Wednesday, September 21, 2011

Teaching binary arithmetic to 12-year-olds

I used to teach my 7th graders how to count to 1023 on their fingers.  It's easy to do:

Your right thumb is 1.
Your right index finger is 2.
Your right middle finger is 4.
Your right ring finger is 8.
Your right pinky finger is 16.

Your left thumb is 32.
Your left index finger is 64.
Your left middle finger is 128.
Your left ring finger is 256.
Your left pinky finger is 512.

Representing a number between 0 and 1023 is simple.  You just hold up the fingers and thumbs whose values add up to the number you're looking for.  For example, 21 is 16 + 4 + 1, so you hold up your right pinky, your right middle finger, and your right thumb.

The kids caught on quickly.  Twelve-year-old minds are sharp.  In no time at all, we were waggling our fingers rapidly as we counted to 100 together.  Some kids went further on their own, finishing triumphantly at 1023.

One time, I told the kids that they had to be really careful when they counted 4 or 128, and that they might get me in trouble if they went around flashing 132 at people.  (Try it yourself; you'll catch on quickly.)  Then little Mickey Cramer got a mischievous grin on her face and said, practicing for when she got home, "Hey Mom, look what Mr. D taught us in math today!"

I miss Mickey.  She was great.  I hope she's having fun in her senior year.  Or college, maybe.

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