Seeing Differently, Teaching Differently

I don’t understand  why certain of my projects with kids get more attention than others. My original post about Sight Word Pockets Book for Kindergarteners  from 2011 still gets viewed every day. My teaching season doesn’t go by without requests for this project. By now I have taught literally thousands of young students how to make origami pockets, but it’s never easy. I’m always looking for a better way to explain this folding method.

A tilted square is still a square

I’ve come into this teaching season thinking differently about folding paper.

For so many years I have been telling students what to do. This year I have prioritized trying to draw their attention towards what to see.

They all recognize a square, but when I tilt it, students say its a diamond, a rhombus, or a kite. Last week I suggested to students that this shape was still a square, then I was relieved when a  classroom teacher chimed in and emphasized that tilt or no tilt, the shape was still a square. The main thing, though, is that this simple rotation and the conversation riveted students’ attention to the shape.

Folding a square point to point, from the top down

I’ve been asking students what happens to the square if I fold it corner to corner. They all seem to be able to predict that folding a square point-to-point can make a triangle. This makes them happy. They seem to like triangles. Then I tell them that with just one fold more I can make many more triangles. What magic can this be? I have their full attention. They are watching to see if this can possibly be true.

Folding just one layer of paper, I fold the tip of the triangle down to the base. The children are delighted. We count the triangles. Are there four triangles? Are there five?

The next step is the tricky step but now students are attached to the shapes that the folds make and have a heightened awareness of triangles. When I talk about tucking the edge of one of the triangles under the flap, they see what I mean. Here, look at this video. It absolutely blows me aware that this five-year-old just learned this folding sequence about a half-hour before I filmed her doing it. Notice how sure her hands are as they move through the steps.

This change in my teaching, prioritizing seeing & predicting over telling & doing feels really good.  It’s happening because I’ve begun to be able to answer a question I’ve been carrying around in my mind for years: I’ve really looked hard at origami , trying to figure out what about it compels some people say that origami is somehow like math.

Now I’m coming to understand that it isn’t origami that I needed to see differently, it’s been my understanding of math that I needed to adjust before I could make the connection. Now that I am seeing math less as addition and subtraction, and more as relationships and transformations, the boundary between origami and math vaporizes.

More and more I am trying  to be  attuned to childrens’ seemingly intuitive connection to ideas that are aligned to a broader understanding math, and I am able to tap into this with great results. I help them see what is already familiar to them, and what happens next is that they better understanding what’s going on, and can figure out what to do next. Yes, even five-year-olds can do this.

 

Endless Accordion

I’m once again revisiting accordions and number lines, because they are both  infinity fun. What I’ve attempted to do here is to create a classroom friendly accordion book whose pages are pockets which can contain changing content, in this case a variety of number lines.

What makes this project classroom friendly is that it is designed to be used with a ubiquitous material: standard sized, standard weight copy paper. It requires a few simple folds, and very few materials. I’ve made templates that can be printed out, but lacking the resource of a copy machine, this can all be easily constructed without my templates.

Endless accordion with pockets.

The accordion is made from units of full-size sheets of paper, folded, then attached together. For the basic number line I recommend using 6 papers, which will result in 12 pockets. Since zero through 10 needs 11 pockets, the extra pocket at the end conveniently implies “dot dot dot …. on and on …to be continued. ”

The shows where the fold lines occur.

A full sheet of 8.5″ x 11″ (or A4) is folded so it ends up looking like the picture below:

Two pockets from one sheet of paper

The tabs at the side are there to create an attachment surface for other the next pockets.

Attaching pockets together

The tabs of adjoining papers can be attached with glue, tape, sewing, paper fasteners, staples or paper clips. I ch0ose paper clips.

One piece of paper, folded, has room for four numbers

The cards with the numbers are also made from sheets of uncut, folded paper. They are folded so that they are just a bit narrower than the pockets.  Once they’ve been folded they can be glued (or taped etc) shut but I don’t bother doing this, as they seem to stay together just fine without gluing.

Counting by 10’s

One set of numbers can make four different number lines.

