Problem Solving Surprises

Recently I’ve made a conscious effort to include a daily problem solving activity into my math class schedule.  I’m guilty of spending too much time on skills-based, procedural instruction and not giving my students enough opportunities to wrestle with more complex problems.

Some of these daily problems are more difficult than others.  Sometimes they are aligned with whatever concept I’m teaching at the time, but more often they are not.  I like this.  Students don’t have a prescribed way to solve the problem and I can put many different work samples under the Elmo to show students how their peers came to the same solution using different strategies.

I thought my students would hate this.  When they see word problems in their homework or class assignments, they assume they can skip them.  Do we have to do number ten? Yes.  We don’t do word problems. For some reason they’ve been loving it.  They actually get excited when the warm-up ends and I start to pass out the problem of the day. When I walk around the room during this time, they are really talking about the problem and not what they saw on Facebook last night.  Some of them like the challenge of solving a more difficult problem.  I also think they like the variety of the problems.  How nice to see a problem about square numbers when we’ve been slogging through fractions for so long.  Some of the problems are less about computation skills and more about logic.

I also haven’t been grading them, and I think this has made their motivation for these problems more intrinsic.  We talk about the ways of starting the problem.  We talk about answers that would make no sense at all.  We talk about strategies that take us down the wrong road and why.  I emphasize the collective effort of making sense of the problem, the willingness to take chances, over finding the correct answer.  Of course they all want to find the correct answer, but in these discussions even students who are making mistakes are helping us arrive at the correct solution.

Often they come up with strategies that I’d never thought of using, even when it should have been glaringly obvious to me.  Check out this problem I gave to my class a couple of days ago:

We were studying ratios and proportions this same week, and I’m embarrassed to admit that when I read this problem I never considered setting up a proportion to find out how much 120 bottles would cost.  Out of all of my sixth grade students, one did.  D, a boy who is constantly turned around trying to start a conversation, who never seems to have any idea about what is going on in class, who is infinitely more concerned with his sneakers or what somebody might have said about his mom than anything we are studying in math, puts this down on his paper in the first 30 seconds:

What!?  How did D do that?  Why couldn’t he do that yesterday in class?  He even labeled his units!  And best question of all, why hadn’t I thought of using proportions to solve this problem?  It truly knocked my socks off.  It took other students a lot longer to solve the same problem using different strategies and the smarties in the room were a little jealous that they hadn’t thought of D’s way.  I even used his work as a springboard to introduce our next concept in the study of ratio and proportions, unit rates.  Who can use D’s strategy to find out how much one bottle of Citrus Sparkle would cost?

I hope my students continue to enjoy the daily problem solving as much as I do.  Well worth the 15 minutes.

Special thanks to Sandy Allen for her guidance and encouragement.


This problem was taken from Problem-Solving Experiences in Mathematics
by Randall I. Charles, Robert P. Mason and Dianne Garner
Dale Seymour Publications – an imprint of Pearson Learning
ISBN 0-201-20641-2