math · Math and Book Arts

Fraction & more Fractions

Many Parts of a circle
Many Parts of a circle

I’ve been working with 9 different grade levels, nine different projects, this month, which is kind of wild, and even more wild because of all the snow days and other unexpected shifts in schedules. Most of the projects we’re doing are things I’ve written about enough on these pages, but I have managed to slide in a couple of new things with the fourth graders.

I had some extra time with some of the students some because they chose to stay after school for some extra time with me. Am still racing to finish prep for tomorrow, but want to quickly post about these two extra projects.

Dividing up a circle project
Dividing up a circle project

I brought in circles and sheets of regular shapes. Student cut up the shapes, and rotated them around a center point. The circles were marked with 12 evenly spaces dots around the circumference. We talked about other cyclic things that are divided up into 12 parts (clock, months) and talked about how 12 has so many divisors.

Rotating Shaper around a circle
Rotating Shape around a circle

I printed the shapes on heavy paper. I hadn’t done this with kids before so I didn’t know if they’d have trouble with this. It was no problem for them at all. They were excited, worked creatively, asked questions and were totally engaged.

Student rotations
Student rotations

Here’s the PDFs that I created for this project.

Circles with 12 dots

shapes to rotate in circles

I casually mentioned that ANY shape can be rotated. Well, they didn’t have to hear me say that twice before they were making new shapes.

Crazy Shape rotation
Crazy Shape rotation

The trick is to retain points that can still line up with the center and with a point on the edge of the circle.

Another Crazy Shape Rotation

During class time, I worked with students on a fractions/ bookmaking project that I’ve written about previously on my Books Are Fractions  post.

Fractions book
Fractions book

I knew some students would finish up early, so I showed them some images I had printed up some twitter posts. (If you want to see many more images like this, type in the words Fraction Museum in the twitter search bar and you will be well rewarded)

The kids were enthusiastic about creating fraction museum pieces, which I then photographed.

Fraction Museum hearts
Fraction Museum hearts

The idea is to collect items, see them as part of a whole, then write fractions that describe the collection.

Fraction Museum books
Fraction Museum books

There was some deeper thinking going on than I expected.

Mixed Fraction Museum
Mixed Fraction Museum

I’ve assembled all their images on to 2 large sheets of papers, and will present them to the kids tomorrow….but only if I stop this blogging and get back to work,

 

Addendum March 26 2018

During my fractions conversations with these kids (who, by the way, had a good grasp of fractions before I ever showed up) I talked about the confusion that can happen when trying to understand why, when the denominator is a bigger number, the unit fraction is smaller. I showed them a piece of paper folded into four sections, then said if I had to fold the same paper into eight sections (which we did) that the number of units had to be smaller to accommodate the larger number of sections. Then I asked “Imagine if we had to divide this paper into 100 sections, how small would those sections have to be? 

Hundreths
Hundreths

Well, that was it. They begged to see a page divided into 100 sections. Each time they saw me, they reminded me. Finally, today, I brought in TWO papers, and asked which one of them had fraction units that were each 1/100. Led by an particularly independent thinker, they figured it out. And figured out why, even though the divisions looked different, that they were all 1/100s.  It was a great conversation. Here’ the PDFs of you can ask kids this question yourself: hundreths

So much fun.

Book Art · Zhen Xian Bao

Workshop at the Met

Metropolitan Museum of Art, NYC
Metropolitan Museum of Art, NYC

The bookbindery at the Metropolitan Museum of Art takes care of many hidden floors of books. It’s like a secret place, mostly below ground level, under the Watson Library, which is entered through a discreetly placed door not far from the great hall. Many years ago, once a week for three years, I volunteered in the bookbindery. A few days ago I visited the Met to do a full day of PD with the staff of the bindery. They wanted to learn about the Zhen Xian Bao

Jenny's Zhen Xian Bao
Jenny’s Zhen Xian Bao

This was my first time teaching the Zhen Xian Bao, aka Chinese Needle Thread Pack, or Chinese Thread Book to a group. We started at 9:30 sharp, broke for an hour of lunch at noon, and worked straight through 4:30. At the end of the day we were completely saturated, and everyone had made exquisite models. This was dream-team group of artists and binders, in a fully equipped bindery. I can’t imagine another group in any other place who would have accomplished so much in one day.

