# Wearing Your Heart – and Some Numbers – on Your Sleeve

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?

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!