October 23, 2014
I like the number line.
The number line is all about relationships: I can look at the number line and actually see and measure the chasm between two quantities, even when, as in the case of negatives, those quantities don’t even exist.
As an adult I’ve realized that I had some misconceptions about the number line, and I have discovered subtleties about it that surprise me.
I’ve been toying with number lines for quite a while. In my opinion the number line needs to be toyed with. The images that I see of it are not captivating. I’m wanting to rigorously play with this arrangement of symbols in way that captures some of its nuances. I intend to try to investigate numerous bookish solutions which means that I suspect that this topic will keep coming up. I hope this will be an ongoing bookmaking/discovery journey. I’m not sure exactly where I will be going with this.
But I do know that a few nights ago , after a disappointing evening of cutting and folding, a way of proceeding finally presented itself, but I was too tired to grab hold of it. The inspiration teased me all night, and before 7 am the next morning I was tending the coffee pot while working out my construction. I’m very pleased with how this particular structure worked out. It was so unexpected and delightful that I am excited to be sharing it.
It’s built from envelopes, the kind we think of as regular envelopes, though, technically, they are called “No. 6 3/4” envelopes.
Here’s are some of the things I like about this piece:
- it’s a zig-zag
- it has pockets
- it scales
- the structure suggests infinity since it can keep going in either direction
- it can fold up into a polite accordion-like book.
The pockets are the most distinguishing feature of this number line. These pockets hold cards, which are printed with different sets, or sequences of numbers. This means that the labeling, or the scaling, of the line is always in flux, subject to the whims of whichever algorithm that’s called for.
That’s the crux of it: the flux.
As students proceed through their grasp of numbers, the labeling of the number line constantly changes in scale as needed. Eventually the number gets integrated into the coordinate plane, and becomes the x-axis. I remember seeing the little graphs in math books, and I thought that when I got to grown-up math that the lines would get longer. It never occurred to me that it would be the scale that changed, not the size of the line.
You can see that there’s intermediate markings between the numbers. These can be interpreted differently depending on which scale is being used. For instance, when counting by tens, the small lines can be counted as ones, when the number line is increasing by one’s, the intermediate lines become tenths. In my mind, the point of doing this is to drive home the concept that the very same line can morph into whatever one needs it to be for the visuals of the relationship at hand. The maker becomes the master of the line.
Then the maker gets to fold up the number line into this accordion-like square. Just my style.
Over the next few days I will be working on designing a set of instructions on how to put this line together. It’s likely, however, that if you picked up some envelopes you ‘d figure this out for yourself.
Addendum Here’s the link to the tutorial: https://bookzoompa.wordpress.com/2014/11/03/the-envelope-number-line-tutorial/
April 9, 2014
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.
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.
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.
March 14, 2013
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.
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.
March 4, 2013
Announcing a new page on my sidebar: Gallery of Student Work .
Now, here’s the back story.
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.
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: https://bookzoompa.wordpress.com/gallery-of-student-work/ 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.