FLAG - Tools: Math 'Creating Measures' Crowded-ness Task, Example #4


Math 'Creating Measures' Crowded-ness Task, Example #4



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 problem gives you the chance to:
  • criticise a given measure for the concept of "crowded-ness"
  • invent your own way of measuring this concept and use it effectively



Group A


Group B


Group C


Group D


Group E


Group F


Warm-up


  1. Someone has suggested that "crowdedness" may be defined as the area of a box that will just enclose all the people in a cluster. So for group A:


    "Crowded-ness" = 7.26 m2


    Use this method to calculate the crowdedness of group F:

    Group F





  2. Write down at least two reasons why this is not a good way of measuring "crowdedness".





  3. Describe a better method for measuring "crowdedness". Explain why it is better.





  4. Use your method to give a numerical value to the "crowdedness" of Groups A to F.
    Use your method to put the groups in order of "crowdedness".





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)