There was so much that I did not have to do to get ready for this workshop. Most significantly, I did not have to do any paper cutting.

In the Bindery at the MET
In the Bindery at the MET

Everyone either brought in their own papers, or they used papers already in the bindery. After explaining how to determine the paper sizes to create the size book that each person wanted, people cut their own papers to size.

 

Yukari's paper
Yukari’s paper

Oh the papers that people brought! From orizomegami papers, to paper-backed fabric, to indigo papers with gold flecks, to Dick Blick assorted papers and more. The gorgeous papers kept coming out!

Mindell making a twist box
Mindell making twist boxes

Here’s a five things I learned from this day of teaching: 1) teaching, then making, four twist boxes takes a good bit of time. After making a gazillion of these, it takes me about 5 minutes to make one of these boxes, but it takes making about 1/2 a gazillion for these to get fast at making them. I assured everyone that the other style boxes we’d be making wouldn’t take as long, and in fact they didn’t take as long. The twist box is a tough one to begin with, but it’s the way to begin.

2) We started the day with people working at their own desks, and much had to be done at these solitary work areas, but not everything.

In the bindery
In the bindery

Crowding around a single work table and working together was incredibly efficient and enjoyable, especially as the day wore on.

Working together
Working together

Folding the second and third layers books while jostling for space around the demonstration desk went surprisingly well.

The four twist box version of the Zhen Xian Bao
Doris’s Zhen Xhen Xian Bao

3) I showed in a variety of different constructions of Chinese Thread Books. I’ve noticed that the most common structure that people teach is this one with four twist boxes on top. I thought I’d encourage people to make all sorts of other different decisions with their structures. It became clear very quickly that  it was incredibly satisfying for everyone to make the exact same structure.

Sophia's Gold Flecked Thread book
Sophia’s Gold Flecked Thread book

Trying to get everyone to do different things would have been too confusing for everyone. Everyone was able to help everyone because we were all doing the same things.

Written directions
Written directions

4) People liked having written directions. I’ve only written out directions for the twist box with a pinwheel top, which is in the current issue of Bound & Lettered, and which everyone had, compliments of the journal’s editor John Neal. I think every single desk had the magazine opened to this page all day, even after we were completely finished with the twist box.

Zhen Xian Bao
Mindell’s Bao, with Green with Gold Pinwheel Twist Boxes and Andrijana’s mostly Indigo Zhen Xian Bao

5) I had thought that if we had the time and energy I would show people how to make the boxes with a flower top. All I can say now is ha ha. There was no way we could have done one thing more. As it was, we ended the day before some people put covers on their creations. I didn’t worry too much about this though, after all, these people are bookbinders. They cover things.

Some with covers, some without
Some with covers, some without

Besides absolutely everything and everyone that made this an incredible workshop day, people who teach (like my friend Susan Share) will appreciate this: I didn’t have to cut any paper for prep, I didn’t have to teach this group anything about cutting, gluing, putting things under weight, and – this was a surprise – when I had to ask people to fold a piece of paper into thirds they could that flawlessly, immediately.. Turns out bookbinders at the Met make hollow spine pieces all the time, which are made by folding paper into thirds. No problem!

 

Miriam's book
Miriam’s book

What a great day. As we walked back out into the world after working all day in the underground, wending our way through the places that remain mostly unseen, we past this most unusual sign:

Underground at the Met
Underground at the Met

Big thanks to Mindell Dubansky for wanting her staff to become familiar with the historical structure called the Zhen Xian Bao, and especially thank you for letting me be the one to show them.

 

 

 

 

 

 

 

 

 

 

 

 

 

Zhen Xian Bao

Between the lines of the Byline

Bound & Lettered, Volume 15, Number 2, March 2018
Bound & Lettered, Volume 15, Number 2, March 2018

Bound & Lettered, the magnificent journal showcasing calligraphy, artists books, and papercrafts, arrived in my mailbox this week, containing an article that I wrote, spanning six pages long, plus photos on both inside covers. Though it’s my name on the byline, when I look at this article that I am so proud of I also what to shout out loud thanks to the village that helped me out.

I had written to John Neal, the Editor of Bound & Lettered, last spring, with the idea that I wanted to write a short, like maybe a one page article, introducing people to the Zhen Xian Bao, a structure I had become enchanted with during the past year. I had already pretty much finished writing the article by the time I first contacted John. My friend book artist Ed Hutchins had encouraged me, had looked over my first draft, and made excellent suggestions to improve the flow of the article.

