Fancy Plane Shapes

April 30, 2017

Second Graders are learning their shapes. What a great age to be composing, decomposing and recomposing.

Bird on the left, hexagon & rectangle on the right

Bird on the left, hexagon & rectangle on the right

These images are the final part of the Wallet+Book project that I began with about 66 students earlier this week. After making images that had a value of 100 we moved on to getting up-close and intimate with parallelograms and trapezoids.

Students got strips of these parallelograms, which I had printed on five different colored papers. We looked at the parallelograms and noticed that they were made of two triangles. After separating a triangle, we fit next to a full parallelogram, to see how the two shapes, together, could make a trapezoid.

Triangle plus parallelogram makes a trapezoid

Triangle plus parallelogram makes a trapezoid

The kids seemed delighted by this discovery. While most students illustrated this connection with three different images…

Three shapes on one

Three shapes on one

…there was one student who took an elegant approach, which was to make just one shape, then label the way it could be broken down into its parts.

Hexagon, rectangles and star

Hexagon, rectangles and star

Next we moved on to hexagons, rectangles, then, finally, a shape of their own choosing. The kids loved noticing how three parallelograms not only are the parts of a hexagon, but also, that their hexagon has the appearance of a cube drawn in perspective. The toughest shape for the students to make was the rectangle, as this meant that they had to divide a triangle in half, the rotate and reflect the pieces. Not so easy. Try it.

Designing

Designing

After making the compulsory curriculum shapes the kids went free-form, designing their own creations. My seventy minutes time slot with each class of 22 students just flew by!

Whale on the water, spouting

Whale on the water, spouting

Some students made abstractions with the shapes, others created scenes or something recognizable.

Playing with shapes

Playing with shapes

Since this was the first time I was doing this project in the classroom, and since I had three classes to work with, I kept changing how I presented the project, getting a better feel each time for better ways to get the kids to interact with the shapes within the time frame I had with them, and within the agenda that needed to be addressed. For each class, though, I kept the curriculum piece at the beginning of my time with the students, ending the class the creative part. I think I’d like to see what happens if I flip that order of working, as perhaps it will let students discover on their own things that I actively try to get them to see.

 

Pieces in pockets of Wallet-Book

Pieces in pockets of Wallet-Book

When we finished, any extra parallelograms were stored in the origami pocket we had made during out last session, looped a humongous rubber band into a hole punched into the front flap, created and ID card for the front, and added some bling, because, well, bling.

wallet-books

wallet-books

The Wallet-folders, by the way, are made from heavy weight 11″ x 17″ paper that has a four-inch fold along the bottom edge, which creates the pockets. There are two 7-inch wide pockets within, and a 3-inch fold-over flap. If you are wondering where I got this awesome paper that is tinted with black, blue, and silver, with a light cast of gold above, well, thank you for wondering. I spray painted the papers (outside, of course, with a mask on) so I could have exactly what I wanted. Yeah, a bit crazy, but that’s what I do.

Making Books with Money

April 27, 2017

Flower

Flower

Oh my gosh, working with second grade students is so rich.

They have skills, they are enthusiastic and uninhibited, and tapping into their learning curve is delightful.

Windshield, with George in the driver's seat

Windshield, with George in the driver’s seat

I’m working with three sections with about 22 students per class, so I’m getting to see about 66 different ways that students are making sense of the 100 cents project that I described in my last post. (oh, there’s an unintended pun in that last sentence, did you get it?

Abstract design

Abstract design

Short recap: students were given images of coins, which added up to $3.00, from which they chose $1.00, or 100 cents, worth of coins to create a design.

These students hadn’t started studying money yet, which was fine. Most students seemed to understand how much coins were worth, though certainly a few students had no idea about the value of coins.

It was fun, when adding up the value of nickels, to say, Now you know why it comes in handy to count by fives.

Person

Person

Making the wallet-book to house the 100 cent images, then making the images was what we got done on the first day. Separating out 100 cents was certainly the most challenging part of the project. The designs flowed freely.

Bug

Bug

Day 2 was a bit more challenging, but I think that the toughest part was just communicating to them what I was looking for, which was for the students to make matching arrays of the coins that they used in their designs, then providing the equation which showed that the value of the coins equal 100.

Aiirplane

airplane

Turns out that this array-making uncovered a few mistakes. For instance the airplane pictures above was five cents short, so he added a nickel on to the bottom and all was well.

Person in landscape

Person in landscape

There was a wide range of simplicity to complication of images.

Flower

Flower

If students didn’t have enough coins of a certain value left from their original 300 cent to making the matching array, they would exchange change with another student, at least that was the plan, which worked fairly well. I did bring lots of extra coins, for moments when it seemed better just to hand students what they needed.

Still, everyone should have had 100 cents left over. These coins got glued on to a pocket of their wallet book, along with a statement of the value of these coins.  That little black folder that contains the 100 cent image now has an enlarged section of a colorful buck glued on to the front. After all that figuring and adding, it was great to end yesterday’s class with some playful coloring in.

Okay, one more day with these students. The next piece that goes into the wallet-book has to do with combining shapes to make other shapes, much in the same way that we combined values of coins to make other values.

