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110011010001001110001!
That wasn't supposed to mean anything in particular, but it's fun nevertheless. At 11:11 on 11/11/11, my 3rd hour math class had a 1:11 minute dance party. "I Need a Hero" was blasting in the background and the students covered my back board with 11/11 graffiti (some of which said Thanks Vets!) and made wishes for the special day.
This would have been the perfect moment to drop everything and teach them how to do binary. It was, after all, the last binary day for a very long time. Instead I dropped a couple binary one-liners and called it good. I guess we'll get there some time in the spring, after MCA's and the rest of our standard curriculum is finished.
Having not learned binary until a few years ago, it was a real eye-opener into a different way of counting. It came up in "The Story of 1", which is a phenomenal DVD about the history of number systems and the evolution of mathematical principles. Surprisingly for a math video, it's actually quite funny too! Towards the end of the movie, the subject of computers and binary counting is introduced with an egg analogy. Using powers of 2, a hard-boiled egg cup is either filled with an egg (switch on!) or it is empty (switch off!).
For example:
1 in binary is 2 to the 0 power. So there is one egg cup, with one egg in it. Or "1" in binary.
2 in binary is 2 to the 1st, but no 2 to the 0. So there are 2 cups, with the first filled. "10".
3 in binary is 2 to the 1st PLUS 2 to the 0, So there are 2 cups, with both filled. "11".
4 in binary is 2 to the 2nd, no 2 to the 1st or 0 power. 3 cups, only the first filled... "100".
and so on... 5 = 101, 6 = 110, 7 = 111...
then at 8 you bump up to 2 to the 3rd power and add a cup. 1000.
This egg analogy makes total sense to kids, especially kinesthetic learners, because they can manipulate a cup or picture of a cup with coins or tiles or actual eggs, and they can practice their powers of two, which in turn helps them to understand the decimal system better. "111" in decimal means something completely different than "111" in binary. This leads to a great discussion on the advantages of various number systems.
Advanced students can be taught how to add and subtract in binary as well, or how to count in hexadecimal or octal. Who knows if they'll ever use it for anything, but it feels kind of like a secret language and makes them feel really smart! So anyway, back to 11/11/11... the fun of it was to tell students that 111111 in binary is 2 to the 5th + 2 to the 4th + 2 to the 3rd + 2 to the 2nd + 2 to the 1st + 2 to the zero power = 63.
I think it is extremely important to pause and elaborate on teachable moments. It may be a subject or conversation that has nothing to do with your goals and objectives for the day, and that's okay. Connecting to humorous, educational, artistic, historical, political and/or occasional controversial ideas in your classroom is what kids actually remember when they look back.
The real challenge is leading the conversation back to math in as meaningful a way as possible, without cutting them off before everyone with their hands up got to share. Funny, isn't it? How many hands go up when you stray off topic to something personal? And how few hands are raised during morning warm-ups or instructional time? Interesting....
