Saturday, November 21, 2015

Beaded Cube Math Lesson for Kids

Several people have asked me to write a math lesson for kids using beading. The challenge is to make something mathematically interesting with bead weaving that can be completed within a single lesson, under an hour, preferably less.

So I wrote this lesson on beaded cubes (PDF). The lesson begins with some background on what a beaded cube is with lots of drawings and a photo. It uses terms like edge, face, vertex, and graph of a cube. The second section gives step-by-step instructions for how to bead weave a cube with a needle, string, and pony beads. After finishing this lesson, students will have practiced basic sewing skills like measuring thread, threading a needle, and tying square knots. The final section provides several math and spatial reasoning "challenges" to extend learners' thinking about beaded cubes.

This lesson teaches several things, especially spatial reasoning, where the learner has to move back and forth between a 2D representation on paper to the 3D model in their hands. It also teaches the importance of carefully following instructions because every step is laid out, and if you skip one of them, your work won't look like what is on the paper. The challenges encourage students to build different symmetric coloring of a cube, extend the construction to a row of cubes, and think about a minimal thread path.

I taught this lesson at the Julia Robinson Math Festival and another version at MoMath. With just 12 beads, this task is not easy, but it is enticing, approachable, and engaging for children, especially girls, and boys like it too, as do their moms and dads. It seems appropriate for children as young as fourth grade, and most of them generally need a good amount of help, but they can do it with coaching. Fifth and six graders have a bit easier time with it.  Interestingly enough, my experience in teaching this lesson to adults and children is that it is not any easier for a typical adult than it is for a typical fifth or sixth grader. In fact, I watched one man get completely lapped by his fifth grade daughter today. GO GIRL MATH POWER!

Here are the materials you need to teach a group of kids:
Pony beads
Size 18 tapestry needles, one per student
String: Cotton is good.  Something thin enough to fit through the eye of the needle, but thick enough to provide some friction.
Magnetic pin cushion: an easy way to collect the needles
Snips or scissors: I tied them to the end of some crazy yarn so they wouldn't disappear.
Beaded samples
Cups or bowls to hold beads
Hand outs: I designed the PDF file to be printed once, and then photocopied onto two sides of a sheet of paper, with one sheet per student.  Print the PDF file for best quality, not the jpgs.

I encourage you to try this lesson with your own students or children. If you have anything meaningful to contribute to making it better, please do not hesitate to send me an email or leave a comment below. If you want to see what else you can do with beaded cubes, you should search for my blog for CRAW or "cubic right angle weave" because a beaded cube forms the basic unit of one of my favorite bead weaving stitches.  Also search Planet Bead to see the many beautiful things that have been beaded with cubes.

If you think this lesson is useful, consider showing your support by perusing my Etsy shop, gwenbeads and buying yourself a little something special. You deserve it.

Thanks for looking. You're awesome. Yes, you!

Edited to add: Emilie Pritchard suggests using long plastic beads, called "spaghetti" beads, to help visualize the edges of the cube. Search the internet to find the for sale.

Thursday, November 12, 2015

New Tutorial - Cellini Flowers and Leaves Beaded with Peyote Stitch

I'm pretty excited about my newest tutorial, Cellini Flowers and Leaves.  With these instructions, you can learn to make earrings and a pendant with sparkling leaves and flowers. Cellini Flowers and Leaves are my original variations on beaded Cellini spiral, combining peyote and herringbone stitches.
Cellini Stitch Spiral
Beading leaves is fast, fun, and easier than it looks. After you master leaves in two sizes, try a flower and a branch, and assemble everything into a cascading corsage pendant. Then bead earrings. And if you still want more, try the large flower beaded bead shown below. Aside from an 8 mm round bead in the small flower, everything is stitched with regular Japanese seed beads, using only a gram or two of each color. So if you collect seed beads, you probably already have everything you need. There's no need to buy more beads; just get right to beading!

Cellini Stitch Spiral
This project is suitable for advanced beginning beaders who want to learn more about peyote and herringbone stitches. For you designer types, the pattern ends with drawings to inspire you to create your own beaded jewelry compositions with Cellini Flowers and Leaves. With so many different designs in one pattern, you could combine the techniques to make your own designs for pendants, bracelets and elaborate necklaces.

Cellini Flowers and Leaves is my third tutorial using the Cellini beading technique, and it won't be the last! The first was Slugs in Love. This is a new Slugfest kit with matching earrings that I assembled. 
Slugs in Love
 I still have a couple kits left before they are all sold out.
Slugs in Love
The second was Snail Shells and Twisty Bits. With this tutorial, you can make a bangle bracelet like this.
Cellini Spiral Stitch
You can also make necklaces and doughnuts like these...
Cellini Beaded Spiral
... as well as pendants in various sizes, like these.
Cellini Spiral Peyote Stitch
And this example shows how Twisty Bits work seamlessly with classic tubular Cellini spiral stitch.
Cellini Spiral Peyote Stitch
As always, thanks for looking.

