'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.

____________________________________________________

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?