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CBSE Notes 2011-2012

Problem Solving

Problem Solving (Homework and Tests)

  • The higher the math class, the more types of problems: in earlier classes, problems often required just one step to find a solution. Increasingly, you will tackle problems which require several steps to solve them. Break these problems down into smaller pieces and solve each piece - divide and conquer!
  • Problem types:
    1. Problems testing memorization (”drill”),
    2. Problems testing skills (”drill”),
    3. Problems requiring application of skills to familiar situations (”template” problems),
    4. Problems requiring application of skills to unfamiliar situations (you develop a strategy for a new problem type),
    5. Problems requiring that you extend the skills or theory you know before applying them to an unfamiliar situation
  • When you work problems on homework, write out complete solutions, as if you were taking a test. Don’t just scratch out a few lines and check the answer in the back of the book. If your answer is not right, rework the problem; don’t just do some mental gymnastics to convince yourself that you could get the correct answer. If you can’t get the answer, get help.
  • The practice you get doing homework and reviewing will make test problems easier to tackle.

Tips on Problem Solving

  • Apply Pólya’s four-step process:
    1. The first and most important step in solving a problem is to understand the problem, that is, identify exactly which quantity the problem is asking you to find or solve for (make sure you read the whole problem).
    2. Next you need to devise a plan, that is, identify which skills and techniques you have learned can be applied to solve the problem at hand.
    3. Carry out the plan.
    4. Look back: Does the answer you found seem reasonable? Also review the problem and method of solution so that you will be able to more easily recognize and solve a similar problem.
  • Some problem-solving strategies: use one or more variables, complete a table, consider a special case, look for a pattern, guess and test, draw a picture or diagram, make a list, solve a simpler related problem, use reasoning, work backward, solve an equation, look for a formula, use coordinates.

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