'Creating Measures' Crowded-ness Task - Example #4 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 In your opinion, which group looks the least "crowded"? Which looks the most "crowded"? Put the groups in order of "crowdedness", just by looking. 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: 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".