Building Symmetry with 4 & 5 year-olds

I have way too many photographs for a single post.  Although only about a dozen 4-and 5-year-olds were with me yesterday playing with symmetry, they were so engaged and made so many beautiful images, both simple and complex, that I got carried away with taking pictures.

Here’s how it went: first I talked with the kids about symmetry, how their own two eyes, two arms, two legs, and two ears are expressions of symmetry in nature.

Building with Symmetry

We also looked at how using symmetry makes things that are built stronger. Then I talked about the visual beauty of symmetry, about reflections, and then about other kinds of symmetry, where something is reflected not just once, but multiple times. I had cut up some reflective mat board and adjusted them to be able to fit around a point of a hexagon.

Reflective mat board, my symmetry makers

The children used colored tiles to make designs that could be reflected.

Symmetry star

They started simple.

Symmetry star

But soon their designs became more complex.

Ready to be reflected as three-fold symmetry

No matter how their explorations went, they were wowed by the reflections.

complex design

After awhile we realized that the designs could be reflected from multiple points, which created different results.

a design that has a couple of points that suggest rotations

 

Reflections around the red hexagon

Reflecting from a different edge

We also looked at different images made by adjusting the angle of the reflective boards.

Triangle waiting for reflective boards

Now prepared to be amazed by the different looks this triangle makes.

Three fold reflection

and next…

Six fold reflection

Even as we created more and more complex designs, the thrill of the simple designs didn’t fade.

Simple Symmetry

This sweet little designs becomes…

Simple Symmetry reflected

…a sweet little reflection.

 

When we had exhausted ourselves with building, it was time to make beaded necklaces. This is the fourth time I’ve worked with these children, and each time I make a different necklace with them. This gives the kids an opportunity to practice counting, to use fine finger control, and to practice making knots. This day, though, we included talk about making a symmetrical design.

symmetry necklace

I offered these children a choice of three kinds of symmetrical patterns to do.  The design that I didn’t photograph was pattern of two alternating colors with a large wooden bead in the middle.

Necklace with symmetry

I’m pretty sure that the ideas I was presenting to these kids was mostly beyond their ability to fully grasp, but they had such a good time playing around with these ideas, and seemed so engaged and excited by them that I have hopes that something about all of this stays with them in some way.

 

Wonky Quadrilaterals

 

Last summer I got caught up with a shape that Martin Holtham started looking at after seeing this vase in a furniture store.

from this fun twitter thread https://twitter.com/GHSMaths/status/757688653795758080

Martin made some paper models of the vase, and I tried it out, too, then explored other ways of decorating, folding and cutting this shape.

Quadrilaterals, decorated

With Martin’s help I made this template for folding:

I kept getting stuck . I liked much of what was happening but was never quite satisfied with what I came up with.

Recently I decided to revisit this shape again. I questioned the materials I was using,  decided to work in a 11″ x 17″ format, started looking more at what the shapes wanted to do than trying to impose my own thoughts on to them.

What’s notable about this shape is that it has an irregularity to it that does not let it fill up a piece of paper in a typically symmetrical way.  It moves somewhat diagonally across the surface. So I went with that and came up with a different template.

Wonky Quadrilateral net

 

Going along with the flow of the shape made all the difference!

 

It folded down into adorable little structure that does a twist-fold , collapsing all the quadrilaterals into this unruly many-sided shape…

 …which untwists in a truly lovely way.

 

I’m still working on this. There are still some thing that I need to work out, not the least of which is to figure out how to make a little video of this structure expanding and contracting again. I have to do it in the right light with a tripod, and I haven’t been able to get it right.

Even though this is still a thought-in-progress, I am so enamored with how it’s progressing that I wanted to share it now.

Idea in motion

Making Shapes with 4-&5-year-olds…

…. which includes blowing bubbles with Platonic Solids

Shapes made with cubed potatoes and toothpicks

The local program for rising kindergartners has begun, and once again I get to hang out with these kids, once a week for 6 weeks, doing all sorts of explorations that have to do with paper projects, with relationship thinking and with numbers.

This group of kids, about 15 of them, seem to have a good grasp of number recognition so we’ve jumped right into playing with shapes.

Circles, squares, rectangles, and triangles are already part of these kids vocabulary. One boy volunteered the alternate name for diamond is rhombus. I’m going to have to work hard to keep ahead of these young scholars.

Pirate hat

Since our first project was going to be making a paper hat, we talked about triangles for a good bit. Some schools that I work with don’t want children to talk about all the different kinds of triangles, as the only one the kids see for quite a few years is the triangle with equal sides. The kindergarten teacher from the local school gave me the go ahead to talk about all kinds of triangles, so that’s what we did.  I heard some really interesting comments from the kids, comments that got me thinking about these shapes in ways that I hadn’t considered before.

Rotations of an Equilateral Triangle

There was some hesitation from the kids about saying that differently proportioned three-sided shapes were all triangles. Then one boy pointed to differently proportioned triangles and suggested that these are different sides of a triangle. This got me wondering if  different triangles could be seen as the same triangle seen from a variety of vantage points.  I came home and tried out rotating equilateral triangles in my Adobe Illustrator program, and, oh my, yes, seeing the same triangle from multiple perspectives gave the same triangle  different appearances. What an interesting discovery!

