Regular Hexagon

Regular Hexagon

One of my all-time favorite paper moments was when I learned how to fold a regular hexagon. Many times, with  protractor or compass in hand,  I had tried to draw hexagons, but  they never worked out just right. This post, which features a tutorial page, is something that I have been wanting to do for a long time, but I needed to stumble upon just the right random instant of blog time. Recently, while musing about life, the universe and everything, well it seemed like the right time to finally put these drawings and steps down on paper. After all, the six goes neatly into 42.

Paper Folding and the Regular Hexagon by Paula Krieg

Paper Folding and the Regular Hexagon


Now, if you go ahead and make a hexagon for yourself, which of course you will because who could possibly resist trying this, you might notice a few splendid things. Then again, you might not notice them, so I will point them out.  First, you will notice that a preliminary step towards hexagonism is that you create an equilateral triangle , which is just the first of the many perks of this activity. The second, most extraordinary flash will be when you realize that the intersection of the three folded lines within your triangle is actually the center of the triangle. The reason that this is so remarkable is that this intersection point in no way looks like it’s at the center of the triangle. It just looks wrong as a center, and you might not believe it. But when you bring the tips of the triangle in to meet the intersection, well, let’s just say you will believe. 

Silently folding a hexagon drawn by Paula Krieg

Silently folding a hexagon

Just for fun, I decided to include this set of directions, too, because, really, it’s a much more attractive page than the one with all the writing on it. And there are plenty of people who will try it out without reading a thing, so here you have it.

Now after you’ve noticed that you’ve made a big equilateral triangle, there are few more shapes to uncover.  First of all, there are all sorts of little equilateral triangles inside of the hexagon. And if you fold the hexagon in half, well, you will have made an isosceles trapezoid. Now, think back, when is the last time you actually held an isosceles trapezoid in your hands? Next, fold back a third of the trapezoid, and there you have a rhombus. And if you can’t remember what any of these shapes are it’s probably because you never learned to spell them. Really, what it is it with this terminology? Wouldn’t these all these shapes be more memorable if we called them lollipops or kiwis?

A special nod here to Christopher Danielson. math teacherblogger who recently had way too much fun using hexagons in his classroom, so I wanted to add something to the virtual hexagon mix. And I want to acknowledge Steve Morris,  who kept me thinking way too long about the edges and shape of the universe: I no long think that the universe is shaped like a hexagon. That was just silly. Now I think it’s the shape that’s made when hexagons and pentagons are fitted together, -but don’t be looking for a post about that. I think I need to get back to making books. Rectangular books.

Anticipating Spring In First Grade

Anticipating Spring In First Grade

One of the best parts of being a guest teaching artist in schools is the relationships that I have with the teachers that I work with. Most of the work that I do is with teachers that I have worked with before.  This means that year after year, as we get to know each other better, we can develop bookmaking projects that can dynamically align to the mandates of the curriculum.  Each year  the projects that I present generally are either repeat projects that are continually refined to serve the classroom needs better, or they are projects that are designed anew, to fit shifting interests of the teachers.

Proposal Sketches for a Healthy Snack Book

Proposal Sketches for a Healthy Snack Book

This past week I started a completely new project with Margo’ s second grade class. I have worked with Margo for years, but this is the first time that she is the primary teacher in the second grade. She said that she wanted to do some research with her students and that she wanted there to be a “global” feel to the project. After brainstorming a bit, we decided that we would reach for the global connection through the children’s snack bags.  Each day for a week the class logged their snacks and noted where they came from. Pineapple from Thailand, bananas from South America, celery from California, Mandarin oranges from Florida, via Chinese origins. We had the concept, then I had to come up with a design that would work in her classroom. What I came up with is illustrated in the drawing above: it includes a pop-up (the snack popping out of the lunch bag), a window to peek through at the habitat of the snack, and two pages for writing. We started the bookmaking yesterday. I look forward to posting images when the books are done!



