The Standard POW Write-Up
Problems of the week are an important part of a math curriculum. They will give you experience in carrying out extended investigations of complex problems. Expect three POWs to be assigned each semester. These problems will not necessarily be connected with the book. You should begin to work on a POW as soon as you get it, since POW’s usually take more time than a regular assignment to complete. POWs also provide you an opportunity to work on your writing, because you will be expected to explain your thinking. “Write-Up” directions will accompany most POWs, often using the categories shown below. Use the descriptions and the checklist below to help you with your POW writeup.
Write-Up Categories:
1. Biographical Facts
This is where you clearly and concisely write (in your own words) about the given mathematician and his/her contributions to mathematics. You may do your research in the library or on the Internet about the mathematician. Give a brief description of his/her life and contributions to math. You may include specific discoveries by the mathematician, quotations attributed to him/her etc. This part of your write-up must be at least a paragraph in length. You must cite your sources.
2. Process
This is where you describe what you did to solve the problem. You can include things that didn’t work out or that seemed like a waste of time. Do this part of the write-up even if you didn’t solve the POW. If you get assistance of any kind, you should indicate what the assistance was and how it helped you.
3. Solution
This is where you state your solution as clearly as possible. Explain how you know that your solution is correct and complete. Part of your explanation should include some kind of “Check”. If you obtained a partial solution, give that. If you were able to generalize the problem, include your more general results. Your explanation should be written in a way that is convincing to someone else.
4. Extension
This is where you get creative and make up your own similar problem. Your problem must be similar to the given POW, but yet different with a different description, different numbers and a different solution. You must state your problem clearly and then show the work and solution to your made up problem. Your problem must be unique, completely different from any other student problem.
5. Evaluation
This is where you write about your personal reaction to the POW. Indicate whether you learned something and what it was. State whether or not the POW was challenging. Rate your performance on a scale of 1 to 5. Include any other comments that come to mind about the POW.
How To Start/Complete A POW (use the checklist to help you work on your POW)
___ A. Search the internet or the library for information on the mathematician.
___ B. Include several contributions by the mathematicians.
___ C. Include quotes that are attributed to the mathematician.
___ D. Your writing must be in your own words. (you may not plagiarize)
___ D. Did you end this part of the POW with your Cited Source ?
III. Process (write about what you did/tried to solve the problem)
___ A. If possible, make a chart, table, in-out table, or diagram to organize the information.
___ B. How does your chart or table relate to the problem? Label all charts, tables & diagrams.
___ C. If you used a calculator, explain how you used it. List your data in an organized table.
___ D. Look for patterns. Describe any that you find.
___ E. State your pattern in math terms.( e.g. Formula A = l*w where A = area, l = length, w =width)
___ F. If you cannot find a pattern, then state situations that can be eliminated. (e.g. The number cannot be
an even number because…. Or….the number cannot be 1 because… etc… )
___ G. Make sure your pattern or rule works for ALL the given information.
___ H. Consult with your family, friends, tutor or a teacher for help. Consult does not mean to copy
someone else’s work.
___ I. Double-check your arithmetic and math ideas. (e.g. Can perimeter be negative)
___ J. Good strategies for solving your POW include organizing your information, working backwards,
using manipulatives, guess/check, finding a pattern, eliminating or narrowing down choices, using
simpler numbers and comparing ideas with others. Always explain and give examples of any strategies
used to solve your POW.
IV. Solution (write and show a check of your answer)
___ A. When you find a solution, double check your work. Make sure it works for all given information.
___ B. Be convincing. Show and explain why/how it works; usually most of this has been covered in your
Process, but it is important to prove that it does indeed answer the problem.
___ C. Define and use variables wherever possible. Express the rule or pattern with math language.
___ D. Note any generalizations that you found in observing the patterns. (e.g. After measuring all the angles
in the different triangles, the sum of the interior angles of any triangle is always equal to 180 degrees)
___ E. If you could not find a solution, be honest and explain what stumped you.
V. Extension (write your own creative similar problem)
___ A. Your problem must be similar to the given POW. You can change the names of people or the
situation, but the essence of the given POW must be same.
___ B. Your problem must use different data (i.e. numbers) and must have the same degree of difficulty.
___ C. You must show your work for your POW, but you may use less detail.
___ D. You must show your solution to your problem so that it can be checked for correctness.
___ E. You problem must be unique. You may not consult with others for this part.
___ F. The purpose of the extension is to indicate your complete understanding of the POW.
VI. Evaluation (write about your feelings towards this POW)
___ A. What is your personal reaction to this problem?
___ B. Write about what you learned from this POW.
___ C. Write about how you would change the POW to make it better.
___ D. Write about whether or not you enjoyed working on the POW, whether it was easy or hard.
___ E. Other comments.
___ A. Start with a draft. Make corrections. Use complete sentences. Use a dictionary or the spell check
features of a computer. You must be neat. Points will be taken off for sloppy work.
___ B. Pace yourself. You should start working on the POW as soon as you get it.
___ C. Turn in your write-up on time. 3 pts per day will be deducted for late POWs.
___ D. Extra credit points will be given for typed POWs.