Eight Jewels

Each child received this array of jewels to use as decoration on their hats.  I asked them to please count the jewels that I gave them to make sure that they each got 8 of them. These children recognize the number 8, they can count to eight, but they counted the amount in the photo above as 6 or 7 or 9 jewels. This was good for me to notice, as it will inform planning for my next session with the kids.

from post https://bookzoompa.wordpress.com/2014/08/04/the-paper-hat-meets-the-shrinking-newspaper/

The hat making went well. I will likely do some kind of paper-folding every time I meet with these kids.

Shadow of a cube

Next (well, after a snack) we went outside and played with the shapes that are featured at the top of this post. The shapes were created with cubed potatoes and toothpicks. We talked about what their shadows might look like, then, mounting them on a knitting needle, looked at all the surprises that showed up on the ground. This was such a great activity (as long as the sun was shining.) It wasn’t easy for them to get this flower-like shadow, but they badly wanted to create it, and did, discovering lots of other surprising shadows along the way.

Dipping 3D shapes

Next we dipped the shapes into bubble mixture that was laced with a bit of glycerin to give the bubbles extra staying power. We talked about what shapes the bubble might make within the confines of the shapes’ boundaries. I can’t even begin to tell express how amazingly rich and interesting this activity is. I highly recommend this. Especially surprising is the shape that forms within the cube. Go try it. Please. Or at least look at this video, made by the Lawler family from their post https://mikesmathpage.wordpress.com/2016/03/16/trying-out-4-dimensional-bubbles/: 

One thing I told the kids at the outset of this project is that Mr. Lawler had warned me that the kids would want to pop the bubbles as soon as the shape emerged from the bubble mixture, so I suggested that we do some running around and popping bubbles before we moved into the observing part of this project. These 4 and 5 year-old were aghast at the suggestion that they might pop the bubbles, and assured that this would not happen. Unbelievably, they did not pop the bubbles.

What shape bubble does a cube make?

Instead, then blew into the shapes and created more bubbles.

What shape bubble does a tetrahedron make?

And more bubbles.

Square bubble maker

When the cube broke apart, bubbles were blown through square shapes.

And then it was time for another snack.

I’m loving this time I’m spending with this age group.

In searching for wisdom to inform my planning I’m revisiting posts on https://mikesmathpage.wordpress.com/ , https://talkingmathwithkids.com/ and http://www.malkerosenfeld.com/ 

 

This morning I came across this video by dad and educator Kent Haines, that I wish every parent would watch.

The next few weeks these kids and I will be talking about numbers, shapes, how when one thing changes, another thing changes (especially with shadows), we’ll be getting those little fingers to fold paper, attempt to tie knots, make patterns, and run around and have fun.

kids in pirate hats

Argh! Shiver me timbers!

 

Susan Share, Penland, and Me

Zip-off Fence, Susan Joy Share

This summer I get to spend a week with Susan J Share at Penland in North Carolina.

I went searching for Susan J Share a good many years ago when we were in our twenties  I had seen some of her bookarts pieces in a show at a Soho Gallery, and had found her work to be so compelling that I immediately wanted to be friends with her. Life-long friends.

I am a patient person. I reasoned that, since we were both part of a small swath of NYC people who were passionately interested in making books, that our paths would cross.

I remember the first time I saw her. She walked into the Center for Book Arts (original Bowery location), but I wasn’t able to BFF her at that moment.  Darn.

Above the Tree Line, Susan J Share

I started volunteering weekly at the bindery at the Metropolitan Museum of Art, under Mindell Dubansky. Susan worked in the bindery as  well, but on a different day than me. She and Mindell became fast friends. Mindell would sometimes chat on the phone with Susan while I was in the bindery. I was so jealous.

At some point, though, Susan and I were at MMA on the same day. I don’t exactly know if there was a defining event in our friendship, but if there was, it was this: Susan was teaching a children’s bookmaking  workshop at the Castle in Central Park, and I asked if I could assist her. Which I did. My first book arts teaching experience. I loved it.

Steel Horizon, Susan J Share

Susan and I went on to share many bookarts experiences. She got me started working with kids in schools through Franklin Furnace’s Sequential Art for Kids program. When she and Henry Pelham-Burns created the bindery at the New-York Historical  Society, I worked with them one day a week. When Susan was looking for studio space, I was able to point her towards a place to rent in the same building I was living in. It was such a gift to be able to chat with her when we’d bump into each other in the course of our days.

Be the Queen Bee, Susan Joy Share

Eventually Susan married Paul and moved to Alaska, and I married Bill and moved upstate. Still, Susan I  see each other, support each other and remain close. As luck would have it, Susan’s brother Ike lives about 45 minutes from me, so I see her here when she comes for family visits.

Now here’s the absolutely most wonderful thing: Susan is teaching a class at Penland  at the end of August. She asked if I would come down and be her assistant for the week. OMG. A week with Susan Share.

Be the Queen Bee (detail), Susan J Share

If anyone would like to be there, here’s the class description:

Susan Joy Share
Books & Boxes

Books and boxes are a natural fit. They may be a set or structurally integrated. They can enhance each other and the experience of opening and discovery. We’ll experiment with formats, including books sewn on tapes, paper enclosures, cloth-covered folding boxes, and Jacob’s Ladder boxes. We’ll generate content with paint, pencil, crayon, and collage. Students will create unique pieces as we fold, sew, glue, wrap, reveal, and engineer. This hands-on workshop includes demonstrations, lectures, and sample books. All levels. Code 07B

Here’s the link

I haven’t been on an adventure like this in a long time. Am so looking forward to it!

OMG a week making art with Susan Share!