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Math Help - Problem Solving Task

  1. #1
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    Problem Solving Task

    I teach Maths in Victoria, Australia. I am obliged to give my students a problem solving task that lasts about 6 to 7 hours. The theme of the task I want to run is on Complex Numbers. Students at this level have only gone as far De Moivre's Theorem, though they could handle Euler's Theorem comfortably. They can also do simple problems of locus in the Argand diagram and solve simple polynomial equations with real and complex coefficients.

    I am wondering if anyone can think of a problem solving task pitched at the level indicated above that students could do over a six to seven hour period.
    The task needs to be broken up into six to seven questions, each question with subsections and such that each question fills about 45 minutes. I note that Mr.Fanastic is Australian and therefore may have a working knowledge of the education system in Victoria. If you do have any ideas that might be useful, please email me at the email address in my profile.

    I posted this thread here rather than in the High School section because the problem solving task required needs the insight of a mathematician as opposed to a teacher.

    Hoping someone out there can help.
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  2. #2
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    Quote Originally Posted by Mr.Chips View Post
    I teach Maths in Victoria, Australia. I am obliged to give my students a problem solving task that lasts about 6 to 7 hours. The theme of the task I want to run is on Complex Numbers. Students at this level have only gone as far De Moivre's Theorem, though they could handle Euler's Theorem comfortably. They can also do simple problems of locus in the Argand diagram and solve simple polynomial equations with real and complex coefficients.

    I am wondering if anyone can think of a problem solving task pitched at the level indicated above that students could do over a six to seven hour period.
    The task needs to be broken up into six to seven questions, each question with subsections and such that each question fills about 45 minutes. I note that Mr.Fanastic is Australian and therefore may have a working knowledge of the education system in Victoria. If you do have any ideas that might be useful, please email me at the email address in my profile.

    I posted this thread here rather than in the High School section because the problem solving task required needs the insight of a mathematician as opposed to a teacher.

    Hoping someone out there can help.
    I can think of several ideas. Ideally, the task would give your students some scope for exploration. Do your students have proficiency in the use of a dynamic geometry software package such as Cabris or Geometers Sketchpad? This would enormously assist exploration of some more difficult loci in the complex plane.

    Some possibilities that you could do other things with as well (start off with a couple of concrete cases and extend to the general case):

    Subsets of the complex plane defined by:

    |z - z1| + |z - z2| = k and |z - z1| - |z - z2| = k

    |z - z1| = k |z - z2| (where k > 0)

    arg(z - z1) - arg(z - z2) = theta.

    The second and third can also incorporate vectors and circle geometry theorems.
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  3. #3
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    Thanks for your suggestion. I am aware of this question. It was presented at the MAV Conference in 2005 at LaTrobe. The problem is that students often have private tutors who know these questions anf the particular question you have suggested is well known among many tutors. I am really after something fresh and new - something that tutors cannot predict the direction the task is going from day to day. We run this Problem Solving Task over eight consecutive school days.
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