'Creating Measures' Steep-ness Task - Example #2

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

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Warm-up

Without measuring anything, put the above staircases in order of "steep-ness."

1.	Someone has suggested that a good measure of "steep-ness" is to calculate the difference:
	
	Height of step - length of step
	
	for each staircase.  Use this definition to put the staircases in order of "steep-ness."  
	Show all your work.

	

2.	Using your results, give reasons why Height of step - length of step is not a suitable measure for "steep-ness."

	

3.	Invent a better way of measuring "steep-ness."  Describe your method carefully below:

	

4.	Place the staircases in order of "steep-ness" using your method. Show all your work.

	

5.	Do you think your measure is a good way of measuring "steep-ness?"  Explain your reasoning carefully.

	

6.	Describe a different way of measuring "steep-ness."
Compare the two methods you invented. Which is best? Why?