Problem of the Week Guidelines

Introduction

Problems of the Week (POW) are not intended to have quick or simple answers. A large part of the learning from attempting problems such as these comes from the in-depth thinking required to address each part and thinking back about how you solved the problem after you have finished it. You will find yourself thinking about how you are thinking about the problem if you fulfill these requirements.

If two or three students wish to work on a POW together, they may, but they will need to identify the contributions of each person to the effort of solving and presenting the problem. If you wish credit, you must have the POW turned in to your teachers before the solution is posted, which generally means Friday. Then, follow the format below to solve the problem. Your final submission must be done on a computer, but you may draw graphics and charts by hand. Prior to turning in the problem, you must use assign yourself a score. The first couple of times you do this, see Ms. Allen or Mr. Fincher to give you a better handle.

Get your problem from the current Middle School POW at the Math Forum, solve it using the guidelines below.

Problem Statement

In your own words, write what the problem is about. Write clearly enough so that someone picking up your paper could understand exactly what you were asked to do.  Be sure to include all the necessary details.

Process

Plan

Before you start solving the problem, make a plan.. How does the problem seem to you?  Describe your first impression of the problem.  Is it similar to others you have done before?  Think about the various problem-solving strategies you have used before.  Describe the mathematical strategies you plan to use to solve this problem. (Reading the problem over ten times and getting out paper/pencil are not mathematical strategies!!) Make a prediction of the answer(s).  If you don't have any idea, make a guess anyway.

Reasoning and Work

Describe in detail how you went about solving the problem, even if you don't think you got a right answer.  Explain your reasoning so that someone else could use your method(s) to solve the problem. Also include a discussion of the following:

Include all work: calculations with explanations, any diagrams, charts, sketches you used, etc.

Solution

State the answer(s) to the problem.  What makes you think you got it right?  Why do you think it makes sense?  How does this answer compare to what you predicted?  Did you find all the possible answers?  How do you know? (Convince the reader! Saying you checked your answer a million times and asked all of your friends is not convincing!) How long did it take you to find an answer?

Evaluation

How did you feel while working on this problem?  What did you like or not like about working on this problem?  Why?  On a scale from 1-5, how would you rate this problem for difficulty?  Why?  What did you learn from this problem that could help you solve other problems?  What new thoughts do you have about the problem after solving it?  How is this problem related to real life?  State your opinions and include reasons.

Problem of the Week Scoring Rubric

4 Well done - Problem Statement in own words.  Demonstrates effective use of strategies.  Explanations are clear and thorough. Reasoning makes sense; effective mathematical arguments are used.  Work contains no computation errors. Fulfills all requirements for submission.
3 Acceptable - Problem Statement in own words.  Some use of strategies.  Explanations could be improved with more detail and/or clarity.  Reasoning makes sense; moderately effective mathematical arguments are used.  Work may contain minor computation errors. Fulfills most requirements for submission; errors and omissions are minor.
2 Revision needed - Problem Statement not in own words.  Limited use of strategies.  Explanations are incomplete and/or unclear in places.  Reasoning makes some sense, but may show misunderstanding or need rethinking.  Work contains computation errors.
1 Restart - Problem Statement is copied.  Little or no use of strategies.  Explanations are incomplete, unclear, inappropriate.  Reasoning shows misunderstanding or doesn't make sense.  Work contains major computation errors.

Does your POW write-up include...

You

Peer

Teacher

Problem statement section

  • Problem Statement
  • Problem rewritten in your own words?
  • All necessary details?
      

Plan

  • First impressions?  Description of similar problems solved?
  • Description of mathematical strategies for solving the problem?
  • Explanation of how the strategies will be used?
  • Prediction of a solution?'
  • Plan that could lead to a solution?
      

Reasoning and Work

  • Description of each step of the reasoning process?
  • Calculations with explanations (where appropriate)?
  • How strategies described in the plan were used?
  • Charts, graphs, diagrams where needed?
  • Description of any help you received?
  • Mathematical understanding of the problem?
      

Solution

  • Solution with label? (Some problems may require multiple answers. Make sure you give all possible answers or, if the number of answers is extremely large, tell how to know when you have found an answer.)
  • Explanation of why solution makes sense (is correct)?
  • Convincing? (Alternate approach used to verify)
  • Consideration of other correct answers?
  • Amount of time spent on problem?
      

Evaluation

  • Description of your thoughts and feelings while working the problem?
  • Rating (1-5, with five being high) with reasons?
  • Explanation of what was learned from doing this problem?
  • Explanation of how this problem is related to real life?
      
POW Evaluator /20 /20 /20

 

Page last updated 10/17/02