Tabellae Ansata, Volume 1, No 4,. Summer 2000
Tabellae Ansata, Volume 1, No 4,. Summer 2000

John Neal wrote back to me about the guidelines of submission, and he also generously provided me with an article about this structure that was written 18 years ago in Tabellae Ansata, the publication that Bound & Lettered has evolved from. Some of what was written in Tabellae Ansata was so surprising that I felt I needed to rewrite my article. It was such a great gift to have received this article, which was written by Gail Rossi.

As I was rewriting the article I also got to work creating new pieces to photograph. I’ve long admired the work that mathematician/teacher/artist Dan Anderson shows on his Open Processing page. I printed some of his images and made them into my version of Chinese thread books, aka Zhen Xian Bao.

Although I sent in many photos, the Zhen Xian Bao made with Dan’s papers was the one that was chosen to fill the whole first page of the article. Yay!

pages 36 and 37 of Bound  Lettered, Volume 15, number 2, March 2018
pages 36 and 37 of Bound Lettered, Volume 15, number 2, March 2018

Other pages had images that featured papers that came to me by way of my friends, Jane Duda and Laurie Cohen, both of whom know how much I like and use beautiful papers. My own stash had begun to run low, so it was a huge boon to me when these two friends separately thought of me when some piles of papers needed a new home.

How to pages for the Chinese Thread Book
How to pages for the Chinese Thread Book

Writing out directions can be tricky, especially if I am super familiar with what I am writing about. It’s so hard to know what is difficult for someone else to understand. I thought my tutorial for this article was perfect. I asked a few people to look at it. Mark Kaercher and John Golden stepped up. John actually asked his group of pre-service teachers to go over my write up. I got some excellent feedback, and made some much-needed improvements. Turns out my first iteration was not so perfect after all.

Before sending in the final article Ed Hutchins looked things over again, and my friend Julie Moline looked it over, too, and made edits using genius skills that fill me with awe and wonder.

Finally, in October, everything was submitted.

Next Dano Keeney, the graphic designer for Bound & Lettered, and John Neal , Editor, worked their magic on the layout and made some final improvements.

Two weeks later, it was in my hands.

Boxes made with Paper printed from Dan Anderson's Open Processing page
Boxes made with Paper printed from Dan Anderson’s Open Processing page

Article by Paula Beardell Krieg, with help from John Neal, Ed Hutchins, Dan Anderson, John Golden, Mark Kaercher, Laurie Cohn, Jane Duda, Jule Moline, and Dano Keeney. Now that’s a great byline.

 

 

 

 

Sewn books

The Weaver’s Knot, finally

Knots & Threads & Books
Knots & Threads & Books

I am a total rock star when it come to making a weaver’s knot – THE knot that bookbinders need when we need to attach more thread to sew signatures together.

The fact that I am like a grande dame of the weaver’s knot should come as no surprise. I love doing exposed sewn bindings, I’m a great admirer of the beauty of knots.

Oh, yeah, and did I mention that until Susan Joy Share showed me the weaver’s knot this past summer at Penland, it was my dark secret that the weaver’s knot eluded me. No matter how many times I looked through my bookbinding books, no matter how many times I studied those diagrams, I couldn’t wrap my brain around it. It didn’t make sense to me.

Exposed Spine Sewing, with many colors of thread
Exposed Spine Sewing, with many colors of thread

Susan knows the secret sauce of the weaver knot. Now I know it.

This is something I have to show you.

When I think of the knots that I know (which I learned from my days of rockclimbing, backpacking and kayaking – yes, kayakers need knots, primarily to tie their long boats to the tops of their tiny cars) it now occurs to me that people showed me how to make all the knots that I know.

An indulgent aside: when I was about 4 years old I watched Captain Kangaroo, on TV, as he demonstrated how to do the knot that ties shoes. Then I went outside to tell my mother, who was in the garage washing her car, that I knew I how to tie my shoes. She told me I didn’t know how to do it. I told her I did. And I did. And that was that.

Now I get to be Captain Kangeroo.

Weavers Knot Video tutorial. It’s the only way to go. Now, watch for the secret sauce. Make knots, be happy.