Perusing Columbus University’s archived Elementary problems of the week, I came across this one:

What three consecutive counting numbers have a sum that is twelve and a half percent of the product of the three consecutive numbers?

Although my first instinct is to represent this algebraically,  my representation would have required finding roots of a cubic equation, which didn’t seem the likely approach intended for a problem for elementary school kids.  So I did what my elementary kids would do (well, actually my elementary kids would not know what to do with 12.5%), which is guess and check, and it was easy to hone in on the correct answer quickly.

1. September 19, 2007 9:10 pm

I get “caught” by problems like this fairly often with my Math Counts students. They will beat me to the answer, because I’ve gone off on an algebraic tangent.

2. September 19, 2007 9:12 pm

Yes, I’m sure both my 11yo and my 14yo would have beaten me to this one. 😉 But the algebra actually helps often enough that it’s usually the first thing I try.

3. September 20, 2007 5:59 am

It is important, when designing problems like these, to use not so easy numbers. If you want algebra, you need to keep it necessary.

In June 1998 (I think) we had a very similar problem on the NY State Regents with answer 1,2,3 or 2,3,4, but full credit only came for an algebraic answer. Do you know how hard it is to perform algebra when you already know the result? for a kid?

One of the meanest things I do, when I want to focus on process, is put up problems with the answers already there…

4. September 20, 2007 8:48 am

In this case, I should have guessed that “they” were not interested in algebra, since it was listed as a problem for elementary students.

You have an interesting point about how the process changes if you know the answer!