Art and Math · design · Geometric Drawings

Copy, Rotate, Reflect and add eggs

In the middle of my arts-in-ed season I’ve kept trying to find time to mess around, trying to make beautiful images.

Today I started a wonderful, week-long math activity folder project with four classes of kindergarten students, am barely able to stay awake right now, but I’ve been wanting to at least throw these  images into my blog here.

I started doing this some time before Easter. Just wanted to make something. Started with a graph that I was able to reduce to just these few lines:

https://www.desmos.com/calculator/gqt97ui6ha

Then I copied, rotated and reflected these lines and came up with a nice tiled surface.

I honestly just loved this image. Parts of it I expected, other parts came as a surprise.

https://twitter.com/PaulaKrieg/status/1117260203421052928

Spent lots of time coloring it in. Mostly used watercolor brushes, SAI Japanese Traditional Colors, but also used some colored pencils.

When it was done, I didn’t much care for the finished result.

It was okay, but didn’t make me as happy as I would have liked.

But then I started playing with it. Put it into Photoshop, isolated squares….

 

…then did some copying, rotating and reflecting…

I kept coming up with all sorts of stuff that surprised me.

 

I kept trying out different combinations…

… and then because Easter was on my mind I started wondering if I could map these on to eggs in Illustrator.

Turns out the answer was yes.

 

These were so fun to do.

I liked how the watercolor translated so well in to the digital environment.

Was very surprised that I ended up with these eggs. But very happy.

OK, that’s it for now. Gotta get ready for tomorrow with kindergarten!

 

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About Halfway There

Equivalent Fractions
Equivalent Fractions

I’ve been interested in creating fractions projects for kids exactly as long as I’ve been working with children in schools (decades). This year, after enjoying,messing around with a hexagon/golden ratio project I wondered if I could modify the idea of using scaled hexagons to help fourth graders make better sense of fractions. My first attempt at this didn’t work out so well.

Making 1, or 100%
Making 1, or 100% out of two halves

I gave students hexagons that were scaled to 1, one-half, a third, a fourth, a fifth, a sixth, an eighth, a tenth, and twelfths. The task was to pair and arrange them so they would span the length of a whole, aka 100% across.

1/3 + 1/6 + 1/6 + 1/3 = 1
1/3 + 1/6 + 1/6 + 1/3 = 1

The project went okay, but it just didn’t snap for me.

I’ve been thinking about how to improve this project. Today I had a chance to work with a small group of kids. I tried a new approach that worked so much better. What was especially great was that it included making a simple book. Yay!

Fractions for a Book
Fractions for a Book

I started kids off with a hexagon that was labeled 1/2. I explained about how the lengths we would be looking at would be the horizontal or vertical length of the hexagon (I didn’t use these words, rather gestured what I meant). Then we layered the hexagon with equivalencies. Here you can see two 1/12ths equals 1/6, three 1/6ths equals 1/2, and 1/6th and two 1/12ths equals 1/3.

Equivalent Fractions
Equivalent Fractions

Nice, right? Snap!

The books we made were just two sheets of paper folded in half, bound with yarn using a modified pamphlet stitch. 

Equivalent Fractions Book
Equivalent Fractions Book

What’s great about using hexagons for this project is that you can still see the labels of the lower layers as the equivalencies are built up. The adults in the room had a bit of trouble with accepting that the hexagons were scaled (similar) versions of each other, but the kids had no problem with it. This reinforces my notion that children have a better intuitive understanding of scale than do adults.

This is the way I explain the scaling to adults: We all know what half a candy bar looks like. That’s one way of thinking of one-half. But when we say a child is half the size of the parent, we don’t envision the child to be half a parent, like they were half a candy bar. Instead, we envision them smaller than the parent in their height as well as width.  This explanation seems to work.

The bullseye view of fractions
The bullseye view of fractions

After doing a bunch of equivalencies, this child decided to nest her fractions.

Okay then. Here, what’s obvious is the hierarchy of the hexagons that are scaled by fractions. Nice!

This project can use a bit more refinement, but this is as far as I’m going with it right now.

I’m including PDF of the hexagons. The labeling includes the colors of the paper I use for printing.  Yeah, it’s lots of files. Welcome to my life.

hexagon-10ths-yellow

hexagon halves blue

hexagon sixths halve grape

hexagon 3rds 12ths chartreusegreen

hexagon 4ths orange

hexagon 5ths 8ths pink

hexagon 6ths halves grape

zhexagon 12ths full page chartreuse

2 pieces to make 12 inch hexagon

12 inch hexagon

Notes about hexagons