November 6, 2014

It’s pretty incredible when a sweater can actually teach math. Sondra Eklund has knitted a super-colorful sweater where each stripe’s colors show what numbers multiply to *make* that number. So the 2nd stripe is blue, the 3rd is red, and then 6 has a stitch of blue, then red, then blue and red because it’s 2×3! 4 has just 2 blue stripes side by side because it’s 2×2, and 8 has 3 blue stripes for 2x2x2. 9 gets 2 red ones, for 3×3. The smaller numbers that you multiply are the “factors,” and when a number has only itself and 1 as factors, it’s a “prime” number. So 2, 3, 5, 7, 11 and other prime numbers each get their own color, and they then show up in bigger numbers. That’s why Sondra calls it her Prime Factorization Cardigan. She took 2 years to knit it, since every stripe knits together its own unique set of colors. After all that work, hopefully she can wear that math for years to come.

*Wee ones:* The 2-stripe uses blue, the 3 uses red, 5 uses yellow and 7 uses maroon. How many prime colors is that?

*Little kids:* Which stripe has a stitch of blue for 2 alternating with a stitch of yellow for 5? *Bonus: *Sondra took 2 years to knit the sweater. In what year did she start? (We’re in 2014 right now.)

*Big kids:* If you’re looking for a stripe that uses a stitch of blue (2), then red (3), then maroon (7), which stripe has them all? *Bonus:* What are the stitches for the 48th stripe?

*The sky’s the limit:* Sondra managed to fit in a total of 78 stripes. How many stripes have multiple rows of all the same color?

Answers:

*Wee ones:* 4 colors.

*Little kids:* The 10, which is 2 x 5. *Bonus:* In 2012.

*Big kids:* The 42. *Bonus:* 4 blue stitches with a red for the 5th, since 48 is 2 x 2 x 2 x 2 x 3.

*The sky’s the limit:* Just 9 stripes. First, the stripes with multiples of all the same color will include most of the perfect squares, where 4 is 2 x 2, 9 is 3 x 3…we then have 16, 25, 49 and 64, giving us 6 stripes (we can’t use 6×6=36 because that has 2 colors, for both 2 and 3). Then there are perfect cubes, including 8 which is 2 x 2 x 2, and 27 (3x 3 x 3). 64 already got counted as a square, so that gives us just 2 more stripes. Then we have the remaining “powers” of 2: 16 (2 x 2 x 2 x 2) already got counted, but we need 32 which is 2 x 2 x 2 x 2 x 2. Again, 64 (2 to the 6th) already got counted, so that’s just 1 more stripe. The next power of 3 is 81 (3 x 3 x 3 x 3) which didn’t make it onto the sweater, so we’re done with 9 stripes in total.

And a big thank-you to Sondra for making this sweater – and for coaching one of Bedtime Math’s Crazy 8s Clubs!

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