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Tools - 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
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Group A
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Group B
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Group C
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Group D
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Group E
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Group F
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Warm-up
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:
"Crowded-ness" = 7.26 m2
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".
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)
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