The most joyful moments during these days is having this opportunity to be a part of these early moments of learning about addition. When students say that they can’t get their numbers to add up to 100, though they know that they do, I can sit with them and help them sort out what’s going on. It’s so illuminating for me hear them tell me what they’ve done, and then to help them see another way of interacting with the numbers.

Addendum: as soon as this post went up the generous and brilliant connector-of-all -things-math offered me this link to some other coin projects http://mathhombre.blogspot.com/2009/08/money-games.html

Simply awesome.

 

100 Cent House

100 Cent House

Tomorrow I will be starting a new project with second graders. Counting money is part of their curriculum, so both the math specialist and teachers liked the idea of addressing money in our book making project. This is a first for me. I’ve never even thought about folding money concepts into bookmaking.

One Hundred Cent flower design

One Hundred Cent flower design

I let my thinking about this be inspired by the idea of the Hundred-Face challenge that Simon Gregg and Malke Rosenfeld have written about, in which students use Cuisenaire Rods to make silly fun faces that have the added value of adding up to 100 (depending on its length, each rod has a value 1 – 10).  Okay, great! We can make designs that out of images of quarters, dimes, nickles and pennies!

I created sheets of coins, being mindful that the coins were the actual size of their reality counterparts.

a Mess of

a Mess of “coins”

The idea will be to count out one dollar worth of coins, then take that mess,

100 Cent Kid

100 Cent Kid

and make something, anything. Could be a pleasing abstract arrangement, could be a face, a person, a rocket ship, letters, but it must add up to one dollar. Then make arrays with coins to make them easy to count.  Since we’re dealing with money, my thought was to make a….

Wallet Book

Wallet Book

…Wallet Book! Put an ID card on the front, a closure, a little bling…

Inside the Wallet Book

Inside the Wallet Book

… and pockets on the inside. There are two folders in the pockets here, the one I’ve written about, and another one that is about shapes, which I will write about at another time.

Something else about this 100 cent folder: its cover is a blow up of a dollar bill. This will be a nice lead-in to talking about a bit of history of printing, that before things were printed in color, making black engravings then coloring them in by hand was all the rage. Here’s a hand-colored hummingbird from Getty Images of a hand painted engravings:

Hand-colored engraving from the Getty Collection

Hand-colored engraving from the Getty Images

Now here’s my hand-colored dollar, which the second graders, as they color their own, will get to know closely.

Hand-colored Engraving

Hand-colored Engraving

Why not? I mean, when else will they be able to color in a dollar? Or course it’s an enlarged copy of just a portion of a dollar bill, so there’s no temptation to try to use it as lunch money.

There’s been many pieces to get together for this project.Here’s the PDF of the coins and the image of the dollar. They are black and white files, which I printed on colored paper.

Now here’s the video that I made of this part of the project, which I hope to show to the classes tomorrow. My thought is that if it’s possible for them to view this on the Smart Boards in the classroom that it will be easier for the students to see. We’ll see how that goes. I’m looking forward to seeing the designs that kids come up with, and wondering how hard this will be for them.

Book, peeking out of its box by Paula Beardell Krieg

Book, peeking out of its box

When Miriam Schaer was assembling her teaching collection to send to Telavi University in the Republic of Georgia, I very much wanted to contribute, but nothing I had on hand seemed right. In the nick of time, some thoughts came colliding together. Polygon Fractal book by Paula Beardell Krieg

This structure started out with an exploration of a shape which I wrote about a few weeks ago after watching family math video made by the Lawlers.

Inside Outside Book by Paula Beardell KriegThe book  opens in an accordion-like fashion, but front and back are structurally different.

Polygon Fractal book by Paula Beardell KriegThe colorful pages rotate open to create these double layered corners. The polygon fractals on the pages here are harvested from Dan Anderson’s openprocessing page then toyed with in Photoshop.

To see the fractals in their full radiant radial symmetry one must rotate the book. There are six completely different images to be seen. But it gets more interesting, because there is a whole other side to see.

The folds of those double layered corners completely reverse to form a cube!

You can’t imagine how excited I was when I saw this cube emerge from the folds!

This folded structure totally suggested that, whatever I use on it, that it be about the dual nature of….something….a suitcase (no, too obvious), a politician’s statements (ugh, too boring)…actually wanted to use images that didn’t imply any hierarchy, hiding, agendas, or judgement about contrasting inner and outer manifestations.

It was this thinking, about duality but equality of visuals, which led me to using Dan’s code along with the polygon fractals that it creates. So perfect. Code and images are perfectly linked, simply completely different ways of seeing the same thing. You know, like Blonde Brunette Redhead 

Now, I do have a lingering unresolved issue with this book. I’m not thrilled with the paper that I’ve used. It’s 32lb Finch Fine Color Copy paper. It takes color beautifully, folds well, but I’m thinking that the folds might be more prone to tearing than is comfortable. Not sure what else to use…am open for suggestions. Miriam’s copy has been shipped, but I’m still happy to check out different papers to use.

I can’t help but wonder if people will be able to figure the transformation of these  pages without seeing this post or reading the brief explanation I’ve provided on the back page of the book? Dunno.

Oh, and here’s my favorite variation:

Hanging a tea light from a pencil so I can see the inside and outside at the same time.

Happy.

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