This! Is exactly what I do!
I'm the head of the Outreach Committee at my fiber arts guild (as well as being vice president) and while we ALSO do demonstrations at historical events, my focus has been bringing in the connections between Fiber Arts and STEM subjects, ESPECIALLY at schools!
Last spring, for example, a nearby middle school had a STEM day and invited us, so I went to the school and set up a display of various Fiber Arts tools and materials, all of which I could use, and a prompt by each one explaining how it uses math or relates to science or whatever, with notes/script I had written out for myself to explain how each one is connected. (The pictures I've included are from the same setup at a different event; I'm not putting up pictures with middle schoolers in them and I didn't catch any before/after.) I had:
A display of silk in different forms ("hankies" or unspun stretched out cocoons, handspun yarn from hankies, rough spun yarn from leftovers, beautiful slippery shiny reeled-and-thrown yarn) and a story about how sick silkworms led to research by Agostino Bassi and his very early work on the Germ Theory, who inspired Louis Pasteur, who inspired Joseph Lister (Science, particularly medical science)
An 8-shaft table loom, with a set of simple punch cards showing how a Jacquard loom would work, and how those punch cards inspired Charles Babbage and Ada Lovelace and how the more complex punch cards were widely used right up through the 60's and 70's (Technology)
A spinning wheel, with a mark on one side of the large wheel so you can see when it had made a complete circle, a bobbin that spun faster, and a discussion on how gearing ratios change the work you do (Engineering)
A display of knitting projects, with a book on fitting different motifs together; for instance, if you have a motif that repeats every 24 stitches, it would be best if your sweater was a multiple of 24 stitches around. But what if you also have a motif that repeats every 7 stitches and another motif that repeats every 15 stitches? This book gets around that problem by having EVERY motif be 24 stitches, but it still brings up the issue. Also, a pair of socks with a ball of similar yarn next to them, so we can talk about different ways to estimate whether or not you've got the right amount of yarn to make another pair of socks. (Math)
As a bonus, an interactive set of drop spindles attached to already-spun yarn, so the kids could spin them themselves without having to worry about messing up the yarn or dropping the spindles on the floor. The spindles were different weights and sizes, so the kids could see how that affected the length of time the spindles would spin. (more Science - physics this time!)
I didn't even get into the math of warping a loom, which usually takes me a couple of pages of scribbling notes and calculations, multiplying by ends-per-inch, adjusting for percentage of shrinkage and percentage of take-up and how much loom waste to allow, and margins of error, and stuff like that.
Oooh I SHOULD'VE brought my tablet loom. I'll have to work that one in.
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