Consecutive Sum-mer

So May is a fun month.  In Minnesota, we can be reasonably certain the sub-40 day temperatures are behind us, the goslings have hatched, and the student countdown to the end of the year has begun.  In my classroom, they not only know that there are 18 days left, but that there are also only 3 Mondays remaining as well.

In John Stevens and Matt Vaudrey’s new book The Classroom Chef, they state that the opposite of bored is not entertained.  It’s curious.  While I agree, I needed some solid evidence to combat the never-ending question of “Can we go outside today?”   (For the record, I’m not totally opposed to taking them outside for math class.  It’s just not warm enough yet.)

Me:  Number your paper from 1 – 30.  (I’m off to an outstanding start, clearly.)  So and So, pick a number (hoping he/she doesn’t pick a power of 2).

Student:  Seven

Me:  Seven is interesting because it can be written as the sum of 2 consecutive numbers, 3 and 4.   What about 6?  Can you think of a way you could make 6 using the sum of consecutive numbers?

We talk about what consecutive numbers are, how many we should be able to sum, which kinds of numbers count as consecutive, whether addition is the only operation allowed, and so on.  Pretty soon, the entire class, (Yes, 100% of my juniors and seniors who have been beaten down by mathematics for 11+ years) is engaged, on task, and curious about the nature of these sums of numbers.

Student:  So you’re telling me that any number, except the powers of 2 which are few in number anyway, can be written as the sum of consecutive numbers?  

Me:  Nope.  I’m not saying that at all.  You discovered it.

Here is the Consecutive Sums problem poster from nrich:


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