Using Yarn Crafts as a Math Teaching Tool

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With 5 colors of yarn and a 5-round crochet motif, how many unique arrangements can you make? Annie Perkins knows, and she has the blanket to prove it.

Above: Permutations Blanket by Annie Perkins. All images courtesy of Annie Perkins.

The Permutations Crochet Blanket

When she wasn’t crocheting classroom models, Annie began crocheting baby blankets and other gifts for friends. Early in the pandemic, she decided it was time to make a blanket for herself. Of course, this wouldn’t be just any blanket.

Permutations are simply the various ways a number of things can be arranged. Annie knew that 5 colors used in a 5-round crochet motif would yield a maximum of 120 different permutations. That meant a blanket with 12 rows of 10 blocks each, with every block unique.

Annie wanted a block with the circle-in-a-square look, and she found a tutorial on YouTube for a Sunburst Granny Square made with 5 rounds instead of the usual 4. Each block measured just under 5″ square before joining. Assembling the blocks using the continuous join as you go method (found in another YouTube video) would add a sixth round to each block. She chose to use the darkest of her 5 colors for this round, giving the entire blanket a sense of continuity it may otherwise have lacked.

Planning and Keeping Track

Annie developed a simple system of assigning a letter for each color, then wrote out all 120 crochet permutations in her notebook. Knowing the bright turquoise would pop against the blues and purples, and wanting to make sure it was evenly distributed throughout the blanket, she used a green dot instead of a letter for this color. Then she started crocheting, checking off each block as it was completed.

It took more than a year, but the day finally arrived when all the blocks were joined, and the blanket was complete. The finished blanket measures about 64″ x 52″.

Other Possibilities . . .

Annie and I discussed ways crocheters and knitters could riff on the permutations theme. Here are some ideas:

• 3 colors in a 3-round block would make 6 permutations. Probably too small for a blanket, but perhaps useful for smaller projects.
• 4 colors in a 4-round block would yield 24 permutations. That means a rectangle 4 blocks wide by 6 blocks long. Annie has also heard about someone who made the set of 24 permutations, then duplicated one for a total of 25 blocks. She assembled these into a blanket 5 blocks wide and 5 blocks long. Her family makes a game of finding the duplicate!
• Knitters can get in on the action using striped mitered squares, or log cabin blocks, or simple striped blocks.

What’s Next for Annie Perkins?

As she settles into her new job, Annie is always looking for new ways to use crochet and other media to make math tangible. In the meantime, she has several friends who are expecting, so you’ll find her crocheting baby blankets. You can follow Annie’s adventures in math, art and crochet on Instagram.

How has crochet impacted your understanding of math? Let us know in the comments!

Sandi Rosner
Technical Content Editor, Yarn

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