Counting by ones

I’m providing links to PDF’s. There’s a PDF for the pocket, which I recommend that you make 6 copies of. This template is in black and white only. I hand colored in the dividing lines.

As for the numbers, I have one full color PDF here, and one that has the black and white outlines of the numbers if you prefer to let have your students color in the numbers themselves. At the moment I only have files for paper measured in inches, but in the next day or two I will update with A4 versions as well.

template for pocket

PDF 8.5 x 11 for accordion pockets lines

Numbers in color

PDF 8.5 x 11 accordion number line, colored numbers

Number to color in yourselves

PDF  8.5 x 1 blank numbers number line for accordion pockets

If you’re interested I’ve posted something about my interest in the number line on my Google+ page https://goo.gl/ScI0nZ

I would love to hear from anyone who constructs this project with a class!

Silly Easy Fast Paper Puppets

Puppet in Progress

I recently taught a workshop in which I was given a good bit of latitude in what I presented. I decided that I would bring a selection of my some of my personal favorite structures, and give people choices of what to make. It was one of the most fun afternoons I’ve had.  This sweet little puppet is another one of those structures that I have forever been wanting to write about, and it was one of the hits of the workshop. It truly takes about one minute to construct. Here’s the tutorial page for it:

Silly Easy Fast Puppet tutorial by Paula Beardell Krieg

The beauty of this structure is that it can be made out of just about any size and proportion of paper. I generally use regular size copy paper, but anything works. It might be hard to tell from these photos, but the mouth of the puppet articulates, and opens in a wide and humorous. way. The workshop participants decorated their creations with all sorts of bits of this and that .

The next photo is a of a puppet that looks it might have much to say. I find myself wishing that there were words on the paper that is cascading out of the mouth.

 

And here are a couple more of my own puppets. I will be teaching  this again at a workshop in the fall, in Waverly, Pennsylvania, so I am going to try to put together a little tribe of these funny faces.

crayon and cut paper decorations on the puppets

Again, the magic of these is the when the mouth open and closes. It’s such a surprise to be able to put together such a whimsical creature so quickly.  If you try this out, please email me a photo!

The Simple Pop-up House, decorated

The Simple House Pop-Up

My last post (if you learn and teach only one pop-up, let it be this one!) provided a page on how to make this pop-up. The goal of this post  is to show off some of the ways that this cut-and-fold shape can be embellished. All the the work shown below is done by kindergarten students.  The card above is the one that I present to students before they get to work. After introducing the project we have a discussion about other ways to interpret the shape. There’s never any shortage of ideas.

Pop-up Bridge

Here’s the pop-up as a bridge, no doubt one of those great bridges going over the Hudson river.

Then there’s the Rocket Ship interpretation….

…as well as other ideas about flying.

This butterfly in the pop-up house is a bit hard to see, but I really love the writing that this kindergarten artist added to her work.

Here are a couple of ingenious young Jedis who have realized that their pop-ups are completely functional arm shields.

Here’s the house as a crown. One thing that might be interesting (or annoying, depending on your mind-set) to note is that it’s likely you would be right if you tried to guess the gender of each of the children whose work I’m showcasing.

Lot of energy here! This child is quite an active kid, and all that movement got focused into this card.

I’m not quite sure how the pop-up inspired this dinosaur drawing…though I do see that the scales on the dino’s back echo the cut shape. Whatever…it works for me.

Of course, many students make home sweet home, often with mom, dad, siblings and a cat. Then there are the barn and cows interpretations, sometimes the shape becomes a pencil or a dog house, a bee hive, or an ocean wave.

One thing to keep in mind when teaching students is that somewhere along the line in school they will be faced with learning about lines of symmetry. Pop-ups like this one are a great hands-on activity to teach the concept of lines of symmetry.

My last post featured the colored tutorial page for this structure. Here’ s the same page, uncolored:

Black and White Simple House Pop-up by Paula Beardell Krieg

Hopefully you’ll color this one in yourself.

If you are interested here are links to a couple more of my posts about pop-ups:

A Nod to Making Pop-Ups   Giving you the World