Thursday, November 5, 2015

Baroque Cube Earrings

Sometimes I like very simple jewelry, like this pair of silver earrings with a touch of blue.  The limited color scheme makes them easy to wear with lots of different outfits. 
Beaded Bead Earrings
I call this design the Baroque Cube. They are mini beaded beads made with peyote stitch.
Beaded Bead Earrings 
Do you want them?  This pair is for sale.
Do you want to make your own?  The Baroque Cube Tutorial is available.

Friday, October 30, 2015

Octahedral Cluster

This is a recent example of one of my all time favorite beaded bead designs, the Octahedral Cluster. Octahedral Clusters all have six stars, like the 6 faces of a cube.  In the beaded bead below, I colored two of the stars silver.

I colored two of the stars black and two of them gold.  Each pair lies on opposite faces.
The points of the stars come together three at a time, one star of each color. There are 8 places on the beaded bead that look just like this.  Four of them are identical, and the other four are mirror images of this.
The beaded bead has the symmetry of an octahedron, which is the same as the symmetry of a cube. Knowing this, you might wonder if this beaded bead is really an octahedron, as I told you, or maybe, it is really a cube. If we look at the largest beads (in green), there are 12 of them.
That could be useful because cubes have 12 edges, but so do octahedrons. In fact, the holes are line segments.  So if you look at the holes of the largest beads, and you extend those lines so that the lines intersect, you will form the 12 edges of an octahedron.  For that reason, I think it is an octahedron, and that is why I call it an Octahedral Cluster.

Here you can see how big it is.
Do you want it?  This beaded bead is for sale.
Do you want to make your own?  The tutorial for the Cube and Octahedral Clusters is available. If you make one of each, then you will really see the difference.

Tuesday, October 27, 2015

Slugs in Love Earrings

Here's a new pair of earrings, Slugs in Love.
Slugs in Love Earrings
I made them using peyote stitch with increases and Cellini Spiral.

Slugs in Love Earrings

Do you want them?  This pair is for sale.
Do you want to make your own?  The Slugs in Love Tutorial is available.
Do you want to learn more about Slugs in Love?  Read my blog post on Slugs in Love.

Thursday, October 22, 2015

Pixel Painting 4 - Tom Davis Cellular Automata

This painting is the fourth large piece in my series of painting using cellular automata on a staggered grid.
Cellular Automata Art
Here you can see the four that I have finished so far. I hope you can some sense the range of designs that are possible using this technique.
Cellular Automata Art

In this series, I am trying to achieve a sense of rhythm, repetition, order and chaos. I like cellular automata because the designs are a balance between organic and geometric.

Each pixel has many layers of paint, making the colors rich and complex. The colors are were inspired by Pantone and Benjamin Moore Color Trends for 2015. Prominently featured are Marsala and Guilford Green. So, if your interior decoration is contemporary, this painting will match the couch. Thirty years from now, when we look back on the two-thousand and teens, these are the colors we will think of, you know, in the same way when you think of the 1970s, you think of avocado green, mustard, and dull orange.
Cellular Automata Art
I named this piece after mathematician Tom Davis, who was likely the first person to discover the rule set I used to design this piece (after I told him where to look). Tom's assistance on my work with cellular automata has been invaluable to me.

20" by 30", unframed. The sides are painted black so it doesn't need a frame.

Signed and dated. I sealed it with three coats of acrylic clear coat to make it a little shiny and protect it from scratches. Looks nice. Want it?  It's for sale here: Pixel Painting 4.

Friday, October 16, 2015

Pixel Painting 3 - Hanging Baskets Cellular Automata

This is an acrylic painting from my new series "Pixel Paintings." In this series, I explore the designs created with cellular automata. This painting is the third large piece in the series.

Cellular Automata Art
In this series, I am trying to achieve a sense of rhythm, repetition, order and chaos. I hope to create a balance between organic and geometric.

Cellular Automata Art
Each pixel has many layers of paint, making the colors rich and complex. The colors are mostly blue, purple and gray with a variety of pinks and burgundies. Here's a close up. 
Cellular Automata Art
20" by 30", unframed. Signed and dated. I sealed it with three coats of acrylic clear coat to make it a little shiny and protect it from scratches. The sides are painted black so it doesn't need a frame. This painting is SOLD.

Have a great weekend. Thanks for looking.
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