Thursday, November 29, 2012

Prblem Solving Top Ten List #2

A good process problem uses no set algorithm to find the solution.  It requires a variety of processes (problem solving strategies) to find the solution.  It is a problem that is easy to understand, is interesting, perhaps even whimsical, and has numbers sufficiently small enough so that lengthy computation is unnecessary.

Standard Word Problem:  Jack's family plans to rent a camping trailer for vacation.  The rent is $22.50 a day.  What will it cost to rent the camping trailer for one week? 

A Problem that Requires Problem Solving:  Drew and Addie are playing a game.  At the end of each game, the loser gives the winner a chip.  When they are done playing several games, Drew has won three games, but Addie has three more chips than she had when the game began.  How many games did Drew and Addie play?

So what happens when your students try to do the process problem above and they have no idea what to do?  In my last posting, I listed ten reasons why students get stuck when problem solving.  Now let's consider why students get stuck in the first place.

Top Ten Reasons for Getting Stuck in the First Place:

  1. You tried to rush through the problem without thinking.
  2. You did not read the problem carefully.
  3. You don't know what the problem is asking for.
  4. You don't have enough information.
  5. You are looking for an answer that the problem isn't asking for.
  6. The strategy you are using doesn't work for this particular problem.
  7. You are not applying or using your strategy correctly.
  8. You failed to combine your strategy with another strategy.
  9. The problem has more than one answer.
  10. The problem cannot be solved.

Next time, we will look at the final Top Ten List entitled The Top Ten Worst Problem Solving Habits.

Since students today tend to be more visual than anything else, a graphic organizer becomes a valuable math tool.  The Triangular Graphic Organizer is generic so that it can be used to solve all kinds of formula problems such as d = rt, A = lw, or c2 = a2 + b2.  This five page handout explains in detail how to use the graphic organizer.  It also contains several examples as well as a page of blank triangular graphic organizers to copy and use in your classroom.
 
Want the answer to the process problem? 
Check out the page above entitled: Answers to Problems.





5 comments :

Mrs. Burke said...

OK - so I'm relatively new to following you. Do you post the solutions to your problems? Just wondering if my processes are correct.

Scipi said...

Mrs. Burke,

Here is the answer: They played 9 games. Did you get the right answer?

Mrs. Burke said...

Yes. Well, it was my first answer. My process was drawing a picture with the chips (then using guess and check) but as I worked it, that was the only scenario. Is there an algorithm or other way to solve?

Mrs. Burke said...

I'm posting a second time. I'm not sure my previous post went through. That is the answer I got although I was unsure of my strategy. I used a guess and check along with drawing chips and cancelling them out as they played. Each player must have started with 6 chips.?. I love solving your problems. It helps me develop my skills as well. I'm not nearly up to your ability and understanding.

Scipi said...

There is no algorithm. That is why this is totally a process or problem that requires a strategy. The way you solved it is PERFECT!