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Welcome to all Elementary Problem Solvers

Mission Statement

     The goal of this page is to provide students with various problems that they can (try to) solve in a non-threatening and somewhat interactive setting. There are some people that are very good at problem solving and then there are the rest of us. This site is for the rest of us. I believe, just as George Polya does, that the art of problem solving can be taught and therefore learned. To master problem solving you will have to practice, by "exercising your mind." Consider this your treadmill and enjoy your run.

     Before attempting any of the problems I suggest that you become familiar with the following 4 Step Problem Solving Plan. You have very likely seen this plan in your mathematics textbooks and/or on the board. You were also very likely told to use it, to which you said, "I don't need that, I can answer anything." I would like to reiterate what your teacher said, "Use it!" This is an expanded version of Polya's original 4 Step Plan. You should go through each of the 4 steps but you don't need to use all of the options in each step. Pick one and go for it. Have fun.

Polya's 4 Step Problem Solving Plan

1. Understand the Problem

• What is the question asking?
• What relevant information have they given you?
• Do you understand all the words in the problem?

  If you are still having trouble figuring out what the question is asking then try some of these approaches.

1. Restate the question in your own words.
2. Make a list of everything you know from the information in the question.
3. List any conditions that are given. These usually come in the form - if ... then.
4. List the relevant facts.
5. Eliminate what isn't relevant.
6. How is the problem similar to other problems you may have already solved?

2. Devise a Plan

  Do not attempt to do any of these unless you Understand the Problem!
  Use whatever you need to apply these strategies. This may include manipulatives and/or pencil and paper.

1. Move It Around

• Look at it in a different order or from a different angle

2. Picture It

• Draw a picture.
• Look for patterns, similarities and/or differences.
• Visualize it.
• Create grids or arrays.
• Tally it.
• Graph it.

3. Take It Apart

• Break it into smaller problems and solve them one at a time.
• Work backwards.
• Search for keywords such as difference, all, and more/less than.

4. Translate It

• Guess and Check.
• Convert the question to equations.

5. Control It

• Create a table.
• Estimate.
• Simplify the question by using smaller numbers and solve.
• Make a prediction.
• Check computation.
• Does the answer make sense?

  If you are still having trouble figuring out how to solve the problem then take a break and let your brain simmer the problem. This does not mean that you can forget about doing the problem. You could also talk about the problem with others.

3. Carry Out the Plan

  At this stage you need to be both persistent and patient.

• Track your work by keeping neat and accurate records.
• Stay with the particular strategy you have chosen until you have either solved the problem or you can prove that it won't work.
• Monitor your work for accuracy.
• If you are still having trouble then take a break and/or discuss the problem with others.

4. Evaluate the Results - Look Back

  This has the potential of being the most important step in the plan if used correctly. Here you can learn from both your successes and your mistakes.

• Check to see that not only does the answer make sense but it is logical.
• Work out the problem in different orders now that you know the answer.
• Consider other problems that could be solved using the same or similar methods.
• If the answer is wrong, reevaluate the problem and try a different strategy.

Enough is enough, now get to work.

Oh yeah, I almost forgot.

GOOD LUCK!

If you have any questions, concerns, suggestions or comments then contact me.

The last time this site was changed was
05/26/99 09:51:07 PM