
Tools  Math 'Creating Measures' Crowdedness Task, Example #4
Squareness, Example #1 (solution)  Steepness, Example #2 (solution)
Compactness, Example #3 (solution)  Crowdedness, Example #4 (solution)
Awkwardness, Example #5 (solution)  Sharpness, 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 "crowdedness"
 invent your own way of measuring this concept and use it effectively

Group A

Group B

Group C

Group D

Group E

Group F

Warmup
In your opinion, which group looks the least "crowded"?
Which looks the most "crowded"?
Put the groups in order of "crowdedness", just by looking.
 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:
"Crowdedness" = 7.26 m^{2}
Use this method to calculate the crowdedness of group F:
Group F
 Write down at least two reasons why this is not a good way of measuring "crowdedness".
 Describe a better method for measuring "crowdedness". Explain why it is better.
 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".
Squareness, Example #1 (solution)  Steepness, Example #2 (solution)
Compactness, Example #3 (solution)  Crowdedness, Example #4 (solution)
Awkwardness, Example #5 (solution)  Sharpness, Example #6 (solution)
