'Creating Measures' Square-ness Task - Example #1


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 "square-ness"
· invent your own ways of measuring this concept
· examine the advantages and disadvantages of different methods.

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Warm-up
Use visual judgements to answer the warm-up questions.
Which rectangle looks the most square?
Which rectangle looks least square?

Without measuring anything, put the rectangles in order of "square-ness."

1. Someone has suggested that a good measure of "square-ness" is to calculate the difference:
 
 Longest side - shortest side
 
 for each rectangle. Use this definition to put the rectangles in order of "square-ness."
 Show all your work.
 
 
 
 
 
2. Using your results, give one good reason why Longest side - shortest side is not a 
suitable measure for "square-ness." 
 
 
 
 
 
3. Invent a different way of measuring "square-ness."  Describe your method carefully below:
 
 
 
 
 
4. Place the rectangles in order of "square-ness" using your method. Show all your work.
 
 
 
 
 
5. Do you think your measure is a good way of measuring "square-ness?"  Explain your 
reasoning carefully.
 
 
 
 
 
6. Find a different way of measuring "square-ness."
Compare the two methods you invented. Which is best? Why?