledÂ two of them at the moment, but he wanted to know if this would be all. I told him I hope to keep doing these for the rest of my life. It’s not that I want to do this project exclusively, but I can see this project being repeated at the summer lunch program for children in our community, at schools that I teach in, and at all sorts of gatherings of people that I am part of. I see this as an on-going project that supports my belief in diversity and unity. There’s no reason to ever consider it ending.

For now, though, my focus will be on getting these first two stars together well. I have to sharpen up some of my computer skills, but that’s happening just fine. The toughest part so far is getting lost in the unexpected patterns that are emerging. At the corners where the different tiles meet, triangles and other shapes come together, colored by different people, and create the most beautifully filled in shapes. This project is fertile ground for surprises as I have not been able to even begin to envision what the final look of the stars will be. One thing that I had hoped is in fact happening, and that is that the underlying geometry of the 12-fold Â rosette is beautifully, gracefully, and effortlessly holding together all the various decisions that people haveÂ overlaidÂ on their own piece of star.

There are stillÂ few small edges that I can send out to people to color. I had planned to color these in myself, but I am happy to send them to anyone who would like to be part of this project. Be in touch by email at paula12fold at gmaildotcom or leave a comment below.

group project

# Virtual Stars are Filling My Inbox

My inbox feels like a treasure chest: People who are coloring pieces of theÂ 12-fold star rosette projectt are sending back their finished pieces.

I’m going to highlight just a few images in thisÂ Â post, which are the ones that have a connection to a child, though not necessarily a young child. The image above is an appropriate one to start with, as Anne, who colored this one in, was the first person to request a tile from me. It was quite late at night when I had finally hit the Publish button on the post that invited people to join me in this project, but Anne lives in Australia, soÂ the post reached in the late afternoon. Â Anne’sÂ  5-year-old neighbor Molly helped Anne with this piece by choosing the colors to color with.

This child-tile belongs to the 23 year-old son of my good friend Jocelyn, whose made coloring in these tiles a family event while they were recently gathered together in their Vermont home. Like her children, each tile that each member of her family gave to me has a unique character.

A few days ago I received a twitter note from John Golden ( I think from Minnesota) showing an image of a colored tile with Â a note pinned to it that said “my daughter’s working on a better one though.” I hadn’t sent one to this gentleman’s daughter so I quickly sent them a second tile to work on, so they could both have tiles included. I have no idea how old John’s daughter is, but she does lovely work. Addendum: John just let me know that Ysabela is freshly 17!

I’m only guessing, but I’m thinking that Janet Reynold’s daughter saw her mother working on her piece of the star and wanted one of her own, Â I’m intriguedÂ by how well theÂ bright carnival-like colors work alongside more muted tones here.

Although it may seem like all the star pieces that I’ve received are brightly colored, this is definitely not the case. I have gotten quite a few that have a more restrained palette. Â Kianan, my friend’s teenage son, used one of my favorite drawing tools, the black sharpie, for his expressiveÂ tile.

My daughter, on the other hand, went nearly psychedelic. I love what she gave me (I am, of course, completely biased and smitten when it comes to anything that she does), but what I am most pleased about is that she actually asked for a tile. I knew she that if she chose to color a tile that she would give me something wonderful, andÂ I’m relieved that she didn’t wait forÂ me beg Â her to do this…which I eventually would have done. I really wanted her to be part of this.

I haven’t begun assembling the star pieces together yet. I will start that process in about a week. I still have some pieces of a second star that I would like people to color in, so if this project interests you at all please take a look at my first and second posts about this project and be in touch.