## Zhen Xian Bao, Post #5: the hidden tray

### September 16, 2016

There’s a hidden box layer in the Zhen Xian Bao.

It can be thought of as the third layer of this structure, but that can be a bit misleading, as there *can* be numerous layers of the masu-type box above it.

Many of the directions I’ve seen for this layer include templates so that you can make simple cuts and folds then do some gluing to create the box. I have nothing against templates (well maybe I do…) but the fact is that the template makes a box that is not nearly as elegant as this origami folded box.

However, if the maker is using paper which is like those made in workshops in the Shiqiao Village, then using a template might make more sense, as it appears to me that using a hardy paper with the origami method would make an overly bulky box. In any case, whatever method you use is your decision. That’s what’s so awesome about the Zhen Xian Bao: there are lots of personal decisions to make.

At the end of the post there’s a video on how to make this box. There’s some key points that I want to emphasize here. The first is that this box is made from a square. If you want the rectangular tray to fit exactly under the boxes above it, which is what seems to be typical, then you must start by first making the boxes of second layer . The width of three of these boxes will be the side measurement for the square. Measuring by using the actual boxes is the only way to go, as different weight papers used for the masu boxes will yield different slightly different measurements. There is no purely numeric way to do this. You need to measure using the actual boxes.

Once you have the correctly sized square, the next step is to fold the square into thirds. Not halves, which is easy, but thirds, which is tricky.

Maybe not so tricky, though. After all, your masu box should be right there with you, and the width of the box is a third of the square, so just line up these boxes on the edge of the paper and fold the far edge to them.

Then fold the other edge to the fold you just made and the paper is folded into three equal sections. Yah!

The two outer thirds will be folded in half again…and this is the last of the pictures of the process. The video at the end of this post to show how to make this, from beginning to end. If I make a one-page tutorial on this, it will eventually show up in my blog.

Here’s that box, with another next to it, hidden under two masu boxes.

Lifting up the masu boxes reveals the rectangular tray below. You can stack many rectangular boxes for more surprises.

The video of the making of this box:

## Zhen Xian Bao Post 4: the second layer box

### September 10, 2016

Finally I am getting to writing about he next second box of the Chinese Thread Book/ Zhen Xian Bao.

For the record, here are links to my previous posts on the Zhen Xian Bao, and to my Pinterest board, which contains sources that I’ve studied:

Zhen Xian Bao, Intro & Examining proportions

Starting with the Finished Size

I know exactly why it has taken my so long to write about this second layer of the Zhen Xian Bao. This box is basically a Masu Box, something that I’ve been making for many years, but that I had never gotten the hang of teaching. I didn’t want to make a post until I figured out how to communicate that step that everyone trips up on.

If you have ever tried to teach this structure to someone you know exactly what I’m talking about. Everything goes just swell until it’s time to make the sides. This is the when I lose all my students…BUT! I’m here to say that I have figured out a way of approaching this step in a way that makes way more sense than I ever thought possible.

There are two key changes I’ve made in my demonstration that make all the difference.

First, and don’t roll your eyes and absolutely do not skip this step: I start with making folds that turn my square piece of paper into a 4 x 4 grid.

Second, when I get to this dreaded step,* instead of folding up the two opposite wall of the box *as is suggested in like, every set of directions that exist, *bring together* the two corners that I’ve marked in the photo above.

What happens next is like origami magic. As those points come together, the structure stands up and, with the slightest bit of nudging, three sides are formed at once.

Oh. if you haven’t tried to make or teach this box already, none of this will make sense to you. Which is a good thing, because you may be spared the experience of totally mind numbing self-esteem draining bewilderment.

I haven’t made a tutorial page just yet. That will come later. But here’s a video. Go for it!

## Two Beautiful

### August 28, 2016

The four-year-old children in my summer workshops made numbers so lovely that I had to make an accordion book out of photographs of the numbers. These images are so exquisite that I don’t expect anyone to believe that they were assembled by such young children, so at the end of this post I’ve embedded video links that show, in fast motion, a couple of the numbers being made. You’ll notice that the children created the assemblages without adult interference.

The materials that students used were mostly from my husband’s garden. One particular harvest of beans had been buried in the back of our pantry for too long and dearest was going to throw it into the compost. These, therefore, are rescued beans. I also picked a selection of flowers (marigolds are the best) Some of the students went outside and brought in leaves from the community garden. There was also pasta in the activity boxes in the room, so we used pasta too.

We worked as a group to make the first number. I pondered over whether to start with zero or one, and took to twitter, asking the math community that shows up there what they thought. There was no definitive consensus but seemed to me that there was more said in favor of starting with zero.

