FLAG - Tools: Math 'Creating Measures' Awkward-ness Task, Example #5


Math 'Creating Measures' Awkward-ness Task, Example #5



Square-ness, Example #1 (solution) || Steep-ness, Example #2 (solution)
Compact-ness, Example #3 (solution) || Crowded-ness, Example #4 (solution)
Awkward-ness, Example #5 (solution) || Sharp-ness, Example #6 (solution)

Malcolm Swan
Mathematics Education
University of Nottingham
Malcolm.Swan@nottingham.ac.uk

Jim Ridgway
School of Education
University of Durham
Jim.Ridgway@durham.ac.uk


This task gives you the chance to
  • invent your own measure for the concept of "awkward-ness"
  • use your measure to put situations in order of "awkward-ness"
  • generalize your measure to work in different situations.



Warm-up


Here are four movie theater situations:

  1. Place the four situations in order of "awkward-ness."

      Which is the easiest situation for people?
      Which is the most awkward?
      Explain how you decided.





  2. Invent a way of measuring "awkward-ness." This should give a number to each situation. Explain carefully how your method works.





  3. Show how you can use your measure to place the four situations in order of "awkward-ness." Show all your work.





  4. Adapt your measure so that the minimum value it can take is 0 (where no-one is made to stand up) and the maximum it can take is 1 (the most awkard situation possible).





  5. Show how your measure in part 4 may be generalised for any number of people entering a row. ( That is when n people enter a row with n available seats).





Square-ness, Example #1 (solution) || Steep-ness, Example #2 (solution)
Compact-ness, Example #3 (solution) || Crowded-ness, Example #4 (solution)
Awkward-ness, Example #5 (solution) || Sharp-ness, Example #6 (solution)