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My beginning students often ask what kind of project they can make after they've learned to cast on, knit, purl, and bind off. I developed a pattern for fingerless mitts that incorporates all of these techniques but doesn't require them to knit to a specific gauge.
Introducing Easy Fingerless Mitts, available as a free download.
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My students learn to knit using worsted weight yarn and size 7 or 8 needles. These mitts can be made using their classroom yarn and needles. The pair will take about 50g of worsted weight yarn (mine actually took a bit less).
The mitts are worked sideways until they are long enough to fit around the hand. The cast on and bind off edges are sewn together, with a gap left for the thumb hole. The garter borders at the cast on and bind off edges keep the thumb hole from rolling, and the garter stitch borders at the sides act as ribbing for the cuff and fingers.
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This pattern is for personal use only and is not to be copied or distributed without prior permission.