I’ve come to a way of thinking about what number to start with. In the course of my five sessions with these students we made or used three different number lines. Each one was different. Our Great Big Number Line went from one to ten. The meandering number line went from zero to 42. This sequence went from zero to 10. Did the children notice the differences? Turns out, yes, they did!… which gave them the opportunity to see that the number line is not a fixed item.

Students worked mostly in pairs of two. It took about 8 to 10 minutes for each number to be made. We did not glue anything down. These assemblages were created to be photographed.

I was a bit worried that these kids would be unhappy about the fact that, as soon as a the picture was taken, the number was undone.

As usual, these kiddos totally surprised me. Dumping the contents of the numbers back into the big bowl was one of their favorite moments!

.My daughter Angela did a great job of photographing this process.

The first thing I did with the photos was, with Photoshop, isolate the numbers from the background, vectorize, then print them up. The next day that I saw these children I showed them the prints and we did a number line clothes line.

I’ve been inspired by Joe Schwartz and Tracy Zager, who have written about facilitating the building of number lines with clothes lines and Post-its, So the first thing we did with our numbers was to hand them out in random order, and have the student estimate where the numbers should be located….

Next stop was Kinko’s to make copies of the numbers on standard sized copy paper, that could be folded into accordion books. I had one problem. I didn’t want to *just* have a line of numbers. I wanted there to be some corresponding items that could be counted, you know, like five *things *associated with the number five. After agonizing over what these things should be I realized that we had already created designs on the backs of the Great Big Number Line, so I recreated, with acceptable accuracy, the students’ designs and made them part of the book.

Now, here’s the little accordion number line book:

What’s great about accordion books is that they have fronts *and* backs. Flipping the book upside down reveals the designs that correspond to the numbers.

Completely opening up the book reveals numbers and images!

I’ll be making a few copies of this book to give to the kindergarten teachers who will have these students in their classes.

Now if you haven’t seen enough images on this project, here are two clips of the children working, in fast-action mode.

Yup, love this project.

## Origami Boats and Meandering Number Line with 4-year olds

### August 24, 2016

Full disclosure: I did not try out teaching 4-year olds how to make origami boats. It’s not that I didn’t want to, or that I chose not to, it was just that there were other things I wanted to do more, and my time with these little ones was limited. Much to my delight, though, after we used the boats in our activity, the children asked me about how they were made. I did a demonstration, with hope that this may encourage an interest in paper-folding.

I chose to use these paper boats because they* stack. *Just for the record, I was curious to see if they floated. Turns out ;Yes! Until the paper absorbs too much water, these vessels are sea worthy. What was more useful for me, though, was that they can stand on their own, so that we could use them as playing pieces for a board game.

During my workshops with these children I noticed that even the most accomplished child in the group could not coordinate counting items with the movement of his hands. In other words, if there was a pile of 8 stones, these children would end up counting inaccurately *because their fingers would move out of sync with the numbers that they were reciting*. I was really interested to see this, partially because I’ve read that there is something about learning to play the piano that helps children be better at math: this now makes sense to me, as playing notes would help train a person to coordinate fingers with intention.

Wanting to try out a simple, and, yes, frugal, made-from-paper activity to encourage accurate counting skills, I worked out a sweet game that the kids seemed to like . What we did mimics classic board games where a die is thrown, and the player advances a certain number of spaces along a line. It was, however, important to me that *I didn’t want to create winners or losers. *This is how it went: the playing pieces were these paper boats, and when two boats land on the same space, they become a team, and stacked together. The point of the game is to get all the boats stacked together as a team before any boat reaches the end of the meandering number line, which, just, for no particular reason other than I ran out of space on my paper, was 42 units long.

Unfortunately, I didn’t get a photo of the kids playing this game, but, they played in groups of three and four, and they seemed to enjoy watching others play as well as playing the game themselves. Counting spaces, counting the dots on the dice, and (especially!) anticipating what throw of the die would yield the desired outcome were all challenging but doable for these kids.

Each of the five sessions that I worked with these students, one-third of my lesson plan was to focused my interpretation of relationship thinking, such as creating patterns from shaped paper, developing finger sense, estimating, discussing what was the same and different about shapes and flowers, and this unit counting game.

Other parts of my time of my time with these kids was artful numbers, which I what my next and last post about my time with these students will be about.

I had to learn how to make these origami boats for this project. I looked many different models, but this one that I’ve shown I found most enchanting. I put together a video of it, that is worth watching because there’s some pointers included that I just can’t fit onto a tutorial page.

Happy boating.