If you haven’t already…Check out The Centre for Education in Mathematics and Computing and their Problems of the Week.

I came across this Problem of the Week below in their book of problems and solutions grades 7/8 for the years 2012-2013.

I modified the task to make it appropriate for the new year 2014.

I planned to use this with a group grade level 8th graders.  I thought it looked like a perfect problem to teach the problem solving strategy of starting with a simpler problem.

Just I had imagined, when I presented them with the problem, they immediately shunned it and put it off by saying they had no idea.  They wanted to try and put it into the calculator (which offers up its own set of learning opportunities).

I asked, “Well, what DO you know?”  Of course they started with $5^3$ is 125.  So, I said well let’s write that down.

Then I asked, “Well, what ELSE do you you know?”  And someone shared $5^2$ is 25.

At this point, we talked about how we organize information in math.

We continued our table, and many students began to recognize the pattern.  I needed to use guiding questions for some to be able to communicate just how the pattern worked.

I think this is a very simple, yet powerful, problem for explicitly teaching a very specific problem solving strategy.

End note:  If you haven’t already read this book…YOU MUST!  It validated many things that I already believed…but gives VERY useful and practical strategies for being explicit about how you teach problem solving.

I’d like to put together a set of tasks that all make use of this problem solving strategy so that students have the opportunity to apply it themselves.

I’d love to hear about how you teach problem solving!