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.

Addendum #2: here’s the link to the final post of this project https://bookzoompa.wordpress.com/2017/04/30/fancy-plane-shapes/

 

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