"Put them in a line and count them": Comments from the Real/Fake World of Math Class

I used this problem with grade 6s yesterday:

An interesting problem, or not? pic.twitter.com/7nB784XGR3

— Matthew Oldridge (@MatthewOldridge) June 20, 2014

I am not sure where this problem came from.  I do know that it stumped me for a while, although a decent number of students eventually got it, and the solution makes sense.

The first thing to note is that we are distinctly operating in the "fake world" here. No such club exists. There is no pressing need to do this particular math. There is no inquiry that can be done here. I defer, as always, to Dan Meyer on this topic.

 The problem is "word problemy", in the fact that it is asking for something simple- a single number of people, which it obscures through the design of its words.  That said, there are no dirty tricks here- it's a fraction problem, of the sort that uses a fraction of a missing whole, then a fraction of a slightly larger whole.

So why give this problem?  Here are some of our usual reasons:

1.  We are doing a fractions unit, and this problem can get us to think about fractions.
2.  To see what kind of thinking our students do on this problem.
3.  This problem is useful in its applications in the real world.
4. Because it's interesting, or beautiful.  These are our best reasons to do math, I think.

#1 didn't apply here.  #2 I am always interested in, although slightly less so when the pressure is off us in late June. As to #4, this problem did hold our interest for a while. It is a tricky one, and it engaged our desire to "puzzle it out".  There were some arguments interpreting the language of the problem, and trying and discarding some possible answers. Multiples of 4 and 7 were clearly involved, somehow.

As to #3, I will defer to my student's comments on the problem.

-you would just line the members of the club up in a line and count them. That's the solution. 

It's difficult to argue with that logic.