Monday, January 4, 2016

Happy New Year - 2016 Fabulous Factoring and a Balrog

During my Christmas break, I began thinking about a good Do Now for the students on their first day back.  What could I do with the number 2016?  Hmmm.  Well, excitingly, it has SO MANY FACTORS!  That would be a great way to get their brains cooking again.  Back in October, my 7th graders explored 504.  We blew out the factor rainbow with a factor "man-oh-war", and proclaimed 504 our favorite number.  It was exhaustingly exciting.  But. Today, 2016 bumped 504 from its pedestal.  This was such a good review of divisibility rules, and dividing, and number patterns, and association.  Once we got into the two digit numbers, the students conjectured whether, for example, 28 would be a factor of 2016.  After all, 2, 4, 7, and 14 were all factors so didn't it make sense?  And they were right.  We're a little stumped why 27 is not a factor of 2016 because 3 and 9 are there.  Someone suggested maybe the larger factor had to be even, but there sat 21 in all its odd glory belying the hypothesis.  We think it might have to do with the fact that 9 is a power of 3 but we're not sure yet, and want to be able to make predictions. 
When you divide 2016 by 4 you get our old friend 504.  That was a huge help when we figured out that if 504 is a factor of 2016, then ALL its factors are also factors of 2016.  Truthfully, took a little convincing on my part, which I demonstrated by showing 36's factors and later on asking for 72's factors.  But, we were rusty from the break.
My 8th graders were worn out by this activity, as they were over a year from factor rainbows, etc.  I told them the sad news that next January, I wouldn't be able to entertain the future 8th graders with a  factoring adventure starring 2017 because, well, 2017 is a factoring dud. "What?!  That's not fair!  Why did we have to have the bad luck to have Jan 2016 in our 8th grade year!!?"  (Did I tell you I love middle school?) I did promise  to inflict 2016 on next year's 8th graders in December just before the break with a "So Long 2016" factoring event. That was some comfort.
So, my 7th graders, who love to factor, loved 2016.  It's not a factor umbrella.  It's not a factor Man-o-War.  It's almost akin to Tolkien's Balrog just before he wraps his sinewy glowing tendrils around Gandalf's leg and drags him into the depths of Moria, but I haven't told them that.  Yet.


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