Last year I worked with Mrs. Kavney’s first grade class, making a  Dinosaur  Diorama. I loved this project and was looking forward to repeating it. This year, however, Mrs. Kavney wanted the book to be more of this world. She worked up a spectacular unit on following the Iditarod in Alaska, incorporating geography, math, and science. She wanted to have our bookmaking project put another spin on this unit, and she had her eye on studying animals and habitat in Alaska.  She liked the Diorama book that we did last year, so I so I reworked the basic design. The animal is now central, a pocket is included that can  hold standard size paper, which will contain the sentences that the first graders will write about their animals, and there is an area to showcase a haiku that students will write. Of course I couldn’t resist the opportunity to somehow incorporate the Northern Lights…which, when I mentioned this to the students, they responded by telling me that these lights are also known as the aurora borealis. I am learning not to talk down to these students…This project was also started this week.  My next post will likely be on the aurora borealis part of the project, and I look forward to seeing how the rest of it goes.

Now, back to prepping.

What I Do

March 4, 2013

Announcing a new page on my sidebar: Gallery of Student Work .

Now, here’s the back story.


A Page from my files

A Page from my files

Last week,  at my daughter’s school. when I was bemoaning that my work schedule precluded my attendance at the next parent meeting,  a parent that I have known for years, and who l very much like, asked me what I do. It is hard to explain to people what it is that I do, which is one reason that I keep a blog.  But I realized that if I sent Lauri a link to my blog she would have to do a good bit of sifting through posts and more posts to see what I do.

Part of Pinterest Page for Bookzoompa

Part of Pinterest Page for Bookzoompa

It occurred to me to direct her to Pinterest, to look at pins from Bookzoompa, but I this didn’t seem like the best solution, either.  It made me sad to realize that this blog hadn’t made it easy to answer the “What do you do?” question. But I had an idea. This is my idea:  It’s a new page on the sidebar of my blog, which simply is photo after photo of work done by students that I have worked with.  Soon I hope to add more pages: one which puts all my tutorials in one place;  and another that shows the work that I do when I am not working with students.

Please take a peek at this new page and let me know what you think. Thanks.

A Shape With Many Wives…

January 5, 2013

          …or talking to teenagers about Geometry


I’ve been having conversations with some high school students about things having to do with math. I thoroughly enjoy these conversations, as I am intrigued by the way students make sense of the sometimes elusive concepts of algebra, geometry and trig. While looking over some problems I asked a young man  Andrew if he knew the definition of a polygon. After letting him flail a bit I resorted to Latin. I know that sounds bizarre, but it seems to me that kids  have a knack for making and retaining connections if can connect to the root of a word. So I put forth the question ‘do you know what poly means” The answer was no. Hmmm…”Well, do you know what polygamy is?”  It turns out that nearly all teenager do have a general (though not precise) understanding of polygamy as having many wives. Great…poly, therefore, means many.  A polygon, therefore, must be a shape with many wives…well, not exactly, but I suspect that this is a close enough definition to help a teenager remember that a polygon is a shape with more than two angles and more than two sides.


A discussion of Isosceles Triangles delighted me beyond measure. When I asked my young friend Lucy about an isosceles triangle, she defined it to me as the one with the two lines.  I knew exactly what she was talking about: each time students see an isosceles triangle in their math books, there are lines on the two equal sides (like on the orange triangle in the drawing above), which is math nomenclature for “hey, look, these two sides are equal.” It turns out that some kids don’t really know that these little lines are code that math people use to show that line segments are equal, or that you can have an isosceles triangle without having those two lines drawn.

It’s a good thing that I didn’t have to resort to Latin to explain isosceles, as the word isosceles comes to us from Greek, and can roughly be translated as “equal legs.’ I mentioned this to my daughter and she declared,


“I’m an Isosccles!”  I suppose it might be more correct to say, “I have isosceles”…?


Thankfully, Equilateral Triangles are Latin-friendly, translating into something like “equal sides.” But this makes me pause and consider some other thoughts about math. Think about this: math is supposedly elegant and logical, however, the name for a triangle with three equal sides comes from Latin, the name for a triangle with two equal sides comes from Greek, and to meaure their lengths the we use Arabic numerals (our 1,2,3,4, 5, etc.), which actually originated in India. No wonder math can be such a challenge! Not only does it seem like a foreign language, fact is, it is many foreign languages!

That said, an understanding of bookbinding (much of which has its roots in Chinese and Japanese cultures) is supported by having a good understanding of geometry.

A bit late, but all the same, I wish you peace in the New Year and may you make connections that support and enrich your life.

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